2007-01-1205-Correlation and Simulation Process

Diffusion and Separation of CO2and CH4in Silicalite,C168Schwarzite, and IRMOF-1:A Comparative Study from Molecular DynamicsSimulationRavichandar Babarao and Jianwen Jiang*Department of Chemical&Biomolecular Engineering,National Uni V ersity of Singapore,Singapore117576Recei V ed No V ember3,2007.Re V ised Manuscript Recei V ed February28,2008Recently we have investigated the storage and adsorption selectivity of CO2and CH4in three different classes of nanoporous materials s silicalite,IRMOF-1,and C168schwarzite through Monte Carlo simulation(Babarao,R.;Hu, Z.;Jiang,ngmuir,2007,23,659).In this work,the self-,corrected,and transport diffusivities of CO2and CH4 in these materials are examined using molecular dynamics simulation.The activation energies at infinite dilution are evaluated from the Arrheniusfits to the diffusivities at various temperatures.As loading increases,the self-diffusivities in the three frameworks decrease as a result of the steric hindrance;the corrected diffusivities remain nearly constant or decrease approximately linearly depending on the adsorbate and framework;and the transport diffusivities generally increase except for CO2in IRMOF-1.The correlation effects are identified to reduce from MFI,C168to IRMOF-1, in accordance with the porosity increasing in the three frameworks.Predictions of self-,corrected,and transport diffusivities for pure CO2and CH4from the Maxwell-Stefan formulation match the simulation results well.In a CO2/CH4mixture,the self-diffusivities decreases with loading,and good agreement is found between simulated and predicted results.On the basis of the adsorption and self-diffusivity in the mixture,the permselectivity is found to be marginal in IRMOF-1,slightly enhanced in MFI,and greatest in C168schwarzite.Although IRMOF-1has the largest storage capacity for CH4and CO2,its selectivity is not satisfactory.I.IntroductionNanoporous materials have been widely utilized in catalysis, ion exchange,gas storage,and purification.1In the nanodomain,fluids diffuse significantly differently from bulkfluids because of spatial confinement and surface interaction.2Understanding such diffusion behavior is not only of fundamental interest but also of central importance for industrial applications.There have been a large number of experimental studies on the determination of diffusivities in zeolites,carbons,and other materials.3,4 Nevertheless,with ever-growing computational power,com-putationally based molecular simulation has played an increas-ingly important role in nanoscience and nanotechnology.5 Simulation on the nanoscale can provide microscopic pictures that are experimentally inaccessible or difficult,if not impossible, to obtain.As a consequence,deeper insight can be gained from molecular simulation,thus assisting the rational design of new materials of increasing complexity.We will give a brief review of simulation studies on diffusion in various nanomaterials,among which zeolites are the most commonly investigated.In the early1990s,Theodorou and co-workers examined the self-diffusion of CH4in silicalite using equilibrium molecular dynamics(MD)6and transport diffusion using both equilibrium and nonequilibrium MD.7Recently,they simulated the self-and transport diffusion of CO2and N2in silicalite over a wide range of occupancies by using various forcefields and made a comparison with experimental data.8,9 Sholl and co-workers computed the transport diffusion of CH4 and CF4in silicalite and found that the Darken approximation is valid only for CH4and deviates strongly for CF4at all temperatures.10From the self-and transport diffusion of seven light gases separately in silicalite at room temperature,they observed that the self-diffusivity decreases with increased loading as a result of steric hindrance;however,the reverse is true for transport diffusivity.11They compared the simulation and experimental results for the permeation of the CH4/CF4mixture through silicalite and found that atomistic modeling correctly predicted silicalite to be more selective for CF4.12From simulation, they investigated the effects of pore shape and connectivity on the diffusion of gases in silica zeolites13and also the effects of the sweep gas and porous support on zeolite membranes using atomic and continuum models.14Recently,Sholl published a comprehensive review on understanding diffusion in crystalline nanoporous materials using simulations.15Snurr and co-workers made thefirst comparison for the self-diffusivities of the CH4/ CF4mixture in silicate between simulation and NMR experiments, and good agreement was observed.16They inspected the structural and transport properties of CF4and n-alkane mixtures in faujasite from MD simulation and found that whereas the main-term transport diffusivities are greater than their self-diffusivity counterparts the cross-term diffusivities are1order of magnitude*Author to whom correspondence should be addressed.Tel:(65)6516 5083.Fax:(65)67791936.E-mail:chejj@.sg.(1)Macilwain,C.Nature2000,405,730.(2)Martin,C.R.;Siwy,Z.Nat.Mater.2004,3,284.(3)Karger,J.;Ruthven,D.Diffusion in Zeolites and Other Microporous Solids; Wiley:New York,1992.(4)Demontis,P.;Suffritti,G.B.Chem.Re V.1997,97,2845.(5)Drexler,put.Theor.Nanosci.2006,3,1.(6)June,R.L.;Bell,A.T.;Theodorou,D.N.J.Phys.Chem.1990,94,8232.(7)Maginn,E.J.;Bell,A.T.;Theodorou,D.N.J.Phys.Chem.1993,97,(8)Makrodimitris,K.;Papadopoulos,G.K.;Theodorou,D.N.J.Phys.Chem. B2001,105,777.(9)Papadopoulos,G.K.;Jobic,H.;Theodorou,D.N.J.Phys.Chem.B2004, 108,12748.(10)Skoulidas,A.I.;Sholl,D.S.J.Phys.Chem.B2001,105,3151.(11)Skoulidas,A.I.;Sholl,D.S.J.Phys.Chem.B2002,106,5058.(12)Skoulidas,A.I.;Bowen,T.C.;Doelling,C.M.;Falconer,J.L.;Noble, R.D.;Sholl,D.S.J.Membr.Sci.2003,227,123.(13)Skoulidas,A.I.;Sholl,D.S.J.Phys.Chem.A2003,107,10132.(14)Skoulidas,A.I.;Sholl,D.S.AIChE J.2005,51,867.(15)Sholl,D.S.Acc.Chem.Res.2006,39,403.5474Langmuir2008,24,5474-5484smaller than the main-term diffusivities.17In addition,they examined the permeances of CH4and CF4through faujasite18 and evaluated the diffusivities for a binary mixture of CH4/CF4, C3H8/CF4,n-C4H10/CF4,and C2H6/n-C4H10in faujasite at300 K.19Krishna and co-workers reported a kinetic Monte Carlo (MC)simulation for the self-diffusion of the CH4/CF4mixture in silicalite,20simulated the self-diffusion of pure CH4and CO2 and an equimolar mixture at a wide range of loading in MFI, CHA,and DDR zeolites,21and screened12different zeolites to determine the best one for separation of CO2and CH4.22 Furthermore,they investigated the correlation effects in the diffusion of CH4and CF4in the MFI zeolite from MD simulation and the Maxwell-Stefan(MS)formulation,respectively.23Jost et al.simulated the diffusion of the CH4/Xe mixture in silicalite and compared it with the pulsedfield gradient nuclear magnetic resonance and found that the simulation and experimental results were in accordance with each other.24Moulijn and co-workers investigated the separation of CH4/C2H6and CH4/C3H8mixtures in silicalite as a function of temperature,pressure,and composi-tion.25The role of adsorption in single and binary permeation of CH4and CO2through a silicalite membrane was further examined by them,in which the generalized MS formulation was adapted in combination with the ideal adsorbed solution theory(IAST)to model binary permeation.26Since its discovery in1991,carbon nanotubes(CNTs)27have stimulated considerable interest,including their potential use for membrane separation as a result of their well-defined nanoscale structures.28Sholl,Johnson,and co-workers simulated the self-and transport diffusivities of light gases such as H2,CH4,Ar,and Ne in CNTs and in two zeolites with comparable pore sizes and found that the diffusion is1-3orders of magnitude faster in CNTs than in silicalite depending on loading.29,30Similar behavior was observed by them for CO2and N2in CNTs at room temperature,in which the linear and spherical models for CO2 were found to give roughly identical diffusivity.31They examined the transport diffusivity in rigid,defect-free CNTs in which an efficient thermostat was employed to account for the influence of nanotubeflexibility.The inclusion offlexibility reduces transport diffusion by roughly1order of magnitude at a pressure close to zero;in contrast,at high pressures the transport diffusion inflexible and rigid nanotubes is very similar,differing by a factor of2on average.32Furthermore,they predicted the binary permeance of the CH4/H2mixture through defect-free CNTs acting as a membrane at room temperature and showed that the mixture diffusion is also rapid as compared to single-component diffusion.33Arora and Sandler studied the mass transport of O2, N2,and their mixture in a CNT and demonstrated that good kinetic selectivity could be achieved for air separation by carefully adjusting the upstream and downstream pressures.34They further investigated the separation of O2and N2in a CNT with a constriction,which leads to high transport resistance to N2while allowing O2to pass at a much higher rate even though these gases have very similar sizes and energetics.35Combining the configurational-bias MC method with the dual control-volume grand canonical MD simulation,Firouzi et al.examined the transport and separation of binary n-alkane mixtures as well as CO2and n-alkane mixtures in CNTs under an external potential gradient.36Jakobtorweihen et al.proposed a novel algorithm for modeling the influence of host latticeflexibility and applied it to the investigation of the diffusion of chain molecules and mixtures in CNTs.37,38Within the past few years,a new family of naonporous materials,namely,metal organic frameworks(MOFs),have been developed.39–41With the well-located metal oxide clusters and organic linkers,MOFs allow the formation of porous frameworks with a wide variety of architecture,topology,and pore size and provide almost unlimited opportunities to develop,control,and tune structures for specific pared to zeolites and CNTs,the simulation studies for diffusion in MOFs are relatively few.Skoulidas found from MD simulation that the transport diffusivity of Ar in Cu-BTC at room temperature differs from the self-diffusivity by2orders of magnitude at high loadings.42Sarkisov et al.simulated the self-diffusivities of CH4, n-C5H12,n-C6H14,n-C7H6,and cyclo-C6H14in MOF-5,which are of the same order of magnitude as in silicalite.43Skoulidas and Sholl examined the self-and transport diffusion of light gases in MOF-2,MOF-3,MOF-5,and Cu-BTC.44Yang and Zhong performed simulations for the adsorption and diffusion of H2in IRMOFs.45Stallmach et al.reported thefirst experimental data on diffusion in MOF-5and demonstrated that organic gas molecules diffuse quite rapidly in MOFs.46Amirjalayer et al. conducted MD simulations of C6H6in IRMOF-1and found that the diffusion and activation energy of C6H6are considerably smaller in theflexible framework compared to those in the rigid one.47To the best of our knowledge,however,there is no simulation work to date for mixture diffusion in MOFs.The above-mentioned studies were primarily from numerical simulations on diffusion in zeolites,CNTs,and MOFs.Analytical predictions of mixture diffusion solely from single components have been a major challenge in the past few decades.Nevertheless, the Maxwell-Stefan(MS)formulation developed by Krishna and co-workers is an advance toward this end,as recently(17)Sanborn,M.J.;Snurr,R.Q.Sep.Purif.Technol.2000,20,1.(18)Sanborn,M.J.;Snurr,R.Q.AIChE J.2001,47,2032.(19)Chempath,S.;Krishna,R.;Snurr,R.Q.J.Phys.Chem.B2004,108, 13481.(20)Paschek,D.;Krishna,ngmuir2001,17,247.(21)Krishna,R.;van Baten,J.M.;Garcia-Perez,E.;Calero,S.Chem.Phys. Lett.2006,429,219.(22)Krishna,R.;van Baten,J.M.Chem.Eng.J.2007,133,121.(23)Skoulidas,A.I.;Sholl,D.S.;Krishna,ngmuir2003,19,7977.(24)Jost,S.;Bar,N.K.;Fritzsche,S.;Haberlandt,R.;Karger,J.J.Phys. Chem.B1998,102,6375.(25)van de Graaf,J.M.;Kapteijn,F.;Moulijn,J.A.AIChE J.1999,45,497.(26)Zhu,W.D.;Hrabanek,P.;Gora,L.;Kapteijn,F.;Moulijn,J.A.Ind.Eng. Chem.Res.2006,45,767.(27)Iijima,S.Nature1991,354,56.(28)Ajayan,P.M.;Zhou,O.Z.Applications of Carbon Nanotubes.In Carbon Nanotubes;Springer-Verlag Berlin:Berlin,2001;Vol.80;p391.(29)Skoulidas,A.I.;Ackerman,D.M.;Johnson,J.K.;Sholl,D.S.Phys.Re V. Lett.2002,89.(30)Ackerman,D.M.;Skoulidas,A.I.;Sholl,D.S.;Johnson,J.K.Mol.(33)Chen,H.B.;Sholl,D.S.J.Membr.Sci.2006,269,152.(34)Arora,G.;Sandler,S.I.J.Chem.Phys.2006,124.(35)Arora,G.;Sandler,S.I.Nano Letters2007,7,565.(36)Firouzi,M.;Nezhad,K.M.;Tsotsis,T.T.;Sahimi,M.J.Chem.Phys. 2004,120,8172.(37)Jakobtorweihen,S.;Verbeek,M.G.;Lowe,C.P.;Keil,F.J.;Smit,B. Phys.Re V.Lett.2005,95,044501.(38)Jakobtorweihen,S.;Lowe,C.P.;Keil,F.J.;Smit,B.J.Chem.Phys. 2007,127,024904.(39)Yaghi,O.M.;O’Keeffe,M.;Ockwig,N.W.;Chae,H.K.;Eddaoudi,M.; Kim,J.Nature2003,423,705.(40)Eddaoudi,M.;Kim,J.;Rosi,N.;Vodak,D.;Wachter,J.;O’Keefe,M.; Yaghi,O.M.Science2002,295,469.(41)Rosi,N.L.;Eckert,J.;Eddaoudi,M.;Vodak,D.T.;Kim,J.;O’Keeffe, M.;Yaghi,O.M.Science2003,300,1127.(42)Skoulidas,A.I.J.Am.Chem.Soc.2004,126,1356.(43)Sarkisov,L.;Duren,T.;Snurr,R.Q.Mol.Phys.2004,102,211.(44)Skoulidas,A.I.;Sholl,D.S.J.Phys.Chem.B2005,109,15760.(45)Yang,Q.Y.;Zhong,C.L.J.Phys.Chem.B2005,109,11862.Diffusion and Separation of CO2and CH4Langmuir,Vol.24,No.10,20085475reviewed.48They used a generalized MS model to predict the permeationfluxes of hydrocarbon mixtures through a silicalite membrane.49,50A general analytical expression for self-diffusivity in a multicomponent mixture was proposed by them.51It has been found that the MS diffusivity in zeolites shows a variety of dependencies on occupancy.As a consequence,they further modeled the occupancy dependence of diffusivity in zeolites by taking into account various factors such as zeolite topology, connectivity,and molecular interactions.52Sholl tested this by predicting binary diffusivity in a lattice model with site heterogeneity.He found that the model is quite accurate in situations where the binding sites are relatively homogeneous but is less accurate for strongly heterogeneous energy distribu-tions.53In addition,Krishna and van Baten carried out MD simulations for pure components and binary,ternary,and quaternary mixtures in FAU at300K over a wide range of loading and found that MS diffusivity for a particular species is nearly identical whether this species is present on its own or in a mixture with other species.54Having tested the MS formulation extensively in zeolite structures for predicting mixture diffusion, they further tested the MS formulation in CNTs for various binary mixtures and found good agreement with simulations.55Whereas the MS formulation to predict mixture diffusion from single components has been tested relatively well in zeolites and CNTs, only recently has such a prediction been attempted in MOF-5 by Keskin and Sholl.56Through MC simulation,we have recently investigated the adsorption of pure CO2and CH4and the separation of their binary mixture in three different families of nanostructured materials s silicalite,C168schwarzite,and IRMOF-1.57The separation of CO2 from CH4,a major component in natural gas,is considered to be an important practical problem.Our simulated adsorption isotherms and isosteric heats closely match the available experimental data. Compared with the adsorption capacities of silicalite and C168 schwarzite,those of CH4and CO2in IRMOF-1are substantially larger.As a typical MOF,IRMOF-1could be a good candidate for gas storage,but its adsorption selectivity does not differ much from silicalite and C168particularly at high pressure.57Nevertheless,the efficacy of membrane-based separation for a gas mixture depends notonlyonthesolubilitydifference,whichisanequilibriumproperty, but also on the diffusivity difference,which is a transport property.58 As a consequence,in this work we investigate the diffusion of CO2,CH4,and their mixture in the three nanostructured adsorbents using MD simulation and examine the permselectivity based on diffusion and adsorption selectivity.This is thefirst simulation study on mixture diffusion in a MOF.In section II, the models used for adsorbents and adsorbates are briefly described and followed in section III by the simulation methodology.In section IV,we present the diffusivities and activation energies at infinite dilution for CO2and CH4.Then the self-,corrected,and transport diffusivities for single component from simulation are presented as a function of loading at300K.The correlation effects are examined from the self-and corrected diffusivities and subsequentlyfitted by an empirical equation.With thefitted correlation effects,the simulated self-, corrected,and transport diffusivities are compared with the theoretical predictions from the MS formulation.Finally,the self-diffusivities in the binary mixture at300K are presented from both simulation and the MS bining the differences in adsorption and diffusion between the two components in a binary mixture,permselectivity is evaluated.In section V,the concluding remarks are summarized.II.ModelsThe atomistic models for three adsorbents(silicalite,C168 schwarzite,and IRMOF-1)and two adsorbates(CH4and CO2) are the same as in our previous study;57therefore,a brief description is given here.Silicalite(MFI)is an Al-free zeolite typically used in membrane processes because of its pore size and ease of preparation.MFI consists of two types of channels with10-membered rings s one is straight,and the other is sinusoidal.These intersecting channels have a diameter of about 5.4Å.The Lennard-Jones potential parameters and partial charges of the Si and O atoms were adapted from the work of Hirotani et al.59Experimentally synthesized nanoporous carbon is amorphous and does not have a well-defined structure;conse-quently,C168schwarzite is used to represent a nanoporous carbon.60Two types of channels exist in C168schwarzite with average diameters of approximately7and9Å.The channels in the same layer are isolated from each other,but they are connected to those in the neighboring layers by channel intersections.Carbon atoms in C168schwarzite were assumed to be neutral,and the Steele potential was used to model the disperse interactions.61 IRMOF-1is an isoreticular MOF that has one type of straight channel with sizes of15and12Åseparately along the channel.62 A universal forcefield(UFF)was used to model the Zn,C,O, and H atoms in IRMOF-1.63On the basis of a fragmented cluster, the atom-centered partial charges were estimated with B3LYP/ 6-31G(d)density-functional theory computation and subsequently fitted using the restrained electrostatic potential(RESP)method.64 CH4was mimicked by the united-atom model with the interaction potential parameters from the TraPPE forcefield developed to reproduce the critical parameters and saturated liquid densities of alkanes.65The interactions between CH4and the adsorbent were modeled using the Lennard-Jones potential,and the Lorentz–Ber-thelot mixing rules were used to calculate the cross interaction parameters.CO2was represented by a three-site moleculefitted to the experimental data of bulk CO2.59The partial charge was0.576e on the C atom and–0.288e on the O atom.The C-O bond length was assumed to be rigid,and the bond length was1.18Å.The OCO bond angle wasflexible and governed by a harmonic potential of 1/2kθ(θ-θ0)2with force constant kθ)1275kJ/mol/rad2and equilibrium angleθ0)180°.CO2-CO2and CO2-adsorbent interactions were modeled by a combination of Lennard-Jones and Coulombic potentials except for C168schwarzite,where only the Lennard-Jones potential was considered.III.MethodologyDiffusion can be characterized into self-,corrected and transport diffusion at different length scales.Self-diffusivity describes the(48)Krishna,R.;Baur,R.Sep.Purif.Technol.2003,33,213.(49)Kapteijn,F.;Moulijn,J.A.;Krishna,R.Chem.Eng.Sci.2000,55,2923.(50)Krishna,R.;Paschek,D.Sep.Purif.Technol.2000,21,111.(51)Krishna,R.;Paschek,D.Phys.Chem.Chem.Phys.2002,4,1891.(52)Krishna,R.;Paschek,D.;Baur,R.Microporous Mesoporous Mater.2004, 76,233.(53)Sholl,ngmuir2006,22,3707.(54)Krishna,R.;van Baten,J.M.J.Phys.Chem.B2005,109,6386.(55)Krishna,R.;van Baten,J.M.Ind.Eng.Chem.Res.2006,45,2084.(56)Keskin,S.;Sholl,D.S.J.Phys.Chem.C2007,111,14055.(59)Hirotani,A.;Mizukami,K.;Miura,R.;Takaba,H.;Miya,T.;Fahmi,A.; Stirling,A.;Kubo,M.;Miyamoto,A.Appl.Surf.Sci.1997,120,81.(60)Jiang,J.W.;Sandler,S.I.J.Am.Chem.Soc.2005,127,11989.(61)Steele,W.Chem.Re V.1993,93,2355.(62)Millward,A.R.;Yaghi,O.M.J.Am.Chem.Soc.2005,127,11989.(63)Rappe,A.K.;Casewit,C.J.;Colwell,K.S.;Goddard,W.A.;Skiff,5476Langmuir,Vol.24,No.10,2008Babarao and Jiangmobility of individual molecules,also called tracer diffusivity,can be estimated from the mean-squared displacement based on the Einstein relation 66D s (c ))lim t f ∞16t 〈1N ∑k )1N|r k (t )-r k (0)|2〉(1)where c is concentration,r k (t )is the position of the k th moleculeat time t ,and N is the number of molecules.This definition applies to both single and multicomponent systems.On a macroscopic scale,Fick’s law of diffusion gives the phenomenological relation between flux J and concentration gradient ∇c ,J )-D t (c )∇c(2)The transport or Fickian diffusivity D t can be evaluated from the corrected diffusivity D c (c )and thermodynamic correction factor Γ(c ),D t (c ))D c (c )Γ(c )(3)withΓ(c ))(∂ln f ⁄∂ln c )T(4)where f is the fugacity of the fluid in equilibrium with the adsorbed phase at a concentration c .Γ(c )at a given temperature T can be evaluated from the equilibrium adsorption isotherm.The corrected diffusivity D c (c ),which is also called the jump diffusivity,can be written asD c (c ))Lk B T ⁄c(5)where L is the phenomenological coefficient and k B is Boltzmann’s constant.Note that the corrected diffusivity is equal to the Maxwell -Stefan diffusivity for a system with only one species.From the linear response theory,L is related to the flux autocorrelation function by 67L )13Vk B T∫0∞〈j (0)·j (t )〉d t(6)where V is the system volume and j (t )is the microscopic current defined as the sum of molecular velocitiesj (t ))∑k )1Nv k (t )(7)The microscopic current is an equilibrium property and can be directly obtained from MD simulation.Equation 6is the Green -Kubo form,and the equivalent Einstein form can be found elsewhere.67The above expression can be extended to multicomponent systems.Self-,corrected,and transport diffu-sivities are concentration-dependent and generally not equal to each other unless at infinite dilution,D s (0))D t (0))D c (0))D (0)(8)In this work,we simulate the diffusion of pure and mixed CH 4and CO 2in MFI,IRMOF-1,and C 168using the MUSIC program.68The simulations were carried out in a canonical ensemble (NVT )with a Nose-Hoover thermostat,and the equations of motion were integrated using a sixth-order Gearpredictor-corrector algorithm.69A time step of 1fs was used for CH 4,and 0.3fs was used for CO 2and the mixture to achieve better energy conservation.A spherical cutoff length of 19.0Åwas used to evaluate the intermolecular Lennard-Jones interactions without the long-range corrections.Cou-lombic interactions between CO 2and adsorbent were calculated using the Ewald summation technique.70For CO 2molecules,Coulombic interactions were calculated directly on the basis of the center-of-mass cutoff of 19.0Åbecause the CO 2molecule is neutral with a quadrupole interaction that converges rapidly with the cutoff distance.To accelerate the simulation,the Lennard-Jones and Coulombic interactions between adsorbate and adsorbent were calculated via a pretabulated energy map that was constructed throughout a unit cell of adsorbent with a grid of 0.2×0.2×0.2Åcubic mesh.The simulation box for MFI contained 12(2×2×3)unit cells,whereas for C 168schwarzite and IRMOF-1,8(2×2×2)unit cells were used.All three adsorbents were assumed to be rigid,and the framework atoms were fixed during simulation.It is important to note,however,that diffusion can be substantially influenced by the framework flexibility.In zeolites,diffusion is usually accelerated in the flexible model by the increased possible number of pathways for the molecular jump.71Nevertheless,a reduction in diffusion is observed in flexible carbon nanotubes by taking into account the energy exchange between diffusing molecules and the nanotube.32The diffusion and activation energy of benzene in IRMOF-1are considerably smaller in the flexible framework compared to those in the rigid one.This is attributed to the correlation motion of benzene with the organic linker phenylene rings,which leads to an increases in the population of benzene in the A-cell pockets.47The final configurations of MC simula-tions for the adsorption of pure CH 4,CO 2,and the equimolar CH 4/CO 2mixture from our previous work 57were taken as the initial configurations for the MD simulations in this work.For pure CH 4and CO 2at 300K,simulations were performed for a total period of 2.5-5.0ns with an equilibration period of 1.0-3.5ns.Ten independent runs were performed at each loading to obtain the desired level of statistical accuracy.During the production run,the atomic coordinates were written to a disk every 1ps and then used to calculate the averaged D s from the Einstein relation.The molecular velocities were written to a disk every 0.1ps and then used to calculate the flux autocorrelation function and phenomenological coefficient using eq 6with an upper limit of 30ps.As demonstrated previously,17,72with an even short limit of 10ps,the flux autocorrelation function decays to zero,and the integral converges to a constant.In addition,we calculated the diffusivities at infinite dilution of CH 4and CO 2in all three adsorbents at various temperatures.To do this,we performed the MD simulation as described above with at least 40molecules in the box by turning off the adsorbate–adsorbate interactions.For the CH 4/CO 2mixture,MD simulations were performed at 300K for a total period of 8ns,with the first half left out for equilibration and the second half left out for the ensemble average.IV.Results and DiscussionFirst we present the simulation results for pure CH 4and CO 2in the three nanostructures at infinite dilution.From the(66)McQuarrie,D.A.Statistical Mechanics;University Science Books:Sausalito,CA,2000.(67)Theodorou,D.N.;Snurr,R.Q.;Bell,A.T.Molecular Dynamics and (69)Allen,M.P.;Tildesley,D.J.Oxford University Press:Oxford,U.K.,1987.Diffusion and Separation of CO 2and CH 4Langmuir,Vol.24,No.10,20085477temperature-dependent diffusivities,the activation energies for diffusion are obtained.Then as a function of loading,the simulated self-,corrected,and transport diffusivities of pure CH4and CO2 at300K are shown.The correlation effects of diffusion are examined and used in the MS formulation for predictions,which in turn are compared with the simulation results.Finally,the simulated and predicted self-diffusivities of the CH4/CO2binary mixture are presented at300K,and the permselectivity for the mixture is evaluated.Diffusivities and Activation Energies at Infinite Dilution. Figure1shows the diffusivities at infinite dilution D(0)for CH4and CO2separately in MFI,C168,and IRMOF-1as a function of the inverse temperature.The results are the average of10independent runs with a standard deviation of within 5%.As estimated in our previous study57and also given in Table1,for the three adsorbents under consideration,the porosity increases in the order of MFI<C168<IRMOF-1.In accordance with the increasing trend in porosity,D(0)generally increases in the same order for both CH4and CO2because of the increased free space for molecules to move.At temperatures lower than 300K,however,D(0)in MFI becomes slightly greater than in C168.Therefore,porosity is not the only factor influencing the diffusivity.Our simulated D(0)at300K given in Table1generally matches the reported simulation and experimental values well. For CH4in MFI,D(0)agrees well with the simulation results from a number of groups.6,7,11,21For CH4in IRMOF-1,D(0)is also in good agreement with the simulation result,44but both are almost an order of magnitude less than the measured value by Stallmach et al.46For CO2in MFI,D(0)is comparable to the measured value from QENS[(0.6-0.7)×10-8m2/s],9though a bit higher than the value simulated by Krishna et al.21For CO2 in IRMOF-1,D(0)is slightly higher than the simulated value of Skoulidas et al.44The discrepancy for CO2might be due to the different potential parameters used.C168schwarzite is a hypothetical structure for nanoporous carbons,and no experi-mental data are available for comparison with our results.In nanoporous materials,the steric effect and surface interaction play a dominant role.Diffusion is normally interpreted as an activated process and can be described by the Arrhenius relationD(0))Dfexp(-E a RT)(9) where D f is the prefactor,E a is the activation energy,and R is the gas constant.Byfitting the simulated D(0)at various temperatures using eq9,D f and E a can be correlated.The lines with CO2.As a result of the high porosity,in IRMOF-1D f for both CH4and CO2is found to be almost1order of magnitude greater than in MFI and C168.Our simulated E a for CH4in MFI(4.45kJ/mol)is in good agreement with the experimental value(5.69kJ/mol).73Stallmach et al.found E a for CH4in IRMOF-1 to be around8.5kJ/mol,46which is almost twice the simulated value(4.88kJ/mol).However,the discrepancy in both D(0)and E a in IRMOF-1may be due to the defects present in the porous structure used in experiments,which was not taken into account in simulations.Our simulated E a for CO2in MFI(3.35kJ/mol) is smaller than one available experimental value(5.8kJ/mol). However,note that the experimental condition was not at infinite dilute;instead,the loading was approximately two molecules/ unit cell.9A molecule must overcome the free-energy barrier to move from one site to another.The barrier as reflected in the activation energy is lower for either CH4or CO2in C168schwarzite compared with that in MFI and IRMOF-1.In particularly,the estimated E a for CO2in C168(1.75kJ/mol)is considerably lower. As further discussed below,this is because CO2is a slender molecule and readily mobile particularly in C168channels. Self-Diffusivities.Figure2shows the loading dependence of the self-diffusivities D s for CH4and CO2in the three adsorbents. The loadings considered here for IRMOF-1are substantially lower than the saturation loading.The error bars indicate the uncertainties in our simulation.As seen,D s for both CH4and CO2in each adsorbent decreases monotonically as loading increases.This is type I behavior as characterized by Karger and Pfeifer in whichfive types of diffusion behavior were demon-strated with increased loading.74The observed type I behavior is very common in nanoporous materials as a result of enhanced steric hindrance of the motion of a tagged particle by neighboring particles as the loading increases.At a loading of around3mmol/g for either CH4or CO2,D s in IRMOF-1is about twice of that in C168and almost1order of magnitude greater than that in MFI. The decreased rate in D s(the slope)is closely related to theFigure1.Diffusivities D(0)at infinite dilution as a function of inverse temperature for pure CH4and CO2in MFI,IRMOF-1,and C168.Symbols are from simulation,and lines are the Arrheniusfits to the symbols.Table1.Diffusivities D(0)at300K(10-8m2/s),Prefactors D f(10-8m2/s),and Activation Energies E a(kJ/mol)at InfiniteDilution for CH4and CO2in MFI,C168,and IRMOF-1adsorbent adsorbate porosity D(0)D f E aMFI CH40.37 1.569.28 4.45CO2 1.31 5.18 3.35C168CH40.67 1.51 6.24 3.50CO2 1.35 2.81 1.75IRMOF-1CH40.82 3.3722.6 4.88CO2 3.0115.4 4.05 5478Langmuir,Vol.24,No.10,2008Babarao and Jiang。

GWAS原理和流程全基因组关联分析Linkagedisequilibrium（LD）连锁不。

GWAS⼊门必看教程：名词解释和基本问题：关联分析：就是AS的中⽂，全称是GWAS。

应⽤基因组中数以百万计的单核苷酸多态；SNP为分⼦遗传标记，进⾏全基因组⽔平上的对照分析或相关性分析，通过⽐较发现影响复杂性状的基因变异的⼀种新策略。

在全基因组范围内选择遗传变异进⾏基因分析，⽐较异常和对照组之间每个遗传变异及其频率的差异，统计分析每个变异与⽬标性状之间的关联性⼤⼩，选出最相关的遗传变异进⾏验证，并根据验证结果最终确认其与⽬标性状之间的相关性。

连锁不平衡：LD，P（AB）= P（A）*P（B）。

不连锁就独⽴，如果不存在连锁不平衡——相互独⽴，随机组合，实际观察到的群体中单倍体基因型 A和B 同时出现的概率。

P (AB) = D + P (A) * P (B) 。

D是表⽰两位点间LD程度值。

曼哈顿图：在⽣物和统计学上，做频率统计、突变分布、GWAS关联分析的时候，我们经常会看到⼀些⾮常漂亮的manhattan plot，能够对候选位点的分布和数值⼀⽬了然。

位点坐标和pvalue。

map⽂件⾄少包含三列——染⾊体号，SNP名字，SNP物理位置。

assoc⽂件包含SNP名字和pvalue。

haploview即可画出。

SNP的本质属性是什么？⼴义上讲是变异：most common type of genetic variation，平级的还有indel、CNV、SV。

Each SNP represents a difference in a single DNA building block, called a nucleotide. 狭义上讲是标记：biological markers，因为SNP是单碱基的，所以SNP⼜是⼀个位点，标记了染⾊体上的⼀个位置。

⼤部分⼈的基因组，99%都是⼀模⼀样的，还有些SNP的位点，就是⼀些可变的位点，在⼈群中有差异。

Calcium fertigation ineffective at increasing fruit yield and quality of muskmelon and honeydew melons in California作者：Johnstone, P. R.Hartz, T. K.May, D. M. 刊名：HortTechnology 年，卷期：2008Vol.18(No.4) 关键词：fruit development flesh firmness fruit yieldCalifornia melon (Cucumis melo) growers commonly apply calcium (Ca) fertilizers during fruit development to increase fruit firmness and improve storage life. Drip-irrigated field trials were conducted in central California in 2005 and 2006 to evaluate the efficacy of this practice on honeydew (C. melo Inodorus group) and muskmelon (C melo Reticulatus group). In the 2005 honeydew trial,three weekly applications of 10 lb/acre Ca from calcium nitrate (CN), calcium thiosulfate (CTS), or calcium chloride (CC) were injected into the irrigation system during early melon development. In the 2006 muskmelon trial, two applications of 15 lb/acre Ca from CTS or CC were made early, or two applications of CC late, in melon development. The effect of these Ca fertigation treatments on fruit yield, soluble solids concentration, flesh firmness, and Ca concentration were compared with an untreated control receiving no Ca fertigation. Calcium fertigation had no effect on marketable yield, quality, or Ca concentration of honeydew or muskmelon fruit regardless of application timing or Ca source applied. Loss of firmness during either 2 weeks (honeydew) or I week (muskmelon) of postharvest storage was unrelated to Ca fertigation treatment and was not correlated with Ca concentration in fruit tissue. We conclude that under conditions representative of the California melon industry, Ca fertigation at typical application rates is ineffective in improving honeydew or muskmelon yield or fruit quality.Changes in ethylene production during preharvest period in quince (Cydonia vulgaris L.) and the use of ethylene production to predict harvest maturity作者：Gunes NT 刊名：European Journal of Horticultural Science 年，卷(期)：200368(5) 分类号：关键词：1-aminocyclopropane-1-carboxylic acid (acc) oxidase Citric acid;Golden delicious apples 1-aminocyclopropane-1-carboxylic acid;Fruit-development Color development Storage Biosynthesis Firmness;Respiration Maturation ConversionThis research was carried out in order to determine changes in respiration rate, internal ethylene, external ethylene, 1-aminocyclopropane-1-carboxylic acid (ACC) oxidase activity, flesh firmness, fruit colour, sugar (sucrose, glucose and fructose) and organic acid (citric and malic) during preharvest maturity period in 'Esme' and 'Cukurgobek' quince cultivars and to present the usability level of especially ethylene production as harvest criterion in quince. For this reason, fruits were sampledat weekly intervals from 90(th) day after full bloom till the beginning of climacteric rise in respiration rate. Either internal or external ethylene production was fluctuated during preharvest period. However, ethylene production did not tend to increase sharply while respiration rate was decreasing. Correlation coefficients and variation between years proved that ethylene production could not be used as harvest criterion. Internal ethylene production of 'Esme' and 'Cukurgobek' cultivars werechanged between0.1-1.7 mul l(-1) and 0.2-4.7 mul l(-1), external ethylene between 0-1.8 mul kg(-1) h(-1) and 0-2.4 mulkg(-1) h(-1), activity of ACC oxidase enzyme between 0-0.9 mul l(-1) and 0-1.9 mul l(-1), respectively. While regular decreases inflesh firmness of quince fruits during preharvest period were observed, increases with fluctuations in sugar and organic acid content were determined. In this research, fructose and malic acid were found as the dominant sugar and organic acid in quince.Storability of orange flesh melons treated with 1-MCP作者：Melo, R. B. deFigueiredo, R. W.Maia, G. A.Alves, R. E.Silva, E. O. 刊名：Acta Horticulturae 年，卷(期)：2008""(No.768) 分类号：关键词：1-methylcyclopropene colour crop quality firmness fruits melons pH plant growth regulators storage life sugar content titratable acidity Cucumis melo Rio Grande do Norte Orange flesh melons from the Mossoro-Acu Region, Rio Grande do Norte, Brazil, were treated with 0, 150, 300 and 600 ppb 1-methylcyclopropene (1-MCP), stored at room temperature of 25+or-3 degrees C and 90+or-5% RH and evaluated at intervals of 0, 3, 6, 9, 12, 15, 18 and 21 d. A 4x8 factorial scheme was used, consisting of four 1-MCP and 8 evaluations, in a completely randomized experimental design, with 4 replications of one fruit each. Evaluations were carried out for external and internal appearance, and peel colour using a subjective rating scale; peel and pulp colour by colorimetry, mass loss, pulp firmness; pH, total soluble solids, total titratable acidity; and total soluble sugar. For most quality parameters evaluated there was no difference between fruits treated with 1-MCP and the controls (Tukey test (P<0.05)). However, shelf-life of the melons stored under room conditions (25+or-3 degrees C and 90+or-5% RH) was 15 d while fruits treated with 1-MCP had the best external appearance and hence better commercial acceptance than the untreated fruits. Postharvest application of 150 ppb 1-MCP to melons extended shelf-life to 18 d and to 21 d when 300 and 600 ppb was appliedReduction of postharvest losses of Galia melon by a short hot-water rinseE. Fallik a *†, Y. Aharoni a , A. Copel a , V. Rodov a , S. Tuvia-Alkalai a , B. Horev a , O. Yekutieli b , A. Wiseblum b and R. Regev ba Department of Postharvest Science of Fresh Produce; andb Institute of Agricultural Engineering, ARO-The V olcani Center, Bet-Dagan, 50250, Israel*To whom correspondence should be addressed.KEYWORDSbrushes • hot water rinse • marketing • storageA rapid method for simultaneously rinsing and disinfecting fresh harvested produce using a hot-water rinse and brushes (HWRB) was tested on Galia melon (Cucumis melo cv. reticulatus) fruit. The optimal treatment to reduce decay while maintaining fruit quality after prolonged storage and marketing simulation was 59 ±1°C for 15 s. Trial shipments by sea transport to Europe demonstrated that treating melon with a commercial-scale HWRB machine (3 tonnes fruit h−1) maintained significantly better overall quality of treated fruit compared with untreated fruit. Exposing spores of Alternaria alternata and Fusarium solani to 60°C for about 15 s in vitro reduced germination by 48% and 42%, respectively. Employing HWRB resulted in a 3-log reduction in total colony-forming units (CFU) of the epiphytic microbial population, compared with untreated fruit. Scanning electron microscopy (SEM) showed that HWRB removed soil, dust and fungal spores from the fruit surface, and partially or entirely sealed natural openings in the epidermis.________________________________________Accepted 3 February 2000.DIGITAL OBJECT IDENTIFIER (DOI)10.1046/j.1365-3059.2000.00467.x About DOIMild heat and calcium treatment effects on fresh-cut cantaloupe melon during storage 作者：Olusola LamikanraMichael A. Watson 刊名：Food Chemistry 年，卷(期)：2007Vol.102(No.4) 分类号：关键词：mild heat pre-treatments postharvest minimal processing calcium heat shock proteins cucumis melo L. fruitThe effect of mild heat fruit pre-treatment on some properties of fresh-cut cantaloupe melon during storage was determined. Whole fruit, previously held at 4℃, was immersed in heated water (60℃) with and without dissolved calcium lactate (1%). Fresh-cut processing was done immediately, either after treatment or after storage at 4℃for 24 h. Headspace gas accumulation during storage indicated reduced respiration in heat-treated fruit. Reduced lipase activity occurred in heat treated fruit during storage at 10℃, while the fruit that was cut 24 h after treatment had a reduced peroxidase activity, unlike fruit that was processed immediately after heating. Isoelectric focussing indicated production of heat shock proteins (PI = 5.1 and 6.5) as a result of heat-treatment. Textural measurements showed increased hardness, chewiness and cohesiveness, but springiness decreased in heat-treated fruit. Presence of calcium in the treatment solution did not affect respiration and textural changes caused by heat treatment. Lipase activity was, however, higher in fruit heated in calcium solutions. Results indicated the potential improvement of shelf life of cut cantaloupe melon by mild heat pre-treatment of the fruit, and that the addition ofcalcium to the treatment water did not further improve product quality.Use of Mild Heat Pre-treatment for Quality Retention of Fresh-cut Cantaloupe Melon 作者：OLUSOLA LAMIKANRAKAREN L. BETT-GARBERDAPHNE A. INGRAMMICHAEL A. WATSON 刊名：Journal of Food Science 年，卷(期)：2005Vol.70(No.1) 分类号：关键词：mild heat pre-treatments postharvest minimal processing sensory evaluation cucumis melo L. fruitThe effect on sensory attributes and shelf life of fresh-cut cantaloupe melon subjected to pre-cut heat treatment at 50 ℃for 60 min, followed by storage at 4 ℃prior to cutting, and then storage at 10 ℃for 8 d was determined. Heat treatment reduced the rate of respiration and moisture loss during storage of the cut fruit. The treatment also reduced total microbial count during the 1st storage d and prevented growth of lactic acid bacteria that occurred in untreated fruit after 8 d in storage. Sensory evaluations indicate that heat treatment increased intensities of desirable attributes such as fruity melon and sweet aromatic flavors, and reduced undesirable flavors such as musty, sour, bitter, chemical and fermented. The study suggeststhat heat treatment would be useful in improving shelf life of fresh-cut fruit.Osmotic treatments in melon (cantaloupe and muskmelon) processing: physicochemical and organoleptical effects.The effects of different osmotic dehydration parameters (pretreatment with calcium salts such as CaCl2, Ca(OH)2 and CaCO3 at 0, 0.5, 1 and 1.5% w/v, and different osmotic solutions such as sucrose, glucose and their mixture) on the pH, sensory attributes, moisture content and water activity (aw) of cantaloupe and muskmelon fruits were evaluated. After osmotic dehydration at 4 degrees C for 12 h, the samples were air dried at 50-60 degrees C. The tests were accomplished in 6 months with 2 months interval. A 5-point hedonic scale was utilized for comparison. Statistical analysis was carried out in a complete randomized design (CRD). The results showed that the moisture content and aw of osmodehydrated cantaloupe and muskmelon decreased as the duration of storage was increased; the pH of cantaloupe decreased and that of muskmelon increased. The aw of cantaloupes pretreated with different calcium salts increased, while the moisture content and pH decreased as the duration of storage was increased. The best sensory attributes were obtained when the fruits were pretreated with CaCO3 (1.5% w/v). Combination of sucrose and glucose led to better flavour and appearance. Heating of samples after immersion in osmotic solutions resulted in higher rate of dehydration. During storage, the flavour intensity of dehydrated cantaloupe samples was enhanced..作者：Shahidi, FGanjloo, AMohebbi, M 刊名：Acta Horticulturae 年，卷(期)：2007""(No.731) 分类号：关键词：calcium carbonate calcium chloride calcium hydroxide dehydration flavour food processing food storage fruit glucose heating melons moisture content organoleptic traits osmosis pH physicochemical propertiespretreatment sucro se water activity 正文语种：eng 基金项目：相似文献(9条) 外文期刊Application of CaCl2 sprays earlier in the season may reduce bitter pit incidence in 'Braeburn; apple. 2005,V ol.40(No.6)外文期刊Effect of Debaryomyces hansenii and calcium salt on fruit rot (Rhizopus macrosporus) of peach. 2004,V ol.12(No.2)外文期刊Synthesis of needle-like aragonite from calcium chloride and sparingly soluble magnesium carbonate 2004,V ol.140(no.1/2)外文期刊Comparison of Shoemaker-McLean-Pratt and modified Mehlich buffer tests for lime requirement on Pennsylvania soils. 2008,Vol.39(No.11-12)期刊论文添加剂条件下氯化钙制备纳米碳酸钙- 合肥工业大学学报（自然科学版）2007,30(9)期刊论文由氯化钙制备纳米碳酸钙研究- 化工矿物与加工2007,36(2)期刊论文用氯化钙制备高纯超细碳酸钙的研究- 化肥工业2002,29(5)外文期刊Preventive effect of mildly altering dietary cation-anion difference on milk fever in dairy cows. 2007,Vol.69(No.2)外文期刊Isotopically exchangeable cobalt in some benchmark alluvial soils of Punjab. 1996,V ol.25(No.2)The postharvest handling system for melon in northwestern China -- status, problems, and prospectsMuskmelon production is an important source of income for farmers in northwestern China, especially those in desert regions. However, the application of postharvest handling techniques to the crop is far from adequate, resulting in substantial lossesin quality and quantity of commodity. Weight loss is directly related to diseases promoted by inadequate postharvest treatments. Quality loss is caused primarily by improper handling practices along the chain from harvesting to retailing. Problems exist in almost all procedures. The application of postharvest technology to the handling of fresh fruits and vegetables in China is still underdeveloped. Cost is considered to be the major obstacle preventing the wider utilisation of available postharvest techniques. In this paper, we overview the present situation, the problems that exist, and the prospects for developing and applying postharvest handling techniques to melons in China, reporting on our research work in ACIAR-supported small project number PHT/1996/152.作者：Nianlai ChenLi AnKeqi Ma 母体文献：ACIAR proceedings,no.105:postharvest handling of fresh vegetables,proceedings of a workship held in Beijing,People's Republic of China,9-11 May 2001 会议名称：会议时间：2001年01月01日会议地点：馆藏号：语种：eng 分类号：关键词：postharvest handlingfresh vegetablesagricultural research 基金项目：相似文献(9条)外文会议Postharvest handling systems assessment for vegetables in China and Australia 2001外文会议Postharvest handling systems assessment of pak choi and Chinese cabbage in eastern-central China 2001外文会议Assessment of postharvest handling systems for vegetables in Beijing 2001外文会议Problems and countermeasures in postharvest handling of fruits and vegetables in China 2001外文会议Postharvest handling of melons in Australia and China 2001外文会议Assessment of the postharvest handling system for broccoli grown in the Lockyer Valley, Queensland, Australia 2001外文会议Trends in China's vegetable exports 2001外文会议Australian postharvest technologies for fresh fruits and vegetables 2001外文会议Australian studies on storage and packaging of Asian leafy vegetables, Chinese waterchestnut, and Kabocha pumpkin 2001。

第四届“QTL作图和育种模拟研讨会”，2009年8月18-20日，山东泰安育种模拟的原理和遗传模拟工具QuLineCIMMYT’s headquarter in MexicoDr. Borlaug and green revolution ¾¾¾¾¾¾¾Mexico CityEl BatanToluca, 19º N, 2640 masl.High rainfall (800-900 mm)Cd. Obregon, 27º N, 39 masl. 8-11 t/ha under irrigation; 1-2t/ha under reduced irrigationCIMMYT’s Shuttle breedingMay to NovemberBreeding methods with self-pollinated cropsBreeding methods in CIMMYT’s wheat breeding program¾¾¾About 40% ofafter F7About 30% of the crosses are discarded in F1About 20% ofof yield trialsWhy do we need tools in breeding?¾¾¾••••Why do we need tools in breeding?¾¾Questions that can be studied by QuLine: A genetic and breeding simulation tool 1.2.3.4.Questions that can be studied by QuLine (mainly for inbred line development) 5.6.QuLine: A simulation tool for genetics and breeding¾QU-GENE (QUantitative GENEtics)A simulation platform for quantitative analysis of genetic models, developed byThe University of Queensland, Australia¾QuCim (funded by GRDC 2000-2004)A QU-GENE application breeding simulation module, specifically designed forCIMMYT’s wheat breeding programsSimulate most breeding programs for developing inbred linesVersion 1.1 released on July, 2003 (Workshop in Brisbane, Australia)More than 100 global requests for QuCim 1.1¾Renamed as QuLine (currently funded by GCP, H+, and Research Programs of China, i.e. 973, 863, and NSF)Landscape representation of a complex GE system (the real GE system is multi-dimensional)What can QuLine do?¾¾¾¾In genetics(implemented by the QU-GENE engine)¾¾¾¾In breeding (implemented by the QuLine module)How does QuLine work?¾•(= input for QuLine•(= input for QuLine(= input for QuLineDefine the QMP file for the selected bulk selection method: an exampleGeneral simulation parameters¾¾¾¾General simulation parameters ¾¾¾¾¾The number of models in the GE system and the number of runs for breeding strategy¾•9»¾Parameters to describe aset of breeding strategies¾¾Definition of a generation ¾¾¾Practical breeding small plot evaluation atVirtual breedingF6F7F8 (T), F8 (B)F8 (YT)F8 small plotFamilies selected14,760 3,8683,868 2,163 1,9741,974 779779An example for seed source indicator 0Bulk in F3 PYEI, F4PYEII, F5Pedigree in F4Families selected 4000 12001200 600600 100100 1000An example (LRC, Toowoomba, Australia) for seed source indicator 1Definition of each selection round¾¾Definition of each selection round ¾pedigree:bulk:Definition of each selection round¾••Definition of each selection round ¾•••9T for top, e.g. yield, tillering, grains per spike and 1000-kernel weight9B for bottom, e.g. lodging and rusts9M for middle, e.g. height and heading9R for random, for some special studies9Roundsof selectionSeedsourceindicatorGenerationtitleSeedpropagationtypeGenerationadvancemethodReplicationsPlotsizeTestlocationsEnvironmenttype10F6self pedigree175012, Toluca 40F7self bulk17011, Obregon F8(T)self bulk17012, TolucaF8(B)self bulk17013, El BatanF8(YT)self bulk110011, Obregon 10F8(SP)self bulk13011, Obregon An example of generation definitionTraitYieldLodg-ingStem rustLeaf rustStripe rustHeightTilleringHeadingGrains per spike1000 kernel weightTotalSelection mode T B B B B M T M T TF6, among 0.990.960.950.90F6, within 0.900.700.900.950.980.100.05F7, among 0.850.700.980.850.960.700.750.25F8(T), among 0.550.700.990.980.990.900.55F8(B), among 0.900.90F8(YT), among 0.400.40Traits, their selection modes andselected proportionsSteps to run QuLineBreeding strategiesGE systemPopulationInput information about the GxE system and populationsQUGENEQuLine*.fit*.var*.fre*.ham*.cro*.his*.rog*.pou *.fixMajor outputs from QuLineWhat has been done using QuLine?¾Crop Science(2003)¾Crop Science(2004)¾Aust. J. Agri. Sci.(2005)¾Crop Science(2007)Comparison of two breeding strategies: modified pedigree (MODPED) andselected bulk (SELBLK)Breeding methods with self-pollinated cropsBreeding methods in CIMMYT’s wheat breeding program¾¾¾methodsTrait, segregating gene number, gene effects and trait heritabilityTrait Genes Gene effecttypeAA Aa aa Trait range h b2(Indiv. plant)Yield20, 40E0, E1, E2Random value from UD (0, 1)0.05 Lodging3additive05100-300.10 Stem rust5additive00.510-50.30 Leaf rust5additive05100-500.30 Yellow rust5additive05100-500.30 Height3additive403020120-600.45 Tillers/plant 3additive53115-30.35 Heading5additive201612100-600.30 Grains/spike5additive1410670-300.35Trait correlation and pleiotropyTraitYieldLodgingStem rustLeaf rust YellowrustHeightTillers/plantHeadingGrains/spikeSeed weightYield-0.50-0.20-0.10-0.10-0.500.400.300.500.40Lodging-0.56Stem rust-0.25Leaf rust-0.05Yellow rust-0.09Height-0.62Tillers/plant-0.08-0.20-0.40Heading0.60Grains/spike 0.09-0.17-0.30Seed weight-0.07-0.30-0.07Estimated by CIMMYT breedersEstimated from the defined genetic modelExperiment design¾12 Genotype and environment (GE) systems¾Initial population¾¾Result 1: Genetic gain in yield from SELBLK is 3.3% higher than MODPED. SELBLK is slightly more efficient.For gains per spike and 1000-kernel weight, SELBLK has a faster genetic gain. For tillers/plant, MODPED has a faster genetic gain.Result 2: SELBLK retained 25% more crosses in the final selected population (more genetic diversity retained)Result 3: SELBLK required 1/3 less land from F1 to F8 than MODPED. SELBLK is more cost-effective.Result 4: SELBLK produced 40% less families (plots) to be planted from F1 to F8 (less labor required)Modeling of the Single Backcrossing Breeding Strategy(SBBS)(Theor. Appl. Genet., 2009, 118: 683-694)Category% favorablegenes Example% totalparentallinesElite adapted lines (EAL)80-85Major released cultivars in targeted mega-environments (MEs) either developed byCIMMYT or by partners10Adapted lines (AL)75-80Elite advanced lines from CIMMYT’sInternational Nursery and Yield Trials60Intermediate adapted lines (IAL)65-75Advanced lines from CIMMYT’s Yield Trialsin Ciudad Obregón and Toluca, Mexico10Un-adapted (or non-adapted) lines (UAL)20-40Land races 2Second generation of re-synthesized wheat (SYNII)40-60Derived lines between the first generation ofre-synthesized wheat derivatives andadapted lines10First generation of re-synthesized wheat (SYNI)20-40Derived lines between primary re-synthesized wheat and adapted lines5Estimated percentages of favourable alleles or gene combinations in different parental lines in wheat breeding at CIMMYTTwo traits defined in QU-GENE •––––•–––。

International Journal of Thermal Sciences46(2007)1311–1317/locate/ijtsPerformance analysis offinned tube and unbaffled shell-and-tubeheat exchangersJoydeep Barman,A.K.Ghoshal∗Department of Chemical Engineering,Indian Institute of Technology,Guwahati,North Guwahati781039,Assam,IndiaReceived15May2006;received in revised form26August2006;accepted6December2006Available online5February2007AbstractThis work considers an optimum design problem for the different constraints involved in the designing of a shell-and-tube heat exchanger consisting of longitudinallyfinned tubes.A Matlab simulation has been employed using the Kern’s method of design of extended surface heat exchanger to determine the behavior on varying the values of the constraints and studying the overall behavior of the heat exchanger with their variation for both cases of triangular and square pitch arrangements,along with the values of pressure drop.It was found out that an optimum fin height existed for particular values of shell and tube diameters when the heat transfer rate was the maximum.Moreover it was found out that the optimumfin height increased linearly with the increase in tube outer diameter.Further studies were also performed with the variation of other important heat exchanger design features and their effects were studied on the behavior of overall performance of the shell-and-tube heat exchanger.The results were thereby summarized which would proclaim to the best performance of the heat exchanger and therefore capable of giving a good idea to the designer about the dimensional characteristics to be used for designing of a particular shell and tube heat exchanger.©2007Elsevier Masson SAS.All rights reserved.Keywords:Fin height;Heat exchanger;Heat transfer rate;Longitudinalfins;Number of tube side passes;Pressure drop;Tube pitch layout1.IntroductionFins have long been recognized as effective means to aug-ment heat transfer.The literature on this subject is sizeable. Shell and tube heat exchanger with its tube eitherfinned or bare is extensively taught in the undergraduate level.Several text and reference books deal with the problems of longitudinalfinned tube in a shell and tube heat exchanger[1–4].It is well under-stood that with increase infin height of a longitudinalfin,heat transfer area increases to increase the heat transfer and at the same time the driving force decreases to decrease the heat trans-fer.However,one important design aspect,which probably is not discussed,is presented here.For a particular shell diameter, capacity of tube numbers is decided depending on tube size and pitch arrangement.In case offinned tube,height of thefin also plays an important role.Therefore,with increase infin height though surface area increases but number of tubes as well as *Corresponding author.E-mail addresses:joydeepb@iitg.ernet.in(J.Barman),aloke@iitg.ernet.in (A.K.Ghoshal).efficiency of thefin decreases.So,there might be an optimum condition of tube number andfin height for a particular tube arrangement and a particular shell diameter for which the heat transfer rate is the maximum[5].A Matlab coding has been de-signed to study the behavior of the overall performance of a heat exchanger on varying the important design features involved in it.The important constraints involved in the designing of a heat exchanger are studied here using the Matlab program.Several results and optimum conditions related to them are briefed out and tabulated in this literature to give a basic idea to the de-signer about the requirements and limitations to be included while designing afinned tube and unbaffled shell-and-tube heat exchanger.In the present article,Kern’s method of design[2]of ex-tended surface heat exchanger is applied for a shell-and-tube heat exchanger problem.Optimum conditions offin height and number of tubes in cases of triangular pitch and square pitch arrangements are found out along with the values of pressure drop.Other results concerning the various constraints of a heat exchanger like number of passes,tube outer diameter and tube pitch layout were also studied and compared in this literature.1290-0729/$–see front matter©2007Elsevier Masson SAS.All rights reserved. doi:10.1016/j.ijthermalsci.2006.12.0051312J.Barman,A.K.Ghoshal/International Journal of Thermal Sciences46(2007)1311–1317 Nomenclaturea s,a tfluidflow area.............................m2 A o,A i tube surface area...........................m2c s,c t specific heat capacity...............J kg−1K−1d thickness of eachfin.........................m de equivalent diameter for heat transfercalculations................................m D,D1inner and outer diameter of tube..............m D2inner diameter of shell.......................m D b tube bundle diameter........................m De s equivalent diameter for pressure dropcalculations................................m f s,f t friction factor offluidh f heat transfer coefficient offins......W m−2K−1 h f i heat transfer coefficient of outside tube surface andfins with respect to the inner tubesurface............................W m−2K−1 h i heat transfer coefficient of inside tubesurface............................W m−2K−1 H f height of eachfin...........................m G s,G t mass velocity offluid...............kg m−2s−1 K s,K t thermal conductivity...............W m−1K−1 L length of each tube..........................m n number of tube side passes N f number offins per tubeN T total number of tubesP t tube pitch..................................m P w wetted perimeter............................m Pr s,Pr t Prandtl numberQ overall heat transfer rate per unit LMTD..W K−1 Re s,Re t Reynolds numbers s,s t specific gravity offluidU overall heat transfer coefficient......W m−2K−1 w tube sidefluid’s massflow rate...........kg s−1 W shell sidefluid’s massflow rate...........kg s−1 P s, P t pressure drop............................Pa Greek symbolsμs,μt,μw viscosity..............................Pa s ηffin efficiencySubscriptsffini inside of tubeo outside of tubes shell sidet tube sidew wall2.The mathematical program model of Kern’s method and solution procedure:determination of tube bundle diameter and maximum number of tubesA shell-and-tube heat exchanger with an internal shell diam-eter,D2,consisting offinned tubes of outer diameter,D1,inner diameter,D,length,L,withfins of height,H f,and thickness, d,is considered here.Total number offins per tube is N f and total number of tubes is N T.Tube bundle diameter is D b:D b=(D1+2H f)×(N T/K)(1/M)(1) The constants,K and M,are determined from Table1for dif-ferent tube passes and tube pitch layouts for a tube pitch,P t=1.25(D1+2H f)[1](2) Tube bundle diameter isfirst calculated by iterative process for bare tubes;henceforth maximum number offinned tubes,N T,is calculated from the derived tube bundle diameter from Eq.(1).3.Shell side calculationsTheflow area,a s,wetted perimeter,P w,equivalent diame-ter,d e,mass velocity,G s,Reynold’s number,Re s and Prandtl number,Pr s are calculated using Eqs.(3)–(8)as follows:a s=πD22/4−N TπD21/4+N f×d×H f(3) P w=N T(πD1−N f×d+2N f×H f)(4) d e=4a s/P w(5) G s=W/a s(6) Re s=d e×G s/μs(7) Pr s=c s×μs/K s(8) The heat transfer coefficient for the outside tube andfin surfaces can be calculated using Sieder–Tate correlation[4],Eqs.(9)and(10)as shown below:h f=1.86(K s/d e)×(Re s×Pr s×d e/L)1/3(9) for laminarflow;Table1Values of constants,K and M[1]Triangular pitch Square pitchNo.of passes1246812468K0.3190.2490.1750.07430.03650.2150.1560.1580.04020.0331 M 2.142 2.207 2.285 2.499 2.675 2.207 2.291 2.263 2.617 2.643J.Barman,A.K.Ghoshal /International Journal of Thermal Sciences 46(2007)1311–13171313h f =0.027(K s /d e )×Re 0.8s ×Pr 1/3s×(μs /μw )0.14(10)for turbulent flow.4.Tube side calculationsThe tube side flow area,a t ,mass velocity,G t ,Reynolds number,Re t and Prandtl number,Pr t ,for tube side fluid are calculated from Eqs.(11)–(14).With the values of viscosity,μt ,specific heat capacity,c t and thermal conductivity,K t ,for tube side fluid and using the Sieder–Tate correlation,the heat transfer coefficient of inside tube surface,h i ,can be calculated.a t =πN T ×D 2 /4n (11)G t =w/a t (12)Re t =DG t /μt (13)Pr t =c t ×μt /K t(14)5.Fin efficiency calculationsThe process is assumed as a steady state one and there isa continuous flow of fluid in the axial direction (both in the shell and tube side).Therefore,for a particular value of radial location,the temperature for any location in the axial direction would be almost same.Further,the angular directional variation of temperature is also neglected.Thus,the problem is reduced to a one-dimensional heat conduction problem.Hence,the fin efficiency is represented as ηf and calculated using Eqs.(15)and (16).ηf =tanh (mH f )/(mH f )(15)wherem =(2h f /K f d)1/2(16)6.Heat transfer calculationsHeat transfer coefficient of outside surface and fins with respect to the inner surface of tubes,h f i and heat transfer coef-ficient of inside surface,h i ,are given as below using Eqs.(17),(21)and (22):h f i =(H f ×P ×N f ×ηf ×N T +A o )h f /A i(17)A o and A i are the outside bare tube surface area and inside surface area of tubes respectively,where P is the perimeter of a fin,as given by Eqs.(18)–(20).A o =(πD 1−N f d)×N T L (18)A i =πDN T L (19)P =2(L +d)(20)The heat transfer coefficient for the inside tube surface can be calculated using Sieder–Tate correlation [4],Eqs.(21)and (22)as shown below:h i =1.86(K t /D)×(Re t ×Pr t ×D/L)1/3(21)for laminar flow;h i =0.027(K t /D)×Re 0.8t ×Pr 1/3t×(μt /μw )0.14(22)for turbulent flow.Thus the overall heat transfer coefficient,U ,with respect to the inside tube surface is given by Eq.(23):U =(h f i ×h i )/(h f i +h i )(23)Finally,the heat transfer rate with respect to the inside tube sur-face area,Q per degree LMTD is calculated using Eq.(24)as follows:Q =U ×A i(24)7.Pressure drop calculationsEquivalent diameter for pressure drop calculations in case of shell side fluid will be different from the diameter used for heat transfer calculations.This diameter is given by Eq.(25):De s =4a s /(P w +πD 2)(25)The pressure drops for shell side and tube side fluid, P s and P t respectively are calculated using Eqs.(26)–(29)as follows:P s = f s ×G 2s ×L / 5.22×1010×De s ×s s (26)f s =16/Re s(27)for laminar flow andf s =0.0035+0.24/Re 0.42s(28)for turbulent flow.Here,Re s =(De s ×G s )/μsP t = f t ×G 2t×L ×n / 5.22×1010×D ×s t (29)where f t is the tube side friction factor and can be calculated as shown above,Eqs.(27)and (28),using tube side Reynolds number,Re t .s s and s t are the specific gravities of shell side and tube side fluids respectively [2].8.Solution basisAn exemplary problem discussed below is used to study the objectives as discussed.Hot fluid (3.8kg s −1)in shell-side is to be cooled by a cold fluid (6.4kg s −1)in tube side.Inner di-ameter of the shell and length of the shell are kept constant as 0.5and 4.88m respectively.Inner and outer diameters of the tube are varied.Number of fins with thickness 9×10−4m per tube is 20and is kept constant for all the calculations.Ther-mal conductivity of the fin material is 45W m −1K −1.Hot and cold fluids are oxygen gas and water respectively.The values for thermal conductivity,viscosity and heat capacity of oxygen gas and water are calculated at an average temperature of 353and 305K respectively.9.Results and discussionsThe Kern’s method of designing of shell and tube heat ex-changers with extended surfaces was used for the designing of the heat exchanger concerned in this paper.The equations in-volved in this method are all simple and well established,and1314J.Barman,A.K.Ghoshal /International Journal of Thermal Sciences 46(2007)1311–1317were incorporated in a Matlab program specially coded for the purpose of this paper.This program is simply a step-wise cal-culation and does not involve any iteration or any optimization technique that may lead to some numerical errors.However,the program was thoroughly checked and thereafter run to arrive at the reasonable conclusions as reported in the manuscript.The results tabulated in Tables 2–5,and results shown graph-ically in Figs.1and 2were found out for a tube outer diameter of 0.0254m.Tables 2and 3present the maximum number of finned tubes of different fin heights for triangular pitch and square pitch arrangements respectively,which can be accom-modated in the shell of inner diameter 0.5m.They also reflect the obvious nature of variations of the shell-side and tube-side pressure drops with variation of fin height keeping one tube pass only.It is well understood that as the number of tubes decreases with the increase in fin height,the tube side fluid flow area is decreased thereby increasing the pressure drop.On the other hand,the shell side flow area increases leading to decrease in pressure drop,which is also shown through Figs.1and 2for tri-angular pitch and square pitch arrangements respectively.The variations of the heat transfer rates for both the pitches with variations of fin height are reported in Tables 2and 3respec-Fig.1.Variation of heat transfer rate and shell-side pressure drop with increase in fin height for triangular pitch arrangement,one tube side pass and for tube outer diameter,0.0254m.tively.The nature of the variations is shown through Figs.1and 2for triangular pitch and square pitch arrangements respec-tively.It is observed from the figures that there exists an opti-mum fin height (0.4572×10−2m for triangular pitch and 0.4826×10−2m for square pitch arrangement),which gives the highest heat transfer rate.Corresponding to these optimum fin heights,optimum number of adjustable finned tubes is 78and 60respectively.Under these optimum conditions,heat transfer rates are 7798.4and 5843.0W K −1,tube side pressure drops are 0.2985and 0.4723kPa and shell side pressure drops are 1.3217and 0.8343kPa for triangular and square pitch arrange-ments respectively.Tables 4and 5show the corresponding values of optimum fin height,total number of tubes,heat transfer rate and pres-sure drop for different values of tube side passes.We notice from these tables (Tables 4and 5)that for a constant shell inner diameter,with increase in the number of tube-side pass the maximum heat transfer rate corresponding to the optimum value of fin height decreases.It is also noticed that as the total number of tubes decreases the tube side pressure drop values in-creases largely which is a major drawback from economicandFig.2.Variation of heat transfer rate and shell-side pressure drop with increase in fin height for square pitch arrangement,one tube side pass and for tube outer diameter,0.0254m.Table 2Capacity of finned tubes of 0.0254m outer diameter in the shell,pressure drops and heat transfer rate values for triangular pitch arrangement and for one tube side passHeight of fin,H f ×102,m 0.2540.3810.43180.45720.5080.55880.6350.762Total number of tubes,N T10286817873696355Shell side—pressure drop, P s ,kPa 1.4341 1.3692 1.3383 1.3217 1.2893 1.2569 1.2093 1.1335Tube side—pressure drop, P t ,kPa0.18820.2530.28270.29850.3330.36950.42950.546Heat transfer rate per unit LMTD,Q ,W K −17469.37767.17797.37798.47777.47730.57622.47371.2Table 3Capacity of finned tubes of 0.0254m outer diameter in the shell,pressure drops and heat transfer rate values for square pitch arrangement and for one tube side pass Height of fin,H f ×102,m 0.2540.3810.40640.43180.45720.48260.5080.5334Total number of tubes,N T8268666462605850Shell side—pressure drop, P s ,kPa 0.87630.86050.85430.8480.84110.83430.82740.8191Tube side—pressure drop, P t ,kPa0.27650.37570.39850.4220.44610.47230.49850.5268Heat transfer rate per unit LMTD,Q ,W K −15522.45797.55820.45835.15842.45843.05837.65826.8J.Barman,A.K.Ghoshal /International Journal of Thermal Sciences 46(2007)1311–13171315optimization point of views.As expected,the shell side pressure drop decreases with decrease in tube number but the decrease is much less in comparison to the increase for the tube side pressure drop.So,in this case,the tube side pressure drop val-ues bear more importance while selecting the number of passes.Hence,from the tabulated data obtained it can be said that one tube side pass is the best choice for the finest results of heat ex-changer performance unless a constraint related to the number of tubes is faced when higher values of tube side pass could be considered.Moreover,it was also noticed that for a particular fin height,the total number of adjustable tubes varies for the pitch arrangements.As the number of tubes that could be ad-justed in a square pitch arrangement were less in number than in triangular pitch arrangement so even the most optimum value of fin height in case of square pitch arrangement could not pro-duce the same heat transfer rate as compared to the other.But the shell side pressure drop is higher in magnitude in triangu-lar pitch than in square pitch arrangement,whereas the relation is just the opposite in case of tube side pressure drop values.So,in the absence of any pressure drop constraints,thetriangu-Fig.3.Variation of optimum fin height with outer diameter of tubes.lar pitch arrangement with the optimum value of fin height will prove to be the best choice.The other tables,i.e.,Tables 6–9give the values of different important parameters such as a s ,A i ,A o ,Re s ,Pr s ,h f ,ηf ,h f i ,h i and U used and determined during the calculations.Fig.3shows the variation of optimum fin height with the change of tube outer diameters for a fixed number of tube side passes and for triangular pitch arrangement.The relation between them is found to be linear and can be expressed by Eq.(30):H f =0.0852×D 1+0.0025(30)Thus by using this equation,an approximate value of optimum fin height for the highest heat transfer rate can be pre-calculated for a tube of particular diameter.Fig.4shows a comparison of the performance of the heat exchanger for one and two tube side passes for triangular pitch arrangement.It is found out that the performance of the heat exchanger based on the heat transfer rate values for two-tube side passes could never meet up with the results for one tube side pass.Also after inspecting thepres-parison of heat transfer rates with fin heights for one and two tubes side passes.Table 4Optimum fin height for maximum heat transfer rate,for different tube-side passes and corresponding values of total number of finned tubes and pressure drops for triangular pitch arrangement and for tube outer diameter as 0.0254m Number of tube side passes,n 12468Optimum fin height,H f ×102,m0.45720.45720.45720.43180.38Heat transfer rate per unit LMTD,Q ,W K −17798.47639.46523.84383.53166.4Total number of finned tubes,N T 7872624740Shell-side pressure drop, P s ,kPa 1.3217 1.12040.84170.50830.3567Tube-side pressure drop, P t ,kPa0.29852.29120.032298.8108297.322Table 5Optimum fin height for maximum heat transfer rate,for different tube-side passes and corresponding values of total number of finned tubes and pressure drops for square pitch arrangement and for tube outer diameter as 0.0254m Number of tube side passes,n 12468Optimum fin height,H f ×102,m0.48260.45720.48260.40640.4064Heat transfer rate per deg.LMTD,Q ,W K −158435476.75286.92911.72503.0Total number of finned tubes,N T 6056513632Shell-side pressure drop, P s ,kPa 0.8340.70310.63640.32520.2773Tube-side pressure drop, P t ,kPa0.47233.557827.9617160.236441.3241316J.Barman,A.K.Ghoshal/International Journal of Thermal Sciences46(2007)1311–1317Table6Values of various parameters involved in determining the important variables of Table2Height offin,H f×102,m0.2540.3810.43180.45720.5080.55880.6350.762 Shell sideflow area,a s,m2 1.41 1.485 1.511 1.523 1.546 1.567 1.596 1.637 Inside tube surface area,A i,m231.326.3724.7123.9422.521.1819.4116.9 Outside tube surface area,A o,m231.10126.2124.5623.79322.3621.0519.2816.8 Shell side 3.988 3.612 3.521 3.483 3.423 3.377 3.33 3.294 Reynolds number,Re s×10−4Shell side0.7010.7010.7010.7000.7010.7010.7010.701 Prandtl number,Pr sFin heat transfer111.8108.26106.96106.34105.14104.01102.42100.05 coefficient,h f,W m−2K−1Fin efficiency,ηf0.98820.97460.9680.96450.95710.94920.93640.9133 Heat transfer coefficient of291.03365.342392.96406.34432.25457.06492.27545.82fins and outside tube surfacewith respect toinside tube surface,h f i,W m−2K−1Inside tube surface heat 1.325 1.52 1.601 1.642 1.726 1.811 1.943 2.17 transfer coefficient,h i×10−3,W m−2K−1Overall heat transfer coefficient238.63294.55315.52325.75345.68364.97392.74436.11 with respect toinside tube surface,U,W m−2K−1Table7Values of various parameters involved in determining the important variables of Table3Height offin,H f×102,m0.2540.3810.40640.43180.45720.48260.5080.5334 Shell sideflow area,a s,m2 1.532 1.595 1.606 1.6162 1.626 1.636 1.645 1.654 Inside tube surface area,A i,m225.0320.9820.28319.6218.9818.3817.8117.26 Outside tube surface area,A o,m224.8820.8520.15719.518.8718.2717.717.16 Shell side 4.987 4.54 4.484 4.434 4.392 4.355 4.323 4.296 Reynolds number,Re s×10−4Shell side0.7010.7010.7010.7010.7010.7010.7010.701 Prandtl number,P r sFin heat transfer98.3796.3295.9195.595.0994.794.393.92 coefficient,h f,W m−2K−1Fin efficiency,ηf0.98960.97730.97440.97130.96810.9650.96130.9577 Heat transfer coefficient of256.3325.67338.81351.72364.38376.81389.0400.96fins and outside tube surface withrespect to insidetube surface,h f i,W m−2K−1Inside tube surface heat 1.585 1.825 1.875 1.926 1.977 2.028 2.081 2.133 transfer coefficient,h i×10−3,W m−2K−1Overall heat transfer coefficient220.62276.36286.96297.4307.67317.78327.73337.52 with respect toinside tube surface,U,W m−2K−1sure drop values(Table4),it can be well concluded that the best option would be to select a heat exchanger with one tube side pass if there is no tube number constraint involved.Hence it can be well summarized by mentioning that a combination of triangular pitch arrangement,one tube side pass and a value of fin height calculated from Eq.(30),when incorporated in the designing of a shell-and-tube heat exchanger with no baffles would certainly proclaim to give the best performance until and unless some restriction is being levied on in terms of pressure drop or number of tubes.10.ConclusionsIn this work the variation of heat transfer rate withfin height for afinned tube shell-and-tube heat exchanger was studied for two different pitch arrangements.It was found out that for par-J.Barman,A.K.Ghoshal/International Journal of Thermal Sciences46(2007)1311–13171317 Table8Values of various parameters involved in determining the optimumfin height and other important variables of Table4Number of tube side passes,n12468 Optimumfin height,H f×102,m0.45720.45720.45720.43180.38 Shell sideflow area,a s,m2 1.523 1.5619 1.6261 1.722 1.7725 Inside tube surface area,A i,m223.9422.0818.9914.512.238 Outside tube surface area,A o,m223.79321.9418.87514.4112.163 Shell side Reynolds number,Re s×10−4 3.483 3.778 4.391 6.0017.798 Fin heat transfer coefficient,h f,W m−2K−1106.34102.0495.184.3777.781 Fin efficiency,ηf0.96450.96590.96810.97460.9817 Heat transfer coefficient offins and outside406.34390.3364.4311.5263.33 tube surface with respect to inside tubesurface,h f i,W m−2K−1Inside tube surface heat transfer coefficient, 1.642 3.051 5.992 1.0285 1.4827 h i×10−3,W m−2K−1Overall heat transfer coefficient with respect325.75346.03343.51302.34258.74 to inside tube surface,U,W m−2K−1Table9Values of various parameters involved in determining the optimumfin height and other important variables of Table5Number of tube side passes,n12468 Optimumfin height,H f×102,m0.48260.45720.48260.40640.4064 Shell sideflow area,a s,m2 1.636 1.6644 1.692 1.795 1.8206 Inside tube surface area,A i,m218.3817.1515.7111.0379.788 Outside tube surface area,A o,m218.2717.0515.61310.979.728 Shell side Reynolds number,Re s×10−4 4.355 4.826 5.0978.249.291 Fin heat transfer coefficient,h f,W m−2K−194.791.0488.7275.9673.118 Fin efficiency,ηf0.9650.96940.9670.97960.9803 Heat transfer coefficient offins and outside376.81349.19353.61269.38259.44 tube surface with respect to inside tubesurface,h f i,W m−2K−1Inside tube surface heat transfer coefficient, 2.028 3.734 6.974 1.28 1.773 h i×10−3,W m−2K−1Overall heat transfer coefficient with respect317.78319.3336.54263.82255.69 to inside tube surface,U,W m−2K−1ticular shell and tube diameters an optimum value offin height exists,which gives the highest heat transfer rate.Moreover it was also found out that on increasing the number of tube side passes while keeping the shell diameter constant,though the number of tubes could be decreased but the performance on the basis of heat transfer rate kept on decreasing and tube side pressure drop values increased substantially.The optimumfin height also increased linearly with the increase of tube outer diameter.It is worth mentioning here that the Matlab coding designed for this problem and the results obtained on using it,might prove quite beneficial in choosing the most appropriatefin height,total number of tubes,tube dimensions,arrangements, number of tube side passes andfin dimensions for a known value of shell diameter as well as keeping the pressure drops in check.In this problem the physical properties of thefluids were assumed constant,tube andfin dimensions were assumed uniform,throughout the entire system.It can be further stated that no experimental verification could be possible due to lack of such experimental data.How-ever,it would be highly appreciated to carry experimental work in this regard.References[1]J.R.Backhurst,J.M.Coulson,J.H.Harkar,J.F.Richardson,Coulson&Richardson’s Chemical Engineering,Butterworth–Heinemann,Oxford, 2004.[2]D.Q.Kern,Process Heat Transfer,McGraw-Hill,New York,2000.[3]P.Harriott,W.L.McCabe,J.C.Smith,Unit Operations of Chemical Engi-neering,McGraw-Hill,New York,2001.[4]S.P.Dusan,R.K.Shah,Fundamentals of Heat Exchanger Design,John Wi-ley and Sons,New York,2003.[5]J.Barman,A.K.Ghoshal,in:Proceedings of Chemcon’05,58th AnnualChemical Engineering Congress,India,2005.。

湍流脉动速度的英文Turbulent Fluctuating Velocity.Turbulence, often described as the "chaos" of fluids, is a common and complex phenomenon encountered in various natural and engineering applications. It is characterized by random fluctuations in various fluid properties, including velocity, pressure, and temperature. Among these fluctuations, turbulent pulsating velocity, or simply turbulent fluctuating velocity, plays a pivotal role in determining the overall behavior of turbulent flows.1. Definition and Characteristics.Turbulent fluctuating velocity refers to the rapid and irregular variations in the velocity of fluid particles within a turbulent flow. These variations are caused by the interaction of eddies, vortices, and other small-scale structures within the flow. These structures constantly form, merge, and break down, leading to the observedfluctuations.The magnitude of these fluctuations is typically much larger than the mean velocity of the flow and can be several orders of magnitude higher. They are also highly uncorrelated, meaning that the velocity at one point in the flow does not depend on the velocity at another point, unless they are separated by a distance comparable to the size of the turbulent eddies.2. Importance of Turbulent Fluctuating Velocity.Turbulent fluctuating velocity is crucial in various fluid dynamics applications. It significantly impacts heat transfer, mass transfer, and the mixing of fluids. For example, in heat exchangers, the turbulent fluctuating velocity enhances the rate of heat transfer between two fluids by increasing the effective surface area for heat exchange.In addition, turbulent fluctuating velocity also plays a key role in determining the overall resistance or dragexperienced by objects placed within a turbulent flow. The fluctuating velocities cause pressure fluctuations on the object's surface, leading to additional drag forces.3. Measurement and Analysis.Measuring turbulent fluctuating velocity is a challenging task due to its random and transient nature. However, several techniques have been developed to capture these fluctuations, including hot-wire anemometry, laser Doppler anemometry, and particle image velocimetry.These measurements provide valuable insights into the characteristics of turbulent flows, such as the statistics of velocity fluctuations, their spatial and temporal correlations, and the energy spectrum of turbulent eddies.4. Modeling and Simulation.Modeling and simulating turbulent fluctuating velocity require sophisticated numerical techniques and computational resources. turbulence models, such as theReynolds-Averaged Navier-Stokes (RANS) model and Large Eddy Simulation (LES), are commonly used to predict the behavior of turbulent flows.These models aim to capture the effects of turbulent fluctuating velocity by introducing additional terms or equations into the governing fluid dynamics equations.While RANS models focus on the statistical properties of turbulence, LES aims to resolve the largest eddies directly and model the smaller ones.5. Conclusion.Turbulent fluctuating velocity is a crucial aspect of turbulent flows, affecting various fluid dynamics phenomena. Understanding its characteristics and behavior is essential for predicting and controlling turbulent flows in various applications, including energy conversion, transportation, and environmental engineering.With ongoing research and the continuous development of new measurement techniques and numerical models, ourunderstanding of turbulent fluctuating velocity and its impact on turbulent flows will continue to deepen.。

英文原文Case StudyTheoretical and practical aspects of the wear of vane pumpsPart A. Adaptation of a model for predictive wear calculationAbstractThe aim of this investigation is the development of a mathematical tool for predicting the wear behaviour of vane pumps uscd in the standard method for indicating the wcar charactcristics of hydraulic fluids according to ASTM D 2882/DIN 51389.The derivation of the corresponding mathematical algorithm is based on the description of the combined abrasive andadhesive wear phenomena occurring on the ring and vanes of the pump by the shear energy hypothesis, in connection withstochastic modelling of the contacting rough surfaces as two-dimensional isotropic random fields. Starting from a comprehensive analysis of the decisive ring-vane tribo contact, which supplies essential input data for the wear calculation, the computational method is adapted to the concrete geometrical, motional and loading conditions of thetribo system vane pump and extended by inclusion of partial elastohydrodynamic lubrication in the mathematical modej.For comparison of the calculated wear behaviour with expenmental results, a test series on a rig described in Part B was carried out. A mineral oil-based lubricant without any additives was used to exclude the influence of additives which cannot be described in the mathematical model. A good qualitative correspondence between calculation and experiment regarding the temporal wear progress and the amount of calculated wear mass was achieved.Keywords: Mathematical modelling; Simulation of wear mechanisms; Wear testing devices; Hydraulic vane pumps; Elastohydrodynamic lubrication;Surface roughness1. IntroductionIn this study, the preliminary results of a newmethodological approach to the development of tribo- meters for complicated tribo sysLems are presented. The basic concept involves the derivation of a mathematical algofithm for wear calculation in an interactive process with experiments, which can be used model of the tribo system to be simulated. In this way, an additional design tool to achieve the correlation of the wear rates of the model and original system is created.The investigations are performed for the Vickers vane pump V104 C usedin the standard method forindicating the wear characteristics of hydraulic fluids according to ASTM D 2882/DIN 51 389. In a first step, a mathematical theory based on the description of abrasive and adhesive wear phenomena by the shear energy hypothesis, and including stochastic modelling of the contacting rough surfaces, is adapted to the tribological reality of the vane pump, extended byaspects of partial elastohydrodynamic lubrication and verified by corresponding experiments.Part A of this study is devoted to the mathematical modelling of the wear behaviour of the vane pump and to the verification of the resulting algorithm; experimental wear investigations represent the focal point of Part B, and these are compared with the results of the computational method derived in Part A.2. Analysis of the tribo contactThe Vickers vane pump V 104 C is constructed as a pump for constant volume flow per revolution. The system pressure is led to the bottom side of the 12 vanes in the rotor slots to seal the cells formed by each pair of vanes, the ring, the rotor and the bushings in the tribologically interesting line contact of the vane and inner curvature of the ring (Fig. 1). Simultaneously, all other vane sides are stressed with different and periodically alternating pressures of the fiuid. A comprehensive structure and stress analysis based on quasistatic modelling of all inertial forces acting on the pump, and considering the inner curvature of the ring, the swivel motion of the vanes in relation to the tangent of curvature and the loading assumptions, is described in Refs. [1-3]. Thereby, a characteristic graph for the contact force Fe as a function of the turn angle can be obtained, which depends on the geometry of the vanes used in each run and the system pressure. From this, the inner curvature of the ring can be divided into four zones of different loading conditions in vane-ring tribo contact (Fig. 2), which is in good agreement with the wear measurements on the rings: in the area of maximum contact force (zone n), the highest linear wear could be found [2,3] (see also PartB).3. Mathematical modelling3.1. Basic relations for wear calculationThe vane and ring show combined abrasive and adhesive wear phenomena (Fig. 3). The basic concepts of the theory for the predictive calculation of such wear phenomena are described in Refs. [4-6].Starting from the assumption that wear is caused by shear effects in the surface regions of contacting bodies in relative motion, the fundamental equation(1)for the linear wear intensity Ih in the stationary wear state can be derived, which contains the specific shear energy density es/ro, interpretable as a material constant, and the real areaArs of the asperity contacts undergoing shear. To determine this real contact area, the de- scription of the contacting rough surfaces as two-dimensional isotropic gaussian fields according to Ref.[7] is included in the modelling. Thus the implicit functional relationwith the weight function(2)is found, which can be used to calculate the surface ratio in Eq. (1) for unlubricated contacts from the hertzian pressure Pa acting in the investigated tribo contact by a complicated iterative process described in Refs. [6,8]. The concrete structure of the functions Fand c depends on the relative motion of the contacting bodies (sliding, rolling). The parameter a- （m0m4）/m22represents the properties of the rough surface by its spectral moments, which can be deter- mined statistically from surface profilometry, and the plasticity index妒= (mOm4)y4(E'/H) is a measure of the ratio of elastic and plastic microcontacts.3.2. Extension to lubricated contactsThe algorithm resulting from the basic relations for wear calculation was applied successfully to unlubricated tribo systems [8]. The first concepts for involving lubrication in the mathematical model are developed in Ref. [8]. They are based on the application of the classical theory of elastohydrodynamic lubrication (EHL) to the microcontacts of the asperities, neglecting the fact that there is also a "macrolubrication film" which separates the contacting bodies and is interrupted in the case of partial lubrication by the asperity microcontacts. Therefore their use for calculating practical wear problems leads to unsatisfactory results [9]. They are extended here by including the following assump- tions in the mathematical model.(1) Lubrication causes the separation of contacting bodies by a macrofilm with a mean thickness u. which can be expressed in terms of the surfaceroughness by [10](3)Where u0 is the mean film thinkness according to classical EHL theory between two ideally smooth bodies, which can be determined for line contact of the vane and ring by[11](2) In the case of partial lubrication, the macrofilm is interrupted during asperity contacts. A plastic microcontact is interpreted as a pure solid state contact, whereas for an elastic contact theroughness is superimposed by a microlubrication film. Because of the modelling of the asperities as spherical indenters, the microfilm thickness can be determined using the EHL theory for sphere-plane contacts, which is represented in the random model by the sliding number [8](5)(3) The hertzian pressure acting in the macrocontact works in two parts: as a hydrodynamic pressure pEH borne by the macrolubrication film and as a pressure pFK borne by the roughness in solid body contact.(4) For pure solid state contacts, it is assumed that the limit for the mean real pressure prFK which an asperity can resist without plastic deformation can be estimated by one-fifth to one-sixth of its hardness(6)Investigations on the contact stiffness in Ref. [11] have led to the conclusion that the elastic properties of the lubrication film cause a relief of the asperities, which means that the real pressure working on the asperity is damped. Therefore, in the mathematical model for lubricated tribo systems, an additional term fffin, which corrects the upper limit of the real pressure as a function of the film thickness, is introduced p,EH =prFK[1 -fcorr(U)] (7)This formula can be used to determine a modified plasticity index {PEH for lubricated contacts according to Ref. [8].Altogether, the basic model for wear calculation can be extended for lubricated tribo systems by replacing relation (2) by(8)(3)3.3. Adaptation to the tribo’system vane pumpTo apply the mathematical model for wear calculation to a concrete tribo system, all material data (specific material and fluid properties, roughness parameters) used by the algorithm must be determined (see Part B). Moreover, the model must be adapted to the mechanical conditions of the wear process investigated. On the one hand, this is related to the relative motion of the bodies in tribo contact, which influences the concrete structure of function f in formulae (2) and (8). In the case of vane-ring contact, sliding with superimposed rolling due to the swivel motion of the vanes was modelled(9)A detailed derivation of the corresponding formulae for fsliding and f.olling can be found in Refs.[8,9].On the other hand, the hertzian presstire Pa acting on tribo contact during the wear process has an esseritial importance in the wear calculation. For the tribo system vane pump, the mean contact force Fe in each loading zone can be regarded as constant, whereas the hertzianpressure decreases with time. The reason for this is the wear debris on the vane, which causes a change 'n the vane tip shape with time,leading to an increased contact radius and, accordingly, a larger contact areaTo describe this phenomenon by the mathematical wear model, the volume removal Wvl of one vane in terms of the respective contact radius Ri(t) at time t and the sliding distance SR(Rl(t》is given by(10)where the constants a and b can be determined by regression from the geometrical data of the tested vanes. The corresponding sliding distance necessary to reach a certain radius Ri due to vane wear can be expressed using the basic equation (1):(11)Thus, applying Eq. (11) together with Eq. (10) to the relation(12)it is possible to derive the following differential equation for the respective volume removal Wvll of the ring, which can be solved by a numerical procedure(13)The required wear intensities of the vane and ring can be calculated by Eq. (8) as a function of the contact radius from the hertzian pressures working in each loading zone, which are available from the contact force by the well-known hertzian formulae.3.4 Possibilities of verificationIf all input data are available for a concrete vane pump run (the concrete geometrical, material and mechanical conditions in the cartridge used and the specific fluid properties, see Part B), the mathematical model for the calculation of the wear of vane pumps derived above can describe quantitatively the following relations.(1) The sliding distance SR(RI) and, if the number of revolutions of the pump and the size of the inner ring surface are known, the respective run time t of the pump which is necessary to reach a certain shape of the vane tips due to wear.(2) The volume removal W,.:uri(t) and the wear masses WmW(t) of the vane and ring as a function of the run time t.(3) The mean local linear wear Wl(t) in every loading zone on the ring at time t.Thus an immediate comparison between the calculated and experimentally established wear behaviour, with regard to the wear progress in time, the local wear progress on the ring and the wear masses at a certain time t, becomes possible.4。

中文摘要中文摘要近年来，由于对信息融合的要求越来越高，使得融合技术不仅在信息处理过程方面大大进步，也在军事领域、故障诊断和目标识别等众多领域得到了成功的研究与应用。

其中，D-S证据理论有着在无先验信息的状态下，可以很好的表示和处理不确定情况的优点，从而通过对问题进行建模，在融合过程中对数据进行更加优化的处理，提高了融合的准确性，使决策结果更加精确。

但若存在冲突证据，运用D-S证据理论进行证据融合就不能达到很好的效果甚至结果有悖常理，所以需要对证据理论进行改进。

当前研究的重点主要集中在修正证据源和修改组合规则，两种方法相对比发现，对证据源进行预处理不会破坏Dempster组合规则的优良性质，这比修改组合规则更有优势。

本文从证据源预处理和证据融合两方面入手，对冲突证据处理并合成，主要研究内容如下：首先，针对融合的不确定性问题进行分析，提出了在证据冲突且存在复合焦元的情况下降低不确定度的逆DP概率转换方法。

基于DP合成规则，通过势的划分，分层逐步降低不确定度，将基本概率分配函数经过转化为概率函数进行融合。

其次，针对冲突证据融合过程中可信度不高的问题，提出一种基于置信距离的加权融合算法。

利用置信距离测度对证据度量，将证据转换为距离矩阵形式，经过矩阵相关计算得到可信度，进而加权进行信度分配以修正证据源，最终进行基础的证据融合。

最后，针对证据冲突程度的衡量问题，提出了基于指数散度的冲突证据融合算法。

利用指数交叉熵进行冲突证据的衡量，并将证据间的冲突系数构建距离矩阵，利用加权融合的方式进行数据融合。

通过大量仿真对比研究，验证了所提算法的有效性与可靠性。

关键词：D-S证据理论；冲突证据；证据融合；概率转换；置信距离测度；指数散度黑龙江大学硕士学位论文AbstractIn recent years, with the increasing demand for information fusion, fusion technology has not only made great progress in information processing, but also been successfully studied and applied in many fields such as military field, fault diagnosis and target identification. Among them, D-S evidence theory has the advantage of expressing and dealing with uncertainties well without prior information, so it can model problems and process data more optimally in the process of fusion, which improves the accuracy of fusion and makes decision results more accurate. However, if there are conflict evidences, the evidence fusion using D-S evidence theory can not achieve good results or even the results are contrary to common sense, so we need to improve the evidence theory.The current research focuses on revising evidence sources and modifying combination rules. However, compared with two methods, it is found that pretreatment of evidence sources will not destroy the good quality of Dempster combination rules, which is more advantageous than revising combination rules. In this paper, the conflict evidences are processed and synthesized from two aspects of evidence source pretreatment and evidence fusion. The main research contents are as follows: Firstly, the uncertainty of fusion is analyzed, and an inverse DP probability conversion method is proposed to reduce the uncertainty in the case of evidence conflict and compound focal elements. Based on DP synthesis rule, the uncertainty is gradually reduced by dividing the potential, and the basic probability assignment function is transformed into probability function to fuse.Secondly, a weighted fusion algorithm based on confidence distance is proposed to solve the problem of low credibility in the process of conflict evidence fusion. Using confidence distance measure to measure evidence, the evidence are transformed into distance matrix form. The credibility is obtained by matrix correlation calculation, and then the reliability is allocated by being weighted to modify the evidence source. In the end, the basic evidence is fused.Finally, aiming at the measurement of evidence conflict degree, a method ofAbstractconflict evidence synthesis based on exponential divergence is proposed. The index cross-entropy is used to measure the conflict evidence, and the conflict coefficient between the evidences is constructed into a distance matrix, and the data fusion is carried out by weighted fusion.A large number of simulation and comparative studies verify the effectiveness and reliability of the proposed algorithm.Keywords: D-S evidence theory; conflict evidences; evidence fusion; probability conversion; confidence distance measure; exponential divergence黑龙江大学硕士学位论文目录中文摘要 (I)Abstract ............................................................................................................................. I I 第1章绪论 .. (1)1.1 课题的研究背景与意义 (1)1.2 证据理论融合算法的研究现状 (2)1.3 证据理论的优点与不足 (4)1.4 本文的主要研究内容 (5)第2章D-S证据理论概述 (7)2.1 D-S证据理论的基本概念 (7)2.1.1 识别框架 (7)2.1.2 基本概率赋值 (7)2.1.3 信任函数 (8)2.1.4 似然函数 (8)2.1.5 贝叶斯信任函数 (9)2.2 D-S证据理论合成规则 (10)2.2.1 两组证据的合成规则 (10)2.2.2 多组证据的合成规则 (10)2.3 D-S证据理论合成存在的冲突问题 (11)2.3.1 经典Zadeh悖论 (11)2.3.2 其他典型悖论问题 (12)2.4 本章小结 (13)第3章基于逆Dubois和Prade合成规则的概率转换方法 (14)3.1 引言 (14)3.2 逆DP转换方法介绍 (15)3.2.1 DP合成规则 (15)目 录3.2.2 逆DP转换方法 (16)3.2.3 不确定性度量指标 (18)3.3 逆DP概率转换方法中比率再分配因子ε的取值分析 (18)3.4 实例分析 (20)3.5 本章小结 (25)第4章基于置信距离的D-S冲突证据融合算法 (26)4.1 引言 (26)4.2 基于置信距离的D-S冲突证据融合算法 (26)4.2.1 置信距离测度 (26)4.2.2 证据方差的判定 (28)4.3 实例验证与对比分析 (31)4.4 本章小结 (38)第5章基于指数散度的D-S冲突证据融合算法 (39)5.1 引言 (39)5.2 熵的理论综述 (39)5.2.1 熵的基本概念 (39)5.2.2 熵的基本性质 (41)5.3 基于熵衡量冲突证据的现有方法 (42)5.4 基于指数散度的D-S冲突证据融合算法 (45)5.4.1 基于指数散度的冲突证据衡量方法 (45)5.4.2 新的证据融合算法及对比分析 (47)5.5 本章小结 (51)结论 (52)参考文献 (54)致谢 (61)攻读学位期间发表论文 (62)独创性声明 (63)黑龙江大学硕士学位论文第1章绪论第1章绪论1.1 课题的研究背景与意义信息融合最早出现在上世纪70年代，自信息融合技术诞生以来就广泛应用在军事与民用领域中[1,2]。

凝聚态物理专业导师简介（以姓氏拼音为序）艾保全，男，副教授，硕士生导师。

主研方向是分子马达运动机制、低维材料（纳米）的能量和热的传输、生物非线性噪声效应。

2004年毕业于中山大学，获博士学位。

随后在香港大学及香港浸会大学从事博士后研究工作，2005年9月起华南师范大学教师。

主要从事理论生物物理的研究，包括生物非线性系统中的噪声效应，肌肉运动微观机制，分子马达的运动机制（线性和旋转马达）以及低维材料的热传导等领域的研究。

他以第一作者在Journal of physical chemistry B, Journal of Chemical physics, Physical Review E等 SCI收录国际重要期刊上发表论文32篇。

论文被引用200多次，其中关于肿瘤生长过程中噪声控制的论文被它引50次,关于微管中粒子定向输运的论文被著名综述期刊Reviews Modern of physics引用并介绍我们的相关工作。

主持国家自然科学基金和广东省自然科学基金各一项，并和澳门科技大学，日本产业科技大学以及香港浸会大学等研究组从事合作研究。

主要荣誉：2006年华南师范大学科研优秀工作者.2006年入选广东省“千百十”人才工程培养对象.2005年获得广东省优秀博士学位论文称号.研究兴趣：1.分子马达的研究: 研究分子马达的运动机制，线性分子马达，旋转分子马达，以及分子马达运动方向的控制，效率及其最大值研究，考虑量子效应的分子马达的运动。

2.低维材料（纳米）的能量和热的传输:一维纳米系统中热传导性质的研究及其应用的研究;热二极管,三级管及热(声子)操纵和控制的研究.3.生物非线性系统中的噪声效应: 基因选择过程中的噪声效应; 噪声对肿瘤生长的影响; 细菌生长过程中的噪声效应。

主持科研项目：1.国家自然科学基金2007.1-2009.12,分子马达运动机制的理论研究（旋转）.2.广东省自然科学基金2007.1-2008.12，线性分子马达运动机制的基础研究.发表代表性论文(if>2.0)1.Bao-quan Ai and Liang-Gang Liu, Brownian pump in nonlinear diffusive media,The Journal of Physical Chemistry B 112(2008)95402.Bao-quan Ai and Liang-Gang Liu, Phase shift induces currents in a periodictube, Journal of Chemical Physics 126(2007) 2047063.Bao-quan Ai and Liang-Gang Liu, A channel Brownian pump powered by anunbiased external force, Journal of Chemical Physics , 128 (2008)0247064.Bao-quan Ai and Liang-Gang Liu, The tube wall fluctuation can induce a netcurrent in a periodic tube, Chemical Physics, 344 (2008)185-188.5.Bao-quan Ai and Liang-Gang Liu, Thermal noise can facilitate energytransformation in the presence of entropic barriers, Phys. Rev.E 75(2007)061126.6.Bao-quan Ai and Liang-Gang Liu, Reply to comment on correlated noise in alogistic growth model, Phys. Rev. E 77(2008)013902.7.Bao-quan Ai and Liang-Gang Liu, Facilitated movement of inertial Brownianmotors driven by a load under an asymmetric potential, Phys. Rev.E 76(2007)042103.8.Bao-quan Ai and Liang-Gang Liu, Current in a three-dimensional periodictube with unbiased forces, Phys. Rev. E 74(2006) 051114.9.Bao-quan Ai, Liqiu Wang and Liang-Gang Liu, Transport reversal in a thermalratchet, Phys. Rev. E 72, (2005) 031101.10.Bao-quan Ai, Xian-ju Wang, Guo-tao Liu and Liang-Gang Liu, Correlatednoise in a logistic growth model, Phys. Rev. E 67 (2003)022903.11.Bao-quan Ai, Xian-Ju Wang, Guo-Tao Liu, and Liang-Gang Liu, Efficiencyoptimization in a correlation ratchet with asymmetric unbiased fluctuations, Phys.Rev. E 68 (2003)061105.12.Xian-Ju Wang, Bao-quan Ai, Liang-Gang Liu, Modeling translocation ofparticles on one-dimensional polymer lattices，Phys. Rev. E 64, (2001)906-910.13.Bao-quan Ai and Liang-Gang Liu, Stochastic resonance in a stochastic bistablesystem,Journal of Statistical Mechanics: theory and experiment (2007)P02019.14.Bao-quan Ai and Liang-gang Liu,Efficiency in a temporally asymmetricBrownian motor with stochastic potentials, Journal of Statistical Mechanics: Theory and Experiment (2006)P09016.15.Bao-quan Ai, Guo-Tao Liu, Hui-zhang Xie and Liang-Gang Liu, Efficiency andCurrent in a correlated ratchet, Chaos 14(4)(2004)95716.Bao-quan Ai, Liqiu Wang and Liang-Gang Liu, Flashing motor at hightransition rate, Chaos, solitons & fractals 34( 2007 ) 1265-1271.17.Bao-quan Ai, and Liang-gang Liu, Transport driven by a spatially modulatednoise in a periodic tube, Journal of Physics: Condensed Matter 19(2007) 266215.Email：aibq@陈浩，男，教授，硕士生导师。