a r X i v :0711.2678v 1 [h e p -l a t ] 16 N o v 2007
Finite density simulations using a determinant estimator
?Speaker.
2π 2π
d φ
e ?ik φdet M (U ,μ=i φT )2.
(1.2)
With the above choice the total net quark number is ?xed,i.e.n u +n d =k .Simulating the above action involves computing the determinant for every phase φ;this is not feasible.We replace the
continuous Fourier transform,det k M 2with a discrete one,det ′k M 2.The error due to this approxi-mation is discussed in
[2]and further analyzed in [3].In the canonical approach we still have to
integrate over a complex integrand;the fermion contribution det k M (U )2is complex when k =0.In our study [2]we used a Monte Carlo method to generate an ensemble based on the weight
W (U )∝e ?S G (U ) Redet ′k M (U )2 ,(1.3)and the removed phase is reintroduced in the observable measurement.To generate an ensemble
with this weight we use Metropolis method where the accept/reject step is based on the ratio of determinants.For more details the reader is referred to the original paper [2].
Calculating the determinant of the fermionic matrix exactly is time consuming;it is only feasi-ble for small lattices.To move to larger lattices we will use a method that involves an estimator for the determinant.This method was proposed in [1];in this work we will investigate it numerically.
2.The algorithm
In this section we will present the algorithm used in our simulations.We start by rewriting the partition function
Z C (V ,T ,k )=
D U e ?S G (U )det ′k M (U )
2
(2.1)
=
D U D ξe ?S G (U )det M (U )2f k (U ,ξ),
where
D ξg (U ,φ,ξ)=
det M (U φ)2
N
∑φi
e ?ik φi
g (U ,φi ,ξ).(2.3)
f k(U,ξ) .The reason for separatin
g out det M(U)2is that the new gauge?eld proposal takes into account the fermionic contribution.As showed in[2]this improves the acceptance rate of this step dramatically.
The second step in the updating process is to refresh the auxiliary variablesξ.To implement the Noisy Monte Carlo algorithm[4],another accept/reject step is used where a new proposal ξ→ξ′is accepted with probability based on the ratio f k(U,ξ′)
(3.2)
c i+M
For our simulations,we used a Pade approximation of order K=30.
We then set up an estimator for the exponent of the right hand side of Eq.(3.1).For the trace, we use an unbiased estimator based on Z(4)noise.We generate random vectorsηand use
h(η)=2η?[ln M(Uφ)?ln M(U)]η,(3.3) as an estimator for2Tr(lnMφ?lnM).It is easy to show that when the elements ofηare picked with equal probability from Z(4)={1,?1,i,?i},the estimator h(η)is unbiased.Unfortunately, without improvement this estimator has a large variance.In[5]it is shown that the variance is proportional with the magnitude of the off-diagonal elements of the matrix.The suggested strategy is to subtract from the matrix of interest matrices that are traceless,so that the estimator remains unbiased,and that emulate the off-diagonal structure of the original matrix,so that the variance is
N TrD k
,where N is the dimension of the matrix.The computational burden is then to compute
TrD k ;to evaluate this we have to compute all closed loops of k steps.For k =4,we have
6such loops at every point corresponding to different plaquette orientations and,on a 44lattice,4Polyakov loops wrapping around the lattice in different directions.As we increase k the number of such loops increases quickly,112for k =6,2884for k =8and 84360for k =10.For the purpose of testing,we carried out the calculation up to order k =11,but this is very expensive.In our simulations we used only improvement up to order 9.
-0.6
-0.4-0.2 0 0.2 0.4 0.6 0.8 0
2
4 6 8 10
12
T r l o g M 1 - T r l o g M 0
improvement order
estimator
exact
0.001 0.01 0.1
1 10 100 0 2
4 6 8 10 12
σ
2
improvement order
Figure 1:Improvement of the trace estimator.Left panel:average and error of 1000different noises with different level of improvement;the line corresponds to the exact value.Right panel:the variance as a function of the improvement order.
Once the estimator for the exponent is set up,we have to design an unbiased estimator for the exponential https://www.doczj.com/doc/555463357.html,ing the exponent estimator h ,we follow
[6]and write
g [h ](η1,η2,...)=1+h (η1)+H (θ1?1
2
)H (θ2?
2
det M 2
.The only problem is that it has a very large
variance.To understand how to address this problem,we plot in Fig.2the variance of the estimator g as a function of the mean value and variance of the estimator h .You can see that the variance of the estimator grows very quickly when the mean value or the variance of h are larger than 1.Unfortunately,we cannot control how big these quantities are;they are dictated by how large the lattice is and the ensemble temperature.
)for a case when h =5and h2 =5.1(small variance for the exponent).We see from the σ2?g
?gure that if we use the naive averaging,the variance would be increased by about a million times when the breakup level is greater than5.
The?rst lesson is that the breakup estimator has a much better variance than the native averag-ing.The second important thing to notice is that when the breakup level is greater than the average value of h the payoff levels off;this means that further reductions in variance come at the same rate as statistical reduction.We derive then a rule of the thumb to help us in setting up the breakup level:the breakup level,n,should be set so that most of the estimates of h are smaller than n.In practice this means that we have to setup n larger than the average value of h plus a few standard deviations.
4.Algorithm check
To verify that the algorithm is correct we run a set of simulations on44lattices at the same parameters as the ensembles we generated in our previous work[2].Before we present the results, we want to discuss the simulations.We had run simulations atβ=5.10,5.15,5.20,5.25and5.30. These simulations correspond to temperatures between153MeV and189MeV.We chose these simulation points since they are close to the transition temperature and this is the area that we are interesting in scanning in our future work.For each temperature,we ran three simulations for zero, one and two baryon numbers.The hopping parameter was set toκ=0.158which corresponds to a pion mass of approximatively1GeV.We tuned the HMC trajectories length so that the acceptance rate of the gauge update is about50%.
Finite Element Simulations with ANSYS Workbench 12 Theory – Applications – Case Studies Huei-Huang Lee SDC PUBLICATIONS Schroff Development Corporation https://www.doczj.com/doc/555463357.html, Better Textbooks. Lower Prices.
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46 Chapter 2 Sketching Chapter 2 Sketching A simulation project starts with the creation of a geometric model. T o be pro0cient at simulations, an engineer has to be pro0cient at geometric modeling 0rst. In a simulation project, it is not uncommon to take the majority of human-hours to create a geometric model, that is particularly true in a 3D simulation. A complex 3D geometry can be viewed as a collection of simpler 3D solid bodies. Each solid body is often created by 0rst drawi ng a sketch on a plane, and then the sketch i s used to generate the 3D soli d body usi ng tools such as extrude, revolve, sweep, etc. In turn, to be pro0cient at 3D bodies creation, an engineer has to be pro0cient at sketching 0rst. Purpose of the Chapter The purpose of this chapter is to provide exercises for the students so that they can be pro0cient at sketching using DesignModeler. Five mechanical parts are sketched in this chapters. Although each sketch is used to generate a 3D models, the generation of 3D models is so trivial that we should be able to focus on the 2D sketches without being distracted. More exercises of sketching will be provided in later chapters. About Each Section Each sketch of a mechani cal part wi ll be completed i n a secti on. Sketches i n the 0rst two secti ons are gui ded i n a step-by-step fashion. Section 1 sketches a cross section of W16x50; the cross section is then extruded to generate a solid model in 3D space. Section 2 sketches a triangular plate; the sketch is then extruded to generate a solid model in 3D space. Secti on 3 does not mean to provi de a hands-on case. It overvi ews the sketchi ng tools i n a systemati c way, attempting to complement what were missed in the 0rst two sections. Sections 4, 5, and 6 provide three cases for more exercises. Sketches in these sections are in a not-so-step-by-step fashion; we purposely leave some room for the students to 0gure out the details.
Vibro-Acoustic Simulations
ACTRAN Training – VIBRO
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Introduction
Pre-requisites - before going through this presentation, the reader should have read and understood the following presentations:
1_BASICS_General_Program_Organization.pdf; Workshop_BASICS_0_Edit_an_ACTRAN_input_file.pdf.
These slides present the basics materials, components and boundary conditions involved in a structural simulation in physical coordinates.
2
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Content
The structural Materials
The visco-elastic and shell Component
The equivalent beam Component and Material
The discrete Component and Material
The Boundary Conditions
Meshing Criteria
3
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A comparison of discrete element simulations and experiments for F sandpiles _composed of spherical particles Yanjie Li a ,Yong Xu a,*,Colin Thornton b a Department of Applied Mechanics,China Agricultural University,Beijing 100083,China b School of Engineering,University of Birmingham,Edgbaston,Birmingham B152TT,UK Received 11April 2005;received in revised form 1August 2005;accepted 6September 2005 Available online 18October 2005 Abstract Discrete element simulations,with the particle–particle interaction model based on classical contact mechanics theory between two non-adhesive spheres,were carried out and compared with F sandpile _experiments using spherical particles in order to assess the validation of the simulation data.The contact interaction model is a combination of Hertzian theory for the normal interaction and Mindlin–Deresiewicz theory for the tangential interaction.To ensure the consistency of the simulations with the experiments,the measurement of sliding friction,a key parameter in DEM simulations,was highlighted.A simple experimental method for establishing the value of the friction coefficient was proposed and used in measuring the friction of the rough glass beads and steel balls to be modelled in the simulations.The simulations were carried out for two cases according to particle arrangements:the first is quasi-two-dimensional (Q2D),with a smaller flat cuboidal box containing the spherical particles inside another box for discharge,and the second case is axisymmetric (3D).For both cases,simulations and experiments were carried out for assemblies of polydisperse rough glass beads under the same https://www.doczj.com/doc/555463357.html,parisons were made that showed that the profiles and hence the measured angles of repose,in each case,were in good agreement,thus supporting the validity of the discrete element model used.Further numerical–experimental comparisons were carried out for 3D conical piles using smooth monodisperse steel balls and the same conclusions were obtained. D 2005Elsevier B.V .All rights reserved. Keywords:Discrete element method;Particles;Sandpiles;Angle of repose;Base pressure distribution 1.Introduction The Discrete Element Method has become a powerful numerical method for analysing discontinuous media since the important work by Cundall and Strack [1].Apart from the advances of applications in civil engineering with block element modelling,the particulate discrete element method for granular materials has developed rapidly in analysing both macroscopic and microscopic behaviours in many applica-tions in chemical engineering,agricultural engineering,etc.Progress has involved both model improvement and intensive simulations.Many investigators have proposed models modified from the original for specific applications.Thornton and Yin [2],Thornton [3,4]developed new particle interac- tion models for spherical particles based on contact mechanics for both nonadhesive and adhesive particles as well as for elastoplastic interactions.Oda et al.[5]modified the conventional linear spring–dashpot model by adding rolling resistance with which he analysed shear band phenomena.Han et al.[6]combined the discrete element method with the finite element method to simulate peen-forming processes.Williams et al.[7]developed a contact detection algorithm for particles with arbitrary geometries.Cleary [8]reported DEM simulations illustrating applications to various industrial processes. However,many researchers have done DEM simulations with their own models without experimental validation.Only a small number of studies have presented their predicted results in comparison with experimental data with enough specified parameters.The ambiguous parameter specification leads to theoretical uncertainty and thus restricts its applicability.For instance,the model based on classical contact mechanics between 0032-5910/$-see front matter D 2005Elsevier B.V .All rights reserved.doi:10.1016/j.powtec.2005.09.002 *Corresponding author.Tel.:+861062736514;fax:+861062736514.E-mail address:xuyong@https://www.doczj.com/doc/555463357.html, (Y .Xu). Powder Technology 160(2005)219– 228 https://www.doczj.com/doc/555463357.html,/locate/powtec
ADS Fundamentals - 2002 LAB 4: AC Simulations Overview - This lab continues the amp_1900 project and uses the same sub-circuit as the previous lab. This exercise teaches the basics of AC simulation, including small signal gain and noise. It also shows many detailed features of the data display for controlling and manipulating data. OBJECTIVES ?Perform AC small signal and noise simulations. ?Adjust pin/wire labels. ?Sweep variables and write equations. ?Control plots, traces, datasets, and AC sources.
Lab 4: AC Simulations 4-2 Table of Contents 1. Copy & Paste (Ctrl+C / Ctrl+V) from one design to another. (3) 2. Modify the copied circuit and pin labels (4) 3. Push and pop to verify the sub circuit. (5) 4. Set up an AC simulation with Noise. (5) 5. Simulate and list the noise data (5) 6. Control the output of equations and node voltages. (6) 7. Simulate without noise. (7) 8. Write a data display equation using a measurement equation (7) 9. Work with measurement and data display equations. (8) 10. Plot the phase and group delay for the ac analysis data (9) 11. Variable Info and the w hat function. (10) 12. OPTIONAL - Sweep Vcc (as if the battery voltage is decreasing) (11)
电力系统仿真软件PSS/E 的直流系统模型及其仿真 研究 黄莹，徐政，贺辉 ( 浙江大学电机系，浙江省杭州市310027) HVDC MODELS OF PSS/E AND THEIR APPLICABILITY IN SIMULATIONS HUA NG Ying ，XU Zheng ，HE Hui (Dept. of Electrical Engineering ，Zhejiang University ，Hangzhou 310027 ，Zhejiang Province ，China) ABS TRACT: The basic principle of dynamic simulation by power system simulation software PSS/E is presented in brief. The HVDC models in PSS/E can be divided into two kinds, in one kind the inductive transient processes in DC trans mission line and the dynamic characteristics of the high frequency DC controller are considered, and in the other kind the above mentioned processes and characteristics are not considered. The effectiveness and adaptability of these DC models are analyzed. Finally, the pseudo steady-state HVDC dynamic model CDC4 is studied in detail and is used to simulate the testing system. The simulation results show that the DC model of PSS/E can meet the need of the simulation of large scale A C/DC power systems, so it is available to apply PSS/E to the transient stability analysis of practical large scale A D/DC power system. KEY WORDS : PSS/E ；HVDC model ；Pseudo steady-state HVDC dynamic model ；HVDC dynamic characteristics ；Power system
Measurements and simulations of transient characteristics of heat pipes Jaros?aw Legierski a ,Bogus?aw Wie ?cek a,* ,Gilbert de Mey b a Technical University of ?o ′dz ′,Institute of Electronics,ul.Wo ′lczanska 223,90-924?o ′dz ′,Poland b University of Ghent,Department of Electronics and Information Systems,Sint Pieternieuwstraat 41,9000Ghent,Belgium Received 1April 2004;received in revised form 13May 2005 Available online 5August 2005 Abstract The rejection of heat generated by components and circuits is a very important aspect in design of electronics sys-tems.Heat pipes are very e?ective,low cost elements,which can be used in cooling systems.This paper presents the modelling and measurements of the heat and mass transfer in heat pipes.The physical model includes the e?ects of liquid evaporation and condensation inside the heat pipe.The internal vapour ?ow was fully simulated using compu-tational ?uid dynamics.The theory has been compared with experimental measurements using thermographic camera and contact thermometers.The main purpose of this study is to determine the e?ective heat pipe thermal conductivity in transient state during start up the pipe operation and temperature increase.ó2005Elsevier Ltd.All rights reserved. 1.Introduction The investigations of heat pipes and their applica-tions into thermal management are known for years,but lately they have become more attractive to transport and dissipate heat in electronics [2,3,6,7].It is mainly due to the high e?ectiveness,small size and compact con-struction.Most of the previous research was made for static thermal conditions,and it resulted in getting the e?ective thermal resistance [6,7,9–11]. Heat pipe is a passive heat transfer device with a high e?ective thermal conductivity.The device is built up as hermetic container that is partially ?lled with a ?uid (typically water for electronic cooling design).The inner surfaces of the heat pipe have a capillary wicking mate- rial.The liquid in the pipe saturates the capillary wick.When one heats up the end of the pipe,the liquid at this place evaporates.Because evaporated medium in the heated section has a higher pressure than in the other part of the pipe,the vapour moves to the colder section,where it is cooled down and condensed.The condensed liquid is then transported back to the hot area thought the capillary wicks.This process causes a transport of heat and mass along the pipe [7,12]. In such a heat sink one can de?ne three sections:–evaporator,–condenser, –adiabatic region in the middle of the pipe. Usually,the heat pipe is modelled as a very high ther-mal conductivity element (k =50000W/m K)[5].The purpose of the measurements and simulations presented in this paper is to determine the e?ective thermal 0026-2714/$-see front matter ó2005Elsevier Ltd.All rights reserved.doi:10.1016/j.microrel.2005.06.003 * Corresponding author. E-mail address:wiecek@p.lodz.pl (B.Wie ?cek). Microelectronics Reliability 46(2006)109–115 https://www.doczj.com/doc/555463357.html,/locate/microrel
TERTS, a generic real-time gas turbine simulation environment W.P.J. Visser, M.J. Broomhead and J. van der Vorst
Nationaal Nationaal Lucht- en Lucht- en Lucht- en Ruimtevaartlaboratorium Ruimtevaartlaboratorium National Aerospace Laboratory NLR NLR-TP-2002-069 TERTS, a generic real-time gas turbine simulation environment W.P.J. Visser, M.J. Broomhead and J. van der Vorst This report is based on a presentation held at the ASME IGTI TurboExpo 2001,New Orleans, June 4-7, 2001 and has also been published as ASME-2001-GT-446.The contents of this report may be cited on condition that full credit is given to NLR and the authors Customer:National Aerospace Laboratory NLR Working Plan number: V.2.A.3Owner:National Aerospace Laboratory NLR Division:Flight Distribution:Unlimited Classification title:Unclassified February 2002
864/JOURNAL OF ENGINEERING MECHANICS/SEPTEMBER2001
JOURNAL OF ENGINEERING MECHANICS /SEPTEMBER 2001/ 865 FIG. 1. Spiral Object in DEM FIG. 3.Calculation Cycle in DEM FIG. 2.Unfolded Figure of Spiral Line at r p 22 r =x ?y (5)?p p p y p ?1 ?=tan (6) p x p If r p is within the range between r spin and r spout ,the particle is able to contact the surface of the spiral. Fig.2shows an unfolded depiction of the spiral line at a distance r p from the z ?-axis.Assuming the spiral has no thick-ness,the distance between the center of the particle and the spiral surface perpendicular to the spiral surface d is given by p d = z ? ?cos ?(7) p p p ? ? 2? By comparing the distance given by (7)and the particle radius R p ,the contact can be judged between the particle and the spiral object d NASA/TM-2003-212145 A Collection of Nonlinear Aircraft Simulations in MATLAB Frederico R. Garza George Washington University Joint Institute for the Advancement of Flight Sciences Langley Research Center, Hampton, Virginia Eugene A. Morelli Langley Research Center, Hampton, Virginia January 2003 The NASA STI Program Office ... in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the lead center for NASA’s scientific and technical information. The NASA STI Program Office provides access to the NASA STI Database, the largest collection of aeronautical and space science STI in the world. The Program Office is also NASA’s institutional mechanism for disseminating the results of its research and development activities. These results are published by NASA in the NASA STI Report Series, which includes the following report types: ? TECHNICAL PUBLICATION. Reports of completed research or a major significant phase of research that present the results of NASA programs and include extensive data or theoretical analysis. Includes compilations of significant scientific and technical data and information deemed to be of continuing reference value. NASA counterpart of peer-reviewed formal professional papers, but having less stringent limitations on manuscript length and extent of graphic presentations. ? TECHNICAL MEMORANDUM. Scientific and technical findings that are preliminary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minimal annotation. Does not contain extensive analysis. ? CONTRACTOR REPORT. Scientific and technical findings by NASA-sponsored contractors and grantees. ?CONFERENCE PUBLICATION. Collected papers from scientific and technical conferences, symposia, seminars, or other meetings sponsored or co-sponsored by NASA. ? SPECIAL PUBLICATION. Scientific, technical, or historical information from NASA programs, projects, and missions, often concerned with subjects having substantial public interest. ? TECHNICAL TRANSLATION. English-language translations of foreign scientific and technical material pertinent to NASA’s mission. Specialized services that complement the STI Program Office’s diverse offerings include creating custom thesauri, building customized databases, organizing and publishing research results ... even providing videos. For more information about the NASA STI Program Office, see the following: ? Access the NASA STI Program Home Page at https://www.doczj.com/doc/555463357.html, ? E-mail your question via the Internet to help@https://www.doczj.com/doc/555463357.html, ? Fax your question to the NASA STI Help Desk at (301) 621-0134 ? Phone the NASA STI Help Desk at (301) 621-0390 ? Write to: NASA STI Help Desk NASA Center for AeroSpace Information 7121 Standard Drive Hanover, MD 21076-1320A Collection of Nonlinear Aircraft Simulations in MATLAB
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