Lattice Green Function (at 0) for the 4d Hypercubic Lattice
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Programming CablesUser’s GuideFeatures•Support for all Lattice programmable products–1.2 V to 3.3 V programming (HW-USBN-2B)–1.2 V to 5 V programming (All other cables)–Ideal for design prototyping and debugging•Connect to multiple PC interfaces–USB (v.1.0, v.2.0)–PC Parallel Port•Easy-to-use programming connectors•Versatile flywire, 2 x 5 (.100”) or 1 x 8 (.100”) connectors•6 feet (2 meters) or more of programming cable length (PC to DUT)•Lead-free/RoHS compliant constructionFigure 1. USB Cable – HW-USBN-2BProgramming CablesLattice Programming Cable products are the hardware connection for in-system programming of all Lattice devices. After completion of the logic design and creation of a programming file with the Lattice Diamond®, ispLEVER® Clas-sic or PAC-Designer® software, the Lattice Diamond Programmer, or Lattice's ispVM™ System software is used to control the programming of devices directly on the PC board. No additional components are required to program a device.After you complete your logic design and create a programming file with the Lattice Diamond/ispLEVER Classic development tools, you can use Diamond Programmer or ispVM™ System software ispVM™ System software or Diamond Programmer to program devices on your board. The ispVM System/Diamond Programmer software auto-matically generates the appropriate programming commands, programming addresses and programming data based on information stored in the programming file and parameters you set in Diamond Programmer/ispVM Sys-tem. Programming signals are then generated from the USB or parallel port of a PC and directed through the Pro-gramming Cable to the device. No additional components are required for programming.Diamond Programmer/ispVM System software is included with all Lattice design tool products and is available for download from the Lattice web site at .Programming Cable Pin DefinitionsThe functions provided by the Programming cables correspond with available functions on Lattice programmable devices. Since some devices contain different programming features, the specific functions provided by the Pro-gramming cable may depend on the selected target device. ispVM System/Diamond Programmer software will automatically generate the appropriate functions based on the selected device. See Table 1 for an overview of the Programming cable functions.Table 1. Programming Cable Pin DefinitionsProgramming Cable Pin NameProgramming CablePin TypeDescriptionVCCProgramming VoltageInputConnect to V CC or V CCJ plane of the target device. T ypical I CC = 10mA. Y our board design supplies the power for V CC . Note: This may not be the same as a target device’s V CCO plane.SDO/TDO Test Data Output Input Used to shift data out via the IEEE1149.1 (JT AG) programming standard.SDI/TDITest Data InputOutput Used to shift data in via the IEEE1149.1 programming standard.ispEN/Enable/PROG/SN EnableOutput Enable device to be programmed.SN = SSPI Chip select for HW-USBN-2B TRST Test Reset Output Optional IEEE 1149.1 state machine reset. DONE DONEInput DONE indicates status of configuration MODE/TMS Test Mode Select Input Output Used to control the IEEE1149.1 state machine.GND GroundInput Connect to ground plane of the target device SCLK/TCK Test Clock Input Output Used to clock the IEEE1149.1 state machineINIT Initialize Input Indicates that ORCA ® device is ready for configuration.I2C: SCL 1I2C SCL Output Provides the I2C signal SCL I2C: SDA 1I2C SDA Output Provides the I2C signal SDA.5V Out 15V OutOutputProvides a 5V signal for the iCEprog M1050 Programmer.1.Only found on the HW-USBN-2B cable.Figure 2. Programming Cable In-System Programming Interface for the PC (HW-USBN-2B)11.Requires Diamond Programmer 3.1 or laterFigure 3. Programming Cable In-System Programming Interface for the PC (HW-USB-1A or HW-USB-2A)1ttice PAC-Designer® software does not support programming with USB cables. To program ispPAC devices with these cables, use the Dia-mond Programmer/ispVM System software.Figure 4. Programming Cable In-System Programming Interface for the PC (HW-DLN-3C and Equivalents)11.HW7265-DL3, HW7265-DL3A, HW-DL-3B, HW-DL-3C and HW-DLN-3C are functionally equivalent products.Figure 5. Programming Cable In-System Programming Interface for the PC (pDS4102-DL2 or pDS4102-DL2A)Figure 6. Programming Cable In-System Programming Interface for the PC (HW7265-DL2 or HW7265-DL2A)1.For reference purposes, the 2x10 connector on the HW7265-DL2 or HW7265-DL2A is equivalent to Tyco 102387-1. This will interface tostandard 100-mil spacing 2x5 headers, or a 2x5 keyed, recessed male connector such as the 3M N2510-5002RB.Programming SoftwareDiamond Programmer and ispVM System for Classic devices is the preferred programming management soft-ware tool for all Lattice devices and download cables. The latest version of Lattice Diamond Program-mer or ispVM System software is available for download from the Lattice web site at /software. Target Board Design ConsiderationsA 4.7K pull-down resistor is recommended on the TCK connection of the target board. This pull-down is recom-mended to avoid inadvertent clocking of the TAP controller induced by fast clock edges or as V CC ramps up. This pull-down is recommended for all Lattice programmable families.The I2C signals SCL and SDA are open drain. A 2.2K pull-up resistor to VCC is required on the target board.For Lattice device families that feature low power, it is recommended to add a 500 ohm resistor between V CCJ and GND during the programming interval when a USB Programming cable is connected to a very low power board design. A FAQ is available that discusses this in more depth at:/en/Support/AnswerDatabase/2/2/0/2205The JTAG programming port speed may need to be governed when using the Programming cables connected to customer PCBs. This is especially important when there is long PCB routing or with many daisy-chained devices. The Lattice programming software can adjust the timing of TCK applied to the JTAG programming port from the cable. This low-precision port setting of TCK depends on many factors, including the PC speed and the type of cable used (parallel port, USB or USB2). This software feature provides an option to slow the TCK for debug or noisy environments. A FAQ is available that discusses this in more depth at:/en/Support/AnswerDatabase/9/7/974.aspxThe USB Download Cable can be used to program Power Manager or ispClock products with Lattice programming software. When using the USB cable with the Power Manager I devices, (POWR604, POWR1208, POWR1208P1), you must slow do TCK by a factor of 2. A FAQ is available that discusses this in more depth at:/en/Support/AnswerDatabase/3/0/306.aspxProgramming Flywire and Connection ReferenceRefer to T able 2 when connecting a flywire download cable to systems that use the 1x8-position or 2x5-position connectors. For newer Lattice FPGA families, a 1x10 connector used in conjunction with the Programming USB cable adds support for the DONE and INITN signals. Both of these signals are inputs to the cable, and can be used to help verify device configuration.Table 2. Flywire Conversion ReferenceFunction FlywireCableWireLabel1x10Connector1x8Connector2x5ConnectorV CC1Red VCC116 TDO/SO/SPI_SO Brown TDO227TDI/SI/SPI_SI Orange TDI335 ispEN2/Enable/PROGRAMN/SN/SPI_SS_B Y ellow ispEN/PROG4410 TRST3/CRESET_B Green TRST/DONE559 TMS/MODE Purple TMS663 GND Black GND77 4 (2 and 8) TCK4/SCLK/CCLK/SPI_SCK White TCK881 DONE3Green TRST/DONE9INITN/CDONE Blue INITN10I2C SCL5, 6Y ellow/White I2C: SCLI2C SDA5,6Green/White I2C: SDATable 3 lists the recommend pin connections. Please contact Lattice technical support for information on unlisted devicefamilies.(e-mail:***************************).Table 3. Recommended Pin ConnectionsDevice FamilyTDITDOTMSTCKispEN/P ROG 1,6TRST 2/D ONE 3,6INITN 3,6VCCGNDSCLSDAECP5™Mandatory Mandatory Mandatory Mandatory Optional Optional Optional Mandatory Mandatory N/A N/A LatticeECP3™Mandatory Mandatory Mandatory Mandatory Optional Optional Optional Mandatory Mandatory N/A N/A LatticeECP2M™/LatticeECP2™Mandatory Mandatory Mandatory Mandatory Optional Optional Optional Mandatory Mandatory N/A N/A LatticeECP™/LatticeEC™Mandatory Mandatory Mandatory Mandatory Optional Optional Optional Mandatory Mandatory N/A N/A LatticeXP2™Mandatory Mandatory Mandatory Mandatory Optional Optional Optional Mandatory Mandatory N/A N/A LatticeXP™Mandatory Mandatory Mandatory Mandatory Optional Optional Optional Mandatory Mandatory N/A N/A LatticeSC™/LatticeSCM™Mandatory Mandatory MandatoryMandatory Optional Optional Optional Mandatory Mandatory N/A N/A iCE40™/iCE40LM/iCE40 Ultra™Mandatory Mandatory N/A Mandatory MandatoryRecom-mended Recom-mended Mandatory Mandatory N/A N/A MachXO2™/MachXO3™Mandatory Mandatory Mandatory Mandatory N/A N/A N/A Mandatory Mandatory Optional Optional MachXO™Mandatory Mandatory Mandatory Mandatory N/A N/A N/A Mandatory Mandatory N/A N/A ORCA ®/FPSC Mandatory Mandatory Mandatory Mandatory Optional Optional Optional Mandatory Mandatory N/A N/A ispXPGA®Mandatory Mandatory Mandatory Mandatory N/A N/A N/A Mandatory Mandatory N/A N/A ispXPLD™Mandatory Mandatory Mandatory Mandatory N/A N/A N/A Mandatory Mandatory N/A N/A ispMACH ®4000Mandatory Mandatory Mandatory Mandatory N/A N/A N/A Mandatory Mandatory N/A N/A ispMACH/ispLSI® 5000Mandatory Mandatory Mandatory Mandatory N/A N/A N/A Mandatory Mandatory N/A N/A MACH ®4A4Mandatory Mandatory Mandatory Mandatory N/A N/A N/A Mandatory Mandatory N/A N/A ispGDX2™Mandatory Mandatory Mandatory Mandatory N/A N/A N/A Mandatory Mandatory N/A N/A ispClock™Mandatory Mandatory Mandatory Mandatory N/A N/A5N/A Mandatory Mandatory N/A N/A Platform Manager™Mandatory Mandatory Mandatory Mandatory N/A Optional 5N/A Mandatory Mandatory N/A N/A Power Manager/Power Manager II Mandatory Mandatory Mandatory Mandatory N/A Optional 5N/A Mandatory Mandatory N/A N/A ispPAC ®MandatoryMandatoryMandatoryMandatoryN/AN/AN/AMandatoryMandatoryN/AN/A1. Refer to the Programming Cable ispEN Pin section below for detailed information on connecting the ispEN/ENABLE pin.2. Refer to the Programming Cable TRST Pin section below for detailed information on connecting the TRST pin.3. The DONE and INITN signals are only available on the Programming USB cable. These signals are inputs to the cable and can be used to help verify deviceconfiguration.4. Please refer to the device data sheet. Not all packages have the ENABLE or TRST pin.5.When using P AC-Designer ® software to program ispPAC devices, do not connect this pin.6.When using these connections, be sure to select the correct settings in the Cable and I/O Port Setup dialog in the ispVM System/Diamond Programmer soft-ware.5V Output 5Red/White5V Out1.For devices that have a V CCJ pin, the V CCJ must be connected to the cable’s V CC, and a 0.1µF decoupling capacitor is required on V CCJ close to the device. Please refer to the device data sheet to determine if the device has a V CCJ pin.2.For older Lattice ISP devices, a 0.01µF decoupling capacitor is required on ispEN/ENABLE of the target board.3.The TRST and DONE pin is multiplexed on the Programming USB cable. If the device TRST signal is available on the board, connect the USB flywire TRST/DONE wire to TRST. If the device DONE signal is available on the board (or if both TRST and DONE are available), con-nect the USB flywire TRST/DONE wire to DONE. Please make sure the correct setting is selected in ispVM/Diamond Programmer (Options, Cable and I/O Port Setup). This will tell ispVM/Diamond Programmer whether the TRST/DONE cable is used as a TRST or a DONE signal.4.A 4.7K pull-down resister is recommended on TCK of the target board.5.Only on the HW-USB2N-2B cable6.Open drain signals. External pull-up ~2.2KOhm resistor to VCC is required.Table 2. Flywire Conversion Reference (Continued)FunctionFlywire Cable Wire Label 1x10 Connector1x8 Connector2x5 ConnectorConnecting the Programming CableThe target board must be un-powered when connecting, disconnecting, or reconnecting the Programming Cable. Always connect the Programming Cable’s GND pin (black wire), before connecting any other JTAG pins. Failure to follow these procedures can result in damage to the target programmable device.Programming Cable TRST PinConnecting the board TRST pin to the cable TRST pin is not recommended. Instead, connect the board TRST pin to Vcc. If the board TRST pin is connected to the cable TRST pin, instruct ispVM/Diamond Programmer to drive the TRST pin high as follows:1.Select the Options menu item.2.Select Cable and I/O Port Setup.3.Check the TRST/Reset Pin Connected checkbox.4.Select the Set High radio button.If the proper option is not selected, the TRST pin will be driven low by ispVM/Diamond Programmer. Consequently, the BSCAN chain will not work because the chain will be locked into RESET state.Programming Cable ispEN PinThe following pins should be grounded:•BSCAN pin of the 2000VE devices•ENABLE pin of MACH4A3/5-128/64, MACH4A3/5-64/64 and MACH4A3/5-256/128 devices.However, the user has the option of having the BSCAN and ENABLE pins driven by the ispEN pin from the cable. In this case, ispVM/Diamond Programmer must be configured to drive the ispEN pin low as follows:1.Select the Options menu item.2.Select Cable and I/O Port Setup.3.Check the ispEN/BSCAN Pin Connected checkbox.4.Select the Set Low radio button.Table 4.Feature HW-USBN-2B HW-USBN-2A HW-USB-2A HW-USB-1A HW-DLN-3CHW7265-DL3,HW7265-DL3A,HW-DL-3B,HW-DL-3C HW7265-DL2HW7265-DL2A PDS4102-DL2PDS4102-DL2AUSB X X X XPC-Parallel X X X X X X 1.2 V Support X X X1.8 V Support X X X X X X X X2.5-3.3 V Support X X X X X X X X X X 5.0 V Support X X X X X X X X X 2x5 Connector X X X X X X X1x8 Connector X X X X X X X Flywire X X X X X XLead-freeConstruction X X XAvailable for order X XProgramming Cable Feature SummaryEach Programming Cable ships with two small connectors that help you keep the flywires organized. The following manufacturer and part number is one possible source for equivalent connectors:•1x8 Connector (e.g. Samtec SSQ-108-02-T-S)•2x5 Connector (e.g. Samtec SSQ-105-02-T-D)The Programming Cable flywire or headers are intended to connect to standard 100-mil spacing headers (pins spaced 0.100 inch apart). Lattice recommends a header with length of 0.243 inches or 6.17 mm. Though, headers of other lengths may work equally well.Ordering InformationDescription Ordering PartNumberChina RoHS Environment-Friendly Use Period (EFUP)Programming cable (USB). Contains 6' USB cable, flywire connectors,8-position (1x8) adapter and 10-position (2x5) adapter, lead-free, RoHScompliant construction.HW-USBN-2BProgramming cable (PC only). Contains parallel port adapter, 6' cable,flywire connectors, 8-position (1x8) adapter and 10-position (2x5) adapter,lead-free, RoHS compliant construction.HW-DLN-3CNote: Additional cables are described in this document for legacy purposes only, these cables are no longer produced. The cables currently available for order are fully equivalent replacement items.Technical Support Assistancee-mail:***************************Internet:Revision HistoryDate Version Change SummaryJanuary 201524.7Updated Programming Cable Pin Definitions section.— In Table 1, Programming Cable Pin Definitions, ispEN/Enable/PROGchanged to ispEN/Enable/PROG/SN and its description revised.— Updated Figure 2, Programming Cable In-System ProgrammingInterface for the PC (HW-USBN-2B).Updated Programming Cable ispEN Pin section.In T able 4, Programming Cable Feature Summary, HW-USBN-2Bmarked as available for order.Updated Ordering Information section. HW-USBN-2A changed to HW-USBN-2BJuly 201424.6Changed document title to Programming Cables User’s GuideChanged ispDOWNLOAD Cables to Programming Cables.Updated Target Board Design Considerations section. Updated FAQlink on ispVM tool control of TCK duty cycle and/or frequency.Updated Table 3, Recommended Pin Connections. Added ECP5,iCE40LM, iCE40 Ultra, and MachXO3 device families.Updated Technical Support Assistance information.October 201224.5Added iCE40 configuration port pin names to the Flywire ConversionReference table.Added iCE40 information to Recommended Cable Connections table.February 201224.4Updated document with new corporate logo.November 201124.3Document transferred to user’s guide format.Added Figure USB Cable – HW-USBN-2A.Updated Recommend Cable Connections table for MachXO2 devices.Updated Target Board Design Considerations section.Added Appendix A.October 200924.2Added information related to the physical specifications of the flywireconnectors.July 200924.1Added Target Board Design Considerations text section.Added Programming Flywire and Connection Reference section head-ing.——Previous Lattice releases.Appendix A. Troubleshooting the USB Driver InstallationIt is essential that you install the drivers before connecting your PC to the USB cable. If the cable is connected before installing the drivers, Windows will try to install its own drivers that may not work.If you have attempted to connect the PC to the USB cable without first installing the appropriate drivers, or have trouble communicating with the Lattice USB cable after installing the drivers, following the steps below:1.Plug in the Lattice USB cable. Choose Start > Settings > Control Panel > System. In the System Propertiesdialog box, click the Hardware tab and Device Manager button. Under Universal Serial Bus controllers, you should see Lattice USB ISP Programmer. If you do not see this, look for the Unknown Device with the yellow flag.2.Double click on the Unknown Device icon.3.Click Reinstall Driver.4.Select Browse for driver software on your computer.For Lattice EzUSB DriverFor FTDI FTUSB Driver5.Browse to the isptools\ispvmsystem directory for the Lattice EzUSB driver or the isptools\ispvmsystem\Drivers\FTDIUSBDriver directory for the FTDI FTUSB driver. For Diamond installations, browse tolscc/diamond/data/vmdata/drivers. Click Next.6.Select Install this Driver software anyway. The system will update the driver.7.Click Close and finish installing the USB driver. Under Control Panel >System >Device Manager > Univer-sal Serial Bus Controllers should include the following:For the Lattice EzUSB Driver: Lattice USB ISP Programmer device installed.For the FTDI FTUSB Driver: USB Serial Converter A and Converter B devices installed.If you are experiencing problems or need additional information, contact Lattice Technical Support.。
Chap 11、Semiconductors11.1 (a) For a semiconductor, show that np product obtained fromEq.(11.27) is proportional to exp(-βE g ) and thus is independent of the position of the chemical potential μ in the bandgap.Eq.(11.27):(b) The law of mass action in semiconductors for reaction creatingpairs of electrons and holes [e.g., Eq.(11.28)] has the form n(T)P(T)∝exp(-βE g ). Explain the significance of this law. (Hint: The law of mass action is described in Section 4.6)Eq.(11.28): (c) Evaluate the np product at T=300K for Si with E g =1.11ev andm eds ﹡=1.05m and m hds ﹡=0.58m.11.2 Using Eq.(11.30) and m eds ﹡=1.05m and m hds ﹡=0.58m for Si,calculate the change in the position of the chemical potential µ in the energy gap of intrinsic Si between T=0 and 300K.Eq.(11.30): 11.3 Calculate the values of N c and N v as defined in Eq.(11.27) for Siat T=300K. The appropriate of density-of-states effective masses for Si are m eds ﹡=1.05m and m hds ﹡=0.58m.11.4 Consider a semiconductor with a bulk energy gap E g =1.5ev andgE v c i i e T N T N T p T n β-=)()()()()()(2/32)()2(2)()(μβμβπ----*===c c E c E B eds i e T N e T k T n T n m )()(2/32)()2(2)()(v v E v E B h ds i e T N e T k T p T p m ----*===μβμβπ **+=eds hdsB g m m T k E T ln 432)(μwith m e﹡=m h﹡=0.1m. Calculate the increase in the energy gap ofthis semiconductor when it is incorporated into the followingstructures:(a) A quantum well (d=2) with L x=10nm.(b) A quantum wire (d=1) with L x=L y=10nm(c) A quantum dot (d=0) with L x=L y=L z=10nm11.5 A Hall effect measurement is carried out on a rectangular barof a semiconductor with dimensions L x=0.04m (the directionof current flow ) and L y=L z=0.002m. When a current I x=5mAflows in the +x direction and a magnetic field B z=0.2T isapplied in the +z direction, the following voltages aremeasured: V x=6V and V y=+0.3mV (i.e., increasing in the +ydirection). Determine the following properties of thesemiconductor bar from these data :(a) The sign of the dominant charge carriers.(b) The concentration of the dominant charge carriers.(c) The electrical conductivity σ.(d) The mobility µ of the dominant charge carriers.11.6Using Eq.(11.59), estimate the increase △n in the electronconcentration in an n-type semiconductor due to the uniformabsorption of light with α=105m-1, I0=1W/m2, and hω=1e V, aquantum efficiency η=1, and a minority-carrier lifetime ηp=10-3s.Eq.(11.59): 11.7 Using the definition of the Hall mobility µH =︱ζR H ︱and theexpression for R H for an intrinsic semiconductor given in Eq.(11.49), show that µH =︱µh -µe ︱.Eq.(11.49): 11.8 Consider the structural transformation of a binary crystal ABfrom the hexagonal wurtzite crystal structure to the cubic zincblende crystal structure in which the density of the atoms remains constant. Find the lattice constant of the resulting cubic crystal if the lattice constants of the initial wurtzite crystal are a =0.3400nm and c =0.5552nm.11.11 List all of the local tetrahedral bonding units, A-B 4, which arepresent in the ternary semiconducting compounds Cu 2SiTe 3, Cu 3PS 4, and CuSi 2P 3. Note that each tetrahedron must contain an average of four bonding electrons per atom.11.13 Derive the expression for the shift △E of the electron energybands from one side of a p-n junction to the other under zero bias as given in Eq.(11.93). Calculate the magnitdde of the built-in electric potential V B =△E/e for Si at T=300K for N d =N a =2×1024m -3. Using these same parameters, calculate the depletion width d and the maximum electric field Q/∈A for a Si p-n junction at T=300 K.ωτηατω pp L I G p n 0)(==∆=∆)(e h eh H ne R μμμμ+-=Eq.(11.93): .Chap 12、Metals and Alloys 12.1 Referring to Section 12.5, show that the condition for the tangencyof the Fermi sphere to the Brillouin zone boundary for the FCC lattice is N =1.36.12.2 Derive Eq.:12.3 Derive Eq.:Chap 13、Ceramics13.1 For the silicon oxynitride compound Si 2N 2O, assume that Si, N,and O atoms have their usual valences (4, 3, and 2) and that the N and O atoms do not form covalent bonds with each other. (a) Given a local bonding unit Si-N x O y for Si with x+y =4,determine x (and y ) for this crystal structure.(b) What are the local bonding units for N and O?13.2 For the Si x N y O z ternary phase diagram, locate the followingcompounds :SiO 2, Si 3N 4, Si 2N 2O, and Si 3N 2O 3.13.3 Find the average number of bridging oxygens, b, and nonbridgingoxygens, n, for the following glasses:(a)CaO•SiO 2, and(b) soda-lime(i.e., 2CaO•3Na 2O•15SiO 2) n ia d B v c a d B g N N T k N N N N T k E E 2ln ln =+=∆)163253(02222∈-=πF F k e m k N U )]1(356[82202ws c ws Coul r r r Nze U --∈=πChap 14、Polymers14.1 A polymer whose viscoelastic properties are described byEq.(14.40) (i.e., the Maxwell model) is subjected to a time-dependent stress σ=σ0exp(-i ωt). Find the steady-state strain. Compare this result to that of a polymer that obeys the Voigt model, given by Eq. (14.37).Eq.(14.40): Eq. (14.37): 14.2 Consider an elastomer consisting of monomers that are opticallyanisotropic [i.e., they have a polarizability α11(ω) for light parallel to the chain axis and α┴(ω) for light polarized perpendicular to the chain axis]. Assume that there are N chains per unit volume. Let )(ωn be the mean index of refraction of the material. The elastomer is stretched with a steching parameter s , as defined in Secti on 14.5. Show that the elastomer will have a birefringence given by)]()()[1()(]2)([452)()()(112211ωαωαωωπωωωδ⊥--⊥--+=-=s s n n N n n nObtain an expression for the stress optical coefficient. C≡δn(ω)/ζ, where ζ is the applied stress.Chap 15、Dielectric and Ferroelectric Materials∙∙=+εησσG ηστεε=+∙15.1 Given the Landau free-energy density for a ferroelectric of the form Where b>c. Let a=a 0(T-T C ) and assume that b and c are constant. Find P z and χ as a function of T for the state of thermal equilibrium. 15.2 Design a piezoelectric actuator that can be used to sweep anSTM head over the surface of a solid. What is the area that can practically be covered?15.3 Adapt Weiss molecular field theory (see Chapter 9) to describe aferroelectric. Assume that there are just two orientations for the electric-dipole moment of a unit cell and that NN cells interact via an exchange interaction. Obtain the hysteresis curve and values for the coercive field E c , saturation polarization P sat , and remanent polarization P rem .15.4 BaTiO 3 is a paraelectric for T>T C =130℃ and has a Curie constantC=76,000K.(a)If the lattice constant for the cubic unit cell of BaTiO 3 is a=0.401nm, calculate the electric-dipole moment µ of this unit cell. (b)What would the corresponding polarization P=µn be at T=0 K?Chap 16、Superconductors16.1 (a) Derive expression for the difference in entropy△S(T)=S n (T)-S s (T) and the difference in specific heatZ y x x z z y z y x o EP P P P P P P c P P P b P a g g -+++++++=)(2)(422222224442△C(T)=C n (T)-C s (T) between the normal and superconducting states in terms of the critical magnetic field H c (T) and its first derivative dH c /dT and second derivative d 2H c /dT 2. [Hint: Use Eq.(16.3) and standard thermodynamic relationships.](b) Evaluate these expressions for △S(T) and △C(T) for the case where H c (T) can be approximated by H c0[1-(T/T c )2] and show that : (ⅰ) △S(T c )=△S(0)=0(ⅱ) △S(T)>0 for 0<T<T c(ⅲ)△C(T c )=-4µ0H c02/T c . Calculate △C(T c ) from this expressionusing T c = 1.175 K and H c0 = 105 Oe = 8360 A/m for Al and compare with the measured result -225 Jm -3K -1 for Al.(ⅳ) △C=0 for T=T c /3 and T=0K.Eq.(16.3): 16.2 (a) Using Eq.(16.5), calculate the condensation energy in J/m 3 and ineV per electron at T=0K for the superconductor Pb for which H c0=6.39×104A/m.(b) Compare your result from part (a) with the expression ε(0)(ε(0)/E F ) where the superconducting energy gap 2ε(0) = 2.6 meV for Pb. Here ε(0)/E F is the fraction of conduction elections whose energies are actually affected by the condensation .Eq.(16.5): 16.3 Consider the London penetration depth λL defined in Eq.(16.10).⎰+=-=H s s s s H T G dH H M T G T H G 02002),0()(),0(),(μμ2)(),0(),0(20T H T G T G c s n μ=-(a) Calculate λL (0K) for the superconducting Al, Pb, and Nb. (b) If a superconductor has a London penetration depth λL (0K)=200nm, what is the concentration n s of superconducting electrons at T=0.5T c .Eq.(16.10): 16.4 When transport current i flows through a superconducting wireof radius R, its path is confined to a region of thickness λ, the penetration depth, just inside the surface of the wire.(a) In this case show that the critical current density J c =i c /A eff is independent of R and can be expressed in terms of the critical field H c by J c =H c /λ. Here A eff is the effective area through which the current flows, with A eff <<πR 2.(b) Calculate J c for superconducting Pb at T=0K. [Note: H c0 = 803 Oe = 63919 A/m and λ(0) = 39 nm](c) Sketch J c (T)/J c (0) from T = 0 K to T c using the temperature dependencies of H c and λ given in Eqs.(16.6) and (16.11), respectively .Eq.(16.6):Eq.(16.11): 16.5 A type Ⅱ superconductor has T c =125k, ΘD =250K, and κ(T c )=50. Onthe basis of standard theories [free-electron model, Debye model, BCS theory, G-L theory, Pauli limit for H c2 given in Eq.(16.33)], 20)()(e T n mT s L μλ=)1()(220c c c T T H T H -=4)/(1)0()(c L L T T T -=λλestimate the following:(a)The superconducting energy gap 2ε(0).(b) The upper critical field H c2(0)=H p .(c)The co herence length ξ(0) and the penetration depth λ(0).(d)The thermodynamic critical field H c0=H c (0).(e)The coefficients γ and A of the electronic and phonon contributions to the specific heat , γT and AT 3, respectively.Eq.(16.33): 16.7 Use Eq.(16.20) to find the limiting values of λ(l ) and ξ(l ) (a) in theclean limit where the electron mean free path l >>ξ0, and (b) in the dirty limit where l <<ξ0.Eq.(16.20): and 16.8 (a) Calculate the density of vortices per unit area B/Φ0 for thefollowing values of B, the average flux density present in the mixed state of a superconductor. Take H c2=1.6MA/m.(i) B = μ0H c2/2. (ii) B ≈ B c2 = μ0H c2.(b)Calculate the average separation d between the vortices from your answers in part (a) and compare your answers with the conherence length ξ. [Hint: You can obtain ξ with the help of Eq.(16.22).]Eq.(16.22): 16.10 Calculate the number of holes N hole per Cu ion in the CuO 2copper-oxygen layers in the superconductor YBa 2Cu 3O 7-x for the Bp T T H μμε0)()(≈l l 11)(10+=ξξll ξλλ+∞=1)()()(2)(2002T T H c ξπμΦ=cases of x = 0, 0.25, and 0.5. Assume the following ionic charge states for the ions in this structure: Y 3+, Ba 2+, Cu 2+, and O 2-.16.11 For the compound with the chemical formula La 1.7Sr 0.3CuO 3.9:(a)what is the total number of electrons per formula unit outside closed shells?(b)How many electrons are contributed by each ion to the CuO 2 layers?(c)what is the average valence of the copper atoms?(d)Assuming that all copper ions have a charge of +2e, what is the number of holes per formula unit?16.12 Derive Eq.(16.33) for the Pauli limiting field H p by settingG n (H)=G s (H) at H=H p and using the Pauli paramagneticsusceptibility χp =µ0µB 2ρ(E F ) of the conduction electrons in thenormal state. [Hint: Use G n (H)-G n (0)=-µ0χp H 2/2, and the BCS resultG n (0)-G s (0)=ρ(E F )ε(0)2/2.]Eq.(16.33):Chap 17、Magnetic Materials17.1 Consider a single-domain uniaxial ferromagnetic particlemagnetized along its easy axis with M=M s in zero applied magnetic field. The magnetic anisotropy energy density is given by E a =K sin 2θ where K >0 and θ is the angle between the B p T T H μμε0)()(≈magnetization M and the easy axis. A magnetic field H is now applied at 90° to the easy axis.(a)Show that the sum of the anisotropy and magnetostatic energy densities for this particle is u(θ)=K sin 2θ-µ0MHsinθ.(b)Find the angle θ be tween M and the easy axis as a function of the magnitude of the field H by minimizing uwith respect to θ .(Note that it will be important to check for the stability of the solution by requiring that ∂2u/∂θ2>0.)(c) Show that the resulting magnetization curve (i.e., the plot of thecomponent of M in the direction of H versus the applied field H ) is a straight line (with slop χ=µ0M 2s /2K ) up to H =H k =2k/µ0M s , at which point the magnetization is saturated in the direction of H . Here H k is the effective magnetic anisotropy field in Eq.(17.14).Eq.(17.14): 17.4 Prove that when the shape anisotropy constant K s is <0 (i.e., whenN ⊥<N 11), the magnetization M for a ferromagnetic film will lie in the plane of the film .17.5 Calculate the radius at which a spherical Fe particle behavessuperparamagnetically at T =300K by setting K 1V=K B T , where K 1≈4.2×104J/m 3 is the first-order magnetocrystalline anisotropy coefficient for Fe and V is the volume of the sphere.17.6 Calculate t he increase in temperature ΔT of a magnetic material withsK M KH 02μ=a square magnetization loop, with M s =1370KA/m and H c =1100kA/m, when the loop is traversed once, Assume that the material is thermally-isolated from its surroundings and that its specific heat is 4×106J/m 3K.17.7 For a magnetically isotropic m aterial with magnetostriction λ, provethat B 2(C 11-C 12)=2B 1C 44. Show, in fact, that if the material is also elastically isotropic, then B 1=B 2. (Hint: See Section 10.8)17.8 Show that B (t) and M (t) both lag the applied magnetic fieldH(t )=H 0e -iωt by the same phas e angle δ when µ0H 0<<B 0cosδ. [Hint: Start by substituting the expressions for B (t) and M (t) from Eq.(17.33) into the expression B =µ0(H+M).]Eq.(17.33): andChap 18、Optical Materials18.1 Suppose that a quantum dot has the shape of a two-dimensionalcircular disk. A model that is often used to describe the potential of an electron confined in such a dot is V(r)=m ﹡ω02r 2/2. Suppose a magnetic induction B is imposed perpendicular to the plane of the dot. Show that the electron energy levels are given by the formula where n=0, 1, 2,…………and l=……, -2, -1, 0, 1, 2,……..18.2 Consider a Lorentz oscillator model for an electron moving in )(0)(δω+-=t i e B t B )(0)(φω+-=t i e M t M **-+++=m eB l m eB l n E l n 2)2()()12(220, ωone-dimensional anharmonic potential described by the Toda potential V(x)=Ae -ax +Bx, where A, a and B are constants. The equation of motion isDerive expressions for the linear polarization P , at frequency ω and the nonlinear polarization at frequency 2ω, P (2ω).18.3 Consider a particle of mass m moving in the anharmonicsymmetric potential V(x)=Acosh[a(x-x o )] subject to a damping force –γv and a driving force qE cosωt . Find the Fourier coefficients for the dipole moment at frequencies ω and 3ω. 18.4 Using Vegard′s law , derive an expression for the bandgap energyE g (x,y) of a layer of In 1-x Ga x As y P 1-y which is lattice matched to an InP substrate. Compare your expression with the experimental result given in Eq.(18.15) and comment on any differences.Eq.(18.15): E g =1.35-0.72y+0.12y 2 eVt qE e e aA dtdx dt x d m o ax ax ωγcos )()(22+-=+--。
电势降落对DNA分子器件电荷输运的影响康大伟;孙孟乐;尤景汉;姬江涛【摘要】基于晶格格林函数和Landauer-Büttiker公式,研究了脱氧核糖核酸分子器件在不同电势降落下的电荷输运性质.界面处的电势降落可以导致负微分电导现象的出现,而且随着电势降落在脱氧核糖核酸分子上的比例的提高,这个效应更加明显.电势降落导致的分子轨道的局域化是产生负微分电导现象的关键因素.%The charge transport properties of deoxyribonucleic acid( DNA) molecular device at different voltage drop were studied based on the lattice Green function and Landauer-Btittiker formula. The voltage drop on the DNA molecule results in the negative differential conductance which becomes more prominent when the voltage drop increases. The localization of molecular orbital is the key point of the negative differential conductance.【期刊名称】《河南科技大学学报(自然科学版)》【年(卷),期】2012(033)003【总页数】4页(P85-88)【关键词】格林函数;脱氧核糖核酸;分子器件;电势降落;局域化【作者】康大伟;孙孟乐;尤景汉;姬江涛【作者单位】河南科技大学物理与工程学院,河南洛阳471003;洛阳理工学院数理部,河南洛阳471023;河南科技大学物理与工程学院,河南洛阳471003;河南科技大学车辆与动力工程学院,河南洛阳471003【正文语种】中文【中图分类】O4690 前言随着器件小型化和电路高集成度的发展,传统的集成电路将走到其物理极限。
厦门“PEP”2024年11版小学四年级下册英语第2单元期末试卷[含答案]考试时间:90分钟(总分:100)A卷考试人:_________题号一二三四五总分得分一、综合题(共计100题)1、What do we call a person who writes books?A. AuthorB. EditorC. PublisherD. Journalist答案: A2、What is the name of the fairy in "Peter Pan"?A. CinderellaB. Tinker BellC. Snow WhiteD. Aurora答案:B3、听力题:Sedimentary rocks often form in layers due to ______ sediment deposition.4、听力题:The _______ of an object can change when it is heated or cooled.5、填空题:A ______ (狼) hunts in packs for food.6、What is the main ingredient in chocolate?A. SugarB. CocoaC. FlourD. Butter7、听力题:His favorite game is ________.8、填空题:We celebrate my brother’s __________ every year. (生日)9、听力题:The chicken is ________ cooked.10、听力题:I want to ___ a sandwich. (make)11、填空题:A raccoon is often seen at ______ (夜间) looking for food.12、听力题:The _____ (tree/house) is tall.13、What is the capital of Peru?A. LimaB. CuscoC. ArequipaD. Trujillo答案: A14、听力题:A ____ has bright colors and is often seen in the forest.15、What do we call a group of penguins?A. ColonyB. GaggleC. PackD. Flock答案: A. Colony16、How many hours are in a day?A. 12B. 24C. 36D. 48答案: B17、填空题:The beach is _______ and sunny.18、Which planet is known for its rings?A. EarthB. SaturnC. MarsD. Venus答案:B19、What do you call a book that tells a fictional story?A. NovelB. BiographyC. AnthologyD. Textbook答案:A20、填空题:The dog digs in the ______.21、填空题:The ________ loves to explore new places.22、填空题:The ant has a strong _______ (合作) ability.23、填空题:The scientist studies _____ (化学) processes in the lab.24、听力题:We have ________ (breakfast) in the morning.25、What is the term for a young cheetah?a. Cubb. Pupc. Kitd. Fawn答案:a26、What is the name of the largest ocean on Earth?A. AtlanticB. IndianC. ArcticD. Pacific27、听力题:The capital of Chile is __________.28、听力题:A __________ is a type of mixture where the components are visible.The arrangement of atoms in a crystal lattice is characteristic of _____ (ionic compounds).30、听力题:A __________ is a mixture that can be separated by evaporation.31、填空题:My favorite pet is a ______ (狗) that loves to cuddle.32、What is the color of an orange?A. RedB. GreenC. OrangeD. Yellow答案: C. Orange33、听力题:A solution that can conduct electricity is called a _______ electrolyte.34、What do you call the place where you go to borrow books?A. BankB. LibraryC. SchoolD. Park答案: B35、填空题:The capital of Belarus is ________ (白俄罗斯的首都是________).36、What is the primary job of a teacher?A. To clean the classroomB. To teach studentsC. To grade papersD. To manage the school答案: B37、选择题:What is the name of the famous mountain in Africa?A. Mount KilimanjaroB. Mount EverestC. Mount FujiD. Mount Elbert38、填空题:We made a ________ out of paper.The llama is known for its soft _________ (毛).40、填空题:I learned about different _____ (植物类型) in science class.41、听力题:A ____ has long whiskers and scurries about.42、填空题:The capital of Turkey is ________ (安卡拉).43、填空题:The ancient Greeks contributed to the development of _____.44、填空题:I want to __________ (动词) my favorite __________ (玩具名) with you!45、听力题:I see a _____ (mouse) in the house.46、听力题:A chemical reaction can involve the breaking and forming of ______.47、听力题:A __________ is a geological feature that can impact transportation routes.48、填空题:Certain plants are known for their ______ properties, like aloe vera.(某些植物以其药用特性而闻名,如芦荟。
小学上册英语第5单元综合卷英语试题一、综合题(本题有100小题,每小题1分,共100分.每小题不选、错误,均不给分)1.I like to ______ (参加) community service.2.What do we call an animal that only eats plants?A. CarnivoreB. HerbivoreC. OmnivoreD. InsectivoreB3.Plants use __________ (光合作用) to make food.4.The bread is ___. (fresh)5.I want to learn how to _______ (技能). It could help me in my future _______ (职业).6.What is the chemical symbol for potassium?A. KB. KrC. PD. Pt7.I see a _____ in the sky. (cloud)8. A ______ (有机农业) promotes healthier ecosystems.9.Acids taste ______.10.What is the main ingredient in pesto sauce?A. BasilB. ParsleyC. CilantroD. Rosemary11.What do you call a large, slow-moving animal with a shell?A. TurtleB. SlothC. SnailD. ArmadilloA12.The rabbit loves to dig in the _________. (土壤)13.I like to wear ___ (hats) in the sun.14.The frog sits on a ______.15.The bridge is very ___ (strong).16.What is the name of the longest river in the world?A. AmazonB. NileC. YangtzeD. MississippiB17.What do we do to express gratitude?A. YellB. ThankC. IgnoreD. FrownB18.Birds build _______ (巢) in trees.19.The _______ (Egyptian Pharaohs) ruled over ancient Egypt for thousands of years.20.The parakeet loves to sing and _______ (跳舞).21.My grandmother tells me __________. (故事)22.The pH scale measures how ______ or basic a solution is.23.The ice cream is ______ on a hot day. (refreshing)24.I see a ________ (彩虹) after the rain.25.What do you wear on your feet?A. HatB. GlovesC. ShoesD. ScarfC26.Which fruit is known for having seeds on the outside?A. GrapesB. StrawberryC. BlueberryD. RaspberryB27.We have a ______ (快乐的) family dinner every Sunday.28.green architecture) promotes sustainable building practices. The ____29.The chemical symbol for tungsten is ________.30.The _______ (The Great Society) aimed to eliminate poverty and racial injustice.31.What is 3 x 4?A. 10B. 11C. 12D. 1332.I want to ________ (influence) positive change.33.What do you call the longest bone in the human body?A. TibiaB. FemurC. HumerusD. Radius34.How many players are there in a basketball team?A. 5B. 6C. 7D. 8A35.What do we call the period of time before written records?A. AncientB. PrehistoricC. MedievalD. ModernB36.What is the name of the famous French landmark known for its iron lattice structure?A. Eiffel TowerB. Louvre MuseumC. Arc de TriompheD. Notre-Dame Cathedral37.I call my friend’s mom __________. (阿姨)38.What do you call a young penguin?A. ChickB. PupC. CalfD. Kit39.How many players are on a soccer team?A. 9B. 10C. 11D. 1240.I enjoy playing outside with my ______.41.I want to travel to ________ (意大利) one day.42.She is _____ (writing) in her notebook.43.My cousin is very __________ (有趣)。
(译林版)2024七年级上册Unit 5 单元综合测试卷一、单词辨音。
(5分)()1. A. school B. chair C. Chinese D. teacher()2. A. thin B. these C. than D. this()3. A. over B. very C. of D. family()4. A. should B. television C. shoe D. shop()5. A. plans B. meals C. sweets D. weekends二、单项选择。
(10分)()1.---Shall we have_________big dinner this evening?---Sorry, but I don't like eating too much for _______dinner.A. the; /B.a; /C./; theD. a; the()2. Good health means not only a strong body but also a healthy mind._____healthy mind, the body cannot work well and may get sick.A. ExceptB. FromC. ToD. Without()3. ---I think she ______a doctor, because she is wearing a white uniform.---I don't think so._________she is a nurse.A. maybe; May beB. may be; MaybeC.maybe; MaybeD. may be; May be()4.---Why do you look so sleepy in class, John?---Sorry, sir. I shouldn't _________to watch the new film The Last Frenzy(《路狂花钱》)last night.A. keep upB. make upC. stay upD. put up()5.---_________? ---Some beef and fish.A. Where do you want to eatB. What would you like to eatC.How do you like beef and fishD. What about some beef and fish()6.---Mum,there________no milk in the fridge.---Oh, but there_________three bottles of orange juice.A. are; isB. are; areC. is; areD. is; is()7.You can see_________on the table and three_________on the chair.A. five kilos of apples; knivesB. three boxes of potatos; knivesC. four kiloes of apples; knivesD. two boxes of tomatoes; knifes()8. ________students are becoming the “Heads-down Tribe(低头族)”. It's________bad for their health and study.A. Too many; much tooB. Too much; much tooC.Much too; too muchD. Too many; too much()9.---Kate, do you have________ to watch the film Spider-Man: Into the Spider-Verse tonight?---Great! It is __________to attract(吸引) so many people to watch it.A. enough time; enough interestingB. enough time; interesting enoughC. time enough; enough interestingD. time enough; interesting enough()10.---The Mint Mambo Style(薄荷曼波穿搭)is simply dressing in shades of fresh green. I would like to have a try. --- _____________A. Me too.B. What about you?C. How do you like it?D. I hope so.三、完形填空。
蚌埠“PEP”2024年10版小学五年级下册英语第6单元期中试卷考试时间:80分钟(总分:140)A卷一、综合题(共计100题)1、填空题:The _______ (老虎) is known for its strength.2、听力题:The __________ can reveal the history of climate changes over time.3、填空题:The __________ makes everything look magical in winter. (雪)4、听力题:I see a _____ (whale) in the ocean.5、What is the name of the largest land animal?A. GiraffeB. ElephantC. RhinoD. Hippopotamus答案: B6、How many legs does an insect have?a. Sixb. Eightc. Fourd. Ten答案:A7、填空题:My favorite movie genre is ______.8、填空题:The sunflowers grow tall in the ________.9、What is the distance around a circle called?A. DiameterB. RadiusC. CircumferenceD. Area答案: C10、听力题:Florence Nightingale is known as the founder of _______.11、What is the term for a baby turkey?a. Chickb. Poultc. Calfd. Kit答案:b12、听力题:I have _____ (two) sisters.13、听力题:She is reading a ___. (book)14、填空题:My brother is a __________ (业务发展经理).15、填空题:My uncle is a great __________ (讲故事的人) with fascinating tales.16、选择题:What is the main ingredient in soup?A. WaterB. VegetablesC. MeatD. All of the above17、填空题:The chemical process of _______ involves combining elements to form compounds. (合成)18、How many players are on a ice hockey team?A. 5B. 6C. 7D. 819、What do we call the process of making a choice?A. Decision-makingB. PlanningC. OrganizingD. Arranging答案:A20、填空题:She is a _____ (作家) contributing to literary magazines.21、填空题:During the summer, I like to go to the _______ (地方) and swim in the _______ (水体).22、填空题:The tiger is a _______ (强壮的) predator in the jungle.23、填空题:__________ (混合物) can be separated into its components.24、听力题:The garden is _______ (blooming) in spring.25、听力题:A buoyant object will float on ______.26、听力题:Glass is an example of a(n) _______ material.27、What do you call the process of learning new things?A. EducationB. TrainingC. TeachingD. Studying答案:A28、填空题:A rabbit has long ______ (耳朵) and is very cute.29、填空题:The __________ (不同地区) have unique features.30、听力题:Pulsars are rotating neutron _______ that emit beams of radiation.The ________ has a big smile and is very friendly.32、填空题:A ______ (植物的保护计划) can help conserve biodiversity.33、填空题:Bamboo is one of the fastest growing _____ (植物).34、What do we call a story that teaches a lesson?A. NovelB. FableC. BiographyD. Fiction答案: B35、What do we call the act of protecting an area of wildlife?A. ConservationB. PollutionC. PreservationD. Restoration答案:A36、听力题:I eat _____ (面包) for breakfast.37、选择题:What is 4 - 1?A. 2B. 3C. 4D. 538、填空题:The ancient Babylonians are known for their advances in ______ (天文学).39、What do we call the food we eat in the morning?A. LunchB. DinnerC. BreakfastD. Snack答案:C40、填空题:I want to _______ (去参加) a workshop.My friend is very ________.42、What is the value of Pi (π. approximately?A. 2.14B. 3.14C. 4.14D. 5.14答案:B43、填空题:A ___ (小老虎) is fierce and strong.44、听力题:The chemical formula for barium hydroxide is _____.45、听力题:I like to ___ new places. (explore)46、听力题:My brother is passionate about ____ (computers).47、填空题:The dog is _______ (在跑) in the yard.48、听力题:The Earth's layers are made up of different types of ______.49、填空题:The __________ (历史的传承渠道) ensure continuity.50、What is the name of the famous detective created by Arthur Conan Doyle?A. Hercule PoirotB. Sam SpadeC. Sherlock HolmesD. Miss Marple答案:C51、What do we call the process of producing offspring?A. GrowthB. ReproductionC. MetabolismD. Evolution答案: BMy dad is a _____ (商人) who travels for work.53、填空题:The __________ (历史的教训) should not be forgotten.54、填空题:My favorite animal is a ______.55、填空题:Different plants have different ______ that affect their growth. (不同的植物有不同的需求,影响它们的生长。
南昌2024年10版小学6年级上册英语第2单元综合卷[有答案]考试时间:100分钟(总分:110)A卷考试人:_________题号一二三四五总分得分一、综合题(共计100题)1、填空题:The squirrel hides its ______.2、听力题:Matter can exist in different ______.3、填空题:Cats have sharp _________ (爪子).4、填空题:The horse rides _________ in the field. (快)5、听力题:The smallest unit of an element is called an __________.6、选择题:What do we call a person who studies diseases?A. BiologistB. EpidemiologistC. MicrobiologistD. Pathologist7、填空题:I like to draw ______.8、填空题:I love to go ______ (滑雪) during winter vacations.9、听力题:The _______ is a negatively charged particle in an atom.10、填空题:A manatee is gentle and loves ______ (水).11、听力题:The first woman to win a Nobel Prize was _______ Curie.12、听力题:The ______ is home to many fish.13、填空题:I want to visit _______ (动物园).14、听力题:The __________ is a region known for its mining.15、填空题:I like to ______ (收集) coins.16、填空题:The _____ (春天) brings new growth and life.17、填空题:The owl looks for food in the _________. (夜晚)18、听力题:A __________ is a place that is protected by law.19、填空题:A _____ (园艺工具) makes planting easier.20、填空题:A __________ (气味) can indicate the presence of certain chemicals.21、What is the name of the famous clock tower in London?A. Big BenB. Tower of LondonC. London EyeD. Buckingham Palace答案: A22、听力题:A solution that has a pH above is considered ______.23、听力题:The _____ (park/garden) is close by.24、Which is a primary color?A. GreenB. BlueC. OrangeD. Purple25、How many wheels does a bicycle have?A. 1B. 2C. 3D. 4答案:B. 226、What do you call a baby cat?A. PuppyB. KittenC. CubD. Calf答案: B27、填空题:We can _______ together to finish the project.28、填空题:A lizard can change color to blend into its ______ (环境).29、填空题:I enjoy listening to ________ (音乐) while studying.30、can Civil Rights Movement aimed for _____ equality. 填空题:The Amer31、填空题:The ________ (生态恢复计划实施) is essential.32、填空题:I love _______ (制作)手工艺品.33、填空题:I love going to ______ (夏令营) during the summer. It’s a chance to make new friends and try new activities.34、听力题:The arrangement of atoms in a crystal lattice is characteristic of _____ (ionic compounds).35、听力题:He is _____ (tall/short) than his sister.36、选择题:What is the capital city of Brazil?A. Rio de JaneiroB. BrasíliaC. São PauloD. Salvador37、填空题:The early human species originated in ________ (非洲).38、填空题:The _______ (The Age of Enlightenment) emphasized reason and scientific thought.39、听力题:The cake is ________ and sweet.40、填空题:I enjoy learning about __________ (历史) and geography.41、What do you call the person who helps you in a store?A. CustomerB. CashierC. ManagerD. Salesperson答案: D42、听力题:A solution is a mixture where one substance is ______ in another.43、听力题:Sound travels faster in water than in ______.44、听力题:My favorite season is _____ (winter/summer).45、听力题:A __________ is formed when a river meets the sea.46、听力题:The children are ________ in the playground.47、听力题:A __________ is a geological feature formed by the erosion of rock.48、What is the name of the dessert made of frozen cream?A. CakeB. JellyC. Ice CreamD. Pie答案:C49、What is the first letter of the English alphabet?A. AB. BC. CD. D50、填空题:_____ (fossil) records show ancient plants.51、填空题:The coach trains the _____ (球队) to win.52、填空题:The trees look beautiful when they are ______ (覆盖着雪).53、What is the primary color of a cantaloupe?A. OrangeB. YellowC. GreenD. Red54、填空题:The ______ (阳光充足的地方) is ideal for flowers.55、填空题:A kitten loves to play with ______ (毛线球).56、填空题:I have a special ______ (盒子) where I keep all my treasures. It is very ______ (珍贵).57、填空题:The ______ (青蛙) croaks by the pond at night.58、听力题:A ______ can live in very cold climates.59、听力题:I wear _____ (帽子) in winter.60、填空题:My friend has a pet _________ (鹦鹉).61、migration) of birds occurs seasonally. 填空题:The ____62、What type of animal is a dolphin?A. FishB. MammalC. ReptileD. Bird答案: B. Mammal63、What do you call the festival celebrated in October?A. ChristmasB. HalloweenC. EasterD. Thanksgiving64、听力题:The weather is _____ (sunny/cloudy) today.65、听力题:Sarah is my ______. We play together every day.66、What do we celebrate on December 25?A. HalloweenB. ThanksgivingC. ChristmasD. Easter答案:C67、填空题:We had a picnic with my _____ (家人).68、填空题:The sunflowers grow tall in the ________.69、填空题:The teacher is _______.70、What do we breathe in?A. WaterB. AirC. FoodD. Light答案:B71、What is the main language spoken in Spain?A. FrenchB. SpanishC. ItalianD. Portuguese答案:B. Spanish72、What is the capital of France?A. BerlinB. RomeC. ParisD. Madrid答案:C73、填空题:I want to visit the __________ (遗址) of ancient civilizations.74、听力题:We will _______ (have) a picnic at the park.75、填空题:The _____ (花香) filled the air as we walked through the garden.76、What is the capital of Kenya?a. Nairobib. Mombasac. Kisumud. Nakuru答案:a77、Which animal lives in a den?A. FoxB. BirdC. FishD. Cow答案:A78、填空题:A ________ (森林) is home to many trees and animals.My family has a tradition of calling each other by our ______ names. (我家有一个传统,称呼彼此的____名字。
a rXiv:c ond-ma t/94897v131Aug1994Lattice Green Function (at 0)for the 4d Hypercubic Lattice M.L.Glasser Department of Physics Clarkson University Potsdam,NY 13699-5820(USA)and A.J.Guttmann Department of Mathematics The University of Melbourne Parkville,Victoria 3052,Australia The generating function for recurrent Polya walks on the four dimensional hypercubic lattice is expressed as a Kamp´e -de-F´e riet function.Various properties of the associated walks are ttice statistics play an important role in many areas of chemistry and statistical physics.Random lattice walks have been investigated extensively,both numerically and analytically,and explicit analytic expressions for recur-rent lattice walks (those that end where they began)are available for several lattices in one,two and three dimensions [1,2].The interest in this prob-lem follows from the numerous connections between random walks and other problems in mathematical physics.They form the basis of certain proofs in the problem of self-avoiding walks [3],they are a key component in the studyof lattice dynamics [4],and they have an extensive following in the mathe-matical literature [1,3].Furthermore,d-dimensional lattice Green functions have recently [5]been shown to underlie the theory of d-dimensional stair-case polygons and to be related to the generating function for d-dimensional multinomial coefficients.The aim of this note is to extend this list to four dimensions by summa-rizing a study of the lattice Green functionP (z )=P 4(z )=11−zwhich generates the statistics for recurrent Polya walks (uniform step prob-abilities)on the 4d hypercubic lattice.From (1)it is clear that P (z )is an analytic function of z 2within the unit circle and has a branch point at z 2=1.It is representable as a single integral in a variety of ways.From the relations in [6],for example,we haveP (z )= ∞0e −x I 40(1π310K (k +)K (k −)1−x 2dx (3)wherek 2±=11−12x 2z 2)√π4 π0[1On the other hand,by expanding the Bessel function in(2),integrating term-by-term,and proceeding as in the appendix in[6],wefinda n=[(1/2)nn!4F3(−n,1/2,1/2,1/2;1/2−n,1/2−n,1/2−n;1)(10) expressing the latter4F3in terms of its series,and noting that(−n)k=(−1)k n!/(n−k)!,(1/2−n)k=(−1)k(1/2)n/(1/2)n−k,(11) we arrive at the double hypergeometric seriesP(z)=∞m,n=0(1/2)m+n(1/2)3n(1/2)3m n!m!(12)which defines a Kamp´e-de F´e riet function[7]:P(z)=F1:3:33:0:0[1,1,1;−;−;z2,z2](13)=F2:1:10:2:2[1/2,1;1/2;1/2−;1,1;1,1;z2/4,z2/4].The quantity a n in(8)is the probability that the random walker ends at its starting point in2n steps(not necessarily for thefirst time).The number of such walks is therefore r n=82n a n,which obeys the recursion relationn4r n−4(20n4−40n3+33n2−13n+2)r n−1+256(4n4−16n3+23n2−14n+3)r n−2=0.(14) Thefirst ten values are given in the table.Number of2n-step recurrent walks3n r n1821683512041901205793900863577136647169937264648839358285480942714450658880102225741588095168For large n,for the d-dimensional hypercubic lattice[8]r(d)n∼2(2d)2n(d/4πn)d/2so in the present case a n∼2/π2n2and r n∼64n(2/n2π2).(For example,this yields a500∼8.10569×10−7,compared to the exact value a500=8.0976×10−7,a difference of less than0.1%).To our knowledge,the only previous studies of P4(z)were by Bender et al.[8],who examined P d(1)as a function of d and by a1/d expansion obtained a value consistent with(6),and by Mayer and Nuttall[9],who derived a differential equation consistent with(5).We have not examined P(z)outside the unit circle,although it is clearly analytic in the z2plane cut along the real axis from z2=1to infinity.While it is doubtful that P(z)can be expressed in terms of elliptic integrals as for the three dimensional cubic lattices[2], it is hoped that further analysis of(13)will lead to a more transparent representation of its analytic properties.AcknowlegementsMLG expresses his thanks to the University of Melbourne for hospital-ity while this work was carried out.AJG acknowleges the support of the Australian Research Council.We are grateful to Dr. E.D.Krupnikov for information about the Kamp´e-de-F´e riet functions.4References[1]M.N.Barber and B.Ninham,Random and Restricted Walks:Theory and Applications.(Gordon and Breach,NY1977).[2]M.L.Glasser and J.I.Zucker,Proc.Nat.Acad.Sci.74,1800(1977).[3]N.Madras and G Slade,The Self-Avoiding Walk.(Birkh¨a user,Boston 1992)[4]G.S.Joyce,Philos.Trans.R.Soc.London273,583(1973)[5]A.J.Guttmann and T.Prellberg,Phys.Rev.E47,R2233(1993)[6]M.L.Glasser and E.Montaldi,Phys.Rev.E46,R2339(1993).(The summation indices on the RHS of(A8)should be n and k.)[7]H.Exton,Multiple Hypergeometric Functions and Applications,(Horwood,Chichester,1976).[8]C.M.Bender,S.Boettcher,and L.Mead,.J.Math.Phys.35,368(1994).[9]I.L.Mayer and J.Nuttall,J.Phys.A:Math.Gen.20,2357(1987).5。