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APPENDIX C. GUIDE TO RTD SIMULATION CODE 147 C.3 Data Files C.3.1 grid.h This is a parameter file that defines the finite difference discretization and the correlation length Lc for the simulation. The user must specify: • nx -Numberofx grid points (Nx). • nk -Numberofk grid points (Nk). • nc - x grid point that is as close to but no larger than the correlation length Lc. • lc - Correlation length Lc. C.3.2 material.dat This files contains a list of numbers that is read in by the routine terms, whichis located in transi.f. These values determine several simulation parameters such as the length of the device L, barrier width, barrier height, etc. To determine the relationship between the numbers and the physical constants, read terms to see how it parses though the list of values. C.4 Compiling and Running The Simulation Included with the RTD simulation code and data files are two makefiles: makeinit and newcompilehopf. These makefiles were made for and tested on the Linux cluster
APPENDIX C. GUIDE TO RTD SIMULATION CODE 148 henry2 maintained by the High Performance Computing division at North Carolina State University. The newcompilehopf is tuned for a particular version of Trilinos, and therefore, must be editted with that in mind. Here are the steps for performing a continuation run through a voltage range for the RTD simulation. 1. Set parameter values in grid.h and material.dat. The values set in grid.h determine the discretization and correlation length used in the simulation while the values set in material.dat determine the physical structure of the device. 2. Copy makeinit to makefile, typemake clean, typemake, and run the compiled program init. Typing make clean will clean up remaining files from previous initializations, and typing make compiles the program init. Run the program by submitting a job to the queue. 3. Set the continuation parameters in RTDContinuationParallel.C and copy the initial guess for the steady-state distribution at the first continuation parameter into the data file initial.out. You will need to set such things as initial voltage parameter, lower and upper bounds on the voltage range, initial step in the voltage parameter, and decide if you want to compute eigenvalues for a stability analysis of the steady-state. If you want to start at V =0,thencopysol.out to initial.out since f0(x, k) is
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Numerical Methods for the Wigner-Po
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NUMERICAL METHODS FOR THE WIGNER-PO
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Acknowledgments First and foremost,
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Table of Contents List of Tables ix
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4.3 ApplicationofSchauder’sFixedP
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List of Tables 1.1 PhysicalConstant
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3.11 I-V Curve with 30 Percent Redu
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CHAPTER 1. OVERVIEW 2 being heavily
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CHAPTER 1. OVERVIEW 4 Doping Spacer
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CHAPTER 1. OVERVIEW 6 and identfyin
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CHAPTER 1. OVERVIEW 8 for predictin
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CHAPTER 1. OVERVIEW 10 by Schrödin
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CHAPTER 1. OVERVIEW 12 ranging term
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CHAPTER 1. OVERVIEW 14 But because
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CHAPTER 1. OVERVIEW 16 = h 2π ,we
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CHAPTER 1. OVERVIEW 18 Table 1.1: P
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CHAPTER 1. OVERVIEW 20 where q is t
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CHAPTER 1. OVERVIEW 22 get K(f)
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CHAPTER 1. OVERVIEW 24 rule. The pr
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CHAPTER 1. OVERVIEW 26 The weights
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Chapter 2 Temporal Integration 2.1
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CHAPTER 2. TEMPORAL INTEGRATION 30
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Chapter 3 Bifurcation Analysis 3.1
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CHAPTER 3. BIFURCATION ANALYSIS 46
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Chapter 4 Theory 4.1 Steady-State T
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CHAPTER 4. THEORY 76 If we write ou
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CHAPTER 4. THEORY 78 So if we write
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CHAPTER 4. THEORY 80 Combining Equa
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CHAPTER 4. THEORY 82 We now estimat
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CHAPTER 4. THEORY 84 pendent of x,
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CHAPTER 4. THEORY 86 interval we ha
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CHAPTER 4. THEORY 88 So an estimate
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CHAPTER 4. THEORY 90 We want to cho
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CHAPTER 4. THEORY 92 The exact same
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CHAPTER 4. THEORY 94 Since un → u
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Page 115 and 116: CHAPTER 4. THEORY 102 Now, we can t
Page 117 and 118: CHAPTER 4. THEORY 104 operator. 4.2
Page 119 and 120: CHAPTER 4. THEORY 106 we have at th
Page 121 and 122: CHAPTER 4. THEORY 108 we have at th
Page 123 and 124: CHAPTER 4. THEORY 110 4.3 Applicati
Page 125 and 126: CHAPTER 4. THEORY 112 We need to fi
Page 127 and 128: Chapter 5 Conclusion In this work,
Page 129 and 130: CHAPTER 5. CONCLUSION 116 • Findi
Page 131 and 132: REFERENCES 118 ODE solver. Technica
Page 133 and 134: REFERENCES 120 [21] C. T. Kelley an
Page 135 and 136: REFERENCES 122 [37] Homer F. Walker
Page 137 and 138: APPENDIX A. NOTATION 124 ˜B Genera
Page 139 and 140: APPENDIX A. NOTATION 126 k Wave num
Page 141 and 142: APPENDIX A. NOTATION 128 ∆t Incre
Page 143 and 144: APPENDIX A. NOTATION 130 ɛc ɛk ɛ
Page 145 and 146: APPENDIX B. TRILINOS 132 user-given
Page 147 and 148: APPENDIX B. TRILINOS 134 Trilinos,
Page 149 and 150: APPENDIX B. TRILINOS 136 Minimum Re
Page 151 and 152: APPENDIX B. TRILINOS 138 A very use
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