Computational Physics

References 603 A.5 Starting from Newton’s interpolation formula, derive the Gauss interpolation formula to order three: xi+t=xi+ ...

604 Appendix A [4] J. Stoer and R. Bulirsch,Introduction to Numerical Analysis. New York, Springer Verlag, 1977. [5] D. Kincaid ...

Appendix B Random number generators B1 Random numbers and pseudo-random numbers Random numbers are used in many simulations, not ...

606 Appendix B Random numbers from standard generators are uniformly distributed over the interval[0, 1]. This means that each n ...

B2 Random number generators 607 different random numbers ism−1. It turns out that there exist special combinations ofaandmallowi ...

608 Appendix B behaviour in any test so far[4]. The sequence lengths in all these examples might seem large, but in practice the ...

B3 Nonuniform random number generators 609 where the numbersciare all equal to 0 or 1. We see that the shift-register generator ...

610 Appendix B density of the numbersy=f(x)is given by 1/f′(x), so this should be equal to the prescribed distributionP(y): 1 /f ...

Exercises 611 01 x h(x) P(x) rejected accepted Figure B.1. The von Neumann method for generating nonuniform random numbers. two ...

612 Appendix B (a) Show that if 0<x<m, botha(xmodq)andr[x/q]lie in the range 0,...,m− 1 ([z]is the largest integer smaller ...

Index ab initio method,seeelectronic structure calculations, 293 Adams’ formula, 578 aluminium,seeband structure, 126 Amdahl’s l ...

614 Index central charge, 346 , 367 , 370 , 415 , 417 central limit theorem, 609 central processing unit (CPU), 541 chaos, 180 c ...

Index 615 energy estimator, 213 , 214 , 256 , 396 , 397 , 406 energy functional, 267 , 268 , 290 – 293 ; see also variational ca ...

616 Index Goedecker–Teter–Hutter (GTH) pseudopotential, 154 gradient corrections,seedensity functional theory (DFT), 96 grand ca ...

Index 617 Lehmann–Symanzik–Zimmermann relation,see quantum field theory, 472 Lie–Trotter–Suzuki formula, 401 , 418 linear combin ...

618 Index multigrid method, 355 , 481 , 504 , 588 – 591 , 604 multigrid Monte Carlo (MGMC) method, 504 Navier–Stokes equations,s ...

Index 619 gluons, 528 , 529 , 532 strong interactions, 527 , 528 quantum electrodynamics (QED), 9 , 467 , 512 – 514 , 517 , 518 ...

620 Index silicon,seeband structure, 146 simple cubic,seecrystal lattices, 123 Simpson’s rule, 567 simulated annealing,seeMonte ...