Nanocomputing computational physics for nanoscience and nanotechnology

Free ebooks ==> www.Ebook777.com James J Y Hsu NANOCOMPUTI NG Computational Physics for Nanoscience and Nanotechnology www.Ebook777.com Free ebooks ==> www.Ebook777.com www.Ebook777.com Published by Pan Stanford Publishing Pte Ltd Toh Tuck Link Singapore 596224 Distributed by World Scientific Publishing Co Pte Ltd Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library NANOCOMPUTING Computational Physics for Nanoscience and Nanotechnology Copyright © 2009 by Pan Stanford Publishing Pte Ltd All rights reserved This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA In this case permission to photocopy is not required from the publisher ISBN-13 978-981-4241-26-7 ISBN-10 981-4241-26-1 Typeset by Research Publishing Services E-mail: enquiries@rpsonline.com.sg Printed in Singapore Free ebooks ==> www.Ebook777.com www.Ebook777.com PREFACE The contents of this book are based on the material of Nano Computing course I taught at National Tsing Hua University since 2004 Nanotechnology is catching attention and gaining importance in both academia and industry alike, and students are very much interested in this emerging topic There is the need to have a coherent presentation on the related disciplines, namely, theoretical physics, computer science, applied mathematics, and engineering study In considering the importance of the four technologies for the future, Nano Technology (NT), Biomedical Technology (BT), Information Technology (IT), and Ecology Technology (ET), the course is designed to give breadth on related subjects, but keep depth on computation and physics On the theoretical side, we cover the Mesoscopic Physics and Nonlinear Many Body Physics On the computer science, Object Oriented Programming and Parallel Computing are incorporated On the applied mathematics, Asymptology and Algorithm are reviewed For the engineering training, some applications and MATLAB are presented Students are introduced to the multiscales and multisciences from this book, and are requested to solve all the problems by either MATLAB or C++ The target audience for the book is students at the senior and graduate level The emphasis of this book is to teach students to solve problems from the features and characteristics of the problem itself, and not from a presumed methodology or a predefined tool It tries Preface to avoid the students from falling into the mind frame of what the old saying, “If you are a hammer, everything else is a nail.” The rightful problem solving mentality is let the problem reveal where the solution might be, and study the clues to find the answers Therefore, start from the asymptotic analysis once the problem is translated into a mathematical equation, and get all the hints possible even if a numerical solution is inevitable This book is organized as follows: It introduces the issues in nanoscience, reviews the mathematical tools both numerical and analytical, and then applies the tools to more advanced problems through a repetition of the ideas and an increase in the level of sophistication so as to allow a deeper understanding of the physics and the problem solving techniques Finally, it applies the scientific knowledge for practical applications The ultimate goal of this book is to prepare students with enough background to start working on a research dissertation in theoretical nanoscience James J Y Hsu March 2008 viii James J Y Hsu ACKNOWLEDGEMENTS I would like to thank Professor T L Lin for suggesting the course title, and ESS faculty and students for giving me the opportunity to teach this course The interaction with Professor C H Tsai’s Carbon Nanotube group was most beneficial Many insightful help from colleagues, post-doctors and students at both NCKU and NTHU are gratefully acknowledged Some derivations and programs were aided byYee Mou Kao,Young-Chung Hsue, Chun Hung Lin, Eugene Pogorelov, Chieh-Wen Lo, Ying-Chi Chung, Chi-Yeh Chen, Robert Weng, Wellin Yang, Lichung Ko, and Cheng Hao Wu This book was proofread by Dr Fay Sheu I also thank my wife, Dr Yen-Hwa Hsu, and my daughters, Ingrid and Jessica, for their support to let me concentrate on research in Taiwan for the past few years Free ebooks ==> www.Ebook777.com CONTENTS Preface v Acknowledgement Chapter One vii Little Big Science 1.1 Tools for Measurement — To See is to Believe 1.2 Carbon Tells Us First 1.3 Mother Nature Knows Best 10 1.4 Challenges in the New Millennium 12 Chapter Two Tools for Analysis 19 2.1 MATLAB 20 2.2 Program Control 29 2.3 Asymptology 33 Chapter Three Mesoscopic Systems 59 3.1 Review on Quantum Physics 59 3.2 Quantum Chemistry 78 3.3 Molecular Biology 88 3.4 Condensed Matter Physics 91 Chapter Four Analytical Chapter 115 4.1 Multiple Time Scales 116 4.2 Multiple Space Scales 124 www.Ebook777.com Reference 117 J Tersoff (1988), Empirical Interatomic Potential for Carbon, with Applications to Amorphous Carbon, Physical Review Letters, 61, 2879 118 D C Tsui, H L Störmer and A C Gossard (1982), Twodimensional Magnetotransport in the Extreme Quantum Limit, Physical Review Letters, 45, 1559-1562 119 R W van Boeyen, N Watanabe, J P Doering, J H Moore, and M A Coplan (2004), Practical Means for the Study of Electron Correlation in Atoms, Physical Review Letters, 92, 223202 120 K von Klitzing, G Dorda, and M Pepper (1980), New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Physical Review Letters, 45, 494 121 S H Vosko, J P Perdew, and A H MacDonald (1975), Ab Initio Calculation of the Spin Susceptibility for the Alkali Metals Using the Density-Functional Formalism, Physical Review Letters, 35, 1725 122 B Wang, S Yin, G Wang, A Buldum, and J Zhao (2001), Novel Structures and Properties of Gold Nanowires, Physical Review Letters, 86, 2046 123 David Wales (1996), Structure, Dynamics, and Thermodynamics of Clusters: Tales from Topographic Potential Surfaces, Science, 271, 925 124 David J Wales and Harold A Scheraga (1999), Global Optimization of Clusters, Crystals, and Biomolecules, Science, 285, 1368 125 P R Wallace (1947), The Band Theory of Graphite, Physical Review, 71, 622 126 Nelson Wax (1954), Selected Papers on Noise and Stochastic Processes, Dover Phoenix Editions 127 C Z Wang and K.M Ho (2005), Environment-dependent Tight-Binding Models, Handbook of Materials Modeling, Vol 1, pages 307-347, Editor S Yip, Springer 128 C Z Wang and K M Ho (2004) Tight-binding molecular dynamics for carbon and applications to nanostructure 342 James J Y Hsu Reference 129 130 131 132 133 134 135 formation, , 1,1.Journal of Computational and Theoretical Nanoscience Jian Wang, Baigeng Wang and Hong Guo (2007), Quantum inductance and negative electrochemical capacitance at finite frequency in a two-plate quantum capacitor, Physical Review B, 75, 155336 Wojciech Hubert Zurek and Juan Pablo Paz, Decoherence, Chaos, and the Second Law, Physical Review Letters, 72, 1994 Yang C K (2005), Doping a C60 molecule with potassium atoms: A theoretical study,Journal of Applied Physics, 98, 116103 T H Yang and Chin Pan (2005), Molecular dynamics simulation of a thin water layer evaporation and evaporation coefficient, International Journal of Heat and Mass Transfer, 48, 3516 D R Yennie (1987), Integer Quantum Hall Effect for Nonspecialists, Reviews of Modern Physics, 59, 781 Yuanbo Zhang,Yan-Wen Tan, Horst L Stormer and Philip Kim (2005), Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature Letter, 438, 201 Y Zhang, Z Jiang, J P Small, M S Purewal, Y.-W Tan, M Fazlollahi, J D Chudow, J A Jaszczak, H L Stormer, and P Kim (2006), Landau-Level Splitting in Graphene in High Magnetic Fields, Physical Review Letters, 96, 136806 Nano Computing 343 FUNCTION INDEX Function Name Page Chapter Purpose AtomicWire 251 Eight BECbl 130 Four Butterfly C60 CCI CGSAT10 298 29 85 153 Nine Two Three Five Correlation Dimension 296 Nine Crystal Electron 293 Nine DOS Energy Dispersion FEM1d FEMH2 312 311 167 175 Ten Ten Five Five FFT Fibonacci Friedel Oscillation 138 30 268 Five Two Nine Graphene Energy Band 306 H2 51 Ten Two H2Energy H2MO Two Three 52 77 quantum wire eigenstates with one atom per site BEC boundary layer of Gross-Pitaeskii equation Hofstadter’s butterfly plot the fullerene structure CCI model for helium like atom coarse-graining simulated annealing based on Tersoff potential to optimize for C60 structure fractal dimension determined by correlation dimension semiclassical trajectory of Bloch electron graphene density of states CNT energy band 1d Finite Element Method 2d Finite Element Method for hydrogen molecule Fast Fourier Transform Fibonacci recursive formula plot Friedel oscillation in Thomas-Fermi Screening graphene energy band symbolic program for hydrogen molecule evaluate the minimum energy of H2 calculate the bond energy and the bond length for H2 Function Index Function Name Page Chapter Purpose H2VB H2W He 80 82 28 Three Three Two He Energy He EnergyC Helical Winding Henon Map Honeycomb Inverse Distance 71 72 28 296 307 74 Three Three Two Nine Ten Three KP KVN 160 83 Three Three lag Landau Landau0 LeapFrog 70 104 107 231 Three Three Three Seven LJEnergyC.c LJForceC.c 231 232 Seven Seven mcH2W 142 Five mc Integration MC Distribution 140 141 Five Five 235 Seven mcPI 140 Five MDH2O MDlf 320 161 Ten Five mex Function 231 Mode Conversion 274 346 James J Y Hsu Seven Nine valence bond model for H2 Weinbaum model for H2 plot energy in terms of variational parameters helium energy components helium energy components with correlation plot helical coil rotating along the axis fractal dimension of Henon map plot graphene sheet spherical harmonic representation of inverse distance Kronig-Penney model kinetic and potential energy components and normalization constant of helium like atom Laguerre polynomials solve for Landau levels — Landau gauge solve for Landau levels — symmetry gauge leap frog routine: converted to dll binary code leap frog routine c source code calculating leap frog routine c source code calculating force Monte Carlo H2 molecule Weinbaum model with correlation integration by MonteCarlo generate a Monte Carlo distribution function calculate the transport coefficients and convert to dll obtain the value π to three digits of accuracy molecular dynamics simulation of water molecular dynamics study of nanocluster showing self organization; leap frog algorithm MATLAB executing dll mode conversion from EM wave to ES plasmon Function Index Function Name Page Chapter Purpose montecarlo.h montecarlo.c Nano Cluster 237 238 256 Seven Seven Eight Nano Particle plotPSI plot Saddle QD QTable 255 27 28 247 254 Eight Two Two Eight Eight Quantum Chaos Quantum Wire 288 250 Nine Eight REF SApGA 70 148 Three Five Simulated Annealing Single Impurity Stairs StandingWave SuperLattice TBJ 147 Five 216 31 285 96 213 Six Two Nine Three Six TBJM 211 Six TightBinding 33 Two TP VanderPol vReadTable vTable 53 120 77 77 Two Four Three Three WELL 49 Two WorkFunction 95 Three header file for MPIC Monte Carlo code MPIC Monte Carlo source code nanoparticle in jellium model with electron-electron interaction nanoparticle in jellium model plot 1s and 2s plot the electrostatic potential quantum dot eigenstates set up table of Q coefficients in Eq(8.14) when expanding in Legendre polynomial quantum trajectory under standing wave quantum wire eigenstates with cylindrical potential radial eigen functions Skeleton program for simulated annealing plus genetic algorithm; pseudo code skeleton program for simulated annealing; pseudo code single quantum dot junction Fibonacci recursive solution stochasticity of standing wave energy band gap for superlattice transport across a molecular junction in tight-binding model: matching boundary conditions transport across a molecular junction in tight-binding model: Green function method eigenvalue solver for sparse tridiagonal matrix transition probability solve the van der Pol equation read the table of Vabab set up a table for the energy component Vabab roots for potential well of constant well depth work function for metals: gold/silver/copper Nano Computing 347 AUTHOR INDEX Abrikosov, A A, 132 Anderson, James B, 182 Ando, Tsuneya, 258 Andreoni, W, 164 Bena, C, 258 Bender, C M, 124 Berber, Savas, 330 Berry M, 103 Bettencourt, M A, 124 Binnig, Gerd, 14 Blasé, Xavier, 330 Blümel, R, 300 Boero, Mauro, 331 Campbell, Neil, 14, 35 Charlier, Jean-Christophe, 330 Chen, Nan-Yow, 108 Chen, Zhihong, 224, 273 Cheng, C Y, 203 Cheng, Runwei, 183 Chu, Kwo Ray, 277 Chou, T T, 132 Curl, Robert F, Dalfovo, F, 129, 132 De Brujin, J D, 54, 250 Davidson, R C, 132 Dresselhaus, M S, 330 Dresselhaus, R G, 330 Ebbesen, T W, Ercolessi, F, 164 Estrada, Richardo, 54 Eustis, Susie, 225, 299 Evans, D J, 331 Feder, David L, 132 Feshback, H, 132 Fetter, Alexander L, 132 Feynman, Richard, Freeman, A J, 196 Fujimoto, K, 97, 256 Galeev, A A, 300 Ganguly, A K, 277 Gasiorowicz, Stephen, 109 Geim, Andrey K, 330 Gen, Mitu, 183 Ginzburg, L, 132 Goddard, W A, 81 Goldhaber-Gordon, D, 258 Gossard, Arthur C, 282 Grassberger, P, 221, 295 Gubanov, V A, 196 Gutzwiller, Martin C, 95 Hall, Edwin, 277 Halperin, B I, 283 Ho, K M, 148, 183 Hofstadter, D R, 278, 297, 298 Hohenberg, P, 200, 252 Hsieh, Li-Ching, 108, 252 Hsu, J Y, 202, 203, 252, 284 Hsu, P J, 183 Hsue, Young-Chung, 197 Hui, B H, 277 Function Index Hummer, G, 331 Hybertsen, Mark S, Iijima, S, 204 J Jain, Jainendra K, 282, 283 Ji, Fengmin, 109 Jorgensen, W L, 314 Kamogawa M, 299 Kanwal, Ram P, 54 Kastner, M A, 246 Ke, S H, 246 Kobayashi, Kensuke, 246 Kohn, W, 78, 183, 188, 191, 200 Koga, Kenichiro, 331 Kroto, Harold W, Kwon, Young-Kyun, 330 Landau, L D, 108 Lai, S K, 183 Laughlin, R B, 108 Lee, H C, 108, 283 Lee, P A, 283 Levine, Ira N, 108 Li, P W, 258 Lifshitz, E M, 108 Lin C H, 203 Lin, M F, 330 Liu, C S, 300 Louie, Steven G, 204 Luo, Liaofu, 108 MacDonald, Allan H, 330 Matsumoto, Yukio, 258 Mitchell, Lawerence, 14, 35 Montgomery, D C, 203, 300 Morse, P M, 132, 255 350 James J Y Hsu Mou, Chung-Yu, 108, 250 Murray, J D, 54, 255 Novikov, D L, 196, 255 Ohtsuki, Y, 299 Oleynik, I I, 224 Park, Key-Taeck, 195 Payne, M C, 183 Procaccia, I, 295 Quinten, M, 299 Rapaport, D C, 183 Read, N, 283 Reece, Jane, 14, 35 Reed, M A, 224 Reinhardt, W P, 226, 300 Roche, Stephan, 330 Rohrer, Heinrich, Rosenbluth, M N, 299 Ruska, Ernst, Sagdeev, R Z, 300 Serebryakova, O N, 299 Stix, Thomas H, 300 Sham, L J, 183, 191 Smalley, Richard E, Stormer, Horst L, 282 Stringari, S, 129, 132, 250 Su, Zheng-Yao, 108, 250 Saito R, 330, 256 Tachikawa, M, 132, 256 Tersoff, J, 331 Tománek, David, 330, 249 Tosatti, E, 164, 251 Author Index Tripathi, V K, 300 Tsui, Daniel C, 282 Uemura, Yasutada, von Klitzing, Klaus, 258, 249 300 Yang, C K, 164 Yang, Chen Ning, 132 Yennie, D R, 279 Yu, L H, 132, 250 Zhang, Yuanbo, 300 Wales, David, 183 Wang, C Z, 183, 273 Wang, Jian, 223 Nano Computing 351 KEYWORD INDEX AB (Aharonov-Bohm) effect, 188 ab initio, 14, 159, 183, 189 atomic force microscopy (AFM), 1, 4, 5, 6, 15 algorithm genetic, 147–150 amino acids, 16, 88–90 aquaporin, 91 asymptology, 33–57, 122, 131–132 Berry phase, 104 beta Function 68 bifurcated solutions 127, 128, 133 Bloch-Floquet theorem phase factor 40, 98, 99, 214, 250 Bloch, 99, 196, 249, 290, 292, 298 frequency momentum wave vector Bohr energy, 52, 63, 70, 73, 97, 191 Bohr radius, 34, 63, 64, 70, 73, 97, 109, 191, 195, 221, 253, 259 Born-Oppenheimer Approximation 120, 122 Bose-Einstein Condensate (BEC), 128–132 boundary layer, 115, 124–132 Brillouin zone, 304, 305, 310, 312 broadband spectra, 147, 184 Brownian motion, 147, 184 canonical distribution, 61, 297 capacitance, 218, 221–222 Chaos quantum, 284–299 carbon nanotube (CNT), 9, 14, 245, 303–303 armchair chiral zigzig coarse graining, 152–154, 198 coherence, 148, 149 commutation relation, 120, 191 composite Fermion (CF), 278, 283, 284 configuration interaction, 73, 83–87 CI correlated confluent hypergeometric functions, 67 cone snails, 10, 16 Cooper pair, 277 correlation dimension, 148, 149, 151 Coulomb blockade, 220, 221, 222, 246, 248 Coulomb staircase, 222 Delaunay triangulation, 32, 137, 152, 158, 185 density functional theory (DFT), 136, 140, 144 density of states (DOS), 39, 101, 102, 205, 221, 223, 281, 310, 312 diamond, 8, 9, 194–199 Dirac cone, 306, 330 distributed computing, 227, 234, 243 divide-and-conquer, 31, 137, 151 DNA, 5, 6, 88, 89, 91, 109, 329 adenine, thymine, guanine, cytosine, 4, 5, 65 Function Index dynamic-link library (DLL), 233, 234, 319 Dyson equation, 205 229– effective mass, 193, 330 energy band conduction gap valence, 32, 34, 56, 91, 92, 95– 97, 100–101, 196, 197, 213, 289, 292, 304, 306 elliptical instability, 284–286 Euler angles, 316, 331 equipartition, 60 Euler’s constant, 43 evaluation local global effective 150–157 exchange interaction energy, 192 Fano effect, 246 Fast Fourier Transform (FFT), 22, 32, 137–138, 285, 289 Fermi level, 92, 94, 248 Fibonacci, 30, 31, 136–137 finite difference method, 110, 133, 164, 198, 225, 251, 257, 259, 275 finite element method (FEM), 21, 152, 158, 164–182, 198 fractal, 290–297, 298, 301 fullerene, 8, 15, 30, 153, 158, 164, 245, 258, 331, 332 full-potential linearized augmentedplane-wave (FLAPW), 196–198 gene therapy, 150, 152 genetic algorithm, 147–150 graphene, 157, 185, 246, 258, 300, 304–312, 330 graphic card process unit (GPU), 242 Green’s function method, 145, 204– 218, 225 354 James J Y Hsu Gutzwiller projection, gyrotron, 277 95 Heisenberg picture, 122, 291 helium, 29, 70–73, 87, 110, 112, 201 Hellmann-Feynman theorem, 258 Hofstadter’s Butterfly, 278, 297–298 hydrogen atom, 47, 63, 65, 73–78, 79, 81, 109, 320 hydrogen molecule, 50, 73–78, 79, 81, 86, 111, 142–145, 174, 185, 186, 187 inductance, 218, 222–223 in-silico, 14 in-vitro, 13 in-vivo, 13 insulator, 92 ionic-covalent resonance, 81 k-point sampling, 199 Kondo effect, 246, 258 Kronig- Penney model (KP model), 98, 99, 100 Landau damping, 266–267 Laplace method for integrals, 46, 48 Legendre Functions Associated, 66, 74, 75, 76, 137, 254 limit cycle 286 Linear Combination of Atomic Orbitals (LCAO), 79, 112 local density approximation, 129, 191–194 lotus effect, 10 magnetic flux quanta, 107, 279, 280, 283, 295, 301 magnetic length, 104, 281 matching procedure, 124, 125 Markov process, 300 Keyword Index materials optimized bio smart, message passing interface (MPI), 227, 230, 233–241 mesoscopic physics, 59 metal, 92, 94, 95 microarray, 6, microscopy, 1, 4, 5, atomic force electron optical scanning soft x-ray tunneling molecular computer, 14, 88–89, 303, 328–300 mode conversion, 271, 273, 274, 300 molecular dynamics (MD), 115, 131, 159–164, 183 ab initio Car-Parrinello tight-binding molecular orbital, 50, 79, 81, 194 Monte Carlo direct simulation, 20, 102, 106, 176, 182 multiple space scales, 124–132 multiple timescales, 116–124 multiphysics, 116, 132 multiscale, 116, 131, 132 near field optics, 5, 6, 38, 299 NP-complete, 107 nucleotides, 89 Object Oriented Programming (OOP), 135, 227–228 openMP, 227, 228, 242 ordering, 34–37 Perierls phase, 297 Planck’s constant, 53–61, 203, 280 plane wave expansion, 196 plasma vapor chemical deposition (PVCD), 14 plasmon dispersion function, 38, 203, 204, 253, 261–277, 330 electromagnetic plasma frequency, 262–263 Plemelj formula, 266 Poincare cycle, 286 potential Tersoff, 152–154, 331–332 Lennard-Jones, 160, 319, 331 pseudo, 124, 128, 184, 196 prion, 12, 91 probability density function (PDF), 56, 101 protein, 3, 5–7, 88–91, 108–109, 299 pruning, 146, 150–153 quantization conductance unit, 217, 219–221 quantization rule, 64, 280, 309, 310 quantum dot, 8, 50, 216, 218, 245– 248, 258 quantum Hall effect, 107–108, 220, 258, 261, 277–284 fractional integer Quantum Monte, 142, 145, 182, 185 Carlo Variational Green’s Function, 135 quantum wire, 56, 110, 199, 214, 245–252 quaternion, 315–318, 331 Raman scattering, random phase approximation (RPA), 264, 276, 277 RNA uracil, 5, 6, 88–89 radial eigenfunction (REF), 69 recursive formula recursion, 30, 31, 136, 137 Riemann Zeta function, 42 Nano Computing 355 Free ebooks ==> www.Ebook777.com Function Index roots, 21, 23, 34, 37, 49, 55, 56, 124, 247, 248, 259 Schrödinger equation, 63–65, 70, 86, 98, 103–105, 109, 112, 182, 187, 192, 199, 203, 204, 246, 249, 251, 263, 264, 270, 276 search deterministic, 150–159 self-energy, 204 self-organization, 161, 329 semiconductor, 4, 88, 92 shared memory model, 227, 242 simulated annealing, 14, 26, 139, 145–150, 152–153, 185 single electron transistor (SET), 246, 258 single hole transistor (SHT), 252, 258 single nucleotide polymorphism (SNP), singular perturbation solution, 37, 124, 125 small angle x-ray scattering (SAXS), spherical harmonics, 66, 69, 74, 198, 246, 253 Stirling’s formula, 47 scanning tunneling microscopy (STM), 1, 356 stochasticity, 284–289 super-polynomial, 146, 151 thermal conductance, 9, 223 Thomas-Fermi approximation, 129, 200, 262, 263, 268, 301 Thomas-Fermi wave number, 197 tight binding approximation (TBA), 32, 42, 56, 110, 183, 184, 207, 297, 304, 331 uncertainty principle, 109, 219, 221 15, 61–62, valence-bond generalized, 79 van der Pol equation, 118–120, 133 van der Waals force, 124, 128, 160, 314 van Hove singularity, 102, 310, 312 virial theorem, 63, 64, 82, 109, 143, 196, 202, 222, 259 Vlasov equation, 266 Wannier ladder, 292 wave-particle duality, 61, 63 Weyl ordering, 124 work function, 15, 94–95 James J Y Hsu www.Ebook777.com ... Data A catalogue record for this book is available from the British Library NANOCOMPUTING Computational Physics for Nanoscience and Nanotechnology Copyright © 2009 by Pan Stanford Publishing Pte... the most powerful and widely employed tools for surface analysis, very useful in characterizing roughness and defects and determining the size and conformation of molecules and aggregates on... importance Nanoscience and nanotechnology have evolved to encompass multi-disciplinary inputs from physics, biology, chemistry and engineering The field is richly benefited from information technology,