COPYRIGHT 2008, PRINCETON UNIVERSITY PRESS

More documents

Recommendations

Info

discrete & continuous nonlinear dynamics 291sequence to another,x i+1 = f(x i ). (12.7)For the logistic map, f(x)=µx(1 − x), with the quadratic dependence of f on xmaking this a nonlinear map, while the dependence on only the one variable x imakes it a one-dimensional map.12.3 Properties of Nonlinear Maps (Theory)Rather than do some fancy mathematical analysis to determine the properties ofthe logistic map [Rash 90], we prefer to have you study it directly on the computerby plotting x i versus generation number i. Some typical behaviors are shown inFigure 12.1. In Figure 12.1A we see equilibration into a single population; in Figure12.1B we see oscillation between two population levels; in Figure 12.1C we seeoscillation among four levels; and in Figure 12.1D we see a chaotic system. Theinitial population x 0 is known as the seed, and as long as it is not equal to zero, itsexact value usually has little effect on the population dynamics (similar to what wefound when generating pseudorandom numbers). In contrast, the dynamics areunusually sensitive to the value of the growth parameter µ. For those values of µat which the dynamics are complex, there may be extreme sensitivity to the initialcondition x 0 as well as to the exact value of µ.12.3.1 Fixed PointsAn important property of the map (12.5) is the possibility of the sequence x i reachinga fixed point at which x i remains or fluctuates about. We denote such fixedpoints as x ∗ .Ataone-cycle fixed point, there is no change in the population fromgeneration i to generation i +1; that is,x i+1 = x i = x ∗ . (12.8)Using the logistic map (12.5) to relate x i+1 to x i yields the algebraic equationµx ∗ (1 − x ∗ )=x ∗ ⇒ x ∗ =0 or x ∗ = µ − 1µ . (12.9)The nonzero fixed point x ∗ =(µ − 1)/µ corresponds to a stable population with abalance between birth and death that is reached regardless of the initial population(Figure 12.1A). In contrast, the x ∗ =0point is unstable and the population remainsstatic only as long as no bugs exist; if even a few bugs are introduced, exponentialgrowth occurs. Further analysis (§12.8) tells us that the stability of a population isdetermined by the magnitude of the derivative of the mapping function f(x i ) at−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 291
292 chapter 120.80.400 10 20Ax nn n0 10 20B0 10 20C0 10 20DFigure 12.1 The insect population x n versus the generation number n for various growthrates. (A) µ = 2.8, a period-one cycle. If the fixed point is x n = 0, the system becomes extinct.(B) µ = 3.3, a period-two cycle. (C) µ = 3.5, a period-four cycle. (D) µ = 3.8, a chaotic regime.If µ3, the square root produces a real number and thus thatphysical solutions exist (complex or negative x ∗ values are nonphysical). We leaveit to your computer explorations to discover how the system continues to doubleperiods as µ continues to increase. In all cases the pattern is the same: One of thepopulations bifurcates into two.−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 292
Page 1 and 2:
COPYRIGHT 2008, PRINCET O N UNIVE R
Page 3 and 4:
−101COPYRIGHT 2008, PRINCET O N U
Page 5 and 6:
Copyright © 2008 by Princeton Univ
Page 7 and 8:
Page 9 and 10:
viiicontents2.3 Experimental Error
Page 11 and 12:
xcontents6.3 Experimentation 1356.4
Page 13 and 14:
xiicontents9.7.1 Friction: Model an
Page 15 and 16:
xivcontents12.8 Signals of Chaos: L
Page 17 and 18:
xvicontents14.15.2Exercise 2: Cache
Page 19 and 20:
xviiicontents18.4 Waves for Variabl
Page 21 and 22:
xxcontentsC.3 DX Tools Summary 576C
Page 23 and 24:
Page 25 and 26:
xxivprefacewhich includes understan
Page 27 and 28:
Page 29 and 30:
2 chapter 1PhysicsCPFigure 1.1 A re
Page 31 and 32:
4 chapter 1Scientific LibrariesPerf
Page 33 and 34:
6 chapter 1C DWe have tried to make
Page 35 and 36:
8 chapter 1possibly when installing
Page 37 and 38:
10 chapter 11.4.1 Structured Progra
Page 39 and 40:
12 chapter 17. Revise Area.java so
Page 41 and 42:
14 chapter 1argv). Because main met
Page 43 and 44:
16 chapter 1Package Class Tree Depr
Page 45 and 46:
18 chapter 1Memory and storage size
Page 47 and 48:
20 chapter 1TABLE 1.4The IEEE 754 S
Page 49 and 50:
22 chapter 1gives 24-bit precision
Page 51 and 52:
24 chapter 1TABLE 1.6Representation
Page 53 and 54:
26 chapter 1The computer fetches th
Page 55 and 56:
28 chapter 1Your problem is to use
Page 57 and 58:
2Errors & Uncertainties in Computat
Page 59 and 60:
32 chapter 2purposes, let us consid
Page 61 and 62:
34 chapter 2can be avoided by combi
Page 63 and 64:
36 chapter 2means that a program ru
Page 65 and 66:
38 chapter 2To be more specific, le
Page 67 and 68:
40 chapter 2Let us assume that an a
Page 69 and 70:
42 chapter 2To see if these assumpt
Page 71 and 72:
44 chapter 2computation. Accordingl
Page 73 and 74:
46 chapter 3is regular practice to
Page 75 and 76:
48 chapter 3to plot for x and y, we
Page 77 and 78:
50 chapter 3Sample PtPlot Data file
Page 79 and 80:
52 chapter 3TABLE 3.1Text Files Gra
Page 81 and 82:
54 chapter 3Figure 3.4 Left: A plot
Page 83 and 84:
56 chapter 3TABLE 3.2Grace Menu and
Page 85 and 86:
58 chapter 33.4.1 Gnuplot Input Dat
Page 87 and 88:
60 chapter 3gnuplot> set output "pl
Page 89 and 90:
62 chapter 3gnuplot> set terminal e
Page 91 and 92:
64 chapter 3By setting terminal to
Page 93 and 94:
66 chapter 33.6 Texturing and 3-D I
Page 95 and 96:
68 chapter 4R R 2RL L 2LC C 2CFigur
Page 97 and 98:
70 chapter 44.3 Resistance Becomes
Page 99 and 100:
72 chapter 4be either static or dyn
Page 101 and 102:
74 chapter 4On line 8 we see a meth
Page 103 and 104:
76 chapter 44.4.3 Static and Nonsta
Page 105 and 106:
78 chapter 42. Compile and execute
Page 107 and 108:
80 chapter 41 / Z0.51400R0400R80021
Page 109 and 110:
82 chapter 4no arguments and return
Page 111 and 112:
84 chapter 42. Define a daughter cl
Page 113 and 114:
86 chapter 4new features without
Page 115 and 116:
88 chapter 4qFigure 4.7 Left: The t
Page 117 and 118:
90 chapter 4with properties differi
Page 119 and 120:
92 chapter 4In a project such as th
Page 121 and 122:
94 chapter 4data types called objec
Page 123 and 124:
96 chapter 46. Change the mass of t
Page 125 and 126:
98 chapter 4Check that all the plot
Page 127 and 128:
100 chapter 43. You should see now
Page 129 and 130:
102 chapter 44.9.11 Complex Object
Page 131 and 132:
104 chapter 4✞/ / KomplexTest : t
Page 133 and 134:
106 chapter 4motion in other direct
Page 135 and 136:
108 chapter 4✝protected double y(
Page 137 and 138:
110 chapter 5Mathematically, the li
Page 139 and 140:
112 chapter 5The linear congruent m
Page 141 and 142:
114 chapter 5TABLE 5.1A Table of a
Page 143 and 144:
116 chapter 55.3 Unit II. Monte Car
Page 145 and 146:
118 chapter 5300y0-10-20R2001000 20
Page 147 and 148:
120 chapter 54100,000log[N(t)]10,00
Page 149 and 150:
122 chapter 5✞/ / Decay . java :
Page 151 and 152:
124 chapter 6f(x)a x i x i+1 x i+2
Page 153 and 154:
126 chapter 6f(x)f(x)parabola 1para
Page 155 and 156:
128 chapter 6evaluate the function
Page 157 and 158:
130 chapter 6⇒ N =( ) 2/91 1(ɛ m
Page 159 and 160:
132 chapter 63. [−∞→∞], sca
Page 161 and 162:
134 chapter 6}public static double
Page 163 and 164:
136 chapter 6the integral of f(x)=1
Page 165 and 166:
138 chapter 6f(x)< f(x) >xFigure 6.
Page 167 and 168:
140 chapter 61. Conduct 16 trials a
Page 169 and 170:
142 chapter 6acceptrejectFigure 6.6
Page 171 and 172:
144 chapter 6The crux of this techn
Page 173 and 174:
7Differentiation & SearchingIn this
Page 175 and 176:
148 chapter 7the forward-difference
Page 177 and 178:
150 chapter 7algorithm (7.7) is O(h
Page 179 and 180:
152 chapter 7algorithms in which de
Page 181 and 182:
154 chapter 7we know a zero occurs.
Page 183 and 184:
156 chapter 7Figure 7.3 Two example
Page 185 and 186:
8Solving Systems of Equationswith M
Page 187 and 188:
160 chapter 8the spheres, and the d
Page 189 and 190:
162 chapter 8We now have a solvable
Page 191 and 192:
164 chapter 8of (8.19) by A −1 :x
Page 193 and 194:
166 chapter 8Row MajorColumn Majora
Page 195 and 196:
168 chapter 8having different varia
Page 197 and 198:
170 chapter 8Matrix objects, add an
Page 199 and 200:
172 chapter 8✞/∗ JamaFit : JAMA
Page 201 and 202:
174 chapter 8( ) α β3. Consider t
Page 203 and 204:
176 chapter 8discarding some inform
Page 205 and 206:
178 chapter 8Lagrange interpolation
Page 207 and 208:
180 chapter 8Figure 8.3 Three fits
Page 209 and 210:
182 chapter 8if you have the abilit
Page 211 and 212:
184 chapter 840fitNumber20dataN(t)0
Page 213 and 214:
186 chapter 8theoretical curve went
Page 215 and 216:
188 chapter 8This is a measure of t
Page 217 and 218:
190 chapter 88.7.4 Linear Quadratic
Page 219 and 220:
192 chapter 8Your problem here is t
Page 221 and 222:
9Differential Equation Applications
Page 223 and 224:
196 chapter 9V(x)HarmonicAnharmonic
Page 225 and 226:
198 chapter 9B(t) are solutions of
Page 227 and 228:
200 chapter 9This expresses the acc
Page 229 and 230:
202 chapter 9derivative:dy(t)dt≃
Page 231 and 232:
204 chapter 9As an example of the u
Page 233 and 234:
206 chapter 9C Dhigh-precision work
Page 235 and 236:
208 chapter 9Amplitude Dependence,
Page 237 and 238:
210 chapter 9Here N is the normal f
Page 239 and 240:
212 chapter 99.9 Unit II. Binding A
Page 241 and 242:
214 chapter 9the Schrödinger equat
Page 243 and 244:
216 chapter 99.11.1 Numerov Algorit
Page 245 and 246:
218 chapter 9}}xl = xl0+i∗h;ul[i]
Page 247 and 248:
220 chapter 9public static double d
Page 249 and 250:
222 chapter 99.13 Unit III. Scatter
Page 251 and 252:
224 chapter 9The equations for the
Page 253 and 254:
226 chapter 9Figure 9.9 The traject
Page 255 and 256:
228 chapter 9fFigure 9.10 Left: The
Page 257 and 258:
230 chapter 99.17.1.1 EXPLORATION:
Page 259 and 260:
232 chapter 10y(t)10Y( )10-1t-10 20
Page 261 and 262:
234 chapter 10As seen in the b n co
Page 263 and 264:
236 chapter 1010.4 Fourier Transfor
Page 265 and 266:
238 chapter 10Regardless of the act
Page 267 and 268: 240 chapter 10for the exponential a
Page 269 and 270: 242 chapter 10102 4 6-1Figure 10.2
Page 271 and 272: 244 chapter 10coefficients a k . If
Page 273 and 274: 246 chapter 104. As always, check t
Page 275 and 276: 248 chapter 10A special case of the
Page 277 and 278: 250 chapter 10Figure 10.4 Input sig
Page 279 and 280: 252 chapter 10Figure 10.5 Left: An
Page 281 and 282: 254 chapter 10A 1.5mp1.0lit 0.5ud 0
Page 283 and 284: 256 chapter 1010.8 Unit III. Fast F
Page 285 and 286: 258 chapter 10Figure 10.9 The basic
Page 287 and 288: 260 chapter 10TABLE 10.1Binary-Reve
Page 289 and 290: 262 chapter 10✞/∗ FFT. java : F
Page 291 and 292: 11Wavelet Analysis & Data Compressi
Page 293 and 294: 266 chapter 11the second derivative
Page 295 and 296: 268 chapter 1111.2.1 Wave Packet As
Page 297 and 298: 270 chapter 11localized in time, su
Page 299 and 300: 272 chapter 11201 Y100Signal0-10-10
Page 301 and 302: 274 chapter 11you have been using f
Page 303 and 304: 276 chapter 11}return Math . sin (8
Page 305 and 306: 278 chapter 11FrequencyTimeFigure 1
Page 307 and 308: 280 chapter 11N SamplesInputN/2(1)c
Page 309 and 310: 282 chapter 11Figure 11.10 The filt
Page 312: wavelet analysis & data compression
Page 315 and 316: 288 chapter 113. Reproduce the scal
Page 317: 290 chapter 12discrete decay law,
Page 321 and 322: 294 chapter 12b. Repeat the simulat
Page 323 and 324: 296 chapter 121b=1.0b=4.0b=5.0X0-1-
Page 325 and 326: 298 chapter 12TABLE 12.1Several Non
Page 327 and 328: 300 chapter 12✞/ / LyapLog . java
Page 329 and 330: 302 chapter 1212.10 Unit II. Pendul
Page 331 and 332: 304 chapter 12In Chapter 9, “Diff
Page 333 and 334: 306 chapter 12Figure 12.6 The data
Page 335 and 336: 308 chapter 12rotating solutionsθ2
Page 337 and 338: 310 chapter 12θ(t)8040.θ(0)=0.314
Page 339 and 340: 312 chapter 12Figure 12.11 Top row:
Page 341 and 342: 314 chapter 12|θ(t)|200 1 2Figure
Page 343 and 344: Angular Velocity of Lower Pendulum3
Page 345 and 346: 318 chapter 12some fraction of a ch
Page 347 and 348: 320 chapter 1212.19 Lotka-Volterra
Page 349 and 350: 322 chapter 12numbers that accounts
Page 351 and 352: 324 chapter 12400200pPopulationpP00
Page 353 and 354: 13Fractals & Statistical GrowthIt i
Page 355 and 356: 328 chapter 1330010,000 points20010
Page 357 and 358: 330 chapter 13Figure 13.2 Left: A f
Page 359 and 360: 332 chapter 13copy of a frond, and
Page 361 and 362: 334 chapter 13The results of this t
Page 363 and 364: 336 chapter 13log N(r) = log C −
Page 365 and 366: 338 chapter 13to determine the slop
Page 367 and 368: 340 chapter 13✞☎import java . i
Page 369 and 370:
342 chapter 13Figure 13.8 Number 8
Page 371 and 372:
344 chapter 13Conway in the 1970s,
Page 373 and 374:
346 chapter 13(x 0, y 1)(x 0, y 0)(
Page 375 and 376:
348 chapter 13yxFigure 13.13 After
Page 377 and 378:
350 chapter 13gradient // Vertical
Page 379 and 380:
14High-Performance Computing Hardwa
Page 381 and 382:
354 chapter 14A(1)A(2)A(3)CPUA(N)M(
Page 383 and 384:
356 chapter 14ADBCFigure 14.4 Multi
Page 385 and 386:
358 chapter 14as Fortran or C, tran
Page 387 and 388:
360 chapter 14TABLE 14.2Computation
Page 389 and 390:
362 chapter 14The processors in a p
Page 391 and 392:
364 chapter 14Figure 14.7 Two views
Page 393 and 394:
366 chapter 14Speedup8Amdahl's Lawp
Page 395 and 396:
368 chapter 1414.11 Parallelization
Page 397 and 398:
370 chapter 14The problem affects p
Page 399 and 400:
372 chapter 14• A race condition
Page 401 and 402:
374 chapter 14yet in order to obtai
Page 403 and 404:
376 chapter 14slightly faster or sm
Page 405 and 406:
378 chapter 14You see (Listing 14.1
Page 407 and 408:
380 chapter 14/optimize:4/optimize:
Page 409 and 410:
382 chapter 14• As indicated in
Page 411 and 412:
384 chapter 1410,000Execution Time
Page 413 and 414:
386 chapter 14as high-performance c
Page 415 and 416:
388 chapter 14✞Dimension Vec( idi
Page 417 and 418:
16Simulating Matter withMolecular D
Page 419 and 420:
426 chapter 16+ +Figure 16.1 The mo
Page 421 and 422:
428 chapter 16the molecules stay cl
Page 423 and 424:
430 chapter 162 3 2 3 2 31 4 1 4 1
Page 425 and 426:
432 chapter 16Velocity-Verlet Algor
Page 427 and 428:
434 chapter 16Energy vs Timefor 36
Page 429 and 430:
436 chapter 16Figure 16.7 A simulat
Page 431 and 432:
thermodynamic simulations & feynman
Page 433 and 434:
Page 435 and 436:
Page 437 and 438:
Page 439 and 440:
Page 441 and 442:
Page 443 and 444:
Page 445 and 446:
Page 447 and 448:
Page 449 and 450:
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
Page 459 and 460:
Page 461 and 462:
Page 463 and 464:
Page 465 and 466:
simulating matter with molecular dy
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
Page 473 and 474:
Page 475 and 476:
Page 477 and 478:
17PDEs for Electrostatics & Heat Fl
Page 479 and 480:
pdes for electrostatics & heat flow
Page 481 and 482:
Page 483 and 484:
Page 485 and 486:
Page 487 and 488:
Page 489 and 490:
Page 491 and 492:
Page 493 and 494:
Page 495 and 496:
Page 497 and 498:
Page 499 and 500:
Page 501 and 502:
Page 503 and 504:
Page 505 and 506:
Page 507 and 508:
Page 509 and 510:
Page 511 and 512:
Page 513 and 514:
Page 515 and 516:
Page 517 and 518:
Page 519 and 520:
θpde waves: string, quantum packet
Page 521 and 522:
pde waves: string, quantum packet,
Page 523 and 524:
Page 525 and 526:
Page 527 and 528:
Page 529 and 530:
Page 531 and 532:
Page 533 and 534:
100pde waves: string, quantum packe
Page 535 and 536:
Page 537 and 538:
Page 539 and 540:
Page 541 and 542:
Page 543 and 544:
Page 545 and 546:
Page 547 and 548:
Page 549 and 550:
solitons & computational fluid dyna
Page 551 and 552:
✞solitons & computational fluid d
Page 553 and 554:
Page 555 and 556:
Page 557 and 558:
Page 559 and 560:
Page 561 and 562:
Page 563 and 564:
Page 565 and 566:
Page 567 and 568:
Page 569 and 570:
Page 571 and 572:
Page 573 and 574:
Page 575 and 576:
Page 577 and 578:
Page 579 and 580:
Page 581 and 582:
integral equations in quantum mecha
Page 583 and 584:
Page 585 and 586:
✞integral equations in quantum me
Page 587 and 588:
Page 589 and 590:
Page 591 and 592:
Page 593 and 594:
Page 595 and 596:
Appendix A: Glossaryabsolute value
Page 597 and 598:
glossary 557control character — A
Page 599 and 600:
glossary 559log in (on) — To sign
Page 601 and 602:
glossary 561supercomputer — The c
Page 603 and 604:
installing ptplot & java developer
Page 605 and 606:
Page 607 and 608:
Page 609 and 610:
industrial-strength data visualizat
Page 611 and 612:
Page 613 and 614:
Page 615 and 616:
Page 617 and 618:
Page 619 and 620:
Page 621 and 622:
Page 623 and 624:
Page 625 and 626:
Page 627 and 628:
Page 629 and 630:
Page 631 and 632:
Page 633 and 634:
Appendix D: An MPI TutorialIn this
Page 635 and 636:
an mpi tutorial 595• Open a shell
Page 637 and 638:
an mpi tutorial 597of all the compu
Page 639 and 640:
an mpi tutorial 599TABLE D.1Some Co
Page 641 and 642:
an mpi tutorial 601jobs to MPI. 2 A
Page 643 and 644:
an mpi tutorial 603✞> cd $HOME Do
Page 645 and 646:
an mpi tutorial 605✞/ / MPIhello
Page 647 and 648:
an mpi tutorial 607Argument Namemsg
Page 649 and 650:
an mpi tutorial 609D.3.4 Broadcast
Page 651 and 652:
an mpi tutorial 611D.4 Parallel Tun
Page 653 and 654:
an mpi tutorial 613✝}MPI_Recv ( &
Page 655 and 656:
an mpi tutorial 615✞/ / Code list
Page 657 and 658:
an mpi tutorial 617-1) does not sen
Page 659 and 660:
an mpi tutorial 619D.6.1 Nonblockin
Page 661 and 662:
an mpi tutorial 621D.9 List of MPI
Page 663 and 664:
Appendix E: Calling LAPACK from CCa
Page 665 and 666:
calling LAPACK from C 625E.2 Compil
Page 667 and 668:
software on the CD 627JavaCodes Con
Page 669 and 670:
software on the CD 629JavaCodes Con
Page 671 and 672:
software on the CD 631Applets Direc
Page 673 and 674:
software on the CD 633Fortran77code
Page 675 and 676:
Appendix G: Compression via DWTwith
Page 677 and 678:
compression via DWT with thresholdi
Page 679 and 680:
compression via DWT with thresholdi
Page 681 and 682:
BIBLIOGRAPHY[Abar 93] Abarbanel, H.
Page 683 and 684:
ibliography 643[Erco] Ercolessi, F.
Page 685 and 686:
ibliography 645[L&F 93] Landau, R.
Page 687 and 688:
ibliography 647[P&W 91] Pinson, L.
Page 689 and 690:
ibliography 649[VdeV 94] van de Vel
Page 691 and 692:
IndexAbstract data structures,70Abs
Page 693 and 694:
index 653drand, 114Driving force, 2
Page 695 and 696:
index 655Libraries, see Subroutines
Page 697 and 698:
index 657structured, 10for virtual
show all

COPYRIGHT 2008, PRINCETON UNIVERSITY PRESS

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?