Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

More documents

Recommendations

Info

208 Monte Carlo Particle Transport Methods: Neutron and Photon CalculationsandC(P',P") = exp[b(P') - b(P")]C(P',P")/A(P') (5.168)where A(P') is such that T(P,P') is normalized to unity. Taking into account the identityb(P') - b(P) d UoVNr + tco) (5.169)(where
functions only, we define the transformed contribution functions f 0(a = a,s,n) by theequationJdP'T(P,P')[f(P,P') + c a(P')f,(P') + c\(P')|dP"C s(P',P")t;(P',P")+ c,(P') I nq„(P')/dP'C n(P',P")f„(P',P")] = J 1(P) (5.174)Note, however, that Equation (5.174) becomes identical to condition (5.158) in Theorem5.10 in the previous Section if one substitutesU(P') =
Page 2 and 3:
Library of Congress Cataloging-in-P
Page 7 and 8:
III. Statistical Considerations •
Page 9 and 10:
IV. Further Generalizations — 183
Page 11:
Appendix 6A:Unbiased Estimation of
Page 14 and 15:
2 Monte Carlo Particle Transport Me
Page 17 and 18:
Chapter 2INTRODUCTIONWhen we starte
Page 19 and 20:
thus,As it is proved" — and is so
Page 21 and 22:
9B. THE PROBABILITY MIXING METHODTh
Page 23 and 24:
11It is easy to prove 15by summing
Page 25 and 26:
13but the most probable values:x, =
Page 27 and 28:
ISand give a random sign (by the us
Page 30 and 31:
18 Monte Carlo Particle Transport M
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
">3
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
100 Monte Carlo Panicle Transport M
Page 114 and 115:
102 Monte Carlo Particle Transport
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171: 158 Monte Carlo Particle Transport
Page 262 and 263: 25!) Monte Carlo Particle Transport
Page 270 and 271:
Page 272 and 273:
Page 274 and 275:
Page 276 and 277:
Page 278 and 279:
Page 280 and 281:
Page 282 and 283:
Page 284 and 285:
Page 286 and 287:
Page 288 and 289:
Page 290 and 291:
Page 292 and 293:
Page 294 and 295:
Page 296 and 297:
Page 298 and 299:
Page 300 and 301:
Page 302 and 303:
Page 304 and 305:
Page 306 and 307:
Page 308 and 309:
Page 310 and 311:
Page 312 and 313:
Page 314 and 315:
Page 317 and 318:
305Chapter 6SPECIAL GAMESIn the maj
Page 319 and 320:
3©7A. CORRELATED MOMENT EQUATIONSI
Page 321 and 322:
309Equation (6.1) will be referred
Page 323 and 324:
311The second moment of the score d
Page 325 and 326:
313andC S(P',P")/C S(P',P") = y(P',
Page 327 and 328:
315introduced in Equation (6.1) for
Page 329 and 330:
317andL„(P 0,P;,...,Pi + 1) = L n
Page 331 and 332:
319whereB„(P„,P; P:, ,) = A*(P
Page 333 and 334:
E. EXAMPLES AND SPECIAL TECHNIQUESL
Page 335 and 336:
323The weight factors associated wi
Page 337 and 338:
325It is seen from Equation (6.37)
Page 339 and 340:
327G. PARAMETRIC PERTURBATIONS: INT
Page 341 and 342:
129Hall 31 gave a constructive deri
Page 343 and 344:
331kernels, which remain unchanged
Page 345 and 346:
333and from Equation (6.51)w';,,(i)
Page 347 and 348:
335According to Equations (6,55) th
Page 349 and 350:
337Minimization is performed by set
Page 351 and 352:
339and letdsdaLet us consider a cor
Page 353 and 354:
341whereis the length of the flight
Page 355 and 356:
and from Equation (6.79)I / ds \ 2
Page 357 and 358:
345Let us assume that we are intere
Page 359 and 360:
347Introduction of this factor also
Page 361 and 362:
3492. Let i|/ n (P) denote the solu
Page 363 and 364:
3SJNow, if ( "> > 0, then k = i an
Page 365 and 366:
353andk„ = S l "VS'" •" (6. if;
Page 367 and 368:
3SSLet k„ denote the normalizatio
Page 369 and 370:
3572. It is then proved that with t
Page 371 and 372:
and start new histories until N new
Page 373 and 374:
361The application of source iterat
Page 375 and 376:
363we haveD 2 [k] = < 2 (k, - k,) )
Page 377 and 378:
365neutron density, S 0 for every
Page 379 and 380:
367if the same relation holds for t
Page 381 and 382:
369Then the multiplication factors
Page 383 and 384:
371in the unperturbed system, the w
Page 385 and 386:
373The perturbation of the effectiv
Page 387 and 388:
375where P" = (r',E'). Multiplying
Page 389 and 390:
377iterate of the derivative of the
Page 391 and 392:
579where P* = (r*,w*,E) = (r*,E*).
Page 393 and 394:
381This estimator, unlike f, in Equ
Page 395 and 396:
383tends to some stable attracting
Page 397 and 398:
3§SIo the case of the next-event e
Page 399 and 400:
387LDFIGURE 6.1.Geometry in scoring
Page 401 and 402:
389Let us denoteThen Equation (6.18
Page 403 and 404:
391is to be increased in order to o
Page 405 and 406:
393Now, since bl(P) = g(P) is bound
Page 407 and 408:
395is scored at every collision wit
Page 409 and 410:
397and its expectation isR — R 1n
Page 411 and 412:
3994. If O > 0 m, then the particle
Page 413 and 414:
401plays a distinguished role), and
Page 415 and 416:
403Theorem 6.7 — If x and s denot
Page 417 and 418:
this a priori information, the best
Page 419 and 420:
40?Thus, the bias introduced into t
Page 421 and 422:
409In view of Equation (6.226) and
Page 423 and 424:
41.1This means that if we use the k
Page 425 and 426:
413Then the whole-sample and rare-s
Page 427 and 428:
41.5According to the results of Sec
Page 429 and 430:
41?(Note that vD 2 [|i|v] is indepe
Page 431 and 432:
419withkOn the other hand, § is an
Page 433 and 434:
421Thus, the expected ratio reads
Page 435 and 436:
423St follows from Equations (6.265
Page 437 and 438:
425Wc start from the observation th
Page 439 and 440:
427Nowi'6.77K)kj„,and therefore(V
Page 441 and 442:
42*3Similarly, for the fourth momen
Page 443 and 444:
43 sOn the other hand, multiplying
Page 445 and 446:
43.¾This will be proven in the lem
Page 447 and 448:
435ThenT.m = EJ.Iy.y.Rjeyiy,,,and s
Page 449 and 450:
6. Brown. F. B. and Martin, W. R.,
Page 451:
67. Rief, H. and Fioretti, A., Mont
Page 454 and 455:
Page 456 and 457:
Page 458 and 459:
Page 460 and 461:
Page 462 and 463:
Page 464 and 465:
Page 466 and 467:
Page 468 and 469:
Page 470 and 471:
Page 472 and 473:
Page 474 and 475:
Page 476 and 477:
Page 478 and 479:
Page 480 and 481:
Page 482 and 483:
Q = iy.M 2 2 (1/T, - 1/1,..,)/1, £
Page 484 and 485:
Page 486 and 487:
Page 488 and 489:
Page 490 and 491:
Page 492 and 493:
48© Monte Carlo Particle Transport
Page 494 and 495:
Page 496 and 497:
Page 498 and 499:
Page 500 and 501:
Page 502 and 503:
Page 504 and 505:
Page 506 and 507:
Page 508 and 509:
Page 510 and 511:
Page 512 and 513:
Page 514 and 515:
Page 516 and 517:
Page 518 and 519:
a ( X506 Monte Carlo Particle Trans
Page 520 and 521:
Page 522 and 523:
Page 525 and 526:
513INDEXAAbsorptiondefined, 25photo
Page 527 and 528:
515score probability in general tim
Page 529:
517path stretching, 447—455splitt
show all

Monte Carlo Particle Transport Methods: Neutron and Photon - gnssn

Create successful ePaper yourself

Delete template?

Save as template?