Physical and Numerical Models in Knot Theory: Including Applications to the Life SciencesThe physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year. This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory. |
Contents
23 | 1 |
24 | 2 |
25 | 3 |
26 | 4 |
27 | 5 |
28 | 6 |
29 | 7 |
30 | 8 |
334 | 302 |
335 | 303 |
336 | 304 |
337 | 305 |
338 | 306 |
339 | 307 |
340 | 308 |
341 | 309 |
31 | 9 |
32 | 10 |
33 | 11 |
34 | 12 |
35 | 13 |
36 | 14 |
37 | 15 |
38 | 16 |
39 | 17 |
40 | 18 |
41 | 19 |
42 | 20 |
43 | 21 |
44 | 22 |
45 | 23 |
46 | 24 |
47 | 25 |
48 | 26 |
49 | 27 |
50 | 28 |
51 | 29 |
52 | 30 |
53 | 31 |
54 | 32 |
55 | 33 |
56 | 34 |
57 | 35 |
58 | 36 |
59 | 37 |
60 | 38 |
61 | 39 |
62 | 40 |
63 | 41 |
64 | 42 |
65 | 43 |
66 | 44 |
67 | 45 |
68 | 46 |
69 | 47 |
70 | 48 |
71 | 49 |
72 | 50 |
73 | 51 |
74 | 52 |
75 | 53 |
76 | 54 |
77 | 55 |
78 | 56 |
79 | 57 |
80 | 58 |
81 | 59 |
82 | 60 |
83 | 61 |
84 | 62 |
85 | 63 |
86 | 64 |
87 | 65 |
88 | 66 |
89 | 67 |
90 | 68 |
91 | 69 |
92 | 70 |
93 | 71 |
94 | 72 |
95 | 73 |
96 | 74 |
97 | 75 |
98 | 76 |
99 | 77 |
100 | 78 |
101 | 79 |
102 | 80 |
103 | 81 |
104 | 82 |
105 | 83 |
106 | 84 |
107 | 85 |
108 | 86 |
109 | 87 |
110 | 88 |
111 | 89 |
112 | 90 |
113 | 91 |
114 | 92 |
115 | 93 |
116 | 94 |
117 | 95 |
118 | 96 |
119 | 97 |
120 | 98 |
121 | 99 |
122 | 100 |
123 | 101 |
124 | 102 |
125 | 103 |
126 | 104 |
127 | 105 |
128 | 106 |
129 | 107 |
130 | 108 |
131 | 109 |
132 | 110 |
133 | 111 |
134 | 112 |
135 | 113 |
136 | 114 |
137 | 115 |
138 | 116 |
139 | 117 |
140 | 118 |
141 | 119 |
142 | 120 |
143 | 121 |
144 | 122 |
145 | 123 |
146 | 124 |
147 | 125 |
148 | 126 |
149 | 127 |
150 | 128 |
151 | 129 |
152 | 130 |
153 | 131 |
154 | 132 |
155 | 133 |
156 | 134 |
157 | 135 |
158 | 136 |
159 | 137 |
160 | 138 |
161 | 139 |
162 | 140 |
163 | 141 |
164 | 142 |
165 | 143 |
166 | 144 |
167 | 145 |
168 | 146 |
169 | 147 |
170 | 148 |
171 | 149 |
172 | 150 |
173 | 151 |
174 | 152 |
175 | 153 |
176 | 154 |
177 | 155 |
178 | 156 |
179 | 157 |
180 | 158 |
181 | 159 |
182 | 160 |
183 | 161 |
184 | 162 |
185 | 163 |
186 | 164 |
187 | 165 |
188 | 166 |
189 | 167 |
190 | 168 |
191 | 169 |
192 | 170 |
193 | 171 |
194 | 172 |
195 | 173 |
196 | 174 |
197 | 175 |
198 | 176 |
199 | 177 |
200 | 178 |
201 | 179 |
202 | 180 |
203 | 181 |
204 | 182 |
205 | 183 |
206 | 184 |
207 | 185 |
208 | 186 |
209 | 187 |
210 | 188 |
211 | 189 |
212 | 190 |
213 | 191 |
214 | 192 |
215 | 193 |
216 | 194 |
217 | 195 |
218 | 196 |
219 | 197 |
220 | 198 |
221 | 199 |
222 | 200 |
223 | 201 |
224 | 202 |
225 | 203 |
226 | 204 |
227 | 205 |
228 | 206 |
229 | 207 |
230 | 208 |
231 | 209 |
232 | 210 |
233 | 211 |
234 | 212 |
235 | 213 |
236 | 214 |
237 | 215 |
238 | 216 |
239 | 217 |
240 | 218 |
241 | 219 |
242 | 220 |
243 | 221 |
244 | 222 |
245 | 223 |
246 | 224 |
247 | 225 |
248 | 226 |
249 | 227 |
250 | 228 |
251 | 229 |
252 | 230 |
253 | 231 |
254 | 232 |
255 | 233 |
256 | 234 |
257 | 235 |
258 | 236 |
259 | 237 |
260 | 238 |
261 | 239 |
262 | 240 |
263 | 241 |
264 | 242 |
265 | 243 |
266 | 244 |
267 | 245 |
268 | 246 |
269 | 247 |
270 | 248 |
271 | 249 |
272 | 250 |
273 | 251 |
274 | 252 |
275 | 253 |
276 | 254 |
277 | 255 |
278 | 256 |
279 | 257 |
280 | 258 |
281 | 259 |
282 | 260 |
283 | 261 |
284 | 262 |
285 | 263 |
286 | 264 |
287 | 265 |
288 | 266 |
289 | 267 |
290 | 268 |
291 | 269 |
292 | 270 |
293 | 271 |
294 | 272 |
295 | 273 |
296 | 274 |
297 | 275 |
298 | 276 |
299 | 277 |
300 | 278 |
301 | 279 |
302 | 280 |
303 | 281 |
304 | 282 |
305 | 283 |
306 | 284 |
307 | 285 |
308 | 286 |
309 | 287 |
310 | 288 |
311 | 289 |
312 | 290 |
313 | 291 |
314 | 292 |
315 | 292 |
316 | 292 |
317 | 292 |
318 | 292 |
319 | 292 |
320 | 292 |
321 | 292 |
322 | 292 |
323 | 292 |
324 | 292 |
325 | 293 |
326 | 294 |
327 | 295 |
328 | 296 |
329 | 297 |
330 | 298 |
331 | 299 |
332 | 300 |
333 | 301 |
342 | 310 |
343 | 311 |
344 | 312 |
345 | 313 |
346 | 314 |
347 | 315 |
348 | 316 |
349 | 317 |
350 | 318 |
351 | 319 |
352 | 320 |
353 | 321 |
354 | 322 |
355 | 323 |
356 | 324 |
357 | 325 |
358 | 326 |
359 | 327 |
360 | 328 |
361 | 329 |
362 | 330 |
363 | 331 |
364 | 332 |
365 | 333 |
366 | 334 |
367 | 335 |
368 | 336 |
369 | 337 |
370 | 338 |
371 | 339 |
372 | 340 |
373 | 341 |
374 | 342 |
375 | 343 |
376 | 344 |
377 | 345 |
378 | 346 |
379 | 347 |
380 | 348 |
381 | 349 |
382 | 350 |
383 | 351 |
384 | 352 |
385 | 353 |
386 | 354 |
387 | 355 |
388 | 356 |
389 | 357 |
390 | 358 |
391 | 359 |
392 | 360 |
393 | 361 |
394 | 362 |
395 | 363 |
396 | 364 |
397 | 365 |
398 | 366 |
399 | 367 |
400 | 368 |
401 | 369 |
402 | 370 |
403 | 371 |
404 | 372 |
405 | 373 |
406 | 374 |
407 | 375 |
408 | 376 |
409 | 377 |
410 | 378 |
411 | 379 |
412 | 380 |
413 | 381 |
414 | 382 |
415 | 383 |
416 | 384 |
417 | 385 |
418 | 386 |
419 | 387 |
420 | 388 |
421 | 389 |
422 | 390 |
423 | 391 |
424 | 392 |
425 | 393 |
426 | 394 |
427 | 395 |
428 | 396 |
429 | 397 |
430 | 398 |
431 | 399 |
432 | 400 |
433 | 401 |
434 | 402 |
435 | 403 |
436 | 404 |
437 | 405 |
438 | 406 |
439 | 407 |
440 | 408 |
441 | 409 |
442 | 410 |
443 | 411 |
444 | 412 |
445 | 413 |
446 | 414 |
447 | 415 |
448 | 416 |
449 | 417 |
450 | 418 |
451 | 419 |
452 | 420 |
453 | 421 |
454 | 422 |
455 | 423 |
456 | 424 |
457 | 425 |
458 | 426 |
459 | 427 |
460 | 428 |
461 | 429 |
462 | 430 |
463 | 431 |
464 | 432 |
465 | 433 |
466 | 434 |
467 | 435 |
468 | 436 |
469 | 437 |
470 | 438 |
471 | 439 |
472 | 440 |
473 | 441 |
474 | 442 |
475 | 443 |
476 | 444 |
477 | 445 |
478 | 446 |
479 | 447 |
480 | 448 |
481 | 449 |
482 | 450 |
483 | 451 |
484 | 452 |
485 | 453 |
486 | 454 |
487 | 455 |
488 | 456 |
489 | 457 |
490 | 458 |
491 | 459 |
492 | 460 |
493 | 461 |
494 | 462 |
495 | 463 |
496 | 464 |
497 | 465 |
498 | 466 |
499 | 467 |
500 | 468 |
501 | 469 |
502 | 470 |
503 | 471 |
504 | 472 |
505 | 473 |
506 | 474 |
507 | 475 |
508 | 476 |
509 | 477 |
510 | 478 |
511 | 479 |
512 | 480 |
513 | 481 |
514 | 482 |
515 | 483 |
516 | 484 |
517 | 485 |
518 | 486 |
519 | 487 |
520 | 488 |
521 | 489 |
522 | 490 |
523 | 491 |
524 | 492 |
525 | 493 |
526 | 494 |
527 | 495 |
528 | 496 |
529 | 497 |
530 | 498 |
531 | 499 |
532 | 500 |
533 | 501 |
534 | 502 |
535 | 503 |
536 | 504 |
537 | 505 |
538 | 506 |
539 | 507 |
540 | 508 |
541 | 509 |
542 | 510 |
543 | 511 |
544 | 512 |
545 | 513 |
546 | 514 |
547 | 515 |
548 | 516 |
549 | 517 |
550 | 518 |
551 | 519 |
552 | 520 |
553 | 521 |
554 | 522 |
555 | 523 |
556 | 524 |
557 | 525 |
558 | 526 |
559 | 527 |
560 | 528 |
561 | 529 |
562 | 530 |
563 | 531 |
564 | 532 |
565 | 533 |
566 | 534 |
567 | 535 |
568 | 536 |
569 | 537 |
570 | 538 |
571 | 539 |
572 | 540 |
573 | 541 |
574 | 542 |
575 | 543 |
576 | 544 |
577 | 545 |
578 | 546 |
579 | 547 |
580 | 548 |
581 | 549 |
582 | 550 |
583 | 551 |
584 | 552 |
585 | 553 |
586 | 554 |
587 | 555 |
588 | 556 |
589 | 557 |
590 | 558 |
591 | 559 |
592 | 560 |
593 | 561 |
594 | 562 |
595 | 563 |
596 | 564 |
597 | 565 |
598 | 566 |
599 | 567 |
600 | 568 |
601 | 569 |
602 | 570 |
603 | 571 |
604 | 572 |
605 | 573 |
606 | 574 |
607 | 575 |
608 | 576 |
609 | 577 |
610 | 578 |
611 | 579 |
612 | 580 |
613 | 581 |
614 | 582 |
615 | 583 |
616 | 584 |
617 | 585 |
618 | 586 |
619 | 587 |
620 | 588 |
621 | 589 |
622 | 590 |
623 | 591 |
624 | 592 |
625 | 593 |
626 | 594 |
627 | 595 |
628 | 596 |
629 | 597 |
630 | 598 |
631 | 599 |
632 | 600 |
633 | 601 |
634 | 602 |
635 | 603 |
636 | 604 |
637 | 605 |
638 | 606 |
639 | 607 |
640 | 608 |
641 | 609 |
642 | 610 |
Other editions - View all
Common terms and phrases
4-regular algorithm analytic approximately arcs asymptotic balls biarc bound chain closed complexity components computed configuration conformations corresponding curve defined denote diagram diagrammatically prime distance entropic force equilateral Figure figure-eight knot finite flux tubes fold geometric global radius glueball graph Hamilton cycle Hopf link Ideal Knots intersect invariant kalottes knot energies knot invariants knot probabilities Knot Theory knot type knots and links lattice length linear loops Math minimal minimum molecules number of edges octree pair parameter Phys physical planar planar graphs plane points polygonal knots polymer polynomial Potts model probability distribution protein quadrisecants radius of curvature random knots random polygons random walks ratio Rawdon rope ropelength RP-graphs scaling segments self-avoiding self-avoiding polygons shown simulation solid knot sphere spin Stasiak structure surface tangent Theorem thickness topological constraint trefoil knot trivial knot umbilical cord unknot values vectors vertex vertices writhe