Knowledge (XXG)

Swift–Hohenberg equation

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Another example where the equation appears is in the study of wrinkling morphology and pattern selection in curved elastic bilayer materials.
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The equation is named after the authors of the paper, where it was derived from the equations for thermal
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Stoop, Norbert; Lagrange, Romain; Terwagne, Denis; Reis, Pedro M.; Dunkel, Jörn (March 2015).
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J. Swift; P.C. Hohenberg (1977). "Hydrodynamic fluctuations at the convective instability".
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noted for its pattern-forming behaviour. It takes the form
361: 37: 119: 381: 8: 213:Dissipative soliton#Theoretical description 388: 374: 199:The Swift–Hohenberg equation leads to the 93: 83: 38: 36: 238: 7: 342: 340: 360:. You can help Knowledge (XXG) by 170:defined on the line or the plane, 80: 49: 41: 14: 344: 186:) is some smooth nonlinearity. 20:(named after Jack B. Swift and 407:Partial differential equations 114: 108: 90: 70: 1: 320:Lewin, Sarah (8 April 2015). 26:partial differential equation 322:"A Grand Theory of Wrinkles" 428: 339: 228:Rayleigh–Bénard convection 412:Applied mathematics stubs 218:Reaction–diffusion system 201:Ginzburg–Landau equation 18:Swift–Hohenberg equation 268:10.1103/PhysRevA.15.319 356:-related article is a 121: 122: 35: 354:applied mathematics 260:1977PhRvA..15..319S 117: 369: 368: 56: 419: 390: 383: 376: 348: 341: 332: 331: 317: 311: 310: 299:10.1038/nmat4202 287:Nature Materials 278: 272: 271: 243: 126: 124: 123: 118: 98: 97: 88: 87: 57: 55: 47: 39: 22:Pierre Hohenberg 427: 426: 422: 421: 420: 418: 417: 416: 397: 396: 395: 394: 337: 335: 327:Quanta Magazine 319: 318: 314: 280: 279: 275: 245: 244: 240: 236: 223:Turing patterns 209: 178:parameter, and 168:scalar function 89: 79: 48: 40: 33: 32: 12: 11: 5: 425: 423: 415: 414: 409: 399: 398: 393: 392: 385: 378: 370: 367: 366: 349: 334: 333: 312: 293:(3): 337–342. 273: 254:(1): 319–328. 237: 235: 232: 231: 230: 225: 220: 215: 208: 205: 128: 127: 116: 113: 110: 107: 104: 101: 96: 92: 86: 82: 78: 75: 72: 69: 66: 63: 60: 54: 51: 46: 43: 13: 10: 9: 6: 4: 3: 2: 424: 413: 410: 408: 405: 404: 402: 391: 386: 384: 379: 377: 372: 371: 365: 363: 359: 355: 350: 347: 343: 338: 329: 328: 323: 316: 313: 308: 304: 300: 296: 292: 288: 284: 277: 274: 269: 265: 261: 257: 253: 249: 242: 239: 233: 229: 226: 224: 221: 219: 216: 214: 211: 210: 206: 204: 202: 197: 194: 192: 187: 185: 181: 177: 173: 169: 165: 161: 157: 153: 149: 145: 141: 137: 133: 111: 105: 102: 99: 94: 84: 76: 73: 67: 64: 61: 58: 52: 44: 31: 30: 29: 27: 23: 19: 362:expanding it 351: 336: 325: 315: 290: 286: 276: 251: 248:Phys. Rev. A 247: 241: 198: 195: 188: 183: 179: 171: 163: 159: 155: 151: 147: 143: 139: 135: 131: 129: 17: 15: 176:bifurcation 401:Categories 234:References 191:convection 174:is a real 307:1476-1122 81:∇ 68:− 50:∂ 42:∂ 207:See also 256:Bibcode 166:) is a 24:) is a 305:  130:where 352:This 146:) or 358:stub 303:ISSN 16:The 295:doi 264:doi 403:: 324:. 301:. 291:14 289:. 285:. 262:. 252:15 250:. 203:. 193:. 162:, 158:, 150:= 142:, 134:= 389:e 382:t 375:v 364:. 330:. 309:. 297:: 270:. 266:: 258:: 184:u 182:( 180:N 172:r 164:t 160:y 156:x 154:( 152:u 148:u 144:t 140:x 138:( 136:u 132:u 115:) 112:u 109:( 106:N 103:+ 100:u 95:2 91:) 85:2 77:+ 74:1 71:( 65:u 62:r 59:= 53:t 45:u

Index

Pierre Hohenberg
partial differential equation
scalar function
bifurcation
convection
Ginzburg–Landau equation
Dissipative soliton#Theoretical description
Reaction–diffusion system
Turing patterns
Rayleigh–Bénard convection
Bibcode
1977PhRvA..15..319S
doi
10.1103/PhysRevA.15.319
"Curvature-induced symmetry breaking determines elastic surface patterns"
doi
10.1038/nmat4202
ISSN
1476-1122
"A Grand Theory of Wrinkles"
Quanta Magazine
Stub icon
applied mathematics
stub
expanding it
v
t
e
Categories
Partial differential equations

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