LEADER 05073nam 2200685Ia 450 001 9910454339403321 005 20200520144314.0 010 $a1-281-93594-8 010 $a9786611935948 010 $a981-279-559-6 035 $a(CKB)1000000000537864 035 $a(EBL)1679680 035 $a(SSID)ssj0000211712 035 $a(PQKBManifestationID)11196121 035 $a(PQKBTitleCode)TC0000211712 035 $a(PQKBWorkID)10134470 035 $a(PQKB)10094522 035 $a(MiAaPQ)EBC1679680 035 $a(WSP)00004747 035 $a(Au-PeEL)EBL1679680 035 $a(CaPaEBR)ebr10255806 035 $a(CaONFJC)MIL193594 035 $a(OCoLC)879023974 035 $a(EXLCZ)991000000000537864 100 $a20040412d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNoise sustained patterns$b[electronic resource] $efluctuations and nonlinearities /$fMarkus Loecher 210 $aRiver Edge, N.J. $cWorld Scientific$d2003 215 $a1 online resource (252 p.) 225 1 $aWorld Scientific lecture notes in physics ;$vv. 70 300 $aDescription based upon print version of record. 311 $a981-02-4676-5 320 $aIncludes bibliographical references and index. 327 $aPreface; Acknowledgements; Contents; Chapter 1 Introduction; 1.1 Stability theory revisited; 1.1.1 Noise and metastability; 1.1.2 Linear stability analysis; 1.2 Instabilities and nonlinear events in everyday life; 1.2.1 Arms race; 1.2.2 Distribution of wealth; 1.2.3 Front nucleation and propagation; 1.2.4 Supply chain dynamics; 1.2.5 A hodgepodge of mechanical instabilities; 1.3 Postscript; Chapter 2 Essentials; 2.1 Probabilistic and information theoretic measures; 2.2 Matrix manipulations; 2.2.1 Circulant matrices; 2.2.2 Singular value decomposition; 2.3 Delay-differential equations 327 $a2.4 The fluctuation-dissipation theorem2.5 The Fokker-Planck equation; 2.6 Numerical techniques for the simulation of stochastic equations; 2.7 Experimental aspects of generating noise; 2.8 Complex integration; Chapter 3 Noise Induced Temporal Phenomena; 3.1 Escape from metastable states; 3.2 Stochastic resonance in bistable systems; 3.2.1 Double-well potential; 3.2.2 Two state theory; 3.2.3 The diode resonator; 3.2.4 The logistic map; 3.3 Postscript; Chapter 4 Adding Spatial Dimensions; 4.1 Spatiotemporal stochastic resonance; 4.1.1 Array enhancement; 4.1.2 Global vs. local dynamics 327 $a4.1.3 Kink nucleation in a O4 model4.1.4 Kink nucleation in the experiment; 4.1.5 Decay rates and kink speeds; 4.1.6 Coupled maps; 4.2 Doubly stochastic resonance; 4.3 Spatial patterns; 4.3.1 Parametric surface waves; 4.4 Postscript; Chapter 5 Stochastic Transport Phenomena; 5.1 Noise-sustained structures in convectively unstable media; 5.1.1 The Ginzburg-Landau equation; 5.1.2 Unidirectionally coupled diode resonators; 5.1.3 Coupled maps; 5.2 Noise sustained front transmission; 5.2.1 Propagation failure in cardiac tissue; 5.2.2 Information theoretic measures revisited: ROC curves; 5.3 Theory 327 $a5.3.1 The continuum limit5.3.2 Kink Brownian motion; 5.3.3 The Peierls-Nabarro potential; 5.4 Noise enhanced wave propagation; 5.4.1 Monostable noise enhanced propagation; 5.5 Stochastic ratchets and Brownian motors; 5.6 Postscript; Chapter 6 Sundry Topics; 6.1 Minority game; 6.1.1 The thermal minority game; 6.2 Traffic dynamics; 6.2.1 Time-continuous model; 6.2.2 Discrete time dynamics; 6.3 Dithering; 6.4 Noise in neural networks; Chapter 7 Afterthoughts; Appendix A Normal Matrices; Appendix B Integrating Colored-Noise Coupled SDEs; B.l Exploiting symmetries of coupled differential equations 327 $aB.2 Coupled Duffing oscillatorsAppendix C Numerical Implementation of the FPT; Appendix D Absolute and Convective Instabilities; Bibliography; Index 330 $aThis book investigates the impact of noise upon the emergence and sustenance of patterns. "Patterns" loosely refers to coherent spatial structures, including fronts, as well as temporal patterns. The crucial role of nonlinearities is highlighted and expanded upon in the context of dynamical system frameworks. The author's familiarity with chaos theory, statistical physics and nonlinear science is reflected in the highly interdisciplinary character of the text. Model equations and experiments taken from fluid dynamics, semiconductor devices, biophysics and statistical mechanics complement theor 410 0$aWorld Scientific lecture notes in physics ;$vv. 70. 606 $aStochastic processes 606 $aRandom noise theory 606 $aStability 608 $aElectronic books. 615 0$aStochastic processes. 615 0$aRandom noise theory. 615 0$aStability. 676 $a530.1 700 $aLoecher$b Markus$0937393 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454339403321 996 $aNoise sustained patterns$92111438 997 $aUNINA