LEADER 04652nam 22007815 450 001 9910739444903321 005 20200702125954.0 010 $a1-4614-7687-9 024 7 $a10.1007/978-1-4614-7687-0 035 $a(CKB)3710000000015757 035 $a(EBL)1398245 035 $a(SSID)ssj0000988062 035 $a(PQKBManifestationID)11534664 035 $a(PQKBTitleCode)TC0000988062 035 $a(PQKBWorkID)10950000 035 $a(PQKB)10977888 035 $a(DE-He213)978-1-4614-7687-0 035 $a(MiAaPQ)EBC6314796 035 $a(MiAaPQ)EBC1398245 035 $a(Au-PeEL)EBL1398245 035 $a(CaPaEBR)ebr10965578 035 $a(OCoLC)858924139 035 $a(PPN)172419735 035 $a(EXLCZ)993710000000015757 100 $a20130812d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBrownian Dynamics at Boundaries and Interfaces $eIn Physics, Chemistry, and Biology /$fby Zeev Schuss 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (340 p.) 225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v186 300 $aDescription based upon print version of record. 311 $a1-4899-9731-8 311 $a1-4614-7686-0 320 $aIncludes bibliographical references and index. 327 $aThe Mathematical Brownian Motion -- Euler Simulation of Ito SDEs -- Simulation of the Overdamped Langevin Equation -- The First Passage Time of a Diffusion Process -- Chemical Reaction in Microdomains -- The Stochastic Separatrix -- Narrow Escape in R2 -- Narrow Escape in R3. 330 $aBrownian dynamics serve as mathematical models for the diffusive motion of microscopic particles of various shapes in gaseous, liquid, or solid environments. The renewed interest in Brownian dynamics is due primarily to their key role in molecular and cellular biophysics: diffusion of ions and molecules is the driver of all life. Brownian dynamics simulations are the numerical realizations of stochastic differential equations that model the functions of biological micro devices such as protein ionic channels of biological membranes, cardiac myocytes, neuronal synapses, and many more. Stochastic differential equations are ubiquitous models in computational physics, chemistry, biophysics, computer science, communications theory, mathematical finance theory, and many other disciplines. Brownian dynamics simulations of the random motion of particles, be it molecules or stock prices, give rise to mathematical problems that neither the kinetic theory of Maxwell and Boltzmann, nor Einstein?s and Langevin?s theories of Brownian motion could predict. This book takes the readers on a journey that starts with the rigorous definition of mathematical Brownian motion, and ends with the explicit solution of a series of complex problems that have immediate applications. It is aimed at applied mathematicians, physicists, theoretical chemists, and physiologists who are interested in modeling, analysis, and simulation of micro devices of microbiology. The book contains exercises and worked out examples throughout. 410 0$aApplied Mathematical Sciences,$x0066-5452 ;$v186 606 $aProbabilities 606 $aPartial differential equations 606 $aPhysics 606 $aBiomathematics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aMathematical and Computational Biology$3https://scigraph.springernature.com/ontologies/product-market-codes/M31000 615 0$aProbabilities. 615 0$aPartial differential equations. 615 0$aPhysics. 615 0$aBiomathematics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 615 24$aMathematical Methods in Physics. 615 24$aMathematical and Computational Biology. 676 $a519.2/33 686 $a60-02, 60J65, 00A69$2msc 700 $aSchuss$b Zeev$4aut$4http://id.loc.gov/vocabulary/relators/aut$0460932 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910739444903321 996 $aBrownian dynamics at boundaries and interfaces$9836880 997 $aUNINA