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020 _a9781461476870
_9978-1-4614-7687-0
024 7 _a10.1007/978-1-4614-7687-0
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aSchuss, Zeev.
_eauthor.
245 1 0 _aBrownian Dynamics at Boundaries and Interfaces
_h[electronic resource] :
_bIn Physics, Chemistry, and Biology /
_cby Zeev Schuss.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXX, 322 p. 45 illus., 9 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v186
505 0 _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.
520 _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.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aDistribution (Probability theory).
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aPartial Differential Equations.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aMathematical and Computational Biology.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461476863
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v186
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-7687-0
912 _aZDB-2-SMA
999 _c95963
_d95963