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This monograph is devoted to random walk based stochastic
algorithms for solving high-dimensional boundary value problems of
mathematical physics and chemistry. It includes Monte Carlo methods
where the random walks live not only on the boundary, but also
inside the domain. A variety of examples from capacitance
calculations to electron dynamics in semiconductors are discussed
to illustrate the viability of the approach. The book is written
for mathematicians who work in the field of partial differential
and integral equations, physicists and engineers dealing with
computational methods and applied probability, for students and
postgraduates studying mathematical physics and numerical
mathematics. Contents: Introduction Random walk algorithms for
solving integral equations Random walk-on-boundary algorithms for
the Laplace equation Walk-on-boundary algorithms for the heat
equation Spatial problems of elasticity Variants of the random walk
on boundary for solving stationary potential problems Splitting and
survival probabilities in random walk methods and applications A
random WOS-based KMC method for electron-hole recombinations Monte
Carlo methods for computing macromolecules properties and solving
related problems Bibliography
The book presents advanced stochastic models and simulation methods
for random flows and transport of particles by turbulent velocity
fields and flows in porous media. Two main classes of models are
constructed: (1) turbulent flows are modeled as synthetic random
fields which have certain statistics and features mimicing those of
turbulent fluid in the regime of interest, and (2) the models are
constructed in the form of stochastic differential equations for
stochastic Lagrangian trajectories of particles carried by
turbulent flows. The book is written for mathematicians,
physicists, and engineers studying processes associated with
probabilistic interpretation, researchers in applied and
computational mathematics, in environmental and engineering
sciences dealing with turbulent transport and flows in porous
media, as well as nucleation, coagulation, and chemical reaction
analysis under fluctuation conditions. It can be of interest for
students and post-graduates studying numerical methods for solving
stochastic boundary value problems of mathematical physics and
dispersion of particles by turbulent flows and flows in porous
media.
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