## Search

Now showing items 11-20 of 87

#### Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory.

(Phys Rev E, 2016-12)

We perform microscopic molecular dynamics simulations of particle chains with an onsite
anharmonicity to study relaxation of spatially homogeneous states to equilibrium,
and directly compare the simulations with the corresponding ...

#### Reactive trajectories and the transition path process

(Probability Theory and Related Fields, 2014-01-01)

© 2014, Springer-Verlag Berlin Heidelberg.We study the trajectories of a solution
(formula presented) to an Itô stochastic differential equation in (formula presented),
as the process passes between two disjoint open sets, ...

#### Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems

(Physical Review B - Condensed Matter and Materials Physics, 2009-03-03)

We propose a multipole representation of the Fermi-Dirac function and the Fermi operator
and use this representation to develop algorithms for electronic structure analysis
of metallic systems. The algorithm is quite simple ...

#### Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: A mathematical justification of fewest switches surface hopping algorithms

(2017-04-23)

We develop a surface hopping algorithm based on frozen Gaussian approximation for
semiclassical matrix Schr\"odinger equations, in the spirit of Tully's fewest switches
surface hopping method. The algorithm is asymptotically ...

#### Randomized sampling for basis functions construction in generalized finite element methods

(2018-02-14)

In the context of generalized finite element methods for elliptic equations with rough
coefficients $a(x)$, efficiency and accuracy of the numerical method depend critically
on the use of appropriate basis functions. This ...

#### Detecting localized eigenstates of linear operators

(2017-11-30)

We describe a way of detecting the location of localized eigenvectors of a linear
system $Ax = \lambda x$ for eigenvalues $\lambda$ with $|\lambda|$ comparatively large.
We define the family of functions $f_{\alpha}: \left\{1.2. ...

#### Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation

(Journal of Computational Physics, 2015-06-05)

© 2015 Elsevier Inc.We develop an efficient algorithm for a spatially inhomogeneous
matrix-valued quantum Boltzmann equation derived from the Hubbard model. The distribution
functions are 2 × 2 matrix-valued to accommodate ...

#### Fast construction of hierarchical matrix representation from matrix-vector multiplication

(Journal of Computational Physics, 2011-05-10)

We develop a hierarchical matrix construction algorithm using matrix-vector multiplications,
based on the randomized singular value decomposition of low-rank matrices. The algorithm
uses O(logn) applications of the matrix ...

#### Orbital-Free Density Functional Theory of Out-of-Plane Charge Screening in Graphene

(Journal of Nonlinear Science, 2015-12-01)

© 2015, Springer Science+Business Media New York.We propose a density functional theory
of Thomas–Fermi–Dirac–von Weizsäcker type to describe the response of a single layer
of graphene resting on a dielectric substrate to ...

#### Efficient rare event simulation for failure problems in random media

(SIAM Journal on Scientific Computing, 2015-01-01)

© 2015 Society for Industrial and Applied Mathematics.In this paper we study rare
events associated to the solutions of an elliptic partial differential equation with
a spatially varying random coefficient. The random coefficient ...