10,764 research outputs found
Effect of dispersion interactions on the properties of LiF in condensed phases
Classical molecular dynamics simulations are performed on LiF in the
framework of the polarizable ion model. The overlap-repulsion and polarization
terms of the interaction potential are derived on a purely non empirical,
first-principles basis. For the dispersion, three cases are considered: a first
one in which the dispersion parameters are set to zero and two others in which
they are included, with different parameterizations. Various thermodynamic,
structural and dynamic properties are calculated for the solid and liquid
phases. The melting temperature is also obtained by direct coexistence
simulations of the liquid and solid phases. Dispersion interactions appear to
have an important effect on the density of both phases and on the melting
point, although the liquid properties are not affected when simulations are
performed in the NVT ensemble at the experimental density.Comment: 8 pages, 5 figure
Exact simulation of the Wright-Fisher diffusion
The Wright-Fisher family of diffusion processes is a widely used class of
evolutionary models. However, simulation is difficult because there is no known
closed-form formula for its transition function. In this article we demonstrate
that it is in fact possible to simulate exactly from a broad class of
Wright-Fisher diffusion processes and their bridges. For those diffusions
corresponding to reversible, neutral evolution, our key idea is to exploit an
eigenfunction expansion of the transition function; this approach even applies
to its infinite-dimensional analogue, the Fleming-Viot process. We then develop
an exact rejection algorithm for processes with more general drift functions,
including those modelling natural selection, using ideas from retrospective
simulation. Our approach also yields methods for exact simulation of the moment
dual of the Wright-Fisher diffusion, the ancestral process of an infinite-leaf
Kingman coalescent tree. We believe our new perspective on diffusion simulation
holds promise for other models admitting a transition eigenfunction expansion.Comment: 36 pages, 2 figure, 2 tables. This version corrects an error in the
proof of Lemma 6.
Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method
Given the matrix polynomial , we
consider the associated polynomial eigenvalue problem. This problem, viewed in
terms of computing the roots of the scalar polynomial , is treated
in polynomial form rather than in matrix form by means of the Ehrlich-Aberth
iteration. The main computational issues are discussed, namely, the choice of
the starting approximations needed to start the Ehrlich-Aberth iteration, the
computation of the Newton correction, the halting criterion, and the treatment
of eigenvalues at infinity. We arrive at an effective implementation which
provides more accurate approximations to the eigenvalues with respect to the
methods based on the QZ algorithm. The case of polynomials having special
structures, like palindromic, Hamiltonian, symplectic, etc., where the
eigenvalues have special symmetries in the complex plane, is considered. A
general way to adapt the Ehrlich-Aberth iteration to structured matrix
polynomial is introduced. Numerical experiments which confirm the effectiveness
of this approach are reported.Comment: Submitted to Linear Algebra App
Quasiseparable Hessenberg reduction of real diagonal plus low rank matrices and applications
We present a novel algorithm to perform the Hessenberg reduction of an
matrix of the form where is diagonal with
real entries and and are matrices with . The
algorithm has a cost of arithmetic operations and is based on the
quasiseparable matrix technology. Applications are shown to solving polynomial
eigenvalue problems and some numerical experiments are reported in order to
analyze the stability of the approac
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