1,237 research outputs found
Multi-Particle Collision Dynamics -- a Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids
In this review, we describe and analyze a mesoscale simulation method for
fluid flow, which was introduced by Malevanets and Kapral in 1999, and is now
called multi-particle collision dynamics (MPC) or stochastic rotation dynamics
(SRD). The method consists of alternating streaming and collision steps in an
ensemble of point particles. The multi-particle collisions are performed by
grouping particles in collision cells, and mass, momentum, and energy are
locally conserved. This simulation technique captures both full hydrodynamic
interactions and thermal fluctuations. The first part of the review begins with
a description of several widely used MPC algorithms and then discusses
important features of the original SRD algorithm and frequently used
variations. Two complementary approaches for deriving the hydrodynamic
equations and evaluating the transport coefficients are reviewed. It is then
shown how MPC algorithms can be generalized to model non-ideal fluids, and
binary mixtures with a consolute point. The importance of angular-momentum
conservation for systems like phase-separated liquids with different
viscosities is discussed. The second part of the review describes a number of
recent applications of MPC algorithms to study colloid and polymer dynamics,
the behavior of vesicles and cells in hydrodynamic flows, and the dynamics of
viscoelastic fluids
Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space
The problem of the invariant classification of the orthogonal coordinate webs
defined in Euclidean space is solved within the framework of Felix Klein's
Erlangen Program. The results are applied to the problem of integrability of
the Calogero-Moser model
Geroch Group Description of Black Holes
On one hand the Geroch group allows one to associate spacetime independent
matrices with gravitational configurations that effectively only depend on two
coordinates. This class includes stationary axisymmetric four- and
five-dimensional black holes. On the other hand, a recently developed inverse
scattering method allows one to factorize these matrices to explicitly
construct the corresponding spacetime configurations. In this work we
demonstrate the construction as well as the factorization of Geroch group
matrices for a wide class of black hole examples. In particular, we obtain the
Geroch group SL(3,R) matrices for the five-dimensional Myers-Perry and
Kaluza-Klein black holes and the Geroch group SU(2,1) matrix for the
four-dimensional Kerr-Newman black hole. We also present certain non-trivial
relations between the Geroch group matrices and charge matrices for these black
holes.Comment: 29 pages, no figures; v2: references added; v3: minor changes,
matches published versio
An algorithm for the rapid numerical evaluation of Bessel functions of real orders and arguments
We describe a method for the rapid numerical evaluation of the Bessel
functions of the first and second kinds of nonnegative real orders and positive
arguments. Our algorithm makes use of the well-known observation that although
the Bessel functions themselves are expensive to represent via piecewise
polynomial expansions, the logarithms of certain solutions of Bessel's equation
are not. We exploit this observation by numerically precomputing the logarithms
of carefully chosen Bessel functions and representing them with piecewise
bivariate Chebyshev expansions. Our scheme is able to evaluate Bessel functions
of orders between and 1\sep,000\sep,000\sep,000 at essentially any
positive real argument. In that regime, it is competitive with existing methods
for the rapid evaluation of Bessel functions and has several advantages over
them. First, our approach is quite general and can be readily applied to many
other special functions which satisfy second order ordinary differential
equations. Second, by calculating the logarithms of the Bessel functions rather
than the Bessel functions themselves, we avoid many issues which arise from
numerical overflow and underflow. Third, in the oscillatory regime, our
algorithm calculates the values of a nonoscillatory phase function for Bessel's
differential equation and its derivative. These quantities are useful for
computing the zeros of Bessel functions, as well as for rapidly applying the
Fourier-Bessel transform. The results of extensive numerical experiments
demonstrating the efficacy of our algorithm are presented. A Fortran package
which includes our code for evaluating the Bessel functions as well as our code
for all of the numerical experiments described here is publically available
Multiconfiguration Time-Dependent Hartree-Fock Treatment of Electronic and Nuclear Dynamics in Diatomic Molecules
The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method is
formulated for treating the coupled electronic and nuclear dynamics of diatomic
molecules without the Born- Oppenheimer approximation. The method treats the
full dimensionality of the electronic motion, uses no model interactions, and
is in principle capable of an exact nonrelativistic description of diatomics in
electromagnetic fields. An expansion of the wave function in terms of
configurations of orbitals whose dependence on internuclear distance is only
that provided by the underlying prolate spheroidal coordinate system is
demonstrated to provide the key simplifications of the working equations that
allow their practical solution. Photoionization cross sections are also
computed from the MCTDHF wave function in calculations using short pulses.Comment: Submitted to Phys Rev
On generalized prolate spheroidal functions
Prolate spheroidal wave functions provide a natural and effective tool for
computing with bandlimited functions defined on an interval. As demonstrated by
Slepian et al., the so called generalized prolate spheroidal functions (GPSFs)
extend this apparatus to higher dimensions. While the analytical and numerical
apparatus in one dimension is fairly complete, the situation in higher
dimensions is less satisfactory. This report attempts to improve the situation
by providing analytical and numerical tools for GPSFs, including the efficient
evaluation of eigenvalues, the construction of quadratures, interpolation
formulae, etc. Our results are illustrated with several numerical examples
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