874 research outputs found
ROS3P---an accurate third-order Rosenbrock solver designed for parabolic problems
In this note we present a new Rosenbrock solver which is third--order accurate for nonlinear parabolic problems. Since Rosenbrock methods suffer from order reductions when they are applied to partial differential equations, additional order conditions have to be satisfied. Although these conditions have been known for a longer time, from the practical point of view only little has been done to construct new methods. {sc Steinebach cite{St95 modified the well--known solver RODAS of {sc Hairer and {sc Wanner cite{HaWa96 to preserve its classical order four for special problem classes including linear parabolic equations. His solver RODASP, however, drops down to order three for nonlinear parabolic problems. Our motivation here was to derive an efficient third--order Rosenbrock solver for the nonlinear situation. Such a method exists with three stages and two function evaluations only. A comparison with other third--order methods shows the substantial potential of our new method
ROS3P : an accurate third-order Rosenbrock solver designed for parabolic problems
In this note we present a new Rosenbrock solver which is third--order accurate for nonlinear parabolic problems. Since Rosenbrock methods suffer from order reductions when they are applied to partial differential equations, additional order conditions have to be satisfied. Although these conditions have been known for a longer time, from the practical point of view only little has been done to construct new methods. {sc Steinebach cite{St95 modified the well--known solver RODAS of {sc Hairer and {sc Wanner cite{HaWa96 to preserve its classical order four for special problem classes including linear parabolic equations. His solver RODASP, however, drops down to order three for nonlinear parabolic problems. Our motivation here was to derive an efficient third--order Rosenbrock solver for the nonlinear situation. Such a method exists with three stages and two function evaluations only. A comparison with other third--order methods shows the substantial potential of our new method
On global error estimation and control for initial value problems
This paper addresses global error estimation and control for initial value problems for ordinary differential equations. The focus lies on a comparison between a novel approach based on the adjoint method combined with a small sample statistical initialization and the classical approach based on the first variational equation. Control is achieved through tolerance proportionality. Both approaches are found to work well and to enable estimation and control in a reliable manner. However, the novel approach is not found to be competitive with the classical approach, mainly because of its huge storage demand for large problems
Galois groups of multivariate Tutte polynomials
The multivariate Tutte polynomial of a matroid is a
generalization of the standard two-variable version, obtained by assigning a
separate variable to each element of the ground set . It encodes
the full structure of . Let \bv = \{v_e\}_{e\in E}, let be an
arbitrary field, and suppose is connected. We show that is
irreducible over K(\bv), and give three self-contained proofs that the Galois
group of over K(\bv) is the symmetric group of degree , where
is the rank of . An immediate consequence of this result is that the
Galois group of the multivariate Tutte polynomial of any matroid is a direct
product of symmetric groups. Finally, we conjecture a similar result for the
standard Tutte polynomial of a connected matroid.Comment: 8 pages, final version, to appear in J. Alg. Comb. Substantial
revisions, including the addition of two alternative proofs of the main
resul
Bipolarons in the Extended Holstein Hubbard Model
We numerically and analytically calculate the properties of the bipolaron in
an extended Hubbard Holstein model, which has a longer range electron-phonon
coupling like the Fr\" ohlich model. In the strong coupling regime, the
effective mass of the bipolaron in the extended model is much smaller than the
Holstein bipolaron mass. In contrast to the Holstein bipolaron, the bipolaron
in the extended model has a lower binding energy and remains bound with
substantial binding energy even in the large-U limit. In comparison with the
Holstein model where only a singlet bipolaron is bound, in the extended
Holstein model a triplet bipolaron can also form a bound state. We discuss the
possibility of phase separation in the case of finite electron doping.Comment: 5 pages, 3 figure
Optimal trapping wavelengths of Cs molecules in an optical lattice
The present paper aims at finding optimal parameters for trapping of Cs
molecules in optical lattices, with the perspective of creating a quantum
degenerate gas of ground-state molecules. We have calculated dynamic
polarizabilities of Cs molecules subject to an oscillating electric field,
using accurate potential curves and electronic transition dipole moments. We
show that for some particular wavelengths of the optical lattice, called "magic
wavelengths", the polarizability of the ground-state molecules is equal to the
one of a Feshbach molecule. As the creation of the sample of ground-state
molecules relies on an adiabatic population transfer from weakly-bound
molecules created on a Feshbach resonance, such a coincidence ensures that both
the initial and final states are favorably trapped by the lattice light,
allowing optimized transfer in agreement with the experimental observation
Net Charge on a Noble Gas Atom Adsorbed on a Metallic Surface
Adsorbed noble gas atoms donate (on the average) a fraction of an electronic
charge to the substrate metal. The effect has been experimentally observed as
an adsorptive change in the electronic work function. The connection between
the effective net atomic charge and the binding energy of the atom to the metal
is theoretically explored.Comment: ReVvTeX 3.1 format, Two Figures, Three Table
A first-principles approach to electrical transport in atomic-scale nanostructures
We present a first-principles numerical implementation of Landauer formalism
for electrical transport in nanostructures characterized down to the atomic
level. The novelty and interest of our method lies essentially on two facts.
First of all, it makes use of the versatile Gaussian98 code, which is widely
used within the quantum chemistry community. Secondly, it incorporates the
semi-infinite electrodes in a very generic and efficient way by means of Bethe
lattices. We name this method the Gaussian Embedded Cluster Method (GECM). In
order to make contact with other proposed implementations, we illustrate our
technique by calculating the conductance in some well-studied systems such as
metallic (Al and Au) nanocontacts and C-atom chains connected to metallic (Al
and Au) electrodes. In the case of Al nanocontacts the conductance turns out to
be quite dependent on the detailed atomic arrangement. On the contrary, the
conductance in Au nanocontacts presents quite universal features. In the case
of C chains, where the self-consistency guarantees the local charge transfer
and the correct alignment of the molecular and electrode levels, we find that
the conductance oscillates with the number of atoms in the chain regardless of
the type of electrode. However, for short chains and Al electrodes the even-odd
periodicity is reversed at equilibrium bond distances.Comment: 14 pages, two-column format, submitted to PR
Fluid Models of Many-server Queues with Abandonment
We study many-server queues with abandonment in which customers have general
service and patience time distributions. The dynamics of the system are modeled
using measure- valued processes, to keep track of the residual service and
patience times of each customer. Deterministic fluid models are established to
provide first-order approximation for this model. The fluid model solution,
which is proved to uniquely exists, serves as the fluid limit of the
many-server queue, as the number of servers becomes large. Based on the fluid
model solution, first-order approximations for various performance quantities
are proposed
On the Relationship between the Uniqueness of the Moonshine Module and Monstrous Moonshine
We consider the relationship between the conjectured uniqueness of the
Moonshine Module, , and Monstrous Moonshine, the genus zero
property of the modular invariance group for each Monster group Thompson
series. We first discuss a family of possible meromorphic orbifold
constructions of based on automorphisms of the Leech
lattice compactified bosonic string. We reproduce the Thompson series for all
51 non-Fricke classes of the Monster group together with a new relationship
between the centralisers of these classes and 51 corresponding Conway group
centralisers (generalising a well-known relationship for 5 such classes).
Assuming that is unique, we then consider meromorphic
orbifoldings of and show that Monstrous Moonshine holds if
and only if the only meromorphic orbifoldings of give
itself or the Leech theory. This constraint on the
meromorphic orbifoldings of therefore relates Monstrous
Moonshine to the uniqueness of in a new way.Comment: 53 pages, PlainTex, DIAS-STP-93-0
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