7,115 research outputs found
Complete integrability versus symmetry
The purpose of this article is to show that on an open and dense set,
complete integrability implies the existence of symmetry
The optimal P3M algorithm for computing electrostatic energies in periodic systems
We optimize Hockney and Eastwood's Particle-Particle Particle-Mesh (P3M)
algorithm to achieve maximal accuracy in the electrostatic energies (instead of
forces) in 3D periodic charged systems. To this end we construct an optimal
influence function that minimizes the RMS errors in the energies. As a
by-product we derive a new real-space cut-off correction term, give a
transparent derivation of the systematic errors in terms of Madelung energies,
and provide an accurate analytical estimate for the RMS error of the energies.
This error estimate is a useful indicator of the accuracy of the computed
energies, and allows an easy and precise determination of the optimal values of
the various parameters in the algorithm (Ewald splitting parameter, mesh size
and charge assignment order).Comment: 31 pages, 3 figure
A Lagrangian kinetic model for collisionless magnetic reconnection
A new fully kinetic system is proposed for modeling collisionless magnetic
reconnection. The formulation relies on fundamental principles in Lagrangian
dynamics, in which the inertia of the electron mean flow is neglected in the
expression of the Lagrangian, rather then enforcing a zero electron mass in the
equations of motion. This is done upon splitting the electron velocity into its
mean and fluctuating parts, so that the latter naturally produce the
corresponding pressure tensor. The model exhibits a new Coriolis force term,
which emerges from a change of frame in the electron dynamics. Then, if the
electron heat flux is neglected, the strong electron magnetization limit yields
a hybrid model, in which the electron pressure tensor is frozen into the
electron mean velocity.Comment: 15 pages, no figures. To Appear in Plasma Phys. Control. Fusio
Z_2-Regge versus Standard Regge Calculus in two dimensions
We consider two versions of quantum Regge calculus. The Standard Regge
Calculus where the quadratic link lengths of the simplicial manifold vary
continuously and the Z_2-Regge Model where they are restricted to two possible
values. The goal is to determine whether the computationally more easily
accessible Z_2 model still retains the universal characteristics of standard
Regge theory in two dimensions. In order to compare observables such as average
curvature or Liouville field susceptibility, we use in both models the same
functional integration measure, which is chosen to render the Z_2-Regge Model
particularly simple. Expectation values are computed numerically and agree
qualitatively for positive bare couplings. The phase transition within the
Z_2-Regge Model is analyzed by mean-field theory.Comment: 21 pages, 16 ps-figures, to be published in Phys. Rev.
Ballistic and Diffuse Electron Transport in Nanocontacts of Magnetics
The transition from the ballistic electron transport to the diffuse one is
experimentally observed in the study of the magnetic phase transition in Ni
nanocontacts with different sizes. It is shown that the voltage needed
for Joule heating of the near-contact region to the critical temperature does
not depend on the contact size only in the diffuse mode. For the ballistic
contact it increases with decrease in the nanocontact size. The reduction of
the transport electron mean free path due to heating of NCs may result in
change of the electron transport mode from ballistic to diffusive one.Comment: 7 pages, 2 figures accepted for the publication in JETPL
(http://www.jetpletters.ac.ru). Will be published on 25 april 201
Colloidal electrophoresis: Scaling analysis, Green-Kubo relation, and numerical results
We consider electrophoresis of a single charged colloidal particle in a
finite box with periodic boundary conditions, where added counterions and salt
ions ensure charge neutrality. A systematic rescaling of the electrokinetic
equations allows us to identify a minimum set of suitable dimensionless
parameters, which, within this theoretical framework, determine the reduced
electrophoretic mobility. It turns out that the salt-free case can, on the Mean
Field level, be described in terms of just three parameters. A fourth
parameter, which had previously been identified on the basis of straightforward
dimensional analysis, can only be important beyond Mean Field. More complicated
behavior is expected to arise when further ionic species are added. However,
for a certain parameter regime, we can demonstrate that the salt-free case can
be mapped onto a corresponding system containing additional salt. The
Green-Kubo formula for the electrophoretic mobility is derived, and its
usefulness demonstrated by simulation data. Finally, we report on
finite-element solutions of the electrokinetic equations, using the commercial
software package COMSOL.Comment: To appear in Journal of Physics: Condensed Matter - special issue on
occasion of the CODEF 2008 conferenc
Polyelectrolyte Bundles
Using extensive Molecular Dynamics simulations we study the behavior of
polyelectrolytes with hydrophobic side chains, which are known to form
cylindrical micelles in aqueous solution. We investigate the stability of such
bundles with respect to hydrophobicity, the strength of the electrostatic
interaction, and the bundle size. We show that for the parameter range relevant
for sulfonated poly-para-phenylenes (PPP) one finds a stable finite bundle
size. In a more generic model we also show the influence of the length of the
precursor oligomer on the stability of the bundles. We also point out that our
model has close similarities to DNA solutions with added condensing agents,
hinting to the possibility that the size of DNA aggregates is under certain
circumstances thermodynamically limited.Comment: 10 pages, 8 figure
Equilibrium solutions of the shallow water equations
A statistical method for calculating equilibrium solutions of the shallow
water equations, a model of essentially 2-d fluid flow with a free surface, is
described. The model contains a competing acoustic turbulent {\it direct}
energy cascade, and a 2-d turbulent {\it inverse} energy cascade. It is shown,
nonetheless that, just as in the corresponding theory of the inviscid Euler
equation, the infinite number of conserved quantities constrain the flow
sufficiently to produce nontrivial large-scale vortex structures which are
solutions to a set of explicitly derived coupled nonlinear partial differential
equations.Comment: 4 pages, no figures. Submitted to Physical Review Letter
ON NON-RIEMANNIAN PARALLEL TRANSPORT IN REGGE CALCULUS
We discuss the possibility of incorporating non-Riemannian parallel transport
into Regge calculus. It is shown that every Regge lattice is locally equivalent
to a space of constant curvature. Therefore well known-concepts of differential
geometry imply the definition of an arbitrary linear affine connection on a
Regge lattice.Comment: 12 pages, Plain-TEX, two figures (available from the author
Monte Carlo Study of Topological Defects in the 3D Heisenberg Model
We use single-cluster Monte Carlo simulations to study the role of
topological defects in the three-dimensional classical Heisenberg model on
simple cubic lattices of size up to . By applying reweighting techniques
to time series generated in the vicinity of the approximate infinite volume
transition point , we obtain clear evidence that the temperature
derivative of the average defect density behaves
qualitatively like the specific heat, i.e., both observables are finite in the
infinite volume limit. This is in contrast to results by Lau and Dasgupta [{\em
Phys. Rev.\/} {\bf B39} (1989) 7212] who extrapolated a divergent behavior of
at from simulations on lattices of size up to
. We obtain weak evidence that scales with the
same critical exponent as the specific heat.As a byproduct of our simulations,
we obtain a very accurate estimate for the ratio of the
specific-heat exponent with the correlation-length exponent from a finite-size
scaling analysis of the energy.Comment: pages ,4 ps-figures not included, FUB-HEP 10/9
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