16,406 research outputs found
Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
We consider a dynamical system described by a system of ordinary differential equations which possesses a compact attracting set Λ of arbitrary shape. Under the assumption of uniform asymptotic stability of Λ in the sense of Lyapunov, we show that discretized versions of the dynamical system involving one-step numerical methods have nearby attracting sets Λ(h), which are also uniformly asymptotically stable. Our proof uses the properties of a Lyapunov function which characterizes the stability of Λ
An Eulerian Approach to the Analysis of Krause's Consensus Models
Abstract. In this paper we analyze a class of multi-agent consensus dynamical systems inspired by Krause’s original model. As in Krause’s, the basic assumption is the so-called bounded confidence: two agents can influence each other only when their state values are below a given distance threshold R. We study the system under an Eulerian point of view considering (possibly continuous) probability distributions of agents and we present original convergence results. The limit distribution is always necessarily a convex combination of delta functions at least R far apart from each other: in other terms these models are locally aggregating. The Eulerian perspective provides the natural framework for designing a numerical algorithm, by which we obtain several simulations in 1 and 2 dimensions
Influence of the quantum zero-point motion of a vortex on the electronic spectra of s-wave superconductors
We compute the influence of the quantum zero-point motion of a vortex on the
electronic quasiparticle spectra of s-wave superconductors. The vortex is
assumed to be pinned by a harmonic potential, and its coupling to the
quasiparticles is computed in the framework of BCS theory. Near the core of the
vortex, the motion leads to a shift of spectral weight away from the chemical
potential, and thereby reduces the zero bias conductance peak; additional
structure at the frequency of the harmonic trap is also observed.Comment: 14 pages, 7 figures; (v2) added refs; (v3) removed discussion on
d-wave superconductors and moved it to cond-mat/060600
Magnetoelectric properties of [FeCl(HO)] with K, Rb, Cs
The compounds [FeCl(HO)] with K, Rb, Cs are identified as
new linear magnetoelectric materials. We present a detailed investigation of
their linear magnetoelectric properties by measurements of pyroelectric
currents, dielectric constants and magnetization. The anisotropy of the linear
magnetoelectric effect of the K-based and Rb-based compound is consistent with
the magnetic point group , already reported in literature. A symmetry
analysis of the magnetoelectric effect of the Cs-based compound allows to
determine the magnetic point group and to develop a model for its
magnetic structure. In addition, magnetic-field versus temperature phase
diagrams are derived and compared to the closely related multiferroic
(NH)[FeCl(HO)].Comment: 17 pages, 10 figures (updated to the weakly revised version that has
been accepted for publication
On the Cholesky Decomposition for electron propagator methods: General aspects and application on C60
To treat the electronic structure of large molecules by electron propagator
methods we developed a parallel computer program called P-RICD. The
program exploits the sparsity of the two-electron integral matrix by using
Cholesky decomposition techniques. The advantage of these techniques is that
the error introduced is controlled only by one parameter which can be chosen as
small as needed. We verify the tolerance of electron propagator methods to the
Cholesky decomposition threshold and demonstrate the power of the
P-RICD program for a representative example (C60). All decomposition
schemes addressed in the literature are investigated. Even with moderate
thresholds the maximal error encountered in the calculated electron affinities
and ionization potentials amount to a few meV only, and the error becomes
negligible for small thresholds.Comment: 30 pages, 6 figures submitted to J.Chem. Phy
Impact of Interatomic Electronic Decay Processes on Xe 4d Hole Decay in the Xenon Fluorides
A hole in a 4d orbital of atomic xenon relaxes through Auger decay after a
lifetime of 3 fs. Adding electronegative fluorine ligands to form xenon
fluoride molecules, results in withdrawal of valence-electron density from Xe.
Thus, within the one-center picture of Auger decay, a lowered Xe 4d Auger width
would be expected, in contradiction, however, with experiment. Employing
extensive ab initio calculations within the framework of many-body Green's
functions, we determine all available decay channels in XeFn and characterize
these channels by means of a two-hole population analysis. We derive a relation
between two-hole population numbers and partial Auger widths. On this basis,
interatomic electronic decay processes are demonstrated to be so strong in the
xenon fluorides that they overcompensate the reduction in intra-atomic Auger
width and lead to the experimentally observed trend. The nature of the relevant
processes is discussed. These processes presumably underlie Auger decay in a
variety of systems.Comment: 11 pages, 5 figures, 3 tables, RevTeX4, extensively revised, the
discussion of single ionization of XeFn was published separately: J. Chem.
Phys. 119, 7763--7771 (2003), preprint arXiv: physics/030612
Effects of boundary conditions on the critical spanning probability
The fractions of samples spanning a lattice at its percolation threshold are
found by computer simulation of random site-percolation in two- and
three-dimensional hypercubic lattices using different boundary conditions. As a
byproduct we find in the cubic lattice.Comment: 8 pages Latex, To appear in Int. J. Mod. Phys.
Anisotropy study of multiferroicity in the pyroxene NaFeGeO
We present a study of the anisotropy of the dielectric, magnetic and
magnetoelastic properties of the multiferroic clinopyroxene NaFeGeO.
Pyroelectric currents, dielectric constants and magnetic susceptibilities as
well as the thermal expansion and the magnetostriction were examined on large
synthetic single crystals of NaFeGeO. The spontaneous electric
polarization detected below K in an
antiferromagnetically ordered state ( K) is mainly lying
within the plane with a small component along , indicating a triclinic
symmetry of the multiferroic phase of NaFeGeO. The electric
polarization can be strongly modified by applying magnetic fields along
different directions. We derive detailed magnetic-field versus temperature
phase diagrams and identify three multiferroic low-temperature phases, which
are separated by a non-ferroelectric, antiferromagnetically ordered state from
the paramagnetic high-temperature phase.Comment: 14 pages, 8 figures. (minor modifications and corrections of the
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