515 research outputs found
Numerical solution and spectrum of boundary-domain integral equation for the Neumann BVP with variable coefficient
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 Taylor & Francis.In this paper, a numerical implementation of a direct united boundary-domain integral equation (BDIE) related to the Neumann boundary value problem for a scalar elliptic partial differential equation with a variable coefficient is discussed. The BDIE is reduced to a uniquely solvable one by adding an appropriate perturbation operator. The mesh-based discretization of the BDIEs with quadrilateral domain elements leads to a system of linear algebraic equations (discretized BDIE). Then, the system is solved by LU decomposition and Neumann iterations. Convergence of the iterative method is discussed in relation to the distribution of eigenvalues of the corresponding discrete operators calculated numerically.The work was supported by the grant EP/H020497/1 "Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients" of the EPSRC, UK
Self-Induced Quasistationary Magnetic Fields
The interaction of electromagnetic radiation with temporally dispersive
magnetic solids of small dimensions may show very special resonant behaviors.
The internal fields of such samples are characterized by
magnetostatic-potential scalar wave functions. The oscillating modes have the
energy orthogonality properties and unusual pseudo-electric (gauge) fields.
Because of a phase factor, that makes the states single valued, a persistent
magnetic current exists. This leads to appearance of an eigen-electric moment
of a small disk sample. One of the intriguing features of the mode fields is
dynamical symmetry breaking
Bose-Einstein condensation in an optical lattice: A perturbation approach
We derive closed analytical expressions for the order parameter
and for the chemical potential of a Bose-Einstein Condensate loaded into
a harmonically confined, one dimensional optical lattice, for sufficiently
weak, repulsive or attractive interaction, and not too strong laser
intensities. Our results are compared with exact numerical calculations in
order to map out the range of validity of the perturbative analytical approach.
We identify parameter values where the optical lattice compensates the
interaction-induced nonlinearity, such that the condensate ground state
coincides with a simple, single particle harmonic oscillator wave function
On the Causality and Stability of the Relativistic Diffusion Equation
This paper examines the mathematical properties of the relativistic diffusion
equation. The peculiar solution which Hiscock and Lindblom identified as an
instability is shown to emerge from an ill-posed initial value problem. These
do not meet the mathematical conditions required for realistic physical
problems and can not serve as an argument against the relativistic
hydrodynamics of Landau and Lifshitz.Comment: 6 page
The anapole moments in disk-form MS-wave ferrite particle
The anapole moments describe the parity-violating parity-odd,
time-reversal-even couplings between elementary particles and the
electromagnetic (EM) field. Surprisingly, the anapole-like moment properties
can be found in certain artificially engineered physical systems. In
microwaves, ferrite resonators with multi-resonance magnetostatic-wave
(MS-wave) oscillations may have sizes two-four orders less than the free-space
EM wavelength at the same frequency. MS-wave oscillations in a ferrite sample
occupy a special place between the pure electromagnetic and spin-wave
(exchange) processes. The energy density of MS-wave oscillations is not the
electromagnetic-wave density of energy and not the exchange energy density as
well. These microscopic oscillating objects -- the particles -- may interact
with the external EM fields by a very specific way, forbidden for the classical
description. To describe such interactions, the quantum mechanical analysis
should be used. The presence of surface magnetic currents is one of the
features of MS oscillations in a normally magnetized ferrite disk resonator.
Because of such magnetic currents, MS oscillations in ferrite disk resonators
become parity violating. The parity-violating couplings between disk-form
ferrite particles and the external EM field should be analyzed based on the
notion of an anapole moment.Comment: 20 pages, 2 figures, PDF (created from MS-Word
Singular Modes of the Electromagnetic Field
We show that the mode corresponding to the point of essential spectrum of the
electromagnetic scattering operator is a vector-valued distribution
representing the square root of the three-dimensional Dirac's delta function.
An explicit expression for this singular mode in terms of the Weyl sequence is
provided and analyzed. An essential resonance thus leads to a perfect
localization (confinement) of the electromagnetic field, which in practice,
however, may result in complete absorption.Comment: 14 pages, no figure
Solid-state synthesis and characterization of ferromagnetic Mn5Ge3 nanoclusters in GeO/Mn thin films
Mn5Ge3 films are promising materials for spintronic applications due to their high spin polarization and a Curie temperature above room temperature. However, non-magnetic elements such as oxygen, carbon and nitrogen may unpredictably change the structural and magnetic properties of Mn5Ge3 films. Here, we use the solid-state reaction between Mn and GeO thin films to describe the synthesis and the structural and magnetic characterization of Mn5Ge3(Mn5Ge3Oy)-GeO2(GeOx) nanocomposite materials. Our results show that the synthesis of these nanocomposites starts at 180°С when the GeO decomposes into elemental germanium and oxygen and the resulting Ge atoms immediately migrate into the Mn layer to form ferromagnetic Mn5Ge3 nanoclusters. At the same time the oxygen atoms take part in the synthesis of GeOx and GeO2 oxides and also migrate into the Mn5Ge3 lattice to form Mn5Ge3Oy Nowotny nanoclusters. Magnetic analysis assumes the general nature of the Curie temperature increase in carbon-doped Mn5Ge3Cx and Mn5Ge3Oy films. Our findings prove that not only carbon, but oxygen may contribute to the increase of the saturation magnetization and Curie temperature of Mn5Ge3-based nanostructures
The Toulose limit of the Multi-Channel Kondo model.
We study the Toulouse limit of the multi-channel Kondo model defined as the
limit of maximal anisotropy which can be achieved without changing the infrared
behaviour of the model. It is shown that when the number of channels exceeds 2,
the interactions do not vanish and the Toulouse limit remains a non-trivial
field theory. Considerable simplifications take place only for k = 2, where the
Bethe ansatz reproduces the results by Emery and Kivelson.Comment: 10 pages, LaTex, a discussion about the magnetic properties is added
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