3,356 research outputs found
Analysis of segregated boundary-domain integral equations for mixed variable-coefficient BVPs in exterior domains
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Birkhäuser Boston.Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.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
Zero curvature representation for a new fifth-order integrable system
In this brief note we present a zero-curvature representation for one of the
new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.Comment: 2 pages, LaTeX 2e, no figure
Nonlinear electromagnetic response of graphene: Frequency multiplication and the self-consistent-field effects
Graphene is a recently discovered carbon based material with unique physical
properties. This is a monolayer of graphite, and the two-dimensional electrons
and holes in it are described by the effective Dirac equation with a vanishing
effective mass. As a consequence, electromagnetic response of graphene is
predicted to be strongly non-linear. We develop a quasi-classical kinetic
theory of the non-linear electromagnetic response of graphene, taking into
account the self-consistent-field effects. Response of the system to both
harmonic and pulse excitation is considered. The frequency multiplication
effect, resulting from the non-linearity of the electromagnetic response, is
studied under realistic experimental conditions. The frequency up-conversion
efficiency is analysed as a function of the applied electric field and
parameters of the samples. Possible applications of graphene in terahertz
electronics are discussed.Comment: 14 pages, 7 figures, invited paper written for a special issue of
JPCM "Terahertz emitters
Evolution of magnetic fields through cosmological perturbation theory
The origin of galactic and extra-galactic magnetic fields is an unsolved
problem in modern cosmology. A possible scenario comes from the idea of these
fields emerged from a small field, a seed, which was produced in the early
universe (phase transitions, inflation, ...) and it evolves in time.
Cosmological perturbation theory offers a natural way to study the evolution of
primordial magnetic fields. The dynamics for this field in the cosmological
context is described by a cosmic dynamo like equation, through the dynamo term.
In this paper we get the perturbed Maxwell's equations and compute the energy
momentum tensor to second order in perturbation theory in terms of gauge
invariant quantities. Two possible scenarios are discussed, first we consider a
FLRW background without magnetic field and we study the perturbation theory
introducing the magnetic field as a perturbation. The second scenario, we
consider a magnetized FLRW and build up the perturbation theory from this
background. We compare the cosmological dynamo like equation in both scenarios
Droplet motion driven by surface freezing or melting: A mesoscopic hydrodynamic approach
A fluid droplet may exhibit self-propelled motion by modifying the wetting
properties of the substrate. We propose a novel model for droplet propagation
upon a terraced landscape of ordered layers formed as a result of surface
freezing driven by the contact angle dependence on the terrace thickness.
Simultaneous melting or freezing of the terrace edge results in a joint
droplet-terrace motion. The model is tested numerically and compared to
experimental observations on long-chain alkane system in the vicinity of the
surface melting point.Comment: 4 pages, 3 figure
Vector, Axial, Tensor and Pseudoscalar Vacuum Susceptibilities
Using a recently developed three-point formalism within the method of QCD Sum
Rules we determine the vacuum susceptibilities needed in the two-point
formalism for the coupling of axial, vector, tensor and pseudoscalar currents
to hadrons. All susceptibilities are determined by the space-time scale of
condensates, which is estimated from data for deep inelastic scattering on
nucleons
Algebraic entropy for semi-discrete equations
We extend the definition of algebraic entropy to semi-discrete
(difference-differential) equations. Calculating the entropy for a number of
integrable and non integrable systems, we show that its vanishing is a
characteristic feature of integrability for this type of equations
Nonequilibrium orientational patterns in two-component Langmuir monolayers
A model of a phase-separating two-component Langmuir monolayer in the
presence of a photo-induced reaction interconvering two components is
formulated. An interplay between phase separation, orientational ordering and
treaction is found to lead to a variety of nonequilibrium self-organized
patterns, both stationary and traveling. Examples of the patterns, observed in
numerical simulations, include flowing droplets, traveling stripes, wave
sources and vortex defects.Comment: Submitted to the Physical Review
- …