697 research outputs found
A note on the polynomial approximation of vertex singularities in the boundary element method in three dimensions
We study polynomial approximations of vertex singularities of the type on three-dimensional surfaces. The analysis focuses on the case when . This assumption is a minimum requirement to guarantee that the above singular function is in the energy space for boundary integral equations with hypersingular operators. Thus, the approximation results for such singularities are needed for the error analysis of boundary element methods on piecewise smooth surfaces. Moreover, to our knowledge, the approximation of strong singularities () by high-order polynomials is missing in the existing literature. In this note we prove an estimate for the error of polynomial approximation of the above vertex singularities on quasi-uniform meshes discretising a polyhedral surface. The estimate gives an upper bound for the error in terms of the mesh size and the polynomial degree
On the convergence of the hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces
In this paper the hp-version of the boundary element method is applied to the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. The underlying meshes are supposed to be quasi-uniform. We use \bH(\div)-conforming discretisations with quadrilateral elements of Raviart-Thomas type and establish quasi-optimal convergence of hp-approximations. Main ingredient of our analysis is a new \tilde\bH^{-1/2}(\div)-conforming p-interpolation operator that assumes only \bH^r\cap\tilde\bH^{-1/2}(\div)-regularity () and for which we show quasi-stability with respect to polynomial degrees
Mismatch of conductivity anisotropy in the mixed and normal states of type-II superconductors
We have calculated the Bardeen-Stephen contribution to the vortex viscosity
for uniaxial anisotropic superconductors within the time-dependent
Ginzburg-Landau (TDGL) theory. We focus our attention on superconductors with a
mismatch of anisotropy of normal and superconducting characteristics. Exact
asymptotics for the Bardeen-Stephen contribution have been derived in two
limits: the cases of small and large electric field penetration depth (as
compared to the coherence length). Also we suggest a variational procedure
which allows us to calculate the vortex viscosity for superconductors with
arbitrary ratio of the coherence lenght to the electric field penetration
depth. The approximate analytical result is compared with numerical
calculations. Finally, using a generalized TDGL theory, we prove that the
viscosity anisotropy and, thus, the flux-flow conductivity anisotropy may
depend on temperature.Comment: 11 pages, 3 figures; typos corrected in Figs. 2 and
Weak Projections onto a Braided Hopf Algebra
We show that, under some mild conditions, a bialgebra in an abelian and
coabelian braided monoidal category has a weak projection onto a formally
smooth (as a coalgebra) sub-bialgebra with antipode; see Theorem 1.12. In the
second part of the paper we prove that bialgebras with weak projections are
cross product bialgebras; see Theorem 2.12. In the particular case when the
bialgebra is cocommutative and a certain cocycle associated to the weak
projection is trivial we prove that is a double cross product, or biproduct
in Madjid's terminology. The last result is based on a universal property of
double cross products which, by Theorem 2.15, works in braided monoidal
categories. We also investigate the situation when the right action of the
associated matched pair is trivial
Band structure of magnetic excitations in the vortex phase of a ferromagnetic superconductor
International audienceMagnetic excitations in a ferromagnetic superconductor in the presence of an Abrikosov vortex lattice have been studied using the phenomenological London and Landau-Lifshitz equations. Due to the periodicity of the vortex field the magnon spectrum has a band structure, similar to the structure of the electon spectrum in a crystal lattice. The gaps between adjacent bands have been calculated using an analog of the weak-binding approximation. When the applied magnetic field is altered the band structure undergoes a qualitative transformation due to commensurability effects, connected with the nonmonotonicity of the magnon spectrum in the Meissner state. In dirty samples the energy gaps may be smeared out because of the dissipation connected with vortex motion. In sufficiently clean samples the gaps manifest themselves as maxima in the frequency dependence of the microwave reflectivity coefficient
Modulational instability in nonlocal Kerr-type media with random parameters
Modulational instability of continuous waves in nonlocal focusing and
defocusing Kerr media with stochastically varying diffraction (dispersion) and
nonlinearity coefficients is studied both analytically and numerically. It is
shown that nonlocality with the sign-definite Fourier images of the medium
response functions suppresses considerably the growth rate peak and bandwidth
of instability caused by stochasticity. Contrary, nonlocality can enhance
modulational instability growth for a response function with negative-sign
bands.Comment: 6 pages, 12 figures, revTeX, to appear in Phys. Rev.
Two dimensional modulational instability in photorefractive media
We study theoretically and experimentally the modulational instability of
broad optical beams in photorefractive nonlinear media. We demonstrate the
impact of the anisotropy of the nonlinearity on the growth rate of periodic
perturbations. Our findings are confirmed by experimental measurements in a
strontium barium niobate photorefractive crystal.Comment: 8 figure
Modulational instability and nonlocality management in coupled NLS system
The modulational instability of two interacting waves in a nonlocal Kerr-type
medium is considered analytically and numerically. For a generic choice of wave
amplitudes, we give a complete description of stable/unstable regimes for zero
group-velocity mismatch. It is shown that nonlocality suppresses considerably
the growth rate and bandwidth of instability. For nonzero group-velocity
mismatch we perform a geometrical analysis of a nonlocality management which
can provide stability of waves otherwise unstable in a local medium.Comment: 15 pages, 12 figures, to be published in Physica Script
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