201 research outputs found
A quasilinear transmission problem with application to Maxwell equations with a divergence-free D-field
Maxwell equations in the absence of free charges require initial data with a divergence-free displacement field D. In materials in which the dependence D=D(E) is nonlinear the quasilinear problem 07 c5D(E)=0 is hence to be solved. In many applications, e.g. in the modelling of wave packets, an approximative asymptotic ansatz of the electric field E is used, which satisfies this divergence condition at t=0 only up to a small residual. We search then for a small correction of the ansatz to enforce 07 c5D(E)=0 at t=0 and choose this correction in the form of a gradient field. In the usual case of a power type nonlinearity in D(E) this leads to the sum of the Laplace and p-Laplace operators. We also allow for the medium to consist of two different materials so that a transmission problem across an interface is produced. We prove the existence of the correction term for a general class of nonlinearities and provide regularity estimates for its derivatives, independent of the L2-norm of the original ansatz. In this way, when applied to the wave packet setting, the correction term is indeed asymptotically smaller than the original ansatz. We also provide numerical experiments to support our analysis
Surface Gap Soliton Ground States for the Nonlinear Schr\"{o}dinger Equation
We consider the nonlinear Schr\"{o}dinger equation , with and and with periodic in each coordinate direction. This problem
describes the interface of two periodic media, e.g. photonic crystals. We study
the existence of ground state solutions (surface gap soliton ground
states) for . Using a concentration compactness
argument, we provide an abstract criterion for the existence based on ground
state energies of each periodic problem (with and ) as well as a more practical
criterion based on ground states themselves. Examples of interfaces satisfying
these criteria are provided. In 1D it is shown that, surprisingly, the criteria
can be reduced to conditions on the linear Bloch waves of the operators
and .Comment: definition of ground and bound states added, assumption (H2) weakened
(sign changing nonlinearity is now allowed); 33 pages, 4 figure
Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential
We address a two-dimensional nonlinear elliptic problem with a
finite-amplitude periodic potential. For a class of separable symmetric
potentials, we study the bifurcation of the first band gap in the spectrum of
the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to
describe this bifurcation. The coupled-mode equations are derived by the
rigorous analysis based on the Fourier--Bloch decomposition and the Implicit
Function Theorem in the space of bounded continuous functions vanishing at
infinity. Persistence of reversible localized solutions, called gap solitons,
beyond the coupled-mode equations is proved under a non-degeneracy assumption
on the kernel of the linearization operator. Various branches of reversible
localized solutions are classified numerically in the framework of the
coupled-mode equations and convergence of the approximation error is verified.
Error estimates on the time-dependent solutions of the Gross--Pitaevskii
equation and the coupled-mode equations are obtained for a finite-time
interval.Comment: 32 pages, 16 figure
Temperature dependence of binary and ternary recombination of D-3(+) ions with electrons
Flowing and stationary afterglow experiments were performed to study the recombination of D-3(+) ions with electrons at temperatures from 77 to 300 K. A linear dependence of apparent (effective) binary recombination rate coefficients on the pressure of the helium buffer gas was observed. Binary (D-3(+)+e(-)) and ternary (D-3(+)+e(-)+He) recombination rate coefficients were derived. The obtained binary rate coefficient agrees with recent theoretical values for dissociative recombination of D-3(+). We describe the observed ternary process by a mechanism with two rate determining steps. In the first step, a rotationally excited long-lived neutral D-3* is formed in D-3(+)-e(-) collisions. As the second step, the D-3* collides with a helium atom that prevents autoionization of D-3*. We calculate lifetimes of D-3* formed from ortho-, para-, or metastates of D-3(+) and use the lifetimes to calculate ternary recombination rate coefficients
Temperature dependence of binary and ternary recombination of H3+ ions with electron
We study binary and the recently discovered process of ternary He-assisted
recombination of H3+ ions with electrons in a low temperature afterglow plasma.
The experiments are carried out over a broad range of pressures and
temperatures of an afterglow plasma in a helium buffer gas. Binary and
He-assisted ternary recombination are observed and the corresponding
recombination rate coefficients are extracted for temperatures from 77 K to 330
K. We describe the observed ternary recombination as a two-step mechanism:
First, a rotationally-excited long-lived neutral molecule H3* is formed in
electron-H3+ collisions. Second, the H3* molecule collides with a helium atom
that leads to the formation of a very long-lived Rydberg state with high
orbital momentum. We present calculations of the lifetimes of H3* and of the
ternary recombination rate coefficients for para and ortho-H3+. The
calculations show a large difference between the ternary recombination rate
coefficients of ortho- and para-H3+ at temperatures below 300 K. The measured
binary and ternary rate coefficients are in reasonable agreement with the
calculated values.Comment: 15 page
Temperature dependence of binary and ternary recombination of H3+ ions with electron
We study binary and the recently discovered process of ternary He-assisted
recombination of H3+ ions with electrons in a low temperature afterglow plasma.
The experiments are carried out over a broad range of pressures and
temperatures of an afterglow plasma in a helium buffer gas. Binary and
He-assisted ternary recombination are observed and the corresponding
recombination rate coefficients are extracted for temperatures from 77 K to 330
K. We describe the observed ternary recombination as a two-step mechanism:
First, a rotationally-excited long-lived neutral molecule H3* is formed in
electron-H3+ collisions. Second, the H3* molecule collides with a helium atom
that leads to the formation of a very long-lived Rydberg state with high
orbital momentum. We present calculations of the lifetimes of H3* and of the
ternary recombination rate coefficients for para and ortho-H3+. The
calculations show a large difference between the ternary recombination rate
coefficients of ortho- and para-H3+ at temperatures below 300 K. The measured
binary and ternary rate coefficients are in reasonable agreement with the
calculated values.Comment: 15 page
Continuation for thin film hydrodynamics and related scalar problems
This chapter illustrates how to apply continuation techniques in the analysis
of a particular class of nonlinear kinetic equations that describe the time
evolution through transport equations for a single scalar field like a
densities or interface profiles of various types. We first systematically
introduce these equations as gradient dynamics combining mass-conserving and
nonmass-conserving fluxes followed by a discussion of nonvariational amendmends
and a brief introduction to their analysis by numerical continuation. The
approach is first applied to a number of common examples of variational
equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including
certain thin-film equations for partially wetting liquids on homogeneous and
heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal
equations. Second we consider nonvariational examples as the
Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard
equations and thin-film equations describing stationary sliding drops and a
transversal front instability in a dip-coating. Through the different examples
we illustrate how to employ the numerical tools provided by the packages
auto07p and pde2path to determine steady, stationary and time-periodic
solutions in one and two dimensions and the resulting bifurcation diagrams. The
incorporation of boundary conditions and integral side conditions is also
discussed as well as problem-specific implementation issues
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Improved Constraints on Sterile Neutrino Mixing from Disappearance Searches in the MINOS, MINOS+, Daya Bay, and Bugey-3 Experiments.
Searches for electron antineutrino, muon neutrino, and muon antineutrino disappearance driven by sterile neutrino mixing have been carried out by the Daya Bay and MINOS+ collaborations. This Letter presents the combined results of these searches, along with exclusion results from the Bugey-3 reactor experiment, framed in a minimally extended four-neutrino scenario. Significantly improved constraints on the Ξ_{ÎŒe} mixing angle are derived that constitute the most constraining limits to date over five orders of magnitude in the mass-squared splitting Îm_{41}^{2}, excluding the 90% C.L. sterile-neutrino parameter space allowed by the LSND and MiniBooNE observations at 90% CL_{s} for Îm_{41}^{2}<13ââeV^{2}. Furthermore, the LSND and MiniBooNE 99% C.L. allowed regions are excluded at 99% CL_{s} for Îm_{41}^{2}<1.6âeV^{2}
A comparison of the neuroprotective efficacy of newly developed oximes (K117, K127) and currently available oxime (obidoxime) in tabun-poisoned rats
The potency of newly developed bispyridinium compounds (K117, K127) to reduce tabun-induced acute neurotoxic signs and symptoms was compared with currently available oxime (obidoxime) using functional observational battery. The neuroprotective effects of atropine alone and atropine combined with one of three bispyridinium oximes (K117, K127, obidoxime) on rats poisoned with tabun at a sublethal dose (180 ÎŒg/kg i.m.; 80% of LD50 value) were studied. Tabun-induced neurotoxicity was monitored using a functional observational battery and automatic measurement of motor activity at 24 h following tabun challenge. The results indicated that all tested oximes combined with atropine enabled tabun-poisoned rats to survive 24 h following tabun challenge while one tabun-poisoned rats died within 24 h after tabun poisoning when the rats were treated with atropine alone. Newly developed oxime K127 combined with atropine was the most effective in decreasing tabun-induced neurotoxicity in the case of sublethal poisonings among all oximes tested. Nevertheless, the differences of neuroprotective efficacy between K127 and obidoxime are not sufficient to replace obidoxime by K127 for the treatment of acute tabun poisonings
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