Higher Order Effects in the Dielectric Constant of Percolative Metal-Insulator Systems above the Critical Point

The dielectric constant of a conductor-insulator mixture shows a pronounced maximum above the critical volume concentration. Further experimental evidence is presented as well as a theoretical consideration based on a phenomenological equation. Explicit expressions are given for the position of the maximum in terms of scaling parameters and the (complex) conductances of the conductor and insulator. In order to fit some of the data, a volume fraction dependent expression for the conductivity of the more highly conductive component is introduced.Comment: 4 pages, Latex, 4 postscript (*.epsi) files submitted to Phys Rev.

Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities

Since the kinetic and the potential energy term of the real time nonlinear Schr\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where $k_{max}=\pi/\Delta x$.Comment: 10 pages, 8 figures, submitted to Phys. Rev.

Any-order propagation of the nonlinear Schroedinger equation

We derive an exact propagation scheme for nonlinear Schroedinger equations. This scheme is entirely analogous to the propagation of linear Schroedinger equations. We accomplish this by defining a special operator whose algebraic properties ensure the correct propagation. As applications, we provide a simple proof of a recent conjecture regarding higher-order integrators for the Gross-Pitaevskii equation, extend it to multi-component equations, and to a new class of integrators.Comment: 10 pages, no figures, submitted to Phys. Rev.

Wide-angle perfect absorber/thermal emitter in the THz regime

We show that a perfect absorber/thermal emitter exhibiting an absorption peak of 99.9% can be achieved in metallic nanostructures that can be easily fabricated. The very high absorption is maintained for large angles with a minimal shift in the center frequency and can be tuned throughout the visible and near-infrared regime by scaling the nanostructure dimensions. The stability of the spectral features at high temperatures is tested by simulations using a range of material parameters.Comment: Submitted to Phys. Rev. Let

Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping

Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the symplectic structure in the case $\epsilon=0$. In the case $0<\epsilon\ll 1$ the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3--D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order

Can Euroscepticism Contribute to a European Public Sphere? The Europeanization of Media Discourses about Euroscepticism across Six Countries

This study compares the media discourses about Euroscepticism in 2014 across six countries (United Kingdom, Ireland, France, Spain, Sweden, and Denmark). We assess the extent to which the mass media's reporting of Euroscepticism indicates the Europeanization of public spheres. Using a mixed-methods approach combining LDA topic modeling and qualitative coding, we find that approximately 70 per cent of print articles mentioning "Euroscepticism" or "Eurosceptic" are framed in a non-domestic (i.e. European) context. In five of the six cases studied, articles exhibiting a European context are strikingly similar in content, with the British case as the exception. However, coverage of British Euroscepticism drives Europeanization in other Member States. Bivariate logistic regressions further reveal three macro-level structural variables that significantly correlate with a Europeanized media discourse: newspaper type (tabloid or broadsheet), presence of a strong Eurosceptic party, and relationship to the EU budget (net contributor or receiver of EU funds).Comment: 29 pages, 2 figures, 4 tables, 2 appendice

Enhanced dispersion interaction in confined geometry

The dispersion interaction between two point-like particles confined in a dielectric slab between two plates of another dielectric medium is studied within a continuum (Lifshitz) theory. The retarded (Casimir-Polder) interaction at large inter-particle distances is found to be strongly enhanced as the mismatch between the dielectric permittivities of the two media is increased. The large-distance interaction is multiplied due to confinement by a factor of $(33\gamma^{5/2}+13\gamma^{-3/2})/46$ at zero temperature, and by $(5\gamma^2+\gamma^{-2})/6$ at finite temperature, \gamma=\ein(0)/\eout(0) being the ratio between the static dielectric permittivities of the inner and outer media. This confinement-induced amplification of the dispersion interaction can reach several orders of magnitude.Comment: 4 page