Density Profiles in a Quantum Coulomb Fluid Near a Hard Wall

Journal of Statistical Physics - Equilibrium particle densities near a hard wall are studied for a quantum fluid made of point charges which interact via Coulomb potential without any...     

Existence and convergence for quasi‐static evolution in brittle fracture

This paper investigates the mathematical well‐posedness of the variational model of quasi‐static growth for a brittle crack proposed by Francfort and Marigo in [15]. The starting point is a time discretized version of that evolution which results in a sequence of minimization problems of Mumford and Shah type functionals. The natural weak setting is that of special functions of bounded variation, and the main difficulty in showing existence of the time‐continuous quasi‐static growth is to pass to the limit as the time‐discretization step tends to 0. This is performed with the help of a jump transfer theorem which permits, under weak convergence assumptions for a sequence {u_n} of SBV‐functions to its BV‐limit u, to transfer the part of the jump set of any test field that lies in the jump set of u onto that of the converging sequence {u_n}. In particular, it is shown that the notion of minimizer of a Mumford and Shah type functional for its own jump set is stable under weak convergence assumptions. Furthermore, our analysis justifies numerical methods used for computing the time‐continuous quasi‐static evolution. © 2003 Wiley Periodicals, Inc.     

Limit Regimes of Braking of Disc-Type Composite Flywheels Made by Filament Winding

A set of invariants describing the limit regimes of braking disk-type wound composite flywheels is suggested. The limit regime is determined by using a linear failure criterion. It is shown that, for generating short-time impulses of very high power, a set of small identical flywheels is more effective than one large flywheel with an equivalent mass. Particular examples illustrating the theory considered are discussed.     

Nonlinear electrohydrodynamic instability of a finitely conducting cylinder: Effect of interfacial surface charges

The nonlinear electrohydrodynamic stability of cylindrical interface, supporting surface charge, among two conducting fluids is investigated. The two fluids are subjected to a radial electric field. The analysis based on the multiple scale technique. It is shown that the evolution of the amplitude is governed by two partial differential equations. These equations are combined to yield two alternate Schrödinger equations with cubic nonlinearity. One of which calculates the nonlinear cutoff electric field, separating stable and unstable disturbances, while the other is used to analyze the stability of the system. The stability criteria are analytically discussed and numerically confirmed. Numerical calculations resulted in set of graphs to indicate the stability picture of the considered system.     

First order dynamic inclusions on time scales

In this paper, we study existence of solutions of first order dynamic inclusions on time scales with general boundary conditions. Both the ∇-derivative and Δ-derivative cases are considered. Examples are presented to illustrate that the Δ-derivative case needs more restrictive assumptions.     

Furtivity and Masking Problems in Time-Dependent Electromagnetic Obstacle Scattering

In this paper, we consider furtivity and masking problems in time-dependent three-dimensional electromagnetic obstacle scattering. That is, we propose a criterion based on a merit function to minimize or to mask the electromagnetic field scattered by a bounded obstacle when hit by an incoming electromagnetic field and, with respect to this criterion, we drive the optimal strategy. These problems are natural generalizations to the context of electromagnetic scattering of the furtivity problem in time-dependent acoustic obstacle scattering presented in Ref. 1. We propose mathematical models of the furtivity and masking time-dependent three-dimensional electromagnetic scattering problems that consist in optimal control problems for systems of partial differential equations derived from the Maxwell equations. These control problems are approached using the Pontryagin maximum principle. We formulate the first-order optimality conditions for the control problems considered as exterior problems defined outside the obstacle for systems of partial differential equations. Moreover, the first-order optimality conditions derived are solved numerically with a highly parallelizable numerical method based on a perturbative series of the type considered in Refs. 2–3. Finally, we assess and validate the mathematical models and the numerical method proposed analyzing the numerical results obtained with a parallel implementation of the numerical method in several experiments on test problems. Impressive speedup factors are obtained executing the algorithms on a parallel machine when the number of processors used in the computation ranges between 1 and 100. Some virtual reality applications and some animations relative to the numerical experiments can be found in the website http://www.econ.unian.it/recchioni/w10/.     

Ground state parameters of BiH3 from infrared and millimeter-wave spectra: ground state and equilibrium structures

Unstable, short-lived BiH₃ has been synthesized and investigated by rotational spectroscopy in the range 158 (J=1-0) to 1280 GHz (J=8-7). Quadrupole and spin-rotation hyperfine structures (eQq=584.676(96) MHz), and the A₁A₂ splitting of the K=3 ground state level, have been resolved. By merging the pure rotational data with 1764 ground state combination differences obtained from the analysis of high resolution Fourier transform infrared spectra of the ν₁-ν₄ bands [J. Mol. Spectrosc. (2004) (in press)] spanning J and K values up to 16 and 14, respectively, with 0?ΔK?9, the ground state rotational and centrifugal distortion constants up to octic and sextic terms for reductions A and B, respectively, have been determined. Of the reductions of the ground state rovibrational Hamiltonian, reduction B including ε rather than h₃ as off-diagonal element is clearly favored. An experimental r₀ structure of the very-near spherical oblate symmetric top BiH₃, r(BiH)=178.82 pm and α(HBiH)=90.320°, has been deduced from the rotational constants B₀=2.64160172(18) and C₀=2.6010403(31) cm⁻¹. The derived experimental r_e structure, r_e(BiH)=177.834(50) pm and α_e(HBiH)=90.321(10)°, was determined. This is in excellent agreement with the most recent ab initio structure, r_e(BiH)=177.84 pm, and α_e(HBiH)=90.12°.     

Photoluminescence of Ge(Si)/Si(0 0 1) self-assembled islands in the near infra-red wavelength range

The dependence of photoluminescence spectra of structures with GeSi/Si(0 0 1) self-assembled nanoislands on growth temperature has been investigated. It was shown that the redshift of the island-related photoluminescence peak with a decrease of the growth temperature is associated with suppression of Si diffusion in the islands and an increase of Ge content in them. For the first time a photoluminescence signal from SiGe islands was observed at energies much lower than the Ge band gap. The energy position of the island-related photoluminescence peak is well described by the model of optical transition, which is indirect in real space. The photoluminescence signal at 1.55 μm from GeSi/Si(0 0 1) self-assembled islands was obtained up to room temperature.