Relaxation to Intermediate Attractors in Nonlinear Wave Equations

We study the dynamics of nonlinear wave equations near the threshold of singularity formation, motivated by some unexpected features observed in the critical gravitational collapse. One of the features, the existence of a universal intermediate attractor in the dynamics at the threshold of singularity formation, is studied in more detail. The result is a scheme of the evolution: for all initial data sufficiently near the threshold, the solutions reach one universal static solution, which plays the role of an intermediate attractor. The solutions remain near the attractor for some time, which scales in a simple way with a parameter of the initial data, and then departs in one of two opposite directions, eventually forming a singularity or dispersing. The relaxation as well as the departure from the attractor is governed in the linear approximation by quasi-normal modes (QNMs) and one growing mode. Moreover, the profiles of the perturbation modes with their oscillation frequencies and damping or amplifying factors, calculated as eigenvalue problems (linear ODEs) have been observed in numerical evolution (nonlinear PDEs). In particular, the exponent of the growing mode determines the lifetime of the intermediate dynamics (near the attractor), and a few least damped QNMs have been observed as ringing in the relaxation process.     

On the behavior of the cathodically polarized Pd/D system: Search for emanating radiation

Evidence for the emission of low intensity X-rays during cathodic polarization of the Pd/D system(s) is presented. The Pd/D system was prepared by charging with electrochemically generated deuterium either palladium foil or palladium electrodeposited from D₂O electrolytes. Experimental and analytical procedures are described in detail.     

Asymptotics from Scaling for Nonlinear Wave Equations

We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the late-time behavior of solutions of the nonlinear problem in timelike and null directions.     

Spontaneous particle creation within the external field approximation of QED

It is expected that strong electromagnetic fields in QED may lead to destabilization of the vacuum, its decay and spontaneous production of an electron-positron pair if the strength of the electric field exceeds some threshold. We study the problem within an external field approximation of QED in presence of time-dependent external fields and define the spontaneous particle creation via the adiabatic limit. We consider some model fields, which we solve analytically or numerically, in order to explain the subtlety of the effect and to recognize problems appearing in its proof. We conclude by characterizing when the effect can exist in a stable way and when it becomes unstable w.r.t. small perturbations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spontaneous emission of light from atoms: the model

We investigate (non‐relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two‐level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal‐coupling Hamiltonian, with the A² term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra‐type equation which governs the time evolution of the amplitude of the excited state. The two‐point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.     

The effect of an external electric field on surface morphology of co-deposited Pd/D films

The polarized PdD electrode undergoes significant morphological changes when exposed to an external electric field. These changes range from minor, e.g. re-orientation and/or separation of weakly connected globules, through forms that result from a combined action of the field as well as that connected with the evolution of gaseous deuterium, to shapes that require substantial energy expenditure.     

Thermal behavior of polarized Pd/D electrodes prepared by co-deposition

Thermal behavior of polarized Pd/D electrode, prepared by the co-deposition technique, serving as a cathode in the Dewar-type electrochemical cell/calorimeter is examined. It is shown that: (i) excess enthalpy is generated during and after the completion of the co-deposition process; (ii) rates of excess enthalpy generation are somewhat higher than when Pd wires or other forms of Pd electrodes are used; (iii) positive feedback and heat-after-death effects were observed; and (iv) rates of excess power generation were found to increase with an increase in both cell current and cell temperature, the latter being higher.     

Global Pointwise Decay Estimates for Defocusing Radial Nonlinear Wave Equations

We prove global pointwise decay estimates for a class of defocusing semilinear wave equations in n = 3 dimensions restricted to spherical symmetry. The technique is based on a conformal transformation and a suitable choice of the mapping adjusted to the nonlinearity. As a result we obtain a pointwise bound on the solutions for arbitrarily large Cauchy data, provided the solutions exist globally. The decay rates are identical with those for small data and hence seem to be optimal. A generalization beyond the spherical symmetry is suggested.