Structural features of the self-action dynamics of ultrashort electromagnetic pulses

Self-focusing dynamics of electromagnetic pulses of arbitrary duration is analyzed numerically and analytically. The wave-field evolution is considered by the wave equation in the reflectionless approximation under quite general assumptions about the dispersion of the medium. Methods for qualitative investigation of the self-focusing dynamics of quasimonochromatic radiation are generalized to the case of wave packets with the length of a few oscillation periods. In particular, sufficient conditions for collapse and many other integral relations are obtained by the momentum method. A self-similar-type transformation is used to show that new structural features are primarily associated with the nonlinear dispersion of the medium (with the dependence of the group velocity of a wave packet on its amplitude). Numerical analysis confirms that the self-focusing of radiation is preceded by an increase in the steepness of the longitudinal profile.     

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.     

Special operator equations

The study addresses the matrix operator equations of a special form which are used in the theory of Markov chains. Solving the operator equations with stochastic transition probability matrices of large finite or even countably infinite size reduces to the case of stochastic matrices of small size. In particular, the case of ternary chains is considered in detail. A Markov model for crack growth in a composite serves as an example of application.     

Capture of excess electrons by triplet-state anthracene molecules in liquid isooctane

Conclusions Rate constants for the reaction of the excess electron with electronically excited acceptor molecules in liquid hydrocarbons have been obtained for the first time through direct measurements.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 5, pp. 989–992, May, 1979.     

Optical metrics and birefringence of anisotropic media

The material tensor of linear response in electrodynamics is constructed out of products of two symmetric second rank tensor fields which in the approximation of geometrical optics and for uniaxial symmetry reduce to “optical” metrics, describing the phenomenon of birefringence. This representation is interpreted in the context of an underlying internal geometrical structure according to which the symmetric tensor fields are vectorial elements of an associated two-dimensional space.     

Non-minimal pp-wave Einstein–Yang–Mills–Higgs model: color cross-effects induced by curvature

Non-minimal interactions in the pp-wave Einstein–Yang–Mills–Higgs (EYMH) model are shown to give rise to color cross-effects analogous to the magneto-electricity in the Maxwell theory. In order to illustrate the significance of these color cross-effects, we reconstruct the effective (associated, color, and color-acoustic) metrics for the pp-wave non-minimal seven-parameter EYMH model with parallel gauge and scalar background fields. Then these metrics are used as hints for obtaining explicit exact solutions of the non-minimally extended Yang–Mills and Higgs equations for the test fields propagating in the vacuum interacting with curvature. The influence of the non-minimal coupling on the test particle motion is interpreted in terms of the so-called trapped surfaces, introduced in the Analog Gravity theory.     

On self-focusing of an ultrashort intense relativistic laser pulse in a plasma

The development of the spatiotemporal (filamentation) instability of a laser pulse upon excitation of a plasma wave is studied numerically and analytically. It is shown that first, as in a medium with inertialless cubic nonlinearity, the filamentation of radiation occurs and then filaments are attracted to each other. The following evolution differs weakly from the evolution of a smoothed wave beam in a medium with inertial nonlinear response.