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The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
We address several extremal problems concerning the spreading property of point sets of Steiner triple systems. This property is closely related to the structure of subsystems, as a set is spreading if and only if there is no proper…
We discuss the laser theory for a single-mode laser with nonlinear gain. We focus in particular on a micromaser which is pumped with a dilute beam of excited atoms crossing the laser cavity. In the weak-coupling regime, an expansion in the…
The principal angles between binary collision subspaces in an $N$-billiard system in $d$-dimensional Euclidean space are computed. These angles are computed for equal masses and arbitrary masses. We then provide a bound on the number of…
A survey of physical parameters and of a ladder of various regimes of laser-matter interactions at extreme intensities is given. Special emphases is made on three selected topics: (i) qualitative derivation of the scalings for probability…
We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period.…
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of…
In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where it can be noticed the diffraction of laser light in…
The radiation loss of small-amplitude radially symmetric oscillons (long-living, spatially localized, time-dependent solutions) in two- and three-dimensional scalar field theories is computed analytically in the small-amplitude expansion.…
We review the recent developments in the field of photonic lattices emphasizing their unique properties for controlling linear and nonlinear propagation of light. We draw some important links between optical lattices and photonic crystals…
Scattering measurements with incident linearly polarized $\gamma$ rays provide information on spins, parities, and $\gamma$-ray multipolarity mixing coefficients, and, therefore, on the nuclear matrix elements involved in the transitions.…
We demonstrate that SDYM equations for the Lie algebra of one-dimensional vector fields represent a natural reduction in the framework of general linearly degenerate dispersionless hierarchy. We define the reduction in terms of wave…
We discuss the main features of a new optical system capable of laser action: the active complex optical network, or lasing network (LANER). The system is experimentally realized with optical fibers linked each other with suitable optical…
We introduce a new dynamical system that we call "tiling billiards," where trajectories refract through planar tilings. This system is motivated by a recent discovery of physical substances with negative indices of refraction. We…
Normal broadband lasers with collinear polychromatic components have immense potential for mitigating laser plasma instabilities (LPIs). However, the projection complexity of collinear polychromatic light (CPL) is a significant challenge…
Linear systems under the influence of nonlinear and random linear perturbations, and with random initial and boundary conditions, are discussed. The notion of states of a system is substituted by the notion of the generating vectors for…
We study coherent backscattering of a monochromatic laser by a dilute gas of cold two-level atoms in the weakly nonlinear regime. The nonlinear response of the atoms results in a modification of both the average field propagation (nonlinear…
An innovative method based on the traversal of rays, originating from detected particles, through a three-dimensional grid of voxels is presented. The methodology has as main advantage that the outcome of the method is independent of the…
We propose a method for designing refractive optical elements for collimated beam shaping. In this method, the problem of finding a ray mapping is formulated as a linear assignment problem, which is a discrete version of the corresponding…