We study the dynamics of the so-called Game of Cards by using tools developed in the context of discrete dynamical systems. We extend a result of [4] and [10] (the last one in the context of distributed systems) that established a necessary and sufficient condition for the game to converge. We precisely describe the lattice structure of the set of configurations and we state bounds for the conv...

The Design Phase of DIAMOND, a 3 generation light source facility, is currently in progress. Earlier studies of a similar storage ring had found a basic lattice structure with low emittance, good dynamic stability and the flexibility to operate in different modes. The lattice has been further developed to meet the evolving demands of the project, delivering very high brightness radiation over a...

Abstract. In this paper we study the existence assertion of the initial boundary value problem for the equation ∂u ∂t = ∆e−∆u. This problem arises in the mathematical description of the evolution of crystal surfaces. Our investigations reveal that the exponent in the equation can have a singular part in the sense of the Lebesgue decomposition theorem, and the exponential nonlinearity somehow “c...

Beamswhich follow curved trajectories are useful in a variety of applications, but up to now have been realized mainly in linear media. We demonstrate theoretically and experimentally the generation of second-harmonic (SH) beams which follow arbitrary convex caustic trajectories. These beams are created in a nonlinear photonic crystal with a second-order susceptibility having a tailored pattern...

Hard sphere colloidal particles are a basic model system for general research into phase behavior, ordering and out-equilibrium glass transitions. Experimentally it has been shown that oscillatory shearing of a monodisperse hard sphere glass, produces two different crystal orientations; a Face Centered Cubic (FCC) crystal with the close packed direction parallel to shear at high strains and an ...

This paper presents a theoretical optical data pathway model. The goal is to evaluate the physics behind photonic crystal/photon relationships and to develop a theoretical model for photonic crystal implementation into VLSI system design. This paper will begin with the exploration of the fundamentals of wave propagation in photonic crystals, development of an optical transmitting device (laser ...

Equations are presented that model diffusion of a protein to the surface of a growing crystal in a convection-free environment. The equations apply to crystal growth solutions that contain both a protein and a protein precipitant. The solutions are assumed ternary and the equations include all four diffusion coefficients necessary for the full description of the diffusion process. The four diff...

In this paper, within the framework of virtual crystal approximation, mathematical modeling dependence density states polariton excitations in a 1D photonic crystal—a system pores (tunnel-coupled microresonators) containing quantum dots—on concentration structural defects is performed.

In this paper we study control systems whose input sets are quantized. We speciically focus on problems relating to the structure of the reachable set of such systems, which may turn out to be either dense or discrete. We report on some recent results on the reachable set of linear quantized systems, and study in detail a particular but interesting class of nonlinear systems, forming the discre...