Propagation of surface waves in a radially inhomogeneous chiral waveguide is considered. The setting reduced to boundary eigenvalue problem for the longitudinal components electromagnetic field Sobolev spaces. To find solution, variational formulation used. analysis an operator-valued function. Discreteness spectrum proved and distribution characteristic numbers function on complex plane determ...

We study the modulational instability in discrete lattices and we show how the discreteness drastically modifies the stability condition. Analytical and numerical results are in very good agreement. We predict also the evolution of a linear wave in the presence of noise and we show that modulational instability is the first step towards energy localization. PACS numbers: 6310, 0340K, 4610, 0545

A complex hyperbolic triangle group is a group generated by three complex reflections fixing complex slices (complex geodesics) in complex hyperbolic space. Our purpose in this paper is to improve the result in [3] and to discuss discreteness of complex hyperbolic triangle groups of type (n, n,∞; k).

This paper is concerned with a class of nonlocal dispersive models – the θ-equation proposed by H. Liu [ On discreteness of the Hopf equation, Acta Math. Appl. Sin. Engl. Ser. 24(3)(2008)423–440]: (1− ∂ x)ut + (1− θ∂ x) ( u2 2 ) x = (1− 4θ) ( ux 2 )

We provide an extension of Fill’s (1998) exact sampler algorithm. Our algorithm is similar to Fill’s, however it makes no assumptions regarding stochastic monotonicity, discreteness of the state space, the existence of densities, etc. We illustrate our algorithm on a simple example.

Lattice effects in ecological time-series are patterns that arise because of the inherent discreteness of animal numbers. In this paper, we suggest a systematic approach for predicting lattice effects. We also show that an explanation of all the patterns in a population time-series may require more than one deterministic model, especially when the dynamics are complex.

Discrete lattice simulations of a one-dimensional φ 4 theory coupled to an external heat bath are being carried out. Great care is taken to remove the effects of lattice discreteness and finite size and to establish the correct correspondence between simulations and the desired, finite-temperature continuum limit.

We demonstrate that discrete solitons are possible in Ginzburg-Landau lattices. As a result of discreteness, we find that this system exhibits a host of features that have no counterpart whatsoever in either the continuous limit or in other conservative discrete models.

We adapt the level set method to simulate the growth of thin lms described by the motion of island boundaries. This island dynamics model involves a continuum in the lateral directions, but retains 1 atomic scale discreteness in the growth direction. Several choices for the island boundary velocity are discussed, and computations of the island dynamics model using the level set method are prese...