Second-order topological modes in two-dimensional continuous media

Two-dimensional solitons with second-order nonlinearities.

We investigate the propagation of intense Gaussian beams in materials with quadratic nonlinearity. Excitation of (2 + 1) solitons is numerically predicted at finite phase mismatch and in the presence of linear walk-off between the fundamental and second-harmonic waves. The numerical results are interpreted in terms of the conserved quantities of the wave evolution, and the appropriate condition...

Anomalous diffusion exponents in continuous two-dimensional multifractal media.

We study diffusion in heterogeneous multifractal continuous media that are characterized by the second-order dimension of the multifractal spectrum D2, while the fractal dimension of order 0, D0, is equal to the embedding Euclidean dimension 2. We find that the mean anomalous and fracton dimensions, d(w) and d(s), are equal to those of homogeneous media showing that, on average, the key paramet...

Topological Mixing in Three-Dimensional Porous Media

The topological complexity inherent to all porous media can impart complicated transport dynamics under steady flow conditions. Recently, it has been established [2] that such topological complexity imparts ubiquitous and persistent chaotic advection via a 3D fluid mechanical analogue of the baker’s map. In the presence of molecular diffusion, chaotic Lagrangian dynamics are well-known to impar...

Two{dimensional Topological Dynamics

Generalized Second-order Two-dimensional Systems: Computing the Transfer Function

In this paper the discrete Fourier transform is used to determine the coefficients of a transfer function of a new twodimensional model of second-order: x(i1 +2, i2 +2) = A0x(i1 +1, i2 +1)+A1x(i1 +1, i2)+A2x(i1, i2 +1). The algorithm is straightforward and has been implemented using the software package Matlab . Two step-by-step examples illustrating the application of the algorithm are presented.