ar X iv : n lin / 0 11 00 43 v 2 [ nl in . C D ] 1 5 Ju l 2 00 2 Families of line - graphs and their quantization

ar X iv : n lin / 0 11 00 43 v 1 [ nl in . C D ] 2 3 O ct 2 00 1 Infinite family of topologically conjugated digraphs and their quantization

We define and analyze families of classical directed graphs, which may be useful in study of quantum chaos. The number of vertices in each graph of a certain family grows to infinity, which corresponds to the semiclassical limit of the quantum system. For any initial directed graph Γ with N vertices and M bonds we define the corresponding edge-graph L(Γ). It consists of M vertices, which repres...

ar X iv : n uc l - th / 0 11 20 08 v 2 1 5 Ju l 2 00 2 Theoretical Study of the 3 He ( μ − , ν μ ) 3 H Capture

ar X iv : n lin / 0 50 70 64 v 1 [ nl in . P S ] 2 8 Ju l 2 00 5 Optical transparency modes in anisotropic media

The modes of nonlinear propagation of the two-component electromagnetic pulses through optically uniaxial media containing resonant particles are studied. The features of their manifestation in the " dense " media and in the media with expressed positive and negative birefringences are discussed. It is shown that exponentially and rationally decreasing solutions of the system of material and wa...

ar X iv : n lin / 0 30 50 20 v 1 [ nl in . C D ] 1 2 M ay 2 00 3 Nodal domains on quantum graphs 8 February 2008

We consider the real eigenfunctions of the Schrödinger operator on graphs, and count their nodal domains. The number of nodal domains fluctuates within an interval whose size equals the number of bonds B. For well connected graphs, with incommensurate bond lengths, the distribution of the number of nodal domains in the interval mentioned above approaches a Gaussian distribution in the limit whe...

ar X iv : n lin / 0 11 10 23 v 1 [ nl in . A O ] 9 N ov 2 00 1 Evolutionary reconstruction of networks

Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present an evolutionary algorithm for reconstruction of graphs from their Laplacian spectra. Through a stochastic process of mutations and selection, evolving test networks converge to a reference graph. Applying th...