Undercompressive shocks for nonstrictly hyperbolic conservation laws

We study 2×2 systems of hyperbolic conservation laws near an umbilic point. These systems have Undercompressive shock wave solutions, i.e., solutions whose viscous profiles are represented by saddle connections in an associated family of planar vector fields. Previous studies near umbilic points have assumed that the flux function is a quadratic polynomial, in which case saddle connections lie on invariant lines. We drop this assumption and study saddle connections using Golubitsky-Schaeffer equilibrium bifurcation theory and the Melnikov integral, which detects the breaking of heteroclinic orbits. The resulting information is used to construct solutions of Riemann problems.     

Exact solutions for network rewiring models

Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.     

1-Soliton solution and conservation laws for nonlinear wave equation in semiconductors

This paper obtains the 1-soliton solution of a nonlinear wave equation that arises in the study of semiconductors. The conserved quantities are also calculated from this equation. Furthermore, additional non-trivial conserved quantities are computed using the invariance and multiplier approach based on the well known result that the Euler-Lagrange operator annihilates the total divergence.     

Features of stable radical generation in lignin on exposure to nitrogen dioxide

The mechanism of stable radical generation in lignin under the action of nitrogen dioxide and NO₂ - air mixture is considered. The formation of phenoxyl, iminoxyl and acylaminoxyl radicals has been detected by EPR. The proposed mechanism involves a primary oxidative reaction of phenol groups with dimers of NO₂ (nitrosyl nitrate) resulting in the formation of phenoxyl radicals and nitric oxide. In the subsequent recombination of phenoxyl radicals and nitric oxide, nitroso compounds and oximes are formed. By reaction of oximes with radicals NO₂, stable iminoxyl radicals are formed. This mechanism is confirmed by kinetic dependencies obtained over a wide range of NO₂ concentrations. From IR spectroscopy measurements it follows that hydroxyl groups of non-phenolic structures of lignin are oxidised to aldehydes producing acylaminoxyl radicals by reaction with NO₂. The kinetic data show that the adsorption of NO₂ on the lignin surface is the rate-determining factor in stable radical formation.     

15-甲基-双环[10,3,0]十五碳-1(12)-烯-13-酮的晶体结构及分子稳定构象

15-甲基-双环[10,3,0]十五碳-1(12)-烯-13-酮的单晶属空间群P2_1/n,晶胞参数:a=0.4838(1)nm,b=1.3949(2)nm,c=2.1645(4)nm,β=92.07(1)°,Z=4.其中平面五员环呈刚性。另一个含烯十二员环的实际构象与分子力学计算的最稳定构象一致。     

A super hierarchy of coupled derivative nonlinear Schrödinger equations and conservation laws

By solving the zero-curvature equation associated with a 3 × 3 matrix spectral problem, a super hierarchy of coupled derivative nonlinear Schrödinger equations is proposed. The corresponding super bi-Hamiltonian structures are established by means of the super trace identity. Then, we derive infinite conservation laws of the super coupled derivative nonlinear Schrödinger equation with the aid of spectral parameter expansions.     

Modeling,simulation and validation of material flow on conveyor belts

In this paper a model comparison approach based on material flow systems is investigated that is divided into a microscopic and a macroscopic model scale. On the microscopic model scale particles are simulated using a model based on Newton dynamics borrowed from the engineering literature. Phenomenological observations lead to a hyperbolic partial differential equation on the macroscopic model scale. Suitable numerical algorithms are presented and both models are compared numerically and validated against real-data test settings.     

ON SINGLE LAWS FOR VARIETIES OF QUASIGROUPS ASSOCIATED WITH EXTENDED CYCLE SYSTEMS

It has been previously shown by Lindner and Rodger that quasigroups associated with 2-perfect extended m-cycle systems can be equationally defined if and only if m ∈ {3, 5, 7}. In this paper we present a single identity for each such m which is equivalent to the identities given for these varieties.