Limiting absorption principle for the dissipative Helmholtz equation

Adapting Mourre's commutator method to the dissipative setting, we prove a limiting absorption principle for a class of abstract dissipative operators. A consequence is the resolvent estimates for the high frequency Helmholtz equation when trapped trajectories meet the set where the imaginary part of the potential is non-zero. We also give the resolvent estimates in Besov spaces

Study on Ultrasonic Degradation of Pentachlorophenol Solution

Pentachlorophenol (PCP) ion was degraded by ultrasound at 25 C. Four aspects that could affect the degradation of PCP were investigated, i.e. initial pH of solution, initial concentration of pentachlorophenol ion, different sound intensity with catalyst and different frequencies of ultrasound. Results showed that PCP ion could be ultrasonic degraded totally after 3 hour treatment if CCl4, which can provide free radical, was added in solution. The mechanism of ultrasonic degradation was considered as free radical oxidation by adding n-butyl alcohol as free radical scavenger

Semi-classical Green kernel asymptotics for the Dirac operator

We consider a semi-classical Dirac operator in arbitrary spatial dimensions with a smooth potential whose partial derivatives of any order are bounded by suitable constants. We prove that the distribution kernel of the inverse operator evaluated at two distinct points fulfilling a certain hypothesis can be represented as the product of an exponentially decaying factor involving an associated Agmon distance and some amplitude admitting a complete asymptotic expansion in powers of the semi-classical parameter. Moreover, we find an explicit formula for the leading term in that expansion.Comment: 46 page

A Self-Consistent First-Principles Technique Having Linear Scaling

An algorithm for first-principles electronic structure calculations having a computational cost which scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this respect it is related to the technique of Li, Nunes and Vanderbilt. The density matrix is expressed in terms of localized support functions, and a matrix of variational parameters, L, having a finite spatial range. The total energy is minimized with respect to both the support functions and the elements of the L matrix. The method is variational, and becomes exact as the ranges of the support functions and the L matrix are increased. We have tested the method on crystalline silicon systems containing up to 216 atoms, and we discuss some of these results.Comment: 12 pages, REVTeX, 2 figure

Weblog patterns and human dynamics with decreasing interest

Weblog is the fourth way of network exchange after Email, BBS and MSN. Most bloggers begin to write blogs with great interest, and then their interests gradually achieve a balance with the passage of time. In order to describe the phenomenon that people's interest in something gradually decreases until it reaches a balance, we first propose the model that describes the attenuation of interest and reflects the fact that people's interest becomes more stable after a long time. We give a rigorous analysis on this model by non-homogeneous Poisson processes. Our analysis indicates that the interval distribution of arrival-time is a mixed distribution with exponential and power-law feature, that is, it is a power law with an exponential cutoff. Second, we collect blogs in ScienceNet.cn and carry on empirical studies on the interarrival time distribution. The empirical results agree well with the analytical result, obeying a special power law with the exponential cutoff, that is, a special kind of Gamma distribution. These empirical results verify the model, providing an evidence for a new class of phenomena in human dynamics. In human dynamics there are other distributions, besides power-law distributions. These findings demonstrate the variety of human behavior dynamics.Comment: 8 pages, 1 figure

Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and L^\infty((0,T)\times\o), where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.Comment: 45page

Transverse instability and its long-term development for solitary waves of the (2+1)-Boussinesq equation

The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multi-symplectic formulation of this equation gives an explicit relation between the parameters for transverse instability when the transverse wavenumber is small. The Evans function is then computed explicitly, giving the eigenvalues for transverse instability for all transverse wavenumbers. To determine the nonlinear and long time implications of transverse instability, numerical simulations are performed using pseudospectral discretization. The numerics confirm the analytic results, and in all cases studied, transverse instability leads to collapse.Comment: 16 pages, 8 figures; submitted to Phys. Rev.