Kinetic limit of a conservative lattice gas dynamics showing long-range correlations

An anisotropic lattice gas dynamics is investigated for which particles on ^d jump to empty nearest neighbor sites with (fast) rate ^–2 in a specified direction and some particular configuration-dependent rates in the other directions. The model is translation and reflection invariant and is particle conserving. The space coordinate in the fast-rate direction is rescaled by ^–1. It follows that the density field converges in probability, as 0, to the corresponding solution of a nonlinear diffusion-type equation. The microscopic fluctuations about the deterministic macroscopic evolution are determined explicitly and it is found that the stationary fluctuations decay via a power law (1/r ^d ) with the direction dependence of a quadrupole field.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

Novel Properties of Photochromic Spirooxazine Nanoparticles

The nanoparticles of a spirooxazine （SPO） and its photomerocyanine （PMC） were prepared through the reprecipitation method. Two distinct features were observed. One is that the decaying lifetime for PMC nanoparticles was 600 times of that for the dispersed molecules, and the other is that the fluorescence intensity of SPO nanoparticles was enhanced by 240 times of that of the dispersed monomer.     

Mass spectrometric analysis of low molecular mass polyesters by laser desorption/ionization on porous silicon

A low molecular mass polyester was analyzed by desorption/ionization on porous silicon (DIOS) mass spectrometry. The results were compared with those of matrix-assisted laser desorption ionization (MALDI) mass spectrometry using matrixes of alpha-cyano-4-hydroxycinnamic acid (CHCA) and 10,15,20-tetrakis(pentafluorophenyl)porphyrin (F20TPP). The CHCA matrix was not suitable for characterization of low molecular mass components of the polyester because the matrix-related ions interfered with the component ions. On the other hand, the F20TPP matrix showed no interference because no matrix-related ions appeared below m/z 822. However, the solvent selection for determining optimal conditions of sample preparation was limited, because F20TPP does not dissolve readily in any of the available organic solvents. In the DIOS spectra, the polymer ions were observed at high sensitivity without a contaminating ion. No matrix is needed for DIOS spectra of low molecular mass polyesters, facilitating sample preparation and selectivity of a precursor ion in post-source decay measurements.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

Simultaneous determination of radionuclides separable into natural decay series by use of time-interval analysis

A delayed coincidence method, time-interval analysis (TIA), has been applied to successive – decay events on the millisecond time-scale. Such decay events are part of the ²²⁰Rn²¹⁶Po (T_1/2 145 ms) (Th-series) and ²¹⁹Rn²¹⁵Po (T_1/2 1.78 ms) (Ac-series). By using TIA in addition to measurement of ²²⁶Ra (U-series) from -spectrometry by liquid scintillation counting (LSC), two natural decay series could be identified and separated. The TIA detection efficiency was improved by using the pulse-shape discrimination technique (PSD) to reject -pulses, by solvent extraction of Ra combined with simple chemical separation, and by purging the scintillation solution with dry N₂ gas. The U- and Th-series together with the Ac-series were determined, respectively, from alpha spectra and TIA carried out immediately after Ra-extraction. Using the ²²¹Fr²¹⁷At (T_1/2 32.3 ms) decay process as a tracer, overall yields were estimated from application of TIA to the ²²⁵Ra (Np-decay series) at the time of maximum growth. The present method has proven useful for simultaneous determination of three radioactive decay series in environmental samples.     

高频超声中带退化记忆项的MGT方程解的衰减估计北大核心CSCD

研究了高频超声应用中带无穷退化记忆项的Moore-Gibson-Thompson方程τu_(ttt)+α(x)u_(tt)-c^(2)Δu-bΔu_(t)+∫^(∞)_(0)g(s)div[a(x)▽u(t-s)]ds=0解的适定性和衰减速率,其中非负函数a(x)和α(x)是可退化的并满足a(x)+α(x)≥δ>0.该系统是由黏性热松弛流体中波传播模型的线性化而得到的.通过使用Faedo-Galerkin逼近和能量估计,证明了解的适定性.在适当的假设下,通过构造适当的李雅普诺夫泛函,建立了能量的指数或一般衰减结果.     

Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

Minimax principles for elliptic mixed hemivariational–variational inequalities

In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent to a mixed hemivariational–variational inequality. While the minimax principle is of independent interest, it is employed in this paper to provide an elementary proof of the solution existence of the mixed hemivariational–variational inequality. Theoretical results are illustrated in the applications of two contact problems.     

Morse Index of Multiple Blow-up Solutions to the Two-Dimensional Sinh-Poisson Equation

In this paper we consider the Dirichlet problemwhere $\rho$ is a small parameter and $\Omega$ is a $C^2$ bounded domain in $\mathbb{R}^2$. In [1], the author proves the existence of a $m$-point blow-up solution $u_\rho$ jointly with its asymptotic behaviour. We compute the Morse index of $u_\rho$ in terms of the Morse index of the associated Hamilton function of this problem. In addition, we give an asymptotic estimate for the first $4m$ eigenvalues and eigenfunctions.