Stable nonequilibrium probability densities and phase transitions for meanfield models in the thermodynamic limit

A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of an infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as non-equilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Grüner-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered.     

Continuation of travelling‐wave solutions of the Navier–Stokes equations

An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first‐order pseudospectral semi‐implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton–Raphson solver and is shown to be highly efficient in performing this task, even when high‐resolution grids are used. This method is well suited to three‐dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Environmental Effect of Macrocyclic Molecules on the Oxidation of Triethylamine by Ferricyanide Ion in Aqueous Solution

The effect of 18-crown-6 and kryptofix (2,2,1) on the oxidation of triethylamine byaqueous ferricyanide ion has been studied at pH 4, 7, and 9.The macrocycle retarded the normal oxidation process at all pH values,the effect depending on the macrocyclic ligand concentration Kryptofix (2,2,1) had a greater effect than 18-crown-6 at all pHvalues in this study. For 18-crown-6, retardation decreases in the order pH 9 > 4 > 7 while forkryptofix it follows the order pH 9 > 7 > 4.     

Two Coulomb waves theory for direct excitation

A theoretical model of Dewangan, in which the total scattering wave function is approximated by a distorted wave containing two Coulomb wave functions, is discussed and its relation with the Brauner-Briggs-Klar model for ionization is examined. An important feature of the theory is that it includes a second Born amplitude naturally and in addition, contains, albeit approximately, both real and imaginary parts of all higher order Born terms. The theory is applied to study the 1s→2s excitation of hydrogen by electrons in the energy range 54.4 to 400eV. The differential and integral cross sections predicted by the theory are compared with the results of other theories and experimental data at 54.4eV and a good agreement is found.     

Two Convergence Problems for Monotone Sequences

Eight measures of rate of convergence of monotone sequences of real numbers have been proposed and discussed in a paper by Beyer, Ebanks, and Qualls (Acta Appl. Math. 20 (1990), 267–284). These rates arose in discussions of dynamical systems. In the comparisons of these rates, two problems remained. A complete answer is given to one of the problems and a partial answer is given to the other problem.     

Large deviations and the generalized processor sharing scheduling for a two-queue system

We establish the optimal asymptotic decay rate of per-session queue length tail distributions for a two-queue system where a single constant rate server serves the two queues using the Generalized Processor Sharing (GPS) scheduling discipline. The result is obtained using the sample-path large deviation principle and has implications in call admission control for high-speed communication networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

A compact shock-assisted free-piston driver for impulse facilities

A free-piston driver that employs entropy-raising shock processes with diaphragm rupture has been constructed, which promises significant theoretical advantages over isentropic compression. Results from a range of conditions with helium and argon driver gases are reported. Significant performance gains were achieved in some test cases. Heat losses are shown to have a strong effect on driver processes. Measurements compare well with predictions from a quasi-one-dimensional numerical code. Received 7 September 1996 / Accepted 5 October 1996     

不良导体热系数和热体散热率测量方法研究(英文)

本文介绍一种直接测量散热率新方法．进而测出不良导体的热系数。该方法，减小了由间接测量散热率所带来的误差，实验装置简单，操作方便，参数少，测量结果的精确性和重复性都有较大提高，更重要的是这一新的实验方法突出了物理思想。     

AN ALTERNATIVE SPECIFICATION FOR MODELING GROUNDWATER DYNAMICS

This research extends previous work with dynamic models to manage groundwater quality by using the consumptive nitrate use rate instead of the nitrate application rate. The analysis indicates that misspecification results in overestimation of economic benefits, and supra-optimum nitrogen fertilizer application rates and groundwater nitrate stocks at a steady state.     

类铜离子的电子碰撞参数及其规律

用准相对论扭曲波方法系统地计算了Ｂａ、Ｎｄ、Ｇｄ、Ｙｂ、Ａｕ、Ｐｂ类铜离子组态能级之间的电子碰撞激发强度Ω（ｎｌ－ｎｌ），３≤ｎ≤７，４≤ｎ≤７，同时给出了高能极限的碰撞强度和外推到阈值的碰撞强度，用最小二乘样条方法拟合了全能域碰撞强度及热平均速率系数。对于一个激发过程，用１０个参数可以得到碰撞电子在任意能量下的碰撞强度以及任意温度下的速率系数。