Computer simulations of critical phenomena and phase behaviour of fluids

Computer simulation techniques such as Monte Carlo (MC) and Molecular Dynamics (MD) methods yield numerically exact information (apart from statistical errors) on model systems of classical statistical mechanics. However, a systematic limitation is the restriction to a finite (and often rather small) particle number N (or box linear dimension L, respectively). This limitation is particularly restrictive near critical points (due to the divergence of the correlation length of the order parameter) and for the study of phase equilibria (possibly involving interfaces, droplets, etc.). Starting out with simple lattice gas (Ising) models, finite size scaling analyses have been developed to overcome this limitation. These techniques work for both simple Lennard-Jones fluids and their mixtures, including generalizations to approximate models for quadrupolar fluids such as carbon dioxide, benzene etc. and various mixtures, whose phase behaviour can be predicted. A combination of MC and MD allows the study of dynamic critical phenomena, and specialised techniques (umbrella sampling plus thermodynamic integration) yield the surface free energy of droplets as function of droplet size. Thus, computer simulation has become a versatile and widely applicable tool for the study of fluids.     

Beyond the LAN: Ethernet’s Evolution into the Public Network

This article details the evolution of Ethernet into Gigabit Ethernet and how this LAN-based technology has undergone major transformations over time. From its data rates and distances to supported media and functionality, Ethernet has greatly improved, enabling it to surmount many of its former limitations and in so doing to expand beyond the LAN into the MAN and now even the WAN. In this article, Pioneer Consulting explores the evolution further by focusing on some of the major technological directions in the Ethernet equipment industry.     

The Failure of Asymmetric Synthesis in Cholesteric Liquid Crystals

A set of selected bimolecular reactions leading to asymmetric and dissymmetric products was carried out in cholesteric solvents with the aim of obtaining asymmetric syntheses.

In all cases, the products did not show significant optical rotation. The reasons for the lack of asymmetric induction are briefly discussed.     

Reaction diffusion and interdiffusion in some binary metallic systems

This paper reviews studies from the Münster laboratory on multiphase and interdiffusion performed on several binary metallic systems. Optical microscopy and electron microprobe analysis were used to study interdiffusion and growth of the intermetallic layer(s) in infinite diffusion couples. Both methods have resolutions at the micron level. Thus, the results summarised in this paper concern the diffusion-controlled regime of the reaction diffusion process. We first remind the reader of some of the basics of multiphase diffusion and interdiffusion. Then we discuss results reported for the following systems: cobalt–niobium, nickel–niobium, nickel–aluminium and magnesium–aluminium. In the case of Co₂Nb we also compare interdiffusion and tracer diffusion of the components. Multiphase diffusion experiments also contain information about solid–solid equilibria of the phase diagram(s).     

Theoretical study on liquid crystal cyanobiphenyls: Phase stability and phase behavior

This article presents a theoretical study on liquid crystalline materials in homologous series of 4'-n-alkyl-4-cyanobiphenyl (nCB) with propyl (3CB), pentyl (5CB), and heptyl (7CB) groups. The atomic net charge and dipole moment components at each atomic center have been evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh–Schrodinger perturbation theory along with the multicentered-multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while a ‘6-exp’ potential function has been assumed for short-range interactions. Further, these interaction energy values have been used as input to calculate the translational entropy, and free energy of nCB (n=3, 5, and 7) molecules during the stacking, and in-plane interactions. The observed results have been correlated with the mesogenic behavior and phase stability based on the thermodynamic parameters introduced in this article. Further, an attempt has been made to elucidate the flexibility of a configuration at a particular temperature, which has a direct relation with phase transition property of the molecules.     

Investigation of ionization equilibria of L-aspartic and L-glutamic acids in water at a microscopic level by DFT method

The pK_a values of different dissociable groups of L-Aspartic and L-Glutamic acids in vacuo and in aqueous medium over a wide pH range have been estimated by DFT/B3LYP/6-31G(d) and 6-31G++(d,p) methods. For both the amino acids discrete water molecules (n?=?0, 3 and 6) have been used to get the first hydration sphere. Starting from a low pH, all possible tautomers resulting from each dissociation step are assumed to exist in a cyclic equilibrium. The structures of the species involved in the dissociation and tautomerization processes have been optimized in vacuo and also in aqueous medium considering H-bonded water molecules under the PCM formalism. For obtaining pK_a in aqueous medium the difference in Gibbs energy of the clusters H₃O⁺.mH₂O and (H₂O) _m+1 (m?=?an integer) is necessary and has been evaluated from computed literature data. Calculations reveal that in vacuo the neutral or less charged species predominate but in aqueous medium the zwitterionic or more chargeable forms contribute appreciably. The Gibbs energy changes for the microscopic cyclic equilibria have been estimated theoretically. These lead to overall (macroscopic) pK_a values for the ionization steps which are in good agreement with available experimental data for both the amino acids.     

Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis

Using Lyapunov functionals the global behaviour of the solutions of a reaction-diffusion system modelling chemotaxis is studied for bounded piecewise smooth domains in the plane. Geometric criteria can be given so that this dynamical system tends to a (not necessarily trivial) stationary state.     

Convergence to equilibria for fluid models of FIFO queueing networks

The qualitative behavior of open multiclass queueing networks is currently a topic of considerable activity. An important goal is to formulate general criteria for when such networks possess equilibria, and to characterize these equilibria when possible. Fluid models have recently become an important tool for such purposes. We are interested here in a family of such models, FIFO fluid models of Kelly type. That is, the discipline is first-in, first-out, and the service rate depends only on the station. To study such models, we introduce an entropy function associated with the state of the system. The corresponding estimates show that if the traffic intensity function is at most 1, then such fluid models converge exponentially fast to equilibria with fixed concentrations of customer types throughout each queue. When the traffic intensity function is strictly less than 1, the limit is always the empty state and occurs after a finite time. A consequence is that generalized Kelly networks with traffic intensity strictly less than 1 are positive Harris recurrent, and hence possess unique equilibria.1991Mathematics Subject Classification, 60K25, 68M20, 90B10. Partially supported by NSF Grant DMS-93-00612.     

一类带有非线性爆炸的粒子增长的数学模型

所建立的数学模型是由可数无穷多个彼此相互关联的非线性常微分方程所组成的自治系统,它刻划了在只有基本粒子和i-粒子(i≥1 ) 进行碰撞反应的系统里,粒子增长过程中密度随时间的变化规律.研究了这一自治系统解的存在性、唯一性、密度守恒以及解的渐近性质.