Gas flow characteristics in straight silicon microchannels

Experiments have been conducted to investigate nitrogen gas flow characteristics through four trapezoidal silicon microchannels with different hydraulic diameters. The volume flow rate and pressure ratio are measured in the experiments. It is found that the friction coefficient is no longer a constant, which is different from the conventional theory. The characteristics are first explained by the theoretical analysis. A simplified rectangular model (rectangular straight channel model) is then proposed. The experimental results are compared with the theoretical predictions based on the simplified rectangular model and the two-dimensional flow between the parallel-plate model which was usually used. The difference between the experimental data and the theoretical predictions is found in the high-pressure ratio cases. The influence of the gas compressibility effect based on the Boltzmann gas kinetic analysis method is studied to interpret the discrepancy. We discuss two important factors affecting the application extent of different prediction models.     

Kinetic models for optimal control of wealth inequalities

We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a finite time horizon approximation, or model predictive control, of the corresponding control problem for the microscopic agents’ dynamic and results in an alternative theoretical approach to the taxation and redistribution policy at a global level. It is shown that in general the control is able to modify the Pareto index of the stationary solution of the corresponding Boltzmann kinetic equation, and that this modification can be exactly quantified. Connections between previous Fokker–Planck based models for taxation-redistribution policies and the present approach are also discussed.     

Hydrodynamics from kinetic models of conservative economies

In this paper, we introduce and discuss the passage to hydrodynamic equations for kinetic models of conservative economies, in which the density of wealth depends on additional parameters, like the propensity to invest. As in kinetic theory of rarefied gases, the closure depends on the knowledge of the homogeneous steady wealth distribution (the Maxwellian) of the underlying kinetic model. The collision operator used here is the Fokker-Planck operator introduced by J.P. Bouchaud and M. Mezard [Wealth condensation in a simple model of economy, Physica A 282 (2000) 536-545], which has been recently obtained in a suitable asymptotic of a Boltzmann-like model involving both exchanges between agents and speculative trading by S. Cordier, L. Pareschi and one of the authors [S. Cordier, L. Pareschi, G. Toscani, On a kinetic model for a simple market economy, J. Stat. Phys. 120 (2005) 253-277]. Numerical simulations on the fluid equations are then proposed and analyzed for various laws of variation of the propensity.     

Description of far-from-equilibrium processes by mean-field lattice gas models

Mean-field kinetic equations are a valuable tool to study the atomic dynamics and spin dynamics of simple lattice gas and Ising models. They can be derived from the microscopic master equation of the system and contain analytical expressions for kinetic coefficients and thermodynamic quantities which are usually introduced phenomenologically. We review several methods to obtain such equations, and discuss applications to the dynamics of order–disorder transitions, spinodal decomposition, and dendritic growth in the isothermal or chemical model. In the case of dendritic growth we show that the mean-field kinetic equations are equivalent to standard continuum equations for this problem and derive expressions for macroscopic quantities, e.g. the surface tension and kinetic coefficients, as functions of the microscopic order parameters. In spinodal decomposition, we focus our attention on the vacancy mechanism, which is a more faithful picture of diffusion in solids than the more widely examined exchange mechanism. We study the interfaces between an unstable mixture and a stable ‘vapour’ phase, and analyse surface modes that lead to specific surface patterns. For order–disorder transitions, studied in the framework of a repulsive two-sublattice model, we derive sets of coupled equations for the mean concentration (a conserved quantity) and for the occupational difference between the two sublattices emerging from the symmetry breaking due to ordering (non-conserved order parameter). These equations are applied to transport in the presence of ordered domains. Finally, we discuss the possibilities of improving the simple mean-field approximation by density functional theories and various forms of the dynamic pair approximation, including the path-probability method.     

Physical description of the impregnation mechanism of dye molecules in contact with porous electrodes

We propose and discuss two models that take into account the decreasing of the bulk density of dyes molecules in contact with a porous electrode. We show that the models based on the standard adsorption phenomenon have to be considered just as fitting models, of limited physical significance. A more physical model has to take into account the diffusion of dye molecules into the channels present in the porous electrode and also the adsorption of dye molecules on the lateral surfaces of these channels. The agreement between the theoretical prediction of such a model and the experimental data is reasonably good.     

Lumps and rouge waves for a $$$$-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluid mechanics

A specific class of singularity-free cosmological model has recently been considered in light of different observational data such as observed Hubble data, BAO data from luminous red galaxy survey by Slowan digital sky survey (SDSS) and CMB data from WMAP. However, it is observed that only 12–14 data points are used to study the viability of the model in late time. In this paper, we discuss the viability of all the models belonging to the same class of EU in light of union compilation data (SNIa) which consists of over a hundred data points, thus getting a more robust test for viability. More importantly, it is crucial that we can distinguish between the various models proposed in the class of solution obtained. We discuss here why with the present observational data it is difficult to distinguish between all of them. We show that the late-time behaviour of the model is typical to any asymptotically de Sitter model.     

Superionic conductors

The so-called superionic conductors represent a class of solid materials showing an unusually high ionic conductivity. Their structure is characterized by strong disorder in the sublattice of conducting ions. We shall describe the dynamic properties of the partially disordered state on the basis of two classes of theoretical models. For stochastic lattice gases we discuss the behavior of various time-correlation functions relevant for inelastic neutron- and light-scattering experiments and for tracer-diffusion measurements. In addition we study a system of interacting Brownian particlés in the presence of a periodic potential as a model for optimized (AgI-type) ionic conductors. A mean-field theory is developed which implies a relationship between the conductivity and structural properties.     

基于Logistic函数模型的纳米自组装动力学分析

利用快速混合停流吸收(stopped-flow absorption)技术,研究了半胱氨酸分子介导的金纳米棒线性自组装过程的动力学性质.通过观测金纳米棒的表面等离激元动态吸收光谱,分析其自组装动力学行为及其与组装结构之间的关系.研究表明,传统的二阶反应动力学理论模型在描述金纳米棒自组装动力学行为上存在明显的局限性.由此,我们提出了基于Logistic函数的新的动力学分析模型.与传统的理论模型相比,新的理论模型具有更好的普适性,不仅适用于定量分析不同速率的金纳米棒自组装动力学特征,还提供了一种更加准确地描述组装初期动力学行为的方法.此外,这种新的动力学分析方法还有助于理解和建立金纳米棒组装动力学特征与组装体结构之间的关联.     

Electron kinetic effects on Raman backscatter in plasmas

We augment the usual three-wave cold-fluid equations governing Raman backscatter (RBS) with a new kinetic thermal correction, proportional to an average of particle kinetic energy weighted by the ponderomotive phase. From closed-form analysis within a homogeneous kinetic three-wave model and ponderomotively averaged kinetic simulations in a more realistic pulsed case, the magnitude of these new contributions is shown to be a measure of the dynamical detuning between the pump laser, seed laser, and Langmuir wave. Saturation of RBS is analyzed, and the role of trapped particles illuminated. Simple estimates show that a small fraction of trapped particles (approximately 6%) can significantly suppress backscatter. We discuss the best operating regime of the Raman plasma amplifier to reduce these deleterious kinetic effects.     

Kinetic and hydrodynamic models of chemotactic aggregation

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean-field Fokker-Planck equation governing the evolution of the distribution function of the system in phase space. By taking the successive moments of this kinetic equation and using a local thermodynamic equilibrium condition, we derive a set of hydrodynamic equations involving a damping term. In the limit of small frictions, we obtain a hyperbolic model describing the formation of network patterns (filaments) and in the limit of strong frictions we obtain a parabolic model which is a generalization of the standard Keller-Segel model describing the formation of clusters (clumps). Our approach connects and generalizes several models introduced in the chemotactic literature. We discuss the analogy between bacterial colonies and self-gravitating systems and between the chemotactic collapse and the gravitational collapse (Jeans instability). We also show that the basic equations of chemotaxis are similar to nonlinear mean-field Fokker-Planck equations so that a notion of effective generalized thermodynamics can be developed.     

Critical phenomena in nonequilibrium phase transitions

We discuss a number of models associated with phase transitions in purely kinetic models where detailed balance does not hold as in thermal equilibrium systems. These models include some of the features of heterogeneous catalysis on a surface, and are used to examine the effect of local correlations on the reaction process. We argue that many models which do not include desorption will show the same kind of critical behavior if they have a continuous transition to a poisoned state. We also present results for a model with a continuous transition to a non-poisoned state. The effect of adding desorption, diffusion, and anisotropy to these idealized models is also discussed.     

Modeling the kinetics of large sets of reactions on metal surfaces

We are concerned with constructing and solving kinetic models for large-scale catalytic mechanisms involving hundreds of reactions. We need reliable estimates for hundreds of rate constants for each project we undertake. In order to obtain reliable estimates of activation barriers with co-adsorbate effects, we employ the UBI-QEP method whenever applicable. We also bring quantum mechanical electronic structure methods to bear when necessary. Herein we describe a new model for obtaining reasonable estimates for rate constants for reactions on metal surfaces that yields rate constants and rate constant parameters without large amounts of computer time. The model is based on a novel approach to surface-phase chemistry and a re-thinking regarding the phases from which surface adsorbates react. We will also discuss recent literature regarding trends in Arrhenius pre-exponential factors (prefactors).     

An almost linear stochastic map related to the particle system models of social sciences

We propose a stochastic map model of economic dynamics. In the past decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of income and wealth. Another area of enquiry is the formation of opinion in a society. The model proposed attempts to produce positively skewed distributions and power law distributions as has been observed in the real data of income and wealth. Also, it shows a non-trivial phase transition in the opinion of a society (opinion formation). A number of physical models also generate similar results. In particular, kinetic exchange models have been successful especially in this regard. Therefore, we compare the results obtained from these two approaches and discuss a number of new features and drawbacks of this model.     

Shock waves by a kinetic model of van der Waals fluids

We present a four-velocity kinetic model of van der Waals fluids. Although, from the physical point of view this model is very simple, mathematically it is quite complicated. Due to this complexity we performed various simplifications, which are also presented. We look for traveling wave solutions for these simplified versions. A discussion of the types of the states of rest is presented. We pay some attention to the monotonicity of the density component of the traveling wave. Finally, we compare the model's kinetic and hydrodynamic shock wave structures. The new feature is that kinetic effects alone are unable to kill the artificial phenomenon of impending shock splitting.     

A Hierarchy of Heuristic-Based Models of Crowd Dynamics

We derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral Individual-Based Model of Ngai et al. (Disaster Med. Public Health Prep. 3:191–195, 2009) where pedestrians are supposed to have constant speeds. This IBM supposes that pedestrians seek the best compromise between navigation towards their target and collisions avoidance. We first propose a kinetic model for the probability distribution function of pedestrians. Then, we derive fluid models and propose three different closure relations. The first two closures assume that the velocity distribution function is either a Dirac delta or a von Mises-Fisher distribution respectively. The third closure results from a hydrodynamic limit associated to a Local Thermodynamical Equilibrium. We develop an analogy between this equilibrium and Nash equilibria in a game theoretic framework. In each case, we discuss the features of the models and their suitability for practical use.     

NMR studies of carrier-mediated transport across lipid bilayer membranes

Two theoretical models are presented which show how the various kinetic steps involved in transport across lipid bilayer membranes affect NMR spectral lineshapes and relaxation times. The first model applies whenever the transported material moves across the membrane by restricted diffusion. The second model applies when the motion can be described as a jump between membrane interfaces. Both carrier-mediated and carrier-independent cases are treated. Special attention is given to the effects of relaxation in the membrane and to morphology. Exact analytical solutions for the simplest one-dimensional geometry are presented. More complicated morphologies are best treated numerically.     

Conserved dynamics and interface roughening in spontaneous imbibition: A critical overview

Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties of the imbibition front, with particular attention to the conservation law associated to the fluid, to problems arising from the actual structure of the embedding medium, and to external influences such as evaporation and gravity. Our main conclusion is that the scaling of moving interfaces includes many crossover phenomena, with competition between the average capillary pressure gradient and its fluctuations setting the maximal lengthscale for roughening. We discuss the physics of both pinned and moving interfaces and the ability of the existing models to account for their properties. Received 17 February 1999 and Received in final form 24 November 1999