Microcanonical ensemble study of a classical fluid of hard rods under gravity

The study of a system of hard rods in a box of finite length in the presence of a uniform gravitational field is made by means of the microcanonical ensemble. Explicit expressions are derived for the phase volume and the density of states, the primary functions of this ensemble. Related statistical quantities are reported, such as the entropy, the temperature, the heat capacity and the forces exerted on the fluid by the bottom and top walls. The microcanonical number density and higher order molecular distribution functions are also derived. Received: 7 April 1998 / Received in final form: 20 July 1998 / Accepted: 28 July 1998     

Microcanonical ensemble extensive thermodynamics of Tsallis statistics

The microscopic foundation of the generalized equilibrium statistical mechanics based on the Tsallis entropy is given by using the Gibbs idea of statistical ensembles of the classical and quantum mechanics. The equilibrium distribution functions are derived by the thermodynamic method based upon the use of the fundamental equation of thermodynamics and the statistical definition of the functions of the state of the system. It is shown that if the entropic index ξ=1/(q−1) in the microcanonical ensemble is an extensive variable of the state of the system, then in the thermodynamic limit the principle of additivity and the zero law of thermodynamics are satisfied. In particular, the Tsallis entropy of the system is extensive and the temperature is intensive. Thus, the Tsallis statistics completely satisfies all the postulates of the equilibrium thermodynamics. Moreover, evaluation of the thermodynamic identities in the microcanonical ensemble is provided by the Euler theorem. The principle of additivity and the Euler theorem are explicitly proved by using the illustration of the classical microcanonical ideal gas in the thermodynamic limit.     

Microcanonical Monte Carlo study of one dimensional self-gravitating lattice gas models

In this study we present a microcanonical Monte Carlo investigation of one dimensional (1 ? d) self-gravitating toy models. We study the effect of hard-core potentials and compare to the results obtained with softening parameters and also the effect of the topology on these systems. In order to study the effect of the topology in the system we introduce a model with the symmetry of motion in a line instead of a circle, which we denominate as 1 /r model. The hard-core particle potential introduces the effect of the size of particles and, consequently, the effect of the density of the system that is redefined in terms of the packing fraction of the system. The latter plays a role similar to the softening parameter ? in the softened particles’ case. In the case of low packing fractions both models with hard-core particles show a behavior that keeps the intrinsic properties of the three dimensional gravitational systems such as negative heat capacity. For higher values of the packing fraction the ring model behaves as the potential for the standard cosine Hamiltonian Mean Field model while for the 1 /r model it is similar to the one-dimensional systems. In the present paper we intend to show that a further simplification level is possible by introducing the lattice-gas counterpart of such models, where a drastic simplification of the microscopic state is obtained by considering a local average of the exact N-body dynamics.     

Microcanonical study of the planar spin model

The planar spin model is simulated by microcanonical and Monte Carlo algorithms. The average action, topological charge density and spin-spin correlation functions are measured on 15 × 15 and 30 × 30 lattices at temperatures surrounding the critical point. In general very good agreement between the methods is found. Accurate runs (5.10⁵ sweeps) expose the finite volume differences between the canonical and microcanonical ensembles. A small shift (of order 1/volume) of the temperature brings the two sets of measurements into excellent agreement.     

二维颗粒气体在堆积过程中的能量耗散

通过高速摄像的方法观测了玻璃颗粒组成的准二维气态颗粒流的冷凝耗散过程,并和理想情况下的均匀耗散的颗粒流体理论作了比较,实验发现气态颗粒部分在耗散堆积过程中近似地满足高斯分布;从动能的结果来看,实际耗散过程和流体理论所预测的不同.实验发现冷凝分为两个阶段：当动能的贡献以气体颗粒为主时,发现颗粒以恒定的速度堆积,动能耗散主要由其中以气态分布的颗粒的沉积速率α,颗粒温度T和气态部分的平动速度ν_g决定;当气态颗粒数目趋向于0,能量耗散主要来自于密堆颗粒的表面层部分 关键词： 离散体系 耗散性     

Microcanonical analysis of a finite three-dimensional Ising system

All singularities which occur at phase transitions are smeared out in finite size systems. It is the purpose of this paper to show that this smearing is a characteristic of the canonical ensemble. It can be greatly reduced if the microcanonical ensemble is used. In order to demonstrate this the density of states of a three-dimensional 10×10×10 Ising system is determined numerically and is analysed in terms of a model entropy. The critical exponents and turn out to be not too far from the values which have been obtained by critical scaling.Dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

Ergodic Properties of Microcanonical Observables

The problem of the existence of a strong stochasticity threshold in the FPU- model is reconsidered, using suitable microcanonical observables of thermodynamic nature, like the temperature and the specific heat. Explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry. Measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density, which is independent of the number of degrees of freedom.     

Microcanonical simulation of nuclear disassembly

We formulate a model for the disassembly of a highly excited finite nuclear source into interacting nuclear fragments. Monte Carlo sampling of the exact microcanonical and canonical ensemble provides many-fragment configurations at the effective freeze-out stage. The effect of including the interaction between the fragments is significant and an elaboration of the model that allows for a nucleon vapor suggests the existence of a first-order phase transition.     

Microcanonical Analysis on a System with Long-Range Interactions

We study a long-range interacting spin chain placed in a staggered magnetic field using microcanonical approach and obtain the global phase diagram. We find that this model exhibits both first order phase transition and second order phase transition separated by a tricritical point, and temperature jump can be observed in the first order phase transition.     

Microcanonical simulation of Ising systems

Numerical simulations of the microcanonical ensemble for Ising systems are described. We explain how to write very fast algorithms for such simulations, relate correlations measured in the microcanonical ensemble to those in the canonical ensemble and discuss criteria for convergence and ergodicity.     

微型填充式气相色谱柱的制备（英文）北大核心CSCD

为了分离永久性气体及低碳轻化合物,基于MEMS技术,研究制备了一种微型填充式的气相色谱柱。为了增加色谱柱的长度以及深宽比,色谱柱的沟道制备采用了激光刻蚀技术,这种技术可以方便的在玻璃基底上刻蚀出深沟道,这是其他化学腐蚀技术无法比拟的。研制的色谱柱其沟道横截面为1.2mm(深度)×0.6mm(宽度),深宽比为2∶1。实验结果表明,这种微型填充柱,具有较大的样品容量,能很好的实现CO和SO_2的分离。     

微型填充式气相色谱柱的制备（英）

为了分离永久性气体及低碳轻化合物,基于MEMS技术,研究制备了一种微型填充式的气相色谱柱。为了增加色谱柱的长度以及深宽比,色谱柱的沟道制备采用了激光刻蚀技术,这种技术可以方便的在玻璃基底上刻蚀出深沟道,这是其他化学腐蚀技术无法比拟的。研制的色谱柱其沟道横截面为1.2 mm(深度)0.6 mm(宽度),深宽比为2∶1。实验结果表明,这种微型填充柱,具有较大的样品容量,能很好的实现CO和SO2的分离。     

Microcanonical analyses of peptide aggregation processes

We propose the use of microcanonical analyses for numerical studies of peptide aggregation transitions. Performing multicanonical Monte Carlo simulations of a simple hydrophobic-polar continuum model for interacting heteropolymers of finite length, we find that the microcanonical entropy behaves convex in the transition region, leading to a negative microcanonical specific heat. As this effect is also seen in first-order-like transitions of other finite systems, our results provide clear evidence for recent hints that the characterization of phase separation in first-order-like transitions of finite systems profits from this microcanonical view.     

Heat transfer in locally heated liquid films moving under the action of gravity and gas flow

Heat transfer in a viscous liquid film moving under the action of gravity and a gas flow on a substrate with a locally heated rectangular area is investigated. The heat exchange coefficient is given on the liquid-gas surface; the heat flux to the liquid is given on the heated area; the substrate surface outside the heated area is heat-insulated. An analytical solution in a form of a convergent series is obtained for the liquid temperature distribution in the film. The influence of the dimensionless criteria on the obtained solution is analyzed. The effect of heat flux inhomogeneity on the temperature distribution is considered.