On the H-theorem for polyatomic gases

The H-theorem for a classical gas of polyatomic molecules of arbitrarily complex structure is examined. A simple use of time reversal invariance of the equations of dynamics is used to circumvent the objections which were raised by Lorentz against Boltzmann's proof (nonexistence of inverse collisions).     

Maximum entropy principle for rarefied polyatomic gases

The aim of this paper is to show that the procedure of maximum entropy principle for the closure of the moments equations for rarefied monatomic gases can be extended also to polyatomic gases. The main difference with respect to the usual procedure is the existence of two hierarchies of macroscopic equations for moments of suitable distribution function, in which the internal energy of a molecule is taken into account. The field equations for 14 moments of the distribution function, which include dynamic pressure, are derived. The entropy and the entropy flux are shown to be a generalization of the ones for classical Grad’s distribution. The results are in perfect agreement with the recent macroscopic approach of extended thermodynamics for real gases.     

The intermolecular pair potential of argon and third virial coefficients

Triplet-triplet (T-T) absorption spectra were measured in the wave-number region between 5000 and 30 000 cm^-1 for the 1,2,4,5-tetracyanobenzene complexes with toluene, mesitylene, durene, and hexamethylbenzene. From the analysis of the observed T-T absorption spectra, with the aid of theoretical considerations based on the interaction among zero-order charge-transfer and locally excited triplet states, the assignment was made and the nature of the lower triplet states of the complexes was clarified. We conclude that the lowest zero-order charge-transfer triplet state and the lowest zero-order locally excited triplet states are close to each other for the complexes, and the charge-transfer character of the lowest state changes from 81 to 15 per cent by changing the electron donor from hexamethylbenzene to toluene.     

The Boltzmann equation for a polyatomic gas

A formulation of the kinetic theory of dilute, classical polyatomic gases is given which parallels the Waldmann development for structureless molecules. In the first section the Boltzmann equation is written in terms of the specific rates of inelastic collision processes and then the properties of these rates and those of the corresponding collision cross sections are examined. The dependence of the distribution function on the dynamical variables is discussed and the equations of change for the gas are derived. Finally, a study is made of the properties of the linearized Boltzmann collision operation. In the second section the Boltzmann equation is deduced from a rigorous statistical-mechanical point of view and discussed in terms of the basic ideas of Bogoliubov. The computationally important special case of impulsive interactions is then considered.This research was supported in part by a grant from the National Science Foundation and in part by the Ames Laboratory of the U. S. Atomic Energy Commission. Contribution No. 2554.     

Monatomic gas as a singular limit of polyatomic gas in molecular extended thermodynamics with many moments

The difference in the theoretical structure between monatomic and polyatomic gases in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (MET) of rarefied gases, which is free from the local equilibrium assumption. The MET theories of these two types of gases are based on the moment balance equations with different hierarchy structures due to whether the internal degrees of freedom of a molecule are incorporated in their distribution functions or not. In particular, the number of balance equations in the MET theory of polyatomic gases is greater than the number in the corresponding theory of monatomic gases. The closure procedure for the system of balance equations of polyatomic gases obtained in a recent paper (Arima et al., 2014) is adopted. We prove that the solutions for polyatomic gases converge, in the limit where the degrees of freedom of a molecule D$D$ tend to 3, to the ones for monatomic gases provided that we impose appropriate initial conditions compatible with monatomic gases. Thus a MET theory of rarefied monatomic gases can be identified as a singular limit of the corresponding MET theory of rarefied polyatomic gases. As illustrative examples, the asymptotic behaviors when D→3$D\to 3$ in the dispersion relation of ultrasonic waves and in the shock wave structure are shown.     

Analysis of the viscosity and second virial coefficients of non-polar polyatomic gases using the m-6-8 potential

Measurements of the catalytic activities of a series of organic radicals regarding the conversion of parahydrogen made it desirable to generalize a model based on a magnetic point dipole which had been proposed by Wigner for ions. The result is that a bilinear form of the spin density of the radical coupled by a geometric expression replaces the square of the dipole strength of the ion. If the sum of the yields of a set of representative collisions is evaluated, a magnitude results which should correspond to the catalytic activity of the radical.

It appears that it is possible to reproduce the relations among the rate constants of the radicals measured experimentally if one uses a spin density built from Hückel orbitals including geometric effects and spin polarization.     

Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent.     

A convergent nonequilibrium statistical mechanical theory for dense gases. III. Transport coefficients to second order in the density

The purpose of this paper is to obtain general expressions for the second-order terms of the transport coefficients of a dense gas. These expressions are obtained using the convergent kinetic theory proposed recently by Braun and Flores.     

Multi-velocity and multi-temperature model of the mixture of polyatomic gases issuing from kinetic theory

In this paper, we consider Euler-like balance laws for mixture components that involve macroscopic velocities and temperatures for each different species. These laws are not conservation laws due to mutual interaction between species. In particular, source terms that describe the rate of change of momentum and energy of the constituents appear. These source terms are computed with the help of kinetic theory for mixtures of polyatomic gases. Moreover, if we restrict the attention to processes which occur in the neighborhood of the average velocity and temperature of the mixture, the phenomenological coefficients of extended thermodynamics can be determined from the computed source terms.     

Mesoscopic transport equations and contemporary thermodynamics: an introduction

The local equilibrium hypothesis is a very successful basis for non-equilibrium thermodynamics over a wide range of phenomena and physical situations. However, the increasing interest in small systems in nanotechnology, in rarefied gases in high-altitude aeronautics, in high-frequency behaviour in information processing, or the search for new materials with sophisticated internal microstructures and tailored thermal properties have led one to ask about the limits of validity of this hypothesis, and to go beyond it. Here we do so in a constructive way, i.e. not only pointing out at these limits, but also embedding the local-equilibrium theory in a more general framework which explicitly exhibits these limits and suggests how to go beyond them, in search for a wider range of applications and a deeper understanding of the foundations.     

On the nonequilibrium statistical mechanics of a binary mixture. II. The transport coefficients

This paper is devoted to the study of the hydrodynamic stage of a two-component dense fluid. Starting from the BBGKY hierarchy obtained earlier, we first derive the expressions for the generalized fluxes. We proceed to set up the generalized kinetic equations, using Bogoliubov's functional assumption. Then we solve these equations by means of a Chapman-Enskog method. The generalized expressions for the transport coefficients are thus obtained. All our results are independent of the existence of density expansions of the relevant quantities.     

Application of the Statistical Rate Theory of interfacial transport to investigate the kinetics of mixed-gas adsorption onto the energetically homogeneous and strongly heterogeneous surfaces

Kinetics of mixed-gas adsorption by using the Statistical Rate Theory is studied. Applying the adsorption lattice model two cases are investigated: when adsorption occurs like on the homogeneous surface and when energetic heterogeneity of adsorption system can be described by the rectangular adsorption energy distribution function. The model of calculations offers possibility of theoretical prediction of the rate of adsorption/desorption of mixture components by using the single-gas equilibrium and kinetic data. Possible changes of adsorbate concentration near the adsorbing surface are also taken into account. The obtained theoretical expressions were verified using real adsorption systems.     

THz radiation generation via the interaction of two‐colour ultra‐short laser pulses with SO2 and NH3 gases

In this work, using a two‐dimensional particle‐in‐cell Monte Carlo collision computation method, terahertz (THz) radiation generation via the interaction of two‐colour, ultra‐short, high‐power laser pulses with the polyatomic molecular gases sulphur dioxide (SO₂) and ammonia (NH₃) is examined. The influence of SO₂ and NH₃ pressures and two‐colour laser pulse parameters, i.e., pulse shape, pulse duration, and beam waist, on the THz radiation generation is studied. It is shown that the THz signal generation from SO₂ and NH₃ increases with the background gas pressure. It is seen that the THz emission intensity for both gases at higher laser pulse durations is higher. Moreover, for these polyatomic gases, the plasma current density increases with increase in the laser pulse beam waist. A more powerful THz radiation intensity with a larger time to peak of the plasma current density is observed for SO₂ compared to NH₃. In addition, many THz signals with small intensities are observed for both polyatomic gases. It is seen that for both SO₂ and NH₃ the generated THz spectral intensity is higher at higher gas pressures.     

Quantum theory of irreversibility

A generalization of the Gibbs–von Neumann entropy is proposed based on the quantum BBGKY (Bogolyubov–Born–Green–Kirkwood–Yvon) hierarchy as the non-equilibrium entropy for an N$N$-body system. By using a generalization of the Liouville–von Neumann equation describing the evolution of a density superoperator, the entropy production for an isolated system is calculated, being non-zero in general. The existence of a non-zero entropy production allows us, following the procedure of non-equilibrium thermodynamics to introduce a master matrix for which a microscopic expression is obtained. After this, as a test of our theory the quantum Boltzmann equation is derived in terms of a transition superoperator related to this master matrix.     

Free cooling and inelastic collapse of granular gases in high dimensions

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velocity field and inelastic collapse when collisions are inelastic enough, showing that the connection with sticky gases needs to be revised. Received 17 April 2000 and Received in final form 7 June 2000     

Energetics of social phenomena: Physics applied to evolutionary biology

Summary The potential usefulness of applications of two physical concepts to evolutionary biology was evaluated on ant societies. The optimization principle, which predicts a more efficient use of energy by more sophisticated societies, was contrasted to that of irreversible thermodynamics, predicting an increase in orderliness and thus an increase in energy consumption per unit of biomass. Our results on oxygen consumption measurements of ant colonies showed a complex and non-linear relationship between colony size and energy consumption per unit mass, that can be explained by irreversible thermodynamics and catastrophe theory, whereas an additional exponential inverse relationship may be explained by optimization principles. Thus, social complexity is related to energy consumption in a discontinuous manner, and seems to be bound by both negentropy content of a society and social-optimization mechanisms.     

Near-surface Brownian motor with synchronously fluctuating symmetric potential and applied force

A model is suggested which accounts for the unidirectional surface-parallel motion of a Brownian particle under the action of fluctuating surface-inclined unbiased external force. The surface-normal force component induces amplitude fluctuations of the symmetric periodic near-surface potential, whereas the surface-parallel component makes the particle move along the surface. The combined effect of synchronous fluctuations of the symmetric potential and the applied force leads to the longitudinal drift of the particle. It is shown that the temperature dependence of the motor velocity is nonmonotonic, with the maximum governed by the range of the near-surface potential.     

n维经典非理想气体的物态方程与热力学函数

求出了n维经典非理想气体的物态方程和热力学函数.由London理论得出了维数n(n<6)不同时的经典非理想气体的物态方程形式基本一样,且与能谱关系无关的结论;当维数n≥6时,如果仍用London理论,巨配分函数发散,此时物态方程及热力学函数将无意义.事实上只要使用刚性球模型,无论是否使用London理论,总存在一个维数n,当维数大于n时巨配分函数发散.     

Cross sections and transport properties of Cl<Superscript>-</Superscript> ions in noble gases

We have used a simple semi-analytic — momentum transfer theory (MTT) to develop negative halogen ions/noble gases momentum transfer integral cross sections based on the available data for reduced mobility at 300 K as a function of E/N. The unfolded cross sections were validated or further improved by assuring a good agreement between our Monte Carlo (MC) calculated transport data and the available experimental results. The data are produced with an aim to provide plasma modellers with cross section data and transport coefficients. We have also calculated the net rates of elastic scattering and detachment.