System-independent release adiabats from shocked states1

Suitable combinations of three parameters of any “linear” material: the initial density, and the coefficients of the linear relationship between shock and particle velocities, are used to define in reduced form most of the variables involved in shock pressures thermodynamic phenomena. This reduced variables formalism is applied, in conjunction with the mirror-image approximation, to obtain pressure-volume relationships for the release adiabats from any given shocked state. The resulting equations are system-independent, that is, they contain only pure numbers and reduced variables. Each adiabat is characterized by the coordinates of the point of crossing with the Hugoniot. Some of the adiabats so obtained for Al, Cu, W, Ti and Cr are in good agreement, at least down to pressures about one half that of the initial shocked state, with those computed using other procedures. A table of adiabats, valid for all “linear” materials, is also included.     

铝热力学特性的晶格动力学研究

在准谐近似下,利用准谐德拜模型通过亥母霍兹自由能构造出了铝在低于熔点温度范围内的物态方程和热力学特性。研究表明,在广泛的温度和压强范围内,铝的体积弹性模量和对应体积与有效的实验值一致,且其静态物态方程以及不同温度和压强下的热容量、熵、热膨胀系数等热力学特性也与有效的实验结果符合的很好。     

Instantaneous Formulation for Transitions Between Two Instantaneous Bound States and Its Gauge Invariance

We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of the equation is instantaneous ＂occasionally＂）. The obtained rigorous instantaneous formulation, in fact, is expressed as an operator sandwiched by two ＂reduced BS wave functions＂ properly, while the reduced BS wave functions appearing in the formulation are the rigorous solutions of the instantaneous BS equation, and they may relate to Schroedinger wave functions straightforwardly. We also show that the rigorous instantaneous formulation is gauge-invariant with respect to the Uem（1） transformation precisely, if the concerned transitions are radiative. Some applications of the formulation are outlined.     

A Positive Formalism for Quantum Theory in the General Boundary Formulation

We introduce a new “positive formalism” for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural and elegant, eliminates operationally irrelevant structure and opens the general boundary formulation to quantum information theory.     

Kinetic equations within the formalism of non-equilibrium thermo field dynamics

After reviewing the real-time formalism of dissipative quantum field theory, i.e. non-equilibrium thermo field dynamics (NETFD), a kinetic equation, a self-consistent equation for the dissipation coefficient and a “mass” or “chemical potential” renormalization equation for non-equilibrium transient situations are extracted out of the two-point Green's function of the Heisenberg field, in their most general forms upon the basic requirements of NETFD. The formulation is applied to the electron-phonon system, as an example, where the gradient expansion and the quasi-particle approximation are performed. The formalism of NETFD is reinvestigated in connection with the kinetic equations.     

Thermodynamics of a Peyrard–Bishop One-Dimensional Lattice with On-site “Hump” Potential

This paper presents a thermodynamic study of DNA through a Peyrard–Bishop one-dimensional lattice with an on-site “hump” potential. The transfer integral operator method was used to obtain the thermodynamic properties of the system and the solution of the Schrödinger-type equation that emerges from this formalism was determined by the variational method. With the parameters of the potential, commonly used in literature, the value obtained for the denaturation temperature was extremely high. This work suggests different parameters to describe the thermodynamics of DNA macromolecule.     

Quantum statistical treatment of multimode self-pulsing in optical systems

We elaborate a formalism which is appropriate to describe the effects of quantum noise in multimode optical instabilities. The multimode Fokker-Planck equation is reformulated in terms of suitable “dressed mode” variables, which diagonalize the linearized part of the drift matrix. We work out explicitly the relations of our formalism with the quantum theory of multiwave mixing.     

Statistical approach to the kinetics of nonuniform fluids

We present a new formalism in Fourier space for the study of spatially nonuniform fluids in nonequilibrium states which generalizes previous work on uniform fluids. Starting from the Liouville equation we obtain a hierarchy of equations for the reduced distribution functions which gives their rate of change at any given order of the system mean density as a sum of a finite number of terms. Using a finite-ranged repulsive interaction potential we derive, as a first application of the formalism, the Boltzmann integrodifferential equation for an infinite system which is initially in a “weakly” inhomogeneous state. This is accomplished introducing an initial statistical assumption, namely initial molecular chaos; this condition is seen to hold during the time evolution described by the resulting kinetic equation.     

Effect of the interaction between the magnetic and phonon subsystems on the magnetic properties of a ferromagnet: Model calculations

Thermodynamical analysis and model calculations for an isotropic ferromagnet show that inclusion of the interaction between the magnetic and phonon subsystems (in particular, through a magnetization-dependent Debye temperature) causes renormalization of the equation of the magnetic state and a temperature dependence of the thermodynamic coefficients of the Landau expansion, which are usually assumed to be constant. One of the consequences of this dependence is, for example, an experimentally observed difference between the “true” and paramagnetic Curie temperatures of a ferromagnet.     

Thermodynamic treatment of nonphysical systems: Formalism and an example (Single-lane traffic)

An effort is made to introduce thermodynamic and statistical thermodynamic methods into the treatment of nonphysical (e.g., social, economic, etc.) systems. Emphasis is placed on the use of theentire thermodynamic framework, not merely entropy. Entropy arises naturally, related in a simple manner to other measurables, but does not occupy a primary position in the theory. However, the maximum entropy formalism is a convenient procedure for deriving the thermodynamic analog framework in which undetermined multipliers are thermodynamic-like variables which summarize the collective behavior of the system. We discuss the analysis of Levine and his coworkers showing that the maximum entropy formalism is the unique algorithm for achieving consistent inference of probabilities. The thermodynamic-like formalism for treating a single lane of vehicular traffic is developed and applied to traffic in which the interaction between cars is chosen to be a particular form of the follow-the-leader type. The equation of state of the traffic, the distributions of velocity and headway, and the various thermodynamic-like parameters, e.g., temperature (collective sensitivity), pressure, etc. are determined for an experimental example (Holland Tunnel). Nearest-neighbor and pair correlation functions for the vehicles are also determined. Many interesting and suggestive results are obtained,     

Fokker-Planck equation approach to fluctuations about nonequilibrium steady states

We examine the properties of steady states in systems which interact at the boundary with a nonequilibrium environment. The examination is based on a nonlinear Fokker-Planck equation, the structure of which is determined by the fact that it also governs the time evolution of the equilibrium fluctuations of the system. The nonlinearities in the Fokker-Planck equation may have two origins: thermodynamic nonlinearities which arise if the thermodynamic potential is not a bilinear function of the state variables, and nonlinear mode coupling which arises if the transport coefficients depend on the state. While these nonlinearities have only a small effect on the equilibrium fluctuations of a system away from critical points, they are shown to be important for the determination of fluctuations about nonequilibrium steady states. In particular the state dependence of the transport coefficients may lead to deviations from local equilibrium and to a breakdown of detail balance. An explicit formula for the time correlations of fluctuations about the nonequilibrium steady state is obtained. The formula leads to long-range correlations in fluids in the presence of a temperature gradient. The result is compared with earlier approaches to the same problem. Finally, we study the linear response to external forces and obtain a generalization of the fluctuation-dissipation formula relating the response functions with the nonequilibrium correlation functions.     

Bulk sound velocity of porous materials at high pressures

A correction of Walsh's method for bulk sound velocity calculation for shocked porous materials is accomplished based on the Wu－Jing thermodynamic equation of state. The corrected bulk velocities for solid and porous samples with low porosities are in good agreement with the corresponding experimental data published previously. On the basis of this corrected equation, the influence of thermoelectrons on the bulk velocity of shocked materials is discussed in detail at pressures of 50, 70 and 200 GPa. Some interesting phenomena are revealed, which seem to be the unique features of a dynamic-pressure-loading process and could not be found in static experiments.     

Nonequilibrium statistical mechanics in the general theory of relativity I. A general formalism

This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The object here is the development of a tractable theory for self-gravitating systems. It is argued that the “state” of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. by mapping the true physics onto a fictitious “background” spacetime, which may be chosen to satisfy some “average” field equations, one then obtains a useful covariant notion of “evolution” in response to a fluctuating “gravitational force.” For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as “localized” in space and time, one obtains a tractable kinetic equation which reduces, in the newtonian limit, to the standard Landau equation.     

On foundation of quantum physics

Some aspects of the interpretation of quantum theory are discussed. It is emphasized that quantum theory is formulated in the Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutator relations between “canonically conjugated” coordinate and momentum operators leads to a wrong version of quantum mechanics. The origin of time is analyzed by the example of atomic collision theory in detail; it is shown that the time-dependent Schrödinger equation is meaningless since in the high-impact-energy limit it transforms into an equation with two time-like variables. Following the Einstein-Rozen-Podolsky experiment and Bell’s inequality, the wave function is interpreted as an actual field of information in the elementary form. The concept “measurement” is also discussed.     

The self-consistent cell model equation of state for solids

An anharmonic equation of state for solids using the Self-Consistent Cell Model (SCCM) is given in a form useful for calculating the usual thermodynamic properties. Following Cowley and Shukla, using the Jaswal-Girifalco potential for copper, calculations are compared with other models and with experiment. The results from the analytic expressions using the SCCM are as good or better than those obtained from far more complicated theories of anharmonicity. Using the Lindemann criterion, the pressure at the melting point was obtained as a function of the melting temperature. A melting line was also obtained for iron and the longitudinal velocity and isothermal bulk modulus along the melting line were calculated. The Hugoniot pressures were calculated and compared with experiment. For both the copper and iron the agreement between theory and experiment is remarkably good considering the empirical nature of the potentials, the simplifying approximations of the SCCM calculations, and the large range of densities and pressures that are compared with experiment.     

Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives.     

Scattering of acoustic waves by macroscopically inhomogeneous poroelastic tubes

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. For planar configurations, the wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently: first in the case of rigid frame inhomogeneous porous materials and then in the case of inhomogeneous poroelastic materials in the framework of Biot's theory. This paper focuses on the solution of the full wave equation in cylindrical coordinates for poroelastic tubes in which the acoustic and elastic properties of the poroelastic tube vary in the radial direction. The reflection coefficient is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method in the case of a two-layer poroelastic tube. As an example, a long bone excited in the sagittal plane is considered. Finally, a discussion is given of ultrasonic time domain scattered field for various inhomogeneity profiles, which could lead to the prospect of long bone characterization.     

THE RELATIVISTIC COVARIANCE OF ONNES EQUATION

On the assumption that Onnes equations meet the requirements of the relativistic covariance, virial coefficients as functions of temperature are derived by using the transformations between thermodynamic variables provided by the vector theory of relativistic thermodynamics, and result in agreement with those obtained from cluster expansions in statistics. This breaks, to some extent, the traditional ideas that the thermodynamic theory is not able to derive equations of state at all and presents a possibly simple and new way of finding theoretically the equation of state.