Nonlocal integral conservation laws and tetradic currents in the Einstein-Cartan theory I. Nonlocal conservation laws

Nonlocal integral conservation laws in the Einstein-Cartan theory for the energy-momentum tensor of general-form sources, in essence being an integral equivalent of convoluted Bianchi identities, are obtained.     

On the statistical theory of spatial structure formation in random media

It is shown that, in parametrically excited stochastic dynamic systems described by partial differential equations, space structures (clustering) can be formed with probability 1 due to rare events occurring with probability tending to zero. Such problems arise in hydrodynamics, magnetohydrodynamics, plasma physics, astrophysics, and radiophysics. … Chaos is the place which serves to contain all things; for if this had not subsisted neither earth nor water nor the rest of the elements, nor the Universe a whole, could have been constructed… Sextus Empiricus, Against the Physics, against the Ethicists, R. G. Bury, p. 217, Harvard University Press, 1997.     

Role of nonequilibrium entropy in Einstein’s theory of gravitation

We employ the covariant version of a systematic framework of nonequilibrium thermodynamics to clarify the role of entropy in the classical theory of gravitation. An expression for the global entropy is identified naturally from the covariant formulation, and a dual role of the Einstein equation as a fundamental evolution equation and as a thermodynamic equation of state follows immediately. The covariant time integral of the entropy is a more fundamental quantity than the entropy itself. In the absence of matter, the gravitational entropy alone cannot generate any irreversible processes. Some implications for the structure of a quantum theory of gravity are discussed.     

Nonlocal effects in diffusive propagation of heat pulses in systems with trapping centers of nonequilibrium phonons

The propagation of heat pulses in systems with defects as trapping centers of nonequilibrium phonons is investigated theoretically. Among these defects are point defects involving two-level systems (TLSs) of different nature. It is demonstrated that, in addition to the principal signal, one more signal can be detected by the bolometer due to reemission of the nonequilibrium TLS energy at a certain ratio of relaxation times in the phonon and TLS subsystems. The temperature and concentration dependences of the time of signal arrival at the bolometer are analyzed. The results of theoretical investigations are compared with experimental data on the propagation of weakly nonequilibrium thermal phonons in solid solutions of the Y_3?x Er_xAl₅O₁₂ rare-earth yttrium aluminum garnets.     

The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transform ) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z= and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover, may be expressed by a Laurent series expansion in positive and negative powers ofz, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions of as obtained from the application of conventional many-body techniques to the calculation of . The expressions are formulated as time scale expansions, which should rapidly converge if macroscopic and microscopic time scales are sufficiently well separated, i.e., if lifetime (memory) effects are not too large.     

On the hydrodynamic theory of a magnetic liquid I. General description

Using Zubarev's method of nonequilibrium statistical operator, the generalized hydrodynamic equations are obtained for a model of magnetic liquid in an inhomogeneous external field. In this model the “liquid” subsystem is treated as a classical one and the “magnetic” subsystem is described by quantum mechanical methods. The properties of the transport equations are analysed in the case of a weak nonequilibrium. The equations for time correlation functions and collective mode spectrum are also found in the same manner. It is shown that the generalized hydrodynamic equations reduce to the well-known results in the limiting cases when the dynamic variables of one subsystem are formally neglected. As an illustration, a simple model of spin relaxation is considered, and the frequency matrix and the matrix of memory functions are calculated. A comparison with previous works is made.     

Reference motion in deformable bodies under rigid body motion and vibration. Part I: theory

This paper examines the motions of reference systems linked to deformable bodies under simultaneously vibration and large translations and rotations. These motions depend on the particular type of linkage between the moving reference system and the deformable body, which is defined by the so-called reference conditions. When using the Rayleigh-Ritz method, the reference conditions also dictate the boundary conditions to be fulfilled by the shape functions used to describe the body's elasticity. This paper analyses three different types of reference conditions, namely: free linkage, rigid linkage and two-point linkage. It is shown that, moving reference frames only evolve at a constant velocity in the absence of external forces when the free linkage is used. The reference velocities for systems with a free linkage are designated rigid body equivalent velocities for the deformable body here. Such velocities can also be calculated under other types of reference conditions and are usually functions of the elastic and reference co-ordinates, and also of their derivatives. Rigid body equivalent velocities are useful for purposes such as estimating the trajectory of deformable bodies moving freely in space without the need to examine the deformations they undergo. Also, their calculation is required with a view to determining the kinematic restitution coefficient for deformable body collisions, which is dealt within Part II of this series.     

Multifractal structure of fully developed hydrodynamic turbulence. I. Kolmogorov's third hypothesis revisited

We discuss intermittency effects in fully developed hydrodynamic turbulence. It is shown that the application of the bounded log-normal distribution to the fluctuations of the local energy dissipation rate resolves some basic difficulties related to Kolmogorov's third hypothesis and gives a good agreement with experiment. The nonlinear interaction of the large-scale and inertial-range turbulent pulsations of the velocities may explain the observable characteristics of the intermittency. We give also a detailed comparison of the results obtained with the use of the bounded log-normal distribution with that obtained in the framework of the homogeneous and random-models, a two-scale Cantor set approximation, and the original unbounded log-normal distribution suggested by Kolmogorov and Obukhov.     

Electromagnetic effects on a molecule at a metal surface: I. Effects of nonlocality and finite molecular size

The electromagnetic effects on a molecule near a metal surface are considered with the view to understanding the surface-enhanced-Raman-scattering (SERS) effect. The image enhancement effect is calculated including the nonlocal response of the metal and finite molecular size. The effect is much reduced (× 10^?5) from that for a point molecule above a local metal but can still give a gain ≈ 10³. The power emitted by a dipole above a smooth surface is also calculated. For an Ag surface the power emitted in the form of photons, surface plasmons, and electron-hole excitations are found to be in the ratio 1 : 3 : 10⁶. The numerical results are calculated using the semi-classical infinite-barrier model of the metal surface with a Lindhard dielectric function modified to take into account finite electron lifetime and core polarization.     

Microscopic theory of superfluid3He-superfluid4He solutions I. Derivation of hydrodynamic equations

The hydrodynamic equations for mixtures of superfluid³He and superfluid⁴He are derived on the basis of the microscopic theory proposed by Bogoliubov.     

Finite correlation time effects in nonequilibrium phase transitions: I. Dynamic equation and steady state properties

We determine an approximate renormalized equation of evolution for an arbitrary nonlinear single-degree-of-freedom system externally driven by Gaussian parametric fluctuations of finite correlation time. The renormalization scheme used here gives a second order equation with a time-and-state-dependent “diffusion coefficient”. We are able to calculate the diffusion coefficient in closed form. The steady-state distribution can easily be obtained from the evolution equation. We are thus able to determine the parameter dependence of the steady-state distribution and, in particular, the influence of a correlation time of the fluctuations, which does not vanish, on the steady-state distribution.     

Correlation effects in the theory of combined doppler and pressure broadening—I. Classical theory

A classical Fourier amplitude theory of combined Doppler and pressure broadening in the impact approximation is developed which treats phase changes changes due ti translation and collision on an equal basis. Radiator motion is accounted for properly by including speed dependence in the collision frequency and velocity dependence in the distribution function for phase shifts and final velocities as the result of a collision. The resulting theory is shown to be equivalent to a previous kinetic equation formulation of the problem. The one-perturber and classical analogue of the quantum one-interacting-level approximations are derived. In the latter case, a simple expression for the line shape in terms of speed dependent width and shift functions is obtained without approximation. Correlation effects are investigated by means of model speed dependent width and shift functions calculated for an inverse power interaction using straight line trajectories. The model shows no departure from a Voigt profile for the r^-3 interaction and for the r^-6 and r^-12 interactions the resulting profile is narrower in the core than the Voigt and in general asymmetric. Analysis of correlated profiles as Voigt profiles is shown under some conditions to lead to non-linear density dependence in the width and shifts resulting in extra- polation anomalies and to significant errors in temperatures inferred from Doppler widths. Results are compared with previous work.     

Multifractal structure of fully developed hydrodynamic turbulence. II. Intermittency effects in the distribution of passive scalar impurities

We discuss intermittency effects in the distribution of scalar passive impurities within fully developed hydrodynamic turbulence. It is shown that the observable stronger intermittency effects in the distribution of passive impurities with respect to that for the energy dissipation rate can naturally be explained in the framework of composite random cascade models. We discuss doubly random bounded and unbounded log-normal models, the doubly random-model, and the two-scale Cantor set approximation. Then the problem of mutual correlations is discussed. The various results are compared with experiments.