Non-equilibrium Part Research Articles

An extended Gibbs relation for the relativistic Boltzmann entropy: classical and quantum gases

In this paper, an extended Gibbs relation is derived for the Boltzmann entropy (per unit volume) from the fundamental principles of general-relativistic kinetic theory of monatomic ideal gases, both classical and quantum. The discussion is based on the well-known extremum property of entropy and the additional observation which has certain elements in common with the infinite-dimensional version of a critical-point theory. As a matter of fact, the joint use of these two concepts enables us to define a privileged class of gas-state variables, the basic role of which is associated with the unique parametrization of the space of distribution functions and the exact decomposition of the relativistic Boltzmann entropy into equilibrium and nonequilibrium parts. By taking the infinitesimal variation of this decomposition, the derivation of an expression for the extended Gibbs relation can be carried out in a step-by-step analogy to the case of equilibrium thermodynamics. In standard textbook treatments of entropy, the method of moments is frequently used to obtain similar results. However, our approach can be viewed as providing a rule for how to understand the notion of an extended Gibbs relation without the need of expressing the distribution function in terms of its all moments.

Dissipation in ferrofluids: Mesoscopic versus hydrodynamic theory

Part of the field dependent dissipation in ferrofluids occurs due to the rotational motion of the ferromagnetic grains relative to the viscous flow of the carrier fluid. The classical theoretical description due to Shliomis (Zh. Eksp. Teor. Fiz. 61, 2411 (1971) [Sov. Phy JETP 34, 1291 (1972)]) uses a mesoscopic treatment of the particle motion to derive a relaxation equation for the nonequilibrium part of the magnetization. Complementary, the hydrodynamic approach of Liu [Phys. Rev. Lett. 70, 3580 (1993)] involves only macroscopic quantities and results in dissipative Maxwell equations for the magnetic fields in the ferrofluid. Different stress tensors and constitutive equations lead to deviating theoretical predictions in those situations, where the magnetic relaxation processes cannot be considered instantaneous on the hydrodynamic time scale. We quantify these differences for two situations of experimental relevance, namely, a resting fluid in an oscillating oblique field and the damping of parametrically excited surface waves. The possibilities of an experimental differentiation between the two theoretical approaches is discussed.

Reconsidering the Concept of Equilibrium in Classical Statistical Mechanics

In the usual procedure of deriving equilibrium thermodynamics from classical statistical mechanics, Gibbsian fine-grained entropy is taken as the analogue of thermodynamical entropy. However, it is well known that the fine-grained entropy remains constant under the Hamiltonian flow. In this paper it is argued that we need not search for alternatives for fine-grained entropy, nor do we have to reject Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, to account for the non-equilibrium part of the laws of thermodynamics. Rather, we have to weaken the requirement that equilibrium be identified with a stationary probability distribution.

Spectrum and Attenuation of Non-Linear Surface Magnetostatic Spin Waves in Ferrite Films

Dispersion and attenuation of non-linear surface magnetostatic waves (MSSW) propagating in thin yttrium-iron-garnet (YIG) ferrite films have been studied both experimentally and theoretically. They were defined from the amplitude and phase alterations of the wave as it traveled along the non-equilibrium part of the film. At the border of such a non-equilibrium part the wave power is equal to the threshold value. The value for the threshold power is defined by the first- and second-order parametric decay processes for the MSSW.

Aging in two-dimensional random-exchange Ising ferromagnets

Domain growth in the two-dimensional random-exchange Ising ferromagnet Rb2Cu0.89Co0.11F4 is studied using ac and dc magnetization measurements. From a scaling analysis of the time and frequency dependences of the nonequilibrium part of the ac susceptibility the ferromagnetic domain size R(t) is found to grow according to R(t) α ⦜ln t]1/gy, with ψ = 14.

Self-consistent temperature waves in Fermi glasses with thermally activated conductivity.

The basic equations of the presented model are the Maxwell heat-conduction equation, the kinetic equation for the thermally activated carriers in Fermi glasses, and the Gauss equation. Assuming, that the temperature and the concentration of the thermally activated carriers may be divided into equilibrium and nonequilibrium parts and that the electric field consists of constant and variable parts, the system of equations is linearized. It is shown that it possesses solutions in the form of nondamped self-consistent temperature waves (STW's) similar to second-sound waves. These solutions are analyzed and it is shown that STW's exist down to some limiting frequency. Numerical calculations are performed for the Fermi-glass phase of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$.

The Fortnightly and Monthly Tides: Resonant Rossby Waves or Nearly Equilibrium Gravity Waves?

The fortnightly and monthly tides are discussed in the light of recent sea level observations and numerical modeling results. Within the tide gauge network of the low-latitude Pacific, the fortnightly tide is shown to possess a large-scale phase lag of roughly 10–40 degrees. Although the nonequilibrium part of the fortnightly tide is traditionally thought to be dominated by Rossby wave dynamics, it is shown, via global shallow-water modeling studies, that this large-scale phase lag is explicable in terms of remotely forced gravity waves whose origin is mainly in the Arctic Ocean. Although future observations outside the low-latitude region of the Pacific may eventually reveal Rossby wave excitation, the fortnightly tidal signal in the tide gauge network at hand appears to reveal at most only weak excitation of Rossby waves compared to the phase lag due to remotely forced gravity waves. The observed monthly tide appears to be only slightly closer to equilibrium than the fortnightly tide. The reason for this remains unclear since the monthly tide is less affected by the remotely forced gravity waves than the fortnightly tide.

The equilibrium pole tide of the anelastic Earth and its effect on the Chandler wobble

According to the perturbation principle of the Love numbers and load Love numbers, the perturbation of mantle anelasticity to the equilibrium pole tide of the elastic Earth and its effect on the period and Q value of the Chandler wobble are discussed by using the elastic Earth model PREM and Zschau's mantle theological model. The results obtained show that the effect of the anelastic perturbation of the equilibrium pole tide on the Chandler wobble is much larger than that of the non-equilibrium part of the pole tide, but it is still in the range of error of the present astronomically observed values.

Revision of the modified moment method and a differential form for the compensated part of entropy

The modified moment method is revised so that the consistency condition is replaced by a differential equation for a dissipation function. This revision given this by a differential form for the compensated part of entropy which is given in terms of substantial usage derivatives of conserved and nonconserved macroscopic variables and derivatives of the former with respect to the latter. In this method the distribution function and the entropy are determined in functionals of the macroscopic variables when the conservation laws and the evolution equations are solved subject to initial and boundary condition and the differential equations for the compensated part of entropy is integrated. The internal consistency of the method is proven. A couple of methods are discussed which allows to determine the distribution function approximately. One of the method is discussed in detail and the results agree with the lowest-order solutions for the consistency condition for the non-equilibrium part of the distribution function in the original version of the modified moment method. Therefore the present revision does not affect the evolution equation using each conditions in the dissipation terms in the previous applications of the modified moment method.

The nonequilibrium part of the photoinduced magnetization in semimagnetic semiconductors

The optical orientation in semimagnetic semiconductors is studied. It is shown that in the absence of an external magnetic field the nonequilibrium photomagnetization is certainly greater than the equilibrium photomagnetization, connected with cooling of the magnetic ions by the oriented electrons.

Features of structure formation in alloy ZhS6U after temperature and time treatment of the melt

1. Use of time and temperature treatment for the melt promotes formation of the combination of structure and properties for cast alloy ZhS6U: dendrite structure is refined, a favorable carbide morphology forms, and mechanical properties are improved. 2. For more complete revelation of the possibilities for cast nickel alloy ZhS6U with carbide and intermetallic strengthening melted with TTT for the melt adjustment is necessary to the existing heat treatment or development of new schedules. 3. Homogenization of alloy ZhS6U TTT for the melt promotes dissolution of the nonequilibrium part of the eutectic and an increase in the amount of secondary strengthening γ′-phase.

The stress state of Venusian crust and variations of its thickness: Implication for tectonics and geodynamics

The data obtained for the heights of the relief and the external gravitational field of Venus for spherical harmonics with degree and order up to 18 allow one to start theoretical analysis of the crust-mantle boundary (Venusian Moho) and stress state of the planetary interior. We suppose that Venusian convection is confined by floating massive crust. Apparently the convection in the upper mantle of Venus is separated from that one in the lower mantle and its lateral scale must be essentially smaller than on Earth. So, the convection is reflected to a larger degree of the gravitational field of the planet than for Earth. The spherical harmonic expansion of the topography for Venus correlates with corresponding expansion of the non-equilibrium part of the gravitational potential for n = 3–18. At the same time the relief of Venus is significantly compensated. It is reasonable to suppose that the gravity field for these harmonics is due to crustal thickness variations and, probably, to variations of crustal density. Thus, in the proposed scheme the Moho's relief causes the partial isostatic compensation of the topography.

Two‐Site/Two‐Region Models for Pesticide Transport and Degradation: Theoretical Development and Analytical Solutions

AbstractAnalytical solutions are presented for two convection‐dispersion type transport models useful for studying simultaneous pesticide sorption and degradation. One solution is for the familiar two‐site sorption model in which adsorption‐desorption proceeds kinetically on one fraction of the sorption sites, and at equilibrium on the remaining sites. Another solution holds for two‐region (or mobile‐immobile liquid phase) transport appropriate for aggregated or fractured media. The transport models account for degradation in both the solution and sorbed phases. The dimensionless analytical solutions for the two‐site and two‐region models are shown to be identical; they contain up to six independent dimensionless parameters: a column Peclet number, a retardation factor, a coefficient partitioning the soil/chemical system in equilibrium and nonequilibrium parts, a rate coefficient, and two dimensionless degradation coefficients. One of the two independent degradation coefficients may be eliminated when the solution and sorbed phase degradation rate coefficients are assumed to be identical, or when, with additional but reasonable assumptions, adsorbed phase degradation is assumed to be negligible.

Modified-moment method for the Fokker-Planck equation and some aspects of the thermodynamics of irreversible processes.

The modified-moment method is applied to solve the Fokker-Planck equation in such a way that the solution is consistent with the requirements of the thermodynamic laws. The formal solution has an attendant mathematical structure for the entropy which is similar to that obtained from the Boltzmann equation. A generalized Gibbs relation is obtained for such a thermodynamic branch of solution. The formalism therefore may be used to study thermodynamic aspects of stochastic processes underlying the Fokker-Planck equation. The method is shown to yield the same analytical results as other methods in the case of linear processes, and in the case of nonlinear processes the moment series converges sufficiently fast to justify a lower-order truncation of the moment series for the distribution function, if the diffusion constant (D) is less than a critical value. In this case the solution of the Fokker-Planck equation tends to the steady-state distribution function. It is shown that the second variation of the nonequilibrium part of the entropy may be used as a Lyapunov function, which provides local criteria of evolution only.

The “harmonic liquid” away from equilibrium: I. Stationary correlation functions

Some aspects of the linear chain of harmonic oscillators (“harmonic liquid”) are studied. In particular we compute the stationary correlation functions of coordinates and momenta of the oscillators for a particular non-equilibrium steady state. We find that the coordinates and momenta autocorrelation functions are analogous to their equilibrium counterparts whereas the coordinates-momenta correlation functions exhibit long-range behaviour due to time reversal symmetry breaking. The non-equilibrium entropy of the chain is also computed. It contains a non-equilibrium part that depends on the temperature of the external sources and on the stationary temperature. A comparison with a non-equilibrium entropy obtained from information theory is made.

Molecular dynamics simulations of the holo and apo forms of retinol binding protein: Structural and dynamical changes induced by retinol removal

The effects of removing retinol from the X-ray structure of holo-retinol binding protein are studied using the molecular dynamics technique. Structural and dynamical properties emerging from an 80 ps simulation of the apo form, for which no crystallographic structure is available, are compared with the results of a 70 ps trajectory of the holo-protein. Dynamical stationarity is attained after roughly 30 ps, and the resulting average structure is proposed as a reasonable model of the apo-protein. Conformational changes are observed for the loops at the β-barrel entrance during the non-equilibrium part of the apo-trajectory. Tryptophan labelling experiments and retinoid reconstitution experiments point towards this part of the molecule as being involved in prealbumin binding. Structural changes in this region may therefore explain the differences in prealbumin affinity between the apo and holo forms. Furthermore, a change in the position of the α-helix, corresponding to a pivot around its C terminus, is observed for the apo-protein. The resulting conformation of the α-helix is found to be similar to that in apo-β-lactoglobulin, which also can bind retinol and for which a crystal structure exists. The results from the holo simulation are compared to the crystallographic data and show good agreement. The dynamics of the secondary and tertiary structural elements are analysed and compared for the two forms. The β-barrel is found to be extremely co-operative in its atomic motions in both simulations, and the top and bottom β-sheets perform collective fluctuations with respect to each other in the low-frequency limit of the simulations. The dynamics of the α-helical region presents clear differences between the two forms; while the holo-protein has a well-defined spectrum for the longitudinal stretching mode, the apo form displays a fairly large bending of the α-helix at several points of the trajectory.

Study of the optical piston.

We report an experimental and theoretical study of the optical piston, a consequence of the phenomenon of light-induced drift (LID), observed in binary mixtures of Na vapor and a buffer gas. Good agreement has been found between experiment and existing theory as far as the shape of the Na density profile in the piston is concerned. The piston velocity is anomalously low; this is accounted for by incorporating the effects of adsorption and desorption into the theory. Furthermore, we introduce a rate-equation model for LID which incorporates the fine and hyperfine structure of the level scheme of the Na absorbers; this gives insight into the sublevel velocity distributions and the nonequilibrium part of the total velocity distribution during LID.

Breakup-fusion description of nonequilibrium protons from ( α, p) reactions

The nonequilibrium part of the proton spectra from a few ( α, p) reactions is calculated, assuming the breakup-fusion (BF) mechanism. It is shown that the calculation reproduces very well the higher-energy parts of the observed spectra, but underestimates the lower-energy parts. The reason why this happens and a plausible mechanism that may fill up this gap are discussed.

Surface plasmon damping due to rough boundary scattering

The surface plasmon damping due to carriers scattering at the statistically rough (semiconductor-dialectric) interface is considered. The specular parameter and the integral relation are used as the boundary condition for a non-equilibrium part of the distribution function. There exist certain cases when the rough surface scattering of carriers is shown to play an important role in the surface plasmon damping.

Neutron emission inC12+Gd158andC13+Gd157reactions between 8 and 12 MeV/nucleon

Neutron spectra in coincidence with evaporation residues and with projectilelike fragments emitted in inelastic scattering reactions have been measured at several bombarding energies for /sup 12/C- and /sup 13/C-induced reactions leading to the same compound nucleus /sup 170/Yb. In the fusion reactions, a nonequilibrium component was observed in the neutron spectra at all beam energies. This component is forward peaked and is associated with a high temperature. The spectra can be parametrized by assuming the nonequilibrium part to result from a hot region (Tapprox.4 MeV) emitting neutrons isotropically and moving with a velocity of approximately 1 cm/ns. This apparent velocity decreases with decreasing beam velocity. Comparisons are made with predictions based on the generalized critical angular momentum model of incomplete fusion of Siwek-Wilczynska et al. No significant difference has been observed between nonequilibrium neutron emission from /sup 12/C- and /sup 13/C-induced reactions. Neutron emission associated with inelastic scattering reactions cannot be described by simple statistical evaporation from two fragments of equal temperature. Effects which may give rise to the observed energy and angular distributions of neutrons in coincidence with inelastic products are discussed.