Realistic equations of state for the primeval universe

Equations of state for the early universe including realistic interactions between constituents are formulated. Under certain hypotheses, these equations are able to generate an inflationary regime prior to the period of the nucleosynthesis. The resulting accelerated expansion is intense enough to solve the flatness and horizon problems. In the cases of a curvature parameter κ equal to 0 or +1, the model is able to avoid the initial singularity and offers a natural explanation for why the universe is in expansion. All the results are valid only for a matter–antimatter symmetric universe.     

Polaron in a strong alternating electric field

The solution is found for the transport equation for a Feynman polaron having arbitrary coupling interacting with the acoustic oscillations in an alternating electric field. In the low-frequency case, this solution cannot be normalized — there are runaway polarons. For high frequencies, this effect is absent. Equations are obtained for the electrical conductivity of polaron semiconductors for various particular cases, including the runaway regime.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 45–49, April, 1979.     

Nonlinear interaction between acoustic and orientation waves in liquid crystals

Taking incompressibility of the medium into account is shown to lead to nonlinear coupling between acoustic and orientation waves in a nematic liquid crystal. Equations for three-wave resonant interaction are derived and the regime of nonlinear excitation of orientation waves in the course of propagation of a powerful high frequency acoustic wave in a liquid crystal is investigated.Branch of the Institute of Machine Management, Russian Academy of Sciences, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 1–2, pp. 146–152, January–February, 1995.     

Spiral Galaxy Rotation Curves Determined from Carmelian General Relativity

Equations of motion, in cylindrical co-ordinates, for the observed rotation of gases within the gravitational potential of spiral galaxies have been derived from Carmeli's Cosmological General Relativity theory. A Tully-Fisher type relation results and rotation curves are reproduced without the need for non-baryonic halo dark matter. Two acceleration regimes are discovered that are separated by a critical acceleration m s⁻². For accelerations larger than the critical value the Newtonian force law applies, but for accelerations less than the critical value the Carmelian regime applies. In the Newtonian regime the accelerations fall off as r ⁻², but in the Carmelian regime the accelerations fall off as r ⁻¹. This is new physics but is exactly what is suggested by Milgrom's phenomenological MOND theory.     

A More General Treatment of Abrasion-Chipping Processes applicable to FAG/SAG Milling

Equations are derived for the rate of loss of mass from a screen interval when the size reduction process is an abrasion-chipping process which follows a wear law of the Bond form or the Davis form, giving cores and fragments. The treatment is extended to steady-state continuous grinding in a fully-mixed reactor, and to the case where first-order disintegrative fracture processes also occur.     

Moment equations and the dynamic equilibrium condition for a relativistic electron beam propagating along an external magnetic field in dense and rarefied gas-plasma media

Equations of transfer of mass, momentum, and energy for a transverse segment of a paraxial relativistic electron beam propagating in dense and rarefied gas-plasma media along an external magnetic field are derived from the kinetic equation. A virial equation is obtained, and the dynamic equilibrium condition that generalizes the wellknown Bennet equation for the cases under study is found.     

矩形微槽道气体流动的速度分布

矩形微槽道的各个流向截面可以局部近似为平面Poiseuille流动,应用信息保存(IP)方法和直接模拟Monte Carlo(DSMC)方法计算了从连续介质区到自由分子流区的平面Poiseuille流动,利用其结果对Beskok-Karniadadis公式和质量流率动理论因子进行修正和重新拟合,给出在整个稀薄气体流动领域都适用的微槽道气体流动速度分布.     

Dynamics of a stochastically driven Brownian particle in one dimension

We present a study on the dynamics of a system consisting of a pair of hardcore particles diffusing with different rates. We solved the drift-diffusion equation for this model in the case when one particle, labeled F, drifts and diffuses slowly toward the second particle, labeled M. The displacements of particle M exhibits a crossover from diffusion to drift at a characteristic time which depends on the rate constants. We show that the positional fluctuation of M exhibits an intermediate crossover regime of subdiffusion separating initial and asymptotic diffusive behavior; this is in agreement with the complete set of Master Equations that describe the stochastic evolution of the model. The intermediate crossover regime can be considerably large depending on the hopping probabilities of the two particles. This is in contrast to the known crossover from diffusive to subdiffusive behavior of a tagged particle that is in the interior of a large single-file system on an unbound real line. We discuss our model with respect to the biological phenomena of membrane protrusions, where polymerizing actin filaments (F) push the cell membrane (M).     

Piston engine driven by a cw laser

The construction and operating principles of a piston laser engine driven by a cw laser and its indicator diagrams are considered under various operating conditions. Equations are given for the indicator efficiency of the engine as a function of the opening angle of the obturator that controls the entry of the laser energy into the cylinder, and recommendations are made for the choice of the optimal regime. Engines with working volumes 2.5 and 45 cm³ driven by a 1-kW CO₂ laser were constructed. The former reached 3600 rpm.Translated from Trudy Fizicheskogo Instituta im. P. N. Lebedeva, Vol. 120, pp. 100–105, 1980.     

Design of Closed-Cycle MHD Generator with Nonequilibrium Ionization and System

A closed-cycle MHD generator topping a steam bottoming plant is analyzed. The combined power plant involves three working fluids in three loops. The MHD loop is investigated more thoroughly since it is the least conventional of the three. Equations are developed to determine the geometric and thermodynamic variables throughout the MHD channel for inlet conditions of mass flow, temperature, pressure, and velocity. Limiting design parameters are output power, channel length, channel aspect ratio, Hall parameter, and interaction parameter. The basic closed-cycle MHD loop working fluid can consist of either argon or helium seeded with cesium. Both non-equilibrium ionization produced by the elevation of the electron temperature from joule heating of the plasma and thermal ionization are considered. Equations used to calculate the electrical conductivity and the elevation of electron temperatures are derived. These equations are coupled with the one-dimentional differential equations applicable to an MHD generator. The chief interest is in determining those MHD channel conditions which result in the most thermodynamically efficient MHD-steam plantcombination. Thus an overall heat balance forthe system is required. Equations are developed to calculate the gas properties at the various stations of the closed loop and to determine the overall efficiency of the cycle. A rather flexible computer program written in Fortran is used to solve the MHD generator equations and to make the overall heat balance. Some typical results presented demonstrate the feasibility and adaptability of the analysis for optimizing the thermal efficiency and the sensitivity of thermal efficiency to various parameters.     

Full phase diagram of the massive Gross-Neveu model

The massive Gross-Neveu model is solved in the large-N limit at finite temperature and chemical potential. The scalar potential is given in terms of Jacobi elliptic functions. It contains three parameters which are determined by transcendental equations. Self-consistency of the scalar potential is proved. The phase diagram for non-zero bare quark mass is found to contain a kink-antikink crystal phase as well as a massive fermion gas phase featuring a cross-over from light to heavy effective fermion mass. For zero bare quark mass, we recover the three known phases kink-antikink crystal, massless fermion gas, and massive fermion gas. All phase transitions are shown to be of second order. Equations for the phase boundaries are given and solved numerically. Implications on condensed matter physics are indicated where our results generalize the bipolaron lattice in non-degenerate conducting polymers to finite temperature.     

Mobile bipolaron

We explore the properties of the bipolaron in a 1D Holstein-Hubbard model with dynamical quantum phonons. Using a recently developed variational method combined with analytical strong coupling calculations, we compute correlation functions, effective mass, bipolaron isotope effect, and the phase diagram. The two site bipolaron has a significantly reduced mass and isotope effect compared to the on-site bipolaron, and is bound in the strong coupling regime up to twice the Hubbard U naively expected. The model can be described in this regime as an effective t-J-V model with nearest neighbor repulsion. These are the most accurate bipolaron calculations to date.     

A theoretical study of the spheroidal droplet evaporation in forced convection

In many applications, the shape of a droplet may be assumed to be an oblate spheroid. A theoretical study is conducted on the evaporation of an oblate spheroidal droplet under forced convection conditions. Closed-form analytical expressions of the mass evaporation rate for an oblate spheroid are derived, in the regime of controlled mass-transfer and heat-transfer, respectively. The variation of droplet size during the evaporation process is presented in the regime of shrinking dynamic model. Comparing with the droplets having the same surface area, an increase in the aspect ratio enhances the mass evaporation rate and prolongs the burnout time.     

Quantum chaos of atoms in a resonant cavity

A system of atoms interacting with a radiation field in a resonant cavity is studied under conditions when the dynamics in the classical limit is stochastic. This situation is called quantum chaos. Equations of motion are obtained for the quantum-mechanical expectation values which take into account the quantum correlation functions. It is shown that in a situation corresponding to quantum chaos, the quantum corrections grow exponentially, making the evolution of the system essentially quantal after a certain time tau( variant Planck's over 2pi ) has elapsed. Analytical and numerical analysis show that in this regime the time tau( variant Planck's over 2pi ) obeys the logarithmic law tau( variant Planck's over 2pi ) approximately ln N (N is the number of atoms), and not the law tau( variant Planck's over 2pi ) approximately N(alpha) (alpha is a certain constant of order unity), as would be the case in the absence of chaos.     

Impact of massive neutrinos on the nonlinear matter power spectrum

We present the first attempt to analytically study the nonlinear matter power spectrum for a mixed dark matter model containing neutrinos of total mass ~0.1 eV, based on cosmological perturbation theory. The suppression in the power spectrum amplitudes due to massive neutrinos is enhanced in the weakly nonlinear regime. We demonstrate that, thanks to this enhanced effect, the use of such a nonlinear model may enable a precision of sigma(m(nu,tot)) ~ 0.07 eV in constraining the total neutrino mass for the planned galaxy redshift survey, a factor of 2 improvement compared to the linear regime.     

Gas flow through a slit into a vacuum in a wide range of rarefaction

Gas flow through a two-dimensional slit into a vacuum is investigated by a direct simulation Monte Carlo method. Results for the mass flow rate are obtained as a function of the rarefaction parameter, which is inversely proportional to the Knudsen number. The distributions of density, temperature and mass velocity, and streamlines are presented. In the free molecular flow regime and in the hydrodynamic limit, our results agree with theoretical asymptotes, and in the transition regime, they compare well with numerical simulations by other authors. The text was submitted by the author in English.     

Metal-insulator transitions in the periodic Anderson model

We solve the periodic Anderson model in the Mott-Hubbard regime, using dynamical mean field theory. Upon electron doping of the Mott insulator, a metal-insulator transition occurs which is qualitatively similar to that of the single band Hubbard model, namely, with a divergent effective mass and a first order character at finite temperatures. Surprisingly, upon hole doping, the metal-insulator transition is not first order and does not show a divergent mass. Thus, the transition scenario of the single band Hubbard model is not generic for the periodic Anderson model, even in the Mott-Hubbard regime.     

Quark-Gluon Interactions at High Temperature and Large Distances

Continuum fourdimensional Quantum Chromodynamics (QCD) including quarks in the regime of high temperature and large distances (the HT regime) is studied to all perturbative orders. The imaginary time (τ) formalism is used. Then, as shown in previous works, QCD is described by a new generating functional Z_HT, in which quark fields retain their dependences on τ, while gluon and ghost fields are τ-independent. The invariance of Z_HT under BRST transformations in the HT regime is exhibited: it closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in Z_HT. Infinite sets of non-abelian Ward identities for the closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in Z_HT are shown to be infrared finite. We prove to all perturbative orders that one can regard as subdominant, and, hence, neglect consistently the contributions of :i) all closed electric gluon loops, ii) all closed quark loops with three or more vertices in diagrams having an even number of electric gluons (or none) in the external lines. In the HT regime, the axial anomalies are obtained: their expressions in terms of τ-independent gluon fields are similar to those for zero temperature. A non-trivial renormalization group (RG) equation in the HT regime, specifically due to the quark-gluon interaction, is presented. A positive beta function is obtained, and it is argued that interactions are not weak in that regime. The RG and the perturbative analysis to all orders appear to indicate that quarks and gluons may be confined in the HT regime (and, in particular in the Early Universe), due to the infrared divergent magnetic gluon sector. Other possibilities are also discussed.     

Anomalous transport regimes in a stochastic advection-diffusion model

A general solution to the stochastic advection-diffusion problem is obtained for a fractal medium with long-range correlated spatial fluctuations. A particular transport regime is determined by two basic parameters: the exponent 2h of power-law decay of the two-point velocity correlation function and the mean advection velocity u. The values of these parameters corresponding to anomalous diffusion are determined, and anomalous behavior of the tracer distribution is analyzed for various combinations of u and h. The tracer concentration is shown to decrease exponentially at large distances, whereas power-law decay is predicted by fractional differential equations. Equations that describe the essential characteristics of the solution are written in terms of coupled space-time fractional differential operators. The analysis relies on a diagrammatic technique and makes use of scale-invariant properties of the medium.