Compressibility and collisional effects on thermal instability of a partially ionized medium

The thermal instability of a finitely conducting hydromagnetic composite and compressible medium is studied to include the frictional effects with neutrals. The effect of compressibility is found to be stabilizing. In contrast to the nonoscillatory modes for (C _p/g)β > 1 in the absence of a magnetic field;C _v, β andg being specific heat at constant pressure, uniform adverse temperature gradient and acceleration due to gravity respectively, the presence of magnetic field introduces oscillatory modes in the system. The overstable case is also discussed. The magnetic field is found to have a stabilizing effect on the system for (C _p/g)β > 1.     

Heat conductivity of a nonlinear β-FPU lattice

In this work, we propose a new approach to the computation of heat conductivity in nonlinear systems. The total heat conductivity process is decomposed into two parts: one part is an equilibrium process at the same temperature T of either end of the lattice, which does not transfer energy and the other is a nonequilibrium process at temperature ΔT of one end and a zero temperature of the opposite end of the lattice. This approach makes it possible to somewhat reduce the time of computation of heat conductivity at ΔT → 0. The threshold temperature T _thr is found to behave as T _thr ∼ N ⁻³, where N is the lattice length. The threshold temperature conventionally separates two mechanisms of heat conductivity: at T < T _thr, phonon heat conductivity is dominant; at T > T _thr, the contribution of soliton heat conductivity increases with increasing temperature. The problem of the computation of heat conductivity in the limit ΔT → 0 reduces to the heat conductivity of a harmonic lattice with time-dependent bond rigidities determined by an equilibrium process at temperature T. An exact expression for the temperature dependence of sound velocity in a lattice with a β-FPU potential at T < 10 is derived. A numerical experiment confirmed the existence of solitons and breathers that correspond to a modified Korteweg-de Vries (KdV) equation. The problem of the quantitative contribution of solitons and breathers to heat conductivity requires further study.     

MHD stagnation point flow towards a stretching sheet

The steady two-dimensional MHD stagnation point flow towards a stretching sheet with variable surface temperature is investigated. The governing system of partial differential equations are transformed into ordinary differential equations, which are then solved numerically using a finite-difference scheme known as the Keller-box method. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that the heat transfer rate at the surface increases with the magnetic parameter when the free stream velocity exceeds the stretching velocity, i.e. ε>1, and the opposite is observed when ε<1.     

Anfachung und Dämpfung von Ionisationswellen in MHD-Kanälen und ihr Einfluß auf die effektive elektrische Leitfähigkeit,den effektiven Hall-Parameter und die mittlere Elektronentemperatur

The phase velocity, the amplification rate and the critical Hall parameter are theoretically determined for ionization waves in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both the magnetic field and the stream velocity. The investigations hold for seeded rare gases at any degree of seed ionization. The critical Hall parameter β_c depends on the degree of ionization, the ionization energy and the temperatures of electron gas T₀ and neutral gas T_g · β_c is always greater than one, if 0 < T₀ — T_g ? T₀ holds. The three-dimensional treatment indicates the existence of waves with a nonvanishing wave vector component in the direction of the magnetic field. The influence of ionization waves on mean current density, mean Hall field intensity and mean electron temperature is determined up to second order terms in the relative fluctuations of the electron temperature. The amplification of ionization waves reduces the effective electric conductivity, the effective Hall parameter and the mean electron temperature compared to the undisturbed state. Similar results are also obtained for steady state homogeneous isotropic turbulence and a special case of axially symmetric turbulence. Furthermore, a component of the electric field in direction or in opposite direction to the magnetic field vector may be generated by non isotropic and non homogeneous turbulence.     

Anomalous behavior of ideal Fermi gas below two dimensions

Normal behavior of the thermodynamic properties of a Fermi gas in d > 2 dimensions, integer or not, means monotonically increasing or decreasing of its specific heat, chemical potential or isothermal sound velocity, all as functions of temperature. However, for 0 < d < 2 dimensions these properties develop a "hump" (or "trough") which increases (or deepens) as d? 0 d\rightarrow 0 . Though not the phase transition signaled by the sharp features ("cusp" or "jump") in those properties for the ideal Bose gas in d > 2 (known as the Bose-Einstein condensation), it is nevertheless an intriguing structural anomaly which we exhibit in detail.     

Viscous modified gravity on a RS brane embedded in AdS<Subscript>5</Subscript>

We consider a modified gravity fluid on a Randall–Sundrum II brane situated at y=0, the action containing a power α of the scalar curvature. As is known from 4D spatially flat modified gravity, the presence of bulk viscosity may drive the cosmic fluid into the phantom region (w<−1) and thereafter inevitably into the Big Rip singularity, even if it is initially nonviscous and lies in the quintessence region (w>−1). The condition for this to occur is that the bulk viscosity contains the power (2α−1) of the scalar expansion. We combine this with the 5D RS II model, and we find that the Big Rip, occurring for α>1/2, carries over to the metric for the bulk metric, |y|>0. Actually, the scale factors on the brane and in the bulk become simply proportional to each other.     

Thermodynamics of Hořava–Lifshitz black holes

We study black holes in the Ho?ava–Lifshitz gravity with a parameter λ. For 1/3≤λ<3, the black holes behave the Lifshitz black holes with dynamical exponent 0<z≤4, while for λ>3, the black holes behave the Reissner–Nordström type black hole in asymptotically flat spacetimes. Hence, these all are quite different from the Schwarzschild–AdS black hole of Einstein gravity. The temperature, mass, entropy, and heat capacity are derived for investigating thermodynamic properties of these black holes.     

Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions

Systems of particles interacting with long range interactions present generically ”quasi-stationary states” (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) ∼ 1/r ^γ with γ > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > d − 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a ”dynamical” classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not.     

Coverage and Structure of Films of Spherical Particles Deposited after Diffusing in a Gravitational Field

We investigate the coverage and structure of a layer of particles deposited on a line after diffusion in a gravitational field. The dynamics of the depositing particles is controlled by the gravity number N _G(=d ⁴ g/6k _B T), where d is the diameter of the particles, is the density difference between the particles and the solution, g is the acceleration due to gravity, k _B is Boltzmann's constant, and T is the temperature. The position-dependent flux of particles in a gap formed by two preadsorbed particles is estimated by superposition of solutions of a steady-state convective diffusion equation for the flux in the presence of a single preadsorbed particle. The saturation coverages are found with a recursion relation and are in good agreement with those obtained from Brownian dynamics simulation. The jamming coverage increases rapidly with increasing particle size, particularly for large values of . An algorithm is presented to generate adsorbed configurations from which the structure of the deposit is determined.     

On confinement of fermions in strongly coupled lattice gauge theory

A lattice theory of Fermi fields of massm coupled to gauge fields in the region wherem and the gauge field coupling constantg are large is studied. It is shown that the energy of some states composed of a fermion and a distant antifermion with a string in between grows at least linearly with the distance if 1<g ⁶<m<g ^logg .On leave from Department of Mathematical Methods of Physcis, Warsaw University, Hoa 74, PL 00-682 Warsaw, Poland     

Quantum interference effects in a multi-driven transition Fg = 3 ↔ Fe = 2

We calculated and studied the quantum coherence effects of a degenerate transition F_g = 3 ↔ F_e = 2 system interacting with a weak linearly polarized (with σ_± components) probe light and a strong linearly polarized (with σ_± components) coupling field. Due to the competition between the drive Rabi frequency and the Zeeman splitting, electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) are appeared at the different values of applied magnetic field in both cases that the Zeeman splitting of excited state Δe is smaller than the Zeeman splitting of ground state Δg (i.e., Δe < Δg) and Δe > Δg. It is shown that the resonance is broader and contrasts are higher for Δe < Δg than that for Δe > Δg at the same Rabi frequencies of probe and coupling fields.     

Anharmonic Oscillator and Double-Well Potential: Approximating Eigenfunctions

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by V=m ² x ²+g x ⁴ at arbitrary g ≥ 0 for m ²>0 and m ²<0, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to an extremely fast convergent perturbation theory Mathematics Subject Classifications(2000) 34L40, 34B08, 41A99     

Numerical Modeling on Heat Transport Across Stochastic Magnetic Field

The heat diffusion across the stochastic magnetic field is studied numerically. The stochastic field is generated by the overlap of two magnetic islands. The parameter w/w_c, is found tobe an important parameter in charactering the transport, where w is the magnetic island width, and w_c is the critical island width for flattening the electron temperature across an island. For w/w_c < 1, the enhanced radial heat diffusivity χ_r is proportional to the parallel heat diffusivity χ_∥, and the heat transport is dominated by the additive effect of individual islands. For w/w_c > 3, χ_r is also proportional to χ_∥ and the additional degradation of the energy confinement due to stochastic magnetic field becomes apparent. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

磁场微重力效应的研究

将导电的液体置于磁场中,使导电液体中浮力驱动的自然对流减弱甚至消失,在导电液体中制造出了二级微重力效应,将这种情况称为磁场微重力效应.通过研究导电液体自然对流驱动力的无量纲Grashof数的变化,发现微重力效应的水平可以用公式g_m＝（β₀/β_m）（ν₀ /ν_m）²g₀ 计算,如果略去一次项,则可用g_m＝（ν₀ /ν_m）²g₀来估算.测量研究了不同磁场条件下硅熔体的磁黏度,估算不同磁场强度对应的磁场微重力水平后,发现估算结果与实验结果基本符合. 关键词： 磁场 二级微重力效应 Grashof数 微重力水平     

Nonlinear effects in gases in the Couette problem

The nonlinear processes of heat and mass transfer in a rarefied gas confined between two infinite parallel plates maintained at different temperatures and moving at a relative velocity are considered. The profiles of the gas macroscopic flow velocity, density, temperature, heat fluxes, and shear stress were calculated on the basis of kinetic equations by the discrete velocity method in a wide range of Knudsen numbers at different values of temperature difference between the plates and plate velocities. It was shown that under certain conditions, the direction of gas flow near the “hot” plate can change to the opposite. It was discovered that the longitudinal and normal components of heat flux at a certain temperature difference between the plates change their orientation to the opposite in transition and nearly free molecular regimes.     

Modeling of supersonic plasma flow in the scrape-off layer

The substantial drop of the plasma temperature along magnetic field lines with increasing plasma density is one of the main features in tokamak divertors. As a result the temperature gradient at the divertor plates becomes very steep and the boundary condition normally applied for the parallel Mach number M at the target, M_t = 1, cannot be satisfied. In this case the value of M_t based on the general form of the Bohm criterion, M_t  1, has to be determined from the continuity of plasma parameters.In the present paper a new approach to resolve the Mach number at the target for such a situation is proposed. This method avoids the singularity problem that arises by treating the particle balance and parallel motion equations in a differential form. Instead, the integral representation of the equations is formulated for an arbitrary form of particle and momentum sources. The approach can also take into account transport perpendicular to the magnetic field lines.The proposed method is demonstrated on the example of a one-dimensional stationary model for the scrape-off layer (SOL) plasma and includes the continuity-, parallel momentum- and heat transfer equations. The recycled neutrals are described in the diffusion approximation. In the case of low density the normal condition M_t = 1 is satisfied and the results are in agreement with the two-point model. At high enough plasma density solutions with the supersonic flow at the divertor plates, M_t > 1, are found. These states correspond to a partially detached plasma with a temperature of a few eV.     

Natural convection heat transfer at reduced pressures

This paper experimentally studies the natural convection heat transfer characteristics on horizontal and vertical plates at pressures lower than atmospheric value. Eight different pressures ranging from 10Pa to 101.325kPa, and three heating loads were used in the experiments. It is found that natural convection heat transfer characteristics at reduced pressures are independent of the plate arrangements and present different behaviors in two pressure ranges, 10Pa < p < 1000Pa and p > 1000Pa. The experimental heat transfer results are correlated into a non-dimensional equation to help the thermal design of stratosphere aircrafts and airborne equipment.     

Low temperature asymptotic behaviours of the correlation functions in the one-dimensional fermi gas

The g-model of the one-dimensional (1-D) Fermi gas including the same site interaction g₄ is investigated in the self-consistent harmonic approximation (SCHA) for the Bosonized Hamiltonian. The asymptotic form of the gap of the spin-density excitation is determined at low temperatures. It is found that the phase transition is of first order and the transition exists if g₁₆ < 0 but does not if g₁₆ > 0. The correlation functions for the order parameters of the charge-density wave (CDW) and singlet-superconductor (SS) are evaluated at low temperatures.