Analysis of creep due to grain-boundary diffusion in hexagonal microstructures

For steady-state deformation caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates are analysed by taking the effects of viscous grain-boundary sliding into account. The maximum normal stress and the extent of stress concentration are shown to decrease as the grain-boundary viscosity increases. For infinite viscosity and/or extremely small grain sizes, the distribution of the normal stress becomes uniform on grain boundaries. The strain rates are predicted by both the stress analysis and the energy balance method, and the two strain rates are consistent with each other. The predicted strain rates also decrease as the grain-boundary viscosity increases. The present analysis reveals that the grain-size exponent is dependent on the grain size and the grain-boundary viscosity: the exponent becomes unity for small grain sizes and/or high viscosity, while it is three for large grain sizes and/or low viscosity. Recent experimental observations that the strain rates of nano-sized grain are much lower than those predicted by grain-boundary diffusion are explained by the increasing contribution of viscous grain-boundary sliding with decreasing grain size.     

Cones of optical axes in gyrotropic crystals with scalar permittivity

A theory is constructed for the degeneracy of electromagnetic waves in gyrotropic crystals near their isotropy points (in temperature and other parameters), in which permittivity ? becomes scalar due to dispersion and optical anisotropy is entirely determined by gyrotropy. It is shown that closed lines of intersection of sheets of the refraction surface, which correspond to the cones and, in particular, planes of the optical axes, are formed for isotropic ?. The polarization characteristics of wave fields experience a jump upon a transition through such lines. The conditions for the existence and geometry of the degeneracy cones under investigation are analyzed for crystals of all symmetry classes permitting optical activity. It is shown that the degeneracy lines disappear for a small deviation of ? from isotropy, while polarization anomalies persist. Isolated (one or two) degeneracy points may retain in place of the lines in the case when the optical axes of a perturbed crystal with “switched-off” gyrotropy belong to the initial cone.     

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.     

Effective temperature scaled dynamics of a flexible polymer in an active bath

Langevin dynamics simulations are employed to study the dynamical properties of a flexible polymer in an active bath. The diffusion of the centre of mass and end-to-end distance fluctuation are particularly analysed. We modulate both active force and active particle size to probe the activity-induced facilitation of polymer dynamics. Results indicate diffusivity and chain relaxation time can be well scaled by the effective temperature of the active bath. In addition, diffusion dynamics demonstrates an anomalous superdiffusive behaviour in short time scales, which becomes more prominent with increasing active particle size. Lastly, we extract the effective viscosity experienced by the probed chain, showing a sharp decrease with increment of effective temperature. The attenuation of effective viscosity due to activity might be responsible for the facilitated polymer dynamics.     

Spectral degeneracy of the lattice dirac equation as a function of lattice shape

We investigate the free Dirac equation in 2 + 1 dimensions on square, triangular, and hexagonal lattices. For each lattice the spectrum exhibits a degeneracy not present in the continuum limit. In the square and hexagonal cases there is a 4-fold degeneracy corresponding to 2 independent symmetries of the Hamiltonian; the degeneracy is eliminated by diagonalizing these symmetries and projecting onto the subspace characterized by a particular pair of eigenvalues. For the triangular case the degeneracy is 6-fold, but the naive Hamiltonian does not possess enough symmetry to eliminate the degeneracy. Certain ambiguities in the lattice Hamiltonian are pointed out and by the addition of terms which vanish in the continuum limit, it is cast in a form with sufficient symmetry to remove the degeneracy entirely, just as was done for the hexagonal and square lattices. It is found that after elimination of the spectral degeneracy the Hamiltonians for the hexagonal and triangular lattices are identical. The solutions to these theories are shown to have the correct continuum limit.     

The stability of the solutions of an anisotropic diffusion equation

Letters in Mathematical Physics - This paper investigates an anisotropic diffusion equation with degeneracy on the boundary. A new kind of weak solution is introduced, and the existence of the...     

Transport properties of degenerate neutrinos and photons

Transport coefficients are presented for a mixture of neutrinos and nuclei, and for a photon-electron system. The expression are valid for arbitrary degeneracy of the massless component, and include generalizations of Weinberg's results for radiative heat conduction and viscosity.     

Bulk viscosity of a reactive (νenpe−) system

The bulk viscosity arising from neutrino absorption by neutrons, and electron capture by protons, is calculated for arbitrary degeneracy of the leptons. These reactions are the primary processes determining the bulk viscosity of collapsing stellar cores. In this context the value found is of the order of 10²⁴ g cm^?1s^?1.     

Features of diffusion of an incident particle

Mechanisms of turbulent diffusion of particles moving in a turbulent medium under the action of gravity and Stokes forces are studied. It is observed that the velocity variance of particles decreases upon an increase in the inertia of the motion. At the same time, the diffusion coefficients of a particle are independent of its inertia. It is shown that, as the velocity of incidence increases, diffusion in the vertical plane becomes stronger than in the horizontal plane, and the ratio of the horizontal and vertical diffusion coefficients decreases to 1: 2.     

Hydrothermal convection in moderately thin spherical shells

Hydrothermal convection of pore water with a temperature-dependent viscosity within a permeable, internally heated, moderately thin spherical shell is investigated by both a perturbation analysis and a direct numerical simulation. The analysis and simulation are mainly focused on a thin spherical shell in that convective instabilities are characterized by the spherical harmonic degree l=6 with a 13-fold mathematical degeneracy. Four different three-dimensional analytical solutions of convection are derived by removing the degeneracy through the nonlinear effect. A direct numerical simulation of the nonlinear problem is also carried out, showing satisfactory agreement between the analytical solutions and the numerical simulations.     

Coulomb Drag of Dipole Excitons in a Hybrid Exciton–Electron System

The effect of Coulomb drag on a gas of dipole excitons in spatially separated two-dimensional quantum wells containing electron and exciton gases is studied theoretically. The Coulomb drag of excitons can be used to control exciton transport in transistor structures whose active element is a two-dimensional gas of dipole excitons. Expressions for the exciton cross conductivity as a function of temperature are obtained for the diffusion and ballistic transport regimes. For each regime, the limiting cases in terms of the ratio of the Coulomb interaction screening length to the distance between the gases are analyzed. It is shown that, at temperatures exceeding considerably the exciton-gas degeneracy temperature, the cross conductivity is independent of the temperature, while in the opposite case it vanishes exponentially.     

Exactly solvable three-body Calogero-type model with translucent two-body barriers

A new exactly solvable alternative to the Calogero three-particle model is proposed. Sharing its confining long-range part, it contains the mere zero-range two-particle barriers. Their penetrability gives rise to a tunneling, tunable via their three independent strengths. Their variability can control the removal of the degeneracy of the energy levels in an innovative, non-perturbative manner.     

Effects of solute-solvent and solvent-solvent attractive interactions on solute diffusion

A study is reported on the diffusion process of a solute molecule in a Lennard-Jones-like liquid near the triple point by a molecular dynamics simulation. Systematic changes were made to the strength of the solute-solvent or solvent-solvent attractive interaction in order to elucidate its effects on the diffusion coefficient. When the solute-solvent attractive interaction is enhanced, the diffusion coefficient of the solute becomes much smaller than that predicted by the Stokes-Einstein relationship with a stick boundary condition. The generalized friction coefficient on the solute molecule was investigated, and the attractive force between solute and solvent is found to be the main cause for the enhancement of the friction. When the attractive interaction between solvent molecules is weakened, the diffusion coefficient of a solute does not change, whereas that of a solvent does. Compared with the shear viscosity of the solvent, the diffusion coefficient of the solute breaks the Stokes-Einstein relationship, whereas the Stokes-Einstein relationship appears to hold in the case of the solvent molecule.     

Systematic characterization of drug release profiles from finite-sized hydrogels

Diffusion is often used as the primary method of molecular transport in drug delivery schemes. We present a systematic investigation of the Weibull and Peppas functions as useful tools in quantifying drug release profiles. The data is obtained from 2D simulated hydrogels and diffusion is modeled using an exact enumeration scheme. We show the fitting parameters to be largely time-dependent and therefore unreliable in indicating fundamental characteristics of the underlying physical mechanism. The parameters in the Weibull function however, have a stable regime when characterizing release profiles; we propose a simple iterative test that can be used to ensure that one is in this stable regime. Also, the mechanism of diffusion is shown to be independent of obstacle density in hydrogels that are larger than their respective characteristic lengths; a homogeneous obstacle distribution can therefore be replaced by an effective viscosity.     

Josephson effect between nanoclusters in resonance conditions

A general expression is derived for the Josephson current between nanoclusters. It is shown that, in the resonance conditions between electron levels of clusters, the expression for the current obtained in the tunnel Hamiltonian model becomes invalid. In the case of degeneracy or close to degeneracy of energy levels in isolated clusters, the critical Josephson current may exceed the value obtained in the model of tunnel Hamiltonian in the large parameter, viz., the ratio of the order parameter |Δ| to the distance between the resonance level and the levels closest to it.     

T-approximation in the theory of normal fermi liquid

The coefficient of viscosity of³He is used as an example for considering the problem of calculating the macrocharacteristics of Fermi systems within the framework of the statistical eikonal T-approximation. It is shown that within the framework of the microscopic theory, it is possible to obtain an expression, without phenomenological parameters, which describes the viscosity not only in the temperature range in which the Landau theory is applicable but also in the range of little degeneracy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 12–16, October, 1978.     

Frequency-dependent shear viscosity, sound velocity, and sound attenuation near the critical point in liquids. III. The shear viscosity

We compare theoretical results for the shear viscosity calculated in one-loop order within the field-theoretical method of the renormalization-group theory with experiments. Our expressions describe the nonasymptotic crossover in both temperature and density, and allow us to consider effects of finite gravitation and finite frequency at which the experiments are performed. In doing so we treat the critical exponent x(eta) of the shear viscosity as an independent parameter, keeping the one-loop value of the Kawasaki amplitude fixed. Within our model we also consider the temperature and density dependence of the thermal diffusion including gravitational effects.     

Linewidth Analysis of Spin Labels in Liquids: II. Experimental

This work demonstrates that homogeneous linewidths can be extracted from continuous wave electron paramagnetic resonance spectra and that they quantitatively agree with the predictions of existing relaxation theory. We suggest that relaxation theory can be used to predict experimental lineshapes provided that the simulations properly include sources of broadening. We have found that the rotational correlation times for spin labels in different percentages of glycerol/water mixtures are best modeled by a power law treatment for the viscosity, similar to that for translational diffusion. The translational diffusion coefficients themselves also have a power law dependence on the viscosity for glycerol/water mixtures. The linewidths were linearly dependent upon both the oxygen and the spin label concentration. The hyperfine splittings of all nuclei were observed to decrease linearly with increasing spin label concentration, completely at odds with existing theory which predicts a quadratic dependence upon concentration. The linear dependence was independent of hyperfine splitting until the magnitude of the hyperfine splitting was less than the homogeneous linewidth.     

Spin diffusion in double-exchange manganites

The theoretical study of spin diffusion in double-exchange magnets by means of dynamical mean-field theory is presented. We demonstrate that the spin-diffusion coefficient becomes independent of the Hund's coupling J(H) in the range of parameters J(H)S>W>T, W being the bandwidth, relevant to colossal magnetoresistive manganites in the metallic part of their phase diagram. Our study reveals a close correspondence as well as some counterintuitive differences between the results on Bethe and hypercubic lattices. Our results are in accord with neutron-scattering data and with previous theoretical work for high temperatures.     

ON THE FALSE DEGENERACY OF THE HELMHOLTZ BOUNDARY INTEGRAL EQUATIONS

In this paper, the false degeneracy of the Helmholtz boundary integral equations is examined. A new theory to explain the false degeneracy of the Helmholtz boundary integral equations is given. In this proposed theory, a false degeneracy of the boundary integral equation is explained as finding a non-trivial source distribution such that it results in trivial field quantities inside the domain interested and non-trivial field quantities for its counter part, i.e., outside the domain interested. It is clearly explained that such a false degeneracy is independent of prescribed boundary conditions but dependent on the integral equation one selects. Moreover, the false degeneracy of the integral equation for the interested domain relates to the eigenproblem for its counter part. Under such a unified theory, the fictitious eigenvalue, spurious eigenvalue and pseudo-fictitious eigenvalue can be explained in a simple mathematical frame. It is concluded from our theoretical analysis that a multiply connected domain results in the pseudo-fictitious eigenvalue even the complex-valued formulations are used. In order to eliminate various kinds of false degeneracy, two methods are employed according to the previous research. A unified view of these two methods is provided such that they can be thought to be equivalent from mathematical point of view. Several numerical examples are given to show the validity of current approach.