Simple theoretical analysis of the Einstein's photoemission from quantum confined superlattices

In this paper, we study the Einstein's photoemission from III-V, II-VI, IV-VI and HgTe/CdTe quantum well superlattices (QWSLs) with graded interfaces and quantum well effective mass superlattices in the presence of a quantizing magnetic field on the basis of newly formulated dispersion relations in the respective cases. Besides, the same has been studied from the afore-mentioned quantum dot superlattices and it appears that the photoemission oscillates with increasing carrier degeneracy and quantizing magnetic field in different manners. In addition, the photoemission oscillates with film thickness and increasing photon energy in quantum steps together with the fact that the solution of the Boltzmann transport equation will introduce new physical ideas and new experimental findings under different external conditions. The influence of band structure is apparent from all the figures and we have suggested three applications of the analyses of this paper in the fields of superlattices and microstructures.

Kinetic characterization of rat brain type IIA sodium channel alpha-subunit stably expressed in a somatic cell line

1. The rat brain type IIA Na+ channel alpha-subunit was stably expressed in Chinese hamster ovary (CHO) cells. Current through the expressed Na+ channels was studied using the whole-cell configuration of the patch clamp technique. The transient Na+ current was sensitive to TTX and showed a bell-shaped peak current vs. membrane potential relation. 2. Na+ current inactivation was better described by the sum of two exponentials in the potential range -30 to +40 mV, with. a dominating fast component and a small slower component. 3. The steady-state inactivation, h(infinity), was related to potential by a Boltzmann distribution, underlying thr ee states of the inactivation gate. 4. Recovery of the channels from inactivation at different potentials in the range -70 to -120 mV were characterized by al? initial delay which decreased with hyperpolarization. The time course was well fitted by the sum of two exponentials. In this case the slower exponential was the major component, and both time constants decreased with hyperpolarization. 5. For a working description of the Na+ channel inactivation in this preparation, with a minimal deviation from the Hodgkin-Huxley model, a three-state scheme of the form O reversible arrow I-1 reversible arrow I-2 was proposed, replacing the original two-state scheme of the Hodgkin-Huxley model, and the rate constants are reported. 6. The instantaneous current-voltage relationship showed marked deviation from linearity and was satisfactorily fitted by the constant-field equation. 7. The time course of activation was described by an m(x) model. However, the best-fitted value of x varied with the membrane potential and had a mean value of 2. 8. Effective gating charge was determined to be 4.7e from the slope of the activation plot, plotted on a logarithmic scale. 9. The rate constants of activation, alpha(m) and beta(m), were determined. Their functional dependence on the membrane potential was investigated.

Rheology of dense sheared granular flows

Rapid granular flows are defined as flows in which the time scales for the particle interactions are small compared to the inverse of the strain rate, so that the particle interactions can be treated as instantaneous collisions. We first show, using Discrete Element simulations, that even very dense flows of sand or glass beads with volume fraction between 0.5 and 0.6 are rapid granular flows. Since collisions are instantaneous, a kinetic theory approach for the constitutive relations is most appropriate, and we present kinetic theory results for different microscopic models for particle interaction. The significant difference between granular flows and normal fluids is that energy is not conserved in a granular flow. The differences in the hydrodynamic modes caused by the non-conserved nature of energy are discussed. Going beyond the Boltzmann equation, the effect of correlations is studied using the ring kinetic approximation, and it is shown that the divergences in the viscometric coefficients, which are present for elastic fluids, are not present for granular flows because energy is not conserved. The hydrodynamic model is applied to the flow down an inclined plane. Since energy is not a conserved variable, the hydrodynamic fields in the bulk of a granular flow are obtained from the mass and momentum conservation equations alone. Energy becomes a relevant variable only in thin 'boundary layers' at the boundaries of the flow where there is a balance between the rates of conduction and dissipation. We show that such a hydrodynamic model can predict the salient features of a chute flow, including the flow initiation when the angle of inclination is increased above the 'friction angle', the striking lack of observable variation of the volume fraction with height, the observation of a steady flow only for certain restitution coefficients, and the density variations in the boundary layers.

Intrinsic limits of subthreshold slope in biased bilayer graphene transistor

In this work, we investigate the intrinsic limits of subthreshold slope in a dual gated bilayer graphene transistor using a coupled self-consistent Poisson-bandstructure solver. We benchmark the solver by matching the bias dependent band gap results obtained from the solver against published experimental data. We show that the intrinsic bias dependence of the electronic structure and the self-consistent electrostatics limit the subthreshold slope obtained in such a transistor well above the Boltzmann limit of 60 mV/decade at room temperature, but much below the results experimentally shown till date, indicating room for technological improvement of bilayer graphene.

Velocity-Space Contours of Collision Integrals

Based on the recently found closed-form expressions of the Boltzmann collision integrals in a rigid-sphere gas for multi-Maxwellian distributions, a few typical sets of contour surfaces of the integrals in the space of molecular velocities are presented. These show graphically the tendency toward equilibrium under the influence of collisions. A brief preliminary comparison with Monte Carlo results is also given.

Non-linear couette flow with heat transfer using the B-G-K model

In recent years a large number of investigators have devoted their efforts to the study of flow and heat transfer in rarefied gases, using the BGK [1] model or the Boltzmann kinetic equation. The velocity moment method which is based on an expansion of the distribution function as a series of orthogonal polynomials in velocity space, has been applied to the linearized problem of shear flow and heat transfer by Mott-Smith [2] and Wang Chang and Uhlenbeck [3]. Gross, Jackson and Ziering [4] have improved greatly upon this technique by expressing the distribution function in terms of half-range functions and it is this feature which leads to the rapid convergence of the method. The full-range moments method [4] has been modified by Bhatnagar [5] and then applied to plane Couette flow using the B-G-K model. Bhatnagar and Srivastava [6] have also studied the heat transfer in plane Couette flow using the linearized B-G-K equation. On the other hand, the half-range moments method has been applied by Gross and Ziering [7] to heat transfer between parallel plates using Boltzmann equation for hard sphere molecules and by Ziering [83 to shear and heat flow using Maxwell molecular model. Along different lines, a moment method has been applied by Lees and Liu [9] to heat transfer in Couette flow using Maxwell's transfer equation rather than the Boltzmann equation for distribution function. An iteration method has been developed by Willis [10] to apply it to non-linear heat transfer problems using the B-G-K model, with the zeroth iteration being taken as the solution of the collisionless kinetic equation. Krook [11] has also used the moment method to formulate the equivalent continuum equations and has pointed out that if the effects of molecular collisions are described by the B-G-K model, exact numerical solutions of many rarefied gas-dynamic problems can be obtained. Recently, these numerical solutions have been obtained by Anderson [12] for the non-linear heat transfer in Couette flow,

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Undamped Oscillations of Collisionless Stellar Systems: Spheres,Spheroids and Discs.

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed.

Undamped oscillations of homogeneous collisionless stellar systems

The Lewis (1968) invariant of the time-dependent harmonic oscillator is used to construct exact time-dependent, uniform density solutions of the collisionless Boltzmann equation. The spatially bound solutions are time-periodic.

Monte carlo simulation for molecular gas dynamics

The dynamics of low-density flows is governed by the Boltzmann equation of the kinetic theory of gases. This is a nonlinear integro-differential equation and, in general, numerical methods must be used to obtain its solution. The present paper, after a brief review of Direct Simulation Monte Carlo (DSMC) methods due to Bird, and Belotserkovskii and Yanitskii, studies the details of theDSMC method of Deshpande for mono as well as multicomponent gases. The present method is a statistical particle-in-cell method and is based upon the Kac-Prigogine master equation which reduces to the Boltzmann equation under the hypothesis of molecular chaos. The proposed Markoff model simulating the collisions uses a Poisson distribution for the number of collisions allowed in cells into which the physical space is divided. The model is then extended to a binary mixture of gases and it is shown that it is necessary to perform the collisions in a certain sequence to obtain unbiased simulation.

Empirical torsional potential functions from protein structure data. Phi- and psi-potentials for non-glycyl amino acid residues.

The torsional potential functions Vt(phi) and Vt(psi) around single bonds N--C alpha and C alpha--C, which can be used in conformational studies of oligopeptides, polypeptides and proteins, have been derived, using crystal structure data of 22 globular proteins, fitting the observed distribution in the (phi, psi)-plane with the value of Vtot(phi, psi), using the Boltzmann distribution. The averaged torsional potential functions, obtained from various amino acid residues in L-configuration, are Vt(phi) = 1.0 cos (phi + 60 degrees); Vt(psi) = 0.5 cos (psi + 60 degrees) - 1.0 cos (2 psi + 30 degrees) - 0.5 cos (3 psi + 30 degrees). The dipeptide energy maps Vtot(phi, psi) obtained using these functions, instead of the normally accepted torsional functions, were found to explain various observations, such as the absence of the left-handed alpha helix and the C7 conformation, and the relatively high density of points near the line psi = 0 degrees. These functions derived from observational data on protein structures, will, it is hoped, explain various previously unexplained facts in polypeptide conformation.

Radiative interactions in boundary layers

A detailed description of radiative interactions in laminar compressible boundary layers for moderate Mach numbers is presented by way of asymptotic analysis and supporting solutions. The radiation field is described by the differential approximation. While the asymptotic analysis is valid for large N (the ratio of photon mean free path to molecular mean free path) and arbitrary Boltzmann number, Bo (the ratio of convective heat flux to radiation heat flux), the solutions are obtained for Bo [double less-than sign] 1, the case of strong radiative interactions. The asymptotic analysis shows the existence of an optically thin boundary layer for large N and all Bo. For Bo [double less-than sign] 1, two outer regions are observed — one optically thin (at short distances from the leading edge) and the other optically thick (at large distances from the leading edge). An interesting feature not pointed out in the previous literature is the existence of a wall layer at large distances from the leading edge where convective heat flux can be ignored to the leading order of approximation. The radiation field in all cases can be very well approximated by a one-dimensional description. The solutions have been constructed using the ideas of matched asymptotic expansions by approximate analytical procedures and numerical methods. It is shown that, to the leading order of approximation, the radiation slip method yields exactly the same result as the more complicated matching procedure. Both the cases of linear and nonlinear radiation have been considered, the former being of interest in developing approximate methods which are subsequently generalized to handle the nonlinear problem. Detailed results are presented for both cases.

Empirical torsional potential functions from protiesn structure DATA Phi- and Psi-Potentials for Non-glycyl Amino Acid Residues

The torsional potential functions Vt(φ) and Vt(ψ) around single bonds N–Cα and Cα-C, which can be used in conformational studies of oligopeptides, polypeptides and proteins, have been derived, using crystal structure data of 22 globular proteins, fitting the observed distribution in the (φ, ψ)-plane with the value of Vtot(φ, ψ), using the Boltzmann distribution. The averaged torsional potential functions, obtained from various amino acid residues in l-configuration, are Vt(φ) = – 1.0 cos (φ + 60°); Vt(ψ) = – 0.5 cos (ψ + 60°) – 1.0 cos (2ψ + 30°) – 0.5 cos (3ψ + 30°). The dipeptide energy maps Vtot(φ, ψ) obtained using these functions, instead of the normally accepted torsional functions, were found to explain various observations, such as the absence of the left-handed alpha helix and the C7 conformation, and the relatively high density of points near the line ψ = 0°. These functions, derived from observational data on protein structures, will, it is hoped, explain various previously unexplained facts in polypeptide conformation.

Analytical and numerical solutions of inward spherical solidification of a superheated melt with radiative-convective heat transfer and density jump at freezing front

Analytical and numerical solutions of a general problem related to the radially symmetric inward spherical solidification of a superheated melt have been studied in this paper. In the radiation-convection type boundary conditions, the heat transfer coefficient has been taken as time dependent which could be infinite, at time,t=0. This is necessary, for the initiation of instantaneous solidification of superheated melt, over its surface. The analytical solution consists of employing suitable fictitious initial temperatures and fictitious extensions of the original region occupied by the melt. The numerical solution consists of finite difference scheme in which the grid points move with the freezing front. The numerical scheme can handle with ease the density changes in the solid and liquid states and the shrinkage or expansions of volumes due to density changes. In the numerical results, obtained for the moving boundary and temperatures, the effects of several parameters such as latent heat, Boltzmann constant, density ratios, heat transfer coefficients, etc. have been shown. The correctness of numerical results has also been checked by satisfying the integral heat balance at every timestep.

Tuning the electronic effective mass in double-doped SrTiO3

We elucidate the relationship between effective mass and carrier concentration in an oxide semiconductor controlled by a double-doping mechanism. In this model oxide system, Sr1-xLaxTiO3-delta, we can tune the effective mass ranging from 6 to 20m(e) as a function of filling (carrier concentration) and the scattering mechanism, which are dependent on the chosen lanthanum-and oxygen-vacancy concentrations. The effective mass values were calculated from the Boltzmann transport equation using the measured transport properties of thin films of Sr1-xLaxTiO3-delta. We show that the effective mass decreases with carrier concentration in this large-band-gap, low-mobility oxide, and this behavior is contrary to the traditional high-mobility, small-effective-mass semiconductors.