Evaluation of Impurity Concentration in Semiconductors from the Relaxation of Thermally Stimulated Currents

The rate equations of thermally stimulated currents due to isothermal detrapping are analyzed. The results demonstrate that, at small trap population, isothermal detrapping follows an exponential law, independent of the trapping rate: fast, slow, or intermediate (the trapping time is comparable to the recombination time). Expressions are derived for determining the density of charged traps in the course of detrapping and assessing the trap density from known trap parameters and thermally stimulated current spectra.     

Modulation of the polarization of semiconductor laser radiation at constant output power

The degree of polarization of “doubly”-modulated (by the pump current and the optical confinement factor) laser radiation is analyzed by applying a method of analyzing the stability of the solutions of systems of Lyapunov differential equations to a system of rate equations. An analysis of the system of rate equations yielded its eigenvalues, also called stability coefficients, which are the characteristic time for a transition of the system from one state to another. The behavior of a doubly modulated laser was modeled mathematically and it was demonstrated that the polarization of the laser output radiation can be controlled with almost constant output power. Pis’ma Zh. Tekh. Fiz. 24, 84–90 (August 26, 1998)     

Peculiarities of transport current penetration in a composite superconductor taking into account different models of flux creep

The flux-creep diffusion of transport current in superconducting composite slab and cylinder based on a hard superconductor is investigated theoretically. Power and exponential current-voltage characteristics were used to define the electric field in the flux-creep regime. Using scaling solutions, the Maxwell equations describing transport current penetration in a one-dimensional superconducting composite are solved analytically. A proposed analysis indicates the existence of special macroscopic distribution of electromagnetic field in superconductor during the flux creep. It is shown that the flux-creep electromagnetic field cannot promptly propagate into the composite and penetrates at the finite rate like in the flux-flow regime. Therefore, a moving current boundary exists in the superconducting composite. It separates the region where the current flows from free current region. Moreover, in the flux creep specific conditions are fulfilled at moving boundary in contrast to the flux-flow regime. According to these conditions the electric and magnetic field induced by current charging smoothly approach to its undisturbed values. They are independent of any parameters of current-voltage characteristics and appear due to zero value of the differential resistivity of the composite at moving boundary. To confirm these results, the numerical calculation based on more general model is executed. The equations describing the violation of stable distribution of fully penetrated current are defined.     

Approximate analytical expressions for pulse modulation response of quantum cascade lasers

Approximate analytical expressions for turn-on delay, rise time and fall time for pulse modulation of the drive current of quantum cascade lasers are presented. These time expressions are obtained using piece-wise analysis of rate equations. From the analytical expressions, the effects of laser parameters and off and on currents are discussed. A numerical analysis shows reasonable agreement with analytical results. It also confirms the predictions from analytical results. The pulse response is compared with that of near-infrared interband lasers.     

Transient behaviour of helium-cooled current leads for superconducting power transmission

Based upon time dependent differential equations, numerical calculations are presented which allow, first, the determination of burn-out condictions for a helium cooled current lead. Secondly, the response of the lead to an overload current may be examined, both during the overload and during subsequent time when the normal current again persists. Representing the temperature dependent resistivity and thermal conductivity of the copper conductor as a function of its purity (residual resistivity ratio), the results are parameterized by dimensionless mass flow rate, current and residual resistivity ratio. Defining the burn-out temperature as 500 K and an operating current as 85% of the burn-out current, it is shown that although all residual resistivity ratios between five and 100 are suitable, there is a limit on the mass flow rate number which can be utilized. This results from secondary temperature surges occurring after the overload, the conditions for which are rather complicated. It is concluded in particular that, within the permissible range of mass flow rates, no damage should result from a 10X current overload for periods up to 0.2 seconds.     

通电瞬时板内半无限长裂纹尖端域的应力场

以导电弹性体的麦克斯威尔方程为出发点,借助于边界条件和初始条件,推得了在向含半无限长直线裂纹的无限大导电薄板内通入电流的瞬时,裂纹尖端附近电流密度的表达式。在此基础上,得到了裂纹尖端区域处温度和应力的具体表达式。算例表明,在电流所产生的焦耳热源的作用下,裂尖区域处的温度将瞬时升高,并伴有压应力的产生,从而可达到阻止裂纹扩展的目的。     

Small-signal-equivalent circuits for a semiconductor laser

Passive electrical circuits whose voltage and current equations are exactly equivalent to the small-signal rate equations of a semiconductor laser are derived to model an electrically modulated laser (verified to be the same as that given in the literature), an optically modulated laser (i.e., a laser used as an optical amplifier), and a multimode laser. These circuits offer a fast and efficient simulation tool with little computational complexity in which the small-signal assumption (i.e., small modulation range) is neither violated nor insufficient for the simulation.     

Power-current hybrid rectangular formulation for interior-point optimal power flow

A non-linear interior-point optimal power flow algorithm based on power?current hybrid mismatch formulation in rectangular coordinates is proposed. In the proposed algorithm, all buses are divided into two types: the buses with non-zero injections and the buses with zero injections. For the buses with non-zero injections, power flow equations are presented by power mismatch formulation. For the buses with zero injections, power flow equations are presented by current mismatch formulation. The proposed power?current hybrid formulation combines the advantages of both power mismatch and current mismatch formulations. For the buses with zero injections, the proposed hybrid formulation shares the advantages of current mismatch formulation: first-order derivatives of power flow equations become constants, second-order derivatives of power flow equations become zeros so that Jacobian and Hessian matrices of power flow equations are easier to compute. The hybrid mismatch formulation is also easier to handle the buses with non-zero injections than current mismatch formulation. Numerical studies on various testing systems indicate that the proposed hybrid formulation has better convergence performance and computational efficiency, especially for large-scale optical power flow problems with a large percentage of zero-injection buses.     

A constitutive model for the deformation induced anisotropic plastic flow of metals

A mathematical framework is established for the equations governing inelastic deformation under multi-dimensional stress states and for the associated evolution equations of the internal state variables. The formulation is based on a generalization of the Prandtl-Reuss flow law. In the evolution equations for the inelastic state variables that control plastic flow, it is assumed that part of the rate of change is isotropic and the remaining part varies according to the sign and orientation of the current rate of deformation vector. This leads to a minimum of twelve components of the internal state tensor which represents resistance to inelastic deformation. In this manner, both initial and load history induced plastic anisotropy can be modeled. A specific set of equations for anisotropic plastic flow is developed consistent with the inelastic state variables.     

Enhancement of superconductivity by quasiparticle injection. I. Model analysis

Nonequilibrium phenomena in the two electrodes of high-current-density superconducting tunnel junctions are analyzed. The quasiparticle injection-induced enhancement of the energy gaps as well as of the critical current of one of the electrodes are considered. A graphic approach is employed to solve the coupled gap equations for both films. Multiple-gap states are found at voltages close to the sum and difference of the two gaps. If a large transport current is passed through one of the electrodes, multiple stable solutions of the gap equations occur at most bias voltages. Because each solution has its own critical current level, the nonequilibrium critical current is no longer a simple single-valued quantity.     

一种实用的多端DC──AC系统潮流计算方法

介绍了一种新的ＭＴＤＣ—ＡＣ潮流计算方法，其特点是将各换流器分别经诺顿定理等效为一带换流内阻的电流源。首先给出各单元直流系统的网络方程和换流器方程，运用给定量经网络方程推出控制方程，再用牛顿法进行潮流选代计算。此方法灵活实用，并附有算例证明。     

An additional loss source in cabled multifilamentary superconductors

It is shown that irregularities in the twist rate of a multifilamentary superconducting strand, which may occur in the cabling or braiding process of a high current conductor, give rise to additional matrix currents and enhanced ac losses. Electrodynamic equations for matrix and filament currents in a strand with a sudden change in twist rate are derived and damped wave solutions are given for an external harmonic field as well as for a ramp field. Inder unfavourable conditions the associated loss enhancement may become comparable to the regular matrix losses. This is also verified experimentally by magnetization measurements. Some recommendations for cable design are given.     

Low-frequency intensity noise in semiconductor lasers

The low-frequency intensity noise at 25 MHz of a Fabry-Perot semiconductor laser is measured as a function of injection current. All the measurements are taken at room temperature and the laser is operated with a commercial current source (the conditions under which laser diodes are often used). At the highest injection current of twice threshold, the intensity noise is 5.5 dB above the shot-noise limit. When the longitudinal side mode suppression of the laser is 20 dB or larger, the intensity noise is modeled adequately by an expression derived from the single-mode, small-signal, linearized, semiclassical rate equations. All the parameters used in the theory are derived or referenced.     

Effects of Combined Heat and Mass Transfer on Entropy Generation due to MHD Nanofluid Flow over a Rotating Frame

The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe3O4 based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.     

Current distribution in a parallel set of conducting strips

The current distribution in a parallel set of thin conducting sheets due to an external applied source is investigated. All sheets are placed in one plane. The source, and all excited fields, are time-harmonic. The frequency is low enough to allow for an electro quasi-static approximation (neglecting the displacement current). The conducting sheets are infinitely long and the current is uniform in the longitudinal direction of the sheets. The sheets have a thin rectangular cross-section, so thin that the current can be assumed uniform in the thickness-direction. Hence, the current distribution only depends on the transverse coordinate. Due to the mutual induction between the sheets, the current distribution over the width of the cross-section becomes non-uniform: it accumulates at the edges of the sheets. It is especially this so-called edge-effect, and its dependence on the applied frequency and the distances between the sheets, that is the aim of this investigation. From the Maxwell equations, a set of integral equations for the current distribution in the sheets is derived. These integral equations are solved, as far as possible by analytical means, by writing the current distribution in each sheet as a series of Legendre polynomials. The general method is worked out for N (N 1) sheets, but explicit results are presented for N=1 and 3. It turns out that the edge-effect becomes stronger for increasing frequencies. For this solution, only a very restricted number of Legendre polynomials are needed.     

Three-dimensional finite element analysis of finite deformation micromorphic linear isotropic elasticity

A finite deformation micromorphic materially linear isotropic elastic model is formulated and implemented for three dimensional finite element analysis. The model is based on the kinematics, balance equations and thermodynamic equations proposed by Eringen and Suhubi (1964). The constitutive equations are calculated in the reference configuration, and the resulting stresses are mapped to the current configuration. The balance of linear momentum and the balance of first moment of momentum are linearized to construct the consistent tangent for three dimensional finite element implementation for solution by the Newton–Raphson method. Three dimensional numerical examples are analyzed to demonstrate preliminarily the implementation.     

Linearized kinetic equations and relaxation processes of a superconductor near T c

Starting from the equation of Gor'kov and Eliashberg in a form introduced by Eilenberger, we derive a set of linearized equations for the deviation from the equilibrium value of the quasiparticle distribution function as well as of the order parameter. These equations resemble the Boltzmann equation and the Ginzburg-Landau equation, respectively, and they form a set of coupled equations. Two different modes can be distinguished, depending on whether the order parameter changes in magnitude or in phase. The equations are solved for the case of a stationary quasiparticle injection into a superconductor and the change in the electrochemical potential of the quasiparticles is calculated. Furthermore, we treat the problem of a current flowing perpendicular to a superconducting-normal interface in which a normal current is converted into a supercurrent, and we calculate the extra resistance of the interface.     

Root function solutions in a nucleation theory considering small cluster mobility

It is shown that discrepancies between current nucleation theory and experimental results for incomplete condensation can be surmounted if dimers and trimers are assumed to be highly mobile on the substrate surface so that most of them are captured by larger clusters. This new conception of nucleation kinetics can be described by a system of rate equations for which approximate analytical solutions are given. A peculiar feature of these solutions is the dependence of the nucleus density on a root of the deposition time. The results are compared with experimental data for gold on NaCl; in spite of some open questions the agreement is fairly good.     

On the structure of the rate equations of materials with internal variables

Summary Rate equations for internal variables are not invariant under transformations to other sets of internal variables if such transformations involve the external variables (deformation, temperature), unless the rate equations include the rates of the external variables as well. The simplest invariant rate equations are linear in the external-variable rates; for materials with such rate equations, thermodynamic relations are studied, and conditions are obtained for the reducibility of such rate equations to a form without external-variable rates. Materials with plastic behavior have rate equations that are piecewise linear in the external-variable rates, and thermodynamic relations for such materials are studied as well.

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Zur Form der Geschwindigkeitsgleichungen für Werkstoffe mit inneren Zustandsvariablen

Zusammenfassung Geschwindigkeitsgleichungen der inneren Zustandsvariablen sind nicht invariant gegen Transformation auf andere innere Zustandsvariable, wenn diese Transformation äußere Zustandsvariable (Deformation, Temperatur) einschließt, außer die Geschwindigkeitsgleichungen enthalten auch Ableitungen äußerer Zustandsvariablen nach der Zeit. Die einfachsten invarianten Geschwindigkeitsgleichungen sind linear in den Ableitungen der äußeren Zustandsvariablen. Für durch solche Gleichungen beschreibbare Werkstoffe werden thermodynamische Beziehungen untersucht und Bedingungen für die Reduzierbarkeit dieser Geschwindigkeitsgleichungen auf Formen, die keine Ableitungen äußerer Zustandsvariablen enthalten, abgeleitet. Werkstoffe mit plastischem Verhalten besitzen Geschwindigkeitsgleichungen, die abschnittsweise linear in den Ableitungen der äußeren Zustandsvariablen sind. Thermodynamische Beziehungen solcher Stoffe werden ebenfalls untersucht.

     

An immersed boundary method to solve fluid–solid interaction problems

We describe an immersed-boundary technique which is adopted from the direct-forcing method. A virtual force based on the rate of momentum changes of a solid body is added to the Navier–Stokes equations. The projection method is used to solve the Navier–Stokes equations. The second-order Adam–Bashford scheme is used for the temporal discretization while the diffusive and the convective terms are discretized using the second-order central difference and upwind schemes, respectively. Some benchmark problems for both stationary and moving solid object have been simulated to demonstrate the capability of the current method in handling fluid–solid interactions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.