Tunnel injection and tunnel stimulation of superconductivity: The role of branch imbalance

The tunnel injection and the tunnel extraction of quasiparticles in a superconductor are considered, taking into account the branch population imbalance. The stability of nonequilibrium states with branch imbalance is discussed. It is shown that if this imbalance is large enough, the nonequilibrium state becomes unstable with respect to spatially homogeneous fluctuations of the order parameter, the characteristic increment being of the order of that for the Cooper instability of the normal state atT>T _c.As a result, states with oscillating order parameter can exist in a superconductor under injection or extraction. The relation of the results obtained to experimental results is discussed.     

Self-Consistent Theory of Transport in Quasi–One-Dimensional Superconducting Wires

We study superconducting transport in quasi–one-dimensional homogeneous wires in the cases of both equilibrium and nonequilibrium quasiparticle populations, using the quasiclassical Green's function technique. We consider superconductors with arbitrary current densities and impurity concentrations ranging from the clean to the dirty limit. Local current conservation is guaranteed by ensuring that the order parameter satisfies the self-consistency equation at each point. For equilibrium transport, we compute the current, the order parameter amplitude, and the quasiparticle density of states as a function of the superfluid velocity, temperature, and disorder strength. Nonequilibrium is characterized by incoming quasiparticles with different chemical potentials at each -end of the superconductor. We calculate the profiles of the electrostratic potential, order parameter, and effective quasiparticle gap. We find that a transport regime of current-induced gapless superconductivity can be achieved in clean superconductors, the stability of this state being enhanced by nonequilibrium.     

Impurities with internal degrees of freedom in superconductors

In this paper we investigate the properties of an electron gas interacting with a system of nonmagnetic impurities having internal degrees of freedom which allow the electrons to be scattered inelastically. We determine the modifications of the Green's functions in the normal and superconducting state due to this inelastic scattering, and calculate the change of the superconducting transition temperature, of the order parameter, and of the density of states. In our model the transition temperature and the order parameter are shown to increase, and the density of states is shown to change its functional behavior drastically. The elastic part of the scattering affects neither the transition temperature, nor the order parameter, nor the density of states.     

Theoretical Study of Specific Heat, Density of States and Free Energy of Itinerant Ferromagnetic Superconductor URhGe

Following the equation of motion method and Green’s function technique, the coexistence of itinerant ferromagnetism (FM) and superconductivity (SC) is investigated in a single band homogeneous system. Self-consistent equations for superconducting order parameter (Δ) and magnetic order parameter (Δ_FM) are derived. It is shown that there generally exists a coexistent (Δ≠0 and Δ_FM≠0) solutions to the coupled equations of the order parameter in the temperature range 0<T<min (T _C,T _FM) where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. Expressions for the specific heat, density of states and free energy are derived. The specific heat has a linear temperature dependence at low temperatures as opposed to the exponential decrease in the BCS theory. The density of states for a finite Δ_FM increases as opposed to that of a standard ferromagnetic metal. The free energy shows that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and therefore is realized at low enough temperature. The theory is applied to explain the observations of URhGe. The agreement between theory and experimental results is quite satisfactory.      

On a weak-coupling theory of superconducting magnetic alloys

The interaction of electrons with magnetic impurities in superconducting magnetic alloys is calculated to second order in the spin exchange coupling. Its effects on the transition temperature, the order parameter, the density of states, and the conductance are studied. The results are as follows. (1) The variation of the transition temperature with impurity concentration is the same as in the Abrikosov-Gor'kov theory; that of the order parameter is similar. (2) The density of states is finite at all nonzero impurity concentrations. Superconductivity with magnetic impurities is always gapless. (3) There are far more states about the Fermi level than in the Abrikosov-Gor'kov theory. At an impurity concentration equal to two-thirds its critical value, the density of states at the Fermi level surpasses one-half the normal value. The conductance curve loses all semblance of an energy gap.     

Theory of periodically driven,current-carrying superconducting filaments. II. Stability limits of the homogeneous state. Periodic and chaotic phase-slip states

Using the generalized time-dependent Ginzburg-Landau equations for dirty superconductors in local equilibrium, we determine the stability limits of the homogeneous superconducting state in high-frequency, current-carrying filaments. For weak pair-breaking by inelastic scattering, the instability sets in when the gap is depressed by the current to the universal ratio (2/3)^1/2. In the unstable region (and beyond it) there exist stable ac phase-slip solutions. In appropriate ranges of frequency and temperature, they exhibit complex time behavior with period-doubling and intermittency-type transition to chaos.     

Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation

We study a scalar reaction-diffusion equation which contains a nonlocal term in the form of an integral convolution in the spatial variable and demonstrate, using asymptotic, analytical and numerical techniques, that this scalar equation is capable of producing spatio-temporal patterns. Fisher's equation is a particular case of this equation. An asymptotic expansion is obtained for a travelling wavefront connecting the two uniform steady states and qualitative differences to the corresponding solution of Fisher's equation are noted. A stability analysis combined with numerical integration of the equation show that under certain circumstances nonuniform solutions are formed in the wake of this front. Using global bifurcation theory, we prove the existence of such non-uniform steady state solutions for a wide range of parameter values. Numerical bifurcation studies of the behaviour of steady state solutions as a certain parameter is varied, are also presented.     

EAM Analysis of the Lattice Parameter Effect in Order-Disorder Transformation

The embedded atom method was used to theoretically analyze the effect of the lattice parameter variation on the order-disorder transformation in binary alloys. The simple model was considered in which the configuration energy E as function of the lattice parameter a and the long-range order parameter sigma was given by Taylor expansion at sigma =0. The following results were found for AB alloy, at T=0 K, the stable state exists in the completely ordered phase which was also found in the case of A(3)B or AB(3) compounds The order-disorder was found to be a second-order transition. Only one kind of order-disorder was found for AB alloy. Three groups of order-disorder transformation can be observed for the A(3)B or AB(3) compound. For the group I when the temperature is below the critical temperature, the order-disorder is a first order transformation. For the group II, the order-disorder transformation is a first order transition. For the group III, the order-disorder transformation is found to be a second order transition. The lattice parameter variations have a significant effect on E-2 coefficient, which is related to the ordering energy. These results are, in a good agreement with those obtained by using EAM (embedded atom method) and CVM (cluster variation method), calculations.     

The Phase Diagram and the Structure of the Charge-Density-Wave State in High Magnetic Field

The properties of a charge-density wave (CDW) state in quasi-one-dimensional metals in magnetic field below the transition temperature are studied using the mean-field theory. We calculate the phase diagram and show that the CDW state with shifted wave vector in high magnetic field (CDW_x phase) has at least double-cosine modulation on the most part of the phase diagram. The transition from CDW₀ to CDW_x state below the critical temperature is accompanied by a jump of the CDW order parameter and of the wave vector rather than by their continuous increase. This implies a first order transition between these CDW states and explains the strong hysteresis accompanying this transition in many experiments. We examine how the phase diagram changes in the case of imperfect nesting. The results are applicable to different families of organic metals.     

On the stability of thermally radiative magnetofluiddynamic channel flow

Summary The stability of three dimensional infinitesimal disturbances is examined for the laminar flow of a thermally radiating, viscous, electrically and heat-conducting fluid between parallel walls with transverse magnetic field. In addition to the classical criteria for the non-radiative case a further system of homogeneous differential equations with mixed boundary conditions arises yielding possible further eigenvalues and requirements for stable flows. For the overall configuration the analogue of Squire's theorem is shown to fail. The eigenvalue problem is of unusual type with the eigenvalue parameter appearing non linearly in both the differential equation and boundary conditions. A study of two-dimensional disturbances is carried out in detail for non-thermally conducting fluids and for a particular wave number the further eigenvalues are shown by exact analysis to be always stable. In channels with black walls at the same temperature extensive numerical calculations for a range of wave-numbers and a variety of other parameters all yield the same result.     

The method of fundamental solutions for inverse source problems associated with the steady‐state heat conduction

This paper presents the use of the method of fundamental solutions (MFS) for recovering the heat source in steady‐state heat conduction problems from boundary temperature and heat flux measurements. It is well known that boundary data alone do not determine uniquely a general heat source and hence some a priori knowledge is assumed in order to guarantee the uniqueness of the solution. In the present study, the heat source is assumed to satisfy a second‐order partial differential equation on a physical basis, thereby transforming the problem into a fourth‐order partial differential equation, which can be conveniently solved using the MFS. Since the matrix arising from the MFS discretization is severely ill‐conditioned, a regularized solution is obtained by employing the truncated singular value decomposition, whilst the optimal regularization parameter is determined by the L‐curve criterion. Numerical results are presented for several two‐dimensional problems with both exact and noisy data. The sensitivity analysis with respect to two solution parameters, i.e. the number of source points and the distance between the fictitious and physical boundaries, and one problem parameter, i.e. the measure of the accessible part of the boundary, is also performed. The stability of the scheme with respect to the amount of noise added into the data is analysed. The numerical results obtained show that the proposed numerical algorithm is accurate, convergent, stable and computationally efficient for solving inverse source problems in steady‐state heat conduction. Copyright © 2006 John Wiley & Sons, Ltd.     

基于可靠指标的稳定安全系数探讨

桥梁结构当第一类稳定安全系数取4时,能否保证结构在更可能出现的第二类失稳发生时的可靠指标达到目标可靠指标值得研究。对单层单跨刚架桥分别进行了第一类和第二类稳定计算,以第一类稳定计算得到的临界荷载,取第一类稳定安全系数为4,采用一次可靠度方法编制程序得出可靠指标。进而采用第一类稳定可靠指标计算时的荷载效应和第二类临界荷载来计算第二类可靠指标。根据可靠指标探讨结构稳定安全系数取值的合理性。在此基础上,对两类稳定临界荷载进行了参数分析,研究临界荷载的变化对可靠指标的影响。结果表明:稳定分析应区分失稳状态,第一类稳定安全系数取4,但当结构发生第二类失稳时,有些情况下不足以保证可靠指标达到目标可靠指标。     

压力对PbTiO3结构和热物性质影响的第一性原理研究

PbTiO₃是一种重要的铁电功能材料, 但压力对其结构、稳定性、力学和热力学性能的影响尚不明确, 从而限制了其在电子通讯领域的应用。本研究采用基于密度泛函理论的第一性原理方法, 研究了压力下四方铁电相钛酸铅(TP-PTO)、立方顺电相钛酸铅(CP-PTO)、四方前驱体相钛酸铅(PP-PTO)结构和热物性质。研究发现, 三种结构可压缩性由大到小依次为PP-PTO>TP-PTO>CP-PTO。能带结构和态密度均表明PTO在研究的压力范围内未发生相变。PTO带隙随着压力增大逐渐降低, TP-PTO在20 GPa由间接带隙半导体转变为直接带隙半导体, 其余两相在压力下恒为直接带隙半导体。PTO在0~30 Gpa范围力学稳定, 且具有各向异性, 其综合力学性能随着压力的增加而增强, 各向异性则是先降低后升高。通过准谐德拜近似理论研究了温度和压力对PTO德拜温度、熵、热容的影响, 结果表明德拜温度随着温度上升而下降, 随着压力增大而上升, 反映出共价键强度依次为CP-PTO>TP-PTO> PP-PTO。熵和热容随着温度上升而上升, 随着压力的增大而下降。     

Parameter identification in constitutive models via optimization with a posteriori error control

In this paper we outline a computational technique for the calibration of macroscopic constitutive laws with automatic error control. In the most general situation the state variables of the constitutive law, as well as the material parameters, are spatially non‐homogeneous. The experimental observations are given in space–time. Based on an appropriate dual problem, we compute a posteriori the discretization error contributions from approximations of the parameter, state and costate fields in space–time for an arbitrarily chosen goal‐oriented error measure of engineering significance. Such a measure can be used in an adaptive strategy (not discussed in this paper) to meet a predefined error tolerance. An important observation is that the Jacobian matrix associated with the resulting Newton method is used (in principle) in solving the dual problem. Rather than treating the Jacobian in a monolithic fashion, we utilize a sequential solution strategy, whereby the FE‐topology of the discretized state problem is used repeatedly. Moreover, the proposed solution strategy lends itself naturally to the computation of first and second order sensitivities, which are obtained with little extra computational effort. Numerical results are given for the prototype model of confined aquifer flow with spatially non‐homogeneous permeability. The efficiency of the optimization strategy and the effectivity of the error computation are assessed. Copyright © 2005 John Wiley & Sons, Ltd.     

Forced vibrations of a body supported by viscohyperelastic shear mountings

The damped, finite-amplitude forced vibration of a rigid body supported symmetrically by simple shear springs and by a smooth inclined bearing surface is studied. The spring material is characterized as a compressible or incompressible, homogeneous and isotropic viscohyperelastic material for which the shear response function in a simple shear deformation is a quadratic function of the amount of shear. The trivial case of constant shear response is included. The equation for the damped motion of the load is a nonlinear, ordinary differential equation of the forced Duffing type with a constant static shift term due to gravity, and for which an exact solution is unknown. An approximate solution is obtained by the method of harmonic balance. Results for the motion of the load relate the system design parameters to the amplitude-frequency response and to the amplitude-driving force intensity response of the system. Regions of stable motion are identified in terms of the amplitude of the motion, driving-force intensity, driving frequency, and system design parameters. Geometrical characterizations of the motion are related schematically to certain cross-sections through the full three-dimensional solution surfaces for the amplitude and for the phase of the motion. A simple diagram maps the loci of all bifurcation points against the static shear deflection, which serves as the system design parameter for the inclined motion. An infinitesimal stability analysis shows that the bifurcation points of the inclined motion fall on the stability boundaries of the numerical solution of a three-parameter Hill equation. The solution provides information that illustrates how the system design parameters affect the motion of the load and how these may be chosen to control the amplitude of the oscillations and the stability of the system. The results are valid for all compressible or incompressible, homogeneous and isotropic, viscohyperelastic materials in the aforementioned class.     

一类准周期参激非线性扭振系统的周期簇发

考虑旋转机械中两种频率不同的周期参数激励同时存在对其传动系统的影响,基于拉格朗日方程,建立一类含准周期参激刚度和摩擦阻尼的非线性扭振系统的动力学方程。运用多尺度法对该扭振系统进行求解,得到系统在1/2亚谐波主参数共振下的幅频特性方程和分岔响应方程。在此基础上,研究了当两种周期参激的频率相差较大时非线性扭振系统的周期簇发现象,分析了快变参激和慢变参激对扭振系统的周期簇发的影响。通过数值仿真,给出了产生周期簇发的参数取值区域。在该区域内系统发生静息态与激发态的相互转迁,当快变激励的幅值减小时,激发态区域扩大,簇发的时间延长,通过调节慢变参激幅值会改变系统簇发的类型和轨迹     

Dynamics of the electrothermal instability of a polar dielectric in the temperature region of maximum relaxation losses

Under the action of an electric field, a polar dielectric may occur in several stable temperature states. Transitions between these states can be induced either by temperature perturbations or by changes in the load parameter depending on the frequency and strength of the electric field. A method is proposed for solving the nonlinear electrothermal problem of the temperature transition dynamics. The results of calculations of the temperature dynamics at the center of a dielectric are in good agreement with the data of numerical experiments.     

Modeling the transition between stable and unstable operation while emptying a silo

In this paper we have examined the stable and unstable states of the operation during the emptying of the silo. Here the state of stable operation of the silo is understood as a smooth mass outflow. The unstable state is manifested by funnel flow or arching. This issues from a moistured granular material. We have focused on the two extreme experimental cases. The first option was considered as a mass flow and the second one was considered as arching. Based on experimental data we have simulated the silo emptying by DEM. Considering the transition between stable and unstable operation we proposed a novel mathematical model of the silo emptying. This model involves a fractional-differential oscillator equation. Analyzing the solution of this equation we have presented how to recognize the state of stable and unstable operation during silo emptying.     

Coexistence of Superconductivity and Itinerant Ferromagnetism in Ferromagnetic Metals UCoGe and UIr

A microscopic coexistence of itinerant ferromagnetism (FM) and superconductivity (SC) is studied in a single band homogenous system, following an equation of motion method and Green’s function technique. Self-consistent equations for superconducting order parameter (Δ) and magnetization parameter (M) are derived. It is shown that there generally exists a coexistent (Δ≠0, M≠0) solution to the coupled equations of the order parameters in the temperature range 0<T<min (T _C,T _FM), where T _C and T _FM are respectively the superconducting and ferromagnetic transition temperatures. The expressions for electronic specific heat (C/T), density of states, free energy, transition probabilities, ultrasonic attenuation, and nuclear relaxation are also derived. The theory is applied to explain the observations in UCoGe and UIr. The specific heat capacity at low temperature shows linear temperature dependence as opposed to the activated behavior. Density of states increases as opposed to the case of a standard ferromagnetic metal. Free energy study reveals that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and, therefore, coexistence of FM and SC realized at a low enough temperature. The agreement between theory and experimental results for UCoGe and UIr is quite encouraging.     

Superconductivity in Itinerant Ferromagnetic Systems

We studied the possible superconducting state in an electronic itinerant ferromagnetic system characterized by a density of states that presents a moderately strong peak that is controlled by a specific parameter a and is positioned near the band edge. Specifically, we investigated the superconducting critical temperature, T _c , and the zero-temperature superconducting gap, ??₀. The analysis is done in a self-consistent way, the BCS mean-field equation being solved together with the electron density equation to trace possible changes in the system??s chemical potential due to the strong correlations between the component electrons. We discussed the density dependence of the superconducting critical temperature and zero-temperature superconducting gap for various values of the control parameter a and of the electron?Celectron attractive interaction. In the zero temperature limit we derive the system??s phase diagram and discuss the possible fermionic and bosonic regimes of the diagram as function of the strength of the attractive interaction.