On the characterization of fluxes in nonlinear irreversible thermodynamics

The linear Onsager theory of irreversible thermodynamics is extended to include nonlinear phenomenological relations by means of Onsager fluxes. Such fluxes satisfy a full system of reciprocity relations, vanish in thermodynamic equilibrium, and give a non-negative production of entropy. A complete characterization of Onsager fluxes is obtained in terms of non-negative scalar valued functions which vanish in thermodynamic equilibrium. These same functions are also shown to characterize all C² fluxes which satisfy the second law of thermodynamics. Each system of Onsager fluxes is shown to derive from a dissipation function which attains its absolute minimum in thermodynamic equilibrium. The reaction rates given by reaction kinetics are shown to be Onsager fluxes and their dissipation functions are explicitly calculated.     

Green's functions for superfluid3He-A in the case of spin hydrodynamics: Influence of the spin-orbit coupling

The spin hydrodynamic equations for superfluid³He-A for the case of external, time-dependent fields are considered. The terms in equations containing these fields are found on the basis of a microscopic approach. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions constructed from operators entering the spin hydrodynamics. The Green's function connected with the order parameter operator has a 1/q ² singularity. Suitable connections between Green's functions lead to relations among kinetic coefficients (Onsager relations). A more detailed consideration of the spin-orbit coupling when the spin waves are not true Goldstone modes removes the mentioned singularity and the Onsager relations remain valid.     

Commutation Rules and Eigenvalues of Spin and Orbital Angular Momentum of Radiation Fields

Abstract

We investigate the separation of the total angular momentum J of the electromagnetic field into a ‘spin’ part S and an ‘orbital’ part L. We show that both ‘spin’ and ‘orbital’ angular momentum are observables. However, the transversality of the radiation field affects the commutation relations for the associated quantum operators. This implies that neither S nor L are angular momentum operators. Moreover their eigenvalues are not discrete. We construct field modes such that each mode excitation (photon) is in a simultaneous eigenstate of S _z and L _z. We consider the interaction of such a photon with an atom and the resulting effect on the internal and external part of the atomic angular momentum.     

On the relation between the kinetic parameters involved in molecular chain breakage and macroscopic failure

Even though the process of macroscopic failure of polymer samples at temperatures below T _g is determined by the kinetics of molecular chain breakage, the kinetic parameters of macroscopic and molecular processes are different from each other. The relations between these parameters are derived for four differently characterized polymer networks. Especially shown is the influence of a distribution n(L/L ₀) of chain segment lengths on the time-to-failure of the network. Fracture criteria involving critical segment lengths, L _c/L ₀, and/or the total number of chain scissions are discussed.     

Boundary conditions for normal-superfluid counterflow and internal Kapitza resistance in superfluids

We calculate the spatial variation of the temperature and the normal fluid velocity of superfluid Fermi and Bose liquids between parallel plates in the presence of a stationary heat flow normal to the plates. The system is modeled by a quasiparticle kinetic equation and a diffuse scattering boundary condition at the walls. We derive integral equations for the hydrodynamic fields, which are solved numerically for arbitrary ratio of the mean free path to the plate separationL. For small /L we recover the hydrodynamic boundary conditions proposed recently by Grabinski and Liu and are able to determine the three surface Onsager coefficients. In the Kundsen regime (large /L), we find the thermal boundary resistance to increase exponentially with decreasing temperature.     

基于感知的城市开放空间声环境评价指标研究

文章从人群主观感知角度出发，针对人口、交通密集型城市开放空间声环境质量评价进行研究，以期从大量的物理、心理声学特征中提取出“有效特征参量”，拓展现有声环境评价指标。该研究基于对上海市开放空间复合混杂的整体声环境特征分析以及实验室主观评价实验，构建了“特征参量”-“主观满意度”样本集，进而提出双重相关系数评估方法，定量评估17种物理、心理声学特征参量间的内在相互影响，以及它们对人群声主观感知的影响，筛选出适应于城市整体声环境主观评价的“有效特征参量”：等效连续A声级LA、噪声中值与环境本底值的差值L50-L90以及尖锐度S，其中，LA是影响声环境主观满意度的决定性因子，它与满意度Sat的负相关性达到88%,L50-L90对Sat的负相关性为25%,S与满意度Sat的正相关程度为33%。进一步，基于它们与满意度Sat的相关系数，计算出3个“有效特征参量”影响“主观满意度”权重系数：0.6,0.17以及0.23。     

Liquid–Liquid–Vapor Equilibria in Binary Families of SF6, CClF3, C2H3F3, and C2H4 with n-Alkanes

Liquid–liquid–vapor equilibria were determined experimentally for binary and quasi-binary systems which consisted of a low-volatile n-alkane or mixture of n-alkanes with a more volatile component, chlorotrifluoromethane, sulfur hexafluoride, 1,1,1-trifluoroethane, and ethene. From the location of the critical end-points L ₂ = L ₁ + V and L ₂ + L ₁ = V of the three-phase curves, the coordinates of the tricritical point and the double critical endpoint of these families were estimated by extrapolation. For the families studied it was found that increasing the carbon number of the n-alkane leads to a transition from type II to type IV to type III fluid phase behavior.     

Grain size correction of welding residual stress measurement in a carbon steel plate using the critical refraction of longitudinal waves

In this, a method to measure welding residual stress in butt-welded joints of carbon steel plates using longitudinal critically refracted wave (L_cr wave) is proposed. Cross-correlation was employed to calculate the difference in time of flight between L_cr wave, and the optimal step length for the measurements is discussed. To determine L_cr wave acoustoelastic coefficient of the heat affected zone (HAZ), the relationship between the L_cr wave acoustoelastic coefficient and the grain size is established. The results show that one cycle is the optimal step length for the difference in the time-of-flight calculation, and with increasing grain size increase, L_cr wave acoustoelastic coefficient decreases in the form of a power function. In addition, grain size can be determined by using amplitude of the L_cr wave, so that the measured value of welding residual stress in HAZ can be corrected. The welding residual stress in melted zone (MZ) is corrected by calibrating acoustoelastic coefficient of the MZ. The acoustoelastic coefficient of the MZ is larger than that of parent material (PM). At last, welding residual stress in the butt-weld joint is measured and corrected with the L_cr wave technique. The results are verified by the hole drilling method.     

Propagation of plasticity bands from the tip of a semiinfinite crack of mixed type

In the framework of the model of plasticity bands, we analyze an elastoplastic fracture-mechanics problem of propagating plasticity bands near the tip of a semiinfinite crack of mixed type. It is assumed that, under the conditions of plane stressed state, plastic strains near the tip of a semiinfinite crack are localized along three plasticity bands (L ₁,L ₂,L ₃) and, under the conditions of plane deformation, they are localized along two bands (L ₁,L ₂). One of these bands (L ₃) is simulated by a line of discontinuity of normal and tangential displacements. The remaining two bands (L ₁,L ₂) are simulated by the lines of discontinuity of tangential displacements. Their lengths and orientations are determined in the process of numerical solution of the problem by the method of singular integral equations. We also present the values of crack tip opening displacements. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 33, No. 6, pp. 55–62, November–December, 1997.     

A cold model study of mass transfer in Q-BOP

At steel-making temperature, chemical kinetics can rarely be the rate-limiting step. Thus most of the reactions are limited by the rate of mass transfer to and from the reaction interface. The overall rate of mass transfer may be controlled by gas phase mass transfer or liquid phase mass transfer. Since in Q-BOP, the rate of reaction may be controlled by the rate of mass transfer in gas phase or in liquid phase, both were studied in a cold model. The different variables studied were tuyere diameter, jet direction, flow rate of gas and tuyere depth. The results of gas phase mass transfer indicate that the effect of tuyere diameter and jet direction is very small. For Reynolds number less than 9000 the effect of flow rate and tuyere depth is given by the equation,K _g A/L ₀ Q = 0·02d ₀ + 0·043, whereas for Reynolds number greater than 9000 the effect of flow rate and tuyere depth is given by the equation,K _g A/L ₀ Q=0·061d ₀+0·046. Similarly the liquid phase mass transfer coefficient is independent of the tuyere diameter and the shrouding gas, and is not much affected by the jet direction. The effect of gas flow rate and tuyere depth is given by the equation,K _L A=0·077 (Q)^0·75(L ₀)^0·61.     

Numerical solution of linear two-point boundary problems via the fundamental-matrix method

A numerical method is presented for the-solution of linear systems of differential equations with initial-value or two-point boundary conditions. For y ′(x) = A (x) y (x) + f (x) the domain of interest [a,b] is divided into an appropriate number L of subintervals. The coefficient matrix A (x) is replaced by its value A_k at a point x_k within the Kth subinterval, thus replacing the original system by the L discretized systems y k(x) = A _k y _k(x) + f _k(x), k = 1,2,…, L. The fundamental matrix solution Φ_k(x, x_k) over each subinterval is found by computing the eigenvalues and eigenvectors of each A _k. By matching the solutions y _k(x) at the L – 1 equispaced grid points defining the limits of the subintervals and the boundary conditions, the two-point problem is reduced to solving a system of linear algebraic equations for the matching constants characterizing the different y _k(x). The values of y ₁(a) and y _L(b) are used to calculate the missing boundary conditions. For initial-value problems this method is equivalent to a one-step method for generating approximate solutions. By means of a coordinate transformation, as in the multiple shooting method,¹ the method becomes particularly suitable for stiff systems of linear ordinary differential equations. Five examples are discussed to illustrate the viability of the method.     

Sparse non-convex Lp regularization for cone-beam X-ray luminescence computed tomography

Cone-beam X-ray luminescence computed tomography (CB-XLCT) is an attractive hybrid imaging modality, and it has the potential of monitoring the metabolic processes of nanophosphors-based drugs in vivo. However, the XLCT imaging suffers from a severe ill-posed problem. In this work, a sparse nonconvex L_p (0?p?L₁ regularization. Further, an iteratively reweighted split augmented lagrangian shrinkage algorithm (IRW_SALSA-L_p) was proposed to efficiently solve the non-convex L_p (0?p?p-values (1/16, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8) in both 3D digital mouse experiments and in vivo experiments. The results demonstrate that the proposed non-convex methods outperform L₂ and L₁ regularization in accurately recovering sparse targets in CB-XLCT. And among all the non-convex p-values, our L_p(1/4?p?相似文献   

Tension of an elastoplastic disk. Part 1. Central crack

Within the framework of the model of plasticity bands, we consider an elastoplastic problem of fracture mechanics of the development of plasticity bands near the tips of a central crack in a disk. We assume that, in the plane stressed state, plastic strains in the vicinity of the crack tip are localized along three plasticity bands (L ₁,L ₂, andL ₃) one of which is located on the continuation of the crack and the other two make nonzero angles with the direction of the crack and that, under the conditions of plane deformation, plastic strains are localized along two plasticity bands (L ₁ andL ₂). The band (L ₃) is modeled by a line of discontinuity of normal and tangential displacements and the bands (L ₁ andL ₂) are modeled by lines of discontinuity of tangential displacements. The lengths and orientations of these lines are determined in the process of numerical solution of the problem by the method of singular integral equations. The values of the crack tip opening displacement are also determined. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 35, No. 5, pp. 7–13, September–October, 1999.     

Tension of an elastoplastic disk. Part 2. Edge crack

Within the framework of the model of plasticity strips, we study the elastoplastic problem of fracture mechanics concerning the development of these strips near the tips of an edge crack in a circular disk. We assume that plastic deformations near the crack tip are localized along three plasticity strips (L ₁,L ₂,L ₃) under the conditions of plane stressed state and along two plasticity strips (L ₁,L ₂) under the conditions of plane deformation. One of these strips (L ₃) is modeled by a line of discontinuity of normal and tangential displacements and the remaining two strips (L ₁,L ₂) are modeled by the lines of discontinuity of tangential displacements. Their lengths and orientations are determined as a result of numerical solution of the problem by the method of singular integral equations. We also present the values of the crack-tip opening displacements. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 1, pp. 17–22, January–February, 2000.     

Generalised critical free-surface flows

Nonlinear waves in a forced channel flow are considered. The forcing is due to a bottom obstruction. The study is restricted to steady flows. A weakly nonlinear analysis shows that for a given obstruction, there are two important values of the Froude number, which is the ratio of the upstream uniform velocity to the critical speed of shallow water waves, F _C>1 and F _L<1 such that: (i) when F<F _L, there is a unique downstream cnoidal wave matched with the upstream (subcritical) uniform flow; (ii) when F=F _L, the period of the cnoidal wave extends to infinity and the solution becomes a hydraulic fall (conjugate flow solution) – the flow is subcritical upstream and supercritical downstream; (iii) when F>F _C, there are two symmetric solitary waves sustained over the site of forcing, and at F=F _C the two solitary waves merge into one; (iv) when F>F _C, there is also a one-parameter family of solutions matching the upstream (supercritical) uniform flow with a cnoidal wave downstream; (v) for a particular value of F>F _C, the downstream wave can be eliminated and the solution becomes a reversed hydraulic fall (it is the same as solution (ii), except that the flow is reversed!). Flows of type (iv), including the hydraulic fall (v) as a special case, are computed here using the full Euler equations. The problem is solved numerically by a boundary-integral-equation method due to Forbes and Schwartz. It is confirmed that there is a three-parameter family of solutions with a train of waves downstream. The three parameters can be chosen as the Froude number, the obstruction size and the wavelength of the downstream waves. This three-parameter family differs from the classical two-parameter family of subcritical flows (i) but includes as a particular case the hydraulic falls (ii) or equivalently (v) computed by Forbes.     

Dynamics of field dislocations and disclinations in a few-mode optical fiber. III. Circularly polarized CP11 modes and L disclinations

It has been found experimentally and theoretically that when a stepped-index few-mode optical fiber is excited by a circularly polarized Gaussian beam, linearly polarized pure edge L _x and L _y disclinations are generated in the guided wave fields. The azimuths of the linear polarization of these disclinations rotate in the direction opposite to the rotation of the disclination axes. When the axes of the L _x and L _y disclinations are mutually orthogonal, a pure screw dislocation is created. When the axes are collinear, the L _x and L _y disclinations annihilate and a pure uniform circularly polarized edge dislocation is generated, its axis coinciding with the axis of the disclinations. Reversal of the circular polarization of the excitation changes the sign of the angles of orientation of the pure edge dislocations and disclinations, and also reverses the azimuth of the linear polarization and reverses the sign of the topological charge of the pure screw dislocation. The physical mechanism for the rotation of the disclination and dislocation axes is attributed to the optical Magnus effect in a few-mode fiber. The rotation of the plane of polarization of the L _x and L _y disclinations and the screw dislocation reflects the appearance of the Berry topological phase accompanied by a cyclic change in the orientation of these disclination axes. Pis’ma Zh. Tekh. Fiz. 23, 14–20 (March 12, 1997)     

Testing reducibility of linear differential operators: A group theoretic perspective

Let k[D] be the ring of differential operators with coefficients in a differential fieldk. We say that an elementL ofk[D] isreducible ifL=L ₁·L ₂ forL ₁,L ₂gEk[D],L ₁,L ₂k. We show that for a certain class of differential operators (completely reducible operators) there exists a Berlekamp-style algorithm for factorization. Furthermore, we show that operators outside this class can never be irreducible and give an algorithm to test if an operator belongs to the above class. This yields a new reducibility test for linear differential operators. We also give applications of our algorithm to the question of determining Galois groups of linear differential equations.Partially supported by NSF Grant 90-24624     

Comparative study of size and distribution of lamellar thicknesses and long periods in polyethylene with a shish-kebab structure

This study contains a combined application of three different techniques for the study of injection moulded polyethylene (PE), showing an oriented shish-kebab structure: small angle X-ray scattering (SAXS), low frequency Raman spectroscopy (LAM) and transmission electron microscopy (TEM), A series of linear PEs and molecular weights in the range 51000–478000 has been investigated and two injection temperatures have been used (T _m=144 and 210 °C). SAXS patterns from the highly oriented regions show the presence of either one axial long period (L ₁) or two (L ₁ and L ₂) depending on molecular weight (¯M _w) and T _m. It is shown that L ₁ and L ₂ increase with ¯M _w up to a given critical molecular weight ¯M _c. Above ¯M _c, L ₁ and L ₂ remain constant. Raman results qualitatively confirm the existence of two separate distributions of straight-length chain segments for those samples having molecular weights above the critical value. Shorter segments are shown to be more abundant than the longer ones. In the lowest molecular weight sample, results from SAXS, TEM and Raman spectroscopy seem to be consistent with each other, although in some cases a tilted molecular arrangement within the lamellae has to be invoked. On the other hand, in case of the highest molecular weight sample, the length of the short straight-chain segments derived from Raman spectroscopy agrees well with the double periodicity obtained from SAXS. On the contrary, long periods measured from TEM only correspond to the shorter SAXS periodicity. This result is discussed by assuming the occurrence of crystalline bridges among adjacent lamellae.     

A nonlinear dynamics of stimulated phonon emission in a nonautonomous acoustic quantum generator under superlow-frequency-modulated pumping conditions

A nonlinear resonance was experimentally observed in a ruby acoustic quantum generator operating in the region of 10¹⁰ Hz with electromagnetic pumping modulated at a superlow frequency. The resonance is manifested by slow regular self-detunings in the microwave spectra of stimulated phonon emission. The self-detuning period T _SD strongly depends on Δ_L≡ω_m-ω_L, where ω_m is the modulation frequency and ω_L is the resonance frequency varying from 9.8 to ∼5 Hz when the magnetic field detuning grows from 0 to 60 Oe. The direction of motion of a mode cluster along the frequency axis is uniquely determined by the sign of Δ_L. As the |Δ_L| value decreases to 0.05 Hz, the self-detuning period increases to very large values T _SD > 100 s. These large-scale collective motions take place against the background of small-scale low-frequency chaotic oscillations in intensity of the generated phonon modes, while the mode widths remain almost as narrow (<1 kHz) as those in the autonomous regime.     

Violation of Schmid's law and tension–compression asymmetry in L12 alloys: role of ordered structure

Abstract

Hypostoichiometric Ni₃Al(B) undergoes a structural transformation from its initial L1₂ structure to DO₂₂ structure during cold rolling. It has been found that this DO₂₂ structure reverts back to L1₂ structureduring annealing. The transformation to DO₂₂ structure as well as back to L1₂ at higher temperature is very much dependent on the degree of cold reduction. Based on thesefindings, the possible reason for abnormal behaviour of these L1₂ordered alloys, i.e. violation of Schmid's law and orientation dependence of flow stress is hypothesised.