Use of pseudopotential towards time-evolution of a nonstationary state: Spatially localized excitation in a crystal

Pseudopotential is used as a formal operator to write the exact time-dependence of a pseudoexciton and hence that of an initial excitation spatially localized in a crystal. The exponential operator where pseudopotential occurs at the argument is readily evaluated using the property of projection operators. Migration of an initially localized excitation is of considerable experimental importance and can be of conceptual use since it should eventually generate the characteristics of a migrating exciton. From the formal time-dependence of a localized excitation, its spread with time can be calculated with relative ease. In a concurrent discussion, the previous work of Merrifield (1958) on the propagation of excitation is criticized and an error is pointed out. The spread, however, remains wavelike and is not dissipative in the absence of a collisional mechanism.     

一种考虑瞬态效应的散热结构导热路径设计的拓扑优化模型

实际工程中,热载荷多数具有短时和周期性特点,瞬态效应显著。目前的散热结构导热路径设计多基于稳态热传导模型,未考虑瞬态效应。本文提出了一种以区域温度控制函数作为设计目标的瞬态热传导问题的拓扑优化模型,能够实现在整个时间历程上特定区域内最高温度最小。使用伴随变量法,推导了目标函数关于设计变量的敏度计算格式。算例表明,基于本文优化模型获得的散热路径设计与基于稳态热传导模型的结果有明显差别,具有更优的散热性能。因此,时变热荷载下的散热结构构型设计需要考虑瞬态响应的影响。     

Aspects of the Theory and Computation of Resonances, with Applications to Field-Free and Field-Dressed Atomic States

A review of certain aspects of the theory and computation of resonance states is presented, from the point of view of the work by the author and his colleagues in atomic physics. Two issues are mainly discussed: one is the understanding and ab initio calculation of resonance states of real systems from a time-dependent point of view. The other is the derivation and application of the complex eigenvalue Schrödinger equation from a superposition of the localized wave packet ₀ with the orthogonal to it scattering wave functions (E), when outgoing-wave boundary conditions are imposed. It is shown how two complex adjoint solutions, the hallmark of resonance state theory, correspond to the Fano solution for a resonance state on the real energy axis, obtained from the application of Hermitian quantum mechanics. The forms of the complex eigenfunctions are used for non-Hermitian calculations of resonance states in polyelectronic atoms. The question of time-asymmetry at the quantum level is tackled by observing that the time-evolution has to be considered with boundary conditions t 0 and > E > 0 and a complex energy distribution given by the diagonal matrix element of the Green's function with respect to ₀. Using a model whereby the self-energy of the decaying state, A(z), is approximated by A(z) A(E ₀), where E ₀ = ₀|H|₀, it is shown that time-asymmetry, if present as defined in this work, should have an effect on the as yet unobserved long-time deviation from exponential decay. Although not described explicitly, it is indicated, via the forms of the trial wave functions and via the references, how poly-electronic calculations have been carried out, for field-free resonance states as well as for resonance states that are created by the presence of an external electromagnetic field.     

The time dependence of chitosan/nonionic surfactant solution viscosity

The measurement of the viscosity of semiconcentrated chitosan (0.08–0.14%) solutions in the system with octaethyleneglycolmonon-dodecylether (C₁₂E₈) was carried out using Cannon-Fenske capillary viscometer. The interaction was—as expected—very weak, vut when the time dependent hydrodynamic behaviour of the system was considered, the interaction has been established at particular surfactant concentrations. The most significant time dependence is shown in a form of sudden viscosity drop in a region close to and above CMC value of the surfactant, which implied existence of the interaction between chitosan and surfactant. At low surfactant concentrations viscosity values vere constant with increasing surfactant concentration, but solution also showed time dependent decrease in the viscosity which has been connected with well known time dependent viscosity of pure chitosan solution.The viscometry enabled monitoring of the extent of chitosan/surfactant association by establishing the viscosity decrease rate constant. The rate constant was derived from the first order constant of the quadratic polynomial curves used for the approximation of experimental values when these are presented in the form of viscosity-time profiles. This method showed the existence of critical surfactant concentration values (C ₁,C ₂ andC ₃). These values are closely connected with the proposed interaction model which is based on the assumption that spherical surfactant micelles are bound by chitosan molecule.On leave from Textile Engineering Dept., Faculty of Technology and Metallurgy, University of Belgrade, Yugoslavia     

黏弹性薄板蠕变屈曲的载荷-时间特性研究

通过对黏弹性薄板压屈的稳定性分析,着重讨论了蠕变屈曲载荷－时间的特性,理论分析表明：黏弹性薄板蠕变屈曲与材料的力学性能密相关,屈曲载荷不像弹性薄板为一定值,而是与时间相关的;在一定载荷下,经过一段时间后出现延迟屈曲,相关的实验研究也证实这一重要结论;这种延迟失稳问题在工程中有其重要的意义。     

Dynamic behavior of polymer surface and the time dependence of contact angle

The increased attention has been focused on the re-searches of soft materials proposed by Pierre-Gilles de Gennes, a Nobel Prize Laureate in Physics. A special issue of “Science” on soft surfaces was published in 2002 to review specific surface properti…     

Quantum Superarrivals: Bohr's Wave-Particle Duality Revisted

The phenomenon of quantum superarrivals is manifested in the probabilities for Schrödinger wave packets scattered from perturbed potential barriers. We argue that both classical wave-like and classical particle-like properties can be exhibited in the same gedanken experimental set-up for obtaining superarrivals through Schrödinger dynamics. An interesting question regarding the tenet of mutual exclusiveness, a la Bohr, of these two properties is raised in the context of this phenomenon.     

The description of reflection coefficients of the scattering problems for finding solutions of the Korteweg–de Vries equations

The results of inverse scattering problem associated with the initial-boundary value problem (IBVP) for the Korteweg–de Vries (KdV) equation with dominant surface tension are formulated. The necessary and sufficient conditions for given functions to be the left- and right-reflection coefficients of the scattering problem are established. The time-dependence t, t > 0 of each element of the scattering matrix s(k,t) is found in respective sector of the k-spectral plane by expansion formulas which are constructed from the known initial and boundary conditions of the IBVP. Knowing the right-reflection coefficient calculated from the elements of s(k,t), we solve the Gelfand–Levitan–Marchenko (GLM) equation in the inverse problem. Then the solution of the IBVP is expressible through the solution of the GLM equation. The asymptotic behavior at infinity of time of the solution of the IBVP is shown