Generating function of a thermoelectric field

It is shown that the state of a thermoelectric medium can be described by a single mathematical object — a generating function for a thermoelectric field. The relation between the generating function and the vector potential of the current density, the temperature distribution, and the potentials for uniform anisotropic and nonuniform isotropic media are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fiziki, No. 5, pp. 21–24, May, 1986.     

耗散系统的准热力学模型

以具有自治系统一般形式的运动方程及其相应的Fokker-Planck方程为出发点,确立了一种适应面比较广的耗散系统的准热力学模型.定义了与驱动项f相共轭的函数X,取代作为上述运动方程的自田变量x(x可代表某种输出或化学反应的产物).以状态参量f,X,C(C为控制参量)对照参量p,V,T,得到一系列涉及准热力学函数及其导数的基本关系式,它们与传统热力学是一一对应的,最后给出一个应用范例. 关键词：     

Shedding Light on the Diverse Reactivity of NacNacAl with N‐Heterocycles

The aluminum(I) compound NacNacAl (NacNac=[ArNC(Me)CHC(Me)NAr]^?, Ar=2,6‐iPr₂C₆H₃, 1 ) shows diverse and substrate‐controlled reactivity in reactions with N‐heterocycles. 4‐Dimethylaminopyridine (DMAP), a basic substrate in which the 4‐position is blocked, induces rearrangement of NacNacAl by shifting a hydrogen atom from the methyl group of the NacNac backbone to the aluminum center. In contrast, C?H activation of the methyl group of 4‐picoline takes place to produce a species with a reactive terminal methylene. Reaction of 1 with 3,5‐lutidine results in the first example of an uncatalyzed, room‐temperature cleavage of an sp² C?H bond (in the 4‐position) by an Al^I species. Another reactivity mode was observed for quinoline, which undergoes 2,2′‐coupling. Finally, the reaction of 1 with phthalazine produces the product of N?N bond cleavage.     

Optimized effective potentials from electron densities in finite basis sets

The Wu-Yang method for determining the optimized effective potential (OEP) and implicit density functionals from a given electron density is revisited to account for its ill-posed nature, as recently done for the direct minimization method for OEP's from a given orbital functional [T. Heaton-Burgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett. 98, 256401 (2007)]. To address the issues on the general validity and practical applicability of methods that determine the Kohn-Sham (local) multiplicative potential in a finite basis expansion, a new functional is introduced as a regularized version of the original work of Wu and Yang. It is shown that the unphysical, highly oscillatory potentials that can be obtained when unbalanced basis sets are used are the controllable manifestation of the ill-posed nature of the problem. The new method ensures that well behaved potentials are obtained for arbitrary basis sets.     

Structural-acoustic modeling for three-dimensional freefield and littoral environments with verification and validation

This paper describes a high-order, finite-element-based, three-dimensional time-harmonic model for large-scale exterior structural-acoustics problems. It is applicable to both freefield and littoral environments. For the freefield case, the infinite exterior is treated as a homogeneous linear acoustic medium. For littoral applications, the water or air and the sediment domains are each treated as linear homogeneous, semi-infinite half-spaces with piecewise-constant properties. Both domains admit complex-valued wave speeds to enable the inclusion of damping. The finite element formulation uses a variational statement which naturally incorporates the transmission-condition at the water or air-sediment interface. The truncation of the infinite exterior is realized using an infinite-element for the freefield case, and the perfectly-matched-layer approximation for littoral applications. Computation of the farfield quantities is done based on an integral representation which, for the littoral cases, uses efficient approximations for the appropriate Green's function. Numerical computations are presented for a series of progressively more complex problems, and are used to verify the model against analytic and other numerical solutions and validate it based on the experimental data for scattering from elastic scatterers as measured in freefield and sediment pool laboratory facilities.