Quasi-localization and quasi-mobility edge for light atoms mixed with heavy ones

A mixture of light and heavy atoms is considered. We study the kinetics of the light atoms, scattered by the heavy ones, the latter undergoing slow diffusive motion. In three-dimensional space we claim the existence of a crossover region (in energy), which separates the states of the light atoms with fast diffusion and the states with slow diffusion; the latter is determined by the dephasing time. For the two dimensional case we have a transition between weak localization, observed when the dephasing length is less than the localization length (calculated for static scatterers), and strong localization observed in the opposite case.     

Localization of elastic deformation in strongly anisotropic, porous, linear materials with periodic microstructures: Exact solutions and dilute expansions

Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading direction, which induces localized (singular) field configurations. The effective elastic moduli are computed as functions of the porosity in each case. Their dilute expansions feature half-integer powers of the porosity, which can be correlated to the localized field patterns. Statistical characterizations of the fields, such as their first moments and their histograms are provided, with particular emphasis on the singularities of the latter. The behavior of the system near the void close-packing fraction is also investigated. The results of this work shed light on corresponding results for strongly non-linear porous media, which have been obtained recently by means of the “second-order” homogenization method, and where the dilute estimates also exhibit fractional powers of the porosity.     

Bournonite PbCuSbS3: Stereochemically Active Lone‐Pair Electrons that Induce Low Thermal Conductivity

An understanding of the structural features and bonding of a particular material, and the properties these features impart on its physical characteristics, is essential in the search for new systems that are of technological interest. For several relevant applications, the design or discovery of low thermal conductivity materials is of great importance. We report on the synthesis, crystal structure, thermal conductivity, and electronic‐structure calculations of one such material, PbCuSbS₃. Our analysis is presented in terms of a comparative study with Sb₂S₃, from which PbCuSbS₃ can be derived through cation substitution. The measured low thermal conductivity of PbCuSbS₃ is explained by the distortive environment of the Pb and Sb atoms from the stereochemically active lone‐pair s² electrons and their pronounced repulsive interaction. Our investigation suggests a general approach for the design of materials for phase‐change‐memory, thermal‐barrier, thermal‐rectification and thermoelectric applications, as well as other functions for which low thermal conductivity is purposefully sought.     

Spectral localization of arbitrarily shaped regions of interest (SLASH) using single voxel signals

A method for obtaining localized spectra from arbitrarily shaped regions of interest is described. When a sample consists of homogeneous compartments or domains, spectra localized in each compartment can be obtained from signals of single voxels with regular shapes by solving a set of simultaneous linear equations. Experimental demonstrations on a phantom and on human brain in vivo for a two compartment, two voxel case are presented. The issue of signal-to-noise ratio is also discussed.     

分次环与局部化

设Ｇ是有限群，Ｒ是有单位元的Ｇ－型分次环，Ｓ是包含在Ｒ的所有齐次元素组成的集合内的乘法封闭子集，Ｓ＝ｘ∈Ｇａｅ（ｇｘ，ｘ）ａ∈Ｓ，Ｄｅｇ（ａ）＝ｇ∈Ｇ｛｝，Ｓ＝＝ｘ∈Ｇａｅ（ｇｘ，ｘｈ）ａ∈Ｓ，Ｄｅｇ（ａ）＝ｇ∈Ｇ，ｈ∈Ｇ｛｝，ＭＧ（Ｒ）表示以Ｇ的元作为行列标的｜Ｇ｜阶矩阵环．本文证明了Ｒ关于Ｓ满足左Ｏｒｅ条件当且仅当Ｒ＃Ｇ关于Ｓ满足左Ｏｒｅ条件当且仅当ＭＧ（Ｒ）关于Ｓ＝满足左Ｏｒｅ条件，而且，Ｓ－１（Ｒ＃Ｇ）≌（Ｓ－１Ｒ）＃Ｇ和Ｓ＝，－１（ＭＧ（Ｒ））≌ＭＧ（Ｓ－１Ｒ）．     

Localization properties of driven disordered one-dimensional systems

We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.     

Behaviors of solutions for a singular diffusion equation

This paper is devoted to some behaviors of solutions of the initial-boundary problem for a singular diffusion equation, namely, localization and large time behavior. After given some special explicit solutions it is proved that solutions of the problem possess the localization property. Next, L² decay estimate as t→∞ is proved by a rather standard energy method. Finally, by comparison with a special solution the expected L^∞ decay estimate is derived.     

Relationship between strain localization and catastrophic rupture

In order to explore a prior warning to catastrophic rupture of heterogeneous media, like rocks, the present study investigates the relationship between surface strain localization and catastrophic rupture. Instrumented observations on the evolution of surface strain field and the catastrophic rupture of a rock under uniaxial compression were carried out. It is found that the evolution of surface strain field displays two phases: at the early stage, the strain field keeps nearly uniform with weak fluctuations increasing slowly; but at the stage prior to catastrophic rupture, a certain accelerating localization develops and a localized zone emerges. Based on the measurements, an analysis was performed with local mean-field approximation. More importantly, it is found that the scale of localized zone is closely related to the catastrophic rupture strain and the rupture strain can be calculated in accord with the local-mean-field model satisfactorily. This provides a possible clue to the forecast of catastrophic rupture.     

Note on a theorem of Bousfield and Friedlander

We examine the proof of a classical localization theorem of Bousfield and Friedlander and we remove the assumption that the underlying model category be right proper. The key to the argument is a lemma about factoring in morphisms in the arrow category of a model category.     

自然定域轨道方法研究

本文报导我们按自然定域轨道原理编制的NLMO程序以及对自然定域轨道计算方法的一些改进。用NLMO程序计算出七个具有不同成键特性分子(包括是否含有孤对或π键,是否含有多中心键等不同情况)的自然定域轨道,结果与用其它定域化方法得出的基本一致。由于自然定域轨道方法基本上具有内禀定域性质,而计算量明显小于其它定域化方法,可以认为它是有效和方便的。