岩土材料应变局部化的有限元分析方法

采用有限单元法分析岩土材料的应变局部化时经常会遇到单元尺寸敏感性问题和网格锁定问题。自适应网格技术能够有效地解决网格锁定问题,但仍然无法克服计算结果对单元尺寸的依赖性,尽管在一维情况下被证明是可行的。复合体理论(均匀化理论)和弱非连续有限元方法可以成功地解决岩土材料的单元尺寸敏感性问题,在一维情况下两类方法实际上是一致的。本文针对岩土材料应变局部化的有限元新技术所存在的若干问题进行了详细的讨论,并给出了有关算例。     

Dynamical localization of two electrons in triple-quantum-dot shuttles

The dynamical localization phenomena in two-electron quantum-dot shuttles driven by an ac field have been investigated and analyzed by the Floquet theory. The dynamical localization occurs near the anti-crossings in Floquet eigenenergy spectrum. The oscillation of the quantum-dot shuttles may increase the possibility of the dynamical localization. Especially, even if the two electrons are initialized in two neighbor dots, they can be localized there for appropriate intensity of the driven field. The studies may help the understanding of dynamical localization in electron shuttles and expand the application potential of nanoelectromechanical devices.     

Characterizing localization properties of two spinless electrons in a one-dimensional Harper model with concurrence

By mapping the Fock space of many local fermionic modes isomorphically onto a many-qubit space and using the measure of concurrence, this paper studies numerically the mode entanglement of two spinless electrons with on-site interaction U moving in the one-dimensional Harper model. Generally speaking, for electrons in extended regimes （potential parameter λ 〈 2）, the spectrum-averaged concurrence N（C） first decreases slowly as A increases until its local minimum, then increases with λ until its peak at λ = 2, while for electrons in localized regimes （λ 〉 2）, N（C） decreases drastically as λ increases. The functions of N（C） versus λ are different for electrons in extended and localized regimes. The maximum of N（C） occurs at the point λ= 2, which is the critical value in the one-dimensional singleparticle Harper model. From these studies it can distinguish extended, localized and critical regimes for the two-particle system. It is also found for the same λ that the interaction U always induce the decreases of concurrence, i.e., the concurrence can reflect the localization effect due to the interaction. All these provide us a new quantity to understand the localization properties of eigenstates of two interacting particles.     

The Integrated Density of States for Some Random Operators with Nonsign Definite Potentials

We study the integrated density of states of random Anderson-type additive and multiplicative perturbations of deterministic background operators for which the single-site potential does not have a fixed sign. Our main result states that, under a suitable assumption on the regularity of the random variables, the integrated density of states of such random operators is locally Hölder continuous at energies below the bottom of the essential spectrum of the background operator for any nonzero disorder, and at energies in the unperturbed spectral gaps, provided the randomness is sufficiently small. The result is based on a proof of a Wegner estimate with the correct volume dependence. The proof relies upon the L^p-theory of the spectral shift function for p?1 (Comm. Math. Phys.218 (2001), 113-130), and the vector field methods of Klopp (Comm. Math. Phys.167 (1995), 553-569). We discuss the application of this result to Schrödinger operators with random magnetic fields and to band-edge localization.     

Dynamical Localization II with an Application to the Almost Mathieu Operator

Several recent works have established dynamical localization for Schrödinger operators, starting from control on the localization length of their eigenfunctions, in terms of their centers of localization. We provide an alternative way to obtain dynamical localization, without resorting to such a strong condition on the exponential decay of the eigenfunctions. Furthermore, we illustrate our purpose with the almost Mathieu operator, H _{, ,} =–+ cos(2(+x)), 15 and with good Diophantine properties. More precisely, for almost all , for all q>0, and for all functions ²( ) of compact support, we show that The proof applies equally well to discrete and continuous random Hamiltonians. In all cases, it uses as input a repulsion principle of singular boxes, supplied in the random case by the multi-scale analysis.     

Reactivity of solids

A review of studies of reactivities of solids is presented, concentrating on localization and autolocalization phenomena. Some examples of feed-back and structure of the reaction zone are given. Plenary lecture     

Determination of the content and localization of magnesium in bioapatite of bone

Using x-ray diffraction, electrothermal atomization atomic absorption spectroscopy, and scanning electron microscopy with an x-ray microanalysis, we have studied the phase decomposition of biogenic and synthetic Mg-containing apatite at 900°C with formation of β-tricalcium-magnesium phosphate (β-TCMP). Employing simplified model representations, we obtained a relation that couples the initial Mg concentration with the degree of transformation of apatite into β-TCMP. It is shown that for the β-TCMP contents measured in bioapatite samples and on replacement of calcium by magnesium to about 8% in this phase the calculated range of Mg concentrations coincides with that available in literature sources (0.2–0.6 wt. %). A comparative investigation of the products of decomposition of biogenic and synthetic apatite by the methods of analysis of the composition and structure has established that the formation of β-TCMP is limited by both the insufficient concentration of magnesium and the small sizes of the crystals. The results of the investigations carried out together with the experimental data known from the literature are indicative of the nonuniform distribution of magnesium in the bulk of crystals of biogenic and synthetic apatite, with its predominant localization at the surface sites of the lattice. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 6, pp. 821–826, November–December, 2005.