Current challenges of Geotechnical Mechanics

The milestones in geotechnical mechanics research conducted at the N. S. Polyakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine are listed. Solutions to the deep-mining challenges faced by the institute as a leading research institution in the industry are outlined. The basic results on the subject achieved by the institute over the years of its existence are summarized To the Beginning of the Third Millennium To the 40th Anniversary of the N. S. Polyakov Institute of Geotechnical Mechanics __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 3–15, September 2006.     

空中交通管理中的地面等待策略研究

就现代空中交通管理中地面等待策略 (GDP)的发展和现状作了简要的总结概括 ,阐述了地面等待对空中交通流量管理的影响与意义 ,分类分析了地面等待策略 ,同时从众多理论研究中归纳出了几种典型模型和求解方法 ,并对各种模型、方法进行了比较分析 ,最后提出了地面等待策略的发展趋势和方向 .     

Exact ground states of Ising spin glasses: New experimental results with a branch-and-cut algorithm

In this paper we study two-dimensional Ising spin glasses on a grid with nearest neighbor and periodic boundary interactions, based on a Gaussian bond distribution, and an exterior magnetic field. We show how using a technique called branch and cut, the exact ground states of grids of sizes up to 100×100 can be determined in a moderate amount of computation time, and we report on extensive computational tests. With our method we produce results based on more than 20,000 experiments on the properties of spin glasses whose errors depend only on the assumptions on the model and not on the computational process. This feature is a clear advantage of the method over other, more popular ways to compute the ground state, like Monte Carlo simulation including simulated annealing, evolutionary, and genetic algorithms, that provide only approximate ground states with a degree of accuracy that cannot be determineda priori. Our ground-state energy estimation at zero field is –1.317.     

3d系列 (TM)4 团簇的结构和磁性

基于第一性原理，在密度泛函理论下，用局域自旋密度近似(LSDA)和广义梯度近似(GGA)对(TM)₄团簇的所有几何构型进行优化、能量、频率和磁性计算.确定出3d系列(TM)₄团簇的基态构型，对其磁性、结合能和平均原子间距作了系统的研究，得出在3d系列(TM)₄团簇中，Mn₄的局域磁矩最大，V₄的局域磁矩最小，并且除Cr₄在LSDA和GGA均为反铁磁性耦合及GGA下的V_{关键词： 4}团簇')" href="#">(TM)₄团簇 基态构型 结合能 局域磁矩 平均原子间距     

关于核多体系统的基态关联效应

对于一个原子核模型系统在不同耦合强度、不同粒子数情况下的基态关联效应进行了研究,结果表明：当具有稳定的静态形变时,基态关联基本上可用基于静态上的零点振动来解释,因此,关于静态性质的自治场计算是至关重要的. 但在开始发生单极形变的临界点附近,它随控制参量的变化显得很复杂、很敏感. 看来,在滴线附近的轻核的进一步研究中,关联效应是需要注意考虑的.     

A conformai,symmetry broken model for gravity

Starting from Padmanabhan's fully conformally invariant action, we obtain gravity as a spontaneously broken theory. Newton's constant and the cosmological constant follow from the breakdown of the conformal symmetry at the tree approximation. For small oscillation of the scalar field about the fundamental state, the matter field degenerates into two decoupled fields.     

The convergence of the one-dimensional ground states to an infinite lattice

For one-dimensional systems interacting via a two-body potential, the sequence of ground states is proved to converge to an infinite lattice, for a large open class of interactions, containing in particular the Lennard-Jones potential.     

The symmetry of ground states under perturbation

We consider a two-body potential which has only periodic ground states and prove that it can be perturbed, by an arbitrarily small perturbation, so as to have only aperiodic ground states.Research supported in part by NSF grant MCS 78-01520-A01.     

A note on exponential decay properties of ground states for quasilinear elliptic equations

We give an explicit formula for exponential decay properties of ground states for a class of quasilinear elliptic equations in the whole space .