Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

Virtual logarithms

The modification of the number field sieve which Joux and Lercier recently used to compute logarithms in a prime field of a record 120 decimal digits makes use of the notion of a virtual logarithm of a prime ideal in a number ring. We provide necessary and sufficient conditions for their method to succeed and give an explicit formula for the virtual logarithm of an ideal.     

相对论平均场理论中各种有效相互作用对中子星性质的影响

基于相对论平均场理论，研究了各种相互作用参数组(NL1、NL3、NLSH、TM1和GL-97)对中子星物质的性质和中子星整体结构的影响．发现参数组NL1、NL3和NLSH所给出的中子星内部的介子场强度、物质的组成比例、物态方程和中子星的整体特点基本相同，但与TM1和GL-97之间有较大的差别．相对于其他参数组，GL-97给出的介子场强度最弱，中子星的相对数密度最大，物态方程也最软，同时采用GL-97参数组计算的中子星的最大质量也最小．     

Transport of Neutrally Buoyant and Dense Variably Sized Colloids in a Two-Dimensional Fracture with Anisotropic Aperture

The transport of monodisperse as well as polydisperse colloid suspensions in a two-dimensional, water saturated fracture with spatially variable and anisotropic aperture is investigated with a particle tracking model. Both neutrally buoyant and dense colloid suspensions are considered. Although flow and transport in fractured subsurface formations have been studied extensively by numerous investigators, the transport of dense, polydisperse colloid suspensions in a fracture with spatially variable and anisotropic aperture has not been previously explored. Simulated snapshots and breakthrough curves of ensemble averages of several realizations of a log-normally distributed aperture field show that polydisperse colloids exhibit greater spreading than monodisperse colloids, and dense colloids show greater retardation than neutrally buoyant colloids. Moreover, it is demonstrated that aperture anisotropy oriented along the flow direction substantially increases colloid spreading; whereas, aperture anisotropy oriented transverse to the flow direction retards colloid movement.     

Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.     

Quantum Teleportation via Hybrid Entangled States

In this paper, we study quantum teleportation of atomic states via a hybrid entangled state (HES) involving an atom and a cavity field. And we investigate how to implement controlled phase (CP) gates between atomic internal Finally, a brief discussion about the feasibility of this scheme in experiment is presented.     

Neutrino propagation in a weakly magnetized medium

Neutrino-photon processes, forbidden in vacuum, can take place in the presence of a thermal medium and/or an external electro-magnetic field, mediated by the corresponding charged leptons (real or virtual). Such interactions affect the propagation of neutrinos through a magnetized plasma. We investigate the neutrino-photon absorptive processes, at the one-loop level, for massless neutrinos in a weakly magnetized plasma. We find that there is no correction to the absorptive part of the axial-vector-vector amplitude due to the presence of a magnetic field, to the linear order in the field strength.     

On computation of the greatest common divisor of several polynomials over a finite field

We propose a probabilistic algorithm to reduce computing the greatest common divisor of m polynomials over a finite field (which requires computing m−1 pairwise greatest common divisors) to computing the greatest common divisor of two polynomials over the same field.     

Stability and Nonlinear Deformation of Cylindrical Grids

The general stability of single-layer cylindrical grids is studied in linear and nonlinear formulations. Dependence of the general buckling load on the geometry and stiffness parameters of a grid is established in an analytical form. Such grids are numerically analyzed for stability. It is established that the general buckling load is much less than the local buckling load. Typical general buckling modes are found. It is shown that such grids are weakly sensitive to imperfections     

Gauss-Manin connections for arrangements, III Formal connections

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices.