Discrete Models of a Class of Isolation Systems

In this paper, a class of isolation systems with rigid limiters has been considered. For this class of systems, some general discrete-time models described by means of some impact Poincaré maps have been established. Two examples: a simple isolation system of one-stage and a real isolation system of two-stages have been investigated. The calculated results show that those models can reveal complex nonlinear behaviors. And even a small random perturbation may change the dynamical character of the system.     

Some solutions (linear in the spatial variables) and generalized Chapman–Enskog functions basic to the linearized Boltzmann equations for a binary mixture of rigid spheres

A Legendre expansion of the (matrix) scattering kernel relevant to the (vector- valued) linearized Boltzmann equation for a binary mixture of rigid spheres is used to define twelve solutions that are linear in the spatial variables {x, y, z}. The twelve (asymptotic) solutions are expressed in terms of three vector-valued functions A ⁽¹⁾(c), A⁽²⁾(c), and B(c). These functions are generalizations of the Chapman–Enskog functions used to define asymptotic solutions and viscosity and heat conduction coefficients for the case of a single-species gas. To provide evidence that the three Chapman–Enskog vectors exist as solutions of the defining linear integral equations, numerical results developed in terms of expansions based on Hermite cubic splines and a collocation scheme are reported for two binary mixtures (Ne-Ar and He-Xe) with various molar concentrations.     

Calculation of rigidly clamped circular plates in the statement of the problem on contact interaction in a two-layer package

The use of a mechanicomathematical model of bending of thick transversely isotropic plates is illustrated, where the plate is divided in an arbitrary number of equally thick conditional layers. This model allows one to approximately reduce the problem of determination of stresses and displacements in the thick plate to a corresponding contact problem for a bent pack age of layers. The axisymmetric bending of a rigidly clamped package consisting of two plates rigidly fastened together is considered. The results of numerical calculations are presented, which are compared with those obtained within the framework of a refined bending model of plates (with account of transverse compression and shear) and of the Timoshenko model, as well as in the statement of the three-dimensional theory of elasticity. The accuracy of satisfying the boundary conditions in each model is analyzed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 93–108, January–February, 2007.     

A new proof of the rigidity problem

In this short note we give a new proof of the boundary rigidity problem in a Euclidean setting proved by Croke. Our method is based on the differentiability of Busemann functions and the characteristic of Euclidean metric on Riemannian manifolds without conjugate points.

     

广义 Rigid环(英文)

本文定义并研究了广义 Rigid环 ,并讨论了环上有限生成投射模的性质     

Fission of Pb nuclei induced by 0.5, 1.0, 1.5, 3.7 and 7.4 GeV protons in the volume of massive U/Pb and Pb targets

Experiments with relativistic protons accelerated at the Synchrophasotron LHE, Dubna, with energies of 0.5, 1.0, 1.5, 3.7 and 7.5 GeV hitting massive targets of (nat. U)/Pb and Pb were carried out using SSNTD during the years 1996–1999. The beam profiles and intensities of both primary particles and fast secondary neutrons were measured inside the massive cylinder blocks of Pb and U by counting fission fragment tracks due to the induced fission of Pb nuclei. The beam diameter typically increases by 20–30% at the depth 10 and 20 cm. With increasing the energy of protons the number of secondary neutrons increases with the depth of the target.

Further studies on beam profile measurements inside the massive heavy metal targets are discussed.     

The axisymmetric mixed boundary-value problem of the vertical vibration of a rigid foundation on saturated layered soil subgrade

Based on the theory of elastic wave propagation in saturated soil subgrade established by the author of this paper, the axisymmetric vertical vibration of a rigid circular foundation resting on partially saturated soil subgrade which is composed of a dry elastic layer and a saturated substratum is studied. The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary-value condition. The results are reduced to the case for saturated half-space. The set of dual integral equations are reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper and plots of the dynamic compliance coefficient C_v versus the dimensionless frequency a₀ are presented. Foundation item: the National Natural Science Foundation of China (59579018) Biography: CHEN Sheng-li (1974-)     

Analysis of a Partially Debonded Conducting Rigid Elliptical Inclusion in a Piezoelectric Matrix

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时变边界的变质量刚体的动力学方程

讨论一类变质量刚体（即在其边界与外部进行质量交换,从而具有时变边界）的动力学问题,并建立了时变边界的刚体动力学普遍方程。