On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid

We consider the motion of a rigid body immersed in a bidimensional incompressible perfect fluid. The motion of the fluid is governed by the Euler equations and the conservation laws of linear and angular momentum rule the dynamics of the rigid body. We prove the existence and uniqueness of a global classical solution for this fluid–structure interaction problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid–structure interaction problem obtained by incorporating some viscosity.     

惯性系中直线运动的常加速度内禀刚性非惯性系

推导相对惯性系作直线运动的常加速度内禀刚性加速系的坐标变换关系式，并讨论该加速系的主要性质。     

Calculation of simply supported circular plates in the statement of the problem of contact interaction in a package of two plates

The possibility of applying the mechanicomathematical model of bending of a package of transversely isotropic plates to approximate calculations of thick plates is investigated. Within the frame work of this model, the problem of axisymmetric bending of a package of two identical plates with simply supported edges is considered. The conditions of rigid contact are given between the plates. Based on the analytical result obtained, the unknown distribution of stresses and displacements across the thickness of the plate is approximated by the distribution of corresponding parameters in the package of two plates. For an isotropic body, the results of numerical calculations are compared with those given by the 3D theory of elasticity. In the case of a transversely isotropic body, a comparison with the results found by the refined bending model of plates (taking into account the transverse compression and shear) and the Timoshenko model is carried out. The accuracy to which the boundary conditions in every model are satisfied is analyzed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 603–616, September–October, 2007.     

Well posedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space ℝ ^d , d = 2 or 3. The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary value problem. We improve the known results by proving a complete wellposedness result: our main result yields a local in time existence and uniqueness of strong solutions for d = 2 or 3. Moreover, we prove that the solution is global in time for d = 2 and also for d = 3 if the data are small enough. Patricio Cumsille’s research was partially supported by CONICYT-FONDECYT grant (No. 3070040) and Takéo Takahashi’s research was partially supported by Grant (JCJC06 137283) of the Agence Nationale de la Recherche.     

Hydrogen bonding,mobility, and structural transitions in aliphatic polyamides

Some salient results in nylon research are reviewed to identify the fundamental principles that are applicable to other strongly interacting or hydrogen‐bonded polymers, including proteins. The effects of hydrogen bonds on stress‐, heat‐, and solvent‐induced changes in macroscopic properties are discussed. These data provide a window into the chain mobility and linkages between the crystalline and amorphous domains, both of which are important for any predictive model. The changes in the characteristics of the amorphous phase with the crystallinity and orientation require that it be modeled with at least two components: a rigid/immobile/anisotropic component and a soft/mobile/isotropic component. The deformation and shrinkage behavior of these polymers are discussed in terms of the relative contributions of the amorphous and crystalline domains and of the interactions between them. The premelting crystalline transition is accompanied by the merging of intersheet and intrasheet diffraction peaks in some nylons, as observed by Brill, and not in others even though the underlying mechanism that gives rise to these transitions, the onset of volume‐increasing librational motion of the crystalline stems, is the same. Because the effects of the temperature, deformation, and solvent have a common origin associated with mobility, a fictive temperature can be associated with a given solvent activity or stress level. The magnitude of this fictive temperature is the amount by which the glass or Brill transition temperature is reduced in the presence of solvents (～50 °C) or stress or by which the annealing temperature can be reduced in the presence of a solvent (or active stress) to achieve the same structural state as that of a dry (or static) polymer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1763–1782, 2006     

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.