Formulas are developed for use in lattice studies of charged hadron polarizabilities. In particular, the valence quark different-flavor component of the charged pion polarizability is examined on a 163 × 24 lattice at β = 6.0 using Wilson fermions. Using the elastic limit results of Part I of this series, it is concluded that this represents a small negative component of the full charged polari...

The problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the diameter of the beam goes to zero, a nonlinear model for strings and a bending-torsion theory for rods are deduced.

We use a simple model to determine the frequency-dependent effective elastic coefficients of a three-dimensional phononic crystal, consisting of periodically arranged solid spheres embedded in fluid host, through theoretical calculations of the transmission coefficient and frequency band structure diagrams, using multiple-scattering techniques. Our results are successfully compared to those obt...

We introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff’s nonlinear bending theory for plates. Different limit models are deduced depending on the relative ratio between the thickness parameter h and the two homogenization scales ε and ε.

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In this paper we consider a elastic vector-valued Allen-Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.

We consider the non-reactive elastic Boltzmann equation for multicomponent gaseous mixtures. We deduce, under the standard diffusive scaling, that well prepared initial conditions lead to solutions satisfying the Maxwell-Stefan diffusion equations in the vanishing Mach and Knudsen numbers limit.

The eeective energy of a mixture of two elastic materials in a thin lm is characterized using Gamma-limit techniques. For cylindrical shaped inclusions it is shown that 3D-2D asymptotics and optimal design commute from a variational viewpoint. Regularity of local minimizers for the resulting design is addressed.

We analyze the asymptotic behavior of a junction problem between a plate and a perpendicular rod made of a nonlinear elastic material. The two parts of this multi-structure have small thicknesses of the same order δ. We use the decomposition techniques obtained for the large deformations and the displacements in order to derive the limit energy as δ tends to 0.