Deformations of duality-symmetric theories

We prove that a sum of free non-covariant duality-symmetric actions does not allow consistent, continuous and local self-interactions that deform the gauge transformations. For instance, non-abelian deformations are not allowed, even in 4 dimensions where Yang–Mills type interactions of 1-forms are allowed in the non-manifestly duality-symmetric formulation. This suggests that non-abelian duality should require to leave the standard formalism of perturbative local field theories. The analyticity of self-interactions for a single duality-symmetric gauge field in four dimensions is also analyzed.     

A Model of Arterial Adaptation to Alterations in Blood Flow

Mechanisms of arterial adaptation to changes in blood flow rates were tested by comparing the predictions of a proposed theoretical model with available experimental data. The artery was modeled as an elastic membrane made of a nonlinear, incompressible, elastic material. Stimulation of the vascular smooth muscle was modeled through the generation of an active component of circumferential stress. The muscular tone was modulated by flow-induced shear stress sensed by the arterial endothelium, and is responsible for the vasomotor adjustment of the deformed arterial diameter in response to changes in blood flow. This study addresses the hypothesis that the synthetic and proliferative activity of smooth muscle cells, leading to a change in arterial dimensions, is shear stress dependent and is associated with changes in the contractile state of the smooth muscle cells and changes in the circumferential wall stress. Remodeling to a step change in flow was formulated as an initial-value problem for a system of first order autonomous differential equations for the evolution of muscular tone and evolution of arterial geometry. The governing equations were solved numerically for model parameters identified from experimental data available in the literature. The model predictions for the time variation of the geometrical dimensions and their asymptotic values were found to be in qualitative agreement with available experimental data. Experiments for validating the introduced hypotheses and further generalizations of the model were discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling and Experimental Characterisation of Hygrothermoelastic Stress in Polymer Matrix Composites

Summary : The present paper is concerned with the modelling and the simulation of hygrothermal deformation of composite laminates. The temperature and moisture fields are established by employing the Fick's law for transient and cyclical environmental conditions, then the Classical Plate Theory (CLT) adapted for taking into account such conditions is applied. The hygrothermoelastic law of the composite is supposed to be constant but the diffusion coefficients depend on the temperature. The paper shows the ability of the model to handle complex environmental loading, close to service conditions. Finally, a model of plate with moderate rotations is introduced to predict the nonlinear deformations of unsymmetric plates under temperature and moisture cycling conditions.     

Maximal Classes of Stored Energies Compatible with Cylindrical Inflations

We consider a family of deformations describing cylindrical inflations within the context of finite, compressible, isotropic elasticity. We pose the problem of finding the maximal class of materials for which these deformations are possible at equilibrium under surface tractions only. We solve this problem for families of cylindrical inflations whose principal strain invariants have a special dependence on the radius. These families comprise and extend all cases considered by Murphy [2]. This revised version was published online in August 2006 with corrections to the Cover Date.     

Invariant star-products on symplectic manifolds

Let (M,F) be a symplectic manifold and consider a Lie subalgebra $\text{G}$ of its Lie algebra of symplectic vector fields. We prove that every one-differentiable deformation of order k of the Poisson Lie algebra of M, which is invariant with respect to $\text{G}$, extends to an invariant one-differentiable deformation of infinite order. If M admits a $\text{G}$-invariant linear connection, a similar result holds true for differentiable deformations and for star-products. In particular, if M admits a $\text{G}$- -invariant linear connection, there always exists a $\text{G}$-invariant star-product.     

Differential realizations of polynomial algebras in finite-dimensional spaces of monomials

We give a complete classification of at most second-order differential ladder operators preserving finite-dimensional spaces of monomials and closing under the Lie bracket to give a cubic polynomial of the diagonal generators.     

Universal Deformations for a Class of Compressible Isotropic Hyperelastic Materials

Differential conditions are derived for a smooth deformation to be universal for a class of isotropic hyperelastic materials that we regard as a compressible variant (a notion we make precise) of Mooney–Rivlin’s class, and that includes the materials studied originally by Tolotti in 1943 and later, independently, by Blatz. The collection of all universal deformations for an incompressible material class is shown to contain, modulo a uniform dilation, all the universal deformations for its compressible variants. As an application of this result, by searching the known families of universal deformations for all incompressible isotropic materials, a nontrivial universal deformation for Tolotti materials is found. This revised version was published online in August 2006 with corrections to the Cover Date.     

Time derivative obtained by applying the Riemannian manifold of Riemannian metrics to kinematics of continuaDérivée temporelle obtenue en utilisant la variété riemannienne des métriques riemanniennes aux cinématiques des milieux continus

The infinite dimensional Riemannian geometry of Riemannian metrics is employed to propose novel objective time derivative by means of covariant derivative. To cite this article: Z. Fiala, C. R. Mecanique 332 (2004).     

Azimuthal Shear in Compressible Finite Elasticity

In an earlier paper, the broadest classes of compressible isotropic strain energies that support irrotational universal deformations were identified and the problems of cylindrical and spherical inflation or compaction were solved in closed form for all of these strain energies. Similar closed form solutions of the problem of azimuthal shear are presented here.      

Evidence for multiple band terminations in Pd

The level structure of ¹⁰²Pd has been investigated using data collected with the Eurogam 2 array. Several cascades of γ-rays have been established up to high spins. Termination of rotational bands has been observed at I^π = 28⁻ and 32⁺, and tentatively at I^π = 38⁺ and 42⁺. The nucleus ¹⁰²Pd is the first case where rotational bands built on valence space configurations are followed from spin close to zero up to termination and, at higher spins, a smooth rotational band which appears to terminate is built on core excited configurations.