Russia's Post-Electoral Landscape

Dubois Patrick. PELLISSIER. In: , . Le dictionnaire de pédagogie et d'instruction primaire de Ferdinand Buisson : répertoire biographique des auteurs. Paris : Institut national de recherche pédagogique, 2002. p. 114. (Bibliothèque de l'Histoire de l'Education, 17

Closing the gap in the solutions of the strong explosion problem: An expansion of the family of second-type self-similar solutions

Shock waves driven by the release of energy at the center of a cold ideal gas sphere of initial density rho\propto r^{-omega} approach a self-similar (SLS) behavior, with velocity \dot{R}\propto R^delta, as R->\infty. For omega>3 the solutions are of the second-type, i.e., delta is determined by the requirement that the flow should include a sonic point. No solution satisfying this requirement exists, however, in the 3\leq omega\leq omega_{g}(gamma) ``gap'' (\omega_{g}=3.26 for adiabatic index gamma=5/3). We argue that second-type solutions should not be required in general to include a sonic point. Rather, it is sufficient to require the existence of a characteristic line r_c(t), such that the energy in the region r_c(t)\infty, and an asymptotic solution given by the SLS solution at r_c(t)<r<R and deviating from it at r<r_c may be constructed. The two requirements coincide for omega>omega_g and the latter identifies delta=0 solutions as the asymptotic solutions for 3\leq omega\leq omega_{g} (as suggested by Gruzinov03). In these solutions, r_c is a C_0 characteristic. It is difficult to check, using numerical solutions of the hydrodynamic equations, whether the flow indeed approaches a delta=0 SLS behavior as R->\infty, due to the slow convergence to SLS for omega~3. We show that in this case the flow may be described by a modified SLS solution, d\ln\dot{R}/d\ln R=delta with slowly varying delta(R), eta\equiv d delta/d\ln R<<1, and spatial profiles given by a sum of the SLS solution corresponding to the instantaneous value of delta and a SLS correction linear in eta. The modified SLS solutions provide an excellent approximation to numerical solutions obtained for omega~3 at large R, with delta->0 (and eta\neq0) for 3\leq omega\leq omega_{g}. (abridged)Comment: 10 pages, 11 figures, somewhat revised, version accepted to Ap

Uniform materials and the multiplicative decomposition of the deformation gradient in finite elasto-plasticity

In this work we analyze the relation between the multiplicative decomposition $\mathbf F=\mathbf F^{e}\mathbf F^{p}$ of the deformation gradient as a product of the elastic and plastic factors and the theory of uniform materials. We prove that postulating such a decomposition is equivalent to having a uniform material model with two configurations - total $\phi$ and the inelastic $\phi_{1}$. We introduce strain tensors characterizing different types of evolutions of the material and discuss the form of the internal energy and that of the dissipative potential. The evolution equations are obtained for the configurations $(\phi,\phi_{1})$ and the material metric $\mathbf g$. Finally the dissipative inequality for the materials of this type is presented.It is shown that the conditions of positivity of the internal dissipation terms related to the processes of plastic and metric evolution provide the anisotropic yield criteria