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

Asymptotic self-similar solutions with a characteristic time-scale

For a wide variety of initial and boundary conditions, adiabatic one dimensional flows of an ideal gas approach self-similar behavior when the characteristic length scale over which the flow takes place, $R$, diverges or tends to zero. It is commonly assumed that self-similarity is approached since in the $R\to\infty(0)$ limit the flow becomes independent of any characteristic length or time scales. In this case the flow fields $f(r,t)$ must be of the form $f(r,t)=t^{\alpha_f}F(r/R)$ with $R\propto(\pm t)^\alpha$. We show that requiring the asymptotic flow to be independent only of characteristic length scales imply a more general form of self-similar solutions, $f(r,t)=R^{\delta_f}F(r/R)$ with $\dot{R}\propto R^\delta$, which includes the exponential ($\delta=1$) solutions, $R\propto e^{t/\tau}$. We demonstrate that the latter, less restrictive, requirement is the physically relevant one by showing that the asymptotic behavior of accelerating blast-waves, driven by the release of energy at the center of a cold gas sphere of initial density $\rho\propto r^{-\omega}$, changes its character at large $\omega$: The flow is described by $0\le\delta<1$, $R\propto t^{1/(1-\delta)}$, solutions for $\omega1$ solutions with $R\propto (-t)^{1/(\delta-1)}$ diverging at finite time ($t=0$) for $\omega>\omega_c$, and by exponential solutions for $\omega=\omega_c$ ($\omega_c$ depends on the adiabatic index of the gas, $\omega_c\sim8$ for $4/3<\gamma<5/3$). The properties of the new solutions obtained here for $\omega\ge\omega_c$ are analyzed, and self-similar solutions describing the $t>0$ behavior for $\omega>\omega_c$ are also derived.Comment: Minor corrections, Accepted to Ap

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

Stability of an Ultra-Relativistic Blast Wave in an External Medium with a Steep Power-Law Density Profile

We examine the stability of self-similar solutions for an accelerating relativistic blast wave which is generated by a point explosion in an external medium with a steep radial density profile of a power-law index > 4.134. These accelerating solutions apply, for example, to the breakout of a gamma-ray burst outflow from the boundary of a massive star, as assumed in the popular collapsar model. We show that short wavelength perturbations may grow but only by a modest factor <~ 10.Comment: 12 pages, 3 figures, submitted to Physical Review

Bosonic String in Affine-Metric Curved Space

The sigma model approach to the closed bosonic string on the affine-metric manifold is considered. The two-loop metric counterterms for the nonlinear two-dimensional sigma model with affine-metric target manifold are calculated. The correlation of the metric and affine connection is considered as the result of the ultraviolet finiteness (or beta-function vanishing) condition for the nonlinear sigma model. The examples of the nonflat nonRiemannian manifolds resulting in the trivial metric beta-function are suggested.Comment: 15 pages, LaTe