393,231 research outputs found
The Gentlest Ascent Dynamics
Dynamical systems that describe the escape from the basins of attraction of
stable invariant sets are presented and analyzed. It is shown that the stable
fixed points of such dynamical systems are the index-1 saddle points.
Generalizations to high index saddle points are discussed. Both gradient and
non-gradient systems are considered. Preliminary results on the nature of the
dynamical behavior are presented
Social and Political Dimensions of Identity
We study the interior regularity of solutions to the Dirichlet problem Lu = g in Omega, u = 0 in R-nOmega, for anisotropic operators of fractional type Lu(x) = integral(+infinity)(0) dp integral(Sn-1) da(w) 2u(x) - u(x + rho w) - u(x - rho w)/rho(1+2s). Here, a is any measure on Sn-1 (a prototype example for L is given by the sum of one-dimensional fractional Laplacians in fixed, given directions). When a is an element of C-infinity(Sn-1) and g is c(infinity)(Omega), solutions are known to be C-infinity inside Omega (but not up to the boundary). However, when a is a general measure, or even when a is L-infinity(s(n-1)), solutions are only known to be C-3s inside Omega. We prove here that, for general measures a, solutions are C1+3s-epsilon inside Omega for all epsilon > 0 whenever Omega is convex. When a is an element of L-infinity(Sn-1), we show that the same holds in all C-1,C-1 domains. In particular, solutions always possess a classical first derivative. The assumptions on the domain are sharp, since if the domain is not convex and the measure a is singular, we construct an explicit counterexample for which u is not C3s+epsilon for any epsilon > 0 - even if g and Omega are C-infinity
Radiative Bulk Viscosity
Viscous resistance to changes in the volume of a gas arises when different
degrees of freedom have different relaxation times. Collisions tend to oppose
the resulting departures from equilibrium and, in so doing, generate entropy.
Even for a classical gas of hard spheres, when the mean free paths or mean
flight times of constituent particles are long, we find a nonvanishing bulk
viscosity. Here we apply a method recently used to uncover this result for a
classical rarefied gas to radiative transfer theory and derive an expression
for the radiative stress tensor for a gray medium with absorption and Thomson
scattering. We determine the transport coefficients through the calculation of
the comoving entropy generation. When scattering dominates absorption, the bulk
viscosity becomes much larger than either the shear viscosity or the thermal
conductivity.Comment: 17 pages. Latex with referee style file of MNRAS (mn.sty). MNRAS, in
pres
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