GASLESS COMBUSTION FRONTS WITH HEAT LOSS

For a model of gasless combustion with heat loss, we use geometric s ingular perturbation theory to show existence of traveling combustion fr onts. We show that the fronts are nonlinearly stable in an appropriate sense if an Evans fun ction criterion, which can be verified numerically, is satisfied. For a solid reactant and exot hermicity parameter that is not too large, we verify numerically that the criterion is satisfi ed

Critical velocity of a mobile impurity in one-dimensional quantum liquids

We study the notion of superfluid critical velocity in one spatial dimension. It is shown that for heavy impurities with mass $M$ exceeding a critical mass $M_\mathrm{c}$, the dispersion develops periodic metastable branches resulting in dramatic changes of dynamics in the presence of an external driving force. In contrast to smooth Bloch Oscillations for $M<M_\mathrm{c}$, a heavy impurity climbs metastable branches until it reaches a branch termination point or undergoes a random tunneling event, both leading to an abrupt change in velocity and an energy loss. This is predicted to lead to a non-analytic dependence of the impurity drift velocity on small forces.Comment: 5 pages, 2 figures; New version with Supplemental Material (3 pages, 6 figures); Accepted to PR

Inviscid dynamical structures near Couette flow

Consider inviscid fluids in a channel {-1<y<1}. For the Couette flow v_0=(y,0), the vertical velocity of solutions to the linearized Euler equation at v_0 decays in time. At the nonlinear level, such inviscid damping has not been proved. First, we show that in any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow, there exist non-parallel steady flows with arbitrary minimal horizontal period. This implies that nonlinear inviscid damping is not true in any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow and for any horizontal period. Indeed, the long time behavior in such neighborhoods are very rich, including nontrivial steady flows, stable and unstable manifolds of nearby unstable shears. Second, in the (vorticity) H^{s}(s>(3/2)) neighborhood of Couette, we show that there exist no non-parallel steadily travelling flows v(x-ct,y), and no unstable shears. This suggests that the long time dynamics in H^{s}(s>(3/2)) neighborhoods of Couette might be much simpler. Such contrasting dynamics in H^{s} spaces with the critical power s=(3/2) is a truly nonlinear phenomena, since the linear inviscid damping near Couette is true for any initial vorticity in L^2

Numerical Simulation of Vortex Crystals and Merging in N-Point Vortex Systems with Circular Boundary

In two-dimensional (2D) inviscid incompressible flow, low background vorticity distribution accelerates intense vortices (clumps) to merge each other and to array in the symmetric pattern which is called ``vortex crystals''; they are observed in the experiments on pure electron plasma and the simulations of Euler fluid. Vortex merger is thought to be a result of negative ``temperature'' introduced by L. Onsager. Slight difference in the initial distribution from this leads to ``vortex crystals''. We study these phenomena by examining N-point vortex systems governed by the Hamilton equations of motion. First, we study a three-point vortex system without background distribution. It is known that a N-point vortex system with boundary exhibits chaotic behavior for N\geq 3. In order to investigate the properties of the phase space structure of this three-point vortex system with circular boundary, we examine the Poincar\'e plot of this system. Then we show that topology of the Poincar\'e plot of this system drastically changes when the parameters, which are concerned with the sign of ``temperature'', are varied. Next, we introduce a formula for energy spectrum of a N-point vortex system with circular boundary. Further, carrying out numerical computation, we reproduce a vortex crystal and a vortex merger in a few hundred point vortices system. We confirm that the energy of vortices is transferred from the clumps to the background in the course of vortex crystallization. In the vortex merging process, we numerically calculate the energy spectrum introduced above and confirm that it behaves as k^{-\alpha},(\alpha\approx 2.2-2.8) at the region 10^0<k<10^1 after the merging.Comment: 30 pages, 11 figures. to be published in Journal of Physical Society of Japan Vol.74 No.