Global exponential convergence to variational traveling waves in cylinders

We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated with scalar reaction-diffusion equations in infinite cylinders is the long-time attractor for the solutions of the initial value problems with front-like initial data. The convergence to this traveling wave is exponentially fast. The obtained result is mainly a consequence of the gradient flow structure of the considered equation in the exponentially weighted spaces and does not depend on the precise details of the problem. It strengthens our earlier generic propagation and selection result for "pushed" fronts.Comment: 23 page

Analysis of enhanced diffusion in Taylor dispersion via a model problem

We consider a simple model of the evolution of the concentration of a tracer, subject to a background shear flow by a fluid with viscosity $\nu \ll 1$ in an infinite channel. Taylor observed in the 1950's that, in such a setting, the tracer diffuses at a rate proportional to $1/\nu$, rather than the expected rate proportional to $\nu$. We provide a mathematical explanation for this enhanced diffusion using a combination of Fourier analysis and center manifold theory. More precisely, we show that, while the high modes of the concentration decay exponentially, the low modes decay algebraically, but at an enhanced rate. Moreover, the behavior of the low modes is governed by finite-dimensional dynamics on an appropriate center manifold, which corresponds exactly to diffusion by a fluid with viscosity proportional to $1/\nu$

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A

Orbital stability of periodic waves for the nonlinear Schroedinger equation

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.Comment: 34 pages, 7 figure

Interaction of vortices in viscous planar flows

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter \nu, and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex system is well-posed on the interval [0,T]. Under these assumptions, we prove that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a superposition of Lamb-Oseen vortices whose centers evolve according to a viscous regularization of the point vortex system. Convergence holds uniformly in time, in a strong topology which allows to give an accurate description of the asymptotic profile of each individual vortex. In particular, we compute to leading order the deformations of the vortices due to mutual interactions. This allows to estimate the self-interactions, which play an important role in the convergence proof.Comment: 39 pages, 1 figur

Development and Evaluation of an Enzyme-Linked Immunosorbent Assay for Dengue Capsid

The astonishing speed with which Dengue has spread across the world and the severity of its infection make Dengue a prime threat to human life worldwide. Unfortunately, to date there are no effective vaccines or treatments against Dengue. Since only a few assays permit rapid and sensitive detection of Dengue, we developed a specific antigen capture enzyme-linked immunosorbent assay (ELISA) for the abundant structural Dengue-2 capsid protein. We showed that the ELISA allows rapid and sensitive detection of Dengue-2 replication in various cell lines including human and mosquito cells. Using anti-capsid antibodies, we demonstrated that the capsid ELISA is as accurate as other well-characterized Dengue assays such as intracellular FACS staining (IFSA) and fluorescent focus (FFA) assays. The capsid ELISA not only represents a useful tool for in vitro basic research, but it may also represent a valuable diagnostic tool for Dengue infection in patients

Coherent vortex structures and 3D enstrophy cascade

Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physical scales. The goal of this paper is to show that the same geometric condition preventing the formation of singularities - 1/2-H\"older coherence of the vorticity direction - coupled with a suitable condition on a modified Kraichnan scale, and under a certain modulation assumption on evolution of the vorticity, leads to existence of 3D enstrophy cascade in physical scales of the flow.Comment: 15 pp; final version -- to appear in CM

SosA inhibits cell division in Staphylococcus aureus in response to DNA damage.

Inhibition of cell division is critical for viability under DNA-damaging conditions. DNA damage induces the SOS response that in bacteria inhibits cell division while repairs are being made. In coccoids, such as the human pathogen, Staphylococcus aureus, this process remains poorly studied. Here, we identify SosA as the staphylococcal SOS-induced cell division inhibitor. Overproduction of SosA inhibits cell division, while sosA inactivation sensitizes cells to genotoxic stress. SosA is a small, predicted membrane protein with an extracellular C-terminal domain in which point mutation of residues that are conserved in staphylococci and major truncations abolished the inhibitory activity. In contrast, a minor truncation led to SosA accumulation and a strong cell division inhibitory activity, phenotypically similar to expression of wild-type SosA in a CtpA membrane protease mutant. This suggests that the extracellular C-terminus of SosA is required both for cell division inhibition and for turnover of the protein. Microscopy analysis revealed that SosA halts cell division and synchronizes the cell population at a point where division proteins such as FtsZ and EzrA are localized at midcell, and the septum formation is initiated but unable to progress to closure. Thus, our findings show that SosA is central in cell division regulation in staphylococci