Instabilities in Zakharov Equations for Laser Propagation in a Plasma

F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard's type, implying that the Cauchy problem is strongly ill-posed

Nonlinear effects in charge stabilized colloidal suspensions

Molecular Dynamics simulations are used to study the effective interactions in charged stabilized colloidal suspensions. For not too high macroion charges and sufficiently large screening, the concept of the potential of mean force is known to work well. In the present work, we focus on highly charged macroions in the limit of low salt concentrations. Within this regime, nonlinear corrections to the celebrated DLVO theory [B. Derjaguin and L. Landau, Acta Physicochem. USSR {\bf 14}, 633 (1941); E.J.W. Verwey and J.T.G. Overbeck, {\em Theory of the Stability of Lyotropic Colloids} (Elsevier, Amsterdam, 1948)] have to be considered. For non--bulklike systems, such as isolated pairs or triples of macroions, we show, that nonlinear effects can become relevant, which cannot be described by the charge renormalization concept [S. Alexander et al., J. Chem. Phys. {\bf 80}, 5776 (1984)]. For an isolated pair of macroions, we find an almost perfect qualitative agreement between our simulation data and the primitive model. However, on a quantitative level, neither Debye-H\"uckel theory nor the charge renormalization concept can be confirmed in detail. This seems mainly to be related to the fact, that for small ion concentrations, microionic layers can strongly overlap, whereas, simultaneously, excluded volume effects are less important. In the case of isolated triples, where we compare between coaxial and triangular geometries, we find attractive corrections to pairwise additivity in the limit of small macroion separations and salt concentrations. These triplet interactions arise if all three microionic layers around the macroions exhibit a significant overlap. In contrast to the case of two isolated colloids, the charge distribution around a macroion in a triple is found to be anisotropic.Comment: 10 pages, 9 figure

Dynamic regimes of hydrodynamically coupled self-propelling particles

We analyze the collective dynamics of self-propelling particles (spps) which move at small Reynolds numbers including the hydrodynamic coupling to the suspending solvent through numerical simulations. The velocity distribution functions show marked deviations from Gaussian behavior at short times, and the mean-square displacement at long times shows a transition from diffusive to ballistic motion for appropriate driving mechanism at low concentrations. We discuss the structures the spps form at long times and how they correlate to their dynamic behavior.Comment: 7 pages, 4 figure

Mobility and Diffusion of a Tagged Particle in a Driven Colloidal Suspension

We study numerically the influence of density and strain rate on the diffusion and mobility of a single tagged particle in a sheared colloidal suspension. We determine independently the time-dependent velocity autocorrelation functions and, through a novel method, the response functions with respect to a small force. While both the diffusion coefficient and the mobility depend on the strain rate the latter exhibits a rather weak dependency. Somewhat surprisingly, we find that the initial decay of response and correlation functions coincide, allowing for an interpretation in terms of an 'effective temperature'. Such a phenomenological effective temperature recovers the Einstein relation in nonequilibrium. We show that our data is well described by two expansions to lowest order in the strain rate.Comment: submitted to EP

Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming

We have formulated the problem of generating periodic dense paritcle packings as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in $d$-dimensional Euclidean space $\mathbb{R}^d$, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential linear programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in $\mathbb{R}^d$ for $d=2,3,4,5$ and $6$ with a diversity of disorder and densities up to the maximally densities. This deterministic algorithm can produce a broad range of inherent structures besides the usual disordered ones with very small computational cost by tuning the radius of the {\it influence sphere}. In three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range $[0.6, 0.7408...]$. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for $d=2,3, 4,5$ and 6. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust and computationally faster at generating maximally dense packings, especially as the space dimension increases.Comment: 34 pages, 6 figure

Enhanced dispersion interaction in confined geometry

The dispersion interaction between two point-like particles confined in a dielectric slab between two plates of another dielectric medium is studied within a continuum (Lifshitz) theory. The retarded (Casimir-Polder) interaction at large inter-particle distances is found to be strongly enhanced as the mismatch between the dielectric permittivities of the two media is increased. The large-distance interaction is multiplied due to confinement by a factor of $(33\gamma^{5/2}+13\gamma^{-3/2})/46$ at zero temperature, and by $(5\gamma^2+\gamma^{-2})/6$ at finite temperature, \gamma=\ein(0)/\eout(0) being the ratio between the static dielectric permittivities of the inner and outer media. This confinement-induced amplification of the dispersion interaction can reach several orders of magnitude.Comment: 4 page

Coulombian Disorder in Periodic Systems

We study the effect of unscreened charged impurities on periodic systems. We show that the long wavelength component of the disorder becomes long ranged and dominates static correlation functions. On the other hand, because of the statistical tilt symmetry, dynamical properties such as pinning remain unaffected. As a concrete example, we focus on the effect of Coulombian disorder generated by charged impurities, on 3D charge density waves with non local elasticity. We calculate the x-ray intensity and find that it is identical to the one produced by thermal fluctuations in a disorder-free smectic-A. We discuss the consequences of these results for experiments.Comment: 11 pages, 3 figures, revtex

Optimal time decay of the non cut-off Boltzmann equation in the whole space

In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space \threed_x with \DgE. We use the existence theory of global in time nearby Maxwellian solutions from \cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to determine the large time decay rates for the soft potential Boltzmann equation in the whole space, with or without the angular cut-off assumption \cite{MR677262,MR2847536}. For perturbative initial data, we prove that solutions converge to the global Maxwellian with the optimal large-time decay rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the L^2_\vel(L^r_x)-norm for any $2\leq r\leq \infty$.Comment: 31 pages, final version to appear in KR

The Challenge of Wide-Field Transit Surveys: The Case of GSC 01944-02289

Wide-field searches for transiting extra-solar giant planets face the difficult challenge of separating true transit events from the numerous false positives caused by isolated or blended eclipsing binary systems. We describe here the investigation of GSC 01944-02289, a very promising candidate for a transiting brown dwarf detected by the Transatlantic Exoplanet Survey (TrES) network. The photometry and radial velocity observations suggested that the candidate was an object of substellar mass in orbit around an F star. However, careful analysis of the spectral line shapes revealed a pattern of variations consistent with the presence of another star whose motion produced the asymmetries observed in the spectral lines of the brightest star. Detailed simulations of blend models composed of an eclipsing binary plus a third star diluting the eclipses were compared with the observed light curve and used to derive the properties of the three components. Our photometric and spectroscopic observations are fully consistent with a blend model of a hierarchical triple system composed of an eclipsing binary with G0V and M3V components in orbit around a slightly evolved F5 dwarf. We believe that this investigation will be helpful to other groups pursuing wide-field transit searches as this type of false detection could be more common than true transiting planets, and difficult to identify.Comment: To appear in ApJ, v. 621, 2005 March 1