Dimensionality of Local Minimizers of the Interaction Energy

In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the imensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.Comment: 27 page

Nonlocal interactions by repulsive-attractive potentials: radial ins/stability

In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse each other in the short range and attract each other in the long range. We prove that under some conditions on the potential, radially symmetric solutions converge exponentially fast in some transport distance toward a spherical shell stationary state. Otherwise we prove that it is not possible for a radially symmetric solution to converge weakly toward the spherical shell stationary state. We also investigate under which condition it is possible for a non-radially symmetric solution to converge toward a singular stationary state supported on a general hypersurface. Finally we provide a detailed analysis of the specific case of the repulsive-attractive power law potential as well as numerical results. We point out the the conditions of radial ins/stability are sharp.Comment: 42 pages, 7 figure

Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous activity, the network displays orderly, perfectly synchronized periodic responses at intermediate level of noise. We show that this phenomenon is fundamentally stochastic and collective in nature. Indeed, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited neurons eventually triggering a chain reaction associated with a macroscopic synchronized excursion and a collective return to rest where this process starts afresh, thus yielding the observed periodic synchronized oscillations. We further uncover a novel anti-resonance phenomenon: noise-induced synchronized oscillations disappear when the system is driven by periodic stimulation with frequency within a specific range. In that anti-resonance regime, the system is optimal for measures of information capacity. This observation provides a new hypothesis accounting for the efficiency of Deep Brain Stimulation therapies in Parkinson's disease, a neurodegenerative disease characterized by an increased synchronization of brain motor circuits. We further discuss the universality of these phenomena in the class of stochastic networks of excitable elements with confining coupling, and illustrate this universality by analyzing various classical models of neuronal networks. Altogether, these results uncover some universal mechanisms supporting a regularizing impact of noise in excitable systems, reveal a novel anti-resonance phenomenon in these systems, and propose a new hypothesis for the efficiency of high-frequency stimulation in Parkinson's disease

X-ray microanalysis in STEM of short-term physico-chemical reactions at bioactive glass particles / biological fluids interface. Determination of O/Si atomic ratios

Short-term physico-chemical reactions at the interface between bioactive glass particles and biological fluids are studied and we focus our attention on the measurements of O/Si atomic ratio. The studied bioactive glass is in the SiO2-Na2O-CaO-P2O5-K2O-Al2O3-MgO system. The elemental analysis is performed at the submicrometer scale by STEM associated with EDXS and EELS. We previously developed an EDXS quantification method based on the ratio method and taking into account local absorption corrections. In this way, we use EELS data to determine, by an iterative process, the local mass thickness which is an essential parameter to correct absorption in EDXS spectra. After different delays of immersion of bioactive glass particles in a simulated biological solution, results show the formation of different surface layers at the bioactive glass periphery. Before one day of immersion, we observe the presence of an already shown (Si,O,Al) rich layer at the periphery. In this paper, we demonstrate that a thin electron dense (Si,O) layer is formed on top of the (Si,O,Al) layer. In this (Si,O) layer, depleted in aluminium, we point out an increase of oxygen weight concentration which can be interpreted by the presence of Si(OH)4 groups, that permit the formation of a (Ca,P) layer. Aluminium plays a role in the glass solubility and may inhibit apatite nucleation. After the beginning of the (Ca,P) layer formation, the size of the electron dense (Si,O) layer decreases and tends to disappear. After two days of immersion, the (Ca,P) layer grows in thickness and leads to apatite precipitatio

GRB Observed by IBIS/PICsIT in the MeV Energy Range

We present the preliminary results of a systematic search for GRB and other transients in the publicly available data for the IBIS/PICsIT (0.2-10 MeV) detector on board INTEGRAL. Lightcurves in 2-8 energy bands with time resolution from 1 to 62.5 ms have been collected and an analysis of spectral and temporal characteristics has been performed. This is the nucleus of a forthcoming first catalog of GRB observed by PICsIT.Comment: 6 pages, 3 figures. Poster presented at COSPAR 2008. Advaces in Space Research, accepted for publicatio

The various manifestations of collisionless dissipation in wave propagation

The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet is Landau damped, so that in the reference frame moving at the group velocity, the wave amplitude decays exponentially with time. In the nonlinear regime, once phase mixing has occurred and when the electron motion is nearly adiabatic, the damping rate is strongly reduced compared to the Landau one, so that the wave amplitude remains nearly constant along the characteristics. Yet, we show here that the electrons are still globally accelerated by the wave packet, and, in one dimension, this leads to a non local amplitude dependence of the group velocity. As a result, a freely propagating wave packet would shrink, and, therefore, so would its total energy. In more than one dimension, not only does the magnitude of the group velocity nonlinearly vary, but also its direction. In the weakly nonlinear regime, when the collisionless damping rate is still significant compared to its linear value, this leads to an effective defocussing effect which we quantify, and which we compare to the self-focussing induced by wave front bowing.Comment: 23 pages, 6 figure

Dynamical Encoding by Networks of Competing Neuron Groups: Winnerless Competition

Following studies of olfactory processing in insects and fish, we investigate neural networks whose dynamics in phase space is represented by orbits near the heteroclinic connections between saddle regions (fixed points or limit cycles). These networks encode input information as trajectories along the heteroclinic connections. If there are N neurons in the network, the capacity is approximately e(N-1)!, i.e., much larger than that of most traditional network structures. We show that a small winnerless competition network composed of FitzHugh-Nagumo spiking neurons efficiently transforms input information into a spatiotemporal output

Penetration and cratering experiments of graphite by 0.5-mm diameter steel spheres at various impact velocities

Cratering experiments have been conducted with 0.5-mm diameter AISI 52100 steel spherical projectiles and 30-mm diameter, 15-mm long graphite targets. The latter were made of a commercial grade of polycrystalline and porous graphite named EDM3 whose behavior is known as macroscopically isotropic. A two-stage light-gas gun launched the steel projectiles at velocities between 1.1 and 4.5 km s 1. In most cases, post-mortem tomographies revealed that the projectile was trapped, fragmented or not, inside the target. It showed that the apparent crater size and depth increase with the impact velocity. This is also the case of the crater volume which appears to follow a power law significantly different from those constructed in previous works for similar impact conditions and materials. Meanwhile, the projectile depth of penetration starts to decrease at velocities beyond 2.2 km s 1. This is firstly because of its plastic deformation and then, beyond 3.2 km s 1, because of its fragmentation. In addition to these three regimes of penetration behavior already described by a few authors, we suggest a fourth regime in which the projectile melting plays a significant role at velocities above 4.1 km s 1. A discussion of these four regimes is provided and indicates that each phenomenon may account for the local evolution of the depth of penetration

The L1-Potts functional for robust jump-sparse reconstruction

We investigate the non-smooth and non-convex $L^1$-Potts functional in discrete and continuous time. We show $\Gamma$-convergence of discrete $L^1$-Potts functionals towards their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer. For the discrete $L^1$-Potts problem, we introduce an $O(n^2)$ time and $O(n)$ space algorithm to compute an exact minimizer. We apply $L^1$-Potts minimization to the problem of recovering piecewise constant signals from noisy measurements $f.$ It turns out that the $L^1$-Potts functional has a quite interesting blind deconvolution property. In fact, we show that mildly blurred jump-sparse signals are reconstructed by minimizing the $L^1$-Potts functional. Furthermore, for strongly blurred signals and known blurring operator, we derive an iterative reconstruction algorithm

Universal Properties of Ferroelectric Domains

Basing on Ginzburg-Landau approach we generalize the Kittel theory and derive the interpolation formula for the temperature evolution of a multi-domain polarization profile P(x,z). We resolve the long-standing problem of the near-surface polarization behavior in ferroelectric domains and demonstrate the polarization vanishing instead of usually assumed fractal domain branching. We propose an effective scaling approach to compare the properties of different domain-containing ferroelectric plates and films.Comment: Phys. Rev. Lett. to be publishe