Ionization fronts in negative corona discharges

In this paper we use a hydrodynamic minimal streamer model to study negative corona discharge. By reformulating the model in terms of a quantity called shielding factor, we deduce laws for the evolution in time of both the radius and the intensity of ionization fronts. We also compute the evolution of the front thickness under the conditions for which it diffuses due to the geometry of the problem and show its self-similar character.Comment: 4 pages, 4 figure

Streamer Propagation as a Pattern Formation Problem: Planar Fronts

Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma. New understanding of this old phenomenon can be gained through modern concepts of (interfacial) pattern formation. As a first step towards an effective interface description, we determine the front width, solve the selection problem for planar fronts and calculate their properties. Our results are in good agreement with many features of recent three-dimensional numerical simulations.Comment: 4 pages, revtex, 3 ps file

Hydrodynamic bidimensional stability of detonation wave solutions for reactive mixtures

The structure of a planar detonation wave is analyzed for an Eulerian mixture of ideal gases undergoing the symmetric reversible explosive reaction A1 + A1 = A2 + A2. The chemical rate law is derived from the reactive Boltzmann equation, showing a detailed chemical kinetics in terms of a second-order reaction rate. The hydrodynamic bidimensional stability of the detonation wave is also investigated using a normal mode approach, when small time-space transverse disturbances affect the shock wave location. A suitable numerical technique is here proposed in order to solve the stability problem and numerical results are provided illustrating the detonation wave structure and its instability spectrum.The paper is partially supported by Brazilian Research Council (CNPq), by Italian Research Council GNFM-INdAM, and by Portuguese Funds of FCT, CMAT project UID/MAT/00013/2013

Nonlinear anomalous diffusion equation and fractal dimension: Exact generalized gaussian solution

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the $N$-dimensional nonlinear diffusion equation $\partial\rho /\partial{t}={\bf \nabla} \cdot (K{\bf \nabla} \rho^{\nu})-{\bf \nabla}\cdot(\mu{\bf F} \rho)-\alpha \rho ,$ where $K=D r^{-\theta}$, $\nu$, $\theta$, $\mu$ and $D$ are real parameters and $\alpha$ is a time-dependent source. This equation unifies the O'Shaugnessy-Procaccia anomalous diffusion equation on fractals ($\nu =1$) and the spherical anomalous diffusion for porous media ($\theta=0$). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.Comment: Latex, 6 pages. To appear in Phys. Rev.

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects

Intervention effects of Ganoderma lucidum spores on epileptiform discharge hippocampal neurons and expression of Neurotrophin-4 and N-Cadherin

Epilepsy can cause cerebral transient dysfunctions. Ganoderma lucidum spores (GLS), a traditional Chinese medicinal herb, has shown some antiepileptic effects in our previous studies. This was the first study of the effects of GLS on cultured primary hippocampal neurons, treated with Mg2+ free medium. This in vitro model of epileptiform discharge hippocampal neurons allowed us to investigate the anti-epileptic effects and mechanism of GLS activity. Primary hippocampal neurons from <1 day old rats were cultured and their morphologies observed under fluorescence microscope. Neurons were confirmed by immunofluorescent staining of neuron specific enolase (NSE). Sterile method for GLS generation was investigated and serial dilutions of GLS were used to test the maximum non-toxic concentration of GLS on hippocampal neurons. The optimized concentration of GLS of 0.122 mg/ml was identified and used for subsequent analysis. Using the in vitro model, hippocampal neurons were divided into 4 groups for subsequent treatment i) control, ii) model (incubated with Mg2+ free medium for 3 hours), iii) GLS group I (incubated with Mg2+ free medium containing GLS for 3 hours and replaced with normal medium and incubated for 6 hours) and iv) GLS group II (neurons incubated with Mg2+ free medium for 3 hours then replaced with a normal medium containing GLS for 6 hours). Neurotrophin-4 and N-Cadherin protein expression were detected using Western blot. The results showed that the number of normal hippocampal neurons increased and the morphologies of hippocampal neurons were well preserved after GLS treatment. Furthermore, the expression of neurotrophin-4 was significantly increased while the expression of N-Cadherin was decreased in the GLS treated group compared with the model group. This data indicates that GLS may protect hippocampal neurons by promoting neurotrophin-4 expression and inhibiting N-Cadherin expression

Anticipating and managing future trade-offs and complementarities between ecosystem services

Peer reviewedPostprin

Control of Rayleigh-Taylor instability by vertical vibration in large aspect ratio containers

We consider a horizontal heavy fluid layer supported by a light, immiscible one in a wide (as compared to depth) container, which is vertically vibrated intending to counterbalance the Rayleigh-Taylor instability of the flat, rigid-body vibrating state. In the simplest case when the density and viscosity of the lighter fluid are small compared to their counterparts in the heavier fluid, we apply a long wave, weakly nonlinear analysis that yields a generalized Cahn-Hilliard equation for the evolution of the fluid interface. This equation shows that the stabilizing effect of vibration is like that of surface tension, and is used to analyze the linear stability of the flat state, the local bifurcation at the instability threshold and some global existence and stability properties concerning the steady states without dry spots. The analysis is extended to two cases of practical interest. Namely, (a) the viscosity of one of the fluids is much smaller than that of the other one, and (b) the densities and viscosities of both fluids are quite close to each other