Non-modal stability analysis and transient growth in a magnetized Vlasov plasma

Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is studied. Our results offer a new scenario of the emergence and development of plasma instabilities on the kinetic scale.Comment: 6 pages, 5 figure

Hydrodynamic Model for the System of Self Propelling Particles with Conservative Kinematic Constraints; Two dimensional stationary solutions

We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we prove that the only types of the stationary planar solutions in the model are either of translational or axial symmetry of the flow. Within the proposed model we differentiate between finite and infinite flocking behavior by the finiteness of the kinetic energy functional.Comment: 12 pages, 1 figur

Continuum limit of self-driven particles with orientation interaction

We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator

On the relation between Vicsek and Kuramoto models of spontaneous synchronization

The Vicsek model for the self-propelled particles is investigated with the respect to the introduction of the stochastic perturbation of the dynamics. It is shown that such a dependence can be thought in terms of the isomorphism of the Vicsek model with the Kuramoto model of spontaneous synchronization. They are isomorphic at least within the mean-field approach. The isomorphism between two models allows to state the dependence of the type of the transition in Vicsek model on the noise perturbation. Two types of noise the scalar and the vector ones lead to qualitatively different behavior with continuous and the discontinuous transition to ordered state correspondingly. New type of the stochastic perturbation - ``mixed`` noise is proposed. It is the weighted superposition of the scalar and vector noises. The corresponding phase diagram ``noise amplitude vs. interaction strength`` is obtained and the tricritical behavior for Vicsek model is demonstrated.Comment: 11 pages, 5 figure

Stability properties of the collective stationary motion of self-propelling particles with conservative kinematic constraints

In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this hydrodynamic model and have shown that two types of stationary flow, linear and radially symmetric (vortical) flow, are possible. In this paper we consider the stability properties of these stationary flows. We show, using a linear stability analysis, that the linear solutions are neutrally stable with respect to the imposed velocity and density perturbations. A similar analysis of the stability of the vortical solution is found to be not conclusive.Comment: 13 pages, 3 figure

Macroscopic limits and phase transition in a system of self-propelled particles

We investigate systems of self-propelled particles with alignment interaction. Compared to previous work, the force acting on the particles is not normalized and this modification gives rise to phase transitions from disordered states at low density to aligned states at high densities. This model is the space inhomogeneous extension of a previous work by Frouvelle and Liu in which the existence and stability of the equilibrium states were investigated. When the density is lower than a threshold value, the dynamics is described by a non-linear diffusion equation. By contrast, when the density is larger than this threshold value, the dynamics is described by a hydrodynamic model for self-alignment interactions previously derived in Degond and Motsch. However, the modified normalization of the force gives rise to different convection speeds and the resulting model may lose its hyperbolicity in some regions of the state space

CLINICAL EXAMPLE OF THE USE OF LIPOFILLING WITH DELAYED RECONSTRUCTION

Malignant breast tumors are one of the causes of disability due to lack of breast or having operational defects. In most cases, the quality of the operation depends on the further social and active patient behavior.This article presents a clinical case of the use of lipofilling with reconstructive plastic surgery in breast cancer patients after complex treatment. In the particular example we show the positive effects after one session of conducted lipofiling in front of the chest wall to the right with Body-Jet hardware techniques. The purpose of this procedure was to improve the quality of cover fabrics in postoperative scar on the anterior chest wall right after comprehensive treatment, including also a cover for the such aggressive tissue treatment, as radiotherapy.It is proved that mesenchymal stromal cells, or cell-messengers that are present in all the fatty tissues, contribute to its regeneration by forming new blood vessels, or act directly on the damaged or exposed to aging structure — restore and rejuvenate the field of lipofilling. Therefore, adipose tissue is laid down by the nature of the human body a source of regeneration. In this clinical example, after successfully conducted one session of lipofilling marked improvement in skin quality in postoperative scar made after mastectomy and radiotherapy. Good autofat graft survival rate is also fixed, which was enough to implement further stages of breast reconstruction

Positive and negative streamers in ambient air: modeling evolution and velocities

We simulate short positive and negative streamers in air at standard temperature and pressure. They evolve in homogeneous electric fields or emerge from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at given streamer length depends only weakly on the initial ionization seed, except in the case of negative streamers in homogeneous fields. We characterize the streamers by length, head radius, head charge and field enhancement. We show that the velocity of positive streamers is mainly determined by their radius and in quantitative agreement with recent experimental results both for radius and velocity. The velocity of negative streamers is dominated by electron drift in the enhanced field; in the low local fields of the present simulations, it is little influenced by photo-ionization. Though negative streamer fronts always move at least with the electron drift velocity in the local field, this drift motion broadens the streamer head, decreases the field enhancement and ultimately leads to slower propagation or even extinction of the negative streamer.Comment: 18 pages, 10 figure

Probing background ionization: Positive streamers with varying pulse repetition rate and with a radioactive admixture

Positive streamers need a source of free electrons ahead of them to propagate. A streamer can supply these electrons by itself through photo-ionization, or the electrons can be present due to external background ionization. Here we investigate the effects of background ionization on streamer propagation and morphology by changing the gas composition and the repetition rate of the voltage pulses, and by adding a small amount of radioactive Krypton 85. We find that the general morphology of a positive streamer discharge in high purity nitrogen depends on background ionization: at lower background ionization levels the streamers branch more and have a more feather-like appearance. This is observed both when varying the repetition rate and when adding Krypton 85, though side branches are longer with the radioactive admixture. But velocities and minimal diameters of streamers are virtually independent of the background ionization level. In air, the inception cloud breaks up into streamers at a smaller radius when the repetition rate and therefore the background ionization level is higher. When measuring the effects of the pulse repetition rate and of the radioactive admixture on the discharge morphology, we found that our estimates of background ionization levels are consistent with these observations; this gives confidence in the estimates. Streamer channels generally do not follow the paths of previous discharge channels for repetition rates of up to 10 Hz. We estimate the effect of recombination and diffusion of ions and free electrons from the previous discharge and conclude that the old trail has largely disappeared at the moment of the next voltage pulse; therefore the next streamers indeed cannot follow the old trail.Comment: 30 pages, 13 figure