Narrow Results

We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high particle number systems give more clear and comprehensive physical descriptions of those systems than purely kinetic approaches, and can be more easily tested experimentally as well as numerically. Also they make it easier to follow perturbations from linear to nonlinear regimes. In particular, we aim at developing a theory that describes both a background nonequilibrium fluid configurations and its perturbations, to be able to account for the backreaction of the latter on the former. Our system of equations includes the usual conservation laws for the energy–momentum tensor and for the electric current, and the equations for two new tensors that encode the information about dissipation. To make contact with kinetic theory, we write the different tensors as the moments of a nonequilibrium one-particle distribution function (1pdf) which, for illustrative purposes, we take in the form of a Grad-like ansatz. Although this choice limits the applicability of the formalism to states not far from equilibrium, it retains the main features of the underlying kinetic theory. We assume the validity of the Vlasov–Boltzmann equation, with a collision integral given by the Anderson–Witting prescription, which is more suitable for highly relativistic systems than Marle’s (or Bhatnagar, Gross and Krook) form, and derive the conservation laws by taking its corresponding moments. We apply our developments to study the emergence of instabilities in an anisotropic, but axially symmetric background. For small departures of isotropy we find the dispersion relation for normal modes, which admit unstable solutions for a wide range of values of the parameter space.

We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions. We show that the nature of the bifurcation, which can be either supercritical or subcritical or even take the form of isola (or detached lobes) strongly depends on the parameters. This dependence is described in a range of parameters numerically accessible (which unfortunately remains remote from geophysical application), and we show how the magnetic Prandtl number and the Ekman number control these transitions.

This paper is devoted to studying of dispersion of waves in the magnetized plasma with the spin and exploring of new methods of the generation wave in the plasma. We consider the dispersion of waves, existed in the plasma in consequence of dynamic of the magnetic moments. It is shown there are nine new waves in the magnetized plasma because of the magnetic moments dynamic. We show there are instabilities at propagation of the neutron beam through the plasma. Increments of instabilities caused by neutron beam are calculated. For studying of this effects we generalize and use the method of the many-particle quantum hydrodynamics. Described processes can play important role at calculation of the stability and the safeness of the nuclear reactors and the studying of the processes in the atmosphere of the neutron stars.

Throughout this paper I will argue that dynamical and structural instabilities are the sources of complexity and pattern formation. The argument can be accomplished by defending two theses. First, a demarcation thesis: two different approaches are predominant in mathematical sciences today — the symmetry-approach and the complexity-approach. Second, a synthesis thesis: although the two approaches differ, they can be connected and, further, to some degree integrated: instabilities are core concepts connecting the two approaches. However, in a specific sense we can say: evolution leads from symmetry to complexity by transitions across borders of instabilities. This paper will provide further arguments in favor of a structural unity in phenomenological diversity [Mainzer, 2005].

A generic stationary instability that arises in quasi-reversible systems is studied. It is characterized by the confluence of three eigenvalues at the origin of complex plane with only one eigenfunction. We characterize the dynamics through the normal form that exhibits in particular, Shilnikov chaos, for which we give an analytical prediction. We construct a simple mechanical system, Shilnikov particle, which exhibits this quasi-reversal instability and displays its chaotic behavior.

In the present paper, we provide results and discussions concerning the processes that lead to local and global chaotic diffusion in the phase space of multidimensional conservative systems. We investigate and provide a measure of the extent of the domain over which diffusion may occur. All these issues are thoroughly discussed by dealing with a multidimensional conservative map that would be representative of the dynamics of a resonance interaction, which is an important mechanism in many dynamical systems.

Quark matter is expected to exist in the interior of compact stellar objects as neutron stars or even the more exotic strange stars, based on the Bodmer–Witten conjecture. Bare strange quark stars and (normal) strange quark-matter stars, those possessing a baryon (electron-supported) crust, are hypothesized as good candidates to explain the properties of a set of peculiar stellar sources such as the enigmatic X-ray source RX J1856.5-3754, some pulsars such as PSR B1828-11 and PSR B1642-03, and the anomalous X-ray pulsars and soft γ-ray repeaters. In the MIT bag model, quarks are treated as a degenerate Fermi gas confined to a region of space having a vacuum energy density B_bag (the Bag constant). In this note, we modify the MIT bag model by including the electromagnetic interaction. We also show that this version of the MIT model implies the anisotropy of the bag pressure due to the presence of the magnetic field. The equations of state of the degenerate quarks gases are studied in the presence of ultra strong magnetic fields. The behavior of a system made up of quarks having (or not) anomalous magnetic moment is reviewed. A structural instability is found, which is related to the anisotropic nature of the pressures in this highly magnetized matter. The conditions for the collapse of this system are obtained and compared to a previous model of neutron stars that is built on a neutron gas having anomalous magnetic moment.

Quark matter is expected to exist in the interior of compact stellar objects as neutron stars or even the more exotic strange stars. In a previous paper [Int. J. Mod. Phys. D14(11) (2005) 1959], the equations of state for a degenerate quark gas were studied in the presence of ultra strong magnetic fields, starting from the modified MIT Bag Model which included the electromagnetic interaction. In the present paper, we revise the behavior of a system made up of quarks with anomalous magnetic moment (AMM) and we discuss its effect in terms of the magnetization and susceptibility. It can be understood as a phase transition or as a criterion of the limited value for the magnetic field in quark stars.

Several general arguments indicate that the event horizon behaves as a stretched membrane. We propose using this relation to understand the gravity and dynamics of black objects in higher dimensions. We provide evidence that:

(i) The gravitational Gregory–Laflamme instability has a classical counterpart in the Rayleigh–Plateau instability of fluids. Each known feature of the gravitational instability can be accounted for in the fluid model. These features include threshold mode, dispersion relation, time evolution and critical dimension of certain phase transitions. Thus, we argue that black strings break in much the same way as water from a faucet breaks up into small droplets.

(ii) General rotating black holes can also be understood with this analogy. In particular, instability and bifurcation diagrams for black objects can easily be inferred.

This correspondence can and should be used as a guiding tool for understanding and exploring the physics of gravity in higher dimensions.

Photon breeding in relativistic jets involves multiplication of high-energy photons propagating from the jet into the external environment and back, with the conversion into electron-positron pairs. The exponential growth of the energy density of these photons is a supercritical process powered by the bulk energy of the jet. The efficient deceleration of the jet outer layers creates a structured jet morphology with a fast spine and slow sheath. In initially fast and high-power jets even the spine can be decelerated efficiently leading to very high radiative efficiencies of conversion of the jet bulk energy into radiation. The decelerating, structured jets have angular distribution of radiation significantly broader than that predicted by a simple blob model with a constant Lorentz factor. This reconciles the discrepancy between the high Doppler factors determined by the fits to the spectra of TeV blazars and the low apparent velocities observed at VLBI scales as well as the low jet Lorentz factors required by the observed statistics and luminosity ratio of Fanaroff-Riley I radio galaxies and BL Lac objects. Photon breeding produces a population of high-energy leptons in agreement with the constraints on the electron injection function required by spectral fits of the TeV blazars. Relativistic pairs created outside the jet and emitting gamma-rays by the inverse Compton process might explain the relatively high level of TeV emission from the misaligned jet in the radio galaxies. The mechanism reproduces basic spectral features observed in blazars including the blazar sequence (shift of the spectral peaks towards lower energies with increasing luminosity). The mechanism is very robust and can operate in various environments characterized by the high photon density.

We discuss the propagation of the hypothetical "combustion" n → SQM in a dense stellar environment. We address the instabilities affecting the flame and a present new results of application to the turbulent regime. The acceleration of the flame, the possible transition to the distributed regime and a further deflagration-to-detonation mechanism are addressed. As a general result, we conclude that the burning happens in (at least) either the turbulent Rayleigh–Taylor or the distributed regime, but not in the laminar regime. In both cases the velocity of the conversion of the star is several orders of magnitude larger than u_lam, making the latter irrelevant in practice for this problem. A transition to a detonation is by no means excluded; actually, it seems to be favored by the physical setting, but a definitive answer would need a full numerical simulation.

Within the framework of magnetohydrodynamics, the Hall effect might become significant either in fully ionized low density plasmas or in cold plasmas with a low ionization fraction. We address the role of the Hall current in the development of the magnetorotational instability. The instability criterion and the instability growth rate are derived from a one-dimensional model.

We have investigated the development of current-driven (CD) kink instability in relativistic jets via 3D RMHD simulations. In this investigation a static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration on the linear and nonlinear evolution of the instability. We found that the initial configuration is strongly distorted but not disrupted by the CD kink instability. The linear growth and nonlinear evolution of the CD kink instability depend moderately on the radial density profile and strongly on the magnetic pitch profile. Kink amplitude growth in the nonlinear regime for decreasing magnetic pitch leads to a slender helically twisted column wrapped by magnetic field. On the other hand, kink amplitude growth in the nonlinear regime nearly ceases for increasing magnetic pitch.

The effect of Brillouin backscattering on the stability of a high power continuously pumped fiber laser is theoretically analyzed in the general framework of two-coupled modes laser model. It is demonstrated that, depending on the cavity losses, different type of instabilities can arise. Low loss cavity favours stable continuous regime in a large range of pumping rates while high loss configuration permits the emergence of different self-pulsing instabilities.

The paper describes how quasi-static, conservative instability problems can be seen in a multi-dimensional context, and how one- and two-dimensional solution manifolds can reveal further information on the structural response. The discussed viewpoint can be seen as the natural extension of the common one-dimensional path-following methods, when additional variables are introduced to describe the parameter dependence in structural response, instability analyses and optimization. The paper describes the general setting of the generalized equilibrium problems, and discusses their numerical treatment for the cases of resulting one- and two-dimensional solution sets. Numerical examples show some applications of these models, and describe the possibilities and properties of the obtained solution sets.

A discussion and an improvement of the Neumann–Kelvin's model are suggested in this paper. This model is used in the simulation of progressive wave phenomenon. As mentioned by several authors ([7, 19, 23, 29]), this model is ill posed unless a capillary energy is introduced. The mathematical explanation is that a compactness inversions' property occurs if the capillary forces are omitted. Theoretical arguments and numerical simulations are used in the following which aims at giving an explanation of what happens from a mechanical point of view.

The nearshore potential vorticity balance of Bowen and Holman (1989) is expanded to include the forcing from wave group induced radiation stresses. Model results suggest that the forcing from these radiation stresses can drive oscillations in the longshore current that have a spatial structure similar to linear shear instabilities of the longshore current. In addition, the forced response is nearly resonant when the forcing has scales (k,σ) similar to the linearly most unstable mode. Thus, we suggest that wave groups may provide an initial perturbation necessary for the generation of shear instabilities of longshore currents and also act as a source of vortical motions on beaches where linear instabilities are completely damped.

Data from the SUPERDUCK (1986) field experiment were analyzed for the presence of spatially coherent wave groups. The analysis confirms that wave groups with periods and longshore spatial structures comparable to the observed shear wave motions were sometimes present on this open coast. This indicates that wave groups with the required spatial and temporal structure to initiate the low frequency oscillations in the longshore current can exist.

Relativistic jets carry energy and particles from compact to very large scales compared with their initial radius. This is possible due to their remarkable collimation despite their intrinsic unstable nature. In this contribution, I review the state-of-the-art of our knowledge on instabilities growing in those jets and several stabilising mechanisms that may give an answer to the question of the stability of jets. In particular, during the last years we have learned that the limit imposed by the speed of light sets a maximum amplitude to the instabilities, contrary to the case of classical jets. On top of this stabilising mechanism, the fast growth of unstable modes with small wavelengths prevents the total disruption and entrainment of jets. I also review several non-linear processes that can have an effect on the collimation of extragalactic and microquasar jets. Within those, I remark possible causes for the decollimation and deceleration of FRI jets, as opposed to the collimated FRII's. Finally, I give a summary of the main reasons why jets can propagate through such long distances.

We have investigated the influence of velocity shear on the linear and non-linear development of the CD kink instability. We follow temporal development of the instability within a periodic computational box. We find that helically distorted density structure propagates along the jet with speed and flow structure dependent on the location of the velocity shear relative to the characteristic radius of the helically twisted force-free magnetic field. At small radius the plasma flows through the kink. The kink propagation speed increases as the radius increases and the kink becomes more embedded in the plasma flow. Larger velocity shear radius leads to slower linear growth, makes a later transition to the nonlinear stage, and with larger maximum amplitude than occurs for a static plasma column. However, when the velocity shear radius is much greater than the characteristic radius of the helical magnetic field, linear and non-linear development become more similar to the development of a static plasma column.

We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the Current-Driven (CD) kink instability as a model of pulsar wind nebulae. In our simulations the CD kink instability was excited by a small initial velocity perturbation and developed turbulent structure inside the hot plasma column. We demonstrated that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter "σ", the ratio of the magnetic energy to the thermal energy for a hot plasma, declined from an initial value of 0.3 to about 0.01 when the CD kink instability saturated. Our simulations demonstrated that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned. The observed structure of the pulsar wind nebulae do not contradict the natural assumption that the magnetic energy flux still remains a good fraction of the total energy flux after dissipation of alternating fields.