Narrow Results

Motivated by the two-scale convergence method introduced by G. Nguetseng and G. Allaire, we study the polarization and relaxation effects induced by two-scale homogenization. By virtue of Boltzmann–Poisson system, we characterize the microscopic properties of electrons in dielectric materials. The homogenized equations are obtained which describe the mean behaviors. By the homogenized equation, we get the polarization and relaxation effects which lead to the modified Gauss law; moreover, the dielectric function and the conductivity are also obtained.

In the current study, a well-known fractional nonlinear differential equation called Zakharov–Kuznetsov equation which has many applications in engineering and physics is investigated. An effective computational techniques namely Daftardar–Jafari Method (DJM) and He’s fractional derivative are employed to model the problem for obtaining a high accuracy of the analytical solution. The governing equations are solved and comparison of the results with exact solutions is presented to evaluate the precision of the presented method. The outcomes reveal that the DJM is efficient and easy to utilize. Further, three-dimensional contour plots are depicted according to the suitable parameters values.

We analyse the two-dimensional MHD configurations characterising the steady state of the accretion disk on a highly magnetised neutron star. The model we describe has a local character and represents the extension of the crystalline structure outlined in Ref. 1, dealing with a local model too, when a specific accretion rate is taken into account. We limit our attention to the linearised MHD formulation of the electromagnetic back-reaction characterising the equilibrium, by fixing the structure of the radial, vertical and azimuthal profiles. Since we deal with toroidal currents only, the consistency of the model is ensured by the presence of a small collisional effect, phenomenologically described by a nonzero constant Nernst coefficient (thermal power of the plasma). Such an effect provides a proper balance of the electron force equation via nonzero temperature gradients, related directly to the radial and vertical velocity components.

We show that the obtained profile has the typical oscillating feature of the crystalline structure, reconciled with the presence of viscosity, associated to the differential rotation of the disk, and with a net accretion rate. In fact, we provide a direct relation between the electromagnetic reaction of the disk and the (no longer zero) increasing of its mass per unit time. The radial accretion component of the velocity results to be few orders of magnitude below the equatorial sound velocity. Its oscillating-like character does not allow a real matter in-fall to the central object (an effect to be searched into nonlinear MHD corrections), but it accounts for the outgoing of steady fluxes, favourable to the ring-like morphology of the disk.

The double pulsar system J0737 – 3039 – a 22.7 ms pulsar in a compact 2.4 hr orbit about a 2.7 s pulsar was one of the long-awaited "holy grails" of pulsar astronomy. After only two years of timing, the system is close to surpassing the original Hulse-Taylor binary as a test of general relativity. On-going timing should soon reveal second-order effects in the post-Newtonian parameters. In addition, the observed interactions of the radio beams of the two pulsars provide a unique laboratory for probing neutron star magnetospheres and relativistic winds. Finally, a revised estimate of the cosmic rate of double neutron star mergers including J0737 – 3039 boosts previous estimates by an order of magnitude and suggests a high detection rate for the advanced LIGO gravitational wave detector.

In the low energy part of an ion accelerator, the ion beam reaches the first accelerating device through a drift tube where a residual neutral gas is present. A process of ionization takes place and secondary electrons and ions are created. We analyze the coupling between these secondary particles, the beam density and the electrical potential.

In a previous article,² we proved that a stationary Vlasov–Poisson problem with ionization source terms, which, at first sight, seems the natural model for this system, does not admit solutions. To overcome this difficulty, we propose here a heuristic model which consists of modifying the electron source term. In this new frame, we prove that the problem can be solved and we give numerical examples.

This paper is concerned with an initial-boundary value problem for screw pinches arisen from plasma physics. We prove the global existence of weak solutions to this physically very important problem. The main difficulties in the proof lie in the presence of 1/x-singularity in the equations at the origin and the additional nonlinear terms induced by the magnetic field. Solutions will be obtained as the limit of the approximate solutions in annular regions between two cylinders. Under certain growth assumption on the heat conductivity, we first derive a number of regularities of the approximate physical quantities in the fluid region, as well as a lot of uniform integrability in the entire spacetime domain. By virtue of these estimates we then argue in a similar manner as that in Ref. 20 to take the limit and show that the limiting functions are indeed a weak solution which satisfies the mass, momentum and magnetic field equations in the entire spacetime domain in the sense of distributions, but satisfies the energy equation only in the compact subsets of the fluid region. The analysis in this paper allows the possibility that energy is absorbed into the origin, i.e. the total energy be possibly lost in the limit as the inner radius goes to zero.

In this paper we prove the existence and uniqueness of classical solution for a system of PDEs recently developed in Refs. 60, 8, 10 and 11 to modelize the nonlinear gyrokinetic turbulence in magnetized plasma. From the analytical and numerical point of view this model is very promising because it allows to recover kinetic features (wave–particle interaction, Landau resonance) of the dynamic flow with the complexity of a multi-fluid model. This model, called the gyro-water-bag model, is derived from two-phase space variable reductions of the Vlasov equation through the existence of two underlying invariants. The first one, the magnetic moment, is adiabatic and the second, a geometric invariant named "water-bag", is exact and is just the direct consequence of the Liouville theorem.

In this paper we consider the relativistic waterbag continuum which is a useful PDE for collisionless kinetic plasma modeling recently developed in Ref. 11. The waterbag representation of the statistical distribution function of particles can be viewed as a special class of exact weak solution of the Vlasov equation, allowing to reduce this latter into a set of hydrodynamic equations (with the complexity of a multi-fluid model) while keeping its kinetic features (Landau damping and nonlinear resonant wave-particle interaction). These models are very promising because they are very useful for analytical theory and numerical simulations of laser-plasma and gyrokinetic physics.^{10–16, 56, 57} The relativistic waterbag continuum is derived from two phase-space variable reductions of the relativistic Vlasov–Maxwell equations through the existence of two underlying exact invariants, one coming from physics properties of the dynamics is the canonical transverse momentum, and the second, named the "water-bag" and coming from geometric property of the phase-space is just the direct consequence of the Liouville Theorem. In this paper we prove the existence and uniqueness of global weak entropy solutions of the relativistic waterbag continuum. Existence is based on vanishing viscosity method and bounded variations (BV) estimates to get compactness while proof of uniqueness relies on kinetic formulation of the relativistic waterbag continuum and the associated kinetic entropy defect measure.

This paper reviews recent results and open problems concerning the existence of steady states to the Maxwell–Schrödinger system. A combination of tools, proofs and results are presented in the framework of the concentration–compactness method.

We study the Maxwellian solutions of the stationary Vlasov-Poisson system, which describes stationary states for plasma. We prove existence, uniqueness and regularity results for these solutions.

We prove that any weak solution (in the sense of Desvillettes and Villani [6]) to the Landau homogeneous equation is smooth and, in particular, that it lies in Schwartz space . Our result has to be compared to [6], where Desvillettes and Villani have shown existence of smooth weak solutions along with a uniqueness result, under further assumptions on initial data. Our method of proof uses the Littlewood–Paley decomposition of velocity space, and elementary Cauchy–Schwarz or Young's inequalities, thus avoiding any use of complex Sobolev interpolation inequalities.

It is shown that the screening of impurities in plasma with Bose-Einstein condensate of electrically charged bosons is drastically different from the usual Debye screening. The polarization operator of photons in plasma becomes infrared singular and the screened potential drops down as a power of distance and even has an oscillating behavior, similar to the Priedel oscillations in plasma with degenerate fermions. The properties of the cosmological plasma with condensed W-bosons are also studied and it is shown that W-bosons condense in ferromagnetic state. The spontaneously generated magnetic fields in such ferromagnetic state may seed the large scale magnetic fields observed in the present-day universe.

As of the year 2018 the Facility for Antiproton and Ion Research (FAIR) will offer access to exotic ion beams and beams of antiproton of unprecedented luminosity. The facility currently under construction in Darmstadt, Germany, adjacent to the existing accelerator at the GSI Helmholtz Centre for Heavy-Ion Research, will serve several collaborations and fields simultaneously: atomic, hadron, nuclear, and plasma physics.