Development of solar wind shock models with tensor plasma pressure for data analysis

The development of solar wind shock models with tensor plasma pressure and the comparison of some of the shock models with the satellite data from Pioneer 6 through Pioneer 9 are reported. Theoretically, difficulties were found in non-turbulent fluid shock models for tensor pressure plasmas. For microscopic shock theories nonlinear growth caused by plasma instabilities was frequently not clearly demonstrated to lead to the formation of a shock. As a result no clear choice for a shock model for the bow shock or interplanetary tensor pressure shocks emerged

Master partial differential equations for a Type II hidden symmetry

AbstractAn approach for determining a class of master partial differential equations from which Type II hidden point symmetries are inherited is presented. As an example a model nonlinear partial differential equation (PDE) reduced to a target PDE by a Lie symmetry gains a Lie point symmetry that is not inherited (hidden) from the original PDE. On the other hand this Type II hidden symmetry is inherited from one or more of the class of master PDEs. The class of master PDEs is determined by the hidden symmetry reverse method. The reverse method is extended to determine symmetries of the master PDEs that are not inherited. We indicate why such methods are necessary to determine the genesis of Type II symmetries of PDEs as opposed to those that arise in ordinary differential equations (ODEs)

Reduction of systems of first-order differential equations via Lambda-symmetries

The notion of lambda-symmetries, originally introduced by C. Muriel and J.L. Romero, is extended to the case of systems of first-order ODE's (and of dynamical systems in particular). It is shown that the existence of a symmetry of this type produces a reduction of the differential equations, restricting the presence of the variables involved in the problem. The results are compared with the case of standard (i.e. exact) Lie-point symmetries and are also illustrated by some examples.Comment: 12 page

Exact Solutions of a Remarkable Fin Equation

A model "remarkable" fin equation is singled out from a class of nonlinear (1+1)-dimensional fin equations. For this equation a number of exact solutions are constructed by means of using both classical Lie algorithm and different modern techniques (functional separation of variables, generalized conditional symmetries, hidden symmetries etc).Comment: 6 page

Lie reduction and exact solutions of vorticity equation on rotating sphere

Following our paper [J. Math. Phys. 50 (2009) 123102], we systematically carry out Lie symmetry analysis for the barotropic vorticity equation on the rotating sphere. All finite-dimensional subalgebras of the corresponding maximal Lie invariance algebra, which is infinite-dimensional, are classified. Appropriate subalgebras are then used to exhaustively determine Lie reductions of the equation under consideration. The relevance of the constructed exact solutions for the description of real-world physical processes is discussed. It is shown that the results of the above paper are directly related to the results of the recent letter by N. H. Ibragimov and R. N. Ibragimov [Phys. Lett. A 375 (2011) 3858] in which Lie symmetries and some exact solutions of the nonlinear Euler equations for an atmospheric layer in spherical geometry were determined.Comment: 10 pages, 1 figure, minor corrections and extension

GaAs Films Prepared by RF-Magnetron Sputtering

The authors reported on the optical absorption, adhesion, and microstructure of RF-magnetron sputtered films of hydrogenated amorphous and microcrystalline GaAs films for the 1 to 25 {micro}m infrared wavelength rate. Sputtering parameters which were varied include sputtering power, temperature and pressure, and hydrogen sputtering-gas concentration. TEM results show a sharp transition from purely amorphous GaAs to a mixture of microcrystalline GaAs in an amorphous matrix at 34 {+-} 2 C. By optimizing the sputtering parameters, the optical absorption coefficient can be decreased below 100 cm{sup -1} for wavelengths greater than about 1.25 {micro}m. These results represent the lowest reported values of optical absorption for sputtered films of GaAs directly measured by spectrophotometry for the near-infrared wavelength region

Exact Vlasov-Maxwell equilibria for asymmetric current sheets

The NASA Magnetospheric Multiscale mission has made in situ diffusion region and kinetic-scale resolution measurements of asymmetric magnetic reconnection for the first time, in the Earth's magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type magnetic field but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric current sheets, with an asymmetric Harris-type magnetic field profile, plus a constant nonzero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution and has different bulk flow properties

Model of supersymmetric quantum field theory with broken parity symmetry

Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form $g(i\phi)^{2+\delta}$, where $\delta$ is a real positive parameter, are physically acceptable in the sense that the energy spectrum is real and bounded below. Such theories possess PT invariance, but they are not symmetric under parity reflection or time reversal separately. This broken parity symmetry is manifested in a nonzero value for $$, even if $\delta$ is an even integer. This paper extends this idea to a two-dimensional supersymmetric quantum field theory whose superpotential is ${\cal S}(\phi)=-ig(i\phi)^{1+\delta}$. The resulting quantum field theory exhibits a broken parity symmetry for all $\delta>0$. However, supersymmetry remains unbroken, which is verified by showing that the ground-state energy density vanishes and that the fermion-boson mass ratio is unity.Comment: 20 pages, REVTeX, 11 postscript figure

On the inverse problem for Channell collisionless plasma equilibria

Vlasov–Maxwell equilibria are described by the self-consistent solutions of the time-independent Maxwell equations for the real-space dynamics of electromagnetic fields and the Vlasov equation for the phase-space dynamics of particle distribution functions (DFs) in a collisionless plasma. These two systems (macroscopic and microscopic) are coupled via the source terms in Maxwell’s equations, which are sums of velocity-space ‘moment’ integrals of the particle DF. This paper considers a particular subset of solutions of the broad plasma physics problem: ‘the inverse problem for collisionless equilibria’ (IPCE), viz. ‘given information regarding the macroscopic configuration of a collisionless plasma equilibrium, what self-consistent equilibrium DFs exist?’ We introduce the constants of motion approach to IPCE using the assumptions of a ‘modified Maxwellian’ DF, and a strictly neutral and spatially one-dimensional plasma, and this is consistent with ‘Channell’s method’ (Channell, 1976, Exact Vlasov-Maxwell equilibria with sheared magnetic fields. Phys. Fluids, 19, 1541–1545). In such circumstances, IPCE formally reduces to the inversion of Weierstrass transformations (Bilodeau, 1962, The Weierstrass transform and Hermite polynomials. Duke Math. J., 29, 293–308). These are the same transformations that feature in the initial value problem for the heat/diffusion equation. We discuss the various mathematical conditions that a candidate solution of IPCE must satisfy. One method that can be used to invert the Weierstrass transform is expansions in Hermite polynomials. Building on the results of Allanson et al. (2016, From one-dimensional fields to Vlasov equilibria: Theory and application of Hermite polynomials. Journal of Plasma Physics, 82, 905820306, http://doi:10.1017/S0022377816000519), we establish under what circumstances a solution obtained by these means converges and allows velocity moments of all orders. Ever since the seminal work by Bernstein et al. (1957, Exact nonlinear plasma oscillations. Phys. Rev., 108, 546–550) on ‘stationary’ electrostatic plasma waves, the necessary quality of non-negativity has been noted as a feature that any candidate solution of IPCE will not a priori satisfy. We discuss this problem in the context of Channell equilibria, for magnetized plasmas