Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

Two-dimensional hygrothermal transfer in porous building materials

A two-dimensional mathematical model for evaluating the simultaneous heat and moisture migration in porous building materials was proposed. Vapor content and temperature were chosen as the principal driving potentials. The numerical solution was based on the control volume finite difference technique with fully implicit scheme in time. Two validation experiments were developed in this study. The evolution of transient moisture distributions in both one-dimensional and two-dimensional cases was measured. A comparison between experimental results and those obtained by the numerical model proves that they are fully consistent with each other. The model can be easily integrated into a whole building heat, air and moisture transfer model. Another main advantage of the present numerical method lies in the fact that the required moisture transport properties are comparatively simple and easy to determine.

Dust lattice wave dispersion relations in two-dimensional hexagonal crystals including the effect of dust charge polarization

A dusty plasma crystalline configuration with equal charge dust grains and mass is considered. Both charge and mass of each dust species are taken to be constant. Two differential equations for a two-dimensional hexagonal crystal on the basis of a Yukawa-type potential energy and a

Nonlinearly modulated dust lattice wave packets in two-dimensional hexagonal dust crystals

The amplitude modulation of dust lattice waves (DLWs) propagating in a two-dimensional hexagonal dust crystal is investigated in a continuum approximation, accounting for the effect of dust charge polarization (dressed interactions). A dusty plasma crystalline configuration with constant dust grain charge and mass is considered. The dispersion relation and the group velocity for DLWs are determined for wave propagation in both longitudinal and transverse directions. The reductive perturbation method is used to derive a (2+1)-dimensional nonlinear Schrodinger equation (NLSE). New expressions for the coefficients of the NLSE are derived and compared, for a Yukawa-type potential energy and for a

Detailed analytical investigation of magnetic field line random walk in turbulent plasmas: I. Two-component slab/two-dimensional turbulence

The random displacement of magnetic field lines in the presence of magnetic turbulence in plasmas is investigated from first principles. A two-component (slab/two-dimensional composite) model for the turbulence spectrum is employes. An analytical investigation of the asymptotic behavior of the field-line mean square displacement (FL-MSD) is carried out. It is shown that the magnetic field lines behave superdifusively for every large values of the position variable z, since the FL-MSD sigma varies as sigma similar to z(4/3). An intermediate diffusive regime may also possible exist for finite values of z under conditions which are explicitly determined in terms of the intrinsic turbulent plasma parameters. The superdiffusie asymptotic result is confirmed numerically via an iterative algorithm. The relevance to previous resuslts is discussed.

Modulated transverse off-plane dust-lattice wave packets in hexagonal two-dimensional dusty plasma crystals

The propagation of nonlinear dust-lattice waves in a two-dimensional hexagonal crystal is investigated. Transverse (off-plane) dust grain oscillatory motion is considered in the form of a backward propagating wave packet whose linear and nonlinear characteristics are investigated. An evolution equation is obtained for the slowly varying amplitude of the first (fundamental) harmonic by making use of a two-dimensional lattice multiple scales technique. An analysis based on the continuum approximation (spatially extended excitations compared to the lattice spacing) shows that wave packets will be modulationally stable and that dark-type envelope solitons (density holes) may occur in the long wavelength region. Evidence is provided of modulational instability and of the occurrence of bright-type envelopes (pulses) at shorter wavelengths. The role of second neighbor interactions is also investigated and is shown to be rather weak in determining the modulational stability region. The effect of dissipation, assumed negligible in the algebra throughout the article, is briefly discussed.

Frequency Steerable Two Dimensional Focusing Using Rectilinear Leaky-Wave Lenses

The concept of frequency steerable two-dimensional electromagnetic focusing by using a tapered leaky-wave line source embedded in a parallel-plate medium is presented. Accurate expressions for analyzing the focusing pattern of a rectilinear leaky-wave lens (LWL) from its constituent leaky-mode tapered propagation constant are described. The influence of the main LWL structural parameters on the synthesis of the focusing pattern is discussed. The ability to generate frequency steerable focusing patterns has been demonstrated by means of an example involving a LWL in hybrid waveguide printed-circuit technology and the results are validated by a commercial full-wave solver.

Comparing the implementation of two-dimensional numerical quadrature on GPU, FPGA and ClearSpeed systems to study electron scattering by atoms

The use of accelerators, with compute architectures different and distinct from the CPU, has become a new research frontier in high-performance computing over the past ?ve years. This paper is a case study on how the instruction-level parallelism offered by three accelerator technologies, FPGA, GPU and ClearSpeed, can be exploited in atomic physics. The algorithm studied is the evaluation of two electron integrals, using direct numerical quadrature, a task that arises in the study of intermediate energy electron scattering by hydrogen atoms. The results of our ‘productivity’ study show that while each accelerator is viable, there are considerable differences in the implementation strategies that must be followed on each.

Two-dimensional particle-in-cell simulation of the expansion of a plasma into a rarefied medium

The expansion of a dense plasma through a more rarefied ionized medium has been studied by means of two-dimensional particle-in-cell simulations. The initial conditions involve a density jump by a factor of 100, located in the middle of an otherwise equally dense electron-proton plasma with uniform proton and electron temperatures of 10 eV and 1 keV, respectively. Simulations show the creation of a purely electrostatic collisionless shock together with an ion-acoustic soliton tied to its downstream region. The shock front is seen to evolve in filamentary structures consistently with the onset of the ion-ion instability. Meanwhile, an un-magnetized drift instability is triggered in the core part of the dense plasma. Such results explain recent experimental laser-plasma experiments, carried out in similar conditions, and are of intrinsic relevance to non-relativistic shock scenarios in the solar and astrophysical systems.

Two-dimensional imaging of low temperature laser produced plasmas

Laser induced fluorescence images of a low temperature laser-produced plasma expanding into vacuum are presented and compared to a computer simulation. The complex nature of a plume expanding into background gas is highlighted, along with a potential means of simplifying the study of such systems.

Two-dimensional Monte Carlo simulations of H i line formation in massive young stellar object disc winds

Massive young stellar objects (YSOs) are powerful infrared Hi line emitters. It has been suggested that these lines form in an outflow from a disc surrounding the YSO. Here, new two-dimensional Monte Carlo radiative transfer calculations are described which test this hypothesis. Infrared spectra are synthesized for a YSO disc wind model based on earlier hydrodynamical calculations. The model spectra are in qualitative agreement with the observed spectra from massive YSOs, and therefore provide support for a disc wind explanation for the Hi lines. However, there are some significant differences: the models tend to overpredict the Bra/Br? ratio of equivalent widths and produce line profiles which are slightly too broad and, in contrast to typical observations, are double-peaked. The interpretation of these differences within the context of the disc wind picture and suggestions for their resolution via modifications to the assumed disc and outflow structure are discussed. © 2005 RAS.

TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE NONRESONANT, COSMIC-RAY-DRIVEN INSTABILITY IN SUPERNOVA REMNANT SHOCKS

In supernova remnants, the nonlinear amplification of magnetic fields upstream of collisionless shocks is essential for the acceleration of cosmic rays to the energy of the "knee" at 10(15.5) eV. A nonresonant instability driven by the cosmic ray current is thought to be responsible for this effect. We perform two-dimensional, particle-in-cell simulations of this instability. We observe an initial growth of circularly polarized nonpropagating magnetic waves as predicted in linear theory. It is demonstrated that in some cases the magnetic energy density in the growing waves can grow to at least 10 times its initial value. We find no evidence of competing modes, nor of significant modification by thermal effects. At late times, we observe saturation of the instability in the simulation, but the mechanism responsible is an artifact of the periodic boundary conditions and has no counterpart in the supernova-shock scenario.