1,069 research outputs found
The extended Malkus-Robbins dynamo as a perturbed Lorenz system
Recent investigations of some self-exciting Faraday-disk homopolar dynamo ([1-4]) have yielded the classic Lorenz equations as a special limit when one of the principal bifurcation parameters is zero. In this paper we focus upon one of those models [3] and illustrate what happens to some of the lowest order unstable periodic orbits as this parameter is increased from zero
A simplified model of the Martian atmosphere - Part 1: a diagnostic analysis
In this paper we derive a reduced-order approximation to the vertical and horizontal structure of a simplified model of the baroclinically unstable Martian atmosphere. The original model uses the full hydrostatic primitive equations on a sphere, but has only highly simplified schemes to represent the detailed physics of the Martian atmosphere, e.g. forcing towards a plausible zonal mean temperature state using Newtonian cooling. Three different norms are used to monitor energy conversion processes in the model and are then compared. When four vertical modes (the barotropic and first three baroclinic modes) are retained in the reduced-order approximation, the correlation norm captures approximately 90% of the variance, while the kinetic energy and total energy norms capture approximately 83% and 78% of the kinetic and total energy respectively. We show that the leading order Proper Orthogonal Decomposition (POD) modes represent the dominant travelling waves in the baroclinically-unstable, winter hemisphere. In part 2 of our study we will develop a hierarchy of truncated POD-Galerkin expansions of the model equations using up to four vertical modes
A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis
In Part I of this study Whitehouse et al. (2005) performed a diagnostic analysis of a simplied model of the Martian atmosphere, in which topography was absent and in which heating was modelled as Newtonian relaxation towards a zonally symmetric equilibrium temperature field. There we derived a reduced-order approximation to the vertical and the horizonal structure of the baroclinically unstable Martian atmosphere, retaining only the barotropic mode and the leading order baroclinic modes. Our objectives in Part II of the study are to incorporate these approximations into a Proper Orthogonal Decomposition-Galerkin expansion of the spherical quasi-geostrophic model in order to derive hierarchies of nonlinear ordinary differential equations for the time-varying coefficients of the spatial structures. Two different vertical truncations are considered, as well as three different norms and 3 different Galerkin truncations. We investigate each in turn, using tools from bifurcation theory, to determine which of the systems most closely resembles the data for which the original diagnostics were performed
Reduced-order models of the Martian atmospheric dynamics
In this paper we explore the possibility of deriving low-dimensional models of the dynamics of the Martian atmosphere. The analysis consists of a Proper Orthogonal Decomposition (POD) of the atmospheric streamfunction after first decomposing the vertical structure with a set of eigenmodes. The vertical modes were obtained from the quasi-geostrophic vertical structure equation. The empirical orthogonal functions (EOFs) were optimized to represent the atmospheric total energy. The total energy was used as the criterion to retain those modes with large energy content and discard the rest. The principal components (PCs) were analysed by means of Fourier analysis, so that the dominant frequencies could be identified. It was possible to observe the strong influence of the diurnal cycle and to identify the motion and vacillation of baroclinic waves
Photonic Band Gaps of Three-Dimensional Face-Centered Cubic Lattices
We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a
viable alternative to the plane-wave method to analyze the spectrum of
electromagnetic waves in a three-dimensional periodic dielectric lattice.
Firstly, in the case of an fcc lattice of homogeneous dielectric spheres, we
reproduce the main features of the spectrum obtained by the plane wave method,
namely that for a sufficiently high dielectric contrast a full gap opens in the
spectrum between the eights and ninth bands if the dielectric constant
of spheres is lower than the dielectric constant of
the background medium. If , no gap is found in the
spectrum. The maximal value of the relative band-gap width approaches 14% in
the close-packed case and decreases monotonically as the filling fraction
decreases. The lowest dielectric contrast for which a
full gap opens in the spectrum is determined to be 8.13. Eventually, in the
case of an fcc lattice of coated spheres, we demonstrate that a suitable
coating can enhance gap widths by as much as 50%.Comment: 19 pages, 6 figs., plain latex - a section on coated spheres, two
figures, and a few references adde
The frictional Schr\"odinger-Newton equation in models of wave function collapse
Replacing the Newtonian coupling G by -iG, the Schrodinger-Newton equation
becomes ``frictional''. Instead of the reversible Schrodinger-Newton equation,
we advocate its frictional version to generate the set of pointer states for
macroscopic quantum bodies.Comment: 6pp LaTeX for J.Phys.Conf.Ser.+2 figs. Talk given at the Int.
Workshop DICE2006 "Quantum Mechanics between Decoherence and Determinism: new
aspects from particle physics to cosmology" Piombino, Sept 11-15, 200
Slow and fast magneto-optical response of magnetite nanoparticles suspension
DC magnetic field applied to Fe3O4 nanoparticle suspension affects its light scattering. Time dependent variations in the light intensity transmitted through a suspension are observed after the magnetic field is switched-on. Two types of variations can be distinguished. Fast response takes less than millisecond while slow variations occur at the time interval from seconds to hundreds of minutes. Possible mechanisms of these variations are discussed
Rashba effect in 2D mesoscopic systems with transverse magnetic field
We present semiclassical and quantum mechanical results for the effects of a
strong magnetic field in Quantum Wires in the presence of Rashba Spin Orbit
coupling. Analytical and numerical results show how the perturbation acts in
the presence of a transverse magnetic field in the ballistic regime and we
assume a strong reduction of the backward scattering interaction which could
have some consequences for the Tomonaga-Luttinger transport. We analyze the
spin texture due to the action of Spin Orbit coupling and magnetic field often
referring to the semiclassical solutions that magnify the singular spin
polarization: results are obtained for free electrons in a twodimensional
electron gas and for electrons in a Quantum Wire.
We propose the systems as possible devices for the spin filtering at various
regimes.Comment: 12 pages, 12 figures, to appear in Phys. Rev.
Field theory of massive and massless vector particles in the Duffin - Kemmer - Petiau formalism
Field theory of massive and massless vector particles is considered in the
first-order formalism. The Hamiltonian form of equations is obtained after the
exclusion of non-dynamical components. We obtain the canonical and symmetrical
Belinfante energy-momentum tensors and their nonzero traces. We note that the
dilatation symmetry is broken in the massive case but in the massless case the
modified dilatation current is conserved. The canonical quantization is
performed and the propagator of the massive fields is found in the Duffin -
Kemmer - Petiau formalism.Comment: 20 pages, typos corrected, a reference added, journal version,
accepted in Int.J.Mod.Phys.
On the equivalence of the Langevin and auxiliary field quantization methods for absorbing dielectrics
Recently two methods have been developed for the quantization of the
electromagnetic field in general dispersing and absorbing linear dielectrics.
The first is based upon the introduction of a quantum Langevin current in
Maxwell's equations [T. Gruner and D.-G. Welsch, Phys. Rev. A 53, 1818 (1996);
Ho Trung Dung, L. Kn\"{o}ll, and D.-G. Welsch, Phys. Rev. A 57, 3931 (1998); S.
Scheel, L. Kn\"{o}ll, and D.-G. Welsch, Phys. Rev. A 58, 700 (1998)], whereas
the second makes use of a set of auxiliary fields, followed by a canonical
quantization procedure [A. Tip, Phys. Rev. A 57, 4818 (1998)]. We show that
both approaches are equivalent.Comment: 7 pages, RevTeX, no figure
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