914 research outputs found
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
Resonance-Induced Effects in Photonic Crystals
For the case of a simple face-centered-cubic photonic crystal of homogeneous
dielectric spheres, we examine to what extent single-sphere Mie resonance
frequencies are related to band gaps and whether the width of a gap can be
enlarged due to nearby resonances. Contrary to some suggestions, no spectacular
effects may be expected. When the dielectric constant of the spheres
is greater than the dielectric constant of the
background medium, then for any filling fraction there exists a critical
above which the lowest lying Mie resonance frequency falls inside
the lowest stop gap in the (111) crystal direction, close to its midgap
frequency. If , the correspondence between Mie
resonances and both the (111) stop gap and a full gap does not follow such a
regular pattern. If the Mie resonance frequency is close to a gap edge, one can
observe a resonance-induced widening of a relative gap width by .Comment: 14 pages, 3 figs., RevTex. For more info look at
http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm
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
A simple formula for the L-gap width of a face-centered-cubic photonic crystal
The width of the first Bragg's scattering peak in the (111)
direction of a face-centered-cubic lattice of air spheres can be well
approximated by a simple formula which only involves the volume averaged
and over the lattice unit cell, being the
(position dependent) dielectric constant of the medium, and the effective
dielectric constant in the long-wavelength limit approximated
by Maxwell-Garnett's formula. Apparently, our formula describes the asymptotic
behaviour of the absolute gap width for high dielectric contrast
exactly. The standard deviation steadily decreases well below
1% as increases. For example for the sphere filling
fraction and . On the interval , our
formula still approximates the absolute gap width (the relative
gap width ) with a reasonable precision, namely with a standard
deviation 3% (4.2%) for low filling fractions up to 6.5% (8%) for the
close-packed case. Differences between the case of air spheres in a dielectric
and dielectric spheres in air are briefly discussed.Comment: 13 pages, 4 figs., RevTex, two references added. For more info see
http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm
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.
A superconvergent representation of the Gersten-Nitzan and Ford-Webber nonradiative rates
An alternative representation of the quasistatic nonradiative rates of
Gersten and Nitzan [J. Chem. Phys. 1981, 75, 1139] and Ford and Weber [Phys.
Rep. 1984, 113, 195] is derived for the respective parallel and perpendicular
dipole orientations. Given the distance d of a dipole from a sphere surface of
radius a, the representations comprise four elementary analytic functions and a
modified multipole series taking into account residual multipole contributions.
The analytic functions could be arranged hierarchically according to decreasing
singularity at the short distance limit d ---> 0, ranging from d^{-3} over
d^{-1} to ln (d/a). The alternative representations exhibit drastically
improved convergence properties. On keeping mere residual dipole contribution
of the modified multipole series, the representations agree with the converged
rates on at least 99.9% for all distances, arbitrary particle sizes and
emission wavelengths, and for a broad range of dielectric constants. The
analytic terms of the representations reveal a complex distance dependence and
could be used to interpolate between the familiar d^{-3} short-distance and
d^{-6} long-distance behaviors with an unprecedented accuracy. Therefore, the
representations could be especially useful for the qualitative and quantitative
understanding of the distance behavior of nonradiative rates of fluorophores
and semiconductor quantum dots involving nanometal surface energy transfer in
the presence of metallic nanoparticles or nanoantennas. As a byproduct, a
complete short-distance asymptotic of the quasistatic nonradiative rates is
derived. The above results for the nonradiative rates translate
straightforwardly to the so-called image enhancement factors Delta, which are
of relevance for the surface-enhanced Raman scattering.Comment: 30 pages including 6 figure
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
Preliminary results of study of infrared spectra of Venus from the orbital spacecraft Venera-9 and Venera-10
The infrared spectrum of Venus in the spectral range 1.6 to 2.8 was measured by means of the spectrometers aboard 'Venera-9' and 'Venera-10' orbital spacecrafts. Approximately 20 series of measurements were made near the pericenter of the orbit, each of which contains 150 spectra for each path intersecting the planet from the terminator to the limb. Phase angles lie within the limits from 60 to 120 deg
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.
- …