4,592 research outputs found
Electromagnetic Energy, Momentum, and Angular Momentum in an Inhomogeneous Linear Dielectric
In a previous work, Optics Communications 284 (2011) 2460--2465, we
considered a dielectric medium with an anti-reflection coating and a spatially
uniform index of refraction illuminated at normal incidence by a
quasimonochromatic field. Using the continuity equations for the
electromagnetic energy density and the Gordon momentum density, we constructed
a traceless, symmetric energy--momentum tensor for the closed system. In this
work, we relax the condition of a uniform index of refraction and consider a
dielectric medium with a spatially varying index of refraction that is
independent of time, which essentially represents a mechanically rigid
dielectric medium due to external constraints. Using continuity equations for
energy density and for Gordon momentum density, we construct a symmetric
energy--momentum matrix, whose four-divergence is equal to a generalized
Helmholtz force density four-vector. Assuming that the energy-momentum matrix
has tensor transformation properties under a symmetry group of space-time
coordinate transformations, we derive the global conservation laws for the
total energy, momentum, and angular momentum.Comment: added publication informatio
Numerical study of multilayer adsorption on fractal surfaces
We report a numerical study of van der Waals adsoprtion and capillary
condensation effects on self-similar fractal surfaces. An assembly of uncoupled
spherical pores with a power-law distributin of radii is used to model fractal
surfaces with adjustable dimensions. We find that the commonly used fractal
Frankel-Halsey-Hill equation systematically fails to give the correct dimension
due to crossover effects, consistent with the findings of recent experiments.
The effects of pore coupling and curvature dependent surface tension were also
studied.Comment: 11 pages, 3 figure
He Scattering from Random Adsorbates, Disordered Compact Islands and Fractal Submonolayers: Intensity Manifestations of Surface Disorder
A theoretical study is made on He scattering from three fundamental classes
of disordered ad-layers: (a) Translationally random adsorbates, (b) disordered
compact islands and (c) fractal submonolayers. The implications of the results
to experimental studies of He scattering from disordered surfaces are
discussed, and a combined experimental-theoretical study is made for Ag
submonolayers on Pt(111). Some of the main theoretical findings are: (1)
Structural aspects of the calculated intensities from translationally random
clusters were found to be strongly correlated with those of individual
clusters. (2) Low intensity Bragg interference peaks appear even for scattering
from very small ad-islands, and contain information on the ad-island local
electron structure. (3) For fractal islands, just as for islands with a
different structure, the off-specular intensity depends on the parameters of
the He/Ag interaction, and does not follow a universal power law as previously
proposed in the literature. In the experimental-theoretical study of Ag on
Pt(111), we use first experimental He scattering data from low-coverage (single
adsorbate) systems to determine an empirical He/Ag-Pt potential of good
quality. Then, we carry out He scattering calculations for high coverage and
compare with experiments. The conclusions are that the actual experimental
phase corresponds to small compact Ag clusters of narrow size distribution,
translationally disordered on the surface.Comment: 36 double-spaced pages, 10 figures; accepted by J. Chem. Phys.,
scheduled to appear March 8. More info available at
http://www.fh.huji.ac.il/~dani
First order wetting of rough substrates and quantum unbinding
Replica and functional renormalization group methods show that, with short
range substrate forces or in strong fluctuation regimes, wetting of a
self-affine rough wall in 2D turns first-order as soon as the wall roughness
exponent exceeds the anisotropy index of bulk interface fluctuations. Different
thresholds apply with long range forces in mean field regimes. For
bond-disordered bulk, fixed point stability suggests similar results, which
ultimately rely on basic properties of quantum bound states with asymptotically
power-law repulsive potentials.Comment: 11 pages, 1 figur
A Theory of Cheap Control in Embodied Systems
We present a framework for designing cheap control architectures for embodied
agents. Our derivation is guided by the classical problem of universal
approximation, whereby we explore the possibility of exploiting the agent's
embodiment for a new and more efficient universal approximation of behaviors
generated by sensorimotor control. This embodied universal approximation is
compared with the classical non-embodied universal approximation. To exemplify
our approach, we present a detailed quantitative case study for policy models
defined in terms of conditional restricted Boltzmann machines. In contrast to
non-embodied universal approximation, which requires an exponential number of
parameters, in the embodied setting we are able to generate all possible
behaviors with a drastically smaller model, thus obtaining cheap universal
approximation. We test and corroborate the theory experimentally with a
six-legged walking machine. The experiments show that the sufficient controller
complexity predicted by our theory is tight, which means that the theory has
direct practical implications. Keywords: cheap design, embodiment, sensorimotor
loop, universal approximation, conditional restricted Boltzmann machineComment: 27 pages, 10 figure
Innovative marketing. The concept and function
This article is theoretical in nature. Any development of innovation begins with the development of creative ideas that will is the starting point for innovation Innovative marketing is aimed at the efficient introduction of these new ideas
Energy-Momentum Tensor for the Electromagnetic Field in a Dielectric
The total momentum of a thermodynamically closed system is unique, as is the
total energy. Nevertheless, there is continuing confusion concerning the
correct form of the momentum and the energy-momentum tensor for an
electromagnetic field interacting with a linear dielectric medium. Here we
investigate the energy and momentum in a closed system composed of a
propagating electromagnetic field and a negligibly reflecting dielectric. The
Gordon momentum is easily identified as the total momentum by the fact that it
is, by virtue of being invariant in time, conserved. We construct continuity
equations for the energy and the Gordon momentum and use the continuity
equations to construct an array that has the properties of a traceless,
diagonally symmetric energy-momentum tensor. Then the century-old
Abraham-Minkowski momentum controversy can be viewed as a consequence of
attempting to construct an energy-momentum tensor from continuity equations
that contain densities that correspond to nonconserved quantities.Comment: added publication informatio
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