1,199 research outputs found
Power loss and electromagnetic energy density in a dispersive metamaterial medium
The power loss and electromagnetic energy density of a metamaterial
consisting of arrays of wires and split-ring resonators (SRRs) are
investigated. We show that a field energy density formula can be derived
consistently from both the electrodynamic (ED) approach and the equivalent
circuit (EC) approach. The derivations are based on the knowledge of the
dynamical equations of the electric and magnetic dipoles in the medium and the
correct form of the power loss. We discuss the role of power loss in
determining the form of energy density and explain why the power loss should be
identified first in the ED derivation. When the power loss is negligible and
the field is harmonic, our energy density formula reduces to the result of
Landau's classical formula. For the general case with finite power loss, our
investigation resolves the apparent contradiction between the previous results
derived by the EC and ED approaches.Comment: 10 pages, 1 figure, Submitted to Phys. Rev.
Energy Requirement of Control: Comments on Szilard's Engine and Maxwell's Demon
In mathematical physical analyses of Szilard's engine and Maxwell's demon, a
general assumption (explicit or implicit) is that one can neglect the energy
needed for relocating the piston in Szilard's engine and for driving the trap
door in Maxwell's demon. If this basic assumption is wrong, then the
conclusions of a vast literature on the implications of the Second Law of
Thermodynamics and of Landauer's erasure theorem are incorrect too. Our
analyses of the fundamental information physical aspects of various type of
control within Szilard's engine and Maxwell's demon indicate that the entropy
production due to the necessary generation of information yield much greater
energy dissipation than the energy Szilard's engine is able to produce even if
all sources of dissipation in the rest of these demons (due to measurement,
decision, memory, etc) are neglected.Comment: New, simpler and more fundamental approach utilizing the physical
meaning of control-information and the related entropy production. Criticism
of recent experiments adde
Electromagnetic energy and energy flows in photonic crystals made of arrays of parallel dielectric cylinders
We consider the electromagnetic propagation in two-dimensional photonic
crystals, formed by parallel dielectric cylinders embedded a uniform medium.
The frequency band structure is computed using the standard plane-wave
expansion method, and the corresponding eigne-modes are obtained subsequently.
The optical flows of the eigen-modes are calculated by a direct computation
approach, and several averaging schemes of the energy current are discussed.
The results are compared to those obtained by the usual approach that employs
the group velocity calculation. We consider both the case in which the
frequency lies within passing band and the situation in which the frequency is
in the range of a partial bandgap. The agreements and discrepancies between
various averaging schemes and the group velocity approach are discussed in
detail. The results indicate the group velocity can be obtained by appropriate
averaging method.Comment: 23 pages, 5 figure
Causality in Propagation of a Pulse in a Nonlinear Dispersive Medium
We investigate the causal propagation of the pulse through dispersive media
by very precise numerical solution of the coupled Maxwell-Bloch equations
without any approximations about the strength of the input field. We study full
nonlinear behavior of the pulse propagation through solid state media like ruby
and alexandrite. We have demonstrated that the information carried by the
discontinuity, {\it i.e}, front of the pulse, moves inside the media with
velocity even though the peak of the pulse can travel either with
sub-luminal or with super-luminal velocity. We extend the argument of
Levi-Civita to prove that the discontinuity would travel with velocity even
in a nonlinear medium.Comment: 4 pages, 4 figures, 2 table
The refractive index and wave vector in passive or active media
Materials that exhibit loss or gain have a complex valued refractive index
. Nevertheless, when considering the propagation of optical pulses, using a
complex is generally inconvenient -- hence the standard choice of
real-valued refractive index, i.e. n_s = \RealPart (\sqrt{n^2}). However, an
analysis of pulse propagation based on the second order wave equation shows
that use of results in a wave vector \emph{different} to that actually
exhibited by the propagating pulse. In contrast, an alternative definition n_c
= \sqrt{\RealPart (n^2)}, always correctly provides the wave vector of the
pulse. Although for small loss the difference between the two is negligible, in
other cases it is significant; it follows that phase and group velocities are
also altered. This result has implications for the description of pulse
propagation in near resonant situations, such as those typical of metamaterials
with negative (or otherwise exotic) refractive indices.Comment: Phys. Rev. A, to appear (2009
Sonic crystal lenses that obey Lensmaker's formula
This paper presents a theoretical study of the phenomenon of acoustic imaging
by sonic crystals, which are made of two-dimensional regular arrays of rigid
cylinders placed in parallel in air. The scattering of acoustic waves is
computed using the standard multiple scattering theory, and the band structures
are computed by the plane-wave expansion method. It is shown that properly
arranged arrays not only can behave as acoustic lenses, but also the focusing
effect can be well described by Lensmaker's formula. Possible applications are
also discussed.Comment: 4 pages, 5 figure
On rational boundary conditions for higher-order long-wave models
Higher-order corrections to classical long-wave theories enable simple and efficient modelling of the onset of wave dispersion and size effects produced by underlying micro-structure. Since such models feature higher spatial derivatives,
one needs to formulate additional boundary conditions when confined to bounded domains. There is a certain controversy associated with these
boundary conditions, because it does not seem possible to justify their choice by purely physical considerations. In this paper an asymptotic model for onedimensional chain of particles is chosen as an exemplary higher-order theory. We demonstrate how the presence of higher-order derivative terms results in
the existence of non-physical “extraneous” boundary layer-type solutions and argue that the additional boundary conditions should generally be formulated to eliminate the contribution of these boundary layers into the averaged solution. Several new methods of deriving additional boundary conditions are presented for essential boundary. The results are illustrated by numerical examples featuring comparisons with an exact solution for the finite chain
Exploiting pattern transformation to tune phononic band gaps in a two-dimensional granular crystal
The band structure of a two-dimensional granular crystal composed of silicone rubber and polytetrafluoroethylene (PTFE) cylinders is investigated numerically. This system was previously shown to undergo a pattern transformation with uniaxial compression by Göncü et al. [Soft Matter 7, 2321 (2011)]. The dispersion relations of the crystal are computed at different levels of deformation to demonstrate the tunability of the band structure, which is strongly affected by the pattern transformation that induces new band gaps. Replacement of PTFE particles with rubber ones reveals that the change of the band structure is essentially governed by pattern transformation rather than particles¿ mechanical properties
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