3,011 research outputs found
Travelling waves and a fruitful `time' reparametrization in relativistic electrodynamics
We simplify the nonlinear equations of motion of charged particles in an
external electromagnetic field that is the sum of a plane travelling wave
F_t(ct-z) and a static part F_s(x,y,z): by adopting the light-like coordinate
ct-z instead of time t as an independent variable in the Action, Lagrangian and
Hamiltonian, and deriving the new Euler-Lagrange and Hamilton equations
accordingly, we make the unknown z(t) disappear from the argument of F_t. We
study and solve first the single particle equations in few significant cases of
extreme accelerations. In particular we obtain a rigorous formulation of a
Lawson-Woodward-type (no-final-acceleration) theorem and a compact derivation
of cyclotron autoresonance, beside new solutions in the presence of uniform
F_s. We then extend our method to plasmas in hydrodynamic conditions and apply
it to plane problems: the system of partial differential equations may be
partially solved and sometimes even completely reduced to a family of decoupled
systems of ordinary ones; this occurs e.g. with the impact of the travelling
wave on a vacuum-plasma interface (what may produce the slingshot effect).
Since Fourier analysis plays no role in our general framework, the method can
be applied to all kind of travelling waves, ranging from almost monochromatic
to socalled "impulses", which contain few, one or even no complete cycle.Comment: Latex file, 35 pages, 6 figures. Final version to appear in J. Phys.
A: Math. Theo
Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver
Due to discretization effects and truncation to finite domains, many
electromagnetic simulations present non-physical modifications of Maxwell's
equations in space that may generate spurious signals affecting the overall
accuracy of the result. Such modifications for instance occur when Perfectly
Matched Layers (PMLs) are used at simulation domain boundaries to simulate open
media. Another example is the use of arbitrary order Maxwell solver with domain
decomposition technique that may under some condition involve stencil
truncations at subdomain boundaries, resulting in small spurious errors that do
eventually build up. In each case, a careful evaluation of the characteristics
and magnitude of the errors resulting from these approximations, and their
impact at any frequency and angle, requires detailed analytical and numerical
studies. To this end, we present a general analytical approach that enables the
evaluation of numerical discretization errors of fully three-dimensional
arbitrary order finite-difference Maxwell solver, with arbitrary modification
of the local stencil in the simulation domain. The analytical model is
validated against simulations of domain decomposition technique and PMLs, when
these are used with very high-order Maxwell solver, as well as in the infinite
order limit of pseudo-spectral solvers. Results confirm that the new analytical
approach enables exact predictions in each case. It also confirms that the
domain decomposition technique can be used with very high-order Maxwell solver
and a reasonably low number of guard cells with negligible effects on the whole
accuracy of the simulation.Comment: 33 pages, 14 figure
Single-image RGB Photometric Stereo With Spatially-varying Albedo
We present a single-shot system to recover surface geometry of objects with
spatially-varying albedos, from images captured under a calibrated RGB
photometric stereo setup---with three light directions multiplexed across
different color channels in the observed RGB image. Since the problem is
ill-posed point-wise, we assume that the albedo map can be modeled as
piece-wise constant with a restricted number of distinct albedo values. We show
that under ideal conditions, the shape of a non-degenerate local constant
albedo surface patch can theoretically be recovered exactly. Moreover, we
present a practical and efficient algorithm that uses this model to robustly
recover shape from real images. Our method first reasons about shape locally in
a dense set of patches in the observed image, producing shape distributions for
every patch. These local distributions are then combined to produce a single
consistent surface normal map. We demonstrate the efficacy of the approach
through experiments on both synthetic renderings as well as real captured
images.Comment: 3DV 2016. Project page at http://www.ttic.edu/chakrabarti/rgbps
Conservative 3+1 General Relativistic Variable Eddington Tensor Radiation Transport Equations
We present conservative 3+1 general relativistic variable Eddington tensor
radiation transport equations, including greater elaboration of the momentum
space divergence (that is, the energy derivative term) than in previous work.
These equations are intended for use in simulations involving numerical
relativity, particularly in the absence of spherical symmetry. The independent
variables are the lab frame coordinate basis spacetime position coordinates and
the particle energy measured in the comoving frame. With an eye towards
astrophysical applications---such as core-collapse supernovae and compact
object mergers---in which the fluid includes nuclei and/or nuclear matter at
finite temperature, and in which the transported particles are neutrinos, we
pay special attention to the consistency of four-momentum and lepton number
exchange between neutrinos and the fluid, showing the term-by-term
cancellations that must occur for this consistency to be achieved.Comment: Version accepted by Phys. Rev.
General Metasurface Synthesis Based on Susceptibility Tensors
A general method, based on susceptibility tensors, is proposed for the
synthesis of metasurfaces transforming arbitrary incident waves into arbitrary
reflected and transmitted waves. The proposed method exhibits two advantages:
1)it is inherently vectorial, and therefore better suited for full vectorial
(beyond paraxial) electromagnetic problems, 2) it provides closed-form
solutions, and is therefore extremely fast. Incidentally, the method reveals
that a metasurface is fundamentally capable to transform up to four independent
wave triplets (incident, reflected and refracted waves). In addition, the paper
provides the closed-form expressions relating the synthesized susceptibilities
and the scattering parameters simulated within periodic boundary conditions,
which allows one to design the scattering particles realizing the desired
susceptibilities. The versatility of the method is illustrated by examples of
metasurfaces achieving the following transformations: generalized refraction,
reciprocal and non-reciprocal polarization rotation, Bessel vortex beam
generation, and orbital angular momentum multiplexing
Realization and Characterization of a Four-Channel Integrated Optical Young Interferometer
In this paper, we report the realization and characterization of a four-channel integrated optical Young interferometer (YI), which enables simultaneous and independent monitoring of three binding processes. The simultaneous and independent measurement of three different glucose concentrations shows the multi-purpose feature of such device. The phase resolution for different pairs of channels was /spl sim/1/spl times/10/sup -4/ fringes, which corresponds to a refractive index resolution of /spl sim/8.5/spl times/10/sup -8/ . The observed errors, which are caused due to mismatching of spatial frequencies of individual interference patterns with those determined from the CCD camera, have been reduced by using different reduction schemes. In addition, we have investigated a novel method for discrimination of the refractive index change from the thickness of a bound layer during an immunoreaction, as well as measuring the temperature change the takes place during such a process
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