241 research outputs found
Perfectly Matched Layers in a Divergence Preserving ADI Scheme for Electromagnetics
For numerical simulations of highly relativistic and transversely accelerated
charged particles including radiation fast algorithms are needed. While the
radiation in particle accelerators has wavelengths in the order of 100 um the
computational domain has dimensions roughly 5 orders of magnitude larger
resulting in very large mesh sizes. The particles are confined to a small area
of this domain only. To resolve the smallest scales close to the particles
subgrids are envisioned. For reasons of stability the alternating direction
implicit (ADI) scheme by D. N. Smithe et al. (J. Comput. Phys. 228 (2009)
pp.7289-7299) for Maxwell equations has been adopted. At the boundary of the
domain absorbing boundary conditions have to be employed to prevent reflection
of the radiation. In this paper we show how the divergence preserving ADI
scheme has to be formulated in perfectly matched layers (PML) and compare the
performance in several scenarios.Comment: 8 pages, 6 figure
Would You Choose to be Happy? Tradeoffs Between Happiness and the Other Dimensions of Life in a Large Population Survey
A large literature documents the correlates and causes of subjective well-being, or happiness. But few studies have investigated whether people choose happiness. Is happiness all that people want from life, or are they willing to sacrifice it for other attributes, such as income and health? Tackling this question has largely been the preserve of philosophers. In this article, we find out just how much happiness matters to ordinary citizens. Our sample consists of nearly 13,000 members of the UK and US general populations. We ask them to choose between, and make judgments over, lives that are high (or low) in different types of happiness and low (or high) in income, physical health, family, career success, or education. We find that people by and large choose the life that is highest in happiness but health is by far the most important other concern, with considerable numbers of people choosing to be healthy rather than happy. We discuss some possible reasons for this preference
A rapidly converging domain decomposition method for the Helmholtz equation
A new domain decomposition method is introduced for the heterogeneous 2-D and
3-D Helmholtz equations. Transmission conditions based on the perfectly matched
layer (PML) are derived that avoid artificial reflections and match incoming
and outgoing waves at the subdomain interfaces. We focus on a subdivision of
the rectangular domain into many thin subdomains along one of the axes, in
combination with a certain ordering for solving the subdomain problems and a
GMRES outer iteration. When combined with multifrontal methods, the solver has
near-linear cost in examples, due to very small iteration numbers that are
essentially independent of problem size and number of subdomains. It is to our
knowledge only the second method with this property next to the moving PML
sweeping method.Comment: 16 pages, 3 figures, 6 tables - v2 accepted for publication in the
Journal of Computational Physic
Multilayer metamaterial absorbers inspired by perfectly matched layers
We derive periodic multilayer absorbers with effective uniaxial properties
similar to perfectly matched layers (PML). This approximate representation of
PML is based on the effective medium theory and we call it an effective medium
PML (EM-PML). We compare the spatial reflection spectrum of the layered
absorbers to that of a PML material and demonstrate that after neglecting gain
and magnetic properties, the absorber remains functional. This opens a route to
create electromagnetic absorbers for real and not only numerical applications
and as an example we introduce a layered absorber for the wavelength of
~m made of SiO and NaCl. We also show that similar cylindrical
core-shell nanostructures derived from flat multilayers also exhibit very good
absorptive and reflective properties despite the different geometry
Open Boundaries for the Nonlinear Schrodinger Equation
We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF)
which is used to solve time dependent Nonlinear Schrodinger Equations (NLS).
The algorithm consists of solving the NLS on a box with periodic boundary
conditions (by any algorithm). Periodically in time we decompose the solution
into a family of coherent states. Coherent states which are outgoing are
deleted, while those which are not are kept, reducing the problem of reflected
(wrapped) waves. Numerical results are given, and rigorous error estimates are
described.
The TDPSF is compatible with spectral methods for solving the interior
problem. The TDPSF also fails gracefully, in the sense that the algorithm
notifies the user when the result is incorrect. We are aware of no other method
with this capability.Comment: 21 pages, 4 figure
Nonlinear force-free reconstruction of the global solar magnetic field: methodology
We present a novel numerical method that allows the calculation of nonlinear
force-free magnetostatic solutions above a boundary surface on which only the
distribution of the normal magnetic field component is given. The method relies
on the theory of force-free electrodynamics and applies directly to the
reconstruction of the solar coronal magnetic field for a given distribution of
the photospheric radial field component. The method works as follows: we start
with any initial magnetostatic global field configuration (e.g. zero, dipole),
and along the boundary surface we create an evolving distribution of tangential
(horizontal) electric fields that, via Faraday's equation, give rise to a
respective normal field distribution approaching asymptotically the target
distribution. At the same time, these electric fields are used as boundary
condition to numerically evolve the resulting electromagnetic field above the
boundary surface, modelled as a thin ideal plasma with non-reflecting,
perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear
force-free configuration that satisfies the given normal field distribution on
the boundary. This is different from existing methods relying on a fixed
boundary condition - the boundary evolves toward the a priori given one, at the
same time evolving the three-dimensional field solution above it. Moreover,
this is the first time a nonlinear force-free solution is reached by using only
the normal field component on the boundary. This solution is not unique, but
depends on the initial magnetic field configuration and on the evolutionary
course along the boundary surface. To our knowledge, this is the first time
that the formalism of force-free electrodynamics, used very successfully in
other astrophysical contexts, is applied to the global solar magnetic field.Comment: 18 pages, 5 figures, Solar Physic
Particle Acceleration in Pulsar Wind Nebulae: PIC modelling
We discuss the role of particle-in-cell (PIC) simulations in unveiling the
origin of the emitting particles in PWNe. After describing the basics of the
PIC technique, we summarize its implications for the quiescent and the flaring
emission of the Crab Nebula, as a prototype of PWNe. A consensus seems to be
emerging that, in addition to the standard scenario of particle acceleration
via the Fermi process at the termination shock of the pulsar wind, magnetic
reconnection in the wind, at the termination shock and in the Nebula plays a
major role in powering the multi-wavelength signatures of PWNe.Comment: 32 pages, 16 figures, to appear in the book "Modelling Nebulae"
edited by D. Torres for Springer, based on the invited contributions to the
workshop held in Sant Cugat (Barcelona), June 14-17, 201
Negative refraction and left-handed behavior in two-dimensional photonic crystals
We systematically examine the conditions of obtaining left-handed (LH)
behavior in photonic crystals. Detailed studies of the phase and group
velocities as well as the phase np and group ng refractive index are given. The
existence of negative refraction does not guarantee the existence of negative
index of refraction and so LH behavior. A wedge type of experiment is suggested
that can unambiguously distiguinsh between cases of negative refraction that
occur when left-handed behavior is present, from cases that show negative
refraction without LH behavior.Comment: 4 pages 4 figures, submitted to Phys. Rev. B Rapid Communication
Exciton-photon interaction in a quantum dot embedded in a photonic microcavity
We present a detailed analysis of exciton-photon interaction in a microcavity
made out of a photonic crystal slab. Here we have analyzed a disk-like quantum
dot where an exciton is formed. Excitonic eigen-functions in addition to their
eigen-energies are found through direct matrix diagonalization, while wave
functions corresponding to unbound electron and hole are chosen as the basis
set for this procedure. In order to evaluate these wave functions precisely, we
have used Luttinger Hamiltonian in the case of hole while ignoring bands
adjacent to conduction band for electron states. After analyzing Excitonic
states, a photonic crystal based microcavity with a relatively high quality
factor mode has been proposed and its lattice constant has been adjusted to
obtain the prescribed resonant frequency. We use finite-difference time-domain
method in order to simulate our cavity with sufficient precision. Finally, we
formulate the coupling constants for exciton-photon interaction both where
intra-band and inter-band transitions occur. By evaluating a sample coupling
constant, it has been shown that the system can be in strong coupling regime
and Rabi oscillations can occur for Excitonic state population.Comment: Journal of Physics B: Atomic and Molecular Physics (to appear
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