71,029 research outputs found
Dispersion in time and space: what propagating optical pulses in time (& not space) forces us to confront
I derive a temporally propagated uni-directional optical pulse equation valid
in the few cycle limit. Temporal propagation is advantageous because it
naturally preserves causality, unlike the competing spatially propagated
models. The exact coupled bi-directional equations that this approach generates
can be efficiently approximated down to a uni-directional form in cases where
an optical pulse changes little over one optical cycle. They also permit a
direct term-to-term comparison of the exact bi-directional theory with its
corresponding approximate uni-directional theory. Notably, temporal propagation
handles dispersion in a different way, and this difference serves to highlight
existing approximations inherent in spatially propagated treatments of
dispersion. Accordingly, I emphasise the need for future work in clarifying the
limitations of the dispersion conversion required by these types of approaches;
since the only alternative in the few cycle limit may be to resort to the much
more computationally intensive full Maxwell equation solvers.Comment: v3: updates and clarifications. arXiv admin note: text overlap with
arXiv:0810.568
Many-body Green's function theory for electron-phonon interactions: the Kadanoff-Baym approach to spectral properties of the Holstein dimer
We present a Kadanoff-Baym formalism to study time-dependent phenomena for
systems of interacting electrons and phonons in the framework of many-body
perturbation theory. The formalism takes correctly into account effects of the
initial preparation of an equilibrium state, and allows for an explicit
time-dependence of both the electronic and phononic degrees of freedom. The
method is applied to investigate the charge neutral and non-neutral excitation
spectra of a homogeneous, two-site, two-electron Holstein model. This is an
extension of a previous study of the ground state properties in the Hartree
(H), partially self-consistent Born (Gd) and fully self-consistent Born (GD)
approximations published in Ref. [arXiv:1403.2968]. We show that choosing a
homogeneous ground state solution leads to unstable dynamics for a sufficiently
strong interaction, and that allowing a symmetry-broken state prevents this.
The instability is caused by the bifurcation of the ground state and understood
physically to be connected with the bipolaronic crossover of the exact system.
This mean-field instability persists in the partially self-consistent Born
approximation but is not found for the fully self-consistent Born
approximation. By understanding the stability properties, we are able to study
the linear response regime by calculating the density-density response function
by time-propagation. This functions amounts to a solution of the Bethe-Salpeter
equation with a sophisticated kernel. The results indicate that none of the
approximations is able to describe the response function during or beyond the
bipolaronic crossover for the parameters investigated. Overall, we provide an
extensive discussion on when the approximations are valid, and how they fail to
describe the studied exact properties of the chosen model system.Comment: 12 figure
Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment
The optical properties of slab-like photonic crystals are often discussed on the basis of effective index (EI) approximations, where a 2-D effective refractive index profile replaces the actual 3-D structure. Our aim is to assess this approximation by analogous steps that reduce finite 2-D waveguide Bragg-gratings (to be seen as sections through 3-D PC slabs and membranes) to 1-D problems, which are tractable by common transfer matrix methods. Application of the EI method is disputable in particular in cases where locally no guided modes are supported, as in the holes of a PC membrane. A variational procedure permits to derive suitable effective permittivities even in these cases. Depending on the structural properties, these values can well turn out to be lower than one, or even be negative. Both the âstandardâ and the variational procedures are compared with reference data, generated by a rigorous 2-D Helmholtz solver, for a series of example structures.\u
Lifted Relax, Compensate and then Recover: From Approximate to Exact Lifted Probabilistic Inference
We propose an approach to lifted approximate inference for first-order
probabilistic models, such as Markov logic networks. It is based on performing
exact lifted inference in a simplified first-order model, which is found by
relaxing first-order constraints, and then compensating for the relaxation.
These simplified models can be incrementally improved by carefully recovering
constraints that have been relaxed, also at the first-order level. This leads
to a spectrum of approximations, with lifted belief propagation on one end, and
exact lifted inference on the other. We discuss how relaxation, compensation,
and recovery can be performed, all at the firstorder level, and show
empirically that our approach substantially improves on the approximations of
both propositional solvers and lifted belief propagation.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
Investigating a simple model of cutaneous wound healing angiogenesis
A simple model of wound healing angiogenesis is presented, and investigated using numerical and asymptotic techniques. The model captures many key qualitative features of the wound healing angiogenic response, such as the propagation of a structural unit into the wound centre. A detailed perturbative study is pursued, and is shown to capture all features of the model. This enables one to show that the level of the angiogenic response predicted by the model is governed to a good approximation by a small number of parameter groupings. Further investigation leads to predictions concerning how one should select between potential optimal means of stimulating cell proliferation in order to increase the level of the angiogenic response
Resonantly Damped Propagating Kink Waves in Longitudinally Stratified Solar Waveguides
It has been shown that resonant absorption is a robust physical mechanism to
explain the observed damping of magnetohydrodynamic (MHD) kink waves in the
solar atmosphere due to naturally occurring plasma inhomogeneity in the
direction transverse to the direction of the magnetic field. Theoretical
studies of this damping mechanism were greatly inspired by the first
observations of post-flare standing kink modes in coronal loops using the
Transition Region And Coronal Explorer (TRACE). More recently, these studies
have been extended to explain the attenuation of propagating coronal kink waves
observed by the Coronal Multi-Channel Polarimeter (CoMP). In the present study,
for the first time we investigate the properties of propagating kink waves in
solar waveguides including the effects of both longitudinal and transverse
plasma inhomogeneity. Importantly, it is found that the wavelength is only
dependent on the longitudinal stratification and the amplitude is simply a
product of the two effects. In light of these results the advancement of solar
atmospheric magnetoseismology by exploiting high spatial/temporal resolution
observations of propagating kink waves in magnetic waveguides to determine the
length scales of the plasma inhomogeneity along and transverse to the direction
of the magnetic field is discussed.Comment: Accepted for publication in Ap
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