364,630 research outputs found
Ultrashort pulses and short-pulse equations in dimensions
In this paper, we derive and study two versions of the short pulse equation
(SPE) in dimensions. Using Maxwell's equations as a starting point, and
suitable Kramers-Kronig formulas for the permittivity and permeability of the
medium, which are relevant, e.g., to left-handed metamaterials and dielectric
slab waveguides, we employ a multiple scales technique to obtain the relevant
models. General properties of the resulting -dimensional SPEs, including
fundamental conservation laws, as well as the Lagrangian and Hamiltonian
structure and numerical simulations for one- and two-dimensional initial data,
are presented. Ultrashort 1D breathers appear to be fairly robust, while rather
general two-dimensional localized initial conditions are transformed into
quasi-one-dimensional dispersing waveforms
Jet evolution from weak to strong coupling
Recent studies, using the AdS/CFT correspondence, of the radiation produced
by a decaying system or by an accelerated charge in the N=4 supersymmetric
Yang-Mills theory, led to a striking result: the 'supergravity backreaction',
which is supposed to describe the energy density at infinitely strong coupling,
yields exactly the same result as at zero coupling, that is, it shows no trace
of quantum broadening. We argue that this is not a real property of the
radiation at strong coupling, but an artifact of the backreaction calculation,
which is unable to faithfully capture the space-time distribution of the
radiation. This becomes obvious in the case of a decaying system ('virtual
photon'), for which the backreaction is tantamount to computing a three-point
function in the conformal gauge theory, which is independent of the coupling
since protected by symmetries. Whereas this non-renormalization property is
specific to the conformal N=4 SYM theory, we argue that the failure of the
three-point function to provide a local measurement is in fact generic: it
holds in any field theory with non-trivial interactions. To properly study a
localized distribution, one should rather compute a four-point function, as
standard in deep inelastic scattering. We substantiate these considerations
with studies of the radiation produced by the decay of a time-like photon at
both weak and strong coupling. We show that by computing four-point functions,
in perturbation theory at weak coupling and, respectively, from Witten diagrams
at strong coupling, one can follow the quantum evolution and thus demonstrate
the broadening of the energy distribution. This broadening is slow when the
coupling is weak but it proceeds as fast as possible in the limit of a strong
coupling.Comment: 49 pages, 6 figure
Weakly Enforced Boundary Conditions for the NURBS-Based Finite Cell Method
In this paper, we present a variationally consistent formulation for the weak enforcement
of essential boundary conditions as an extension to the finite cell method, a fictitious
domain method of higher order. The absence of boundary fitted elements in fictitious domain or
immersed boundary methods significantly restricts a strong enforcement of essential boundary
conditions to models where the boundary of the solution domain coincides with the embedding
analysis domain. Penalty methods and Lagrange multiplier methods are adequate means to
overcome this limitation but often suffer from various drawbacks with severe consequences for
a stable and accurate solution of the governing system of equations. In this contribution, we
follow the idea of NITSCHE [29] who developed a stable scheme for the solution of the Laplace
problem taking weak boundary conditions into account. An extension to problems from linear
elasticity shows an appropriate behavior with regard to numerical stability, accuracy and an
adequate convergence behavior. NURBS are chosen as a high-order approximation basis to
benefit from their smoothness and flexibility in the process of uniform model refinement
Data-Optimized Coronal Field Model: I. Proof of Concept
Deriving the strength and direction of the three-dimensional (3D) magnetic
field in the solar atmosphere is fundamental for understanding its dynamics.
Volume information on the magnetic field mostly relies on coupling 3D
reconstruction methods with photospheric and/or chromospheric surface vector
magnetic fields. Infrared coronal polarimetry could provide additional
information to better constrain magnetic field reconstructions. However,
combining such data with reconstruction methods is challenging, e.g., because
of the optical-thinness of the solar corona and the lack and limitations of
stereoscopic polarimetry. To address these issues, we introduce the
Data-Optimized Coronal Field Model (DOCFM) framework, a model-data fitting
approach that combines a parametrized 3D generative model, e.g., a magnetic
field extrapolation or a magnetohydrodynamic model, with forward modeling of
coronal data. We test it with a parametrized flux rope insertion method and
infrared coronal polarimetry where synthetic observations are created from a
known "ground truth" physical state. We show that this framework allows us to
accurately retrieve the ground truth 3D magnetic field of a set of force-free
field solutions from the flux rope insertion method. In observational studies,
the DOCFM will provide a means to force the solutions derived with different
reconstruction methods to satisfy additional, common, coronal constraints. The
DOCFM framework therefore opens new perspectives for the exploitation of
coronal polarimetry in magnetic field reconstructions and for developing new
techniques to more reliably infer the 3D magnetic fields that trigger solar
flares and coronal mass ejections.Comment: 14 pages, 6 figures; Accepted for publication in Ap
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