152,402 research outputs found
Stable embedded solitons
Stable embedded solitons are discovered in the generalized third-order
nonlinear Schroedinger equation. When this equation can be reduced to a
perturbed complex modified KdV equation, we developed a soliton perturbation
theory which shows that a continuous family of sech-shaped embedded solitons
exist and are nonlinearly stable. These analytical results are confirmed by our
numerical simulations. These results establish that, contrary to previous
beliefs, embedded solitons can be robust despite being in resonance with the
linear spectrum.Comment: 2 figures. To appear in Phys. Rev. Let
Accuracy of the domain method for the material derivative approach to shape design sensitivities
Numerical accuracy for the boundary and domain methods of the material derivative approach to shape design sensitivities is investigated through the use of mesh refinement. The results show that the domain method is generally more accurate than the boundary method, using the finite element technique. It is also shown that the domain method is equivalent, under certain assumptions, to the implicit differentiation approach not only theoretically but also numerically
Antiferromagnetic Alignment and Relaxation Rate of Gd Spins in the High Temperature Superconductor GdBa_2Cu_3O_(7-delta)
The complex surface impedance of a number of GdBaCuO
single crystals has been measured at 10, 15 and 21 GHz using a cavity
perturbation technique. At low temperatures a marked increase in the effective
penetration depth and surface resistance is observed associated with the
paramagnetic and antiferromagnetic alignment of the Gd spins. The effective
penetration depth has a sharp change in slope at the N\'eel temperature, ,
and the surface resistance peaks at a frequency dependent temperature below 3K.
The observed temperature and frequency dependence can be described by a model
which assumes a negligibly small interaction between the Gd spins and the
electrons in the superconducting state, with a frequency dependent magnetic
susceptibility and a Gd spin relaxation time being a strong function
of temperature. Above , has a component varying as , while below it increases .Comment: 4 Pages, 4 Figures. Submitted to Phys. Rev.
Revealing local failed supernovae with neutrino telescopes
We study the detectability of neutrino bursts from nearby direct black
hole-forming collapses (failed supernovae) at Megaton detectors. Due to their
high energetics, these bursts could be identified - by the time coincidence of
N >= 2 or N >= 3 events within a ~ 1 s time window - from as far as ~ 4-5 Mpc
away. This distance encloses several supernova-rich galaxies, so that failed
supernova bursts could be detected at a rate of up to one per decade,
comparable to the expected rate of the more common, but less energetic, neutron
star-forming collapses. Thus, the detection of a failed supernova within the
lifetime of a Mt detector is realistic. It might give the first evidence of
direct black hole formation, with important implications on the physics of this
phenomenon.Comment: LaTeX, 4 pages, 4 figures; minor changes to the text, results
unchange
A scalar nonlocal bifurcation of solitary waves for coupled nonlinear Schroedinger systems
An explanation is given for previous numerical results which suggest a
certain bifurcation of `vector solitons' from scalar (single-component)
solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcation
in question is nonlocal in the sense that the vector soliton does not have a
small-amplitude component, but instead approaches a solitary wave of one
component with two infinitely far-separated waves in the other component. Yet,
it is argued that this highly nonlocal event can be predicted from a purely
local analysis of the central solitary wave alone. Specifically the
linearisation around the central wave should contain asymptotics which grow at
precisely the speed of the other-component solitary waves on the two wings.
This approximate argument is supported by both a detailed analysis based on
matched asymptotic expansions, and numerical experiments on two example
systems. The first is the usual coupled NLS system involving an arbitrary ratio
between the self-phase and cross-phase modulation terms, and the second is a
coupled NLS system with saturable nonlinearity that has recently been
demonstrated to support stable multi-peaked solitary waves. The asymptotic
analysis further reveals that when the curves which define the proposed
criterion for scalar nonlocal bifurcations intersect with boundaries of certain
local bifurcations, the nonlocal bifurcation could turn from scalar to
non-scalar at the intersection. This phenomenon is observed in the first
example. Lastly, we have also selectively tested the linear stability of
several solitary waves just born out of scalar nonlocal bifurcations. We found
that they are linearly unstable. However, they can lead to stable solitary
waves through parameter continuation.Comment: To appear in Nonlinearit
Emergent Geometry and Quantum Gravity
We explain how quantum gravity can be defined by quantizing spacetime itself.
A pinpoint is that the gravitational constant G = L_P^2 whose physical
dimension is of (length)^2 in natural unit introduces a symplectic structure of
spacetime which causes a noncommutative spacetime at the Planck scale L_P. The
symplectic structure of spacetime M leads to an isomorphism between symplectic
geometry (M, \omega) and Riemannian geometry (M, g) where the deformations of
symplectic structure \omega in terms of electromagnetic fields F=dA are
transformed into those of Riemannian metric g. This approach for quantum
gravity allows a background independent formulation where spacetime as well as
matter fields is equally emergent from a universal vacuum of quantum gravity
which is thus dubbed as the quantum equivalence principle.Comment: Invited Review for Mod. Phys. Lett. A, 17 page
Shape optimization of three-dimensional stamped and solid automotive components
The shape optimization of realistic, 3-D automotive components is discussed. The integration of the major parts of the total process: modeling, mesh generation, finite element and sensitivity analysis, and optimization are stressed. Stamped components and solid components are treated separately. For stamped parts a highly automated capability was developed. The problem description is based upon a parameterized boundary design element concept for the definition of the geometry. Automatic triangulation and adaptive mesh refinement are used to provide an automated analysis capability which requires only boundary data and takes into account sensitivity of the solution accuracy to boundary shape. For solid components a general extension of the 2-D boundary design element concept has not been achieved. In this case, the parameterized surface shape is provided using a generic modeling concept based upon isoparametric mapping patches which also serves as the mesh generator. Emphasis is placed upon the coupling of optimization with a commercially available finite element program. To do this it is necessary to modularize the program architecture and obtain shape design sensitivities using the material derivative approach so that only boundary solution data is needed
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