3,184 research outputs found
Fermion self-trapping in the optical geometry of Einstein-Dirac solitons
Funding: St Leonards scholarship from the University of St Andrews and from UKRI under EPSRC Grant No. EP/R513337/1 (P.E.D.L).We analyze gravitationally localized states of multiple fermions with high angular momenta, in the formalism introduced by Finster, Smoller, and Yau [Phys Rev. D 59, 104020 (1999)]. We show that the resulting solitonlike wave functions can be naturally interpreted in terms of a form of self-trapping, where the fermions become localized on shells the locations of which correspond to those of âbulgesâ in the optical geometry created by their own energy density.Publisher PDFPeer reviewe
Nonlinear effects in the excited states of many-fermion Einstein-Dirac solitons
Funding: P. E. D. L. acknowledges funding from a St Leonards scholarship from the University of St Andrews and from UKRI under EPSRC Grant No. EP/R513337/1.We present an analysis of excited-state solutions for a gravitationally localized system consisting of a filled shell of high-angular-momentum fermions, using the Einstein-Dirac formalism introduced by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)]. We show that, even when the particle number is relatively low (Nf â„ 6), the increased nonlinearity in the system causes a significant deviation in behavior from the two-fermion case. Excited-state solutions can no longer be uniquely identified by the value of their central redshift, with this multiplicity producing distortions in the characteristic spiraling forms of the mass-radius relations. We discuss the connection between this effect and the internal structure of solutions in the relativistic regime.Publisher PDFPeer reviewe
Differential approximation for Kelvin-wave turbulence
I present a nonlinear differential equation model (DAM) for the spectrum of
Kelvin waves on a thin vortex filament. This model preserves the original
scaling of the six-wave kinetic equation, its direct and inverse cascade
solutions, as well as the thermodynamic equilibrium spectra. Further, I extend
DAM to include the effect of sound radiation by Kelvin waves. I show that,
because of the phonon radiation, the turbulence spectrum ends at a maximum
frequency where
is the total energy injection rate, is the speed of sound and
is the quantum of circulation.Comment: Prepared of publication in JETP Letter
Modeling Kelvin wave cascades in superfluid helium
We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM
Gain-scheduled controller design: An analytic framework directly incorporating non-equilibrium plant dynamics
Solution to the twin image problem in holography
While the invention of holography by Dennis Gabor truly constitutes an
ingenious concept, it has ever since been troubled by the so called twin image
problem limiting the information that can be obtained from a holographic
record. Due to symmetry reasons there are always two images appearing in the
reconstruction process. Thus, the reconstructed object is obscured by its
unwanted out of focus twin image. Especially for emission electron as well as
for x- and gamma-ray holography, where the source-object distances are small,
the reconstructed images of atoms are very close to their twin images from
which they can hardly be distinguished. In some particular instances only,
experimental efforts could remove the twin images. More recently, numerical
methods to diminish the effect of the twin image have been proposed but are
limited to purely absorbing objects failing to account for phase shifts caused
by the object. Here we show a universal method to reconstruct a hologram
completely free of twin images disturbance while no assumptions about the
object need to be imposed. Both, amplitude and true phase distributions are
retrieved without distortion
Predictability in Systems with Many Characteristic Times: The Case of Turbulence
In chaotic dynamical systems, an infinitesimal perturbation is exponentially
amplified at a time-rate given by the inverse of the maximum Lyapunov exponent
. In fully developed turbulence, grows as a power of the
Reynolds number. This result could seem in contrast with phenomenological
arguments suggesting that, as a consequence of `physical' perturbations, the
predictability time is roughly given by the characteristic life-time of the
large scale structures, and hence independent of the Reynolds number. We show
that such a situation is present in generic systems with many degrees of
freedom, since the growth of a non-infinitesimal perturbation is determined by
cumulative effects of many different characteristic times and is unrelated to
the maximum Lyapunov exponent. Our results are illustrated in a chain of
coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed
with uufile
Improved linear response for stochastically driven systems
The recently developed short-time linear response algorithm, which predicts
the average response of a nonlinear chaotic system with forcing and dissipation
to small external perturbation, generally yields high precision of the response
prediction, although suffers from numerical instability for long response times
due to positive Lyapunov exponents. However, in the case of stochastically
driven dynamics, one typically resorts to the classical fluctuation-dissipation
formula, which has the drawback of explicitly requiring the probability density
of the statistical state together with its derivative for computation, which
might not be available with sufficient precision in the case of complex
dynamics (usually a Gaussian approximation is used). Here we adapt the
short-time linear response formula for stochastically driven dynamics, and
observe that, for short and moderate response times before numerical
instability develops, it is generally superior to the classical formula with
Gaussian approximation for both the additive and multiplicative stochastic
forcing. Additionally, a suitable blending with classical formula for longer
response times eliminates numerical instability and provides an improved
response prediction even for long response times
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