25,107 research outputs found
Bayesian Coronal Seismology
In contrast to the situation in a laboratory, the study of the solar
atmosphere has to be pursued without direct access to the physical conditions
of interest. Information is therefore incomplete and uncertain and inference
methods need to be employed to diagnose the physical conditions and processes.
One of such methods, solar atmospheric seismology, makes use of observed and
theoretically predicted properties of waves to infer plasma and magnetic field
properties. A recent development in solar atmospheric seismology consists in
the use of inversion and model comparison methods based on Bayesian analysis.
In this paper, the philosophy and methodology of Bayesian analysis are first
explained. Then, we provide an account of what has been achieved so far from
the application of these techniques to solar atmospheric seismology and a
prospect of possible future extensions.Comment: 19 pages, accepted in Advances in Space Researc
Dark-in-Bright Solitons in Bose-Einstein Condensates with Attractive Interactions
We demonstrate a possibility to generate localized states in effectively
one-dimensional Bose-Einstein condensates with a negative scattering length in
the form of a dark soliton in the presence of an optical lattice (OL) and/or a
parabolic magnetic trap. We connect such structures with twisted localized
modes (TLMs) that were previously found in the discrete nonlinear
Schr{\"o}dinger equation. Families of these structures are found as functions
of the OL strength, tightness of the magnetic trap, and chemical potential, and
their stability regions are identified. Stable bound states of two TLMs are
also found. In the case when the TLMs are unstable, their evolution is
investigated by means of direct simulations, demonstrating that they transform
into large-amplitude fundamental solitons. An analytical approach is also
developed, showing that two or several fundamental solitons, with the phase
shift between adjacent ones, may form stable bound states, with
parameters quite close to those of the TLMs revealed by simulations. TLM
structures are found numerically and explained analytically also in the case
when the OL is absent, the condensate being confined only by the magnetic trap.Comment: 13 pages, 7 figures, New Journal of Physics (in press
How does an interacting many-body system tunnel through a potential barrier to open space?
The tunneling process in a many-body system is a phenomenon which lies at the
very heart of quantum mechanics. It appears in nature in the form of
alpha-decay, fusion and fission in nuclear physics, photoassociation and
photodissociation in biology and chemistry. A detailed theoretical description
of the decay process in these systems is a very cumbersome problem, either
because of very complicated or even unknown interparticle interactions or due
to a large number of constitutent particles. In this work, we theoretically
study the phenomenon of quantum many-body tunneling in a more transparent and
controllable physical system, in an ultracold atomic gas. We analyze a full,
numerically exact many-body solution of the Schr\"odinger equation of a
one-dimensional system with repulsive interactions tunneling to open space. We
show how the emitted particles dissociate or fragment from the trapped and
coherent source of bosons: the overall many-particle decay process is a quantum
interference of single-particle tunneling processes emerging from sources with
different particle numbers taking place simultaneously. The close relation to
atom lasers and ionization processes allows us to unveil the great relevance of
many-body correlations between the emitted and trapped fractions of the
wavefunction in the respective processes.Comment: 18 pages, 4 figures (7 pages, 2 figures supplementary information
Adiabatic Compression of Soliton Matter Waves
The evolution of atomic solitary waves in Bose-Einstein condensate (BEC)
under adiabatic changes of the atomic scattering length is investigated. The
variations of amplitude, width, and velocity of soliton are found for both
spatial and time adiabatic variations. The possibility to use these variations
to compress solitons up to very high local matter densities is shown both in
absence and in presence of a parabolic confining potential.Comment: to appear in J.Phys.
Statistical state dynamics of weak jets in barotropic beta-plane turbulence
Zonal jets in a barotropic setup emerge out of homogeneous turbulence through
a flow-forming instability of the homogeneous turbulent state (`zonostrophic
instability') which occurs as the turbulence intensity increases. This has been
demonstrated using the statistical state dynamics (SSD) framework with a
closure at second order. Furthermore, it was shown that for small
supercriticality the flow-forming instability follows Ginzburg-Landau (G-L)
dynamics. Here, the SSD framework is used to study the equilibration of this
flow-forming instability for small supercriticality. First, we compare the
predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD
dynamics closed at second order for a wide ranges of parameters. A new branch
of jet equilibria is revealed that is not contiguously connected with the G-L
branch. This new branch at weak supercriticalities involves jets with larger
amplitude compared to the ones of the G-L branch. Furthermore, this new branch
continues even for subcritical values with respect to the linear flow-forming
instability. Thus, a new nonlinear flow-forming instability out of homogeneous
turbulence is revealed. Second, we investigate how both the linear flow-forming
instability and the novel nonlinear flow-forming instability are equilibrated.
We identify the physical processes underlying the jet equilibration as well as
the types of eddies that contribute in each process. Third, we propose a
modification of the diffusion coefficient of the G-L dynamics that is able to
capture the asymmetric evolution for weak jets at scales other than the
marginal scale (side-band instabilities) for the linear flow-forming
instability.Comment: 27 pages, 17 figure
Preconditioned fully implicit PDE solvers for monument conservation
Mathematical models for the description, in a quantitative way, of the
damages induced on the monuments by the action of specific pollutants are often
systems of nonlinear, possibly degenerate, parabolic equations. Although some
the asymptotic properties of the solutions are known, for a short window of
time, one needs a numerical approximation scheme in order to have a
quantitative forecast at any time of interest. In this paper a fully implicit
numerical method is proposed, analyzed and numerically tested for parabolic
equations of porous media type and on a systems of two PDEs that models the
sulfation of marble in monuments. Due to the nonlinear nature of the underlying
mathematical model, the use of a fixed point scheme is required and every step
implies the solution of large, locally structured, linear systems. A special
effort is devoted to the spectral analysis of the relevant matrices and to the
design of appropriate iterative or multi-iterative solvers, with special
attention to preconditioned Krylov methods and to multigrid procedures.
Numerical experiments for the validation of the analysis complement this
contribution.Comment: 26 pages, 13 figure
Nonlinear dynamics of Bose-condensed gases by means of a low- to high-density variational approach
We propose a versatile variational method to investigate the spatio-temporal
dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this
end we employ a \emph{q}-Gaussian trial wave-function that interpolates between
the low- and the high-density limit of the ground state of a Bose-condensed
gas. Our main result consists of reducing the Gross-Pitaevskii equation, a
nonlinear partial differential equation describing the T=0 dynamics of the
condensate, to a set of only three equations: \emph{two coupled nonlinear
ordinary differential equations} describing the phase and the curvature of the
wave-function and \emph{a separate algebraic equation} yielding the generalized
width. Our equations recover those of the usual Gaussian variational approach
(in the low-density regime), and the hydrodynamic equations that describe the
high-density regime. Finally, we show a detailed comparison between the
numerical results of our equations and those of the original Gross-Pitaevskii
equation.Comment: 11 pages, 12 figures, submitted to Phys. Rev. A, January 200
Generation of highly inclined protoplanetary discs through single stellar flybys
We study the three-dimensional evolution of a viscous protoplanetary disc
which is perturbed by a passing star on a parabolic orbit. The aim is to test
whether a single stellar flyby is capable to excite significant disc
inclinations which would favour the formation of so-called misaligned planets.
We use smoothed particle hydrodynamics to study inclination, disc mass and
angular momentum changes of the disc for passing stars with different masses.
We explore different orbital configurations for the perturber's orbit to find
the parameter spaces which allow significant disc inclination generation.
Prograde inclined parabolic orbits are most destructive leading to significant
disc mass and angular momentum loss. In the remaining disc, the final disc
inclination is only below . This is due to the removal of disc
particles which have experienced the strongest perturbing effects. Retrograde
inclined parabolic orbits are less destructive and can generate disc
inclinations up to . The final disc orientation is determined by the
precession of the disc angular momentum vector about the perturber's orbital
angular momentum vector and by disc orbital inclination changes.
We propose a sequence of stellar flybys for the generation of misalignment
angles above . The results taken together show that stellar flybys
are promising and realistic for the explanation of misaligned Hot Jupiters with
misalignment angles up to 60\degr.Comment: 15 pages, 15 figures, accepted for publication in MNRA
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