6,197 research outputs found
Moser-Trudinger inequality on conformal discs
We show that the Moser-Trudinger inequality holds in a conformal disc if and
only if the metric is bounded from above by the Hyperbolic metric. We also find
a necessary and sufficient condition for the Moser-Trudinger inequality to hold
in an unbounded subset of the two dimensional Euclidean space
Modeling quasi-static magnetohydrodynamic turbulence with variable energy flux
In quasi-static MHD, experiments and numerical simulations reveal that the
energy spectrum is steeper than Kolmogorov's spectrum. To explain
this observation, we construct turbulence models based on variable energy flux,
which is caused by the Joule dissipation. In the first model, which is
applicable to small interaction parameters, the energy spectrum is a power law,
but with a spectral exponent steeper than -5/3. In the other limit of large
interaction parameters, the second model predicts an exponential energy
spectrum and flux. The model predictions are in good agreement with the
numerical results.Comment: 16 pages, 5 figure
Mobile vector soliton in a spin-orbit coupled spin- condensate
We study the formation of bound states and three-component bright vector
solitons in a quasi-one-dimensional spin-orbit-coupled hyperfine spin
Bose-Einstein condensate using numerical solution and variational approximation
of a mean-field model. In the antiferromagnetic domain, the solutions are
time-reversal symmetric, and the component densities have multi-peak structure.
In the ferromagnetic domain, the solutions violate time-reversal symmetry, and
the component densities have single-peak structure. The dynamics of the system
is not Galelian invariant. From an analysis of Galelian invariance, we
establish that the single-peak ferromagnetic vector solitons are true solitons
and can move maintaining constant component densities, whereas the
antiferromagnetic solitons cannot move with constant component densities
Vector solitons in a spin-orbit coupled spin- Bose-Einstein condensate
Five-component minimum-energy bound states and mobile vector solitons of a
spin-orbit-coupled quasi-one-dimensional hyperfine-spin-2 Bose-Einstein
condensate are studied using the numerical solution and variational
approximation of a mean-field model. Two distinct types of solutions with
single-peak and multi-peak density distribution of the components are
identified in different domains of interaction parameters. From an analysis of
Galilean invariance and time-reversal symmetry of the Hamiltonian, we establish
that vector solitons with multi-peak density distribution preserve
time-reversal symmetry, but cannot propagate maintaining the shape of
individual components. However, those with single-peak density distribution
violate time-reversal symmetry of the Hamiltonian, but can propagate with a
constant velocity maintaining the shape of individual components
Nonesophageal Eosinophilic Gastrointestinal Disorders: Clinical Care and Future Directions
Eosinophilic gastrointestinal disorders are a set of conditions with a wide range of clinical manifestations and treatment modalities. The disorders are suspected to result from an abnormal inflammatory response to allergen(s), and individuals may develop a relapsing or chronic disease, if the allergen is not eliminated. Mechanisms of disease pathogenesis, including the humoral immune response, need to be fully elucidated. A variety of therapies are used, though there is a lack of well-defined randomized, prospective studies. Other therapeutic options are needed as the current treatments have potential concerns; elimination diets may impair a child’s quality of life, and corticosteroids have adverse risks with long-term use. We review what is known about non-esophageal eosinophilic gastrointestinal disorders, and discuss research investigations which need to be conducted to facilitate diagnosis and enhance treatment methods
Phase separation in a spin-orbit coupled Bose-Einstein condensate
We study a spin-orbit (SO) coupled hyperfine spin-1 Bose-Einstein condensate
(BEC) in a quasi-one-dimensional trap. For a SO-coupled BEC in a
one-dimensional box, we show that in the absence of the Rabi term, any non-zero
value of SO coupling will result in a phase separation among the components for
a ferromagnetic BEC, like Rb. On the other hand, SO coupling favors
miscibility in a polar BEC, like Na. In the presence of a harmonic trap,
which favors miscibility, a ferromagnetic BEC phase separates, provided the
SO-coupling strength and number of atoms are greater than some critical value.
The Rabi term favors miscibility irrespective of the nature of the spin
interaction: ferromagnetic or polar
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