3,282 research outputs found
Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice
We predict new generic types of vorticity-carrying soliton complexes in a
class of physical systems including an attractive Bose-Einstein condensate in a
square optical lattice (OL) and photonic lattices in photorefractive media. The
patterns include ring-shaped higher-order vortex solitons and supervortices.
Stability diagrams for these patterns, based on direct simulations, are
presented. The vortex ring solitons are stable if the phase difference \Delta
\phi between adjacent solitons in the ring is larger than \pi/2, while the
supervortices are stable in the opposite case, \Delta \phi <\pi /2. A
qualitative explanation to the stability is given.Comment: 9 pages, 4 figure
Stable two-dimensional solitons in nonlinear lattices
We address the existence and stability of two-dimensional solitons in optical
or matter-wave media, which are supported by purely nonlinear lattices in the
form of a periodic array of cylinders with self-focusing nonlinearity, embedded
into a linear material. We show that such lattices can stabilize
two-dimensional solitons against collapse. We also found that stable multipoles
and vortex solitons are also supported by the nonlinear lattices, provided that
the nonlinearity exhibits saturation.Comment: 12 pages, 3 figures, to appear in Optics Letter
Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index
We address vortex solitons supported by optical lattices featuring modulation
of both the linear and nonlinear refractive indices. We find that when the
modulation is out-of-phase the competition between both effects results in
remarkable shape transformations of the solitons which profoundly affect their
properties and stability. Nonlinear refractive index modulation is found to
impose restrictions on the maximal power of off-site solitons, which are shown
to be stable only below a maximum nonlinearity modulation depth.Comment: 11 pages, 3 figures, to appear in Optics Letter
Model for hypernucleus production in heavy ion collisions
We estimate the production cross sections of hypernuclei in projectile like
fragment (PLF) in heavy ion collisions. The discussed scenario for the
formation cross section of hypernucleus is: (a) Lambda particles are produced
in the participant region but have a considerable rapidity spread and (b)
Lambda with rapidity close to that of the PLF and total momentum (in the rest
system of PLF) up to Fermi motion can then be trapped and produce hypernuclei.
The process (a) is considered here within Heavy Ion Jet Interacting Generator
HIJING-BBbar model and the process (b) in the canonical thermodynamic model
(CTM). We estimate the production cross-sections for light hypernuclei for C +
C at 3.7 GeV total nucleon-nucleon center of mass energy and for Ne+Ne and
Ar+Ar collisions at 5.0 GeV. By taking into account explicitly the impact
parameter dependence of the colliding systems, it is found that the cross
section is different from that predicted by the coalescence model and large
discrepancy is obtained for 6_He and 9_Be hypernuclei.Comment: 9 pages, 4 figures, 3 tables, revtex4, added reference
The Auxiliary Field Method in Quantum Mechanical Four-Fermi Models -- A Study Toward Chiral Condensation in QED
A study for checking validity of the auxiliary field method (AFM) is made in
quantum mechanical four-fermi models which act as a prototype of models for
chiral symmetry breaking in Quantum Electrodynamics. It has been shown that
AFM, defined by an insertion of Gaussian identity to path integral formulas and
by the loop expansion, becomes more accurate when taking higher order terms
into account under the bosonic model with a quartic coupling in 0- and
1-dimensions as well as the model with a four-fermi interaction in 0-dimension.
The case is also confirmed in terms of two models with the four-fermi
interaction among species in 1-dimension (the quantum mechanical four-fermi
models): higher order corrections lead us toward the exact energy of the ground
state. It is found that the second model belongs to a WKB-exact class that has
no higher order corrections other than the lowest correction. Discussions are
also made for unreliability on the continuous time representation of path
integration and for a new model of QED as a suitable probe for chiral symmetry
breaking.Comment: 30 pages, 12 figure
Ratio control in a cascade model of cell differentiation
We propose a kind of reaction-diffusion equations for cell differentiation,
which exhibits the Turing instability. If the diffusivity of some variables is
set to be infinity, we get coupled competitive reaction-diffusion equations
with a global feedback term. The size ratio of each cell type is controlled by
a system parameter in the model. Finally, we extend the model to a cascade
model of cell differentiation. A hierarchical spatial structure appears as a
result of the cell differentiation. The size ratio of each cell type is also
controlled by the system parameter.Comment: 13 pages, 7 figure
Resonant nonlinearity management for nonlinear-Schr\"{o}dinger solitons
We consider effects of a periodic modulation of the nonlinearity coefficient
on fundamental and higher-order solitons in the one-dimensional NLS equation,
which is an issue of direct interest to Bose-Einstein condensates in the
context of the Feshbach-resonance control, and fiber-optic telecommunications
as concerns periodic compensation of the nonlinearity. We find from
simulations, and explain by means of a straightforward analysis, that the
response of a fundamental soliton to the weak perturbation is resonant, if the
modulation frequency is close to the intrinsic frequency of the
soliton. For higher-order -solitons with and 3, the response to an
extremely weak perturbation is also resonant, if is close to the
corresponding intrinsic frequency. More importantly, a slightly stronger drive
splits the 2- or 3-soliton, respectively, into a set of two or three moving
fundamental solitons. The dependence of the threshold perturbation amplitude,
necessary for the splitting, on has a resonant character too.
Amplitudes and velocities of the emerging fundamental solitons are accurately
predicted, using exact and approximate conservation laws of the perturbed NLS
equation.Comment: 14 pages, 6 figure
Shock structures in time averaged patterns for the Kuramoto-Sivashinsky equation
The Kuramoto-Sivashinsky equation with fixed boundary conditions is
numerically studied. Shocklike structures appear in the time-averaged patterns
for some parameter range of the boundary values. Effective diffusion constant
is estimated from the relation of the width and the height of the shock
structures.Comment: 6 pages, 7 figure
Cascade Failure in a Phase Model of Power Grids
We propose a phase model to study cascade failure in power grids composed of
generators and loads. If the power demand is below a critical value, the model
system of power grids maintains the standard frequency by feedback control. On
the other hand, if the power demand exceeds the critical value, an electric
failure occurs via step out (loss of synchronization) or voltage collapse. The
two failures are incorporated as two removal rules of generator nodes and load
nodes. We perform direct numerical simulation of the phase model on a
scale-free network and compare the results with a mean-field approximation.Comment: 7 pages, 2 figure
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