649 research outputs found
Dissipative Dynamics of Matter Wave Soliton in Nonlinear Optical Lattice
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein
condensates (BEC), with low-dimensional (1D) conservative plus dissipative
nonlinear optical lattices are investigated. In the case of focusing media
(with attractive atomic systems) the collapse of the wave packet is arrested by
the dissipative periodic nonlinearity. The adiabatic variation of the
background scattering length leads to metastable matter-wave solitons.
When the atom feeding mechanism is used, a dissipative soliton can exist in
focusing 2D media with 1D periodic nonlinearity. In the defocusing media
(repulsive BEC case) with harmonic trap in one dimension and one dimensional
nonlinear optical lattice in other direction, the stable soliton can exist.
This prediction of variational approach is confirmed by the full numerical
simulation of 2D Gross-Pitaevskii equation.Comment: 9 pages, 8 figure
Modelling segmental duplications in the human genome
Background: Segmental duplications (SDs) are long DNA sequences that are repeated in a genome and have high sequence identity. In contrast to repetitive elements they are often unique and only sometimes have multiple copies in a genome. There are several well-studied mechanisms responsible for segmental duplications: non-allelic homologous recombination, non-homologous end joining and replication slippage. Such duplications play an important role in evolution, however, we do not have a full understanding of the dynamic properties of the duplication process. Results: We study segmental duplications through a graph representation where nodes represent genomic regions and edges represent duplications between them. The resulting network (the SD network) is quite complex and has distinct features which allow us to make inference on the evolution of segmantal duplications. We come up with the network growth model that explains features of the SD network thus giving us insights on dynamics of segmental duplications in the human genome. Based on our analysis of genomes of other species the network growth model seems to be applicable for multiple mammalian genomes. Conclusions: Our analysis suggests that duplication rates of genomic loci grow linearly with the number of copies of a duplicated region. Several scenarios explaining such a preferential duplication rates were suggested
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.
Stable two-dimensional dispersion-managed soliton
The existence of a dispersion-managed soliton in two-dimensional nonlinear
Schr\"odinger equation with periodically varying dispersion has been explored.
The averaged equations for the soliton width and chirp are obtained which
successfully describe the long time evolution of the soliton. The slow dynamics
of the soliton around the fixed points for the width and chirp are investigated
and the corresponding frequencies are calculated. Analytical predictions are
confirmed by direct PDE and ODE simulations. Application to a Bose-Einstein
condensate in optical lattice is discussed. The existence of a
dispersion-managed matter-wave soliton in such system is shown.Comment: 4 pages, 3 figures, Submitted to Phys. Rev.
Pulse confinement in optical fibers with random dispersion
Short range correlated uniform noise in the dispersion coefficient, inherent
in many types of optical fibers, broadens and eventually destroys all initially
ultra-short pulses. However, under the constraint that the integral of the
random component of the dispersion coefficient is set to zero, or pinned,
periodically or quasi-periodically along the fiber, the nature of the pulse
propagation changes dramatically. For the case that randomness is added to
constant positive dispersion, the pinning restriction significantly reduces
pulse broadening. If the randomness is added to piecewise constant periodic
dispersion, the pinning may even provide probability distributions of pulse
parameters that are numerically indistinguishable from the statistically steady
case. The pinning method can be used to both manufacture better fibers and
upgrade existing fiber links.Comment: 4 pages, 2 figure
Faraday waves in quasi-one-dimensional superfluid Fermi-Bose mixtures
Generation of Faraday waves in superfluid Fermi-Bose mixtures in elongated
traps is investigated. The generation of waves is achieved by periodically
changing a parameter of the system in time. Two types of modulations of
parameters are considered, first a variation of the fermion-bosons scattering
length, and secondly the boson-boson scattering length. We predict the
properties of the generated Faraday patterns and study the parameter regions
where they can be excited.Comment: Final published versio
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