5,056 research outputs found
Vortex stability in nearly two-dimensional Bose-Einstein condensates with attraction
We perform accurate investigation of stability of localized vortices in an
effectively two-dimensional ("pancake-shaped") trapped BEC with negative
scattering length. The analysis combines computation of the stability
eigenvalues and direct simulations. The states with vorticity S=1 are stable in
a third of their existence region, , where is
the number of atoms, and is the corresponding collapse
threshold. Stable vortices easily self-trap from arbitrary initial
configurations with embedded vorticity. In an adjacent interval, , the unstable vortex
periodically splits in two fragments and recombines. At , the fragments do not recombine, as each one collapses by
itself. The results are compared with those in the full 3D Gross-Pitaevskii
equation. In a moderately anisotropic 3D configuration, with the aspect ratio
, the stability interval of the S=1 vortices occupies
of their existence region, hence the 2D limit provides for a reasonable
approximation in this case. For the isotropic 3D configuration, the stability
interval expands to 65% of the existence domain. Overall, the vorticity
heightens the actual collapse threshold by a factor of up to 2. All vortices
with are unstable.Comment: 21 pages, 8 figures, to appear in Physical Review
Slow Quenches Produce Fuzzy, Transient Vortices
We examine the Zurek scenario for the production of vortices in quenches of
liquid in the light of recent experiments. Extending our previous
results to later times, we argue that short wavelength thermal fluctuations
make vortices poorly defined until after the transition has occurred. Further,
if and when vortices appear, it is plausible that that they will decay faster
than anticipated from turbulence experiments, irrespective of quench rates.Comment: 4 pages, Revtex file, no figures Apart from a more appropriate title,
this paper differs from its predecessor by including temperature, as well as
pressure, quenche
Non-Ground-State Bose-Einstein Condensates of Trapped Atoms
The possibility of creating a Bose condensate of trapped atoms in a
non-ground state is suggested. Such a nonequilibrium Bose condensate can be
formed if one, first, obtains the conventional Bose condensate in the ground
state and then transfers the condensed atoms to a non-ground state by means of
a resonance pumping. The properties of ground and non-ground states are
compared and plausible applications of such nonequilibrium condensates are
discussed.Comment: 1 file, 16 pages, RevTe
DNA methylation in human epigenomes depends on local topology of CpG sites
In vertebrates, methylation of cytosine at CpG sequences is implicated in stable and heritable patterns of gene expression. The classical model for inheritance, in which individual CpG sites are independent, provides no explanation for the observed non-random patterns of methylation. We first investigate the exact topology of CpG clustering in the human genome associated to CpG islands. Then, by pooling genomic CpG clusters on the basis of short distances between CpGs within and long distances outside clusters, we show a strong dependence of methylation on the number and density of CpG organization. CpG clusters with fewer, or less densely spaced, CpGs are predominantly hyper-methylated, while larger clusters are predominantly hypo-methylated. Intermediate clusters, however, are either hyper- or hypo-methylated but are rarely found in intermediate methylation states. We develop a model for spatially-dependent collaboration between CpGs, where methylated CpGs recruit methylation enzymes that can act on CpGs over an extended local region, while unmethylated CpGs recruit demethylation enzymes that act more strongly on nearby CpGs. This model can reproduce the effects of CpG clustering on methylation and produces stable and heritable alternative methylation states of CpG clusters, thus providing a coherent model for methylation inheritance and methylation patterning.Cecilia Lövkvist, Ian B. Dodd, Kim Sneppen and Jan O. Haerte
Mixed perturbative expansion: the validity of a model for the cascading
A new type of perturbative expansion is built in order to give a rigorous
derivation and to clarify the range of validity of some commonly used model
equations.
This model describes the evolution of the modulation of two short and
localized pulses, fundamental and second harmonic, propagating together in a
bulk uniaxial crystal with non-vanishing second order susceptibility
and interacting through the nonlinear effect known as ``cascading'' in
nonlinear optics.
The perturbative method mixes a multi-scale expansion with a power series
expansion of the susceptibility, and must be carefully adapted to the physical
situation. It allows the determination of the physical conditions under which
the model is valid: the order of magnitude of the walk-off, phase-mismatch,and
anisotropy must have determined values.Comment: arxiv version is already officia
Bose-Einstein condensation in a two-dimensional, trapped,interacting gas
We study Bose-Einstein condensation phenomenon in a two-dimensional (2D)
system of bosons subjected to an harmonic oscillator type confining potential.
The interaction among the 2D bosons is described by a delta-function in
configuration space. Solving the Gross-Pitaevskii equation within the two-fluid
model we calculate the condensate fraction, ground state energy, and specific
heat of the system. Our results indicate that interacting bosons have similar
behavior to those of an ideal system for weak interactions.Comment: LaTeX, 4 pages, 4 figures, uses grafik.sty (included), to be
published in Phys. Rev. A, tentatively scheduled for 1 October 1998 (Volume
58, Number 4
Conservation laws of scaling-invariant field equations
A simple conservation law formula for field equations with a scaling symmetry
is presented. The formula uses adjoint-symmetries of the given field equation
and directly generates all local conservation laws for any conserved quantities
having non-zero scaling weight. Applications to several soliton equations,
fluid flow and nonlinear wave equations, Yang-Mills equations and the Einstein
gravitational field equations are considered.Comment: 18 pages, published version in J. Phys. A:Math. and Gen. (2003).
Added discussion of vorticity conservation laws for fluid flow; corrected
recursion formula and operator for vector mKdV conservation law
Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulence
Size-selective concentration of particles in a weakly turbulent
protoplanetary nebula may be responsible for the initial collection of
chondrules and other constituents into primitive body precursors. This paper
presents the main elements of this process of turbulent concentration. In the
terrestrial planet region, both the characteristic size and size distribution
of chondrules are explained. "Fluffier" particles would be concentrated in
nebula regions which were at a lower gas density and/or more intensely
turbulent. The spatial distribution of concentrated particle density obeys
multifractal scaling}, suggesting a close tie to the turbulent cascade process.
This scaling behavior allows predictions of the probability distributions for
concentration in the protoplanetary nebula to be made. Large concentration
factors (>10^5) are readily obtained, implying that numerous zones of particle
density significantly exceeding the gas density could exist. If most of the
available solids were actually in chondrule sized particles, the ensuing
particle mass density would become so large that the feedback effects on gas
turbulence due to mass loading could no longer be neglected. This paper
describes the process, presenting its basic elements and some implications,
without including the effects of mass loading.Comment: 34 pages, 7 figures; in press for Astrophys. J; expected Jan 01 2001
issu
Linearizability of the Perturbed Burgers Equation
We show in this letter that the perturbed Burgers equation is equivalent, through a near-identity transformation and
up to order \epsilon, to a linearizable equation if the condition is satisfied. In the case this
condition is not fulfilled, a normal form for the equation under consideration
is given. Then, to illustrate our results, we make a linearizability analysis
of the equations governing the dynamics of a one-dimensional gas.Comment: 10 pages, RevTeX, no figure
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