1,457 research outputs found
Vortex lattice stability and phase coherence in three-dimensional rapidly rotating Bose condensates
We establish the general equations of motion for the modes of a vortex
lattice in a rapidly rotating Bose-Einstein condensate in three dimensions,
taking into account the elastic energy of the lattice and the vortex line
bending energy. As in two dimensions, the vortex lattice supports Tkachenko and
gapped sound modes. In contrast, in three dimensions the Tkachenko mode
frequency at long wavelengths becomes linear in the wavevector for any
propagation direction out of the transverse plane. We compute the correlation
functions of the vortex displacements and the superfluid order parameter for a
homogeneous Bose gas of bounded extent in the axial direction. At zero
temperature the vortex displacement correlations are convergent at large
separation, but at finite temperatures, they grow with separation. The growth
of the vortex displacements should lead to observable melting of vortex
lattices at higher temperatures and somewhat lower particle number and faster
rotation than in current experiments. At zero temperature a system of large
extent in the axial direction maintains long range order-parameter correlations
for large separation, but at finite temperatures the correlations decay with
separation.Comment: 10 pages, 2 figures, Changes include the addition of the particle
density - vortex density coupling and the correct value of the shear modulu
Vortex Lattice Inhomogeneity in Spatially Inhomogeneous Superfluids
A trapped degenerate Bose gas exhibits superfluidity with spatially
nonuniform superfluid density. We show that the vortex distribution in such a
highly inhomogeneous rotating superfluid is nevertheless nearly uniform. The
inhomogeneity in vortex density, which diminishes in the rapid-rotation limit,
is driven by the discrete way vortices impart angular momentum to the
superfluid. This effect favors highest vortex density in regions where the
superfluid density is most uniform (e.g., the center of a harmonically trapped
gas). A striking consequence of this is that the boson velocity deviates from a
rigid-body form exhibiting a radial-shear flow past the vortex lattice.Comment: 5 RevTeX pgs,2 figures, published versio
Giant Vortex Lattice Deformations in Rapidly Rotating Bose-Einstein Condensates
We have performed numerical simulations of giant vortex structures in rapidly
rotating Bose-Einstein condensates within the Gross-Pitaevskii formalism. We
reproduce the qualitative features, such as oscillation of the giant vortex
core area, formation of toroidal density hole, and the precession of giant
vortices, observed in the recent experiment [Engels \emph{et.al.}, Phys. Rev.
Lett. {\bf 90}, 170405 (2003)]. We provide a mechanism which quantitatively
explains the observed core oscillation phenomenon. We demonstrate the clear
distinction between the mechanism of atom removal and a repulsive pinning
potential in creating giant vortices. In addition, we have been able to
simulate the transverse Tkachenko vortex lattice vibrations.Comment: 5 pages, 6 figures; revised description of core oscillation, new
subfigur
A Generalized Theory of DNA Looping and Cyclization
We have developed a generalized semi-analytic approach for efficiently
computing cyclization and looping factors of DNA under arbitrary binding
constraints. Many biological systems involving DNA-protein interactions impose
precise boundary conditions on DNA, which necessitates a treatment beyond the
Shimada-Yamakawa model for ring cyclization. Our model allows for DNA to be
treated as a heteropolymer with sequence-dependent intrinsic curvature and
stiffness. In this framework, we independently compute enthlapic and entropic
contributions to the factor and show that even at small length scales
entropic effects are significant. We propose a simple
analytic formula to describe our numerical results for a homogenous DNA in
planar loops, which can be used to predict experimental cyclization and loop
formation rates as a function of loop size and binding geometry. We also
introduce an effective torsional persistence length that describes the coupling
between twist and bending of DNA when looped.Comment: 6 pages, 4 figures, submitted to EP
Vortices in Spatially Inhomogeneous Superfluids
We study vortices in a radially inhomogeneous superfluid, as realized by a
trapped degenerate Bose gas in a uniaxially symmetric potential. We show that,
in contrast to a homogeneous superfluid, an off-axis vortex corresponds to an
anisotropic superflow whose profile strongly depends on the distance to the
trap axis. One consequence of this superflow anisotropy is vortex precession
about the trap axis in the absence of an imposed rotation. In the complementary
regime of a finite prescribed rotation, we compute the minimum-energy vortex
density, showing that in the rapid-rotation limit it is extremely uniform,
despite a strongly inhomogeneous (nearly) Thomas-Fermi condensate density
. The weak radially-dependent contribution () to the vortex distribution, that vanishes with the
number of vortices as , arises from the interplay between
vortex quantum discretness (namely their inability to faithfully support the
imposed rigid-body rotation) and the inhomogeneous superfluid density. This
leads to an enhancement of the vortex density at the center of a typical
concave trap, a prediction that is in quantitative agreement with recent
experiments (cond-mat/0405240). One striking consequence of the inhomogeneous
vortex distribution is an azimuthally-directed, radially-shearing superflow.Comment: 22 RevTeX pages, 20 figures, Submitted to PR
Pinning and collective modes of a vortex lattice in a Bose-Einstein condensate
We consider the ground state of vortices in a rotating Bose-Einstein
condensate that is loaded in a corotating two-dimensional optical lattice. Due
to the competition between vortex interactions and their potential energy, the
vortices arrange themselves in various patterns, depending on the strength of
the optical potential and the vortex density. We outline a method to determine
the phase diagram for arbitrary vortex filling factor. Using this method, we
discuss several filling factors explicitly. For increasing strength of the
optical lattice, the system exhibits a transition from the unpinned hexagonal
lattice to a lattice structure where all the vortices are pinned by the optical
lattice. The geometry of this fully pinned vortex lattice depends on the
filling factor and is either square or triangular. For some filling factors
there is an intermediate half-pinned phase where only half of the vortices is
pinned. We also consider the case of a two-component Bose-Einstein condensate,
where the possible coexistence of the above-mentioned phases further enriches
the phase diagram. In addition, we calculate the dispersion of the low-lying
collective modes of the vortex lattice and find that, depending on the
structure of the ground state, they can be gapped or gapless. Moreover, in the
half-pinned and fully pinned phases, the collective mode dispersion is
anisotropic. Possible experiments to probe the collective mode spectrum, and in
particular the gap, are suggested.Comment: 29 pages, 4 figures, changes in section
Математична модель фінансової динаміки страхової компанії
This paper is devoted to the construction of a mathematical model of financial dynamics of life insurance company. The methods of calculating insurance amounts, payments, net premium reserve are studied, their generalization is carried out taking into account various types of insurer's expenses for ensuring the activities of the insurance company, the sensitivity of the financial dynamics of the insurance company depending on the input parameters of the model is analyzed. The results of the work are of great practical importance for modeling the work of the insurance company, because the National Bank of Ukraine implements mandatory monitoring of the solvency of the insurance company on the basis of the insurer's reporting data.
Pages of the article in the issue: 28 - 36
Language of the article: UkrainianДана робота присвячена побудові математичної моделі фінансової динаміки страхової компанії зі страхування життя. Вивчено методи обчислення страхових сум, платежів, резерву нетто-премій, здійснено їх узагальнення із врахуванням різних типів витрат страховика на забезпечення діяльності страхової компанії, проаналізовано чутливість фінансової динаміки страхової компанії в залежності від вхідних параметрів моделі. Результати роботи мають важливе практичне значення для моделювання роботи страхової компанії, адже Національний банк України впроваджує обов’язковий моніторинг забезпечення платоспроможності страхової компанії на основі звітних даних страховика.
Сторінки у випуску: 28 - 36
Мова статті: українськ
Rapidly rotating Bose-Einstein condensates in anharmonic potentials
Rapidly rotating Bose-Einstein condensates confined in anharmonic traps can
exhibit a rich variety of vortex phases, including a vortex lattice, a vortex
lattice with a hole, and a giant vortex. Using an augmented Thomas-Fermi
variational approach to determine the ground state of the condensate in the
rotating frame -- valid for sufficiently strongly interacting condensates -- we
determine the transitions between these three phases for a
quadratic-plus-quartic confining potential. Combining the present results with
previous numerical simulations of small rotating condensates in such anharmonic
potentials, we delineate the general structure of the zero temperature phase
diagram.Comment: 5 pages, 5 figure
Colloids with key-lock interactions: non-exponential relaxation, aging and anomalous diffusion
The dynamics of particles interacting by key-lock binding of attached
biomolecules are studied theoretically. Experimental realizations of such
systems include colloids grafted with complementary single-stranded DNA
(ssDNA), and particles grafted with antibodies to cell-membrane proteins.
Depending on the coverage of the functional groups, we predict two distinct
regimes. In the low coverage localized regime, there is an exponential
distribution of departure times. As the coverage is increased the system enters
a diffusive regime resulting from the interplay of particle desorption and
diffusion. This interplay leads to much longer bound state lifetimes, a
phenomenon qualitatively similar to aging in glassy systems. The diffusion
behavior is analogous to dispersive transport in disordered semiconductors:
depending on the interaction parameters it may range from a finite
renormalization of the diffusion coefficient to anomalous, subdiffusive
behavior. We make connections to recent experiments and discuss the
implications for future studies.Comment: v2: substantially revised version, new treatment of localized regime,
19 pages, 10 figure
Tkachenko oscillations and the compressibility of a rotating Bose gas
The elastic oscillations of the vortex lattice of a cold Bose gas (Tkachenko
modes) are shown to play a crucial role in the saturation of the
compressibility sum rule, as a consequence of the hybridization with the
longitudinal degrees of freedom. The presence of the vortex lattice is
responsible for a behavior of the static structure factor at small
wavevectors , which implies the absence of long range order in 2D
configurations at zero temperature. Sum rules are used to calculate the
Tkachenko frequency in the presence of harmonic trapping. Results are derived
in the Thomas-Fermi regime and compared with experiments as well as with
previous theoretical estimates.Comment: 4 pages, 2 figure
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