389,762 research outputs found
Quantized mirror curves and resummed WKB
Based on previous insights, we present an ansatz to obtain quantization
conditions and eigenfunctions for a family of difference equations which arise
from quantized mirror curves in the context of local mirror symmetry of toric
Calabi-Yau threefolds. It is a first principles construction, which yields
closed expressions for the quantization conditions and the eigenfunctions when
. The key ingredient is the modular duality structure
of the underlying quantum integrable system. We use our ansatz to write down
explicit results in some examples, which are successfully checked against
purely numerical results for both the spectrum and the eigenfunctions.
Concerning the quantization conditions, we also provide evidence that, in the
rational case, this method yields a resummation of conjectured quantization
conditions involving enumerative invariants of the underlying toric Calabi-Yau
threefold.Comment: 37 pages, 8 figures, 1 table; v2: minor corrections, more details
added in section
Eigen-analysis of a Fully Viscous Boundary-Layer flow Interacting with a Finite Compliant Surface
A method and preliminary results are presented for the determination of eigenvalues and eigenmodes from fully viscous boundary layer flow interacting with a finite length one-sided compliant wall. This is an extension to the analysis of inviscid flow-structure systems which has been established in previous work. A combination of spectral and finite-difference methods are applied to a linear perturbation form of the full Navier-Stokes equations and one-dimensional beam equation. This yields a system of coupled linear equations that accurately define the spatio-temporal development of linear perturbations to a boundary layer flow over a finite-length compliant surface. Standard Krylov subspace projection methods are used to extract the eigenvalues from this complex system of equations. To date, the analysis of the development of Tollmien-Schlichting (TS) instabilities over a finite compliant surface have relied upon DNS-type results across a narrow (or even singular) spectrum of TS waves. The results from this method have the potential to describe conclusively the role that a finite length compliant surface has in the development of two-dimensional TS instabilities and other FSI instabilities across a broad spectrum
Numerical Simulation of Vortex Crystals and Merging in N-Point Vortex Systems with Circular Boundary
In two-dimensional (2D) inviscid incompressible flow, low background
vorticity distribution accelerates intense vortices (clumps) to merge each
other and to array in the symmetric pattern which is called ``vortex
crystals''; they are observed in the experiments on pure electron plasma and
the simulations of Euler fluid. Vortex merger is thought to be a result of
negative ``temperature'' introduced by L. Onsager. Slight difference in the
initial distribution from this leads to ``vortex crystals''. We study these
phenomena by examining N-point vortex systems governed by the Hamilton
equations of motion. First, we study a three-point vortex system without
background distribution. It is known that a N-point vortex system with boundary
exhibits chaotic behavior for N\geq 3. In order to investigate the properties
of the phase space structure of this three-point vortex system with circular
boundary, we examine the Poincar\'e plot of this system. Then we show that
topology of the Poincar\'e plot of this system drastically changes when the
parameters, which are concerned with the sign of ``temperature'', are varied.
Next, we introduce a formula for energy spectrum of a N-point vortex system
with circular boundary. Further, carrying out numerical computation, we
reproduce a vortex crystal and a vortex merger in a few hundred point vortices
system. We confirm that the energy of vortices is transferred from the clumps
to the background in the course of vortex crystallization. In the vortex
merging process, we numerically calculate the energy spectrum introduced above
and confirm that it behaves as k^{-\alpha},(\alpha\approx 2.2-2.8) at the
region 10^0<k<10^1 after the merging.Comment: 30 pages, 11 figures. to be published in Journal of Physical Society
of Japan Vol.74 No.
Regular networks of Luttinger liquids
We consider arrays of Luttinger liquids, where each node is described by a
unitary scattering matrix. In the limit of small electron-electron interaction,
we study the evolution of these scattering matrices as the high-energy single
particle states are gradually integrated out. Interestingly, we obtain the same
renormalization group equations as those derived by Lal, Rao, and Sen, for a
system composed of a single node coupled to several semi-infinite 1D wires. The
main difference between the single node geometry and a regular lattice is that
in the latter case, the single particle spectrum is organized into periodic
energy bands, so that the renormalization procedure has to stop when the last
totally occupied band has been eliminated. We therefore predict a strongly
renormalized Luttinger liquid behavior for generic filling factors, which
should exhibit power-law suppression of the conductivity at low temperatures
E_{F}/(k_{F}a) >
1. Some fully insulating ground-states are expected only for a discrete set of
integer filling factors for the electronic system. A detailed discussion of the
scattering matrix flow and its implication for the low energy band structure is
given on the example of a square lattice.Comment: 16 pages, 7 figure
Relation between the eigenfrequencies of Bogoliubov excitations of Bose-Einstein condensates and the eigenvalues of the Jacobian in a time-dependent variational approach
We study the relation between the eigenfrequencies of the Bogoliubov
excitations of Bose-Einstein condensates, and the eigenvalues of the Jacobian
stability matrix in a variational approach which maps the Gross-Pitaevskii
equation to a system of equations of motion for the variational parameters. We
do this for Bose-Einstein condensates with attractive contact interaction in an
external trap, and for a simple model of a self-trapped Bose-Einstein
condensate with attractive 1/r interaction. The stationary solutions of the
Gross-Pitaevskii equation and Bogoliubov excitations are calculated using a
finite-difference scheme. The Bogoliubov spectra of the ground and excited
state of the self-trapped monopolar condensate exhibits a Rydberg-like
structure, which can be explained by means of a quantum defect theory. On the
variational side, we treat the problem using an ansatz of time-dependent
coupled Gaussians combined with spherical harmonics. We first apply this ansatz
to a condensate in an external trap without long-range interaction, and
calculate the excitation spectrum with the help of the time-dependent
variational principle. Comparing with the full-numerical results, we find a
good agreement for the eigenfrequencies of the lowest excitation modes with
arbitrary angular momenta. The variational method is then applied to calculate
the excitations of the self-trapped monopolar condensates, and the
eigenfrequencies of the excitation modes are compared.Comment: 15 pages, 12 figure
Analytical study of the liquid phase transient behavior of a high temperature heat pipe
The transient operation of the liquid phase of a high temperature heat pipe is studied. The study was conducted in support of advanced heat pipe applications that require reliable transport of high temperature drops and significant distances under a broad spectrum of operating conditions. The heat pipe configuration studied consists of a sealed cylindrical enclosure containing a capillary wick structure and sodium working fluid. The wick is an annular flow channel configuration formed between the enclosure interior wall and a concentric cylindrical tube of fine pore screen. The study approach is analytical through the solution of the governing equations. The energy equation is solved over the pipe wall and liquid region using the finite difference Peaceman-Rachford alternating direction implicit numerical method. The continuity and momentum equations are solved over the liquid region by the integral method. The energy equation and liquid dynamics equation are tightly coupled due to the phase change process at the liquid-vapor interface. A kinetic theory model is used to define the phase change process in terms of the temperature jump between the liquid-vapor surface and the bulk vapor. Extensive auxiliary relations, including sodium properties as functions of temperature, are used to close the analytical system. The solution procedure is implemented in a FORTRAN algorithm with some optimization features to take advantage of the IBM System/370 Model 3090 vectorization facility. The code was intended for coupling to a vapor phase algorithm so that the entire heat pipe problem could be solved. As a test of code capabilities, the vapor phase was approximated in a simple manner
Iteration Stability for Simple Newtonian Stellar Systems
For an equation of state in which pressure is a function only of density, the
analysis of Newtonian stellar structure is simple in principle if the system is
axisymmetric, or consists of a corotating binary. It is then required only to
solve two equations: one stating that the "injection energy", , a
potential, is constant throughout the stellar fluid, and the other being the
integral over the stellar fluid to give the gravitational potential. An
iterative solution of these equations generally diverges if is held
fixed, but converges with other choices. We investigate the mathematical reason
for this convergence/divergence by starting the iteration from an approximation
that is perturbatively different from the actual solution. A cycle of iteration
is then treated as a linear "updating" operator, and the properties of the
linear operator, especially its spectrum, determine the convergence properties.
For simplicity, we confine ourselves to spherically symmetric models in which
we analyze updating operators both in the finite dimensional space
corresponding to a finite difference representation of the problem, and in the
continuum, and we find that the fixed- operator is self-adjoint and
generally has an eigenvalue greater than unity; in the particularly important
case of a polytropic equation of state with index greater than unity, we prove
that there must be such an eigenvalue. For fixed central density, on the other
hand, we find that the updating operator has only a single eigenvector, with
zero eigenvalue, and is nilpotent in finite dimension, thereby giving a
convergent solution.Comment: 16 pages, 3 figure
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