Dynamics of a BEC bright soliton in an expulsive potential

We theoretically investigate the dynamics of a matter-wave soliton created in a harmonic potential, which is attractive in the transverse direction but expulsive in the longitudinal direction. This Bose-Einstein-condensate (BEC) bright soliton made of $^7$Li atoms has been observed in a recent experiment (Science {\bf 296}, 1290 (2002)). We show that the non-polynomial Schr\"odinger equation, an effective one-dimensional equation we derived from the three-dimensional Gross-Pitaevskii equation, is able to reproduce the main experimental features of this BEC soliton in an expulsive potential.Comment: 5 pages, 4 figures (2 of them with colors

Simulation of a stationary dark soliton in a trapped zero-temperature Bose-Einstein condensate

We discuss a computational mechanism for the generation of a stationary dark soliton, or black soliton, in a trapped Bose-Einstein condensate using the Gross-Pitaevskii (GP) equation for both attractive and repulsive interaction. It is demonstrated that the black soliton with a "notch" in the probability density with a zero at the minimum is a stationary eigenstate of the GP equation and can be efficiently generated numerically as a nonlinear continuation of the first vibrational excitation of the GP equation in both attractive and repulsive cases in one and three dimensions for pure harmonic as well as harmonic plus optical-lattice traps. We also demonstrate the stability of this scheme under different perturbing forces.Comment: 7 pages, 15 ps figures, Final version accepted in J Low Temp Phy

Solitary Wave Interactions In Dispersive Equations Using Manton's Approach

We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150}, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized solutions. The approach is illustrated using as examples solitons in the Korteweg-de Vries equation, standing waves in the nonlinear Schr{\"o}dinger equation and kinks as well as breathers of the sine-Gordon equation.Comment: 5 pages, 4 figures, slightly modified version to appear in Phys. Rev.

A two-fluid single-column model of the dry, shear-free, convective boundary layer

This is the final version. Available on open access from Wiley via the DOI in this record.A single-column model of the dry, shear-free, convective boundary layer is presented in which nonlocal transports by coherent structures such as thermals are represented by the partitioning of the fluid into two components, updraft and environment, each with a full set of prognostic dynamical equations. Local eddy diffusive transport and entrainment and detrainment are represented by parameterizations similar to those used in Eddy Diffusivity Mass Flux schemes. The inclusion of vertical diffusion of the vertical velocity is shown to be important for suppressing an instability inherent in the governing equations. A semi-implicit semi-Lagrangian numerical solution method is presented and shown to be stable for large acoustic and diffusive Courant numbers, though it becomes unstable for large advective Courant numbers. The solutions are able to capture key physical features of the dry convective boundary layer. Some of the numerical challenges posed by sharp features in the solution are discussed, and areas where the model could be improved are highlighted.Natural Environment Research Council (NERC

Nonlinear analysis of a simple model of temperature evolution in a satellite

We analyse a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite's temperature is analysed by qualitative, perturbation and numerical methods, which show that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.Comment: 13 pages, 4 figures (5 EPS files

Oscillatory oblique stagnation-point flow toward a plane wall

Two-dimensional oscillatory oblique stagnation-point flow toward a plane wall is investigated. The problem is a eneralisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier-Stokes equations is sought for which the flow streamfunction depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis

Nonlinear analysis of spacecraft thermal models

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.Comment: 29 pages, 4 figure

Stationary solutions of the one-dimensional nonlinear Schroedinger equation: I. Case of repulsive nonlinearity

All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the attractive case. Our solutions take the form of stationary trains of dark or grey density-notch solitons. Real stationary states are in one-to-one correspondence with those of the linear Schr\"odinger equation. Complex stationary states are uniquely nonlinear, nodeless, and symmetry-breaking. Our solutions apply to many physical contexts, including the Bose-Einstein condensate and optical pulses in fibers.Comment: 11 pages, 7 figures -- revised versio

Presupernova Structure of Massive Stars

Issues concerning the structure and evolution of core collapse progenitor stars are discussed with an emphasis on interior evolution. We describe a program designed to investigate the transport and mixing processes associated with stellar turbulence, arguably the greatest source of uncertainty in progenitor structure, besides mass loss, at the time of core collapse. An effort to use precision observations of stellar parameters to constrain theoretical modeling is also described.Comment: Proceedings for invited talk at High Energy Density Laboratory Astrophysics conference, Caltech, March 2010. Special issue of Astrophysics and Space Science, submitted for peer review: 7 pages, 3 figure

Dressing with Control: using integrability to generate desired solutions to Einstein's equations

21 pages, no figures21 pages, no figures21 pages, no figures21 pages, no figuresMotivated by integrability of the sine-Gordon equation, we investigate a technique for constructing desired solutions to Einstein's equations by combining a dressing technique with a control-theory approach. After reviewing classical integrability, we recall two well-known Killing field reductions of Einstein's equations, unify them using a harmonic map formulation, and state two results on the integrability of the equations and solvability of the dressing system. The resulting algorithm is then combined with an asymptotic analysis to produce constraints on the degrees of freedom arising in the solution-generation mechanism. The approach is carried out explicitly for the Einstein vacuum equations. Applications of the technique to other geometric field theories are also discussed