The ground state of a Gross–Pitaevskii energy with general potential in the Thomas–Fermi limit

We study the ground state which minimizes a Gross–Pitaevskii energy with general non-radial trapping potential, under the unit mass constraint, in the Thomas–Fermi limit where a small parameter tends to 0. This ground state plays an important role in the mathematical treatment of recent experiments on the phenomenon of Bose–Einstein condensation, and in the study of various types of solutions of nonhomogeneous defocusing nonlinear Schrodinger equations. Many of these applications require delicate estimates for the behavior of the ground state near the boundary of the condensate, as the singular parameter tends to zero, in the vicinity of which the ground state has irregular behavior in the form of a steep corner layer. In particular, the role of this layer is important in order to detect the presence of vortices in the small density region of the condensate, understand the superfluid flow around an obstacle, and also has a leading order contribution in the energy. In contrast to previous approaches, we utilize a perturbation argument to go beyond the classical Thomas–Fermi approximation and accurately approximate the layer by the Hastings–McLeod solution of the Painleve–II equation. This settles an open problem, answered very recently only for the special case of the model harmonic potential. In fact, we even improve upon previous results that relied heavily on the radial symmetry of the potential trap. Moreover, we show that the ground state has the maximal regularity available, namely it remains uniformly bounded in the 1/2-Holder norm, which is the exact Holder regularity of the singular limit profile, as the singular parameter tends to zero. Our study is highly motivated by an interesting open problem posed recently by Aftalion, Jerrard, and Royo-Letelier, and an open question of Gallo and Pelinovsky, concerning the removal of the radial symmetry assumption from the potential trap

Stylistics on the Linguistics Text Applied in a Social Approach to Get a Certain Goal

The stylistics on the linguistics has an important role in the text applied. The social approach is one way how to get a certain goal. In this case, the brilliant solution to solve the problem based on the new method and procedure that can we did. For the public person in the word, the common way can not be avoided a social behavior as well as the community interaction. The current paper explained and explore how it can be done based on a certain way. Of course, the basic concept should be maintained, therefore, in solving the problem those are two principle concept must be had. The first is a success and the second is study

Global-in-time behavior of the solution to a Gierer-Meinhardt system

Gierer-Meinhardt system is a mathematical model to describe biological pattern formation due to activator and inhibitor. Turing pattern is expected in the presence of local self-enhancement and long-range inhibition. The long-time behavior of the solution, however, has not yet been clarified mathematically. In this paper, we study the case when its ODE part takes periodic-in-time solutions, that is, $\tau=s+1$. Under some additional assumptions on parameters, we show that the solution exists global-in-time and absorbed into one of these ODE orbits. Thus spatial patterns eventually dis- appear if those parameters are in a region without local self-enhancement or long-range inhibition

Digital Repositories and the Semantic Web: Semantic Search and Navigation for DSpace

4th International Conference on Open RepositoriesThis presentation was part of the session : DSpace User Group PresentationsDate: 2009-05-21 08:30 AM – 10:00 AMIn many digital repository implementations, resources are often described against some flavor of metadata schema, popularly the Dublin Core Element Set (DCMES), as is the case with the DSpace system. However, such an approach cannot capture richer semantic relations that exist or may be implied, in the sense of a Semantic Web ontology. Therefore we first suggest a method in order to semantically intensify the underlying data model and develop an automatic translation of the flatly organized metadata information to this new ontology. Then we propose an implementation that provides for inference-based knowledge discovery, retrieval and navigation on top of digital repositories, based on this ontology. We apply this technique to real information stored in the University of Patras Institutional Repository that is based on DSpace, and confirm that more powerful, inference-based queries can indeed be performed

Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation

We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It\^o calculus to derive the stochastic dynamics of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a sufficiently small noise strength, we establish stochastic stability of a neighborhood of the manifold of droplets in $L^2$ and $H^1$, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales