Matter-wave solitons of collisionally inhomogeneous condensates

We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii equation. The numerical results are shown to be in very good agreement with the predictions of the effective equations of motion derived by adiabatic perturbation theory. The spatially dependent nonlinearity leads to a gravitational potential that allows to influence the motion of both fundamental as well as higher order solitons.Comment: 19 pages, 4 figure

Avoiding Infrared Catastrophes in Trapped Bose-Einstein Condensates

This paper is concerned with the long wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in ``cigar-shaped'' (1D) attractive BECs and the transverse instability of dark solitons in ``pancake'' (2D) repulsive BECs. We suggest mechanisms, and give explicit estimates, on how to ``engineer'' the trapping conditions of the condensate to avoid such instabilities: the main result being that a tight enough trapping potential suppresses the instabilities present in the homogeneous limit. We compare the obtained estimates with numerical results and we highlight the relevant regimes of dynamical behavior

Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates

We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also studied numerically. Both cases of purely one-dimensional and ``cigar-shaped'' condensates are studied by means of different mean-field models, and the oscillation frequencies of the pertinent solitons are found and compared with the results obtained by the linear stability analysis.Numerical results are shown to be in very good agreement with the corresponding analytical predictions

Ring Dark Solitons and Vortex Necklaces in Bose-Einstein Condensates

We introduce the concept of ring dark solitons in Bose-Einstein condensates. We show that relatively shallow rings are not subject to the snake instability, but a deeper ring splits into a robust ring-like cluster of vortex pairs, which performs oscillations in the radial and azimuthal directions, following the dynamics of the original ring soliton.Comment: Phys. Rev. Lett., in pres

Matrix proteoglycans are markedly affected in advanced laryngeal squamous cell carcinoma

AbstractProteoglycans (PGs) are implicated in the growth and progression of malignant tumors. In this study, we examined the concentration and localization of PGs in advanced (stage IV) laryngeal squamous cell carcinoma (LSCC) and compared with human normal larynx (HNL). LSCC and HNL sections were examined immunohistochemically with a panel of antibodies, and tissues extracts were analyzed by biochemical methods including immunoblotting and high performance liquid chromatography (HPLC). The results demonstrated significant destruction of cartilage in LSCC, which was followed by marked decrease of aggrecan and link protein. In contrast to the loss of aggrecan in LSCC, accumulation of versican and decorin was observed in the tumor-associated stroma. Biochemical analyses indicated that aggrecan, versican, decorin and biglycan comprise the vast majority of total PGs in both healthy and cancerous tissue. In LSCC the absolute amounts of KS/CS/DS-containing PGs were dramatically decreased about 18-fold in comparison to HNL. This decrease is due to the loss of aggrecan. Disaccharide analysis of CS/DSPGs from LSCC showed a significant reduction of 6-sulfated Δ-disaccharides (Δdi-6S) with a parallel increase of 4-sulfated Δ-disaccharides (Δdi-4S) as compared to HNL. The obtained data clearly demonstrate that tumor progression is closely related to specific alteration of matrix PGs in LSCC. The altered composition of PGs in cartilage, as well as in tumor-associated stroma, is crucial for the biological behaviour of cancer cells in the diseased tissue

Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials

Motivated by recent experimental studies of matter-waves and optical beams in double well potentials, we study the solutions of the nonlinear Schr\"{o}dinger equation in such a context. Using a Galerkin-type approach, we obtain a detailed handle on the nonlinear solution branches of the problem, starting from the corresponding linear ones and predict the relevant bifurcations of solutions for both attractive and repulsive nonlinearities. The results illustrate the nontrivial differences that arise between the steady states/bifurcations emerging in symmetric and asymmetric double wells

Acoustic solitons in waveguides with Helmholtz resonators: transmission line approach

We report experimental results and study theoretically soliton formation and propagation in an airfilled acoustic waveguide side loaded with Helmholtz resonators. Our theoretical approach relies on a transmission-line description of this setting, which leads to a nonlinear dynamical lattice model. The latter is treated analytically, by means of dynamical systems and multiscale expansion techniques, and leads to various soliton solutions for the pressure. These include Boussinesq-like and Korteweg-de Vries pulse-shaped solitons, as well as nonlinear Schr\"{o}odinger envelope solitons. The analytical predictions are in excellent agreement with direct numerical simulations and in qualitative agreement with the experimental observations.Comment: 10 pages, 9 figure