Discrete Breathers in One-Dimensional Diatomic Granular Crystals

We report the experimental observation of discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both theoretically and experimentally. We then illustrate theoretically and numerically the modulational instability of the lower edge of the optical band. This leads to the dynamical formation of long-lived breather structures, whose families of solutions we compute throughout the linear spectral gap. Finally, we observe experimentally such localized breathing modes with quantitative characteristics that agree with our numerical results.Comment: 5 pages, 4 figure

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

Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals with Three-Particle Unit Cells

We investigate the tunable vibration filtering properties of one-dimensional diatomic granular crystals composed of arrays of stainless steel spheres and cylinders interacting via Hertzian contact. The arrays consist of periodically repeated three-particle unit cells (steel-cylinder-sphere) in which the length of the cylinder is varied systematically. We apply static compression to linearize the dynamic response of the crystals and characterize their linear frequency spectrum. We find good agreement between theoretical dispersion relation analysis (for infinite systems), state-space analysis (for finite systems), and experiments. We report the observation of up to three distinct pass bands and two finite band gaps and show their tunability for variations in cylinder length and static compression

Impact of anisotropy on vortex clusters and their dynamics

We investigate the effects of anisotropy on the stability and dynamics of vortex cluster states which arise in Bose-Einstein condensates. Sufficiently strong anisotropies are shown to stabilize states with arbitrary numbers of vortices that are highly unstable in the isotropic limit. Conversely, anisotropy can be used to destabilize states which are stable in the isotropic limit. Near the linear limit, we identify the bifurcations of vortex states including their emergence from linear eigenstates, while in the strongly nonlinear limit, a particle-like description of the dynamics of the vortices in the anisotropic trap is developed. Both are in very good agreement with numerical results. Collective modes of stabilized many vortex cluster states are demonstrated.Comment: 6 pages, 6 figure