Transfer of BECs through discrete breathers in an optical lattice

We study the stability of a stationary discrete breather (DB) on a nonlinear trimer in the framework of the discrete nonlinear Schr\"odinger equation (DNLS). In previous theoretical investigations of the dynamics of Bose-Einstein condensates in leaking optical lattices, collisions between a DB and a lattice excitation, e.g. a moving breather (MB) or phonon, were studied. These collisions lead to the transmission of a fraction of the incident (atomic) norm of the MB through the DB, while the DB can be shifted in the direction of the incident lattice excitation. Here we show that there exists a total energy threshold of the trimer, above which the lattice excitation can trigger the destabilization of the DB and that this is the mechanism leading to the movement of the DB. Furthermore, we give an analytic estimate of upper bound to the norm that is transmitted through the DB. Our analysis explains the results of the earlier numerical studies and may help to clarify functional operations with BECs in optical lattices such as blocking and filtering coherent (atomic) beams.Comment: 8 pages, 5 figure

The discretised harmonic oscillator: Mathieu functions and a new class of generalised Hermite polynomials

We present a general, asymptotical solution for the discretised harmonic oscillator. The corresponding Schr\"odinger equation is canonically conjugate to the Mathieu differential equation, the Schr\"odinger equation of the quantum pendulum. Thus, in addition to giving an explicit solution for the Hamiltonian of an isolated Josephon junction or a superconducting single-electron transistor (SSET), we obtain an asymptotical representation of Mathieu functions. We solve the discretised harmonic oscillator by transforming the infinite-dimensional matrix-eigenvalue problem into an infinite set of algebraic equations which are later shown to be satisfied by the obtained solution. The proposed ansatz defines a new class of generalised Hermite polynomials which are explicit functions of the coupling parameter and tend to ordinary Hermite polynomials in the limit of vanishing coupling constant. The polynomials become orthogonal as parts of the eigenvectors of a Hermitian matrix and, consequently, the exponential part of the solution can not be excluded. We have conjectured the general structure of the solution, both with respect to the quantum number and the order of the expansion. An explicit proof is given for the three leading orders of the asymptotical solution and we sketch a proof for the asymptotical convergence of eigenvectors with respect to norm. From a more practical point of view, we can estimate the required effort for improving the known solution and the accuracy of the eigenvectors. The applied method can be generalised in order to accommodate several variables.Comment: 18 pages, ReVTeX, the final version with rather general expression

Dimension dependent energy thresholds for discrete breathers

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. We study the existence of energy thresholds for discrete breathers, i.e., the question whether, in a certain system, discrete breathers of arbitrarily low energy exist, or a threshold has to be overcome in order to excite a discrete breather. Breather energies are found to have a positive lower bound if the lattice dimension d is greater than or equal to a certain critical value d_c, whereas no energy threshold is observed for d<d_c. The critical dimension d_c is system dependent and can be computed explicitly, taking on values between zero and infinity. Three classes of Hamiltonian systems are distinguished, being characterized by different mechanisms effecting the existence (or non-existence) of an energy threshold.Comment: 20 pages, 5 figure

Etude expérimentale d'une couche de mélange anisotherme

Une couche de mélange anisotherme plane est étudiée dans différentes configurations de gradients forcés de vitesse et de température. L'écoulement est mis en oeuvre dans une soufflerie spécialement conçue pour générer des écoulements à basse vitesse avec génération séparée de deux courants à vitesses et températures contrôlées séparément. L'étude utilise une nouvelle technique d'anémométrie par fil chaud à surchauffe programmable dénommée PCTA. Le capteur permet de mesurer simultanément la vitesse et la température à haute fréquence en un même point. Les profils transversaux de vitesse et de température mesurés le long de la direction principale de l'écoulement donnent accès aux paramètres d'expansion de la couche de mélange. Les expansions de l'épaisseur de vorticité et de l'épaisseur de mélange thermique sont comparées, en fonction du paramètre de cisaillement dynamique et du nombre de Richardson. L'utilisation de l'anémomètre PCTA ouvre des perspectives d'analyse fine des interactions vitesse-température dans le mélange turbulent

Homoclinic standing waves in focussing DNLS equations --Variational approach via constrained optimization

We study focussing discrete nonlinear Schr\"{o}dinger equations and present a new variational existence proof for homoclinic standing waves (bright solitons). Our approach relies on the constrained maximization of an energy functional and provides the existence of two one-parameter families of waves with unimodal and even profile function for a wide class of nonlinearities. Finally, we illustrate our results by numerical simulations.Comment: new version with revised introduction and improved condition (A3); 16 pages, several figure

Periodontal treatment to improve glycaemic control in diabetic patients: study protocol of the randomized, controlled DIAPERIO trial

<p>Abstract</p> <p>Background</p> <p>Periodontitis is a common, chronic inflammatory disease caused by gram-negative bacteria leading to destruction of tissues supporting the teeth. Epidemiological studies have consistently shown increased frequency, extent and severity of periodontitis among diabetic adults. More recently, some controlled clinical trials have also suggested that periodontal treatment could improve glycaemic control in diabetic patients. However current evidence does not provide sufficient information on which to confidently base any clinical recommendations. The main objective of this clinical trial is to assess whether periodontal treatment could lead to a decrease in glycated haemoglobin levels in metabolically unbalanced diabetic patients suffering from chronic periodontitis.</p> <p>Methods</p> <p>The DIAPERIO trial is an open-label, 13-week follow-up, randomized, controlled trial. The total target sample size is planned at 150 participants, with a balanced (1:1) treatment allocation (immediate treatment vs delayed treatment). Periodontal treatment will include full mouth non-surgical scaling and root planing, systemic antibiotherapy, local antiseptics (chlorhexidine 0.12%) and oral health instructions. The primary outcome will be the difference in change of HbA1c between the two groups after the 13-weeks' follow-up. Secondary outcomes will be the difference in change of fructosamine levels and quality of life between the two groups.</p> <p>Discussion</p> <p>The DIAPERIO trial will provide insight into the question of whether periodontal treatment could lead to an improvement in glycaemic control in metabolically unbalanced diabetic patients suffering from periodontitis. The results of this trial will help to provide evidence-based recommendations for clinicians and a draft framework for designing national health policies.</p> <p>Trial registration</p> <p>Current Controlled Trials ISRCTN15334496</p