A study of resonance tongues near a Chenciner bifurcation using MatcontM

MatcontM is a matlab toolbox for numerical analysis of bifurcations of fixed points and periodic orbits of maps. It computes codim 1 bifurcation curves and supports the computation of normal coefficients including branch switching from codim 2 points to secondary curves. Recently, the initialization and computation of connecting orbits was improved. Moreover, a graphical user interface was added enabling interactive control of all these computations. To further support these computations it allows to compute orbits of the map and its iterates and to represent them in 2D, 3D and numeric windows. We demonstrate the use of the toolbox in a study of Arnol'd tongues near a degenerate Neimark-Sacker (Chenciner) bifurcation. Here we illustrate the recent theory of [Baesens&Mackay,2007] how resonance tongues interact with a quasi-periodic saddle-node bifurcation of invariant curves in maps. Using normal form coefficients we find evidence for one of their cases, but not the other. Actually, we find another unfolding, i.e. a third possibility. We also find a structure that resembles a quasi-periodic cusp bifurcation of invariant curves

Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs

The paper provides full algorithmic details on switching to the continuation of all possible codim 1 cycle bifurcations from generic codim 2 equilibrium bifurcation points in n-dimensional ODEs. We discuss the implementation and the performance of the algorithm in several examples, including an extended Lorenz-84 model and a laser system.Comment: 17 pages, 7 figures, submitted to Physica

A imigração e a língua de acolhimento em Portugal: questões de identidade e integração

A imigração, a diversidade e a multiculturalidade estão cada vez mais presentes nas sociedades modernas e a gestão desta realidade representa um enorme desafio, tanto para as sociedades de acolhimento como para os próprios imigrantes. Esse desafio implica um processo de adaptação e integração que apenas pode funcionar havendo vontade e esforço de ambas as partes envolvidas. O país (sociedade) de acolhimento deve trabalhar no sentido de promover um ambiente onde nativos e imigrantes possam conviver pacificamente garantindo a todos o respeito por direitos e deveres, bem como pelas suas identidades. Quanto aos imigrantes, têm que se adaptar a uma nova vida e uma nova realidade longe dos seus países de origem, devendo também eles respeitar o meio em que se encontram e do qual passam a fazer parte, ao mesmo tempo que tentam preservar as suas identidades e os laços com o seu país de origem. É um processo que envolve muitas mudanças, particularmente para os imigrantes. O país, a sociedade, os costumes, a cultura, o clima, as crenças, a língua, etc, fazem parte de um conjunto de novas experiências e novas aprendizagens para o imigrante. Essas novas experiências trazidas pela imigração têm a potencialidade de gerar mudança identitária. Através de um estudo que pretendeu dar voz aos próprios imigrantes, procurei neste trabalho perceber se há realmente mudanças ao nível da identidade provocadas pelo processo de imigração e de que modo atuam alguns elementos nessa mudança e no processo de integração, nomeadamente a língua – língua materna e língua de acolhimento.Abstract: Immigration, diversity and multiculturalism are every day more present in the modern society and dealing with this reality represents a big challenge for both, host society and the immigrants. It requires a process of adaptation and integration that can only work if both parts are involved and willing to make things work. The host society must promote an environment where natives and immigrants can live together peacefully and also guarantee that all legal rights and obligations are respected as well as people’s identities. When it comes to the immigrants, they have to adapt to a new culture and environment, making sure they respect the society which they are now part of, and also try to preserve their identities and the bound with their own country and people. It's a process that involves many changes, more so to the immigrants. The nation, society, habits, culture, weather, beliefs, language, etc., are all new experiences to them. These integration and experiences could have the potential to generate identity changes. Through a study that wanted to listen to the immigrants opinions and experiences, I’ve tried to understand if there are actually changes in immigrants identities as a result of the migration process and how do some elements take place in that change, particularly the language - language from the host society and language from the origin country

Влияние трансплантации островковых клеток поджелудочной железы плодов кролика на течение индуцированного сахарного диабета у лабораторных животных

This article is about the trial of transplantation of fetal cells of pancreas to laboratory mice with streptosotozin diabetes. Cells were infused into liver in the dose of 105 cells/0,5 ml. Mices that received rabbit β-cells had normal level blood glucose within 2 months after xenotransplantation.В данной работе показан опыт по трансплантации островковых клеток поджелудочной железы плодов кролика лабораторным мышам со стрептозотоцин-индуцированным сахарным диабетом. Клетки были трансплантированы в печень в дозе 105 кл./0,5 мл. В течение 2 месяцев после ксенотрансплантации у мышей отмечалась стойкая нормогликемия

Early Stages of Homopolymer Collapse

Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this Paper a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the theta temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages respectively scale as the zeroth, 1/5 and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure

Instanton propagator and instanton induced processes in scalar model

The propagator in the instanton background in the $(- \lambda \phi^{4})$ scalar model in four dimensions is studied.Leading and sub-leading terms of its asymptotics for large momenta and its on-shell double residue are calculated analytically. These results are applied to the analysis of the initial-state and initial-final-state corrections and the calculation of the next-to-leading (propagator) correction to the exponent of the cross section of instanton induced multiparticle scattering processes.Comment: 44 pages, 7 postscript figures, LaTe

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Integrable systems on the sphere associated with genus three algebraic curves

New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the variables of separation and vice versa, calculate the corresponding quadratures and discuss some possible integrable deformations of initial systems.Comment: 19 pages, LaTeX with AMS font

Demonstration of the temporal matter-wave Talbot effect for trapped matter waves

We demonstrate the temporal Talbot effect for trapped matter waves using ultracold atoms in an optical lattice. We investigate the phase evolution of an array of essentially non-interacting matter waves and observe matter-wave collapse and revival in the form of a Talbot interference pattern. By using long expansion times, we image momentum space with sub-recoil resolution, allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure