Additive noise effects in active nonlinear spatially extended systems

We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first focus on a regime close to the instability onset (primary bifurcation), where the system can be described by a single dominant mode. We show analytically that the resulting noise in the equation describing the amplitude of the dominant mode largely depends on the nature of the stochastic forcing. For a highly degenerate noise, in the sense that it is acting on the first stable mode only, the amplitude equation is dominated by a pure multiplicative noise, which in turn induces the dominant mode to undergo several critical state transitions and complex phenomena, including intermittency and stabilisation, as the noise strength is increased. The intermittent behaviour is characterised by a power-law probability density and the corresponding critical exponent is calculated rigorously by making use of the first-passage properties of the amplitude equation. On the other hand, when the noise is acting on the whole subspace of stable modes, the multiplicative noise is corrected by an additive-like term, with the eventual loss of any stabilised state. We also show that the stochastic forcing has no effect on the dominant mode dynamics when it is acting on the second stable mode. Finally, in a regime which is relatively far from the instability onset, so that there are two unstable modes, we observe numerically that when the noise is acting on the first stable mode, both dominant modes show noise-induced complex phenomena similar to the single-mode case

Self-similarity of solitary waves on inertia-dominated falling liquid films

We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re=20–120 and surface tension coefficients σ=0.0512–0.072Nm−1 on substrates with inclination angles β=19◦ − 90◦. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence

Os roedores das ilhas Flores e Corvo : distribuição, fertilidade e morfometria

XIII Expedição Científica do Departamento de Biologia - Flores e Corvo 2007.O conhecimento da biologia e ecologia das espécies de roedores dos Açores é escasso. Integrado na XIII Expedição Científica do Departamento de Biologia da Universidade dos Açores, realizámos uma amostragem de roedores em três habitats distintos (pastagem, floresta e lixeira) na ilha das Flores, durante três noites, e num habitat (lixeira) na ilha do Corvo, durante uma noite. A espécie Mus musculus foi capturada nos três habitats, Rattus rattus foi capturada na floresta e na pastagem e Rattus norvegicus só foi capturada na lixeira. Na ilha do Corvo não conseguimos efectuar nenhuma captura de animais destas espécies. Apresentamos os dados da fertilidade potencial das fêmeas prenhas capturados e dados sobres as medidas de algumas características da morfologia externa. Sugerimos um padrão de distribuição das três espécies para o Arquipélago dos Açores e apresentamos uma forma simples e expedita para a identificação das espécies de Rodentia nos Açores

Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation

We analyze the effect of pure additive noise on the long-time dynamics of the noisy Kuramoto-Sivashinsky (KS) equation in a regime close to the instability onset. We show that when the noise is highly degenerate, in the sense that it acts only on the first stable mode, the solution of the KS equation undergoes several transitions between different states, including a critical on-off intermittent state that is eventually stabilized as the noise strength is increased. Such noise-induced transitions can be completely characterized through critical exponents, obtaining that both the KS and the noisy Burgers equation belong to the same universality class. The results of our numerical investigations are explained rigorously using multiscale techniques.Comment: 4 pages, 4 figure

A new mode reduction strategy for the generalized Kuramoto–Sivashinsky equation

Consider the generalized Kuramoto–Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction–diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS equation. For this purpose, we approximate it by a renormalization group equation which is qualitatively characterized by rigorous error bounds. This formulation allows for a new stochastic mode reduction guaranteeing optimality in the sense of maximal information entropy. Herewith, noise is systematically added to the reduced gKS equation and gives a rigorous and analytical explanation for its origin. These new results would allow one to reliably perform low-dimensional numerical computations by accounting for the neglected degrees of freedom in a systematic way. Moreover, the presented reduction strategy might also be useful in other applications where classical mode reduction approaches fail or are too complicated to be implemented

Uniformity transition for ray intensities in random media

This paper analyses a model for the intensity of distribution for rays propagating without absorption in a random medium. The random medium is modelled as a dynamical map. After N iterations, the intensity is modelled as a sum S of N contributions from different trajectories, each of which is a product of N independent identically distributed random variables xk, representing successive focussing or de-focussing events. The number of ray trajectories reaching a given point is assumed to proliferate exponentially: N=ΛN, for some Λ>1. We investigate the probability distribution of S. We find a phase transition as parameters of the model are varied. There is a phase where the fluctuations of S are suppressed as N → ∞, and a phase where the S has large fluctuations, for which we provide a large deviation analysis

Efectos de un entrenamiento pliométrico sobre el rendimiento en la salida de natación en deportistas adolescentes

En la natación el rendimiento depende de diversos factores atendiendo a la distancia de la prueba. La fuerza explosiva puede resultar un elemento clave en pruebas de distancia corta por su relevancia en la fase de salida. El objetivo de este estudio fue analizar la efectividad que posee un entrenamiento pliométrico sobre la fuerza explosiva del tren inferior y su posible transferencia en el rendimiento de la fase de salida. 16 nadadores adolescentes fueron distribuidos aleatoriamente en dos grupos: control (GC) y experimental (GE). El GC realizó un entrenamiento de fuerza resistencia del tren inferior y el GE de pliometría. Tras 6 semanas se analizaron diferentes variables físicas (CMJ y ABK) y cinemáticas (ángulo de salida, ángulo de entrada al agua, distancia de salto, tiempo de vuelo y tiempo en 5 m). El análisis intragrupo no mostró cambios en el GC mientras que el GE experimentó un incremento en la altura de los saltos CMJ (p<0,005) y ABK (p<0,001), y en la variable técnica del ángulo de salida (p<0,03). En las comparaciones intergrupo el GE aumentó el ángulo de salida (p<0,05). El entrenamiento pliométrico mejora la altura de salto vertical pudiendo tener una transferencia positiva sobre el rendimiento de la salida de natación. Se hace necesaria la realización de nuevos estudios en donde se corroboren los resultados obtenidos en esta investigación

Controlling spatiotemporal chaos in active dissipative-dispersive nonlinear systems

We present a new methodology for the stabilization and control of infinite-dimensional dynamical systems exhibiting low-dimensional spatiotemporal chaos. We show that with an appropriate choice of time-dependent controls we are able to stabilize and/or control all stable or unstable solutions, including steady solutions, traveling waves (single and multipulse ones/bound states) and spatiotemporal chaos. We exemplify our methodology with the generalized Kuramoto-Sivashinsky equation, a paradigmatic model of spatiotemporal chaos, which is known to exhibit a rich spectrum of wave forms and wave transitions and a rich variety of spatiotemporal structures

Dynamics of Fattening and Thinning 2D Sessile Droplets

We investigate the dynamics of a droplet on a planar substrate as the droplet volume changes dynamically due to liquid being pumped in or out through a pore. We adopt a diffuse-interface formulation which is appropriately modified to account for a localized inflow–outflow boundary condition (the pore) at the bottom of the droplet, hence allowing to dynamically control its volume, as the droplet moves on a flat substrate with a periodic chemical pattern. We find that the droplet undergoes a stick–slip motion as the volume is increased (fattening droplet) which can be monitored by tracking the droplet contact points. If we then switch over to outflow conditions (thinning droplet), the droplet follows a different path (i.e., the distance of the droplet midpoint from the pore location evolves differently), giving rise to a hysteretic behavior. By means of geometrical arguments, we are able to theoretically construct the full bifurcation diagram of the droplet equilibria (positions and droplet shapes) as the droplet volume is changed, finding excellent agreement with time-dependent computations of our diffuse-interface model