Aspects of the stochastic Burgers equation and their connection with turbulence

We present results for the 1 dimensional stochastically forced Burgers equation when the spatial range of the forcing varies. As the range of forcing moves from small scales to large scales, the system goes from a chaotic, structureless state to a structured state dominated by shocks. This transition takes place through an intermediate region where the system exhibits rich multifractal behavior. This is mainly the region of interest to us. We only mention in passing the hydrodynamic limit of forcing confined to large scales, where much work has taken place since that of Polyakov. In order to make the general framework clear, we give an introduction to aspects of isotropic, homogeneous turbulence, a description of Kolmogorov scaling, and, with the help of a simple model, an introduction to the language of multifractality which is used to discuss intermittency corrections to scaling. We continue with a general discussion of the Burgers equation and forcing, and some aspects of three dimensional turbulence where - because of the mathematical analogy between equations derived from the Navier-Stokes and Burgers equations - one can gain insight from the study of the simpler stochastic Burgers equation. These aspects concern the connection of dissipation rate intermittency exponents with those characterizing the structure functions of the velocity field, and the dynamical behavior, characterized by different time constants, of velocity structure functions. We also show how the exponents characterizing the multifractal behavior of velocity structure functions in the above mentioned transition region can effectively be calculated in the case of the stochastic Burgers equation.Comment: 25 pages, 4 figure

Instability of rotating chiral solitons

We show that spherically symmetric chiral SU(2)×SU(2) solitons are unstable under spin-isospin rotations. Namely, the effective potential including the effects of quantizing the collective coordinate corresponding to such a rotation has no minimum in the class of functions used to describe such solitons. © 1984 The American Physical Society

Analyses cinématique et dynamique de la théorie des déterminants de la marche

Colloque avec actes et comité de lecture. Internationale.International audienceIl a été démontré que le modèle compass gait, de par ses caractéristiques, surestime l'amplitude verticale de la trajectoire du CoM et ne prédit pas correctement la force verticale d'appui au sol. Ainsi, sur la base du modèle compass gait, Saunders émet l'hypothèse que 6 déterminants de la marche permettraient de réduire cette amplitude et donc d'approcher la trajectoire de référence du CoM. L'objectif de cet article est d'évaluer l'influence respective de ces déterminants sur la trajectoire du CoM et leur influence respective sur la force verticale d'appui à l'aide d'un modèle mathématique 3D. La flexion du genou en appui ainsi que l'obliquité du bassin influencent de façon importante a la diminution de l'amplitude verticale de déplacement du CoM uniquement au cours du double appui, contribuant de fa con importante a l'apparition du premier pic de la force verticale d'appui. Au cours du simple appui, la flexion dorsale de la cheville en appui contribue plutôt a l'excursion verticale du CoM at la flexion plantaire en n de simple appui est responsable de l'apparition du second pic. La contribution la plus importante a la minimisation de l'amplitude verticale du CoM apparaît en tenant compte des mécanismes du pied dans le modèle proposé

Diffusion regimes in Levy flights with trapping

The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is assumed to avoid the divergence of the mean squared displacement. Using the limit theorems of the theory of Levy stable distributions we have provided a characterization of the different diffusion regimes.Comment: 1 figure, submitted to Physica

Stochasticity of gene products from transcriptional pulsing

Transcriptional pulsing has been observed in both prokaryotes and eukaryotes and plays a crucial role in cell-to-cell variability of protein and mRNA numbers. An important issue is how the time constants associated with episodes of transcriptional bursting and mRNA and protein degradation rates lead to different cellular mRNA and protein distributions, starting from the transient regime leading to the steady state. We address this by deriving and then investigating the exact time-dependent solution of the master equation for a transcriptional pulsing model of mRNA distributions. We find a plethora of results. We show that, among others, bimodal and long-tailed (power-law) distributions occur in the steady state as the rate constants are varied over biologically significant time scales. Since steady state may not be reached experimentally we present results for the time evolution of the distributions. Because cellular behavior is determined by proteins, we also investigate the effect of the different mRNA distributions on the corresponding protein distributions using numerical simulations

Hydrothermal Surface-Wave Instability and the Kuramoto-Sivashinsky Equation

We consider a system formed by an infinite viscous liquid layer with a constant horizontal temperature gradient, and a basic nonlinear bulk velocity profile. In the limit of long-wavelength and large nondimensional surface tension, we show that hydrothermal surface-wave instabilities may give rise to disturbances governed by the Kuramoto-Sivashinsky equation. A possible connection to hot-wire experiments is also discussed.Comment: 11 pages, RevTex, no figure

Defect-Mediated Stability: An Effective Hydrodynamic Theory of Spatio-Temporal Chaos

Spatiotemporal chaos (STC) exhibited by the Kuramoto-Sivashinsky (KS) equation is investigated analytically and numerically. An effective stochastic equation belonging to the KPZ universality class is constructed by incorporating the chaotic dynamics of the small KS system in a coarse-graining procedure. The bare parameters of the effective theory are computed approximately. Stability of the system is shown to be mediated by space-time defects that are accompanied by stochasticity. The method of analysis and the mechanism of stability may be relevant to a class of STC problems.Comment: 34 pages + 9 figure