Descripción: We study the large time behavior of nonnegative solutions of the Cauchy problem ut =R J(x,y)(u(y; t),u(x; t)) dy,up, u(x; 0) = u0(x) 2 L∞, where |x|αu0(x) → A < 0 as |x| → 1. One of our main goals is the study of the critical case p = 1+2=ff for 0 > ff > N, left open in previous articles, for which we prove that tff=2ju(x; t) , U(x; t)j → 0 where U is the solution of the heat equation with absorption with initial datum U(x; 0) = CA;N |x|,α. Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u0 in the supercritical case and also in the critical case (p = 1 + 2=N) for bounded and integrable u0.

Descripción: Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two-dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale L f, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the inverse cascade range at a small but fixed Rossby number, Ro f≈0.05. Several numerical simulations with helical and nonhelical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with reasonably large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a ∼k⊥-5/3 scaling, and the other that corresponds to a steeper ∼k⊥-3 spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to the 2D modes. The spectrum that emerges depends on the anisotropy of the forcing function, the former solution prevailing for forcings in which more energy is injected into the 2D modes while the latter prevails for isotropic forcing. In the case of anisotropic forcing, whence the energy goes from the 2D to the 3D modes at low wave numbers, large-scale shear is created, resulting in a time scale τ sh, associated with shear, thereby producing a ∼k -1 spectrum for the total energy with the horizontal energy of the 2D modes still following a ∼k⊥-5/3 scaling. © 2012 American Physical Society.

Descripción: A simple model based on the Hasegawa-Mima equation is used to study dipole vortex interactions and turbulence of electrostatic drift waves in a plasma. It is shown that if nonlinear effects are important during vortex collisions, dipoles are broken into monopoles. Nonadiabatic effects also affect dipole behavior, which can be destroyed by the instability of emitted waves (dipole vortex radiation). Simulations of turbulence in both decaying and driven cases show the appearance of long-lived monopole structures. These coherent structures contribute to stop the cascade of energy to large scales, and then to reach a self-organized stationary state. Some numerical evidence is done that Hasegawa-Mima turbulence has a long-time behavior that is much richer than the thermodynamic equilibrium state observed in two-dimensional hydrodynamics. In driven turbulence, an important departure from Gaussian statistics of vorticity fluctuations is found, giving some indication of intermittency. Using various analyzing techniques, in particular the proper orthogonal decomposition, we show that the turbulence can be characterized by a field of coherent structures, which dominates the dynamics of the system, and random waves interacting weakly with the coherent structures. (c) 1995 The American Physical Society © 1995 The American Physical Society.

Descripción: Experimental observations on the plasma dynamics inside the nozzle of a 30 A oxygen cutting torch operated at conditions close to the double arcing are reported. It is employed a technique previously developed in our laboratory consisting in using the nozzle as a large-sized Langmuir probe. Based on the behavior of the ion current signal and simple estimations, it is concluded that (1) the non-equilibrium plasma inside the nozzle is far from the steady state in time, in contrast to what is frequently assumed. The power supply ripple was identified as the main fluctuations source and (2) large-scale plasma fluctuations inside the nozzle could cause transient (total duration of the order of 100 μs) Townsend avalanches developing in the space-charge layer located between the arc plasma and the nozzle wall. Such events trigger the so called non-destructive double-arcing phenomena without appealing to the presence of insulating films deposited inside the nozzle orifice, as was previously proposed in the literature. © 2011 American Institute of Physics.

Descripción: The displacement of particles or probes in the cell cytoplasm as a function of time is characterized by different anomalous diffusion regimes. The transport of large cargoes, such as organelles, vesicles or large proteins, involves the action of ATP-consuming molecular motors. We investigate the motion of pigment organelles driven by myosin-V motors in Xenopus laevis melanocytes using a high spatio-temporal resolution tracking technique. By analyzing the turning angles (φ) of the obtained 2D trajectories as a function of the time lag, we determine the critical time of the transition between anticorrelated and directed motion as the time when the turning angles begin to concentrate around φ 0. We relate this transition with the crossover from subdiffusive to superdiffusive behavior observed in a previous work [5]. We also assayed the properties of the trajectories in cells with inhibited myosin activity, and we can compare the results in the presence and absence of active motors. © 2010 IOP Publishing Ltd.

Descripción: The effect of rotation is considered to become important when the Rossby number is sufficiently small, as is the case in many geophysical and astrophysical flows. Here we present direct numerical simulations to study the effect of rotation in flows with moderate Rossby numbers (down to Ro ≈ 0.03) but at Reynolds numbers large enough to observe the beginning of a turbulent scaling at scales smaller than the energy injection scale. We use coherent forcing at intermediate scales, leaving enough room in the spectral space for an inverse cascade of energy to also develop. We analyze the spectral behavior of the simulations, the shell-to-shell energy transfer, scaling laws and intermittency, as well as the geometry and the anisotropy of the structures in the flow. At late times, the direct transfer of energy at small scales is mediated by interactions with the largest scale in the system, the energy containing eddies with k⊥ ≈ 1, where ⊥ refers to wavevectors perpendicular the axis of rotation. The transfer between modes with wavevector parallel to the rotation is strongly quenched. The inverse cascade of energy at scales larger than the energy injection scale is nonlocal, and energy is transferred directly from small scales to the largest available scale. We observe both a direct and inverse cascade of energy at high rotation rate, indicative that these cascades can take place simultaneously. Also, as time evolves and the energy piles up at the large scales, the intermittency of the direct cascade of energy is preserved while corrections due to intermittency are found to be the same (within error bars) as in homogeneous nonrotating turbulence. © 2009 American Institute of Physics.

Descripción: The variability of atmospheric midlatitudinal ozone between 1980 and 2000 over the Southern Hemisphere is discussed. The distribution of ozone and ozone change during the seasonal cycle is discussed using Total Ozone Mapping Spectrometer Nimbus and Earth Probe data binned at 72 (30° longitude by 5° latitude) bins, between 60° and 30°S. Rather than using a standard trend approach, the annual mean time series for each bin were fitted with a cubic polynomial. The results show that in the zonal mean sense there is a sizable, latitude-dependent slowdown of the ozone loss from the early 1990s onward, but when individual bins are considered, significant longitudinal patterns of ozone change appear, with both positive (enhancement) and negative (depletion) changes in total ozone. Thus regional evolution remains important as an indicator both of chemical depletion evolution and the relation with climate. Such longitudinal behavior is limited in the subtropics and grows toward the subpolar edge of the sampled region. For example, a large decrease was observed over southern South America in the 1990s, but during the 1990s there was only a limited change. The analysis for January, June, and October over the 20-year period shows changes in the evolution along the year, both in time and space. Furthermore, such seasonally dependent changes reach a peak in October, as would be expected. The October pattern of interannual variability could be linked to Southern Annular Mode, though there probably are some other processes driving it. Copyright 2005 by the American Geophysical Union.