121318465
Time averaged energy dissipation rate for shear driven flows in R n
Abstract We drive an upper bound of the time averaged energy dissipation rate for boundary driven flows directly from the Navier-Stokes equations in R n . The upper bound is independent of the kinematic viscosity in accordance with Kolomogorov's scaling result.
122233992
Effect of tangential derivative in the boundary layer on time averaged energy dissipation rate
Abstract We show that for shear driven flows the energy dissipation rate per unit volume is dominated by a function of the energy dissipation rate in the boundary layer due to the tangential derivatives of the tangential velocities or the tangential derivatives of the normal velocity. Hence if the energy dissipation rate in a (thick enough) boundary layer due to the tangential derivatives of the tangential velocities or the tangential derivatives of the normal velocity is small, the energy dissipation rate per unit volume has to be small as well. This leads to a possible explanation of the sub-Kolmogorov bound to the energy dissipation rate per unit volume for shear driven flows observed in laboratory data. However, the smallness of these tangential derivatives in the boundary layer in the averaged sense still needs to be proved rigorously from the Navier–Stokes equations. We hope that our result will stimulate discussion on modeling, numerical simulation and laboratory experiment on these tangential derivatives in the boundary layer.
120708868
An energy equation for the weakly damped driven nonlinear Schro¨dinger equations and its application to their attractors
Abstract In this note we present an energy equation concerning the H 2 norm of a forced one-dimensional nonlinear Schrodinger equation. As an application we are able to corroborate recent results on attractors of weakly damped forced nonlinear Schrodinger equation, by proving that the attractor is an attractor in the strong topology of H 2 and its Hausdorff and fractal dimensions are finite in H 2 . The energy equation for the H 1 norm can be derived in the same fashion and it implies corresponding results for the attractor in H 1 .
122609601
Attractor dimension estimates for two-dimensional shear flows
Abstract We study the large time behavior of boundary and pressure-gradient driven incompressible fluid flows in elongated two-dimensional channels with emphasis on estimates for their degrees of freedom, i.e., the dimension of the attractor for the solutions of the Navier-Stokes equations. For boundary driven shear flows and flux driven channel flows we present upper bounds for the degrees of freedom of the form cα Re 3 2 where c is a universal constant, α denotes the aspect ratio of the channel (length/width), and Re is the Reynolds number based on the channel width and the imposed “outer” velocity scale. For fixed pressure gradient driven channel flows we obtain an upper bound of form c'α Re2, where c' is another universal positive constant and the Reynolds number is based on a velocity defined by the infimum, over all possible trajectories, of the time averaged mass flux per unit channel width. We discuss these results in terms of physical arguments based on small length scales in turbulent flows.
3479727
p-Percent Coverage Schedule in Wireless Sensor Networks
We investigate the p-percent coverage problem in this paper and propose two algorithms to prolong network lifetime based on the fact that for some applications full coverage is not necessary and different subareas of the monitored area may have different coverage requirements. The first algorithm, CPCA, is a centralized algorithm which selects the least number of nodes to monitor p-percent of the monitored area. The second algorithm, DPCP, is a distributed algorithm which can determine a set of nodes in a distributed manner to cover p-percent of the monitored area. Both of the algorithms guarantee network connectivity. The simulation results show that our algorithms can remarkably prolong network lifetime, have less than 5% unrequired coverage for large networks and employ nodes fairly for most cases.
29379375
Boundary layers in channel flow with injection and suction
We present a rigorous result regarding the boundary layer associated with the incompressible Newtonian channel flow with injection and suction.
11132243
Layered access control for MPEG-4 FGS video
MPEG-4 has recently adopted the fine granularity scalability (FGS) video coding technology which enables easy and flexible adaptation to bandwidth fluctuations and device capabilities. Encryption for FGS should preserve such adaptation capabilities and allow intermediate stages in the delivery to process the media on the ciphertext directly. In this paper, we propose a novel scalable access control scheme with this property for the MPEG-4 FGS format. It offers free browsing of the low-quality base layer video but controls the access to the enhancement layer at different service levels based on either PSNR or bitrates. Both types of service levels are supported simultaneously without jeopardizing each other's security. The scheme is fast and degrades neither compression efficiency nor error resilience of the MPEG-4 FGS. The approach is also applicable to other scalable multimedia.
205494087
A uniformly dissipative scheme for stationary statistical properties of the infinite Prandtl number model
The purpose of this short communication is to announce that a class of numerical schemes, uniformly dissipative approximations, which uniformly preserve the dissipativity of the continuous infinite dimensional dissipative complex (chaotic) systems possess desirable properties in terms of approximating stationary statistics properties. In particular, the stationary statistical properties of these uniformly dissipative schemes converge to those of the continuous system at vanishing mesh size. The idea is illustrated on the infinite Prandtl number model for convection and semi-discretization in time, although the general strategy works for a broad class of dissipative complex systems and fully discretized approximations. As far as we know, this is the first result on rigorous validation of numerical schemes for approximating stationary statistical properties of general infinite dimensional dissipative complex systems.
5609899
Large Prandtl number behavior of the Boussinesq system of Rayleigh-Bénard convection
Abstract We establish the validity of the inifinite Prandtl number model as an approximation of the Boussinesq system at large Prandtl number on finite and infinite time interval, as well as in some statistical sense.