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.
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.
3391053
Wealth-Based Evolution Model for the Internet AS-Level Topology
In this paper, we seek to understand the intrinsic reasons for the well-known phenomenon of heavy-tailed degree in the Internet AS graph and argue that in contrast to traditional models based on preferential attachment and centralized opti- mization, the Pareto degree of the Internet can be explained by the evolution of wealth associated with each ISP. The proposed topology model utilizes a simple multiplicative stochastic process that determines each ISP's wealth at different points in time and several "maintenance" rules that keep the degree of each node proportional to its wealth. Actual link formation is determined in a decentralized fashion based on random walks, where each ISP individually decides when and how to increase its degree. Simulations show that the proposed model, which we call Wealth-based Internet Topology (WIT), produces scale-free random graphs with tunable exponent α and high clustering coefficients (between 0.35 and 0.5) that stay invariant as the size of the graph increases. This evolution closely mimics that of the Internet observed since 1997.
37286032
A Random Key Management Scheme for Wireless Sensor Networks
The establishment of shared keys between communicating neighbor nodes in wireless sensor networks is a challenge due to resource-constrained sensor networks. Several key pre-distribution schemes have been proposed in literatures to establish pairwise keys between sensor nodes. However, many of them are either too complicated to fit for wireless sensor networks or insecure for some common aggressions. In this paper, we propose a random key management scheme based on random key pre-distribution for wireless sensor networks. To achieve better performance and security, the proposed scheme employs two different phases to establish enhanced pairwise keys between neighboring nodes. Compared with other existing random key pre-distribution schemes, our scheme has better resilience against node capture and also performs better in terms of network connectivity and scalability with appropriate memory, computation and communication overheads.
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.
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.
1669034
Modeling Heterogeneous User Churn and Local Resilience of Unstructured P2P Networks
Previous analytical results on the resilience of unstructured P2P systems have not explicitly modeled heterogeneity of user churn (i.e., difference in online behavior) or the impact of in-degree on system resilience. To overcome these limitations, we introduce a generic model of heterogeneous user churn, derive the distribution of the various metrics observed in prior experimental studies (e.g., lifetime distribution of joining users, joint distribution of session time of alive peers, and residual lifetime of a randomly selected user), derive several closed-form results on the transient behavior of in-degree, and eventually obtain the joint in/out degree isolation probability as a simple extension of the out-degree model.