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.
6175305
On Static and Dynamic Partitioning Behavior of Large-Scale P2P Networks
In this paper, we analyze the problem of network disconnection in the context of large-scale P2P networks and understand how both static and dynamic patterns of node failure affect the resilience of such graphs. We start by applying classical results from random graph theory to show that a large variety of deterministic and random P2P graphs almost surely (i.e., with probability 1-o(1)) remain connected under random failure if and only if they have no isolated nodes. This simple, yet powerful, result subsequently allows us to derive in closed-form the probability that a P2P network develops isolated nodes, and therefore partitions, under both types of node failure. We finish the paper by demonstrating that our models match simulations very well and that dynamic P2P systems are extremely resilient under node churn as long as the neighbor replacement delay is much smaller than the average user lifetime.
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 .
33294789
An Optimal Algorithm for Minimizing Cluster Overlap of ACE
In order to reduce channel contention, support scalability and prolong the lifetime of the sensor networks, sensor nodes are often grouped into clusters. Algorithm for Cluster Establishment (ACE) is a clustering algorithm for sensor networks that uses three rounds of feedback to induce the formation of a highly efficient cover of uniform clusters over the network. In this paper, we present an optimizing algorithm for minimizing the cluster overlap of ACE. Simulation shows the proposed algorithm can efficiently eliminate the redundant cluster heads and minimize the cluster overlap.
8744802
On static and dynamic partitioning behavior of large-scale networks
In this paper, we analyze the problem of network disconnection in the context of large-scale P2P networks and understand how both static and dynamic patterns of node failure affect the resilience of such graphs. We start by applying classical results from random graph theory to show that a large variety of deterministic and random P2P graphs almost surely (i.e., with probability 1-o(1)) remain connected under random failure if and only if they have no isolated nodes. This simple, yet powerful, result subsequently allows us to derive in closed-form the probability that a P2P network develops isolated nodes, and therefore partitions, under both types of node failure. We finish the paper by demonstrating that our models match simulations very well and that dynamic P2P systems are extremely resilient under node churn as long as the neighbor replacement delay is much smaller than the average user lifetime
2819336
Optimal harvesting problems for an age-dependent n-dimensional food chain model with diffusion
We investigate the optimal harvesting problems of an age-dependent n-dimensional food chain model with spartially structured, which is controlled by harvesting. The existence and uniqueness of solution for the system are proven using Banach fixed-point theorem. We establish existence result of optimal control and necessary optimality conditions.