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.
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.
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 .
37107541
Ant Colony Optimization-Based Location-Aware Routing for Wireless Sensor Networks
The routing for Wireless Sensor Networks (WSNs) is a key and hard problem, and it is a research topic in the field of WSN applications. Based on Ant Colony Optimization (ACO), this paper proposes a novel adaptive intelligent routing scheme for WSNs. Following the proposed scheme, a high performance routing algorithm for WSNs is designed. The proposed routing scheme is very different from the existing ACO based routing schema for WSNs. On one hand, in the proposed scheme, the search range for an ant to select its next-hop node is limited to a subset of the set of the neighbors of the current node. On the other hand, by fusing the residual energy and the global and local location information of nodes, the new probability transition rules for an ant to select its next-hop node are defined. Compared with other ACO based routing algorithms for WSNs, the proposed routing algorithm has a better network performance on aspects of energy consumption, energy efficiency, and packet delivery latency.
3442104
Node Isolation Model and Age-Based Neighbor Selection in Unstructured P2P Networks
Previous analytical studies of unstructured P2P resilience have assumed exponential user lifetimes and only considered age-independent neighbor replacement. In this paper, we overcome these limitations by introducing a general node-isolation model for heavy-tailed user lifetimes and arbitrary neighbor-selection algorithms. Using this model, we analyze two age-biased neighbor-selection strategies and show that they significantly improve the residual lifetimes of chosen users, which dramatically reduces the probability of user isolation and graph partitioning compared with uniform selection of neighbors. In fact, the second strategy based on random walks on age-proportional graphs demonstrates that, for lifetimes with infinite variance, the system monotonically increases its resilience as its age and size grow. Specifically, we show that the probability of isolation converges to zero as these two metrics tend to infinity. We finish the paper with simulations in finite-size graphs that demonstrate the effect of this result in practice.
3413304
On Node Isolation Under Churn in Unstructured P2P Networks with Heavy-Tailed Lifetimes
Previous analytical studies [12], [18] of unstructured P2P resilience have assumed exponential user lifetimes and only considered age-independent neighbor replacement. In this paper, we overcome these limitations by introducing a general node-isolation model for heavy-tailed user lifetimes and arbitrary neighbor-selection algorithms. Using this model, we analyze two age-biased neighbor-selection strategies and show that they significantly improve the residual lifetimes of chosen users, which dramatically reduces the probability of user isolation and graph partitioning compared to uniform selection of neighbors. In fact, the second strategy based on random walks on age-weighted graphs demonstrates that for lifetimes with infinite variance, the system monotonically increases its resilience as its age and size grow. Specifically, we show that the probability of isolation converges to zero as these two metrics tend to infinity. We finish the paper with simulations in finite-size graphs that demonstrate the effect of this result in practice.
47232248
Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience
This paper examines graph-theoretic properties of existing peer-to-peer networks and proposes a new infrastructure based on optimal-diameter de Bruijn graphs. Since generalized de Bruijn graphs exhibit very short average distances and high resilience to node failure, they are well suited for distributed hash tables (DHTs). Using the example of Chord, CAN, and de Bruijn, we study the routing performance, graph expansion, clustering properties, and bisection width of each graph. Having confirmed that de Bruijn graphs offer the best diameter and highest connectivity among the existing peer-to-peer structures, we offer a very simple incremental building process that preserves optimal properties of de Bruijn graphs under uniform user joins/departures. We call the combined peer-to-peer architecture optimal diameter routing infrastructure.