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.
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.
19093181
Threshold Proxy Signature Scheme with Strong Real-Time Efficiency
The threshold proxy signature scheme with strong real-time efficiency is proposed based on a trapdoor hash function and the sharing secret technology. In the scheme, the procedure of generating threshold proxy signature is performed in two phases. The off-line phase generates a threshold proxy pre-signature before the message to be signed is even known. The pre-signature is independent of the particular message to be signed and is stored for future in the on-line phase. While on-line phase generates quickly a threshold proxy signature using the pre-signature once the message to be signed is presented. The on-line phase is typically very fast and strong real-time efficiency since it only needs a few modular additions and multiplications and one round of communication among proxy signers. Furthermore, the scheme not only has strong real-time efficiency, but also withstands the conspiracy attack existed in the previous schemes and requires no trusted third party. The scheme is particularly useful for requiring the strong real-time efficiency and fully distributed networks such as electric wallet or smart cards etc.
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.
17025259
A level-set based variational method for design and optimization of heterogeneous objects
Abstract A heterogeneous object is referred to as a solid object made of different constituent materials. The object is of a finite collection of regions of a set of prescribed material classes of continuously varying material properties. These properties have a discontinuous change across the interface of the material regions. In this paper, we propose a level-set based variational approach for the design of this class of heterogeneous objects. Central to the approach is a variational framework for a well-posed formulation of the design problem. In particular, we adapt the Mumford–Shah model which specifies that any point of the object belongs to either of two types: inside a material region of a well-defined gradient or on the boundary edges and surfaces of discontinuities. Furthermore, the set of discontinuities is represented implicitly, using a multi-phase level set model. This level-set based variational approach yields a computational system of coupled geometric evolution and diffusion partial differential equations. Promising features of the proposed method include strong regularity in the problem formulation and inherent capabilities of geometric and material modeling, yielding a common framework for optimization of the heterogeneous objects that incorporates dimension, shape, topology, and material properties. The proposed method is illustrated with several 2D examples of optimal design of multi-material structures and materials.
41225271
On Internal Cardinal Direction Relations
Internal Cardinal Direction (ICD) relations can be considered as the refinement to the contains/within topological relation. It is widely used to describe the position of an object in a region. In this paper, three ICD models with varying degrees of details are presented – ICD-5, ICD-9 and ICD-13. In each of these, the notion of a “middle part” is defined using Minimum Bounding Rectangles (MBR). Then focusing on ICD-9, three representation methods are discussed. They are major portion, point set of intersections and proportions of intersections respectively. The ICD-9 model is validated by a cognitive experiment, which helped to determine the size of the middle part in ICD-9 and validate the MBR-based partition method. Based on a psychological theory about vague predicates, conceptual neighborhood and intersection of ICD relations are also discussed briefly.
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.