45747323
Generalized algebraic method and new exact traveling wave solutions for (2+1)-dimensional dispersive long wave equation
Abstract With the help of the symbolic computation system Maple , a new generalized algebraic method to uniformly construct solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz. As an application of the method, we choose a (2 + 1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by the method proposed by Fan [E.G. Fan, Phys. Lett. A 300 (2002) 243] and find other new and more general solutions at the same time, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solutions, hyperbolic, and soliton solutions, Jacobi, and Weierstrass doubly periodic wave solutions.
27234161
Two-dimensional symmetry reduction of (2 + 1)-dimensional nonlinear Klein-Gordon equation
In this paper, one-dimensional optimal system of group invariant solutions of (2+1)-dimensional Klein-Gordon system is constructed. Then the classification of group invariant solutions is given out and the corresponding two-dimensional symmetry reduced equations are obtained. At last some symmetry transformations are gained in detail. Especially, we obtain the most general solution from a given solution by use of six variable one-parameter subgroups transformations.
41322043
New exact travelling wave solutions for the shallow long wave approximate equations
Based upon a generally projective Riccati equation method, which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the shallow long wave approximate equations. New and more general form solutions are obtained, including kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions. The properties of the new formal solitary wave solutions are shown by some figures.
12162530
A new general algebraic method with symbolic computation to construct new doubly-periodic solutions of the (2 + 1)-dimensional dispersive long wave equation
For constructing more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations, a new direct and unified algebraic method, named Jacobi elliptic function rational expansion method, is presented and implemented in a computer algebraic system. Compared with most of the existing Jacobi elliptic function expansion methods, the proposed method can be expected to obtain new and more general formal solutions. We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method.
20461063
The function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems
The function cascade synchronization scheme for the hyperchaotic systems is proposed to make the states of two identical the hyperchaotic systems both with and without uncertain parameters asymptotically synchronized. Based on Lyapunov stability theory and the proposed scheme, the Lu system and Chen hyperchaotic system with and without uncertain parameters are chosen to achieve the function cascade synchronization simultaneously. Numerical simulations are used to verify the effectiveness and feasibility of the presented control scheme.
18967560
Generalized Cascade Synchronization of Discrete-time Henon-like Map
This Letter addresses the generalized cascade synchronization problem of discrete-time hyperchaotic systems. By choosing a general kind of proportional scaling error functions and based on rigorous control theory, we take the discrete-time Henon-like map as a example to achieve the generalized cascade synchronization. Numerical simulations are used to show the effectiveness of the proposed technique.
16744851
Using Trust for Secure Collaboration in Uncertain Environments
The SECURE project investigates the design of security mechanisms for pervasive computing based on trust. It addresses how entities in unfamiliar pervasive computing environments can overcome initial suspicion to provide secure collaboration.
206370432
An accurate sampling-based method for approximating geometry
We present a sampling-based method for approximating the boundary of a geometry defined by various geometric operations. Based on a novel adaptive sampling condition, we first construct volumetric grids such that an error-minimizing point can be found in each cell to capture all the geometric objects inside the cell. We then construct a polygonal model from the grid. We guarantee the boundary approximation has the same topology as the exact surfaces, and the maximum approximation error from the exact surfaces is bounded by a user specified tolerance. Our method is robust and easy to implement. We have applied it in various applications such as remeshing of polygonal models, Boolean operations, and offsetting operations. We report experimental results on a variety of CAD models.
17024398
Runtime parallel incremental scheduling of DAGs
A runtime parallel incremental DAG scheduling approach is described in this paper. A DAG is expanded incrementally, scheduled, and executed on a parallel machine. A DAG scheduling algorithm is parallelized to scale to large systems. In this approach, a large DAG can be executed without consuming large amount of memory space. Inaccurate estimation of task execution time and communication time can be tolerated. This runtime approach can also execute dynamic DAGs. Implementation of this parallel incremental system demonstrates the feasibility of this approach. Preliminary results show that it is superior to other approaches.
43007315
The impact of smart disks and spatial reuse property on RAID-5 storage systems
RAID storage systems using SCSI and traditional disk drives cannot meet the growing demand of new I/O intensive applications. New technologies such as smart disks and SSA are being proposed to improve the performance, scalability, and reliability of RAID systems. The objective of this work is to investigate the impact of smart disks and SSA's spatial reuse property on the performance of RAID-5 storage systems. In order to perform this work, we have enhanced CMU's RAIDframe simulator so that it accurately models the overhead of current SCSI and SSA protocols, and we have created smart disk models which include on-drive XOR logic and on-drive caches. We observe that neither smart disks alone nor spatial reuse property alone has much impact on RAID system performance. However, if smart disks and spatial reuse property are properly used in combination, RAID-5 system performance and scalability can be further enhanced. In particular, we propose a parity caching approach to improve the performance of small writes.
8082956
Statistical Neurodynamics for Sequence Processing Neural Networks with Finite Dilution
We extend the statistical neurodynamics to study transient dynamics of sequence processing neural networks with finite dilution, and the theoretical results are supported by extensive numerical simulations. It is found that the order parameter equations are completely equivalent to those of the Generating Functional Method, which means that crosstalk noise follows normal distribution even in the case of failure in retrieval process. In order to verify the gaussian assumption of crosstalk noise, we numerically obtain the cumulants of crosstalk noise, and third- and fourth-order cumulants are found to be indeed zero even in non-retrieval case.