On the parallel solution of parabolic equations

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented

Efficient solution of parabolic equations by Krylov approximation methods

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms

Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR

A Time Dependent Multi-Determinant approach to nuclear dynamics

We study a multi-determinant approach to the time evolution of the nuclear wave functions (TDMD). We employ the Dirac variational principle and use as anzatz for the nuclear wave-function a linear combination of Slater determinants and derive the equations of motion. We demonstrate explicitly that the norm of the wave function and the energy are conserved during the time evolution. This approach is a direct generalization of the time dependent Hartree-Fock method. We apply this approach to a case study of ${}^6Li$ using the N3LO interaction renormalized to 4 major harmonic oscillator shells. We solve the TDMD equations of motion using Krylov subspace methods of Lanczos type. We discuss as an application the isoscalar monopole strength function.Comment: 38 pages, additional calculations included. Accepted for publication, Int. J. of Mod. Phys.

Strengthening the role of civil society in water sector governance towards climate change adaptation in African cities – Durban, Maputo, Nairobi

Water resources management is one of the most important climate change-related issues on international, national and urban public policy agendas. Income inequality in South Africa, Mozambique, and Kenya is among the largest in the world; in all three countries, equity struggles related to water are growing in social, political and ecological significance, which is both a symptom and a cause of urban vulnerabilities related to climate change. Democratic mediation of these conflicts, and sustainable long-term management of water resources in the face of climate change, requires public participation. But those most affected by water issues such as scarcity and flooding are also those least likely to be able to participate in governance and policy institutions. In particular, members of economically disadvantaged groups – especially women, in general – tend to be gravely impacted by poor water management, but also face great difficulties in participating effectively in governance bodies. This project responded to that particular need, and has developed practical strategies for strengthening urban governments in planning investments in climate change adaptation. The project linked university researchers with community-based NGOs conducting environmental education and organizing participatory workshops in low-income urban areas with pressing climate change and water-related problems; built on proven methods of community-university collaboration to strengthen urban watershed governance; increased equity in public participation processes related to urban climate change adaptation; and fostered progressive local, national and international policy development on climate change-related water management – while training students, university researchers, NGO staff members, and community participants. The major research outcome of the project is its contribution to understanding effective ways of strengthening local governments, NGOs and civil society organizations involved in environmental education and organizing for improved public participation in watershed governance and climate change adaptation in African urban areas.This research was supported by the International Development Research Centre, grant number IDRC GRANT NO. 106002-00

Exploring the democratic potential of online social networking: The scope and limitations of e-participation

Copyright © 2012 by the Association for Information Systems.The availability and promise of social networking technologies with their perceived open philosophy has increasingly inspired citizens around the world to participate in political activity on the Web. Recent examples range from opposing public policies, such as government funding cuts, to organizing revolutionary social movements, such as those in the Middle East and North Africa. Although online spaces create remarkable opportunities for various forms of political action, there are concerns over the power of existing institutions to control and even censor such interaction spaces. The objective of this article is to draw together different insights on the online engagement phenomenon, highlighting both its potential and limitations as a mechanism for fostering democratic debate and influencing policy making. We examine recent examples from Europe, the Middle East and Latin America. Finally, we summarize the implications of our work and outline directions for further research

Laboratory implementations of PMSM drive in hybrid electric vehicles applications

Field Programmable Gate Arrays (FPGAs) are one of the today\u27s most successful technologies for developing systems that require real time operation and providing additional flexibility to the designer. This research is focused on developing a control board for a permanent magnet synchronous machine (PMSM) using an FPGA module. The board is configured for individual use of an FPGA, digital signal processor (DSP) or in combination to control the PMSM by generating the required Pulse Width Modulator (PWM) to the inverter in order to drive and control the speed of the PMSM. Since, the exact rotor position and speed are required to control the motor; a useful method is developed digitally and implemented in the FPGA hardware module. The speed observer (SO), in which the Hall effect signals were used to calculate the speed and the angle of the rotor. In this thesis, three different techniques of PWM generation were developed and combined with rotor position and speed method. The project is implemented in Altera FPGA using Quartus II software V11.0 with VHDL as the supporting language. The design achieved high performance and accuracy of the detection estimation and control scheme for the Permanent Magnet Synchronous Machine. Error and design analysis has been done also --Abstract, page iii

Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

Optimisation of on-line principal component analysis

Different techniques, used to optimise on-line principal component analysis, are investigated by methods of statistical mechanics. These include local and global optimisation of node-dependent learning-rates which are shown to be very efficient in speeding up the learning process. They are investigated further for gaining insight into the learning rates' time-dependence, which is then employed for devising simple practical methods to improve training performance. Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure