The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

A Combined Renormalization Group-Multiple Scale Method for Singularly Perturbed Problems

This paper introduces a straightforward method to asymptotically solve a variety of initial and boundary value problems for singularly perturbed ordinary differential equations whose solution structure can be anticipated. The approach is simpler than conventional methods, including those based on asymptotic matching or on eliminating secular terms. © 2010 by the Massachusetts Institute of Technology.

Computation of Mathematical Models for Complex Industrial Processes

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios.

A numerical method for the fractional Fitzhugh–Nagumo monodomain model

A fractional FitzHugh–Nagumo monodomain model with zero Dirichlet boundary conditions is presented, generalising the standard monodomain model that describes the propagation of the electrical potential in heterogeneous cardiac tissue. The model consists of a coupled fractional Riesz space nonlinear reaction-diffusion model and a system of ordinary differential equations, describing the ionic fluxes as a function of the membrane potential. We solve this model by decoupling the space-fractional partial differential equation and the system of ordinary differential equations at each time step. Thus, this means treating the fractional Riesz space nonlinear reaction-diffusion model as if the nonlinear source term is only locally Lipschitz. The fractional Riesz space nonlinear reaction-diffusion model is solved using an implicit numerical method with the shifted Grunwald–Letnikov approximation, and the stability and convergence are discussed in detail in the context of the local Lipschitz property. Some numerical examples are given to show the consistency of our computational approach.

DroplIT, an improved image analysis method for droplet identification in high-throughput crystallization trials

The application of robotics to protein crystallization trials has resulted in the production of millions of images. Manual inspection of these images to find crystals and other interesting outcomes is a major rate-limiting step. As a result there has been intense activity in developing automated algorithms to analyse these images. The very first step for most systems that have been described in the literature is to delineate each droplet. Here, a novel approach that reaches over 97% success rate and subsecond processing times is presented. This will form the seed of a new high-throughput system to scrutinize massive crystallization campaigns automatically. © 2010 International Union of Crystallography Printed in Singapore-all rights reserved.

A novel tuning method for advanced line drop compensator and its application to response coordination of distributed generation with voltage regulating devices

Nowadays, integration of small-scale electricity generators, known as Distributed Generation (DG), into distribution networks has become increasingly popular. This tendency together with the falling price of DG units has a great potential in giving the DG a better chance to participate in voltage regulation process, in parallel with other regulating devices already available in the distribution systems. The voltage control issue turns out to be a very challenging problem for distribution engineers, since existing control coordination schemes need to be reconsidered to take into account the DG operation. In this paper, a control coordination approach is proposed, which is able to utilize the ability of the DG as a voltage regulator, and at the same time minimize the interaction of DG with another DG or other active devices, such as On-load Tap Changing Transformer (OLTC). The proposed technique has been developed based on the concepts of protection principles (magnitude grading and time grading) for response coordination of DG and other regulating devices and uses Advanced Line Drop Compensators (ALDCs) for implementation. A distribution feeder with tap changing transformer and DG units has been extracted from a practical system to test the proposed control technique. The results show that the proposed method provides an effective solution for coordination of DG with another DG or voltage regulating devices and the integration of protection principles has considerably reduced the control interaction to achieve the desired voltage correction.