Dissipative particle dynamics (DPD) originated as a tool for performing fluid dynamics simulations of complex fluids and amongst other things has been used to simulate dilute polymer solutions. The technique employed an Euler time-stepping technique up until recently, when a velocity-Verlet type algorithm was proposed. This paper presents a more accurate velocity-Verlet and analyses the equilibrium properties of this new technique for finite time-steps. An expression for the temperature in terms of the basic DPD parameters is derived for this scheme. Int. J. Mod. Phys. C 1999.10:241-261. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/07/15. For personal use only.

Image restoration is an inverse problem that has been widely studied in recent years. The total variation based model by Rudin-Osher-Fatemi (1992) is one of the most effective and well known due to its ability to preserve sharp features in restoration. This paper addresses an important and yet outstanding issue for this model in selection of an optimal regularization parameter, for the case of image deblurring.We propose to compute the optimal regularization parameter along with the restored image in the same variational setting, by considering a Karush Kuhn Tucker (KKT) system. Through establishing analytically the monotonicity result, we can compute this parameter by an iterative algorithm for the KKT system. Such an approach corresponds to solving an equation using discrepancy principle, rather than using discrepancy principle only as a stopping criterion. Numerical experiments can show that the algorithm is efficient and effective for image deblurring problems and yet is competitive to a related selection method.

This 1999 book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package MATLAB. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with MATLAB, no starting knowledge of the package being assumed. The range of material is wide: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations form the basic mathematics. This is applied to a large number of investigations and modelling problems, from sequences of real numbers to cafeteria queues, from card shuffling to models of fish growth. All extras to the standard MATLAB package are supplied on the World Wide Web.

In this paper, we consider the problem of restoring blurred noisy vectorial images where the blurring model involves contributions from the different image channels (cross-channel blur). The proposed method restores the images by solving a sequence of quadratic constrained minimization problems where the constraint is automatically adapted to improve the quality of the restored images. In the present case, the constraint is the Total Variation extended to vectorial images, and the objective function is the 2 norm of the residual. After proving the convergence of the iterative method, we report the results obtained on a wide set of test images, showing that this approach is efficient for recovering nearly optimal results.

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