An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type

We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time. We derive optimal $hp$-version error estimates and show that exponential rates of convergence can be achieved for solutions with singular (temporal) behavior near $t=0$ caused by the weakly singular kernel. Moreover, we prove that by using nonuniformly refined time steps, optimal algebraic convergence rates can be achieved for the $h$-version DG method. We then combine the DG time-stepping method with a standard finite element discretization in space, and present an optimal error analysis of the resulting fully discrete scheme. Our theoretical results are numerically validated in a series of test problems

A study of local approximation for polarization potentials

We discuss the derivation of an equivalent \textit{l}-independent polarization potential for use in the optical Schr\"{o}dinger equation that describes the elastic scattering of heavy ions. Three diffferent methods are used for this purpose. Application of our theory to the low energy scattering of the halo nucleus $^{11}$Li from a $^{12}$C target is made. It is found that the notion of \textit{l}-independent polarization potential has some validity but can not be a good substitute for the \textit{l}-dependent local equivalent Feshbach polarization potential.Comment: 8 pages, 4 figure

Influence of the halo upon angular distributions for elastic scattering and breakup

The angular distributions for elastic scattering and breakup of halo nuclei are analysed using a near-side/far-side decomposition within the framework of the dynamical eikonal approximation. This analysis is performed for 11Be impinging on Pb at 69 MeV/nucleon. These distributions exhibit very similar features. In particular they are both near-side dominated, as expected from Coulomb-dominated reactions. The general shape of these distributions is sensitive mostly to the projectile-target interactions, but is also affected by the extension of the halo. This suggests the elastic scattering not to be affected by a loss of flux towards the breakup channel.Comment: 11 pages, 3 figures, accepted for publication in Phys. Lett.

Effective Management of Human Resource in Schools of the Future: the Superleadership Paradigm

The impact of technology on education has generated varying possibilities of approaches and techniques in the teaching-learning process in the Malaysian educational setting. In effect, the impact has been pervasive in the management and administrative culture in schools to the extent that there is a growing demand toward a continual building of competency, capacity and capability of educational leaders and managers through various training program

Identification of the time-dependent conductivity of an inhomogeneous diffusive material

In this paper, we consider a couple of inverse problems of determining the time-dependent thermal/hydraulic conductivity from Cauchy data in the one-dimensional heat/diffusion equation with space-dependent heat capacity/ specific storage. The well-posedness of these inverse problems in suitable spaces of continuously differentiable functions are studied. For the numerical realisation, the problems are discretised using the finite-difference method and recast as nonlinear least-squares minimization problems with a simple positivity lower bound on the unknown thermal/ hydraulic conductivity. Numerically, this is effectively solved using the lsqnonlin routine from the MATLAB toolbox. Regularization is included wherever necessary. Numerical results are presented and discussed for several benchmark test examples showing that accurate and stable numerical solutions are achieved. The outcomes of this study will be relevant and of importance to the applied mathematics inverse problems community working on thermal/hydraulic property determination in heat transfer and porous media

Deformed Gaussian Orthogonal Ensemble Analysis of the Interacting Boson Model

A Deformed Gaussian Orthogonal Ensemble (DGOE) which interpolates between the Gaussian Orthogonal Ensemble and a Poissonian Ensemble is constructed. This new ensemble is then applied to the analysis of the chaotic properties of the low lying collective states of nuclei described by the Interacting Boson Model (IBM). This model undergoes a transition order-chaos-order from the $SU(3)$ limit to the $O(6)$ limit. Our analysis shows that the quantum fluctuations of the IBM Hamiltonian, both of the spectrum and the eigenvectors, follow the expected behaviour predicted by the DGOE when one goes from one limit to the other.Comment: 10 pages, 4 figures (avaiable upon request), IFUSP/P-1086 Replaced version: in the previous version the name of one of the authors was omitte