Large deviations of the empirical current for the boundary driven Kawasaki process with long range interaction

We consider a lattice gas evolving in a bounded cylinder of length 2N + 1 and interacting via a Neuman Kac interaction of range N, in contact with particles reservoirs at different densities. We investigate the associated law of large numbers and large deviations of the empirical current and of the density. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by a nonlocal, nonlinear evolution equation with Dirichlet boundary conditions

Development of a PC interfaced blood pressure meter (E-BPMS)

Blood pressure is one of the fundamental vital signs, and its measurement is of great importance to medical professionals and the general public alike. Nowadays, there are several types of blood pressure meter available manufactured from various companies. In order to meet the demand on telemedicine and technology advancement, a new form of blood pressure meter is desirable. This prototype of blood pressure meter is interfaced with a personal computer (PC) which able to simulate the measurement process in real time. The proposed system was named e-BPMS (Electronic Blood Pressure Measurement System) suggests the usage of both hardware and software in determining blood pressure reading. Hardware elements operate on oscillometric principle which gives the results in terms of systolic, diastolic and MAP (Mean Arterial Pressure). Furthermore, these results will be presented and simulated on the software. The e-BPMS interface was developed by using Visual Basic 6.0 language which highlights the user friendly attributes. Moreover, the simulated waveform will evaluate the blood pressure and gives the blood pressure value. This application shows significant improvement on the overall performance and gives reliable results. The framework used to design e-BPMS is easy to understand and it can be extended further to endorse new application area

Gaussian estimates for spatially inhomogeneous random walks on Zd{\mathbf{Z}}^d

It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on ${\mathbf{Z}}^d$ admits upper and lower Gaussian estimates.Comment: Published at http://dx.doi.org/10.1214/009117905000000440 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

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