Optimal L2-error estimates for the semidiscrete Galerkin\ud approximation to a second order linear parabolic initial and\ud boundary value problem with nonsmooth initial data

In this article, we have discussed a priori error estimate for the semidiscrete Galerkin approximation of a general second order parabolic initial and boundary value problem with non-smooth initial data. Our analysis is based on an elementary energy argument without resorting to parabolic duality technique. The proposed technique is also extended to a semidiscrete mixed method for parabolic problems. Optimal L2-error estimate is derived for both cases, when the initial data is in L2

An hp-Local Discontinuous Galerkin method for Parabolic\ud Integro-Differential Equations

In this article, a priori error analysis is discussed for an hp-local discontinuous Galerkin (LDG) approximation to a parabolic integro-differential equation. It is shown that the L2 -norm of the gradient and the L2 -norm of the potential are optimal in the discretizing parameter h and suboptimal in the degree of polynomial p. Due to the presence of the integral term, an introduction of an expanded mixed type Ritz-Volterra projection helps to achieve optimal estimates. Further, it is observed that a negative norm estimate of the gradient plays a crucial role in our convergence analysis. As in the elliptic case, similar results on order of convergence are established for the semidiscrete method after suitably modifying the numerical fluxes. The optimality of these theoretical results is tested in a series of numerical experiments on two dimensional domains

Optimal L2 estimates for semidiscrete Galerkin methods for\ud parabolic integro-differential equations with nonsmooth data

In this article, we discuss an alternate approach to a priori error estimates for the semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equation with nonsmooth initial data. It is based on energy arguments and on a repeated use of time integration, but without using parabolic type duality technique. Optimal L2-error estimate is derived for the semidiscrete approximation, when the initial data is in L2

An a posteriori error analysis of a mixed finite element Galerkin approximation to second order linear parabolic problems

In this article, a posteriori error estimates are derived for a mixed finite element Galerkin approximation to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstruction method, a posteriori error estimates in $L^\infty(L^2)$ and $L^2(L^2)$-norms with optimal order of convergence for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on backward Euler method, a completely discrete scheme is analyzed and a posteriori bounds are derived, which improves earlier results on a posteriori estimates for mixed parabolic problems

Optimal error estimates of a mixed finite element method for\ud parabolic integro-differential equations with non smooth initial data

In this article, a new mixed method is proposed and analyzed for parabolic integro-differential equations (PIDE) with nonsmooth initial data. Compared to mixed methods for PIDE, the present method does not bank on a reformulation using a resolvent operator. Based on energy arguments and without using parabolic type duality technique, optimal L2-error estimates are derived for semidiscrete approximations, when the initial data is in L2. Due to the presence of the integral term, it is, further, observed that estimate in dual of H(div)-space plays a role in our error analysis. Moreover, the proposed analysis follows the spirit of the proof technique used for deriving optimal error estimates of finite element approximations to PIDE with smooth data and therefore, it unifies both the theories, i.e., one for smooth data and other for nonsmooth data. Finally, the proposed analysis can be easily extended to other mixed method for PIDE with rough initial data and provides an improved result

A priori error estimates for the optimal control of laser surface hardening of steel

A priori error estimates for the optimal control of laser surface hardening of stee

Studies of the performance of different front-end systems for flat-panel multi-anode PMTs with CsI(Tl) scintillator arrays

We have studied the performance of two different types of front-end systems for our gamma camera based on Hamamatsu H8500 (flat-panel 64 channels multi-anode PSPMT) with a CsI(Tl) scintillator array. The array consists of 64 pixels of $6\times6\times20{\rm mm}^3$ which corresponds to the anode pixels of H8500. One of the system is based on commercial ASIC chips in order to readout every anode. The others are based on resistive charge divider network between anodes to reduce readout channels. In both systems, each pixel (6mm) was clearly resolved by flood field irradiation of $^{137}$Cs. We also investigated the energy resolution of these systems and showed the performance of the cascade connection of resistive network between some PMTs for large area detectors.Comment: 9 pages, 6 figures, proceedings of the 7th International Workshop on Radiation Imaging Detectors (IWORID7), submitted to NIM

Model independent tests of the Kerr bound with extreme mass ratio inspirals

An outstanding prediction of general relativity is the fact that the angular momentum S of an isolated black hole with mass μ is limited by the Kerr bound, S≤Gμ2/c. Testing this cornerstone is challenging due to the difficulty in modeling spinning compact objects that violate this bound. We argue that precise, model-independent tests can be achieved by measuring gravitational waves from an extreme mass ratio inspiral around a supermassive object, one of the main targets of the future LISA mission. In the extreme mass ratio limit, the dynamics of the small compact object depends only on its multipole moments, which are free parameters. At variance with the comparable-mass case, accurate waveforms are valid also when the spin of the small object greatly exceeds the Kerr bound. By computing the orbital dephasing and the gravitational-wave signal emitted by a spinning point particle in circular, nonprecessing, equatorial motion around a Kerr black hole, we estimate that LISA will be able to measure the spin of the small compact object at the level of 10%. Together with mass measurements, this will allow for theory-agnostic, unprecedented constraints on string-theory inspired objects such as “superspinars”, almost in their entire parameter space

Cholesterol homeostasis: a key to prevent or slow down neurodegeneration

Neurodegeneration, a common feature for many brain disorders, has severe consequences on the mental and physical health of an individual. Typically human neurodegenerative diseases are devastating illnesses that predominantly affect elderly people, progress slowly, and lead to disability and premature death; however they may occur at all ages. Despite extensive research and investments, current therapeutic interventions against these disorders treat solely the symptoms. Therefore, since the underlying mechanisms of damage to neurons are similar, in spite of etiology and background heterogeneous, it will be of interest to identify possible trigger point of neurodegeneration enabling development of drugs and/or prevention strategies that target many disorders simultaneously. Among the factors that have been identified so far to cause neurodegeneration, failures in cholesterol homeostasis are indubitably the best investigated. The aim of this review is to critically discuss some of the main results reported in the recent years in this field mainly focusing on the mechanisms that, by recovering perturbations of cholesterol homeostasis in neuronal cells, may correct clinically relevant features occurring in different neurodegenerative disorders and, in this regard, also debate the current potential therapeutic interventions

A multi-layer edge-on single photon counting silicon microstrip detector for innovative techniques in diagnostic radiology

A three-layer detector prototype, obtained by stacking three edge-on single photon counting silicon microstrip detectors, has been developed and widely tested. This was done in the framework of the Synchrotron Radiation for Medical Physics/Frontier Radiology (SYRMEP/FRONTRAD) collaboration activities, whose aim is to improve the quality of mammographic examinations operating both on the source and on the detector side. The active surface of the device has been fully characterized making use of an edge-scanning technique and of a well-collimated laminar synchrotron radiation beam. The obtained data (interlayer distances, channel correspondence, etc.) have then been used to combine information coming from each detector layer, without causing any loss in spatial and contrast resolution of the device. Contrast and spatial resolution have also been separately evaluated for each detector layer. Moreover, imaging techniques (phase contrast, refraction, and scatter imaging), resulting in an increased visibility of low absorbing details, have been implemented, and their effectiveness has been tested on a biological sample. Finally, the possibility of simultaneously acquiring different kind of images with the different detector layers is discussed. This would result in maximizing the information extracted from the sample, while at the same time the high absorption efficiency of the detector device would allow a low dose delivery