Relativistic QRPA calculation of muon capture rates

The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of total muon capture rates on a large set of nuclei from $^{12}$C to $^{244}$Pu, for which experimental values are available. The microscopic theoretical framework is based on the Relativistic Hartree-Bogoliubov (RHB) model for the nuclear ground state, and transitions to excited states are calculated using the PN-RQRPA. The calculation is fully consistent, i.e., the same interactions are used both in the RHB equations that determine the quasiparticle basis, and in the matrix equations of the PN-RQRPA. The calculated capture rates are sensitive to the in-medium quenching of the axial-vector coupling constant. By reducing this constant from its free-nucleon value $g_A = 1.262$ by 10% for all multipole transitions, the calculation reproduces the experimental muon capture rates to better than 10% accuracy.Comment: 19 pages, 5 figures, submitted to Phys. Rev.

Numerical Approximations Using Chebyshev Polynomial Expansions

We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the Chebyshev polynomial of order N (El-gendi's method). The solutions are exact at these points, apart from round-off computer errors and the convergence of other numerical methods used in connection to solving the linear system of equations. Applications to initial value problems in time-dependent quantum field theory, and second order boundary value problems in fluid dynamics are presented.Comment: minor wording changes, some typos have been eliminate

Efficient Entropy Estimation for Mutual Information Analysis Using B-Splines

International audienceThe Correlation Power Analysis (CPA) is probably the most used side-channel attack because it seems to fit the power model of most standard CMOS devices and is very efficiently computed. However, the Pearson correlation coefficient used in the CPA measures only linear statistical dependences where the Mutual Information (MI) takes into account both linear and nonlinear dependences. Even if there can be simultaneously large correlation coefficients quantified by the correlation coefficient and weak dependences quantified by the MI, we can expect to get a more profound understanding about interactions from an MI Analysis (MIA). We study methods that improve the non-parametric Probability Density Functions (PDF) in the estimation of the entropies and, in particular, the use of B-spline basis functions as pdf estimators. Our results indicate an improvement of two fold in the number of required samples compared to a classic MI estimation. The B-spline smoothing technique can also be applied to the rencently introduced Cramér-von-Mises test

An approach to convert vertex-based 3D representations to combinatorial B-splines for real-time visual collaboration

Scientific Visualization and Virtual Reality are increasingly being used for the design of complex systems. These technologies offer powerful capabilities to make decisions that are cost and time effective. The next logical extension is to collaborate with these visual models in real-time, where parts of a design team are geographically separated. Specifically, visual collaboration enables ideas and proposed changes to be discussed exactly on a virtual model of a product. However, high-end visualization hardware and Internet technologies impede widespread use of real-time visual collaboration due to the large amount of data from which these representations are created. These data are typically in the form of 3D vertex-based models, which offer a high degree of realism when displayed, but at a price of storage, rendering speeds and processing efficiency. The more realistic the representation desired, the larger the number of vertices required and hence the higher the file size. In this paper, we propose a new data modeling and handling technique where traditional vertex-based models are converted into combinatorial B-Spline based wire-frame models that allow realtime visual collaboration in the context of typical virtual reality systems. Using appropriate filtering methods, parametric equations are computed for each curved segment in a vertexbased representation and bundled together with sampled linear segments of the model. The computed parametric equation based models occupy only a fraction of the size when compared to the original vertex-based models. These lightweight models can easily be transmitted over the Internet, in real-time, for viewing with a platform independent visual client program. The proposed methods were tested on several example data files to prove the method’s effectiveness

Smoothness-Increasing Accuracy-Conserving (SIAC) filtering and quasi interpolation: A unified view

Filtering plays a crucial role in postprocessing and analyzing data in scientific and engineering applications. Various application-specific filtering schemes have been proposed based on particular design criteria. In this paper, we focus on establishing the theoretical connection between quasi-interpolation and a class of kernels (based on B-splines) that are specifically designed for the postprocessing of the discontinuous Galerkin (DG) method called Smoothness-Increasing Accuracy-Conserving (SIAC) filtering. SIAC filtering, as the name suggests, aims to increase the smoothness of the DG approximation while conserving the inherent accuracy of the DG solution (superconvergence). Superconvergence properties of SIAC filtering has been studied in the literature. In this paper, we present the theoretical results that establish the connection between SIAC filtering to long-standing concepts in approximation theory such as quasi-interpolation and polynomial reproduction. This connection bridges the gap between the two related disciplines and provides a decisive advancement in designing new filters and mathematical analysis of their properties. In particular, we derive a closed formulation for convolution of SIAC kernels with polynomials. We also compare and contrast cardinal spline functions as an example of filters designed for image processing applications with SIAC filters of the same order, and study their properties