GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations

We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial differential equations and are widely used in the simulation of tsunami wave propagations. Our algorithms are tailored to take advantage of the single instruction multiple data (SIMD) architecture of graphic processing units. The time integration is accelerated by local time stepping based on a multi-rate Adams-Bashforth scheme. A total variational bounded limiter is adopted for nonlinear stability of the numerical scheme. This limiter is coupled with a mass and momentum conserving positivity preserving limiter for the special treatment of a dry or partially wet element in the triangulation. Accuracy, robustness and performance are demonstrated with the aid of test cases. We compare the performance of the kernels expressed in a portable threading language OCCA, when cross compiled with OpenCL, CUDA, and OpenMP at runtime.Comment: 26 pages, 51 figure

A first step to accelerating fingerprint matching based on deformable minutiae clustering

Fingerprint recognition is one of the most used biometric methods for authentication. The identification of a query fingerprint requires matching its minutiae against every minutiae of all the fingerprints of the database. The state-of-the-art matching algorithms are costly, from a computational point of view, and inefficient on large datasets. In this work, we include faster methods to accelerating DMC (the most accurate fingerprint matching algorithm based only on minutiae). In particular, we translate into C++ the functions of the algorithm which represent the most costly tasks of the code; we create a library with the new code and we link the library to the original C# code using a CLR Class Library project by means of a C++/CLI Wrapper. Our solution re-implements critical functions, e.g., the bit population count including a fast C++ PopCount library and the use of the squared Euclidean distance for calculating the minutiae neighborhood. The experimental results show a significant reduction of the execution time in the optimized functions of the matching algorithm. Finally, a novel approach to improve the matching algorithm, considering cache memory blocking and parallel data processing, is presented as future work.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions

We compute the Coleman Weinberg effective potential for the Higgs field in RS Gauge-Higgs unification scenarios based on a bulk SO(5) x U(1)_X gauge symmetry, with gauge and fermion fields propagating in the bulk and a custodial symmetry protecting the generation of large corrections to the T parameter and the coupling of the Z to the bottom quark. We demonstrate that electroweak symmetry breaking may be realized, with proper generation of the top and bottom quark masses for the same region of bulk mass parameters that lead to good agreement with precision electroweak data in the presence of a light Higgs. We compute the Higgs mass and demonstrate that for the range of parameters for which the Higgs boson has Standard Model-like properties, the Higgs mass is naturally in a range that varies between values close to the LEP experimental limit and about 160 GeV. This mass range may be probed at the Tevatron and at the LHC. We analyze the KK spectrum and briefly discuss the phenomenology of the light resonances arising in our model.Comment: 31 pages, 9 figures. Corrected typo in boundary condition for gauge bosons and top mass equation. To appear in PR

On a class of minimum contrast estimators for Gegenbauer random fields

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.Comment: 23 pages, 8 figure

Stripe to spot transition in a plant root hair initiation model

A generalised Schnakenberg reaction-diffusion system with source and loss terms and a spatially dependent coefficient of the nonlinear term is studied both numerically and analytically in two spatial dimensions. The system has been proposed as a model of hair initiation in the epidermal cells of plant roots. Specifically the model captures the kinetics of a small G-protein ROP, which can occur in active and inactive forms, and whose activation is believed to be mediated by a gradient of the plant hormone auxin. Here the model is made more realistic with the inclusion of a transverse co-ordinate. Localised stripe-like solutions of active ROP occur for high enough total auxin concentration and lie on a complex bifurcation diagram of single and multi-pulse solutions. Transverse stability computations, confirmed by numerical simulation show that, apart from a boundary stripe, these 1D solutions typically undergo a transverse instability into spots. The spots so formed typically drift and undergo secondary instabilities such as spot replication. A novel 2D numerical continuation analysis is performed that shows the various stable hybrid spot-like states can coexist. The parameter values studied lead to a natural singularly perturbed, so-called semi-strong interaction regime. This scaling enables an analytical explanation of the initial instability, by describing the dispersion relation of a certain non-local eigenvalue problem. The analytical results are found to agree favourably with the numerics. Possible biological implications of the results are discussed.Comment: 28 pages, 44 figure

Full transmission through perfect-conductor subwavelength hole arrays

Light transmission through 2D subwavelength hole arrays in perfect-conductor films is shown to be complete (100%) at some resonant wavelengths even for arbitrarily narrow holes. Conversely, the reflection on a 2D planar array of non-absorbing scatterers is shown to be complete at some wavelengths regardless how weak the scatterers are. These results are proven analytically and corroborated by rigorous numerical solution of Maxwell's equations. This work supports the central role played by dynamical diffraction during light transmission through subwavelength hole arrays and it provides a systematics to analyze more complex geometries and many of the features observed in connection with transmission through hole arrays.Comment: 5 pages, 4 figure