An exact general remeshing scheme applied to physically conservative voxelization

We present an exact general remeshing scheme to compute analytic integrals of polynomial functions over the intersections between convex polyhedral cells of old and new meshes. In physics applications this allows one to ensure global mass, momentum, and energy conservation while applying higher-order polynomial interpolation. We elaborate on applications of our algorithm arising in the analysis of cosmological N-body data, computer graphics, and continuum mechanics problems. We focus on the particular case of remeshing tetrahedral cells onto a Cartesian grid such that the volume integral of the polynomial density function given on the input mesh is guaranteed to equal the corresponding integral over the output mesh. We refer to this as "physically conservative voxelization". At the core of our method is an algorithm for intersecting two convex polyhedra by successively clipping one against the faces of the other. This algorithm is an implementation of the ideas presented abstractly by Sugihara (1994), who suggests using the planar graph representations of convex polyhedra to ensure topological consistency of the output. This makes our implementation robust to geometric degeneracy in the input. We employ a simplicial decomposition to calculate moment integrals up to quadratic order over the resulting intersection domain. We also address practical issues arising in a software implementation, including numerical stability in geometric calculations, management of cancellation errors, and extension to two dimensions. In a comparison to recent work, we show substantial performance gains. We provide a C implementation intended to be a fast, accurate, and robust tool for geometric calculations on polyhedral mesh elements.Comment: Code implementation available at https://github.com/devonmpowell/r3

Nonlinear singular perturbations of the fractional Schr\"odinger equation in dimension one

The paper discusses nonlinear singular perturbations of delta type of the fractional Schr\"odinger equation $\imath\partial_t\psi=\left(-\triangle\right)^s\psi$, with $s\in(\frac{1}{2},1]$, in dimension one. Precisely, we investigate local and global well posedness (in a strong sense), conservations laws and existence of blow-up solutions and standing waves.Comment: 28 pages. Some minor revisions have been made with respect to the previous versio

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Rev. iberoam. bioecon. cambio clim. Vol.1(1) 2015; 95-114Los cambios medioambientales globales hacen pensar en un aumento futuro de la aridez, por ello es necesario buscar alternativas que permitan un uso más eficiente del agua y reducir su consumo, teniendo en cuenta que es un recurso limitado. En la actualidad, aproximadamente el 59,7% del total de agua planificada para todos los usos en Cuba se utiliza en la agricultura, pero no más del 50% de esa agua se convierte directamente en productos agrícolas. El estudio de las funciones agua-rendimiento y su uso dentro de la planificación del agua para riego es una vía importante para trazar estrategias de manejo que contribuyan al incremento en la producción agrícola. Utilizando los datos de agua aplicada por riego y los rendimientos obtenidos en más de 100 experimentos de campo realizados fundamentalmente en suelo Ferralítico Rojo de la zona sur de La Habana y con ayuda de herramientas de análisis de regresión en este trabajo se estiman las funciones agua aplicada-rendimientos para algunos cultivos agrícolas y se analizan las posibles estrategias de optimización del riego a seguir en función de la disponibilidad de agua. Seleccionar una estrategia de máxima eficiencia del riego puede conducir a reducciones de agua a aplicar entre un 21,6 y 46,8%, incrementos de la productividad del agua entre 17 y 32% y de la relación beneficios/costo estimada de hasta un 3,4%. Lo anterior indica la importancia desde el punto de vista económico que puede llegar a alcanzar el uso de esta estrategia en condiciones de déficit hídrico. El conocimiento de las funciones agua aplicada por riego-rendimiento y el uso de la productividad del agua, resultan parámetros factibles de introducir como indicadores de eficiencia en el planeamiento del uso del agua en la agricultura, con lo cual es posible reducir los volúmenes de agua a aplicar y elevar la relación beneficio-costo actual.Rev. iberoam. bioecon. cambio clim. Vol.1(1) 2015; 95-11

A Computational Method for Solving a Class of Fractional-Order Non-Linear Singularly Perturbed Volterra Integro-Differential Boundary-Value Problems

In this thesis, we present a computational method for solving a class of fractional singularly perturbed Volterra integro-differential boundary-value problems with a boundary layer at one end. The implemented technique consists of solving two problems which are a reduced problem and a boundary layer correction problem. The reproducing kernel method is used to the second problem. Pade’ approximation technique is used to satisfy the conditions at infinity. Existence and uniformly convergence for the approximate solution are also investigated. Numerical results provided to show the efficiency of the proposed method

Review of Some Promising Fractional Physical Models

Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and differentiation of non-integer orders, i.e., by methods of the fractional calculus. This paper is a review of physical models that look very promising for future development of fractional dynamics. We suggest a short introduction to fractional calculus as a theory of integration and differentiation of non-integer order. Some applications of integro-differentiations of fractional orders in physics are discussed. Models of discrete systems with memory, lattice with long-range inter-particle interaction, dynamics of fractal media are presented. Quantum analogs of fractional derivatives and model of open nano-system systems with memory are also discussed.Comment: 38 pages, LaTe

Hitchhiker's guide to the fractional Sobolev spaces

This paper deals with the fractional Sobolev spaces W^[s,p]. We analyze the relations among some of their possible definitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results. Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains

Intrinsic alignment-lensing interference as a contaminant of cosmic shear

Cosmic shear surveys have great promise as tools for precision cosmology, but can be subject to systematic errors including intrinsic ellipticity correlations of the source galaxies. The intrinsic alignments are believed to be small for deep surveys, but this is based on intrinsic and lensing distortions being uncorrelated. Here we show that the gravitational lensing shear and intrinsic shear need not be independent: correlations between the tidal field and the intrinsic shear cause the intrinsic shear of nearby galaxies to be correlated with the gravitational shear acting on more distant galaxies. We estimate the magnitude of this effect for two simple intrinsic-alignment models: one in which the galaxy ellipticity is linearly related to the tidal field, and one in which it is quadratic in the tidal field as suggested by tidal torque theory. The first model predicts a gravitational-intrinsic (GI) correlation that can be much greater than the intrinsic-intrinsic (II) correlation for broad redshift distributions, and that remains when galaxies pairs at similar redshifts are rejected. The second model, in its simplest form, predicts no gravitational-intrinsic correlation. In the first model, and assuming a normalization consistent with recently claimed detections of intrinsic correlations, we find that the GI correlation term can exceed the usual II term by >1 order of magnitude and the intrinsic correlation induced B-mode by 2 orders of magnitude. These interference effects can suppress the lensing power spectrum for a single broad redshift bin by of order ∼10% at zs=1 and ∼30% at zs=0.5. We conclude that, depending on the intrinsic-alignment model, the GI correlation may be the dominant contaminant of the lensing signal and can even affect cross spectra between widely separated bins. We describe two ways to constrain this effect, one based on density-shear correlations and one based on scaling of the cross correlation tomography signal with redshift