Minimal energy problems for strongly singular Riesz kernels

We study minimal energy problems for strongly singular Riesz kernels on a manifold. Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such problems by switching to Hadamard's partie finie integral operator which defines a strongly elliptic pseudodifferential operator on the manifold. The measures with finite energy are shown to be elements from the corresponding Sobolev space, and the associated minimal energy problem admits a unique solution. We relate our continuous approach also to the discrete one, which has been worked out earlier by D.P. Hardin and E.B. Saff.Comment: 31 pages, 2 figure

Multi-Level quasi-Newton methods for the partitioned simulation of fluid-structure interaction

In previous work of the authors, Fourier stability analyses have been performed of Gauss-Seidel iterations between the flow solver and the structural solver in a partitioned fluid-structure interaction simulation. These analyses of the flow in an elastic tube demonstrated that only a number of Fourier modes in the error on the interface displacement are unstable. Moreover, the modes with a low wave number are most unstable and these modes can be resolved on a coarser grid. Therefore, a new class of quasi-Newton methods with more than one grid level is introduced. Numerical experiments show a significant reduction in run time

Agronomical performance of common bean inoculated with new rhizobial isolates.

This work aimed to evaluate the agronomic efficiency of rhizobia isolates under field conditions in two sites: Guapó and Santo Antônio de Goiás, by comparison of their results with the commercial strains SEMIA 4077, 4080 and SEMIA SEMIA 4088 of Rhizobium tropici

Computational model of one-dimensional flow of water in an unsaturated soil

O estudo do fluxo de água em zonas não saturadas do solo é de grande importância para pesquisas relacionadas à disponibilidade hídrica para o desenvolvimento das plantas. Devido ao alto custo, ao tempo demandado e ao esforço humano nas investigações de campo, os modelos matemáticos, aliados às técnicas numéricas e avanços computacionais, constituem-se em uma ferramenta importante na previsão desses estudos. No presente trabalho, objetivou-se solucionar a equação diferencial parcial não linear de Richards mediante a aplicação do Método de Elementos Finitos. Na aproximação espacial, foi empregada a adaptatividade com refinamento "h" na malha de elementos finitos e, na derivada temporal, foi aplicado o esquema de Euler Explícito. A função interpolação polinomial utilizada foi de grau 2, e a que garantiu a conservação de massa da estratégia de adaptação. Para a validação do modelo, foram utilizados dados disponíveis em literatura. A utilização da função interpolação polinomial de grau 2 e o refinamento "h", com considerável redução do tempo de execução da rotina computacional, permitiram uma boa concordância do modelo em comparação a soluções disponíveis na literatura.Study of water flow in the unsaturated soil zone is of great importance for research related to the water availability for crop development. Due to the high cost, the time required and the human effort in the field investigations, mathematical models combined with numerical techniques and computational advances are important tools in the prediction of these studies. This work aimed to solve the Richards's non-linear partial differential equation by applying the Finite Element Method. Adaptability with "h" refinement of the finite element mesh was used in the spatial approximation, while Explicit Euler scheme was applied for the time derivative. The polynomial interpolation function used was of degree two, and ensured the mass conservation of the adaptation strategy. To validate the model, data available in the literature were used. Use of the polynomial interpolation function with degree two and the "h" refinement, with considerable reduction of the computational runtime allowed good agreement in comparison to solutions available in the literature

Essentially translation invariant pseudodifferential operators on manifolds with cylindrical ends

We study two classes (or calculi) of pseudodifferential operators defined on manifolds with cylindrical ends: the class of pseudodifferential operators that are ``translation invariant at infinity'' and the class of ``essentially translation invariant operators'' that have appeared in the study of layer potential operators on manifolds with straight cylindrical ends. Both classes are close to the $b$-calculus considered by Melrose and Schulze and to the $c$-calculus considered by Melrose and Mazzeo-Melrose. Our calculi, however, are different and, while some of their properties follow from those of the $b$- or $c$-calculi, many of their properties do not. In particular, the ``essentially translation invariant calculus'' is spectrally invariant, a property not enjoyed by the ``translation invariant at infinity'' calculus or the $b$-calculus. For our calculi, we provide easy, intuitive proofs of the usual properties: stability for products and adjoints, mapping and boundedness properties for operators acting between Sobolev spaces, regularity properties, existence of a quantization map and topological properties of our algebras, the Fredholm property. Since our applications will be to the Stokes operator, we systematically work in the setting of Agmon-Douglis-Nirenberg-elliptic operators.Comment: 39 page

A Statistical Model for Simultaneous Template Estimation, Bias Correction, and Registration of 3D Brain Images

Template estimation plays a crucial role in computational anatomy since it provides reference frames for performing statistical analysis of the underlying anatomical population variability. While building models for template estimation, variability in sites and image acquisition protocols need to be accounted for. To account for such variability, we propose a generative template estimation model that makes simultaneous inference of both bias fields in individual images, deformations for image registration, and variance hyperparameters. In contrast, existing maximum a posterori based methods need to rely on either bias-invariant similarity measures or robust image normalization. Results on synthetic and real brain MRI images demonstrate the capability of the model to capture heterogeneity in intensities and provide a reliable template estimation from registration

On the Dirichlet problem in elasticity for a domain exterior to an arc

AbstractWe consider here a Dirichlet problem for the two-dimensional linear elasticity equations in the domain exterior to an open arc in the plane. It is shown that the problem can be reduced to a system of boundary integral equations with the unknown density function being the jump of stresses across the arc. Existence, uniqueness as well as regularity results for the solution to the boundary integral equations are established in appropriate Sobolev spaces. In particular, asymptotic expansions concerning the singular behavior for the solution near the tips of the arc are obtained. By adding special singular elements to the regular splines as test and trial functions, an augmented Galerkin procedure is used for the corresponding boundary integral equations to obtain a quasi-optimal rate of convergence for the approximate solutions