University of California, Irvine

About: University of California, Irvine is a education organization based out in Irvine, California, United States. It is known for research contribution in the topics: Population & Galaxy. The organization has 47031 authors who have published 113602 publications receiving 5521832 citations. The organization is also known as: UC Irvine & UCI.

A fast sweeping method for Eikonal equations

Abstract: In this paper a fast sweeping method for computing the numerical solution of Eikonal equations on a rectangular grid is presented. The method is an iterative method which uses upwind difference for discretization and uses Gauss-Seidel iterations with alternating sweeping ordering to solve the discretized system. The crucial idea is that each sweeping ordering follows a family of characteristics of the corresponding Eikonal equation in a certain direction simultaneously. The method has an optimal complexity of O(N) for N grid points and is extremely simple to implement in any number of dimensions. Monotonicity and stability properties of the fast sweeping algorithm are proven. Convergence and error estimates of the algorithm for computing the distance function is studied in detail. It is shown that 2 n Gauss-Seidel iterations is enough for the distance function in n dimensions. An estimation of the number of iterations for general Eikonal equations is also studied. Numerical examples are used to verify the analysis.

Boundary conditions for the diffusion equation in radiative transfer

Abstract: Using the method of images, we examine the three boundary conditions commonly applied to the surface of a semi-infinite turbid medium. We find that the image-charge configurations of the partial-current and extrapolated-boundary conditions have the same dipole and quadrupole moments and that the two corresponding solutions to the diffusion equation are approximately equal. In the application of diffusion theory to frequency-domain photon-migration (FDPM) data, these two approaches yield values for the scattering and absorption coefficients that are equal to within 3%. Moreover, the two boundary conditions can be combined to yield a remarkably simple, accurate, and computationally fast method for extracting values for optical parameters from FDPM data. FDPM data were taken both at the surface and deep inside tissue phantoms, and the difference in data between the two geometries is striking. If one analyzes the surface data without accounting for the boundary, values deduced for the optical coefficients are in error by 50% or more. As expected, when aluminum foil was placed on the surface of a tissue phantom, phase and modulation data were closer to the results for an infinite-medium geometry. Raising the reflectivity of a tissue surface can, in principle, eliminate the effect of the boundary. However, we find that phase and modulation data are highly sensitive to the reflectivity in the range of 80-100%, and a minimum value of 98% is needed to mimic an infinite-medium geometry reliably. We conclude that noninvasive measurements of optically thick tissue require a rigorous treatment of the tissue boundary, and we suggest a unified partial-current--extrapolated boundary approach.

Scaling environmental change through the community-level: a trait-based response-and-effect framework for plants

Abstract: Predicting ecosystem responses to global change is a major challenge in ecology. A critical step in that challenge is to understand how changing environmental conditions influence processes across levels of ecological organization. While direct scaling from individual to ecosystem dynamics can lead to robust and mechanistic predictions, new approaches are needed to appropriately translate questions through the community level. Species invasion, loss, and turnover all necessitate this scaling through community processes, but predicting how such changes may influence ecosystem function is notoriously difficult. We suggest that community-level dynamics can be incorporated into scaling predictions using a trait-based response-effect framework that differentiates the community response to environmental change (predicted by response traits) and the effect of that change on ecosystem processes (predicted by effect traits). We develop a response-and-effect functional framework, concentrating on how the relationships among species' response, effect, and abundance can lead to general predictions concerning the magnitude and direction of the influence of environmental change on function. We then detail several key research directions needed to better scale the effects of environmental change through the community level. These include (1) effect and response trait characterization, (2) linkages between response-and-effect traits, (3) the importance of species interactions on trait expression, and (4) incorporation of feedbacks across multiple temporal scales. Increasing rates of extinction and invasion that are modifying communities worldwide make such a research agenda imperative.