Adaptive BDDC in Three Dimensions

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of variables. The effectiveness of the method is illustrated on several engineering problems.Comment: 28 pages, 9 figures, 9 table

The limiting absorption principle for periodic differential operators and applications to nonlinear Helmholtz equations

We prove an $L^p$-version of the limiting absoprtion principle for a class of periodic elliptic differential operators of second order. The result is applied to the construction of nontrivial solutions of nonlinear Helmholtz equations with periodic coefficient functions

Transform-Limited-Pulse Representation of Excitation with Natural Incoherent Light

We study the natural excitation of molecular systems, applicable to, for example, photosynthetic light-harvesting complexes, by natural incoherent light. In contrast with the conventional classical models, we show that the light need not have random character to properly represent the resultant linear excitation. Rather, thermal excitation can be interpreted as a collection of individual events resulting from the system's interaction with individual, deterministic pulsed realizations that constitute the field. The derived expressions for the individual field realizations and excitation events allow for a wave function formalism, and therefore constitute a useful calculational tool to study dynamics following thermal-light excitation. Further, they provide a route to the experimental determination of natural incoherent excitation using pulsed laser techniques.Comment: 5 pages, 3 figures, 1 page supplementary information. Comments welcom

Parameter estimation on gravitational waves from multiple coalescing binaries

Future ground-based and space-borne interferometric gravitational-wave detectors may capture between tens and thousands of binary coalescence events per year. There is a significant and growing body of work on the estimation of astrophysically relevant parameters, such as masses and spins, from the gravitational-wave signature of a single event. This paper introduces a robust Bayesian framework for combining the parameter estimates for multiple events into a parameter distribution of the underlying event population. The framework can be readily deployed as a rapid post-processing tool