2004 — 2007 
Beetle, Christopher 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Mathematical Physics For Gravitational Wave Astronomy @ Florida Atlantic University
The NSF's two LIGO gravitational wave detectors are among a number of new and planned facilities around the globe designed to detect gravitational waves. Once operating at their optimal design sensitivities, these detectors are expected to open a new vista in highenergy astrophysics, gravitational wave astronomy, in which gravitational radiation incident on Earth could be analyzed to extract previously inaccessible information about its sources. A great deal of work must yet be done to make gravitational wave astronomy a reality. This award sponsors the development of mathematical techniques needed to calculate approximations to the gravitational wave signals arising from an astrophysical inspiral of pairs of black holes or neutron stars. These are likely to be among the strongest signals for detection and are consequently among the most critical to understand theoretically. The research funded here will be conducted in concert with three other groups around the U.S., and will tightly integrate the development of new mathematical techniques and the generation of computer codes implementing them. In addition to the main goal of producing a reliable template for the gravitational wave signal arising from binary systems, this work aims to produce new, astrophysicallyrealistic initialdata sets describing binary systems for other numerical relativity efforts around the country and around the world.
The mathematical terrain underlying this project is largely unexplored. As a result, there are many educational opportunities for undergraduate and graduate students participating in this work. Students need little preparation beyond their course work to begin contributing, and the chance to become involved in timely and important research in relativity theory  a prominent subfield of physics in the popular imagination  could help attract young people to the field. In addition, this research will be conducted by a young PI in a young relativity effort at a young research institution, Florida Atlantic University. The award will help establish a new group in gravitational theory and foster close research ties between it and established groups around the U.S. This new group will help raise the profile of physics research, particularly in relativity theory, throughout southern Florida via its members' planned vigorous public outreach efforts.

0.942 
2006 — 2008 
Tichy, Wolfgang [⬀] Marronetti, Pedro (coPI) [⬀] Beetle, Christopher 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Orbiting Binary Black Holes  From the PostNewtonian Regime to the Innermost Stable Circular Orbit by Combining Initial Data Sequences and Numerical Evolutions @ Florida Atlantic University
The NSF's LIGO gravitational wave detectors are among a number of new and planned facilities all over the world which are designed to directly detect and measure gravitational waves. The observation of gravitational waves will open a new window on the universe by enabling us to study exotic objects such as black holes, supernovae, neutron stars, collapsars and gammaray bursts in a completely different way. The work in this project is aimed at continuing the development of a generic numerical code capable of simulating what is expected to be one of the most important sources of gravitational radiation, namely binary systems consisting of black holes. The specific focus of this project is to improve such binary black hole simulations by (i) providing more realistic initial conditions for the simulations, (ii) improving the quality and accuracy of the simulations and (iii) studying the validity and utility of approximation schemes such as the periodic standingwave approximation. This work is important because only accurate simulations, which start from realistic initial conditions, will be able to produce reliable theoretical predictions of the gravitational waves which will be observed in the near future. In addition, this investigation makes key contributions to synergistic efforts, ranging from numerical and mathematical relativity to gravitational wave astrophysics. It is carried out in collaboration with the relativity groups at the University of Texas in Brownsville and the University of Jena in Germany. Regular exchanges benefit students from all three institutions.

0.942 
2021 
Beetle, Christopher Tognoli, Emmanuelle [⬀] Williams, Christine L (coPI) [⬀] 
R56Activity Code Description: To provide limited interim research support based on the merit of a pending R01 application while applicant gathers additional data to revise a new or competing renewal application. This grant will underwrite highly meritorious applications that if given the opportunity to revise their application could meet IC recommended standards and would be missed opportunities if not funded. Interim funded ends when the applicant succeeds in obtaining an R01 or other competing award built on the R56 grant. These awards are not renewable. 
The Mathematics of Relatedness @ Florida Atlantic University
Social interactions are beneficial for aging individuals, be they healthy or affected by degenerative disease. Social engagement not only brings support but also acts on brain structure, behavior and cognition to slow aging. The aging process, however, produces multiple changes that compromise people?s ability to interact with others (person too slow or frail to keep to regular outings with family; thought processes and verbal fluency too sluggish, and hearing too feeble, to secure sufficiently frequent turnsattalk in group conversation with younger individuals; etc.), leading to attrition of numerous and varied social links. The goal of this research program, to be conducted by an interdisciplinary team of sociocognitive scientists, mathematical physicists and geriatric nursing experts, is to gain understanding on first principles underlying preservation or loss of social interaction in aging. This is accomplished by mathematically modeling the underpinnings of social integration and segregation within heterogeneous groups of older and younger individuals, and by conducting observational studies of group activities involving elderly and younger adults in a memory and wellness center (storytelling, gentle yoga, music making). Our mathematical model of social coordination (empirically validated in young adults) allows to vary each agent?s ?coupling? capabilities, (behavioral or cognitive) slowing pace, the memory process of social adaptation and behavioral noise level. Preliminary evidence suggests that pace discrepancy and weak coupling lead to briefer, less frequent periods of coordination, which are fundamentally scale and contextdependent. Theory also suggests that noise enhances the stability of heterogenous groups, while tending to disrupt that of more homogenous ones. All of those preliminary findings point to systemic effects: interactional opportunities not only depend on individuals, but also nontrivially on the match or mismatch between individuals and their social environment. Therefore, the contribution of this research on methodology and measurement in the behavioral and social sciences lies in a muchneeded emphasis on this systemic of social behavior, that is, the effect that the whole exerts on the parts, a key property of complex systems. It leads to an exemplary framework for quantifying individual and collective behavior; provides analysis strategies to characterize their entanglement; and identifies cues to recognize when systemic effects are likely at play. The specific aims of this projects are, first and via models, to quantify the effect that the social environment exerts on elderly social interactions and second, via empirical observations, to develop translational work that connects the model?s first principle with verified outcomes so as to engineer social interactions that maximize connectedness. All of those advances will help to sustain behavioral and cognitive reserve and extend the span of healthy and functional aging. Because of its foundation in a general mathematical model of coordination, the findings and their methodology can also apply in a broad range of translational contexts, including the many facets of communicable health and communicable disease.

0.942 