Entropy Production in Random Billiards

We introduce a class of random mechanical systems called random billiards to study the problem of quantifying the irreversibility of nonequilibrium macroscopic systems. In a random billiard model, a point particle evolves by free motion through the interior of a spatial domain, and reflects according to a reflection operator, specified in the model by a Markov transition kernel, upon collision with the boundary of the domain. We derive a formula for entropy production rate that applies to a general class of random billiard systems. This formula establishes a relation between the purely mathematical concept of entropy production rate and textbook thermodynamic entropy, recovering in particular Clausius' formulation of the second law of thermodynamics. We also study an explicit class of examples whose reflection operator, referred to as the Maxwell-Smolukowski thermostat, models systems with boundary thermostats kept at possibly different temperatures. We prove that, under certain mild regularity conditions, the class of models are uniformly ergodic Markov chains and derive formulas for the stationary distribution and entropy production rate in terms of geometric and thermodynamic parameters.Comment: 30 pages, 9 figure

Zero gravity apparatus Patent

Zero gravity apparatus utilizing pneumatic decelerating means to create payload subjected to zero gravity conditions by dropping its heigh

Establishing a Sustainable Occupational Therapy Student-Led Pro Bono Clinic at the University of Saint Augustine in Austin, Texas

Under-resourced and underserved communities across the United States experience significant health disparities. These communities lack access to valuable services resulting in health inequities that impinge on their health, quality of life, and engagement in meaningful occupations. There is a need for occupational therapy to provide valuable services to the under-resourced and underserved community to address the historical inequity that impacts their overall quality of life. Universities have the potential to fulfill the gaps within these communities by establishing a pro bono clinic. The purpose of this capstone project is to establish a sustainable occupational therapy pro bono clinic at the University of Saint Augustine for Health Science Austin campus. The intent of the pro bono clinic is twofold. The first, is to provide students with the opportunity to advance their clinical skills and graduate as leaders with insights on the causes of health disparities and the skills to address them. Second, is to address the gap in services experienced by the under-resourced community, and the underserved such as those with disabilities and chronic conditions who do not meet the “reasonable and necessary clause” and those who have maximized their benefits and do not qualify for preventative and chronic rehabilitation services. The significance of this project will impact the university, students, faculty, and the community to yield several positive outcomes. The project plan is to establish an occupational therapy pro bono clinic by organizing the student body and developing a website to meet the needs of the students, clients, and community stakeholders

Are Securities Laws Effective Against Climate Change? A Proposal for Targeted Climate Related Disclosure and GHG Reduction

The New York Attorney General filed a lawsuit against Exxon Mobil on October 24, 2018, claiming the company committed securities fraud in order to prop up the value of the company by publicly disclosing a higher proxy cost—or projected future cost—of climate change regulation than the internal cost used. Following this lawsuit, a federal class action was filed utilizing the same legal theory on the same facts. These lawsuits should be viewed as part of the larger history of lawsuits against large fossil fuel companies for climate change-related harms. Public nuisance theory largely captured a set of lawsuits against these companies, before being nullified as an actionable federal claim by AEP and Kivalina on displacement grounds. There are several issues with using securities fraud to address climate change. First, securities laws suffer from circularity, as harmed investors are recouped by other stakeholders and the corporation, thereby also harming the shareholder group, and leaving no net gain. Second, quantifying proxy costs poses a challenge, as future regulations are not yet in existence. Third, climate change disclosure is not mandated by the SEC, which leads to a range of disclosure, often inadequate, from the use of varied accounting frameworks or the lack of disclosure entirely. Finally, securities law fails to address the societal cost of climate change, instead focusing on reimbursing the internal harmed shareholder group while excluding externally harmed groups. This Note proposes a legislative solution through comparison to the Dodd-Frank Wall Street Reform Act of 2010 as a societal-focused law. Through the proposed legislation, this Note seeks to help refine securities fraud as a tool to combat climate change-related financial fraud to capture negative externalities