The Immanent Contingency of Physical Laws in Leibniz’s Dynamics

This paper focuses on Leibniz’s conception of modality and its application to the issue of natural laws. The core of Leibniz’s investigation of the modality of natural laws lays in the distinction between necessary, geometrical laws on the one hand, and contingent, physical laws of nature on the other. For Leibniz, the contingency of physical laws entailed the assumption of the existence of an additional form of causality beyond mechanical or efficient ones. While geometrical truths, being necessary, do not require the use of the principle of sufficient reason, physical laws are not strictly determined by geometry and therefore are logically distinct from geometrical laws. As a consequence, the set of laws that regulate the physical laws could have been created otherwise by God. However, in addition to this, the contingency of natural laws does not consist only in the fact that God has chosen them over other possible ones. On the contrary, Leibniz understood the status of natural laws as arising from the action internal to physical substances. Hence the actuality of physical laws results from a causal power that is inherent to substances rather than being the mere consequence of the way God arranged the relations between physical objects. Focusing on three instances of Leibniz’s treatment of contingency in physics, this paper argues that, in order to account for the contingency of physical laws, Leibniz maintained that final causes, in addition to efficient and mechanical ones, must operate in physical processes and operations

Virtual Reality Games for Motor Rehabilitation

This paper presents a fuzzy logic based method to track user satisfaction without the need for devices to monitor users physiological conditions. User satisfaction is the key to any product’s acceptance; computer applications and video games provide a unique opportunity to provide a tailored environment for each user to better suit their needs. We have implemented a non-adaptive fuzzy logic model of emotion, based on the emotional component of the Fuzzy Logic Adaptive Model of Emotion (FLAME) proposed by El-Nasr, to estimate player emotion in UnrealTournament 2004. In this paper we describe the implementation of this system and present the results of one of several play tests. Our research contradicts the current literature that suggests physiological measurements are needed. We show that it is possible to use a software only method to estimate user emotion

Combined analysis of KamLAND and Borexino neutrino signals from Th and U decays in the Earth's interior

The KamLAND and Borexino experiments have detected electron antineutrinos produced in the decay chains of natural thorium and uranium (Th and U geoneutrinos). We analyze the energy spectra of current geoneutrino data in combination with solar and long-baseline reactor neutrino data, with marginalized three-neutrino oscillation parameters. We consider the case with unconstrained Th and U event rates in KamLAND and Borexino, as well as cases with fewer degrees of freedom, as obtained by successively assuming for both experiments a common Th/U ratio, a common scaling of Th+U event rates, and a chondritic Th/U value. In combination, KamLAND and Borexino can reject the null hypothesis (no geoneutrino signal) at 5 sigma. Interesting bounds or indications emerge on the Th+U geoneutrino rates and on the Th/U ratio, in broad agreement with typical Earth model expectations. Conversely, the results disfavor the hypothesis of a georeactor in the Earth's core, if its power exceeds a few TW. The interplay of KamLAND and Borexino geoneutrino data is highlighted.Comment: 12 pages, including 6 figure

Introductory Lectures on Turbulence: Physics, Mathematics and Modeling

From Chapter 1: The understanding of turbulent behavior in flowing fluids is one of the most intriguing, frustrating— and important—problems in all of classical physics. The problem of turbulence has been studied by many of the greatest physicists and engineers of the 19th and 20th Centuries, and yet we do not understand in complete detail how or why turbulence occurs, nor can we predict turbulent behavior with any degree of reliability, even in very simple (from an engineering perspective) flow situations. Thus, study of turbulence is motivated both by its inherent intellectual challenge and by the practical utility of a thorough understanding of its nature.https://uknowledge.uky.edu/me_textbooks/1001/thumbnail.jp

Correlation function of spin noise due to atomic diffusion

We use paramagnetic Faraday rotation to study spin noise spectrum from unpolarized Rb vapor in a tightly focused probe beam in the presence of N$_2$ buffer gas. We derive an analytical form for the diffusion component of the spin noise time-correlation function in a Gaussian probe beam. We also obtain analytical forms for the frequency spectrum of the spin noise in the limit of a tightly focused or a collimated Gaussian beam in the presence of diffusion. In particular, we find that in a tightly focused probe beam the spectral lineshape can be independent of the buffer gas pressure. Experimentally, we find good agreement between the calculated and measured spin noise spectra for N$_2$ gas pressures ranging from 56 to 820 torr.Comment: 6 pages, 4 figure

Lectures in Computational Fluid Dynamics of Incompressible Flow: Mathematics, Algorithms and Implementations

From Prologue: The present lecture notes are written to emphasize the mathematics of the Navier–Stokes (N.–S.) equations of incompressible flow and the algorithms that have been developed over the past 30 years for solving them.https://uknowledge.uky.edu/me_textbooks/1003/thumbnail.jp

Lectures on Computational Numerical Analysis of Partial Differential Equations

From Chapter 1: The purpose of these lectures is to present a set of straightforward numerical methods with applicability to essentially any problem associated with a partial differential equation (PDE) or system of PDEs independent of type, spatial dimension or form of nonlinearity.https://uknowledge.uky.edu/me_textbooks/1002/thumbnail.jp

Lectures In Elementary Fluid Dynamics: Physics, Mathematics and Applications

From Chapter 1: It takes little more than a brief look around for us to recognize that fluid dynamics is one of the most important of all areas of physics—life as we know it would not exist without fluids, and without the behavior that fluids exhibit. It is the goal of these lecture notes to help students in this process of gaining an understanding of, and an appreciation for, fluid motion—what can be done with it, what it might do to you, how to analyze and predict it.https://uknowledge.uky.edu/me_textbooks/1000/thumbnail.jp