Physical Sciences and Mathematics Commons^™

Primordial Black Hole Evaporation And Spontaneous Dimensional Reduction, Jonas R. Mureika

Physics Faculty Works

Several different approaches to quantum gravity suggest the effective dimension of spacetime reduces from four to two near the Planck scale. In light of such evidence, this Letter re-examines the thermodynamics of primordial black holes (PBHs) in specific lower-dimensional gravitational models. Unlike in four dimensions, (1 + 1)-D black holes radiate with power P ∼ M²_BH, while it is known no (2+1)-D (BTZ) black holes can exist in a non-anti-de Sitter universe. This has important relevance to the PBH population size and distribution, and consequently on cosmological evolution scenarios. The number of PBHs that have evaporated to …

Forecasting The Effect Of The Amethyst Initiative On College Drinking, Ben G. Fitzpatrick, Richard Scribner, Azmy S. Ackleh, Jawaid Rasul, Geoffrey Jacquez, Neal Simonsen, Robert Rommel

Mathematics Faculty Works

Background

A number of college presidents have endorsed the Amethyst Initiative, a call to consider lowering the minimum legal drinking age (MLDA). Our objective is to forecast the effect of the Amethyst Initiative on college drinking.

Methods

A system model of college drinking siumlates MLDA changes through (1) a decrease in heavy episodic drinking (HED) due to the lower likelihood of students drinking in unsupervised settings where they model irresponsible drinking (misperception), and (2) an increase in overall drinking among currently underage students due to increased social availability of alcohol (wetness).

Results

For the proportion of HEDs on campus, effects …

Simulating A Guitar With A Conventional Sonometer, Zily Burstein, Christina M. Gower, Gabriele U. Varieschi

Physics Faculty Works

In this paper we present a simple way to convert a conventional sonometer into a simulated fretted instrument, such as a guitar or similar, by adding a fingerboard to the sonometer. In particular, we use this modified apparatus in relation to the problem of the instrument intonation, i.e., how to obtain correctly tuned notes on these string instruments. The experimental procedures presented in this study can become a more structured laboratory activity to be used in general physics courses or acoustics classes.

Noncontact Ultrasound Imaging Applied To Cortical Bone Phantoms, John Bulman, K. S. Ganezer, P. W. Halcrow, Ian Neeson

Physics Faculty Works

Purpose: The purpose of this paper was to take the first steps toward applying noncontact ultrasound (NCU) to the tasks of monitoring osteoporosis and quantitative ultrasound imaging (QUS) of cortical bone. The authors also focused on the advantages of NCU, such as its lack of reliance on a technologist to apply transducers and a layer of acoustical coupling gel, the ability of the transducers to operate autonomously as specified by preprogrammed software, and the likely reduction in statistical and systematic errors associated with the variability in the pressure applied by the clinician to the transmitting transducer that NCU might provide. …

Computational Modeling And Numerical Methods For Spaciotemporal Calcium Cycling In Ventricular Myocytes, Robert Rovetti

Mathematics Faculty Works

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain …

Computational Modeling And Numerical Methods For Spatiotemporal Calcium Cycling In Ventricular Myocytes, Michael Nivala, Enno De Lange, Robert J. Rovetti, Zhilin Qu

Mathematics Faculty Works

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain …

Could Any Black Holes Be Produced At The Lhc?, Jonas R. Mureika, Piero Nicolini, Euro Spallucci

Physics Faculty Works

We introduce analytical quantum gravity modifications of the production cross section for terascale black holes by employing an effective ultraviolet cut off l. We find the new cross sections approach the usual "black disk" form at high energy, while they differ significantly near the fundamental scale from the standard increase with respect to s. We show that the heretofore discontinuous step function used to represent the cross section threshold can realistically be modeled by two functions representing the incoming and final parton states in a high energy collision. The growth of the cross section with collision energy is …

Conformal Cosmology And The Pioneer Anomaly, Gabriele U. Varieschi

Physics Faculty Works

No abstract provided.

Metals And Bacteria Partitioning To Various Size Particles In Ballona Creek Storm Water Runoff, John Dorsey, Jeffrey S. Brown, Eric D. Stein, Drew Ackerman, Jessica Lyon, Patrick M. Carter

Civil and Environmental Engineering Faculty Works

Many storm water best management practice (BMP) devices function primarily by capturing particulate matter to take advantage of the well-documented association between storm water particles and pollutants. The hydrodynamic separation or settling methods used by most BMP devices are most effective at capturing medium to large particles; however, these may not be the most predominant particles associated with urban runoff. The present study examined particle size distribution in storm water runoff from an urban watershed in southern California and investigated the pollutant-particle associations of metals (Cu, Pb, Ni, and Zn) and bacteria (enterococci and Escherichia coli). During small storm events …

Effects Of Visual, Auditory, And Kinesthetic Imagery Interventions On Dancers’ Plié Arabesques, Teresa Heiland, Robert Rovetti

Mathematics Faculty Works

The goal of this study was to examine the influence of visual, auditory, and kinesthetic delivery modes of Franklin Method images (anatomical bone rhythms, metaphorical image, and tactile aid, respectively) on the performance of college dancers’ Plié Arabesques by assessing its influence on three measures: plié depth; maintenance of rotation; and simultaneous use of hip, knee, and ankle (Tri-fold). Eighteen participants performed a series of Plié Arabesques during three visits over a period of two months; at each visit, pliés were performed before and after an image intervention, and the change in mean Likert scale rating was calculated for each …

Enhancements Of Rack Counting Invariants Via Dynamical Cocycles, Alissa S. Crans, Sam Nelson, Aparna Sarkar

Mathematics Faculty Works

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

The Double Cover Of The Real Symplectic Group And A Theme From Feynman’S Quantum Mechanics, Michael Berg

Mathematics Faculty Works

We present a direct connection between the 2-cocycle defining the double cover of the real symplectic group and a Feynman path integral describing the time evolution of a quantum mechanical system.

Upper Bounds In The Ohtsuki-Riley-Sakuma Partial Order On 2-Bridge Knots, Scott M. Garrabrant, Jim Hoste, Patrick D. Shanahan

Mathematics Faculty Works

In this paper we use continued fractions to study a partial order on the set of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We establish necessary and sufficient conditions for any set of 2-bridge knots to have an upper bound with respect to the partial order. Moreover, given any 2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has an upper bound. As an application we answer a question of Suzuki, showing that there is no upper bound for the set consisting of the trefoil and figure-eight knots.

How Well Do The Nsf Funded Elementary Mathematics Curricula Align With The Gaise Report Recommendations?, Anna E. Bargagliotti

Mathematics Faculty Works

Statistics and probability have become an integral part of mathematics education. Therefore it is important to understand whether curricular materials adequately represent statistical ideas. The Guidelines for Assessment and Instruction in Statistics Education (GAISE) report (Franklin, Kader, Mewborn, Moreno, Peck, Perry, & Scheaffer, 2007), endorsed by the American Statistical Association, provides a two-dimensional (process and level) framework for statistical learning. This paper examines whether the statistics content contained in the NSF funded elementary curricula Investigations in Number, Data, and Space, Math Trailblazers, and Everyday Mathematics aligns with the GAISE recommendations. Results indicate that there are differences in the approaches used …

Characterization Of Radially Symmetric Finite Time Blowup In Multidimensional Aggregation Equations, Andrea L. Bertozzi, John B. Garnett, Thomas Laurent

Mathematics Faculty Works

This paper studies the transport of a mass $\mu$ in $\mathbb{R}^d, d \geq 2,$ by a flow field $v= -\nabla K*\mu$. We focus on kernels $K=|x|^\alpha/ \alpha$ for $2-d\leq \alpha<2$ for which the smooth densities are known to develop singularities in finite time. For this range we prove the existence for all time of radially symmetric measure solutions that are monotone decreasing as a function of the radius, thus allowing for continuation of the solution past the blowup time. The monotone constraint on the data is consistent with the typical blowup profiles observed in recent numerical studies of these singularities. We prove monotonicity is preserved for all time, even after blowup, in contrast to the case $\alpha >2$ where radially symmetric solutions are known to lose monotonicity. In the case of the Newtonian potential ($\alpha=2-d$), under the assumption of radial symmetry the equation can be transformed into the inviscid Burgers equation on a half line. This enables us to prove preservation of monotonicity using the classical theory of conservation laws. In the case $2 -d < \alpha < 2$ and at the critical exponent p we exhibit initial data in $L^p$ for which the solution immediately develops a Dirac mass singularity. This extends recent work on the local ill-posedness of solutions at the critical exponent.

Spatial Graphs With Local Knots, Erica Flapan, Blake Mellor, Ramin Naimi

Mathematics Faculty Works

It is shown that for any locally knotted edge of a 3-connected graph in S³, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in S³.

A New Topological Perspective On Quantization In Physics, Hooman Rahimizadeh, Stan Sholar, Michael Berg

Mathematics Faculty Works

We propose a new characterization of classical quantization in physics in terms of sheaf cohomology on the site of spacetime as a smooth 4-manifold. The perspective of sheaf cohomology is motivated by a presentation of the Aharonov-Bohm effect in terms of the integration of differential forms.

On Levi-Civita’S Alternating Symbol, Schouten’S Alternating Unit Tensors, Cpt, And Quantization, Evert Jan Post, Stan Sholar, Hooman Rahimizadeh, Michael Berg

Mathematics Faculty Works

The purpose of the present article is to demonstrate that by adopting a unifying differential geometric perspective on certain themes in physics one reaps remarkable new dividends in both microscopic and macroscopic domains. By replacing algebraic objects by tensor-transforming objects and introducing methods from the theory of differentiable manifolds at a very fundamental level we obtain a Kottler-Cartan metric-independent general invariance of the Maxwell field, which in turn makes for a global quantum superstructure for Gauss-Amp`ere and Aharonov-Bohm “quantum integrals.” Beyond this, our approach shows that postulating a Riemannian metric at the quantum level is an unnecessary concept and our …

Convergence Of A Steepest Descent Algorithm For Ratio Cut Clustering, Xavier Bresson, Thomas Laurent, David Uminsky, James H. Von Brecht

Mathematics Faculty Works

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In this paper, we present an explicit-implicit gradient flow scheme for the relaxed ratio cut problem, and prove that the algorithm converges to a critical point of the energy. We also show the efficiency of the proposed algorithm on the two moons dataset.

Linear Rank Tests Of Uniformity: Understanding Inconsistent Outcomes And The Construction Of New Tests, Anna E. Bargagliotti

Mathematics Faculty Works

Several nonparametric tests exist to test for differences among alternatives when using ranked data. Testing for differences among alternatives amounts to testing for uniformity over the set of possible permutations of the alternatives. Well-known tests of uniformity, such as the Friedman test or the Anderson test, are based on the impact of the usual limiting theorems (e.g. central limit theorem) and the results of different summary statistics (e.g. mean ranks, marginals, and pairwise ranks). Inconsistencies can occur among statistical tests' outcomes - different statistical tests can yield different outcomes when applied to the same ranked data. In this paper, we …

Congrats You’Re Abd! Now What?, Alissa Crans

Mathematics Faculty Works

No abstract provided.