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One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov 2014 Dublin Institute of Technology

One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

Articles

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.


Free Energies In A General Non-Local Theory Of A Material With Memory, Giovambattista Amendola, Mauro Fabrizio, Murrough Golden 2014 Dublin Institute of Technology

Free Energies In A General Non-Local Theory Of A Material With Memory, Giovambattista Amendola, Mauro Fabrizio, Murrough Golden

Articles

A general theory of non-local materials, with linear constitutive equations and memory effects, is developed within a thermodynamic framework. Several free energy and dissipation functionals are constructed and explored. These include an expression for the minimum free energy and a functional that is a free energy for important categories of memory kernels and is explicitly a functional of the minimal state. The functionals discussed have a similar general form to the corresponding expressions for simple materials. A number of new results are derived for them, most of which apply equally to both types of material. In particular, detailed formulae are ...


Traditional Lecture Versus An Activity Approach For Teaching Statistics: A Comparison Of Outcomes, Jennifer L. Loveland 2014 Utah State University

Traditional Lecture Versus An Activity Approach For Teaching Statistics: A Comparison Of Outcomes, Jennifer L. Loveland

All Graduate Theses and Dissertations

Many educational researchers have proposed teaching statistics with less lecture and more active learning methods. However, there are only a few comparative studies that have taught one section of statistics with lectures and one section with activity-based methods; of those studies, the results are contradictory. To address the need for more research on the actual effectiveness of active learning methods in introductory statistics, this research study was undertaken.

An introductory, university level course was divided into two sections. One section was taught entirely with traditional lecture. The other section was taught using active learning methods and a minimal amount of ...


Bayes, Brains & Babies: Electrophysiology And Mathematics Of Infant Holistic Processing And Selective Inhibition, Matthew Singh 2014 University of Tennessee, Knoxville

Bayes, Brains & Babies: Electrophysiology And Mathematics Of Infant Holistic Processing And Selective Inhibition, Matthew Singh

EURēCA: Exhibition of Undergraduate Research and Creative Achievement

Poster presentation at 2014 Exhibition of Undergraduate Research and Creative Achievement


Fan-Linear Maps And Fan Algebras, John Hull 2014 Georgia State University

Fan-Linear Maps And Fan Algebras, John Hull

Georgia State Undergraduate Research Conference

No abstract provided.


Dynamics Of Traveling Waves In Neural Networks In Presence Of Period Inhomogeneities, Rosahn Bhattarai 2014 Georgia State University

Dynamics Of Traveling Waves In Neural Networks In Presence Of Period Inhomogeneities, Rosahn Bhattarai

Georgia State Undergraduate Research Conference

No abstract provided.


A Cellular Automaton Model For Traffic Flow - Investigating The Effect Of Turning, Tracy Finner, Matthew A. Beauregard 2014 Indiana University – Purdue University Fort Wayne

A Cellular Automaton Model For Traffic Flow - Investigating The Effect Of Turning, Tracy Finner, Matthew A. Beauregard

American Journal of Undergraduate Research

A cellular automaton model is proposed, modeling vehicular traffic flow on a two dimensional lattice in which the vehicles turn at an intersection with a given probability. It is shown that the introduction of turning reduces the long-term average velocity, and can be predicted by a power law depending on the probability of a vehicle turning and the density of cars. The reduction in speed decreases rapidly once the light cycle length surpasses a certain threshold, the value of which can be predicted from the observed power law.


On The Hamming Distance Between Base-N Representations Of Whole Numbers, Anunay Kulshrestha 2014 Indiana University – Purdue University Fort Wayne

On The Hamming Distance Between Base-N Representations Of Whole Numbers, Anunay Kulshrestha

American Journal of Undergraduate Research

We first talk about the Hamming Distance between two strings. Then, we apply this concept to the representations of whole numbers in base n for all positive integers n > 2. We claim that a closed-form formula exists that helps us find the sum of all such Hamming Distances. Later, we derive the formula. We also state and prove other interesting results on the aforementioned topic.


The Scientist–Reporter Collaboration: A Guide To Working With The Press, Rachel Levy, Flora Lichtman, David L. Hu 2014 Claremont Colleges

The Scientist–Reporter Collaboration: A Guide To Working With The Press, Rachel Levy, Flora Lichtman, David L. Hu

All HMC Faculty Publications and Research

Science, technology, engineering, and mathematics (STEM) to the public can be challenging. Often, the language that researchers use among themselves is technical and difficult for non-experts to decipher. But as you probably know, communicating your research to non-experts is becoming mandatory. In a direct sense, funding agencies often require outreach for grant fulfillment. There are indirect benefits as well: Conveying the joy of discovery and the relevance of scientific results builds scientific literacy among the public---which of course includes both students who will eventually do research of their own and people who elect the policy makers who allocate funding. How ...


An Analysis Of The Practical Dpg Method, Jay Gopalakrishnan, Weifeng Qiu 2014 Portland State University

An Analysis Of The Practical Dpg Method, Jay Gopalakrishnan, Weifeng Qiu

Mathematics and Statistics Faculty Publications and Presentations

We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree p on each mesh element. Earlier works showed that there is a "trial-to-test" operator T, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator T is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply T. In practical computations ...


Aftermath: Every Math Major Should Take A Public-Speaking Course, Rachel Levy 2014 Claremont Colleges

Aftermath: Every Math Major Should Take A Public-Speaking Course, Rachel Levy

All HMC Faculty Publications and Research

Rachel Levy argues that all mathematics majors should learn the art of public speaking.


Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov 2014 Dublin Institute of Technology

Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov

Conference papers

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g with respect to the pairing provided by the variational derivatives of the Lagrangian ...


Steam Inspired By Insight, Diana Vizcarra 2014 Claremont Colleges

Steam Inspired By Insight, Diana Vizcarra

The STEAM Journal

Innovators of the 21st century might come from unexpected places. Visual impairment is no barrier when technology and creativity intersect. The world needs blind innovators! The blind input data without visual association and download blueprints of their surroundings to format a mental database. They categorize patterns, textures, and conditions to perceive their location in space. They are able to capture the beauty of the world through poetry and predict future trends through past experience – all without visual access to the physical world they inhabit.

This writing was possible because of collaboration with Angie Menjivar.


The Efficacy Of Mathematics Education, Eric Geimer 2014 Claremont Colleges

The Efficacy Of Mathematics Education, Eric Geimer

The STEAM Journal

Evidence supports the notion that mathematics education in the United States is inadequate. There is also evidence that mathematics education deficiencies extend internationally. The worldwide mathematics education deficit appears large enough that improving student performance in this educational problem area could yield great economic benefit. To improve the efficacy of mathematics education, education’s root problems must first be understood. Often supposed educational root problems are considered and contrasted against potential deficiencies of mathematics methodologies and curricula that are based on mainstream educational philosophies. The educational philosophies utilized to form early-grade mathematics methodologies and related curricula are judged to be ...


Session B-1: Geometry In Art & Architecture, Julie Dowling 2014 Illinois Mathematics and Science Academy

Session B-1: Geometry In Art & Architecture, Julie Dowling

Professional Learning Day

Math is all around us! Discover how to implement geometry lessons using art and architecture that the students see around them every day.


Session B-2: Build Student Engagement, Mental Math, And Reasoning With "Math Talks", Sendhil Revuluri 2014 Illinois Mathematics and Science Academy

Session B-2: Build Student Engagement, Mental Math, And Reasoning With "Math Talks", Sendhil Revuluri

Professional Learning Day

"Math talks" are quick routines that you can implement in your classroom within days. They can raise engagement, build efficient, accurate, and flexible mental math strategies, and help students construct arguments and critique reasoning. We will engage in math talks, analyzing how they can be enacted in the classroom and designed for specific goals or respond to specific misconceptions. Participants will learn about math talks that support understanding of number, algebra, and other domains.


Session A-2: Cycloids!, Ruth Dover 2014 Illinois Mathematics and Science Academy

Session A-2: Cycloids!, Ruth Dover

Professional Learning Day

This session includes a hands-on exploration to see graphs of different types of cycloids. Participants will use trigonometry to create the parametric equations for the graphs. This topic lends itself nicely to projects for pre-calculus students. Software will be shown to help see more examples and patterns.


The Nature And Nurture Of Intuition, Thomas Q. Sibley 2014 College of Saint Benedict and Saint John’s University

The Nature And Nurture Of Intuition, Thomas Q. Sibley

Forum Lectures

Are people just innately good at mathematics or not? My teaching experience suggests mathematical ability is not just fate: Students develop their mathematical abilities by doing mathematics. In particular we discuss geometric intuition, its connection with geometric reasoning and the possibility of developing them, using examples to get the listeners actively thinking about their own geometric thinking.


The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre 2014 Utah State University

The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre

Charles G. Torre

We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from ...


The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre 2014 Utah State University

The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre

Presentations and Publications

We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein–Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field ...


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