Physical Sciences and Mathematics Commons^™

Universal Scaling And Intrinsic Classification Of Electro-Mechanical Actuators, Sambit Palit, Ankit Jain, Muhammad A. Alam

Birck and NCN Publications

Actuation characteristics of electromechanical (EM) actuators have traditionally been studied for a few specific regular electrode geometries and support (anchor) configurations. The ability to predict actuation characteristics of electrodes of arbitrary geometries and complex support configurations relevant for broad range of applications in switching, displays, and varactors, however, remains an open problem. In this article, we provide four universal scaling relationships for EM actuation characteristics that depend only on the mechanical support configuration and the corresponding electrode geometries, but are independent of the specific geometrical dimensions and material properties of these actuators. These scaling relationships offer an intrinsic classification for …

Turrent Configurations And Particle Paths, Zihao Lawrence Jian

Undergraduate Research Conference

The research originated from the question of how many rows of soldiers or turrets could be placed and allow for all turrets to have a projectile path. We find the relationship between the safe radius for each turret/soldier and the number of rows for which each soldier will have a clear projectile path. As shown, we place turrets in a grid configuration in the Cartesian plane.

Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives, Xiao-Jun Yang

Xiao-Jun Yang

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.

Simulating Exoplanet Detection Of Kepler Via Monte-Carlo Techniques, Manuel Marcano, Mario Yuuji Harper

Mario Yuuji Harper

The Kepler mission was launched in 2009 with the intent to find earth-like planets around other star systems. Since it's launch, the number of known (and suspected) exoplanets have increased substantially from 200 to 3000. With this increase in data now available, we have chosen to model through a monte-carlo simulation, the possibility of being able to see exoplanets in a random part of the sky (using the parameters of the Kepler spacecraft). We show that there is a 0.18 to 0.01 percent chance of being able to detect exoplanets.

Research And Development Of The Positron Damping Rings For The Proposed International Linear Collider, And At Cern In Geneva, Switzerland For The Large Hadron Collider Atlas Experiment's Integrated Simulation Framework, Ryan Badman

Renée Crown University Honors Thesis Projects - All

Abstract not available. Please download the full Capstone for abstract.

Novel Algorithms And Instrumentation For Vibrational Spectroscopic Methods Of Analysis, Mohamed F. Abdelkader

Chemistry & Biochemistry Theses & Dissertations

Raman spectroscopy is a form of vibrational spectroscopy that has been increasingly applied to qualitative analysis of chemicals, explosives, pharmaceuticals, and fuels due to its non-invasive and non-destructive nature; its ease of sampling; and its high molecular specificity. These characteristics of Raman spectroscopy also facilitate its use for both in-line and at-line analysis. The principle limitation of Raman spectroscopy is optical interference arising from both analyte and non-analyte fluorescence. In this dissertation, a solution to this problem is presented in the form of a novel spectrometer design which operates in a sequentially shifted excitation mode to eliminate fluorescence backgrounds, fixed …

A Radial Basis Functions Method For Fractional Diffusion Equations, Cecile M. Piret, Emmanuel Hanert

Cecile M Piret

A Method For Simulating Burr Type Iii And Type Xii Distributions Through L-Moments And L-Correlations, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate L-moments and the L-correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that L-moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also …

Stable, Tunable, Quasimonoenergetic Electron Beams Produced In A Laser Wakefield Near The Threshold For Self-Injection, Sudeep Banerjee, Serguei Y. Kalmykov, Nathan D. Powers, Gregory Golovin, Vidiya Ramanathan, Nathan J. Cunningham, Kevin J. Brown, Shouyuan Chen, Isaac Ghebregziabher, Bradley A. Shadwick, Donald P. Umstadter, Benjamin A. Cowan, David L. Bruhwiler, Arnaud Beck, Erik Lefebvre

Donald P. Umstadter

Stable operation of a laser-plasma accelerator near the threshold for electron self-injection in the blowout regime has been demonstrated with 25–60 TW, 30 fs laser pulses focused into a 3–4 millimeter length gas jet. Nearly Gaussian shape and high nanosecond contrast of the focused pulse appear to be critically important for controllable, tunable generation of 250–430 MeV electron bunches with a low energy spread, ~ 10 pC charge, a few-mrad divergence and pointing stability, and a vanishingly small low-energy background. The physical nature of the near-threshold behavior is examined using three-dimensional particle-in-cell simulations. Simulations indicate that properly locating the nonlinear …

Stable, Tunable, Quasimonoenergetic Electron Beams Produced In A Laser Wakefield Near The Threshold For Self-Injection, Sudeep Banerjee, Serguei Y. Kalmykov, Nathan D. Powers, Gregory Golovin, Vidiya Ramanathan, Nathan J. Cunningham, Kevin J. Brown, Shouyuan Chen, Isaac Ghebregziabher, Bradley A. Shadwick, Donald P. Umstadter, Benjamin A. Cowan, David L. Bruhwiler, Arnaud Beck, Erik Lefebvre

Serge Youri Kalmykov

Stable operation of a laser-plasma accelerator near the threshold for electron self-injection in the blowout regime has been demonstrated with 25–60 TW, 30 fs laser pulses focused into a 3–4 millimeter length gas jet. Nearly Gaussian shape and high nanosecond contrast of the focused pulse appear to be critically important for controllable, tunable generation of 250–430 MeV electron bunches with a low energy spread, ~ 10 pC charge, a few-mrad divergence and pointing stability, and a vanishingly small low-energy background. The physical nature of the near-threshold behavior is examined using three-dimensional particle-in-cell simulations. Simulations indicate that properly locating the nonlinear …

Distributional Monte Carlo Methods For The Boltzmann Equation, Christopher R. Schrock

Theses and Dissertations

Stochastic particle methods (SPMs) for the Boltzmann equation, such as the Direct Simulation Monte Carlo (DSMC) technique, have gained popularity for the prediction of flows in which the assumptions behind the continuum equations of fluid mechanics break down; however, there are still a number of issues that make SPMs computationally challenging for practical use. In traditional SPMs, simulated particles may possess only a single velocity vector, even though they may represent an extremely large collection of actual particles. This limits the method to converge only in law to the Boltzmann solution. This document details the development of new SPMs that …

On Divisibility Properties Of Some Differences Of The Central Binomial Coefficients And Catalan Numbers, Tamas Lengyel

Tamas Lengyel

We discuss divisibility properties of some differences of the central binomial coeffi- cients and Catalan numbers. The main tool is the application of various congruences modulo high prime powers for binomial coefficients combined with some recurrences relevant to these combinatorial quantities.

Propeller, Joel Kahn

The STEAM Journal

This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.

The Effect Of The R1648h Sodium Channel Mutation On Neuronal Excitability: A Model Study, Christopher Locandro, Robert Clewley

Georgia State Undergraduate Research Conference

No abstract provided.

Simulation Insights Using R, Boyan Kostadinov

Publications and Research

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software R for Statistical Computing. The author illustrates the computer simulation approach by focusing on several problems of increasing difficulty. The simulation techniques and the specific problems discussed in this article would be of interest to STEM students and instructors, teaching courses in Monte Carlo simulations, stochastic modeling, probability and statistics. The R code for all problems is discussed in full detail so that the reader can get a taste of …

Battery Energy Storage System In Solar Power Generation, Radhey Shyam Meena Er., Deepa Sharma

Radhey Shyam Meena

Grid-connected solar PV dramatically changes the load profile of an electric utility customer. The expected widespread adoption of solar generation by customers on the distribution system poses significant challenges to system operators both in transient and steady state operation, from issues including voltage swings, sudden weather-induced changes in generation, and legacy protective devices designed with one-way power flow in mind

Duncan, Benjamin, 1772-1809 (Sc 678), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid only for Manuscripts Small Collection 678. Cipher book kept by Benjamin Duncan, of Culpeper County, Virginia and Fayette County, Kentucky. Includes samples of legal forms and letters.

Fractal Heat Conduction Problem Solved By Local Fractional Variation Iteration Method, Yang Xiaojun

Xiao-Jun Yang

This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.

Isomorphisms Of Lattices Of Bures-Closed Bimodules Over Cartan Masas, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

For i = 1; 2, let (Mi;Di) be pairs consisting of a Cartan MASA Di in a von Neumann algebra Mi, let atom(Di) be the set of atoms of Di, and let Si be the lattice of Bures-closed Di bimodules in Mi. We show that when Mi have separable preduals, there is a lattice isomorphism between S1 and S2 if and only if the sets

f(Q1;Q2) 2 atom(Di) atom(Di) : Q1MiQ2 6= (0)g

have the same cardinality. In particular, when Di is nonatomic, Si is isomorphic to the lattice of projections in L1([0; 1];m) where m is Lebesgue measure, regardless …

On The Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev

Articles

We develop the direct scattering problem for quadratic bundles associated to Hermitian symmetric spaces. We adapt the dressing method for quadratic bundles which allows us to find special solutions to multicomponent derivative Schrodinger equation for instance. The latter is an infinite dimensional Hamiltonian system possessing infinite number of integrals of motion. We demonstrate how one can derive them by block diagonalization of the corresponding Lax pair.

How To Find Killing Vectors, Charles G. Torre

How to... in 10 minutes or less

We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.

A Local Fractional Variational Iteration Method For Laplace Equation Within Local Fractional Operators, Xiao-Jun Yang

Xiao-Jun Yang

The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators.The obtained results reveal that the method is very effective.

An H1 Model For Inextensible Strings, Stephen Preston, Ralph Saxton

Ralph Saxton

We study geodesics of the H1 Riemannian metric (see article for equation) on the space of inextensible curves (see article for equation). This metric is a regularization of the usual L2 metric on curves, for which the submanifold geometry and geodesic equations have been analyzed already. The H1 geodesic equation represents a limiting case of the Pochhammer-Chree equation from elasticity theory. We show the geodesic equation is C∞ in the Banach topology C1 ([0,1], R2), and thus there is a smooth Riemannian exponential map. Furthermore, if we hold one of the curves fixed, we have global-in-time solutions. We conclude with …

Blow-Up Of Solutions To The Generalized Inviscid Proudman-Johnson Equation, Alejandro Sarria, Ralph Saxton

Ralph Saxton

For arbitrary values of a parameter --- finite-time blowup of solutions to the generalized, inviscid Proudman Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to the problem.

Influence Of Damping On Hyperbolic Equations With Parabolic Degeneracy, Katarzyna Saxton, Ralph Saxton

Ralph Saxton

This paper examines the effect of damping on a nonstrictly hyperbolic 2 x 2 system. It is shown that the growth of singularities is not restricted as in the strictly hyperbolic case where dissipation can be strong enough to preserve the smoothness of solutions globally in time. Here, irrespective of the stabilizing properties of damping, solutions are found to break down in finite time on a line where two eigenvalues coincide in state space.

A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn

Mathematics Faculty Publications

In this paper we extend the spectral order of Coecke and Martin to infinite-dimensional quantum states. Many properties present in the finite-dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analysed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and that part is not a closed subset of the model. The finite parts of the lattices used by Birkhoff and von Neumann as models for classical and quantum logic appear as subsets of the models for infinite …

Some Minor-Closed Classes Of Signed Graphs, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We define four minor-closed classes of signed graphs in terms of embeddability in the annulus, projective plane, torus, and Klein bottle. We give the full list of 20 excluded minors for the smallest class and make a conjecture about the largest class.

Parametric Catalan Numbers And Catalan Triangles, Tian-Xiao He

Scholarship

Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered as an extension of large Schroder numbers and small Schroder numbers, respectively. Using the characterization sequences of Bell-type Riordan arrays, some properties and expressions including the Taylor expansions of generalized Catalan numbers are given. A few combinatorial interpretations of the generalized Catalan numbers are also provided. Finally, a generalized Motzkin numbers …

Parametric Catalan Numbers And Catalan Triangles, Tian-Xiao He

Tian-Xiao He

Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered as an extension of large Schroder numbers and small Schroder numbers, respectively. Using the characterization sequences of Bell-type Riordan arrays, some properties and expressions including the Taylor expansions of generalized Catalan numbers are given. A few combinatorial interpretations of the generalized Catalan numbers are also provided. Finally, a generalized Motzkin numbers …

Sloane’S Gap: Do Mathematical And Social Factors Explain The Distribution Of Numbers In The Oeis?, Nicolas J.-P. Gauvrit, Jean-Paul Delahaye, Hector Zenil

Journal of Humanistic Mathematics

The Online Encyclopedia of Integer Sequences (OEIS) is a catalog of integer sequences. We are particularly interested in the number of occurrences of N(n) of an integer n in the database. This number N(n) marks the importance of n and it varies noticeably from one number to another, and from one number to the next in a series. “Importance” can be mathematically objective (2^10 is an example of an “important” number in this sense) or as the result of a shared mathematical culture (10^9 is more important than 9^10 because we use a decimal notation). The concept of algorithmic complexity …