Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Selected Works

Mathematics

2015

Articles 1 - 30 of 165

Full-Text Articles in Physical Sciences and Mathematics

Full Isolation Number Of Matrices: Some Extremal Results, David Tate, David Brown Dec 2015

Full Isolation Number Of Matrices: Some Extremal Results, David Tate, David Brown

David C. Brown

A set of nonzero entries of a (0,1)-matrix is an isolated set if no two entries belong to the same row, no two entries belong to the same column, and no two entries belong to a submatrix of the form [1 1; 1 1]. The isolation number of a matrix is the maximum size over all isolated sets. The isolation number of a matrix is a well-known and well-used lower bound for the matrix's Boolean rank. We will discuss the isolation number of the adjacency matrix of various graphs and develop some extremal results for n x n matrices with …

Go to article

Bipartite Probe Interval Graphs, Interval Point Bigraphs, And Circular Arcgraphs, David Brown, J. Lundgren Dec 2015

Bipartite Probe Interval Graphs, Interval Point Bigraphs, And Circular Arcgraphs, David Brown, J. Lundgren

David C. Brown

No abstract provided.

Go to article

Forbidden Subgraph Characterization Of Bipartite Unit Probe Interval Graphs, David Brown, L. Langley Dec 2015

Forbidden Subgraph Characterization Of Bipartite Unit Probe Interval Graphs, David Brown, L. Langley

David C. Brown

No abstract provided.

Go to article

Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, Sean A. Broughton Dec 2015

Quasi-Platonic Psl2(Q)-Actions On Closed Riemann Surfaces, Sean A. Broughton

S. Allen Broughton

This paper is the first of two papers whose combined goal is to explore the dessins d'enfant and symmetries of quasi-platonic actions of PSL2(q). A quasi-platonic action of a group G on a closed Riemann S surface is a conformal action for which S/G is a sphere and S->S/G is branched over {0, 1,infinity}. The unit interval in S/G may be lifted to a dessin d'enfant D, an embedded bipartite graph in S. The dessin forms the edges and vertices of a tiling on S by dihedrally symmetric polygons, generalizing the idea of a …

Go to article

Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz Oct 2015

Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz

Lori Beth Ziegelmeier

No abstract provided.

Go to article

Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz Oct 2015

Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz

Chad M. Topaz

No abstract provided.

Go to article

Form Domains And Eigenfunction Expansions For Differential Equations With Eigenparameter Dependent Boundary Conditions, Branko Ćurgus, Paul Binding Sep 2015

Form Domains And Eigenfunction Expansions For Differential Equations With Eigenparameter Dependent Boundary Conditions, Branko Ćurgus, Paul Binding

Branko Ćurgus

Form domains are characterized for regular 2n-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the eigenparameter. Corresponding modes of convergence for eigenfunction expansions are studied, including uniform convergence of the first n - 1 derivatives.

Go to article

An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett Sep 2015

An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett

Branko Ćurgus

Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f′(t)=f(t)-f(t-1) for t>1. We also consider four other solutions of this equation that are related to the above selection process.

Go to article

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young Sep 2015

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young

Gerald W Young

The objective of this work was to develop the foundation for an interactive corrosion risk management tool for assessing the probability of failure of equipment/infrastructure as a function of threats (such as pitting corrosion and coating degradation) and mitigation schemes (such as inhibitors and coatings). The application of this work was to assist with corrosion management and maintenance planning of equipment/infrastructure given dynamic changes in environmental conditions. Markov models are developed to estimate pitting damage accumulation density distributions as a function of input parameters for pit nucleation and growth rates. The input parameters are selected based upon characterization with experimental …

Go to article

One-Dimensional Approach To Modeling Damage Evolution In Galvanic Corrosion, Aaron Stenta, S. Basco, A. Smith, Curtis Clemons, Dimitry Golovaty, Kevin Kreider, Joseph Wilder, Gerald Young, Robert Lillard Sep 2015

One-Dimensional Approach To Modeling Damage Evolution In Galvanic Corrosion, Aaron Stenta, S. Basco, A. Smith, Curtis Clemons, Dimitry Golovaty, Kevin Kreider, Joseph Wilder, Gerald Young, Robert Lillard

Gerald W Young

A one-dimensional mathematical model is developed to describe time-dependent damage evolution in well-mixed (spatially uniform species concentrations) galvanic systems using an IR drop approach. An asymptotic procedure taking advantage of disparity in length scales (thin film approximation for the electrolyte thickness) is used to derive the model. Limitations that result from the reduction of dimension are described, along with an analysis demonstrating the ability of the 1D model to capture physical phenomena, such as area ratio effects. Computed potential, current density, and corrosion damage profiles are compared and verified with experimental data available in the literature and 2D galvanic corrosion …

Go to article

An Adaptive Level Set Approach For Modeling Damage Due To Galvanic Corrosion, Joseph Wilder, Curtis Clemons, Dmitry Golovaty, Kevin Kreider, Gerald Young, R. Lillard Sep 2015

An Adaptive Level Set Approach For Modeling Damage Due To Galvanic Corrosion, Joseph Wilder, Curtis Clemons, Dmitry Golovaty, Kevin Kreider, Gerald Young, R. Lillard

Gerald W Young

This article presents an approach to solving problems related to galvanic corrosion that involve moving boundaries (due to preferential corrosion of one of the metals in the system). The method incorporates an adaptive (node based, finite difference) grid technique for the treatment of boundary-related singularities that arise in the calculation of the electric potential. Simulation of the time evolution of the damage done by the corroding interface is performed using of a level set formulation. An analysis of the convergence of the method and a comparison with experimental data from the literature are included.

Go to article

Fixed Point Theory For Non-Self Maps, Linda Saliga Sep 2015

Fixed Point Theory For Non-Self Maps, Linda Saliga

Linda Saliga

No abstract provided.

Go to article

Global Magnetic Confinement For The 1.5d Vlasov-Maxwell System, Toan Nguyen, Truyen Nguyen, Walter Strauss Sep 2015

Global Magnetic Confinement For The 1.5d Vlasov-Maxwell System, Toan Nguyen, Truyen Nguyen, Walter Strauss

Truyen V. Nguyen

We establish the global-in-time existence and uniqueness of classical solutions to the ``one and one-half'' dimensional relativistic Vlasov--Maxwell systems in a bounded interval, subject to an external magnetic field which is infinitely large at the spatial boundary. We prove that the large external magnetic field confines the particles to a compact set away from the boundary. This excludes the known singularities that typically occur due to particles that repeatedly bounce off the boundary. In addition to the confinement, we follow the techniques introduced by Glassey and Schaeffer, who studied the Cauchy problem without boundaries.

Go to article

One-Dimensional Pressureless Gas Systems With/Without Viscosity, Truyen Nguyen, Adrian Tudorascu Sep 2015

One-Dimensional Pressureless Gas Systems With/Without Viscosity, Truyen Nguyen, Adrian Tudorascu

Truyen V. Nguyen

A general global existence result for one-dimensional pressureless Euler/Euler-Poisson systems with or without viscosity is obtained by employing the “sticky particles” model. We first construct entropy solutions for some appropriate scalar conservation laws, then we show that these solutions encode all the information necessary to obtain solutions for the pressureless systems. Another novel contribution is the stability and uniqueness of solutions, which is obtained via a contraction principle in the Wasserstein metric.

Go to article

One-Dimensional Approach To Modeling Damage Evolution In Galvanic Corrosion, Aaron Stenta, S. Basco, A. Smith, Curtis Clemons, Dimitry Golovaty, Kevin Kreider, Joseph Wilder, Gerald Young, Robert Lillard Sep 2015

One-Dimensional Approach To Modeling Damage Evolution In Galvanic Corrosion, Aaron Stenta, S. Basco, A. Smith, Curtis Clemons, Dimitry Golovaty, Kevin Kreider, Joseph Wilder, Gerald Young, Robert Lillard

Kevin L. Kreider

A one-dimensional mathematical model is developed to describe time-dependent damage evolution in well-mixed (spatially uniform species concentrations) galvanic systems using an IR drop approach. An asymptotic procedure taking advantage of disparity in length scales (thin film approximation for the electrolyte thickness) is used to derive the model. Limitations that result from the reduction of dimension are described, along with an analysis demonstrating the ability of the 1D model to capture physical phenomena, such as area ratio effects. Computed potential, current density, and corrosion damage profiles are compared and verified with experimental data available in the literature and 2D galvanic corrosion …

Go to article

An Adaptive Level Set Approach For Modeling Damage Due To Galvanic Corrosion, Joseph Wilder, Curtis Clemons, Dmitry Golovaty, Kevin Kreider, Gerald Young, R. Lillard Sep 2015

An Adaptive Level Set Approach For Modeling Damage Due To Galvanic Corrosion, Joseph Wilder, Curtis Clemons, Dmitry Golovaty, Kevin Kreider, Gerald Young, R. Lillard

Kevin L. Kreider

This article presents an approach to solving problems related to galvanic corrosion that involve moving boundaries (due to preferential corrosion of one of the metals in the system). The method incorporates an adaptive (node based, finite difference) grid technique for the treatment of boundary-related singularities that arise in the calculation of the electric potential. Simulation of the time evolution of the damage done by the corroding interface is performed using of a level set formulation. An analysis of the convergence of the method and a comparison with experimental data from the literature are included.

Go to article

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young Sep 2015

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young

Kevin L. Kreider

The objective of this work was to develop the foundation for an interactive corrosion risk management tool for assessing the probability of failure of equipment/infrastructure as a function of threats (such as pitting corrosion and coating degradation) and mitigation schemes (such as inhibitors and coatings). The application of this work was to assist with corrosion management and maintenance planning of equipment/infrastructure given dynamic changes in environmental conditions. Markov models are developed to estimate pitting damage accumulation density distributions as a function of input parameters for pit nucleation and growth rates. The input parameters are selected based upon characterization with experimental …

Go to article

One-Dimensional Approach To Modeling Damage Evolution In Galvanic Corrosion, Aaron Stenta, S. Basco, A. Smith, Curtis Clemons, Dimitry Golovaty, Kevin Kreider, Joseph Wilder, Gerald Young, Robert Lillard Sep 2015

One-Dimensional Approach To Modeling Damage Evolution In Galvanic Corrosion, Aaron Stenta, S. Basco, A. Smith, Curtis Clemons, Dimitry Golovaty, Kevin Kreider, Joseph Wilder, Gerald Young, Robert Lillard

Dimitry Golovaty

A one-dimensional mathematical model is developed to describe time-dependent damage evolution in well-mixed (spatially uniform species concentrations) galvanic systems using an IR drop approach. An asymptotic procedure taking advantage of disparity in length scales (thin film approximation for the electrolyte thickness) is used to derive the model. Limitations that result from the reduction of dimension are described, along with an analysis demonstrating the ability of the 1D model to capture physical phenomena, such as area ratio effects. Computed potential, current density, and corrosion damage profiles are compared and verified with experimental data available in the literature and 2D galvanic corrosion …

Go to article

On A Conjecture Of Gluck, James Cossey, Zoltan Halasi, Attila Maroti, Hung Nuguyen Sep 2015

On A Conjecture Of Gluck, James Cossey, Zoltan Halasi, Attila Maroti, Hung Nuguyen

James P. Cossey

Let F(G) and b(G) respectively denote the Fitting subgroup and the largest degree of an irreducible complex character of a finite group G. A well-known conjecture of D. Gluck claims that if G is solvable then |G:F(G)|≤b(G)2. We confirm this conjecture in the case where |F(G)| is coprime to 6. We also extend the problem to arbitrary finite groups and prove several results showing that the largest irreducible character degree of a finite group strongly controls the group structure.

Go to article

One-Dimensional Approach To Modeling Damage Evolution In Galvanic Corrosion, Aaron Stenta, S. Basco, A. Smith, Curtis Clemons, Dimitry Golovaty, Kevin Kreider, Joseph Wilder, Gerald Young, Robert Lillard Sep 2015

One-Dimensional Approach To Modeling Damage Evolution In Galvanic Corrosion, Aaron Stenta, S. Basco, A. Smith, Curtis Clemons, Dimitry Golovaty, Kevin Kreider, Joseph Wilder, Gerald Young, Robert Lillard

Curtis B. Clemons

A one-dimensional mathematical model is developed to describe time-dependent damage evolution in well-mixed (spatially uniform species concentrations) galvanic systems using an IR drop approach. An asymptotic procedure taking advantage of disparity in length scales (thin film approximation for the electrolyte thickness) is used to derive the model. Limitations that result from the reduction of dimension are described, along with an analysis demonstrating the ability of the 1D model to capture physical phenomena, such as area ratio effects. Computed potential, current density, and corrosion damage profiles are compared and verified with experimental data available in the literature and 2D galvanic corrosion …

Go to article

An Adaptive Level Set Approach For Modeling Damage Due To Galvanic Corrosion, Joseph Wilder, Curtis Clemons, Dmitry Golovaty, Kevin Kreider, Gerald Young, R. Lillard Sep 2015

An Adaptive Level Set Approach For Modeling Damage Due To Galvanic Corrosion, Joseph Wilder, Curtis Clemons, Dmitry Golovaty, Kevin Kreider, Gerald Young, R. Lillard

Curtis B. Clemons

This article presents an approach to solving problems related to galvanic corrosion that involve moving boundaries (due to preferential corrosion of one of the metals in the system). The method incorporates an adaptive (node based, finite difference) grid technique for the treatment of boundary-related singularities that arise in the calculation of the electric potential. Simulation of the time evolution of the damage done by the corroding interface is performed using of a level set formulation. An analysis of the convergence of the method and a comparison with experimental data from the literature are included.

Go to article

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young Sep 2015

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young

Curtis B. Clemons

The objective of this work was to develop the foundation for an interactive corrosion risk management tool for assessing the probability of failure of equipment/infrastructure as a function of threats (such as pitting corrosion and coating degradation) and mitigation schemes (such as inhibitors and coatings). The application of this work was to assist with corrosion management and maintenance planning of equipment/infrastructure given dynamic changes in environmental conditions. Markov models are developed to estimate pitting damage accumulation density distributions as a function of input parameters for pit nucleation and growth rates. The input parameters are selected based upon characterization with experimental …

Go to article

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young Sep 2015

Localized Corrosion Risk Assessment Using Markov Analysis, K Mccallum, J Zhao, M Workman, M Iannuzzi, M Kappes, Joe Payer, Curtis Clemons, S Chawla, Kevin Kreider, Nao Mimoto, Gerald Young

Nao Mimoto

The objective of this work was to develop the foundation for an interactive corrosion risk management tool for assessing the probability of failure of equipment/infrastructure as a function of threats (such as pitting corrosion and coating degradation) and mitigation schemes (such as inhibitors and coatings). The application of this work was to assist with corrosion management and maintenance planning of equipment/infrastructure given dynamic changes in environmental conditions. Markov models are developed to estimate pitting damage accumulation density distributions as a function of input parameters for pit nucleation and growth rates. The input parameters are selected based upon characterization with experimental …

Go to article

Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik Aug 2015

Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik

Catherine Kublik

We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order 2n. The fourth order (n=2) version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). The second order equation (n=1) corresponds to another famous model from image processing, namely Perona and Malik's anisotropic diffusion, and was studied in earlier papers. The equations studied in this paper are high order analogues of the Perona-Malik equation, and like the …

Go to article

Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler Aug 2015

Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler

Catherine Kublik

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.

Go to article

An Implicit Interface Boundary Integral Method For Poisson’S Equation On Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, Richard Tsai Aug 2015

An Implicit Interface Boundary Integral Method For Poisson’S Equation On Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, Richard Tsai

Catherine Kublik

We propose a simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with smooth boundaries defined through their signed distance function. Our formulation is based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain, where the integrations are carried out in the level set framework using an appropriate Jacobian. By the coarea formula, the algorithm operates in the Euclidean space and does not require any explicit parameterization of the boundaries. We present numerical results in two and three dimensions.

Go to article

Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul Aug 2015

Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul

Catherine Kublik

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation. Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.

Go to article

Foliations And Global Inversion, Eduardo C. Balreira Aug 2015

Foliations And Global Inversion, Eduardo C. Balreira

Eduardo Cabral Balreira

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism f : M → Rn is bijective if and only if Hn−1(M) = 0 and the pre-image of every affine hyperplane is non-empty and acyclic. The proof is based on some geometric constructions involving foliations and tools from intersection theory. This topological result generalizes in finite dimensions the classical analytic theorem of Hadamard-Plastock, including its recent improvement by Nollet-Xavier. The main theorem also relates to a conjecture of the aforementioned authors, involving the well known Jacobian Conjecture in …

Go to article

Skew-Product Dynamical Dystems: Applications To Difference Equations, Saber Elaydi, Robert Sacker Aug 2015

Skew-Product Dynamical Dystems: Applications To Difference Equations, Saber Elaydi, Robert Sacker

Saber Elaydi

No abstract provided.

Go to article

Asymptotic Solutions Of A Discrete Schrödinger Equation Arising From A Dirac Equation With Random Mass, Bernd Aulbach, Saber Elaydi, Klaus Ziegler Aug 2015

Asymptotic Solutions Of A Discrete Schrödinger Equation Arising From A Dirac Equation With Random Mass, Bernd Aulbach, Saber Elaydi, Klaus Ziegler

Saber Elaydi

For a Dirac particle in one dimension with random mass, the time evolution for the average wavefunction is considered. Using the supersymmetric representation of the average Green’s function, we derive a fourth order linear difference equation for the low-energy asymptotics of the average wavefunction. This equation is of Poincar´e type, though highly critical and therefore not amenable to standard methods. In this paper we show that, nevertheless, asymptotic expansions of its solutions can be obtained.

Go to article

Next Last