Physical Sciences and Mathematics Commons^™

Multiple Subject Barycentric Discriminant Analysis (Musubada): How To Assign Scans To Categories Without Using Spatial Normalization, Hervé Abdi, Lynne J. Williams, Andrew C. Connolly, M. Ida Gobbini

Dartmouth Scholarship

We present a new discriminant analysis (DA) method called Multiple Subject Barycentric Discriminant Analysis (MUSUBADA) suited for analyzing fMRI data because it handles datasets with multiple participants that each provides different number of variables (i.e., voxels) that are themselves grouped into regions of interest (ROIs). Like DA, MUSUBADA (1) assigns observations to predefined categories, (2) gives factorial maps displaying observations and categories, and (3) optimally assigns observations to categories. MUSUBADA handles cases with more variables than observations and can project portions of the data table (e.g., subtables, which can represent participants or ROIs) on the factorial maps. Therefore MUSUBADA can …

Petawatt-Laser-Driven Wakefield Acceleration Of Electrons To 2 Gev In 10^{17} Cm^{-3} Plasma, Xiaoming Wang, Rafal B. Zgadzaj, Neil Fazel, Sunghwan A. Yi, X. Zhang, Watson Henderson, Yen-Yu Zhang, Rick Korzekwa, Hai-En Tsai, C.-H. Pai, Zhengyan Li, Hernan Quevedo, Gilliss Dyer, Erhard W. Gaul, Mikael Martinez, Aaron Bernstein, Ted Borger, M. Spinks, M. Donovan, Serguei Y. Kalmykov, Vladimir N. Khudik, Gennady Shvets, Todd Ditmire, Michael C. Downer

Serge Youri Kalmykov

Electron self-injection into a laser-plasma accelerator (LPA) driven by the Texas Petawatt (TPW) laser is reported at plasma densities 1.7 - 6.2 x 10^{17} cm^{-3}. Energy and charge of the electron beam, ranging from 0.5 GeV to 2 GeV and tens to hundreds of pC, respectively, depended strongly on laser beam quality and plasma density. Angular beam divergence was consistently around 0.5 mrad (FWHM), while shot-to-shot pointing fluctuations were limited to ±1.4 mrad rms. Betatron x-rays with tens of keV photon energy are also clearly observed.

Sub-Millimeter-Scale, 100-Mev-Class Quasi-Monoenergetic Laser Plasma Accelerator Based On All-Optical Control Of Dark Current In The Blowout Regime, Serguei Y. Kalmykov, Xavier Davoine, Bradley A. Shadwick

Serge Youri Kalmykov

It is demonstrated that by negatively chirping the frequency of a 20-fs, 15-TW driving laser pulse with an ultrabroad bandwidth (corresponding to a sub-2-cycle transform-limited duration it is possible to prevent early compression of the pulse into an optical shock, thus reducing expansion of the accelerating plasma bucket (electron density "bubble") and delaying dephasing of self-injected and accelerated electrons. These features help suppress unwanted continuous self-injection (dark current) in the blowout regime, making possible to use the entire dephasing length to generate low-background, quasi-monoenergetic 200-MeV-scale electron beams from sub-mm-length, dense plasmas (n_{e0} = 1.3 x 10^{19} cm^{−3}).

The Reasonable Effectiveness Of Mathematics In The Natural Sciences, Nicolas Fillion

Electronic Thesis and Dissertation Repository

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements a strategy to show that the applicability of mathematics is very reasonable indeed.

I distinguish three forms of the …

A Constructive Proof Of Fundamental Theory For Fuzzy Variable Linear Programming Problems, A. Ebrahimnejad

Applications and Applied Mathematics: An International Journal (AAM)

Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generalize the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof using a numerical example.

Numerical Solution Of A Reaction-Diffusion System With Fast Reversible Reaction By Using Adomian’S Decomposition Method And He’S Variational Iteration Method, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.

Mohammed O. Al-Amr

In this paper, the approximate solution of a reaction-diffusion system with fast reversible reaction is obtained by using Adomian decomposition method (ADM) and variational iteration method (VIM) which are two powerful methods that were recently developed. The VIM requires the evaluation of the Lagrange multiplier, whereas ADM requires the evaluation of the Adomian polynomials. The behavior of the approximate solutions and the effects of different values of t are shown graphically.

Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman

Masters Theses

Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …

Stability And Convergence For Nonlinear Partial Differential Equations, Oday Mohammed Waheeb

Boise State University Theses and Dissertations

If used cautiously, numerical methods can be powerful tools to produce solutions to partial differential equations with or without known analytic solutions. The resulting numerical solutions may, with luck, produce stable and accurate solutions to the problem in question, or may produce solutions with no resemblance to the problem in question at all. More such numerical computations give no hope of solving this troublesome feature and one needs to resort to investing time in a theoretical approach. This thesis is devoted not solely to computations, but also to a theoretical analysis of the numerical methods used to generate computationally the …

Nabla Fractional Calculus And Its Application In Analyzing Tumor Growth Of Cancer, Fang Wu

Masters Theses & Specialist Projects

This thesis consists of six chapters. In the first chapter, we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to prove that there exists a solution for up to the first order nabla fractional difference equation with an initial condition. In chapter three, we define a lower and an upper solution for up to the first order nabla fractional difference equation with an initial condition. Under certain …

Numerical Studies For Solving Fractional Riccati Differential Equation, N. H. Sweilam, M. M. Khader, A. M. S. Mahdy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, finite difference method (FDM) and Pade'-variational iteration method (Pade'- VIM) are successfully implemented for solving the nonlinear fractional Riccati differential equation. The fractional derivative is described in the Caputo sense. The existence and the uniqueness of the proposed problem are given. The resulting nonlinear system of algebraic equations from FDM is solved by using Newton iteration method; moreover the condition of convergence is verified. The convergence's domain of the solution is improved and enlarged by Pade'-VIM technique. The results obtained by using FDM is compared with Pade'-VIM. It should be noted that the Pade'-VIM is preferable because …

Local Fractional Fourier Series With Application To Wave Equation In Fractal Vibrating String, Yang Xiaojun

Xiao-Jun Yang

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag- Leffler function.

The Octonions And The Exceptional Lie Algebra G2, Ian M. Anderson

Research Vignettes

The octonions O are an 8-dimensional non-commutative, non-associative normed real algebra. The set of all derivations of O form a real Lie algebra. It is remarkable fact, first proved by E. Cartan in 1908, that the the derivation algebra of O is the compact form of the exceptional Lie algebra G2. In this worksheet we shall verify this result of Cartan and also show that the derivation algebra of the split octonions is the split real form of G2.

PDF and Maple worksheets can be downloaded from the links below.

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, Nabeel Butt

Electronic Thesis and Dissertation Repository

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility …

Hard And Soft Error Resilience For One-Sided Dense Linear Algebra Algorithms, Peng Du

Doctoral Dissertations

Dense matrix factorizations, such as LU, Cholesky and QR, are widely used by scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This dissertation develops fault tolerance algorithms for one-sided dense matrix factorizations, which handles Both hard and soft errors.

For hard errors, we propose methods based on diskless checkpointing and Algorithm Based Fault Tolerance (ABFT) to provide full matrix protection, including the left and right factor that are normally seen in …

Degree Constrained Triangulation, Roshan Gyawali

UNLV Theses, Dissertations, Professional Papers, and Capstones

Triangulation of simple polygons or sets of points in two dimensions is a widely investigated problem in computational geometry. Some researchers have considered variations of triangulation problems that include minimum weight triangulation, de-launay triangulation and triangulation refinement. In this thesis we consider a constrained version of the triangulation problem that asks for triangulating a given domain (polygon or point sites) so that the resulting triangulation has an increased number of even degree vertices. This problem is called Degree Constrained Triangulation (DCT). We propose four algorithms to solve DCT problems. We also present experimental results based on the implementation of the …

Numerical Analysis Of First And Second Order Unconditional Energy Stable Schemes For Nonlocal Cahn-Hilliard And Allen-Cahn Equations, Zhen Guan

Doctoral Dissertations

This PhD dissertation concentrates on the numerical analysis of a family of fully discrete, energy stable schemes for nonlocal Cahn-Hilliard and Allen-Cahn type equations, which are integro-partial differential equations (IPDEs). These two IPDEs -- along with the evolution equation from dynamical density functional theory (DDFT), which is a generalization of the nonlocal Cahn-Hilliard equation -- are used to model a variety of physical and biological processes such as crystallization, phase transformations, and tumor growth. This dissertation advances the computational state-of-the-art related to this field in the following main contributions: (I) We propose and analyze a family of two-dimensional unconditionally energy …

Trajectory Generation In High-Speed, High-Precision Micromilling Using Subdivision Surfaces, Athulan Vijayaraghavan, Angela Sodemann, Aaron Hoover, J. Mayor, David Dornfeld

Aaron M. Hoover

Motion control in high-speed micromilling processes requires fast, accurate following of a specified curvilinear path. The accuracy with which the path can be followed is determined by the speed at which individual trajectories can be generated and sent to the control system. The time required to generate the trajectory is dependent on the representations used for the curvilinear trajectory path. In this study, we introduce the use of subdivision curves as a method for generating high-speed micromilling trajectories. Subdivision curves are discretized curves which are specified as a series of recursive refinements of a coarse mesh. By applying these recursive …

The Block Aor Iterative Methods For Solving Fuzzy Linear Systems, Hs Najafi, Sa Edalatpanah

SA Edalatpanah

In this article the block AOR Iterative methods are used for solving fuzzy linear systems. The convergence of the methods and functional relationship between eigenvalues in block AOR is investigated.

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Department of Mathematics: Dissertations, Theses, and Student Research

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to …

Computationally Efficient Methods For Modelling Laser Wakefield Acceleration In The Blowout Regime, Benjamin M. Cowan, Serguei Y. Kalmykov, Arnaud Beck, Xavier Davoine, Kyle Bunkers, Agustin F. Lifschitz, Erik Lefebvre, David L. Bruhwiler, Bradley A. Shadwick, Donald P. Umstadter

Donald P. Umstadter

Electron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100-terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, 3D particle-in-cell modelling are examined. First, the Cartesian code VORPAL (Nieter, C. and Cary, J. R. 2004 VORPAL: a versatile plasma simulation code. J. Comput. Phys. 196, 538) using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while …

Computationally Efficient Methods For Modelling Laser Wakefield Acceleration In The Blowout Regime, Benjamin M. Cowan, Serguei Y. Kalmykov, Arnaud Beck, Xavier Davoine, Kyle Bunkers, Agustin F. Lifschitz, Erik Lefebvre, David L. Bruhwiler, Bradley A. Shadwick, Donald P. Umstadter

Serge Youri Kalmykov

Electron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100-terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, 3D particle-in-cell modelling are examined. First, the Cartesian code VORPAL (Nieter, C. and Cary, J. R. 2004 VORPAL: a versatile plasma simulation code. J. Comput. Phys. 196, 538) using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while …

Variational Iteration Method For Q-Difference Equations Of Second Order, Guo-Cheng Wu

G.C. Wu

Recently, Liu extended He's variational iteration method to strongly nonlinear q-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. The q-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.

Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.

Mhd Mixed Convective Flow Of Viscoelastic And Viscous Fluids In A Vertical Porous Channel, R. Sivaraj, B. R. Kumar, J. Prakash

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyze the problem of steady, mixed convective, laminar flow of two incompressible, electrically conducting and heat absorbing immiscible fluids in a vertical porous channel filled with viscoelastic fluid in one region and viscous fluid in the other region. A uniform magnetic field is applied in the transverse direction, the fluids rise in the channel driven by thermal buoyancy forces associated with thermal radiation. The equations are modeled using the fully developed flow conditions. An exact solution is obtained for the velocity, temperature, skin friction and Nusselt number distributions. The physical interpretation to these expressions is examined …

Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on …

A New Cg-Algorithm With Self-Scaling Vm-Update For Unconstraint Optimization, Abbas Y. Al-Bayati, Ivan S. Latif

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new combined extended Conjugate-Gradient (CG) and Variable-Metric (VM) methods is proposed for solving unconstrained large-scale numerical optimization problems. The basic idea is to choose a combination of the current gradient and some pervious search directions as a new search direction updated by Al-Bayati's SCVM-method to fit a new step-size parameter using Armijo Inexact Line Searches (ILS). This method is based on the ILS and its numerical properties are discussed using different non-linear test functions with various dimensions. The global convergence property of the new algorithm is investigated under few weak conditions. Numerical experiments show that the …

A Duhamel Integral Based Approach To Identify An Unknown Radiation Term In A Heat Equation With Non-Linear Boundary Condition, R. Pourgholi, M. Abtahi, A. Saeedi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider the determination of an unknown radiation term in the nonlinear boundary condition of a linear heat equation from an overspecified condition. First we study the existence and uniqueness of the solution via an auxiliary problem. Then a numerical method consisting of zeroth-, first-, and second-order Tikhonov regularization method to the matrix form of Duhamel's principle for solving the inverse heat conduction problem (IHCP) using temperature data containing significant noise is presented. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method. Some numerical experiments confirm the …

Introducing An Efficient Modification Of The Variational Iteration Method By Using Chebyshev Polynomials, M. M. Khader

Applications and Applied Mathematics: An International Journal (AAM)

In this article an efficient modification of the variational iteration method (VIM) is presented using Chebyshev polynomials. Special attention is given to study the convergence of the proposed method. The new modification is tested for some examples to demonstrate reliability and efficiency of the proposed method. A comparison of our numerical results those of the conventional numerical method, the fourth-order Runge-Kutta method (RK4) are given. The comparison shows that the solution using our modification is fast-convergent and is in excellent conformance with the exact solution. Finally, we conclude that the proposed method can be applied to a large class of …

A New Four Point Circular-Invariant Corner-Cutting Subdivision For Curve Design, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

A 4-point nonlinear corner-cutting subdivision scheme is established. It is induced from a special C-shaped biarc circular spline structure. The scheme is circular-invariant and can be effectively applied to 2-dimensional (2D) data sets that are locally convex. The scheme is also extended adaptively to non-convex data. Explicit examples are demonstrated.

Pointwise Schauder Estimates Of Parabolic Equations In Carnot Groups, Heather Arielle Griffin

Graduate Theses and Dissertations

Schauder estimates were a historical stepping stone for establishing uniqueness and smoothness of solutions for certain classes of partial differential equations. Since that time, they have remained an essential tool in the field. Roughly speaking, the estimates state that the Holder continuity of the coefficient functions and inhomogeneous term implies the Holder continuity of the solution and its derivatives. This document establishes pointwise Schauder estimates for second order parabolic equations where the traditional role of derivatives are played by vector fields generated by the first layer of the Lie algebra stratification for a Carnot group. The Schauder estimates are shown …