Physical Sciences and Mathematics Commons^™

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 …

Generation Of Tunable, 100–800 Mev Quasi-Monoenergetic Electron Beams From A Laser-Wakefield Accelerator In The Blowout Regime, Sudeep Banerjee, Nathan D. Powers, Vidiya Ramanathan, Isaac Ghebregziabher, Kevin J. Brown, Chakra M. Maharjan, Shouyuan Chen, Arnaud Beck, Erik Lefebvre, Serguei Y. Kalmykov, Bradley A. Shadwick, Donald P. Umstadter

Donald P. Umstadter

In this paper, we present results on a scalable high-energy electron source based on laser wakefield acceleration. The electron accelerator using 30 - 80 TW, 30 fs laser pulses, operates in the blowout regime, and produces high-quality, quasi-monoenergetic electron beams in the range 100 - 800 MeV. These beams have angular divergence of 1 - 4 mrad, and 5 - 25 percent energy spread, with a resulting brightness 10^{11} electrons mm^{-2} MeV^{-1} mrad^{-2}. The beam parameters can be tuned by varying the laser and plasma conditions. The use of a high-quality laser pulse and appropriate target conditions enables optimization of …

Generation Of Tunable, 100–800 Mev Quasi-Monoenergetic Electron Beams From A Laser-Wakefield Accelerator In The Blowout Regime, Sudeep Banerjee, Nathan D. Powers, Vidiya Ramanathan, Isaac Ghebregziabher, Kevin J. Brown, Chakra M. Maharjan, Shouyuan Chen, Arnaud Beck, Erik Lefebvre, Serguei Y. Kalmykov, Bradley A. Shadwick, Donald P. Umstadter

Serge Youri Kalmykov

In this paper, we present results on a scalable high-energy electron source based on laser wakefield acceleration. The electron accelerator using 30 - 80 TW, 30 fs laser pulses, operates in the blowout regime, and produces high-quality, quasi-monoenergetic electron beams in the range 100 - 800 MeV. These beams have angular divergence of 1 - 4 mrad, and 5 - 25 percent energy spread, with a resulting brightness 10^{11} electrons mm^{-2} MeV^{-1} mrad^{-2}. The beam parameters can be tuned by varying the laser and plasma conditions. The use of a high-quality laser pulse and appropriate target conditions enables optimization of …

Variances For Maximum Penalized Likelihood Estimates Obtained Via The Em Algorithm, Mark Segal, Peter Bacchetti, Nicholas Jewell

Mark R Segal

We address the problem of providing variances for parameter estimates obtained under a penalized likelihood formulation through use of the EM algorithm. The proposed solution represents a synthesis of two existent techniques. Firstly, we exploit the supplemented EM algorithm developed in Meng and Rubin (1991) that provides variance estimates for maximum likelihood estimates obtained via the EM algorithm. Their procedure relies on evaluating the Jacobian of the mapping induced by the EM algorithm. Secondly, we utilize a result from Green (1990) that provides an expression for the Jacobian of the mapping induced by the EM algorithm applied to a penalized …

The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun

Xiao-Jun Yang

The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform, used in Yang-Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail.

Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a generalized Newton iteration method derived from the generalized local fractional Taylor series with the local fractional derivatives is reviewed. Operators on real line numbers on a fractal space are induced from Cantor set to fractional set. Existence for a generalized fixed point on generalized metric spaces may take place.

Random Number Generation: Types And Techniques, David F. Dicarlo

Senior Honors Theses

What does it mean to have random numbers? Without understanding where a group of numbers came from, it is impossible to know if they were randomly generated. However, common sense claims that if the process to generate these numbers is truly understood, then the numbers could not be random. Methods that are able to let their internal workings be known without sacrificing random results are what this paper sets out to describe. Beginning with a study of what it really means for something to be random, this paper dives into the topic of random number generators and summarizes the key …

Laser Plasma Acceleration With A Negatively Chirped Pulse: All-Optical Control Over Dark Current In The Blowout Regime, Serguei Y. Kalmykov, Arnaud Beck, Xavier Davoine, Erik Lefebvre, Bradley A. Shadwick

Serge Youri Kalmykov

Recent experiments with 100 terawatt-class, sub-50 femtosecond laser pulses show that electrons self-injected into a laser-driven electron density bubble can be accelerated above 0.5 gigaelectronvolt energy in a sub-centimetre length rarefied plasma. To reach this energy range, electrons must ultimately outrun the bubble and exit the accelerating phase; this, however, does not ensure high beam quality. Wake excitation increases the laser pulse bandwidth by red-shifting its head, keeping the tail unshifted. Anomalous group velocity dispersion of radiation in plasma slows down the red-shifted head, compressing the pulse into a few-cycle-long piston of relativistic intensity. Pulse transformation into a piston causes …

Preconditioning Strategy To Solve Fuzzy Linear Systems (Fls), Sa Edalatpanah

SA Edalatpanah

In this article, the preconditioning methods are used for fuzzy linear systems and especially some new preconditioners are introduced. Moreover, the preconditioned iterative methods are studied from the point of view of rate of convergence and the convergence properties of the proposed methods have been analyzed and compared with the classical methods. Finally, the methods are tested by numerical example that shows a good improvement on the convergence speed.

The Zero-Mass Renormalization Group Differential Equations And Limit Cycles In Non-Smooth Initial Value Problems, Yang Xiaojun

Xiao-Jun Yang

In the present paper, using the equation transform in fractal space, we point out the zero-mass renormalization group equations. Under limit cycles in the non-smooth initial value, we devote to the analytical technique of the local fractional Fourier series for treating zero-mass renormalization group equations, and investigate local fractional Fourier series solutions.

Preconditioning Visco-Resistive Mhd For Tokamak Plasmas, Daniel R. Reynolds, Ravi Samtaney, Hilari C. Tiedeman

Mathematics Research

No abstract provided.

Some Approaches For Using Stationary Iterative Methods To Linear Equations Generated From The Boundary Element Method, Hs Najafi, Sa Edalatpanah, B Parsa Moghaddam

SA Edalatpanah

For linear equations, there are numerous stationary iterative methods. However, these methods are not applicable in some important problems such as linear system arising from the boundary element method (BEM). In this paper, we proposed two approaches for using stationary iterative methods to linear equations arising from the BEM for the Laplace and convective diffusion with first-order chemical reaction problems. Our proposed methods are simple and graceful. Finally, numerical example is given to show the efficiency of our results.

A Kind Of Symmetrical Iterative Methods To Solve Special Class Of Lcp (M, Q), Sa Edalatpanah, Hs Najafi

SA Edalatpanah

No abstract provided.

Nash Equilibrium Solution Of Fuzzy Matrix Game Solution Of Fuzzy Bimatrix Game, Sa Edalatpanah, Hs Najafi

SA Edalatpanah

In this paper, we propose a method for finding Nash equilibrium of fuzzy games. This method is based on ranking function of fuzzy linear programming which simplifies the solving process of fuzzy Nash equilibrium. Numerical results show that the proposed method is competitive to the state-of-the-art algorithms.

A New Two-Phase Method For The Fuzzy Primal Simplex Algorithm, Sa Edalatpanah, S Shahabi

SA Edalatpanah

Recently, Nasseri et al., [1, 2] proposed fuzzy two-phase method involving fuzzy artificial variables and fuzzy big-M method to obtain an initial fuzzy basic feasible solution to solve the linear programming with fuzzy variables (FVLP) problems. In this paper, we propose a new two-phase method for solving fuzzy linear programming. Our method needs not any artificial variables and has an advantage of the simple implementation. Furthermore this method is more effective and faster than above methods.

New Model For Preconditioning Techniques With Application To The Boundary Value Problems, Sa Edalatpanah, Hs Najafi

SA Edalatpanah

No abstract provided.

A Novel Approach To Processing Fractal Dynamical Systems Using The Yang-Fourier Transforms, Yang Xiaojun

Xiao-Jun Yang

In the present paper, local fractional continuous non-differentiable functions in fractal space are investigated, and the control method for processing dynamic systems in fractal space are proposed using the Yang-Fourier transform based on the local fractional calculus. Two illustrative paradigms for control problems in fractal space are given to elaborate the accuracy and reliable results.

Numerical Solution Of Integral Equations In Solidification And Laser Melting, Elizabeth Case, Johannes Tausch

Mathematics Research

No abstract provided.

Multilevel Schur Complement Preconditioner For Multi-Physics Simulations, Hilari Tiedeman, Daniel Reynolds

Mathematics Research

No abstract provided.

The Immersed Interface Method For Two-Fluid Problems, Miguel Uh, Sheng Xu

Mathematics Research

No abstract provided.

Block Preconditioning Of Stiff Implicit Models For Radiative Ionization In The Early Universe, Daniel R. Reynolds, Robert Harkness, Geoffrey So, Michael L. Norman

Mathematics Research

No abstract provided.

On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski

Publications

Abstract

The asymptotic stability of solutions of the Mindlin-type microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly non-convex free energy dependence on microdeformation.

Research highlights

The Mindlin-type microstructure model cannot describe properly short wave propagation in laminates. A modified Mindlin-type microstructure model with weakly non-convex free energy resolves this discrepancy. It is shown that the improved model with weakly non-convex free energy is asymptotically stable for short waves.

Reformulation Of The Muffin-Tin Problem In Electronic Structure Calculations Within The Feast Framework, Alan R. Levin

Masters Theses 1911 - February 2014

This thesis describes an accurate and scalable computational method designed to perform nanoelectronic structure calculations. Built around the FEAST framework, this method directly addresses the nonlinear eigenvalue problem. The new approach allows us to bypass traditional approximation techniques typically used for first-principle calculations. As a result, this method is able to take advantage of standard muffin-tin type domain decomposition techniques without being hindered by their perceived limitations. In addition to increased accuracy, this method also has the potential to take advantage of parallel processing for increased scalability.

The Introduction presents the motivation behind the proposed method and gives an overview …

Spatial And Temporal Correlations Of Freeway Link Speeds: An Empirical Study, Piotr J. Rachtan

Masters Theses 1911 - February 2014

Congestion on roadways and high level of uncertainty of traffic conditions are major considerations for trip planning. The purpose of this research is to investigate the characteristics and patterns of spatial and temporal correlations and also to detect other variables that affect correlation in a freeway setting. 5-minute speed aggregates from the Performance Measurement System (PeMS) database are obtained for two directions of an urban freeway – I-10 between Santa Monica and Los Angeles, California. Observations are for all non-holiday weekdays between January 1st and June 30th, 2010. Other variables include traffic flow, ramp locations, number of lanes and the …

Singular Solutions Of Coss-Coupled Epdiff Equations: Waltzing Peakons And Compacton Pairs, Colin Cotter, Darryl Holm, Rossen Ivanov, James Percival

Conference papers

We introduce EPDiff equations as Euler-Poincare´ equations related to Lagrangian provided by a metric, invariant under the Lie Group Diff(Rⁿ). Then we proceed with a particular form of EPDiff equations, a cross coupled two-component system of Camassa-Holm type. The system has a new type of peakon solutions, 'waltzing' peakons and compacton pairs.

Controlling Nanoparticles Formation In Molten Metallic Bilayers By Pulsed-Laser Interference Heating, Mikhail Khenner, Sagar Yadavali, Ramki Kalyanaraman

Mathematics Faculty Publications

The impacts of the two-beam interference heating on the number of core-shell and embedded nanoparticles and on nanostructure coarsening are studied numerically based on the non-linear dynamical model for dewetting of the pulsed-laser irradiated, thin (< 20 nm) metallic bilayers. The model incorporates thermocapillary forces and disjoining pressures, and assumes dewetting from the optically transparent substrate atop of the reflective support layer, which results in the complicated dependence of light reflectivity and absorption on the thicknesses of the layers. Stabilizing thermocapillary effect is due to the local thickness-dependent, steady- state temperature profile in the liquid, which is derived based on the mean substrate temperature estimated from the elaborate thermal model of transient heating and melting/freezing. Linear stability analysis of the model equations set for Ag/Co bilayer predicts the dewetting length scales in the qualitative agreement with experiment.

Interpolation Of Fuzzy Data By Using Quadratic Piecewise Polynomial Induced Form E(3) Cubic Splines, H. Behforooz, R. Ezzati, Saeid Abbasbandy

Saeid Abbasbandy

In this paper, we will consider the interpolation of fuzzy data by using the fuzzy-valued piecewise quartic polynomials Qy0,y1,..., yn (x) induced from E(3) cubic spline functions.

Effective Calculation Of Multiple Solutions Of Mixed Convection In A Porous Medium, Saeid Abbasbandy, E. Shivanian

Saeid Abbasbandy

This paper considers an important model of boundary value problem with a condition at infinity namely combined free and forced convection over a plane of arbitrary shape embedded in a fluid-saturated porous medium; this model admits dual solutions, and uses a technique, which is to some extent modification of homotopy analysis method (HAM), in order to obtain dual solutions analytically with high accuracy.

Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li

Ji-Huan He

A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.

Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He

Ji-Huan He

This review is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations . Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace Transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this review article are first appeared. …