Application Of Optimization Methods To Crack Profile Inversion Using Eddy Currents, 2017 Iowa State University

#### Application Of Optimization Methods To Crack Profile Inversion Using Eddy Currents, John R. Bowler, Wei Zhang, Aleksandar Dogandžić

*John R. Bowler*

A numerical scheme for finding crack shapes from eddy current measurements has been developed based on a startdard iterative inversion approach in which a nonlinear least squares objective function quantifying the overall difference between predictions and measurements is minimized. In this paper, steepest descent and conjugate‐gradient methods for minimizing the objective function are investigated and compared. Cramér‐Rao lower bounds on the crack parameters are derived to quantify the accuracy of the estimated crack shape. Cramér‐Rao bounds are also used to indicate improvements in the design of eddy‐current nondestructive evaluation systems.

Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, 2017 State University of New York at New Paltz

#### Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, 2017 State University of New York at New Paltz

#### Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, Anca R. Radulescu, Emily R. Hannon

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Application Of Symplectic Integration On A Dynamical System, 2017 East Tennessee State University

#### Application Of Symplectic Integration On A Dynamical System, William Frazier

*Electronic Theses and Dissertations*

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic ...

Comparing Methods Of Measuring Chaos In The Symbolic Dynamics Of Strange Attractors, 2017 Georgia State University

#### Comparing Methods Of Measuring Chaos In The Symbolic Dynamics Of Strange Attractors, James J. Scully

*Georgia State Undergraduate Research Conference*

No abstract provided.

Center Manifold Theory And Computation Using A Forward Backward Approach, 2017 College of William and Mary

#### Center Manifold Theory And Computation Using A Forward Backward Approach, Emily E. Schaal

*Undergraduate Honors Theses*

The center manifold, an object from the field of differential equations, is useful in describing the long time behavior of the system. The most common way of computing the center manifold is by using a Taylor approximation. A different approach is to use iterative methods, as presented in Fuming and Kupper, 1994, Dellnitz and Hohmann, 1997, and Jolly and Rosa, 2005. In particular, Jolly and Rosa present a method based on a discretization of the Lyapunov-Perron (L-P) operator. One drawback is that this discretization can be expensive to compute and have error terms that are difficult to control. Using a ...

P26. Global Exponential Stabilization On So(3), 2017 sberkane@uwo.ca

#### P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

*Western Research Forum*

Global Exponential Stabilization on SO(3)

Nestt: A Nonconvex Primal-Dual Splitting Method For Distributed And Stochastic Optimization, 2017 Iowa State University

#### Nestt: A Nonconvex Primal-Dual Splitting Method For Distributed And Stochastic Optimization, Davood Hajinezhad, Mingyi Hong, Tuo Zhao, Zhaoran Wang

*Mingyi Hong*

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists a sum *N/* nonconvex *Li/N/ *smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into *N/ * subproblems, and utilizes an augmented Lagrangian based primal-dual scheme to solve it in a distributed and stochastic manner. With a special non-uniform sampling, a version of NESTT achieves *e-1* stationary solution using...gradient evaluations, which can be up to *O(N)/ * times better than the (proximal) gradient descent methods. It also achieves Q-linear convergence rate for nonconvex l1 penalized quadratic problems with polyhedral ...

Parallel Successive Convex Approximation For Nonsmooth Nonconvex Optimization, 2017 Stanford University

#### Parallel Successive Convex Approximation For Nonsmooth Nonconvex Optimization, Mesiam Razaviyayn, Mingyi Hong, Zhi-Quan Luo, Jong-Shi Pang

*Mingyi Hong*

Consider the problem of minimizing the sum of a smooth (possibly non-convex) and a convex (possibly nonsmooth) function involving a large number of variables. A popular approach to solve this problem is the block coordinate descent (BCD) method whereby at each iteration only one variable block is updated while the remaining variables are held fixed. With the recent advances in the developments of the multi-core parallel processing technology, it is desirable to parallelize the BCD method by allowing multiple blocks to be updated simultaneously at each iteration of the algorithm. In this work, we propose an inexact parallel BCD approach ...

Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, 2017 University of Kentucky

#### Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

*Theses and Dissertations--Mathematics*

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.

Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, 2017 Dublin Institute of Technology

#### Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

*Articles*

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion ...

A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, 2017 University of Kentucky

#### A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

*Theses and Dissertations--Mechanical Engineering*

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model ...

Proceedings Of The 2nd Resrb 2017 Conference, June 19-21, Wrocław, Poland, 2016 Wroclaw University of Technology

#### Proceedings Of The 2nd Resrb 2017 Conference, June 19-21, Wrocław, Poland, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, 2016 Wroclaw University of Technology

#### Call For Abstracts - Resrb 2018, June 18-20, Brussels, Belgium, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Order Form Resrb 2018, 2016 Wroclaw University of Technology

#### Order Form Resrb 2018, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Abstract Template Resrb 2018, 2016 Wroclaw University of Technology

#### Abstract Template Resrb 2018, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Renewable Energy And Sustainable Development (Resd) Group, 2016 Wroclaw University of Technology

#### Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

C.V. - Wojciech Budzianowski, 2016 Wroclaw University of Technology

Noise, Chaos, And The Verhulst Population Model, 2016 University of Wyoming

#### Noise, Chaos, And The Verhulst Population Model, Laurel J. Leonhardt

*Honors Theses AY 16/17*

The history of Verhulst's logistic equation is discussed. Bifurcation diagrams and the importance of the discrete logistic equation in chaos theory are introduced. The results of adding noise to the discrete logistic equation are computed. Surprising linearity is discovered in the relationship between error bounds placed on the period two region and the amount of noise added to the system.

(Un)Stable Manifold Computation Via Iterative Forward-Backward Runge-Kutta Type Methods, 2016 College of William and Mary

#### (Un)Stable Manifold Computation Via Iterative Forward-Backward Runge-Kutta Type Methods, Dmitriy Zhigunov

*Undergraduate Honors Theses*

I present numerical methods for the computation of stable and unstable manifolds in autonomous dynamical systems. Through differentiation of the Lyapunov-Perron operator in [Casteneda, Rosa 1996], we find that the stable and unstable manifolds are boundary value problems on the original set of differential equation. This allows us to create a forward-backward approach for manifold computation, where we iteratively integrate one set of variables forward in time, and one set of variables backward in time. Error and stability of these methods is discussed.