Numerical Analysis and Computation Commons^™

Numerical Simulation Of Residual Stress In Low-Temperature Colossal Carburized Layer On Austenitic Stainless Steel, Dongsong Rong, Yong Jiang, Jianming Gong, Yawei Peng

The 8th International Conference on Physical and Numerical Simulation of Materials Processing

No abstract provided.

On Some Optimal Stopping Problems With Constraint, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

We consider the optimal stopping problem of a Markov process {x_t : t ≤ 0} when the controller is allowed to stop only at the arrival times of a signal, that is, at a sequence of instants {τ_n : n ≤ 1} independent of {x_t : t ≤ 0}. We solve in detail this problem for general Markov–Feller processes with compact state space when the interarrival times of the signal are independent identically distributed random variables. In addition, we discuss several extensions to other signals and to other cases of state spaces. These results …

Essays In Market Structure And Liquidity, Adrian J. Walton

Electronic Thesis and Dissertation Repository

Market structure concerns the mechanisms for negotiating trades and the composition of trading participants, and can affect liquidity and price efficiency. More gains from trade can be realized from an asset that is more liquid, and a better allocation of risk and capital can be achieved when an asset’s price is more efficient so it is important to understand market structure. This thesis uses theory and empirical methods to examine the effects of a few specific aspects of market structure.

In Chapter 1, we study a novel market structure on the New York Stock Exchange (NYSE), the Retail Liqudity Program …

Breakdown Of Itcz-Like Pv Patterns, Ajay Raghavendra, Thomas A. Guinn

Beyond: Undergraduate Research Journal

The Inter-Tropical Convergence Zone (ITCZ) is a zonal belt of intense convection, responsible for the genesis of over 80% of all tropical cyclones. This region of intense diabatic heating and shear results in a maximum of Ertel's potential vorticity (PV) meeting Rayleigh's necessary condition for barotropic instability. A fundamental issue is understanding the necessary precursor events leading to the breakdown of the ITCZ and subsequent formation of tropical cyclones. Our research examines the non-linear PV dynamics of the breakdown of both finite-length and infinite-length vorticity strips of varying widths and shapes, simulating the ITCZ found near the tropical eastern Pacific …

A Comparison Of Solution Methods For Mandelbrot-Like Polynomials, Eunice Y. S. Chan

Electronic Thesis and Dissertation Repository

We compare two different root-finding methods, eigenvalue methods and homotopy methods, using three test problems: Mandelbrot polynomials, Fibonacci-Mandelbrot polynomials, and Narayana-Mandelbrot polynomials. For the eigenvalue methods, using both MATLAB and Maple, we computed the eigenvalues of a specialized recursively-constructed, supersparse, upper Hessenberg matrix, inspired by Piers Lawrence's original construction for the Mandelbrot polynomials, for all three families of polynomials. This led us to prove that this construction works in general. Therefore, this construction is genuinely a new kind of companion matrix. For the homotopy methods, we used a special-purpose homotopy, in which we used an equivalent differential equation to solve …

Multi-Objective Optimization Under Uncertainty Using The Hyper-Volume Expected Improvement, Martin Figura, Piyush Pandita, Rohit K. Tripathy, Ilias Bilionis

The Summer Undergraduate Research Fellowship (SURF) Symposium

The design of real engineering systems requires the optimization of multiple quantities of interest. In the electric motor design, one wants to maximize the average torque and minimize the torque variation. A study has shown that these attributes vary for different geometries of the rotor teeth. However, simulations of a large number of designs cannot be performed due to their high cost. In many problems, design optimization of multi-objective functions is a very challenging task due to the difficulty to evaluate the expectation of the objectives. Current multi-objective optimization (MOO) techniques, e.g., evolutionary algorithms cannot solve such problems because they …

Design Optimization Of A Stochastic Multi-Objective Problem: Gaussian Process Regressions For Objective Surrogates, Juan Sebastian Martinez, Piyush Pandita, Rohit K. Tripathy, Ilias Bilionis

The Summer Undergraduate Research Fellowship (SURF) Symposium

Multi-objective optimization (MOO) problems arise frequently in science and engineering situations. In an optimization problem, we want to find the set of input parameters that generate the set of optimal outputs, mathematically known as the Pareto frontier (PF). Solving the MOO problem is a challenge since expensive experiments can be performed only a constrained number of times and there is a limited set of data to work with, e.g. a roll-to-roll microwave plasma chemical vapor deposition (MPCVD) reactor for manufacturing high quality graphene. State-of-the-art techniques, e.g. evolutionary algorithms; particle swarm optimization, require a large amount of observations and do not …

A Fast Model For The Simulation Of External Gear Pumps, Zechao Lu, Xinran Zhao, Andrea Vacca

The Summer Undergraduate Research Fellowship (SURF) Symposium

External gear pump is an important category of positive displacement fluid machines used to perform the mechanical–hydraulic energy conversions in many fluid power applications. An efficient numerical simulation program is needed to simulate the system in order to provide a direction for design purpose. The model consists of a lumped parameter fluid dynamic model and a model that simulates the radial micro-motions of the gear’s axes of rotation. The system consists of a set of ordinary differential equations related to the conservation on mass of the internal control volumes of the pump, which are given by the tooth space volumes …

An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

Electronic Theses and Dissertations

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R³, but also to the general case of finding minimal functionals on hypersurfaces in Rⁿ associated with an arbitrary metric.

Numerical Computing With Functions On The Sphere And Disk, Heather Denise Wilber

Boise State University Theses and Dissertations

A new low rank approximation method for computing with functions in polar and spherical geometries is developed. By synthesizing a classic procedure known as the double Fourier sphere (DFS) method with a structure-preserving variant of Gaussian elimination, approximants to functions on the sphere and disk can be constructed that (1) preserve the bi-periodicity of the sphere, (2) are smooth over the poles of the sphere (and origin of the disk), (3) allow for the use of FFT-based algorithms, and (4) are near-optimal in their underlying discretizations. This method is used to develop a suite of fast, scalable algorithms that exploit …

Krylov Subspace Spectral Method With Multigrid For A Time-Dependent, Variable-Coefficient Partial Differential Equation, Haley Renee Dozier

Master's Theses

Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.

This thesis will demonstrate how one can make KSS methods even more efficient by using a Multigrid-like approach for low-frequency components. The essential ingredients of Multigrid, such as restriction, residual correction, and prolongation, are adapted to the timedependent case. Then a comparison of KSS, KSS with Multigrid, KSS-EPI and standard Krylov projection methods will be demonstrated.

Optimizing The Mix Of Games And Their Locations On The Casino Floor, Jason D. Fiege, Anastasia D. Baran

International Conference on Gambling & Risk Taking

We present a mathematical framework and computational approach that aims to optimize the mix and locations of slot machine types and denominations, plus other games to maximize the overall performance of the gaming floor. This problem belongs to a larger class of spatial resource optimization problems, concerned with optimizing the allocation and spatial distribution of finite resources, subject to various constraints. We introduce a powerful multi-objective evolutionary optimization and data-modelling platform, developed by the presenter since 2002, and show how this software can be used for casino floor optimization. We begin by extending a linear formulation of the casino floor …

Stationary And Time-Dependent Optimization Of The Casino Floor Slot Machine Mix, Anastasia D. Baran, Jason D. Fiege

International Conference on Gambling & Risk Taking

Modeling and optimizing the performance of a mix of slot machines on a gaming floor can be addressed at various levels of coarseness, and may or may not consider time-dependent trends. For example, a model might consider only time-averaged, aggregate data for all machines of a given type; time-dependent aggregate data; time-averaged data for individual machines; or fully time dependent data for individual machines. Fine-grained, time-dependent data for individual machines offers the most potential for detailed analysis and improvements to the casino floor performance, but also suffers the greatest amount of statistical noise. We present a theoretical analysis of single …

Estimation Of Performance Airspeeds For High-Bypass Turbofans Equipped Transport-Category Airplanes, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model …

Black Holes Modeled As Fluid Droplets On Membranes, Anthony Bardessono

Physics

No abstract provided.

Cobb-Douglas Based Firm Production Model Under Fuzzy Environment And Its Solution Using Geometric Programming, Palash Mandal, Arindam Garai, Tapan K. Roy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider Cobb-Douglas production function based model in a firm under fuzzy environment, and its solution technique by making use of geometric programming. A firm may use many finite inputs such as labour, capital, coal, iron etc. to produce one single output. It is well known that the primary intention of using production function is to determine maximum output for any given combination of inputs. Also, the firm may gain competitive advantages if it can buy and sell in any quantities at exogenously given prices, independent of initial production decisions. On the other hand, in reality, constraints …

Construction Of Energy Preserving Qmf, Jian-Ao Lian, Yonghui Wang

Applications and Applied Mathematics: An International Journal (AAM)

Recently, a family of perfect reconstruction (PR) quadrature mirror filterbanks (QMF) with finite impulse response filters (FIR) from systems of biorthogonal refinable functions and wavelets were introduced and also applied to image processing. However, a detailed procedure was absent. The main objective of this paper is to present extensive examples that will provide a thorough process of construction of the new family of PR QMF with FIR filterbanks. These new filters are linearphase due to the symmetry property of their corresponding biorthogonal refinable functions and wavelets. In addition, these filters have odd lengths so that the symmetric extension can be …

Color Image Encryption And Decryption Using Hill Cipher Associated With Arnold Transform, Rakesh Ranjan, R. K. Sharma, M. Hanmandlu

Applications and Applied Mathematics: An International Journal (AAM)

Image security over open network transmission is a big concern nowadays. This paper proposes another methodology for color image encoding and decoding using two stage Hill Cipher method which is connected with Arnold Transformation. The forgoing created a strategy for encryption and decryption of color image information and touched on just the premise of keys. In this plan, keys and the agreement of Hill Cipher (HC) are basic. Moreover, keys multiplication (pre or post) over an RGB image information framework is inevitable to know to effectively decrypt the first image information. We have given a machine simulation with a standard …

Priority Queueing System With A Single Server Serving Two Queues M[X1],M[X2]/G1,G2/1 With Balking And Optional Server Vacation, G. Ayyappan, P. Thamizhselvi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study a vacation queueing system with a single server simultaneously dealing with an M^{[x₁] _/}G₁/1 and an M^{[x₂] /}G₂/1 queues. Two classes of units, priority and non-priority, arrive at the system in two independent compound Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority and non-priority units. We further assume that the server may take a vacation of random length just after serving the last customer in the priority unit present in the system. If the server …

Non-Newtonian Prandtl Fluid Over Stretching Permeable Surface, N. R. Jain, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

An analysis is made of the velocity and temperature distribution in the flow of a viscous incompressible fluid caused by the stretching permeable surface which issues in the Prandtl fluid. Parandtl fluid is a pseudoplastic visco-inelastic non-Newtonian fluid. The governing partial differential equations are reduced to ordinary differential equations using deductive group transformation and similarity solution is derived. Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity and temperature profiles. The corresponding skin friction …