Numerical Analysis and Computation Commons^™

Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

Singular control for multidimensional Gaussian-Poisson processes with a long-run (or ergodic) and a discounted criteria are discussed. The dynamic programming yields the corresponding Hamilton-Jacobi-Bellman equations, which are discussed. Full details on the proofs and further extensions are left for coming works.

Stress Analysis Of Ramberg-Osgood And Hollomon 1-D Axial Rods, Ronald J. Giardina Jr

LSU New Orleans Theses and Dissertations

In this paper we present novel analytic and finite element solutions to 1-D straight rods made of Ramberg-Osgood and Hollomon type materials. These material models are studied because they are a more accurate representation of the material properties of certain metals used often in manufacturing than the simpler composite linear types of stress/strain models. Here, various types of loads are considered and solutions are compared against some linear models. It is shown that the nonlinear models do have manageable solutions, which produce important differences in the results - attributes which suggest that these models should take a more prominent place …

Influence Of Microstructure On Thermoelastic Wave Propagation, Arkadi Berezovski, Mihhail Berezovski

Publications

Numerical simulations of the thermoelastic response of a microstructured material on a thermal loading are performed in the one-dimensional setting to examine the influence of temperature gradient effects at the microstructure level predicted by the thermoelastic description of microstructured solids (Berezovski et al. in J. Therm. Stress. 34:413–430, 2011). The system of equations consisting of a hyperbolic equation of motion, a parabolic macroscopic heat conduction equation, and a hyperbolic evolution equation for the microtemperature is solved by a finite-volume numerical scheme. Effects of microtemperature gradients exhibit themselves on the macrolevel due to the coupling of equations of the macromotion …

Hardy Space Properties Of The Cauchy Kernel Function For A Strictly Convex Planar Domain, Belen Espinosa Lucio

Graduate Theses and Dissertations

This work is based on a paper by Edgar Lee Stout, where it is shown that for every strictly pseudoconvex domain $D$ of class $C^2$ in $\mathbb{C}^N$, the Henkin-Ram\'irez Kernel Function belongs to the Smirnov class, $E^q(D)$, for every $q\in(0,N)$.

The main objective of this dissertation is to show an analogous result for the Cauchy Kernel Function and for any strictly convex bounded domain in the complex plane. Namely, we show that for any strictly convex bounded $D\subset\mathbb{C}$ of class $C^2$ if we fix $\zeta$ in the boundary of $D$ and consider the Cauchy Kernel Function

\mathcal{K}(\zeta,z)=\frac{1}{2\pi i}\frac{1}{\zeta-z}

as a …

Refining Environmental Satellite Data Using A Statistical Approach, Md Zahidur Rahman, Leonid Roytman, Abdelhamid Kadik

Publications and Research

The proposed approach in this article applies an efficient and novel statistical technique to accurately describe radiometric data measured by Advanced Very High Resolution Radiometers (AVHRR) onboard the National Oceanic and Atmospheric Administration’s (NOAA) Polar Orbiting Environmental Satellites (POES). The corrected data set will then be applied to improve the strength of NOAA Global Vegetation Index (GVI) data set for the 1982- 2003 period produced from AVHRR. The GVI is used extensively for studying and monitoring land surface, atmosphere and recently for analyzing climate and environmental changes. The POES AVHRR data, though useful, cannot be directly used in climate change …

Propeller, Joel Kahn

The Transdisciplinary STEAM+ Journal

This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.

Sloane’S Gap: Do Mathematical And Social Factors Explain The Distribution Of Numbers In The Oeis?, Nicolas J.-P. Gauvrit, Jean-Paul Delahaye, Hector Zenil

Journal of Humanistic Mathematics

The Online Encyclopedia of Integer Sequences (OEIS) is a catalog of integer sequences. We are particularly interested in the number of occurrences of N(n) of an integer n in the database. This number N(n) marks the importance of n and it varies noticeably from one number to another, and from one number to the next in a series. “Importance” can be mathematically objective (2^10 is an example of an “important” number in this sense) or as the result of a shared mathematical culture (10^9 is more important than 9^10 because we use a decimal notation). The concept of algorithmic complexity …

Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene

Publications and Research

In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.

Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene

Publications and Research

Ordinary least-squares regression suffers from a fundamental lack of symmetry: the regression line of y given x and the regression line of x given y are not inverses of each other. Alternative symmetric regression methods have been developed to address this concern, notably: orthogonal regression and geometric mean regression. This paper presents in detail a variety of least squares regression methods which may not have been known or fully explicated. The derivation of each method is made efficient through the use of Ehrenberg's formula for the ordinary least-squares error and through the extraction of a weight function g(b) which characterizes …

Near-Optimal Compressed Sensing Guarantees For Anisotropic And Isotropic Total Variation Minimization, Deanna Needell, Rachel Ward

CMC Faculty Publications and Research

Consider the problem of reconstructing a multidimensional signal from partial information, as in the setting of compressed sensing. Without any additional assumptions, this problem is ill-posed. However, for signals such as natural images or movies, the minimal total variation estimate consistent with the measurements often produces a good approximation to the underlying signal, even if the number of measurements is far smaller than the ambient dimensionality. Recently, guarantees for two-dimensional images were established. This paper extends these theoretical results to signals of arbitrary dimension and to both the anisotropic and isotropic total variation problems. To be precise, we show that …

Simulations Of Surfactant Driven Thin Film Flow, Shreyas Kumar

HMC Senior Theses

This thesis is intended to fulfill the requirements of the Math and Physics departments at Harvey Mudd College. We begin with a brief introduction to the study of surfactant dynamics followed by some background on the experimental framework our work is related to. We then go through a derivation of the model we use, and explore in depth the nature of the Equation of State (EoS), the relationship between the surface tension on a fluid and the surfactant concentration. We consider the effect of using an empirical equation of state on the results of the simulations and compare the new …

Hydrodynamic Modeling Of Ns-Laser Ablation, David Autrique, Vasilios Alexiades, Harihar Khanal

Publications

Laser ablation is a versatile and widespread technique, applied in an increasing number of medical, industrial and analytical applications. A hydrodynamic multiphase model describing nanosecond-laser ablation (ns- LA) is outlined. The model accounts for target heating and mass removal mechanisms as well as plume expansion and plasma formation. A copper target is placed in an ambient environment consisting of helium and irradiated by a nanosecond-laser pulse. The effect of variable laser settings on the ablation process is explored in 1-D numerical simulations.

Time-Stepping For Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades

Publications

Nanosecond laser ablation is a popular technique, applied in many areas of science and technology such as medicine, archaeology, chemistry, environmental and materials sciences. We outline a computational model for radiative and collisional processes occurring during ns-laser ablation, and compare the performance of various low and high order time-stepping algorithms.

Two-Dimensional Hydrodynamic Modeling Of Two-Phase Flow For Understanding Geyser Phenomena In Urban Stormwater System, Zhiyu S. Shao

Theses and Dissertations--Civil Engineering

During intense rain events a stormwater system can fill rapidly and undergo a transition from open channel flow to pressurized flow. This transition can create large discrete pockets of trapped air in the system. These pockets are pressurized in the horizontal reaches of the system and then are released through vertical vents. In extreme cases, the transition and release of air pockets can create a geyser feature.

The current models are inadequate for simulating mixed flows with complicated air-water interactions, such as geysers. Additionally, the simulation of air escaping in the vertical dropshaft is greatly simplified, or completely ignored, in …

Sampling From The Hardcore Process, William C. Dodds

CMC Senior Theses

Partially Recursive Acceptance Rejection (PRAR) and bounding chains used in conjunction with coupling from the past (CFTP) are two perfect simulation protocols which can be used to sample from a variety of unnormalized target distributions. This paper first examines and then implements these two protocols to sample from the hardcore gas process. We empirically determine the subset of the hardcore process's parameters for which these two algorithms run in polynomial time. Comparing the efficiency of these two algorithms, we find that PRAR runs much faster for small values of the hardcore process's parameter whereas the bounding chain approach is vastly …

Full Newton Step Interior Point Method For Linear Complementarity Problem Over Symmetric Cones, Andrii Berdnikov

College of Graduate Studies: Theses & Dissertations

In this thesis, we present a new Feasible Interior-Point Method (IPM) for Linear Complementarity Problem (LPC) over Symmetric Cones. The advantage of this method lies in that it uses full Newton-steps, thus, avoiding the calculation of the step size at each iteration. By suitable choice of parameters we prove the global convergence of iterates which always stay in the the central path neighborhood. A global convergence of the method is proved and an upper bound for the number of iterations necessary to find ε-approximate solution of the problem is presented.

Computational Fluid Dynamics (Cfd) Modeling Of A Laboratory Scale Coal Gasifier, Kiel S. Schultheiss

College of Graduate Studies: Theses & Dissertations

Furthering gasification technology is an essential part of advancing clean coal technologies. In order to seek insight into the appropriate operations for the formation of synthetic gas (syngas) a numerical simulation was performed to predict the phenomena of coal gasification in a laboratory scale entrained-flow coal gasifier. The mesh for the model was developed with ICEM CFD software and the chemical and physical phenomena were modeled using the fluid flow solver ANSYS FLUENT. Mesh independence was verified. The model was validated with experimental data from several studies performed on a laboratory scale gasifier.

Systematic examination of the model was performed …

Pressure Poisson Method For The Incompressible Navier-Stokes Equations Using Galerkin Finite Elements, John Cornthwaite

College of Graduate Studies: Theses & Dissertations

In this thesis we examine the Navier-Stokes equations (NSE) with the continuity equation replaced by a pressure Poisson equation (PPE). Appropriate boundary conditions are developed for the PPE, which allow for a fully decoupled numerical scheme to recover the pressure. The variational form of the NSE with PPE is derived and used in the Galerkin Finite Element discretization. The Galerkin finite element method is then used to solve the NSE with PPE. Moderate accuracy is shown.

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 …

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 …