Physical Sciences and Mathematics Commons^™

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mikhail Khenner

A mathematical model for the evolution of pulsed laser-irradiated, molten metallic films has been developed using the lubrication theory. The heat transfer problem that incorporates the absorbed heat from a single laser beam or the interfering laser beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the reflectivity, the peak laser beam …

Random Walks With Elastic And Reflective Lower Boundaries, Lucas Clay Devore

Masters Theses & Specialist Projects

No abstract provided.

Geometric Build-Up Solutions For Protein Determination Via Distance Geometry, Robert Tucker Davis

Masters Theses & Specialist Projects

Proteins carry out an almost innumerable amount of biological processes that are absolutely necessary to life and as a result proteins and their structures are very often the objects of study in research. As such, this thesis will begin with a description of protein function and structure, followed by brief discussions of the two major experimental structure determination methods. Another problem that often arises in molecular modeling is referred to as the Molecular Distance Geometry Problem (MDGP). This problem seeks to find coordinates for the atoms of a protein or molecule when given only a set of pair-wise distances between …

Comic Books That Teach Mathematics, Bruce Kessler

Bruce Kessler

During the 2008--2009 academic year, the author embarked on an extremely non-standard curriculum path: developing comic books with embedded mathematics appropriate for 3rd through 6th grade students. With the help of an education professor to measure impact, an elementary-school principal, and talented undergraduate illustrators, this project came to fruition and the comics were implemented in elementary classrooms at Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky. This talk gives the motivation for the idea, introduces the characters, and how the comics integrated the math content into the stories.

Comic Books That Teach Mathematics, Bruce Kessler

Bruce Kessler

During the 2008--2009 academic year, the author embarked on an extremely non-standard curriculum path: developing comic books with embedded mathematics appropriate for 3rd through 6th grade students. With the help of an education professor to measure impact, an elementary-school principal, and talented undergraduate illustrators, this project came to fruition and the comics were implemented in elementary classrooms at Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky. This manuscript gives the history of this idea, the difficulties of developing the content of the comics and getting them illustrated, and the implementation plan in the school.

A …

Using Works Of Visual Art To Teach Matrix Transformations, James Luke Akridge, Rachel Bowman, Peter Hamburger, Bruce Kessler

Bruce Kessler

The authors present a modern technique for teaching matrix transformations on $\R^2$ that incorporates works of visual art and computer programming. Two of the authors were undergraduate students in Dr. Hamburger's linear algebra class, where this technique was implemented as a special project for the students. The two students generated the images seen in this paper, and the movies that can be found on the accompanying webpage www.wku.edu/\~bruce.kessler/.

Using Works Of Visual Art To Teach Matrix Transformations, James Luke Akridge, Rachel Bowman, Peter Hamburger, Bruce Kessler

Mathematics Faculty Publications

The authors present a modern technique for teaching matrix transformations on $\R^2$ that incorporates works of visual art and computer programming. Two of the authors were undergraduate students in Dr. Hamburger's linear algebra class, where this technique was implemented as a special project for the students. The two students generated the images seen in this paper, and the movies that can be found on the accompanying webpage www.wku.edu/\~{\space}bruce.kessler/.

Elementary-Level Mathematics Content In Comic Book Format, Bruce Kessler, Janet Tassell, Mary Evans, Cathy Willoughby, Melissa Zimmer

Mathematics Faculty Publications

No abstract provided.

Elementary-Level Mathematics Content In Comic Book Format, Bruce Kessler, Janet Tassell, Mary Evans, Cathy Willoughby, Melissa Zimmer

Bruce Kessler

No abstract provided.

Generalized Probabilistic Bowling Distributions, Jennifer Lynn Hohn

Masters Theses & Specialist Projects

Have you ever wondered if you are better than the average bowler? If so, there are a variety of ways to compute the average score of a bowling game, including methods that account for a bowler’s skill level. In this thesis, we discuss several different ways to generate bowling scores randomly. For each distribution, we give results for the expected value and standard deviation of each frame's score, the expected value of the game’s final score, and the correlation coefficient between the score of the first and second roll of a single frame. Furthermore, we shall generalize the results in …

Fractional Calculus: Definitions And Applications, Joseph M. Kimeu

Masters Theses & Specialist Projects

No abstract provided.

Multiwavelets For Quantitative Pattern Matching, Bruce Kessler

Mathematics Faculty Publications

This was my presentation in Hawaii that accompanied my paper on pattern matching, published in the conference proceedings.

Multiwavelets For Quantitative Pattern Matching, Bruce Kessler

Bruce Kessler

This was my presentation in Hawaii that accompanied my paper on pattern matching, published in the conference proceedings.

Wavelet Decompositions For Quantitative Pattern Matching, Bruce Kessler

Mathematics Faculty Publications

The purpose of this paper is to provide an introduction to the concepts of wavelets and multiwavelets, and explain how these tools can be used by the analyst community to find patterns in quantitative data. Three multiwavelet bases are introduced, the GHM basis from \cite{GHM}, a piecewise polynomial basis with approximation order 4 from \cite{DGH}, and a smoother approximation-order-4 basis developed by the author in previous work \cite{K}. The technique of using multiwavelets to find patterns is illustrated in a traffic-analysis example. Acknowledgements: This work supported in part by the NACMAST consortium under contract EWAGSI-07-SC-0003.

Multiwavelets For Quantitative Pattern Matching, Bruce Kessler

Bruce Kessler

The purpose of this paper is to provide an introduction to the concepts of wavelets and multiwavelets, and explain how these tools can be used by the analyst community to find patterns in quantitative data. Three multiwavelet bases are introduced, the GHM basis from \cite{GHM}, a piecewise polynomial basis with approximation order 4 from \cite{DGH}, and a smoother approximation-order-4 basis developed by the author in previous work \cite{K}. The technique of using multiwavelets to find patterns is illustrated in a traffic-analysis example. Acknowledgements: This work supported in part by the NACMAST consortium under contract EWAGSI-07-SC-0003.

Comic Books That Teach Mathematics, Bruce Kessler

Mathematics Faculty Publications

During the 2008--2009 academic year, the author embarked on an extremely non-standard curriculum path: developing comic books with embedded mathematics appropriate for 3rd through 6th grade students. With the help of an education professor to measure impact, an elementary-school principal, and talented undergraduate illustrators, this project came to fruition and the comics were implemented in elementary classrooms at Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky. This manuscript gives the history of this idea, the difficulties of developing the content of the comics and getting them illustrated, and the implementation plan in the school.

My Trig Book, Bruce Kessler

Mathematics Faculty Publications

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Math and Science sections of the course. The text has also been used in two online course offerings.

My Trig Book, Bruce Kessler

Mathematics Faculty Publications

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Academy sections of the course. The text has also been used in two online course offerings.

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mathematics Faculty Publications

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mathematics Faculty Publications

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …

Thermocapillary Effects In Driven Dewetting And Self-Assembly Of Pulsed Laser-Irradiated Metallic Films, Agegnehu Atena, Mikhail Khenner

Mikhail Khenner

In this paper the lubrication-type dynamical model is developed of a molten, pulsed laser-irradiated metallic film. The heat transfer problem that incorporates the absorbed heat from a single beam or interfering beams is solved analytically. Using this temperature field, we derive the 3D long-wave evolution PDE for the film height. To get insights into dynamics of dewetting, we study the 2D version of the evolution equation by means of a linear stability analysis and by numerical simulations. The stabilizing and destabilizing effects of various system parameters, such as the peak laser beam intensity, the film optical thickness, the Biot and …