Mathematics Faculty Publications Copyright (c) 2013 Western Kentucky University All rights reserved. http://digitalcommons.wku.edu/math_fac_pub Recent documents in Mathematics Faculty Publications en-us Wed, 10 Apr 2013 21:45:32 PDT 3600 Operation Comics http://digitalcommons.wku.edu/math_fac_pub/39 http://digitalcommons.wku.edu/math_fac_pub/39 Fri, 17 Jun 2011 08:53:09 PDT Bruce Kessler et al. A “Peak” at the Algorithm Behind “Peaklet Analysis” Software http://digitalcommons.wku.edu/math_fac_pub/38 http://digitalcommons.wku.edu/math_fac_pub/38 Mon, 09 May 2011 12:56:41 PDT In response to a problem posed by faculty at the Applied Physics Institute at Western Kentucky University, the speaker has developed an algorithm for providing an automated analysis of spectrum data for the purpose of determining the elemental composition of the item generating the data. A full, non-provisional patent application has been filed on the idea, and a full marketing campaign has started to license software implementing the algorithm. This presentation will give a brief explanation of the mathematics in use in the algorithm, and will give some examples of the software in action.

]]> Bruce Kessler Wavelets “Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) with Comic Books http://digitalcommons.wku.edu/math_fac_pub/37 http://digitalcommons.wku.edu/math_fac_pub/37 Mon, 09 May 2011 11:53:57 PDT During Spring 2009, Dr. Kessler created and published a comic book series that embedded math content into the story for 4th-6th grade students. The comics were well received in the classrooms at Cumberland Trace Elementary. Dr. Kessler contends that this approach to teaching and learning can be used in any content area, and is useful for engaging students who might not be as interested otherwise. This session will explore ways of utilizing the skills of your students to construct learning comics in your classes, regardless of the funds, technology, and artistic experience at your disposal. The session will include a brief origin of the math comics, an open forum on strategies for making the idea work in your class, and an implementation of those strategies, with participants beginning their own “comics.”

]]> Bruce Kessler Mathematics Education Wavelet-Based Analysis of Neutron-Induced Photon Spectral Data http://digitalcommons.wku.edu/math_fac_pub/36 http://digitalcommons.wku.edu/math_fac_pub/36 Mon, 09 May 2011 11:53:47 PDT Neutron-based methods of non-destructive inter- rogation of objects for the purpose of their characterization are well-established techniques, employed in the field of bulk material analysis, contraband detection, unexploded ordnance, etc. The characteristic gamma rays produced in nuclear reactions initiated by neutrons in the volume of the irradiated object (inelastic neutron scattering, thermal neutron capture, and activation) are used for the elemental identification. In many real-world applications, an automated spectral analysis is needed, and many algorithms are used for that purpose. The Applied Physics Institute at Western Kentucky University has recently started to employ a mathematical spectrum analysis technique based on wavelets that simultaneously provides quick, accurate, and objective analysis of gamma ray spectra.

This paper will provide a brief overview of wavelets and multiwavelets, and of the wavelet-based analysis algorithm. Examples will be given using neutron- induced photon spectra measured using high resolution and low resolution detectors.

]]> Bruce Kessler et al. Wavelets Operation Comics: The Story Continues http://digitalcommons.wku.edu/math_fac_pub/35 http://digitalcommons.wku.edu/math_fac_pub/35 Mon, 09 May 2011 11:53:37 PDT During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the initial cohort of students using the comics, and the project has been given new life with an infusion of money from an anonymous corporate donor and a new illustrator, author Tu. This manuscript will give an abbreviated summary of our initial findings, and will show how Tu. is addressing the presentation of mathematical content in her illustrations in three new comics. We will also outline the 2-1/2 year study we are beginning during the Spring 2011 semester, and how the project is spawning other outreach activities.

]]> Bruce Kessler et al. Mathematics Education A Primer on Chaos and Fractals http://digitalcommons.wku.edu/math_fac_pub/34 http://digitalcommons.wku.edu/math_fac_pub/34 Mon, 14 Mar 2011 10:10:19 PDT This is a prelude to a performance of the play "Arcadia" exclusively for the science and math majors of Lipscomb University. One of the main characters of the story is a mathematical genius, and has realized the power and limitations of iterations in generating mathematical models and structures, although she is living in the early 1800's. This talk gives an introduction to the ideas of chaos theory, fractals, and randomness.

]]> Bruce Kessler Mathematics Education WKU Professor Develops Comic Book Series http://digitalcommons.wku.edu/math_fac_pub/33 http://digitalcommons.wku.edu/math_fac_pub/33 Mon, 14 Mar 2011 09:02:11 PDT Dan Modlin, WKYU-FM et al. Stability of a strongly anisotropic thin epitaxial film in a wetting interaction with elastic substrate http://digitalcommons.wku.edu/math_fac_pub/32 http://digitalcommons.wku.edu/math_fac_pub/32 Tue, 11 Jan 2011 08:37:36 PST The linear dispersion relation for longwave surface perturbations, as derived by Levine et al. Phys. Rev. B 75, 205312 (2007) is extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak to strong, such that sharp corners and slightly curved facets occur on the corresponding Wulff shape). Through detailed parametric studies it is shown that a combination of a wetting interaction and strong anisotropy, and even a wetting interaction alone results in complicated linear stability characteristics of strained and unstrained films.

]]> Mikhail Khenner et al. Selected recent publications Thermocapillary effects in driven dewetting and self-assembly of pulsed laser-irradiated metallic films http://digitalcommons.wku.edu/math_fac_pub/31 http://digitalcommons.wku.edu/math_fac_pub/31 Tue, 26 Oct 2010 06:49:02 PDT 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 intensity, the film optical thickness, the Biot and Marangoni numbers, etc. are elucidated. It is observed that the film stability is promoted for such parameters variations that increase the heat production in the film. Moreover, when the heat conduction in the thin substrate is taken into account, the film with non-zero reflectivity is stable with respect to small perturbations in some interval of the optical thickness parameter. In the numerical simulations the impacts of different irradiation modes are investigated. In particular, we obtain that in the interference heating mode the spatially periodic irradiation results in a spatially periodic film rupture with the same, or nearly equal period. Small values of the capillary number result in ring rupture. The 2D model qualitatively reproduces the experimental observations to-date and displays some new effects (Phys. Rev. B 80, 075402 (2009)).

]]> Mikhail Khenner Presentations Thermocapillary effects in driven dewetting and self-assembly of pulsed laser-irradiated metallic films http://digitalcommons.wku.edu/math_fac_pub/30 http://digitalcommons.wku.edu/math_fac_pub/30 Mon, 16 Aug 2010 08:15:37 PDT 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 Marangoni numbers, etc. are elucidated. It is observed that the film stability is promoted for such parameters variations that increase the heat absorption in the film. In the numerical simulations the impacts of different irradiation modes are investigated. In particular, we obtain that in the interference heating mode the spatially periodic irradiation results in a spatially periodic film rupture with the same, or nearly equal period. The 2D model qualitatively reproduces, for the first time, the results of the experimental observations of a film stability and spatial ordering of a re-solidified nanostructures.

]]> Agegnehu Atena et al. Selected recent publications Oscillatory and monotonic modes of long-wave Marangoni convection in a thin film http://digitalcommons.wku.edu/math_fac_pub/29 http://digitalcommons.wku.edu/math_fac_pub/29 Mon, 16 Aug 2010 08:15:36 PDT We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=OBi, where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.

]]> Sergey Shklyaev et al. Selected recent publications Enhanced stability of a dewetting thin liquid film in a single-frequency vibration field http://digitalcommons.wku.edu/math_fac_pub/28 http://digitalcommons.wku.edu/math_fac_pub/28 Mon, 16 Aug 2010 08:15:35 PDT Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description is reasonable and the amplitude equation holds. The linear and nonlinear analyses of the amplitude equation and the numerical computations show that such vibration stabilizes the film against dewetting and rupture.

]]> Sergey Shklyaev et al. Selected recent publications Morphologies and kinetics of a dewetting ultrathin solid film http://digitalcommons.wku.edu/math_fac_pub/26 http://digitalcommons.wku.edu/math_fac_pub/26 Mon, 17 May 2010 12:54:27 PDT The surface evolution model based on geometric partial differential equation is used to numerically study the kinetics of dewetting and dynamic morphologies for the localized pinhole defect in the surface of the ultrathin solid film with the strongly anisotropic surface energy. Depending on parameters such as the initial depth and width of the pinole, the strength of the attractive substrate potential and the strength of the surface energy anisotropy, the pinhole may either extend to the substrate and thus rupture the film, or evolve to the quasiequilibrium shape while the rest of the film surface undergoes phase separation into a hill-and-valley structure followed by coarsening. Overhanging (non-graph) morphologies are possible for deep, narrow (slit-like) pinholes.

]]> Mikhail Khenner Selected recent publications Enhanced stability of a dewetting thin liquid film in a single-frequency vibration field http://digitalcommons.wku.edu/math_fac_pub/25 http://digitalcommons.wku.edu/math_fac_pub/25 Mon, 17 May 2010 12:54:25 PDT Dynamics of a thin dewetting liquid film on a vertically oscillating substrate is considered. We assume moderate vibration frequency and large (compared to the mean film thickness) vibration amplitude. Using the lubrication approximation and the averaging method, we formulate the coupled sets of equations governing the pulsatile and the averaged fluid flows in the film, and then derive the nonlinear amplitude equation for the averaged film thickness. We show that there exists a window in the frequency-amplitude domain where the parametric and shear-flow instabilities of the pulsatile flow do not emerge. As a consequence, in this window the averaged description is reasonable and the amplitude equation holds. The linear and nonlinear analyses of the amplitude equation and the numerical computations show that such vibration stabilizes the film against dewetting and rupture.

]]> Mikhail Khenner Selected recent publications Thermocapillary effects in driven dewetting and self-assembly of pulsed laser-irradiated metallic films http://digitalcommons.wku.edu/math_fac_pub/24 http://digitalcommons.wku.edu/math_fac_pub/24 Mon, 10 May 2010 19:03:14 PDT 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 intensity, the film optical thickness, the Biot and Marangoni numbers, etc. are elucidated. It is observed that the film stability is promoted for such parameters variations that increase the heat production in the film. Moreover, when the heat conduction in the thin substrate is taken into account, the film with non-zero reflectivity is stable with respect to small perturbations in some interval of the optical thickness parameter. In the numerical simulations the impacts of different irradiation modes are investigated. In particular, we obtain that in the interference heating mode the spatially periodic irradiation results in a spatially periodic film rupture with the same, or nearly equal period. Small values of the capillary number result in ring rupture. The 2D model qualitatively reproduces the experimental observations to-date and displays some new effects (Phys. Rev. B 80, 075402 (2009)).

]]> Mikhail Khenner Morphological evolution of single-crystal ultrathin solid films http://digitalcommons.wku.edu/math_fac_pub/23 http://digitalcommons.wku.edu/math_fac_pub/23 Mon, 10 May 2010 19:03:13 PDT An introduction to mathematical modeling of ultrathin solid films and the role of such modeling in nanotechnologies: Educational presentation for senior physics majors

]]> Mikhail Khenner An Algorithm for Wavelet–Based Elemental Spectrum Analysis http://digitalcommons.wku.edu/math_fac_pub/22 http://digitalcommons.wku.edu/math_fac_pub/22 Mon, 15 Mar 2010 18:52:39 PDT At the previous Approximation Theory XII meeting, I discussed some preliminary work with the Applied Physics Institute at Western Kentucky University in using multiwavelets to provide an objective analysis of gamma-ray spectrum generated from fast neutron bombardment of objects, for the purpose of identifying the elemental composition of the object. The method discussed at the time worked moderately well with the limited amount of data provided, but subsequent use with data sets of different compounds and with different detectors brought to light serious flaws with its implementation.

This talk will illustrate those issues and will address how they have been corrected in the current implementation. The algorithm has potential commercial application in analyzing gamma-ray, X-ray, fluorescence, etc. spectra, and is protected by provisional patent. It is currently being used in the grant-funded development of a prototype device for analyzing the active/inactive status of small (less than 2 kg in weight) unexploded ordnance.

]]> Bruce Kessler Wavelets Mathematical Modeling My Trig Book http://digitalcommons.wku.edu/math_fac_pub/21 http://digitalcommons.wku.edu/math_fac_pub/21 Mon, 25 Jan 2010 07:10:02 PST 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.

]]> Bruce Kessler Mathematics Education Improved automated monitoring and new analysis algorithm for circadean phototaxis rhythms in Chlamydomonas http://digitalcommons.wku.edu/math_fac_pub/20 http://digitalcommons.wku.edu/math_fac_pub/20 Mon, 25 Jan 2010 07:10:00 PST Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported to be specific for phototaxis and by choosing an algal strain, which does not need background illumination between test light cycles for proper expression of the rhythm. As a result, period and phase of the rhythm are now unaffected by the time a culture is placed into the machine. Analysis of the rhythm data was also optimized through a new algorithm, whose robustness was demonstrated using virtual rhythms with various noises. The algorithm differs in particular from other reported algorithms by maximizing the fit of the data to a sinusoidal curve that dampens exponentially. The algorithm was also used to confirm the reproducibility of rhythm monitoring by the machine. Machine and algorithm can now be used for a multitude of circadian clock studies that require unambiguous period and phase determinations such as light pulse experiments to identify the photoreceptor(s) that reset the circadian clock in C. reinhardtii.

]]> Christa Gaskill et al. Mathematical Modeling Multiwavelets for Quantitative Pattern Matching http://digitalcommons.wku.edu/math_fac_pub/19 http://digitalcommons.wku.edu/math_fac_pub/19 Sun, 26 Jul 2009 16:27:55 PDT This was my presentation in Hawaii that accompanied my paper on pattern matching, published in the conference proceedings.

]]> Bruce Kessler Mathematical Modeling