• - 3:30pm - Allen 411
    CAM seminar
    Hodge decomposition of the dynamic Ginzburg-Landau equations in multi-connected nonsmooth domains
    Dr. Buyang Li, The Hong Kong Polytechnic University,

    Title:  Hodge decomposition of the dynamic Ginzburg-Landau equations in multi-connected nonsmooth domains
    Abstract:  In a general polygonal domain, possibly nonconvex and multi-connected (with holes), the time-dependent Ginzburg-Landau equation is reformulated into a new system of equations by using the Hodge decomposition: decomposing the magnetic potential into its divergence-free part, curl-free part and harmonic part, separately. Global well-posedness of the new system and its equivalence to the original problem are proved. A linearized and decoupled Galerkin finite element method is proposed for solving the new system. The convergence of numerical solutions is proved based on a compactness argument by utilizing the maximal Lp-regularity of the discretized equations. Several numerical examples are provided to illustrate the efficiency of the proposed numerical method in both simply connected and multi-connected nonsmooth domains.
    Link: http://cam.math.msstate.edu/sem20180426BL.html


  • - 3:30pm - Allen 411
    CAM seminar
    Localizing uncertainty with gaussian Markov random field models
    Dr. Hans Werner Van Wyk, Mathematics, Auburn University,

    Title:  Localizing uncertainty with gaussian Markov random field models
    Abstract:  The high computational cost of stochastic simulations involving partial differential equations (PDEs) with uncertain input parameters is often attributable to a combination of two bottlenecks: i) the steep cost of evaluating sample paths and ii) the complexity of the underlying parameter space. In this talk we relate both of these problems to the computational mesh, by using Gaussian Markov random fields to model the spatially varying input parameters for a simple PDE. This allows us to exploit readily available local dependency information of the parameter field in conjunction with standard finite element error estimates to identify spatial regions that contribute statistically to the error in the computed quantity of interest.
    Link: http://cam.math.msstate.edu/sem20180412HW.html


  • - 3:30pm - Allen 411
    CAM seminar
    Mathematical studies of extraordinary field enhancement in subwavelength structures
    Dr. Junshan Lin, Mathematics, Auburn University,

    Title:  Mathematical studies of extraordinary field enhancement in subwavelength structures
    Abstract:  Since the discovery of the extraordinary optical transmission through nanohole arrays in metallic films by Ebbesen, a wealth of research has been sparked in the experimental and theoretical investigation of localized electromagnetic field enhancement in subwavelength nanostructures. This remarkable phenomenon can lead to potentially significant applications in near-field imaging, bio-sensing, etc. However, there has been a long debate on the interpretation of the enhancement effect since Ebbesen's work. In addition, a quantitative analysis of the field enhancement in subwavelength structures is still widely open. In this talk, using two-dimensional slits as a prototype, I will present mathematical studies of the field enhancement in the subwavlength structures. Based upon the layer potential technique, asymptotic analysis and homogenization theory, the enhancement mechanisms for both the single slit and an array of slits are studied quantitatively.
    Link: http://cam.math.msstate.edu/sem20180405JL.html


  • - 3:30pm - Allen 411
    CAM seminar
    Gene regulation and spatial mechanisms control layer formation in epidermis
    Dr. Huijing Du, Mathematics, University of Nebraska, Lincoln,

    Title:  Gene regulation and spatial mechanisms control layer formation in epidermis
    Abstract:  Epidermal morphogenesis, which occurs during the second half of embryogenesis, is the developmental process that generates a skin permeability barrier essential for terrestrial survival. Defects with this barrier are associated with common skin disorders such as atopic dermatitis. Study of mechanisms that control epidermal development and differentiation is therefore highly relevant to human health. Motivated by recent experimental observations on the role of Ovol transcription factors in regulating epidermal development, we developed a multiscale model to investigate the underlying mechanisms responsible for epidermal layer formation and homeostasis. We report that regulation of proliferation and differentiation by Ovol plays an important role in epidermal development. In addition, our computational analysis shows that asymmetric cell division, selective cell adhesion, and morphogen regulation work in a synergetic manner to produce the well-stratified epidermal layers. Taken together, our results demonstrate that robust epidermal morphogenesis involves a balance between proliferation and differentiation, and an interplay between short- and long-range spatial control mechanisms. This principle may also be applicable to other complex systems of tissue development or regeneration.
    Link: http://cam.math.msstate.edu/sem20180329HD.html


  • Past Seminars

Graduate Student Seminars

  • - 3:00pm - Allen 14
    Master's Presentation
    Analysis of diabetic incidence
    Yiyuan Ma, Statistics, Msstate,

    Title:  Analysis of diabetic incidence

  • - 3:30pm - Allen 14
    Master's Presentation
    Better metrics: AUC or AP?
    Matthew Kilpatrick, Statistics, Msstate,

    Title:  Better metrics: AUC or AP?

  • - 3:00pm - Allen 14
    Master's Presentation
    Fractal geometry in music
    Carly Herm, Mathematics, Msstate,

    Title:  Fractal geometry in music

  • - 3:30pm - Allen 14
    Master's Presentation
    Lightning strikes on aircraft
    Derrick Jones, Mathematics, Msstate,

    Title:  Lightning strikes on aircraft

  • Past Graduate Student Seminars

Research Seminars

  • - 3:30pm - Allen 411
    CAM seminar
    Hodge decomposition of the dynamic Ginzburg-Landau equations in multi-connected nonsmooth domains
    Dr. Buyang Li, The Hong Kong Polytechnic University,

    Title:  Hodge decomposition of the dynamic Ginzburg-Landau equations in multi-connected nonsmooth domains
    Abstract:  In a general polygonal domain, possibly nonconvex and multi-connected (with holes), the time-dependent Ginzburg-Landau equation is reformulated into a new system of equations by using the Hodge decomposition: decomposing the magnetic potential into its divergence-free part, curl-free part and harmonic part, separately. Global well-posedness of the new system and its equivalence to the original problem are proved. A linearized and decoupled Galerkin finite element method is proposed for solving the new system. The convergence of numerical solutions is proved based on a compactness argument by utilizing the maximal Lp-regularity of the discretized equations. Several numerical examples are provided to illustrate the efficiency of the proposed numerical method in both simply connected and multi-connected nonsmooth domains.
    Link: http://cam.math.msstate.edu/sem20180426BL.html

  • - 3:30pm - Allen 411
    CAM seminar
    Localizing uncertainty with gaussian Markov random field models
    Dr. Hans Werner Van Wyk, Mathematics, Auburn University,

    Title:  Localizing uncertainty with gaussian Markov random field models
    Abstract:  The high computational cost of stochastic simulations involving partial differential equations (PDEs) with uncertain input parameters is often attributable to a combination of two bottlenecks: i) the steep cost of evaluating sample paths and ii) the complexity of the underlying parameter space. In this talk we relate both of these problems to the computational mesh, by using Gaussian Markov random fields to model the spatially varying input parameters for a simple PDE. This allows us to exploit readily available local dependency information of the parameter field in conjunction with standard finite element error estimates to identify spatial regions that contribute statistically to the error in the computed quantity of interest.
    Link: http://cam.math.msstate.edu/sem20180412HW.html

  • - 3:30pm - Allen 411
    CAM seminar
    Mathematical studies of extraordinary field enhancement in subwavelength structures
    Dr. Junshan Lin, Mathematics, Auburn University,

    Title:  Mathematical studies of extraordinary field enhancement in subwavelength structures
    Abstract:  Since the discovery of the extraordinary optical transmission through nanohole arrays in metallic films by Ebbesen, a wealth of research has been sparked in the experimental and theoretical investigation of localized electromagnetic field enhancement in subwavelength nanostructures. This remarkable phenomenon can lead to potentially significant applications in near-field imaging, bio-sensing, etc. However, there has been a long debate on the interpretation of the enhancement effect since Ebbesen's work. In addition, a quantitative analysis of the field enhancement in subwavelength structures is still widely open. In this talk, using two-dimensional slits as a prototype, I will present mathematical studies of the field enhancement in the subwavlength structures. Based upon the layer potential technique, asymptotic analysis and homogenization theory, the enhancement mechanisms for both the single slit and an array of slits are studied quantitatively.
    Link: http://cam.math.msstate.edu/sem20180405JL.html

  • - 3:30pm - Allen 411
    CAM seminar
    Gene regulation and spatial mechanisms control layer formation in epidermis
    Dr. Huijing Du, Mathematics, University of Nebraska, Lincoln,

    Title:  Gene regulation and spatial mechanisms control layer formation in epidermis
    Abstract:  Epidermal morphogenesis, which occurs during the second half of embryogenesis, is the developmental process that generates a skin permeability barrier essential for terrestrial survival. Defects with this barrier are associated with common skin disorders such as atopic dermatitis. Study of mechanisms that control epidermal development and differentiation is therefore highly relevant to human health. Motivated by recent experimental observations on the role of Ovol transcription factors in regulating epidermal development, we developed a multiscale model to investigate the underlying mechanisms responsible for epidermal layer formation and homeostasis. We report that regulation of proliferation and differentiation by Ovol plays an important role in epidermal development. In addition, our computational analysis shows that asymmetric cell division, selective cell adhesion, and morphogen regulation work in a synergetic manner to produce the well-stratified epidermal layers. Taken together, our results demonstrate that robust epidermal morphogenesis involves a balance between proliferation and differentiation, and an interplay between short- and long-range spatial control mechanisms. This principle may also be applicable to other complex systems of tissue development or regeneration.
    Link: http://cam.math.msstate.edu/sem20180329HD.html

  • Past Research Seminars