CSU Math HomeManuchehr Aminian's home page
CSU Math Postdoc Seminar
Fall 2019 Schedule
  • September 16
  • Who: Everyone
  • Title: Organizational meeting
  • Abstract:
Fall 2018 Schedule
  • November 28, Weber 223, 3pm
  • Who: Dr. Sophie Giffard-Roisin, University of Colorado Boulder ( Webpage )
  • Title: Deep learning for hurricane forecasting
  • Abstract: The forecast of hurricane trajectories is crucial for the protection of people and property, but machine learning techniques have been scarce for this so far. I will present a method that we developed recently, a fusion of neural networks, that is able to combine past trajectory data and reanalysis of atmospheric images (wind and pressure 3D fields). Our network is trained to estimate the longitude and latitude displacement of hurricanes and depressions from a large database from both hemispheres (more than 3000 storms since 1979, sampled at a 6 hour frequency). Finally, I will give an overview of the hackathon that I organized on a very close topic at the Climate Informatics Workshop in September.
  • November 12
  • Who: Dr. Sara Calandrini, Florida State University
  • Co-authors: Konstantin Pieper, Max Gunzburger
  • Title: Exponential Time Differencing for the Tracer Equations Appearing in Primitive Equation Ocean Models
  • Abstract: In the field of ocean modeling, a great focus is given to the development of efficient and parallelizable time-stepping methods in the presence of highly nonuniform grids which are needed for the modeling of coastal regions. To achieve this goal, time-stepping schemes have been designed that remain stable and accurate even for time steps considerably larger than those required by the CFL condition for standard methods. Exponential time differencing (ETD) methods are a compelling choice since they have been proven to be very effective for solving stiff evolution problems in the past decades. In this work, we focus on the tracer equations that are part of the primitive equations used in ocean modeling. These equations describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several equations may be added to and coupled to the dynamics system. In many relevant situations, the time-step requirements of explicit methods caused by the transport and mixing in the vertical direction are more restrictive than the ones for the horizontal. We propose an ETD solver where the vertical transport is treated with a matrix exponential, whereas the horizontal is dealt with in an explicit way, leading to less restrictive CFL conditions. We investigate numerically the accuracy and computational speed-ups that can be obtained over an explicit or a fully exponential method. Results for the complete set of primitive equations are also shown, where a tracer system is coupled to the dynamics. Here, the tracer and dynamics equations are decoupled in each time-step, and a second-order ETD solver is employed for the dynamics system.
  • November 5
  • Who: Dr. Giacomo Capodaglio, Florida State University ( Google scholar )
  • Title: Approximation of probability density functions for SPDEs using truncated series expansions
  • Abstract: The probability density function (PDF) of a random variable associated with the solution of a stochastic partial differential equation (SPDE) is approximated using a truncated series expansion. The SPDE is solved using two stochastic finite element (SFEM) methods, Monte Carlo sampling and the stochastic Galerkin method with global polynomials. The random variable is a functional of the solution of the SPDE, such as the average over the physical domain. The truncated series are obtained considering a finite number of terms in the Gram-Charlier (GC) or Edgeworth (ED) series expansions. These expansions approximate the PDF of a random variable in terms of another PDF, and involve coefficients that are functions of the known cumulants of the random variable. While the GC and ED series have been employed in a variety of fields such as chemistry, astrophysics and finance, their use in the framework of SPDEs has not yet been explored. This is a joint work with Max Gunzburger and Henry P. Wynn.
  • October 22, 2018
  • Who: Dr. Valeria Barra, CU Boulder ( https://csel.cs.colorado.edu/~vaba3353/ )
  • Title: Numerical investigation of thin viscoelastic films and membranes
  • Abstract: This study focuses on numerical simulations of the dynamics of thin viscoelastic films, in different settings. The first part of this work presents a computational investigation of thin viscoelastic films and drops, that are subjected to the van der Waals interaction force, in two spatial dimensions. The liquid films are deposited on a flat solid substrate that can have a zero or nonzero inclination with respect to the base. The equation that governs the interfacial dynamics of the thin films and drops is obtained within the long-wave approximation of the Navier-Stokes equations, with Jeffreys model for viscoelastic stresses. The effects of viscoelasticity and the substrate slippage on the dynamics of thin viscoelastic films and drops that spread or recede on a prewetted substrate are analyzed. The second part of this work presents a numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes, not necessarily deposited on solid substrates. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic response to deformations of Maxwell type. A penalty method is utilized to enforce near incompressibility of the viscoelastic media, in which the penalty constant is proportional to the viscosity of the fluid. A finite element method is used, in which the slender geometry representing the liquid membrane is discretized by linear three-node triangular elements under plane stress conditions. Two applications of interest are considered for the numerical framework provided: shear flow and extensional flow in drawing processes.