epshteyn (at) math.utah.edu)September 11
Speaker: Ornella Mattei, Department of Mathematics, University of Utah
Title: Field patterns: A new type of wave
Abstract: Field patterns are a new type of wave propagating in
one-dimensional linear media with moduli that vary both in space and time.
Specifically, the geometry of these space-time materials is commensurate
with the slope of the characteristic lines so that a disturbance does not
generate a complicate cascade of subsequent disturbances, but rather
concentrates on a periodic space-time pattern, that we call field pattern.
Field patterns present spectacularly novel features. One of the most
interesting ones is the appearance of a wave generated from an
instantaneous source, whose amplitude, unlike a conventional wake, does not
tend to zero away from the wave front. Furthermore, very interestingly, the
band structure associated with these special space-time geometries is
infinitely degenerate: associated with each point on the dispersion diagram
is an infinite space of Bloch functions, a basis for which are generalized
functions each concentrated on a field pattern.
September 15. Note Room is LCB 222. Time is Friday September 15 4pm - 5pm.
Speaker: Roland Pulch,
Institute for Mathematics and Informatics, University of Greifswald
Title: Model order reduction for linear dynamical systems with quadratic
outputs
Abstract: We investigate model order reduction (MOR) for linear dynamical systems,
where a quadratic output is de ned as a quantity of interest. The system
can be transformed into a linear dynamical system with many linear
outputs. MOR is feasible by the method of balanced truncation, but
suffers from the large number of outputs. Alternatively, we derive an
equivalent quadratic-bilinear system with a single linear output. The
properties of the quadratic-bilinear system are analyzed. We examine an
MOR by the technique of balanced truncation, where a stabilization of
the system is required. Therein, the solution of quadratic Lyapunov
equations is traced back to the solution of linear Lyapunov equations.
We present numerical results for several test examples comparing the two
MOR approaches.
September 18
Speaker: Christel Hohenegger, Department of Mathematics, University of Utah
Title: Diffusion in complex fluids
Abstract: Complex fluids are omnipresent in our everyday life, as they
encompass material from polymer melts, to mucus, blood, cake batter, and
sill putty. Depending on the applied stress, they can exhibit a liquid or
solid like response. As a result, immersed and passive particles show
subdiffusive behavior, which is to say the variance of the particle
displacement grows sublinearly with time. Passive microrheology records
displacement of such particles and extract mechanical properties of the
bulk fluid. It is premised on the idea that statistics of particles
trajectories can reveal fundamental information about the fluid
environment. We probe this hypothesis on two fronts. First, we present a
Landau-Lifshitz-Navier-Stokes model of a passive particle advected in a
viscoelastic fluid and show how the mean square displacement and first step
auto-correlation in the increment process are related to those of the
fluid's modes. Second, we address the uncertainty in reconstructing loss
and storage moduli which characterize the elastic and viscous properties of
the fluid from simulated data as an inverse problem.
September 25
Speaker: Andrej Cherkaev, Department of Mathematics, University of Utah
Title: Modeling of damage spread in beam lattices and robust design of
fault-tolerant lattices
Abstract: We discuss modeling of unstable process of damage spread in triangular and
hexagonal lattices, introduce quantitative criteria for measurement of
lattice damage, simulate the damage spread, and suggest a fault tolerant
design of isotropic periodic lattice that is a hybrid between triangular
and hexagonal structures.
Joint work with M. Ryvkin (Tel Aviv University)
October 16
Speaker: Chiu-Yen Kao,
Department of Mathematics, Claremont Mckenna College
Title: Extremal Eigenvalues for Inhomogeneous Rods and Plates
Abstract:
Optimizing eigenvalues of biharmonic equations appears in the frequency
control based on density distribution of composite rods and thin plates
with clamped or simply supported boundary conditions. We use a
rearrangement algorithm to find the optimal density distribution which
minimizes a specific eigenvalue. We answer the open question regarding
optimal density configurations to minimize k-th eigenvalue for clamped rods
and analytically show that the optimal configurations are distinct for
clamped rods and simply supported rods. Many numerical simulations in both
one and two dimensions demonstrate the robustness and efficiency of the
proposed approach.
October 23
Speaker: Akil Narayan,
Department of Mathematics and SCI, University of Utah
Title: Multivariate polynomial quadrature for parameterized problems
Abstract: Numerical quadrature rules that use point values are ubiquitous tools for
approximating integrals. Some of the most popular rules achieve accuracy by
enforcing exactness for integrands in a finite-dimensional polynomial space. When
the integration domain is one-dimensional, classical rules are available and
plentiful. In multidimensional domains with non-standard polynomial spaces and
weights, the situation is far more complicated. We will present a general
methodology for numerically generating approximate quadrature rules in the
multidimensional case. The need for flexible multivariate quadrature rules will be
motivated by solutions to parametric partial differential equations, and the
efficacy of our approach will be shown on various test problems in scientific
computing.
October 30
Speaker: Frank Stenger,
School of Computing, University of Utah
Title: Stenger's proof of the Riemann hypothesis
Abstract: This talk will be about the speaker's proof of the Riemann hypothesis
November 27
Speaker: Varun Shankar,
Department of Mathematics, University of Utah
Title: A high-order meshfree framework for solving PDEs on irregular
domains
Abstract: We present meshfree methods based on Radial Basis Function (RBF)
interpolation for solving partial differential equations (PDEs) on
irregular domains in O(N) complexity. First, we present the Overlapped
RBF-Finite Difference (RBF-FD) method, a recent generalization of RBF-FD
methods that exploits certain properties of RBF interpolants to
dramatically reduce the cost of high-order methods, both on serial and
parallel architectures. To rectify the spectra of RBF-FD differentiation
matrices on scattered node sets, we develop a quasi-analytic
hyperviscosity-based stabilization technique based on a semi-discrete
Von-Neumann analysis applied to differential operators that are continuous
analogues of the discrete RBF-FD differentiation matrices. We also
introduce a simple ghost node technique to ameliorate boundary-related
instabilities seen in RBF-FD methods. We verify high-order convergence
rates on some model problems on domains with curved boundaries, and
demonstrate the solution of some PDEs inspired by biological applications
on more irregular domains.
epshteyn (at) math.utah.edu).
Past lectures: Spring 2017, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.