This set of lectures will provide a basic introduction to hyperbolic systems of conservation laws in one space dimension. The main topics covered will be: Meaning of the conservation equations and definition of weak solutions.Shocks, Rankine-Hugoniot equations and admissibilityconditions.The Riemann problem. Wave interaction estimates.Weak solut...
Creator:
Chen, Gui-Qiang G. (Northwestern University)
Created:
2009-07-15
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We consider control and inverse problems on metric graphs for severaltypes of PDEs includingthe wave, heat and Schr\'odinger equations. We demonstrate that, forgraphs without cycles,unknown coefficients of the equations together with the topology of thegraph and lengths of the edgescan be recovered from the dynamical Dirichlet-to-Neumann map ass...
Creator:
Avdonin, Sergei (University of Alaska)
Created:
2015-11-12
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Forecasts will play an increasingly important role in the next generation of control systems. In nominal conditions, predictions of system dynamics, human behavior and environmental conditions can be used by the control algorithm to improve the performance of the resulting system. However, in practice, constraint satisfaction, performance guaran...
Creator:
Borrelli, Francesco (University of California, Berkeley)
Created:
2013-06-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In this talk we discuss aspects of the physics and mathematics of a quantum control system interacting with its environment. In particular we discuss the control of an finite-dimensional Lindblad system by considering the geometry of its orbit and interorbit dynamics. This entails considering the geometry of flag manifolds, the structure of the ...
Creator:
Bloch, Anthony (University of Michigan)
Created:
2016-04-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In the last decades, advances in pulse shaping techniques have openedup the possibility of manipulation of systems whose evolution followsthe laws of quantum mechanics. Moreover, novel applications, such as inquantum information processing, have offered further motivation forthis study.From a mathematical point of view, the field which is now kn...
Creator:
D'Alessandro, Domenico (Iowa State University)
Created:
2015-10-15
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We present an overview of our recent work on the modeling and control of collective dynamics. This work provides implementable solutions to the Schroedinger bridge problem and has potential application to stochastic optimal control, optimal transport, and various generalizations. We discuss the case of degenerate constant diffusion coefficients ...
Creator:
Chen, Yongxin (University of Minnesota, Twin Cities)
Created:
2015-11-23
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Geophysical hazards such as tsunamis, storm surges, debris flows, and landslides pose a significant risk to a large fraction of the world's population. Mathematical models and computer simulations of these hazards are critical in developing a better understanding of past events, both recent and pre-historic. They are also used to assess hazards,...
Creator:
LeVeque, Randall J.
Created:
2016-03-10
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Energy networks are becoming increasingly decentralized and exhibit new forms of coupling. For instance, during the polar vortex of 2014, sustained low temperatures in the Midwest region of the U.S. resulted in unusually high gas demands from buildings in urban areas. This led to shortages of natural gas that propagated to California, Massachuse...
Creator:
Zavala, Victor M. (University of Wisconsin, Madison)
Created:
2016-05-11
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
We investigate the problem of optimizing the shape and location of actuators or sensors for evolution systems driven by a partial differential equation, like for instance a wave equation, a Schrödinger equation, or a parabolic system, on an arbitrary domain Omega, in arbitrary dimension, with boundary conditions if there is a boundary, which ca...
Creator:
Privat, Yannick (Universite de Paris VI (Pierre et Marie Curie))
Created:
2017-09-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The modern view of the nervous system as layering distributedcomputation and communication for the purpose of sensorimotorcontrol and homeostasis has much experimental evidence butlittle theoretical foundation, leaving unresolved the connectionbetween diverse components and complex behavior. As a simple startingpoint, we address a fundamental tr...
Creator:
Nakahira, Yorie (California Institute of Technology)
Created:
2015-11-09
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The North American electric power grid is a large existing distributed network that will present new stability and control problems should the penetration of distributed renewable sources, controllable loads, and local-area energy storage capabilities become a significant portion of the overall grid. Roof-top solar panels and small wind turbines...
Creator:
Polis, Michael (Oakland University)
Created:
2018-05-18
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
There is a several decade history demonstrating that electrical polarization of neurons can modulate neuronal firing, and that such polarization can suppress (or excite) spiking activity and seizures. In recent years, we uncovered a unification in the computational biophysics of spikes, seizures, and spreading depression (Wei et al J Neurosci 34...
Creator:
Schiff, Steven (The Pennsylvania State University)
Created:
2018-02-12
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.