Math

Browse all posts in the Math category.

49 to 54 of 82

09MAY 2022
Math
Uniform Turnpike Property
Uniform Turnpike Property 1 Introduction In this post, we analyze a heat equation with rapidly oscillating coefficients dependent on a parameter , with a distributed control. We show that the uniform null controllability implies the uniform turnpike property, i.e., the turnpike property with constants independent of the -parameter. The main conclusions of this post are […]
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07APR 2022
Hub
The interplay of control and deep learning
The interplay of control and Deep Learning It is superﬂuous to state the impact deep (machine) learning has had on modern technology, as it powers many tools of modern society, ranging from web searches to content ﬁltering on social networks. It is also increasingly present in consumer products such as cameras, smartphones and automobiles. […]
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24FEB 2022
Math
Nonlinear hyperbolic systems: Modeling, controllability and applications
Nonlinear hyperbolic systems: Modeling, controllabiliy and applications The control theory of hyperbolic systems is an important topic in continuum and fluid mechanics. Networks of nonlinear hyperbolic systems arise in real world applications, e.g. planar or out-of-plane networks of vibrating strings, shearable beams, gas networks and shallow water systems. On these typical 1d hyperbolic networks, the […]Nonlinear hyperbolic systems: Modeling, controllabiliy and applications The control theory of hyperbolic systems is an important topic in continuum and fluid mechanics. Networks of nonlinear hyperbolic systems arise in real world applications, e.g. planar or out-of-plane networks of vibrating strings, shearable beams, gas networks and shallow water systems. On these typical 1d hyperbolic networks, the […]
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20JAN 2022
Math
Kinetic theory of Bose Einstein Condensates
Kinetic theory of Bose Einstein Condensates If a dilute gas of bosons, about one-hundred-thousandth the density of normal air, is cooled to a temperature very close to absolute zero (0 K or -273.15C), the gas will be changed into a new state of matter, called Bose-Einstein condensate (BEC). This state of matter was predicted by […]
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03JAN 2022
EZuazua
pyGasControls library (simulation software)
Martin Gugat, Enrique Zuazua, Aleksey Sikstel, FAU DCN-AvH Code: [HINT] To run the software on your computer, you may have to install additional standard software packages (like cmake and a c++ compiler) and additional libraries (lapack, PETSc). In order to optimize the operation of gas transportation networks, as a first step a powerful […]
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16DEC 2021
Hub
Hamilton-Jacobi Equations: Inverse Design
Carlos Esteve, Deusto CCM Code: In a previous post “Inverse Design For Hamilton-Jacobi Equations“, described all the possible initial states that agree with the given observation of the system at time on the reconstruction of the initial state in many evolution models. Our goal here is to study the inverse design problem associated to Hamilton […]
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