Math

Browse all posts in the Math category.

43 to 48 of 82

01DEC 2022
Math
Stability results for the KdV equation with time-varying delay
Stability results for the KdV equation with time-varying delay Introduction The Korteweg-de Vries equation (KdV), is a third-order nonlinear one-dimensional equation given by . It was introduced in [6] to model the propagation of long water waves in a channel. In the last few years, the controllability and stabilization properties of the KdV have been […]
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30SEP 2022
Akademy
Approximating the 1D wave equation using Physics Informed Neural Networks (PINNs)
Approximating the 1D wave equation using Physics Informed Neural Networks (PINNs) Internship under the “Women in Mathematics of Data” program Date: September 2022 Supervisors: Enrique Zuazua Institution: FAU MoD, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) Code: • See the complete report by Dania Sana Introduction Accurate and fast predictions of numerical solutions are of significant interest in […]Approximating the 1D wave equation using Physics Informed Neural Networks (PINNs) Internship under the “Women in Mathematics of Data” program Date: September 2022 Supervisors: Enrique Zuazua Institution: FAU MoD, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) Code: • See the complete report by Dania Sana Introduction Accurate and fast predictions of numerical solutions are of significant interest in […]
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05AUG 2022
All
Gas networks at stationary states: Analysis, software and visualization
Gas networks at stationary states: Analysis, software and visualization Code: Files to run: nocircle.m, onecircle.m or twocircles.m 1 Introduction This post presents the results of my Bachelor thesis about the modeling and implementation of gas networks at stationary states. Using the isothermal Euler equations to describe the gas flow through a single pipe, algebraic […]
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30JUL 2022
Hub
Sheep Herding Game
Author: Daniël Veldman, FAU DCN-AvH Code: A sheep herding game in MATLAB developed for the Long Night of Science #NdW22 (Lange Nacht der Wissenschaft) Erlangen-Furth-Nuernberg 2022. Main rules • The dog should drive sheep to the target (red). • You can steer the dog with the arrow keys. • The sheep are afraid of the […]
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23JUL 2022
Hub
Lloyd’s Algorithm
Author: Martín Hernández, FAU DCN-AvH Code: In this repository, we show a code for Lloyd’s algorithm. Also called Voronoid iteration, this is an iterative algorithm finding for equispaced convex cells in euclidean space. Lloyd’s algorithm finds the distribution of the cells computing their center of mass and iteratively applying the Voronoid tessellation. Like the closely […]
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12JUL 2022
Math
Using the support function for optimal shape design
Using the support function for optimal shape design 1 Motivation Led by problems of optimal placement and design of sensors, we are interested in considering the following shape optimization problem where is the Hausdorff distance between and defined as follows with is the distance from to the set . Figure 1. The Hausdorff distance […]
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