Publications related to Riemann mapping theorem

Extremal Distance And Conformal Radius Of A Cle4 Loop

Consider CLE4 in the unit disk, and let l be the loop of the CLE4 surrounding the origin. Schramm, Sheffield and Wilson determined the law of the conformal radius seen from the origin of the domain surrounded by l. We complement their result by determining ...

INST MATHEMATICAL STATISTICS-IMS2022

From kirigami to hydrogels: a tutorial on designing conformally transformable surfaces

Tian Chen, Yingying Ren, Yue Wang

Elastic surfaces that morph between multiple geometrical configurations are of significant engineering value, with applications ranging from the deployment of space-based PV arrays, the erection of temporary shelters, and the realization of flexible displa ...

2022

Spherical cap harmonic analysis (SCHA) for characterising the morphology of rough surface patches

Katrin Beyer, Mahmoud S. M. Shaqfa

We use spherical cap harmonic (SCH) basis functions to analyse and reconstruct the morphology of scanned genus-0 rough surface patches with open edges. We first develop a novel one-to-one conformal mapping algorithm with minimal area distortion for paramet ...

2021

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

MATHICSE Technical Report: Constraint-Aware Neural Networks for Riemann Problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satised to obtain ...

MATHICSE2019

The index of singular zeros of harmonic mappings of anti-analytic degree one

Robert Gerhard Jérôme Luce

We study harmonic mappings of the form , where h is an analytic function. In particular, we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the critical set of f, where the Jacobian of f is non-vanishing, it ...

TAYLOR & FRANCIS LTD2019

Primary invariants of Hurwitz Frobenius manifolds

Nicolas Gerson Orantin

Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds and t ...

AMER MATHEMATICAL SOC2018

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Elisabetta Chiodaroli

We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157-90), and based on the techniques of De Lellis and Szekelyhidi (2010 Arch. Ra ...

IOP PUBLISHING LTD2018

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

Drazen Dujic, Francisco Daniel Freijedo Fernández, Uzair Javaid

Impedance stability methods are suitable for assessing the dynamics of power converters controllers, but also for ac/dc microgrids system level studies. This work proposes the combination of impedance modeling and conformal mapping for the identification o ...

2017

MATHICSE Technical Report : The index of singular zeros of harmonic mappings of anti-analytic degree one

Robert Gerhard Jérôme Luce

We study harmonic mappings of the form f(z) = h(z) 􀀀 z, where h is an analytic function. In particular we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the critical set of f, where the Jacobian of f is non ...

MATHICSE2017

Riemann mapping theorem

Extremal Distance And Conformal Radius Of A Cle4 Loop

From kirigami to hydrogels: a tutorial on designing conformally transformable surfaces

Spherical cap harmonic analysis (SCHA) for characterising the morphology of rough surface patches

Constraint-aware neural networks for Riemann problems

MATHICSE Technical Report: Constraint-Aware Neural Networks for Riemann Problems

The index of singular zeros of harmonic mappings of anti-analytic degree one

Primary invariants of Hurwitz Frobenius manifolds

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

MATHICSE Technical Report : The index of singular zeros of harmonic mappings of anti-analytic degree one

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The index of singular zeros of harmonic mappings of anti-analytic degree one

From kirigami to hydrogels: a tutorial on designing conformally transformable surfaces

Constraint-aware neural networks for Riemann problems

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Primary invariants of Hurwitz Frobenius manifolds

MATHICSE Technical Report : The index of singular zeros of harmonic mappings of anti-analytic degree one

Conformal Mapping of Impedance Stability Models for System-Level Dynamics Assessments

Extremal Distance And Conformal Radius Of A Cle4 Loop

MATHICSE Technical Report: Constraint-Aware Neural Networks for Riemann Problems

Spherical cap harmonic analysis (SCHA) for characterising the morphology of rough surface patches