Universität Bonn

Trimester Program: "Mathematics for Complex Materials"


January 3 - April 14, 2023

Organizers: Xavier Lamy, Luc Nguyen, Angkana Rüland, Arghir Zarnescu

Description: The world of materials is undergoing a revolution as the number of materials, their sophistication and applications are witnessing an unprecedented boom. A particularly important class of materials which are driving this process and which pose key mathematical challenges are the so-called “complex materials”. These materials have extraordinary features and capabilities that have been intensively exploited technologically including many of the most impressive technological applications of our modern living.

The program aims to contribute to the long-term development of the mathematical tools relevant to the study of complex materials, starting from existing known mathematical models. A key objective will be to identify the physically relevant analytical challenges and problems that are common to a large class of complex materials and provide basic steps for addressing them.

The trimester program will include two workshops and one Spring school between them with the following preliminary titles and dates:

Workshop: Current challenges in complex materials: modelling and analysis (January 9-13, 2023)
"SPP meets TP" Workshop: Variational methods for complex phenomena in solids (February 21-24, 2023)
School: Recent trends in the mathematics of complex materials (March 20-24, 2023) separate application process
Workshop: Topological and geometrical aspects in complex materials (March 27-31, 2023)


Participants

PERSON
AFFILIATION
PERIOD OF STAY
Amit Acharya Carnegie Mellon University 08.01.2023 – 14.01.2023
Amit Acharya Carnegie Mellon University 01.02.2023 – 28.02.2023
Roberto Alicandro Università di Cassino e del Lazio Meridionale 02.04.2023 – 06.04.2023
Douglas Arnold University of Minnesota 02.03.2023 – 19.03.2023
Annika Bach Sapienza University of Rome 08.01.2023 – 13.01.2023
Annika Bach Sapienza University of Rome 26.02.2023 – 18.03.2023
Hendrik Baers Universität Heidelberg 01.03.2023 – 14.04.2023
John Ball Heriot-Watt University 22.01.2023 – 11.02.2023
Valeria Banica Sorbonne Université 20.03.2023 – 24.03.2023
Valeria Banica Sorbonne Université 27.03.2023 – 31.03.2023
Paolo Bonicatto University of Warwick 05.02.2023 – 10.02.2023
Maria-Carme Calderer University of Minnesota 02.03.2023 – 19.03.2023
Giacomo Canevari Dipartimento di Informatica, Università di Verona 08.01.2023 – 14.01.2023
Giacomo Canevari Dipartimento di Informatica, Università di Verona 12.02.2023 – 27.02.2023
Razvan-Dumitru Ceuca Basque Center for Applied Mathematics (BCAM) 07.01.2023 – 04.02.2023
Xian Chen (Sherry) Hong Kong University of Science and Technology 09.01.2023 – 14.01.2023
Sergio Conti Universität Bonn
Giovanni Di Fratta Università degli Studi di Napoli 08.01.2023 – 13.01.2023
Giovanni Di Fratta Università degli Studi di Napoli 02.03.2023 – 22.03.2023
Federico Luigi Dipasquale Università degli Studi di Napoli 08.01.2023 – 14.01.2023
Federico Luigi Dipasquale Università degli Studi di Napoli 12.03.2023 – 01.04.2023
Georg Dolzmann Universität Regensburg 19.02.2023 – 31.03.2023
Jonathan Fabiszisky University of Münster 20.02.2023 – 25.02.2023
Jonathan Fabiszisky University of Münster 20.03.2023 – 01.04.2023
Irene Fonseca Carnegie Mellon University 08.01.2023 – 10.01.2023
Martino Fortuna La Sapienza università di Roma 08.01.2023 – 04.02.2023
Adriana Garroni Sapienza, Università di Roma 08.01.2023 – 14.01.2023
Adriana Garroni Sapienza, Università di Roma 24.01.2023 – 03.02.2023
Maria Stella Gelli Università di Pisa 20.02.2023 – 25.02.2023
Maria Stella Gelli Università di Pisa 06.03.2023 – 14.04.2023
Zhiyuan Geng BCAM- Basque Center for Applied Mathematics 08.01.2023 – 15.02.2023
Janusz Ginster Humboldt-Universität zu Berlin 19.02.2023 – 03.03.2023
Rossella Giorgio Technische Universität Wien 09.01.2023 – 13.01.2023
Rossella Giorgio Technische Universität Wien 19.03.2023 – 24.03.2023
Dmitry Golovaty University of Akron 08.01.2023 – 31.01.2023
Andreea Grecu “Gheorghe Mihoc – Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy 19.03.2023 – 01.04.2023
André Guerra Institute for Theoretical Studies ETH-ITS 26.02.2023 – 19.03.2023
Leon Happ Technische Universität Wien 08.01.2023 – 13.01.2023
Leon Happ Technische Universität Wien 19.03.2023 – 24.03.2023
Davit Harutyunyan University of California Santa Barbara 05.01.2023 – 14.01.2023
Melanie Hassler Medical University of Vienna 02.03.2023 – 14.03.2023
Matthias Hieber TU Darmstadt
Radu Ignat Institut de Mathématiques de Toulouse 06.01.2023 – 14.04.2023
Robert Jerrard University of Toronto 11.02.2023 – 18.02.2023
Illia Karabash the University of Bonn, Institute for Applied mathematics
Dorothee Knees University of Kassel 20.02.2023 – 03.03.2023
Niklas Knobel Karlsruher Institut für Technologie 27.02.2023 – 11.03.2023
Herbert Koch Universität Bonn
Thibault Lacombe UT3 Paul Sabatier 13.03.2023 – 01.04.2023
Xavier Lamy Université Paul Sabatier 09.01.2023 – 15.04.2023
Tim Laux Universität Bonn
Chiara Leone University Federico II of Naples 02.04.2023 – 06.04.2023
Marta Lewicka University of Pittsburgh 17.01.2023 – 31.03.2023
Peter Lewintan University of Duisburg-Essen 19.02.2023 – 18.03.2023
Cy Maor Hebrew University of Jerusalem 19.02.2023 – 25.02.2023
Elio Marconi Università di Padova 29.01.2023 – 11.02.2023
Alice Marveggio Institute of Science and Technology Austria (ISTA) 02.02.2023 – 29.03.2023
Roberta Marziani TU Dortmund 26.02.2023 – 18.03.2023
Alexander Mielke WIAS 20.02.2023 – 03.03.2023
Maria-Giovanna Mora Università di Pavia 19.02.2023 – 25.02.2023
Stefan Müller Universität Bonn
Mickaël Nahon Max Planck Institute for Mathematics in the Sciences 05.02.2023 – 18.02.2023
Mickaël Nahon Max Planck Institute for Mathematics in the Sciences 19.03.2023 – 25.03.2023
Gokul Gopan Nair Cornell University 01.02.2023 – 31.03.2023
Isaac Newell University of Oxford 19.03.2023 – 01.04.2023
Luc Nguyen University of Oxford 13.03.2023 – 14.04.2023
Barbara Niethammer Universität Bonn
Michael Ortiz Universität Bonn
Felix Otto Max Planck Institute for Mathematics in the Sciences 08.01.2023 – 14.01.2023
Anastasija Pesic Humboldt-Universitaet zu Berlin 08.01.2023 – 14.01.2023
Bogdan Raita Scuola Normale Superiore di Pisa 23.03.2023 – 13.04.2023
Sandra Ried Universität Leipzig 05.02.2023 – 11.02.2023
Tobias Ried Max Planck Institute for Mathematics in the Sciences 08.01.2023 – 21.01.2023
Tobias Ried Max Planck Institute for Mathematics in the Sciences 05.02.2023 – 11.02.2023
Arnab Roy TU Darmstadt 02.03.2023 – 18.03.2023
Angkana Rüland Ruprecht-Karls-Universität Heidelberg 05.01.2023 – 10.01.2023
Angkana Rüland Ruprecht-Karls-Universität Heidelberg 13.02.2023 – 14.04.2023
Lucia Scardia Heriot-Watt University 19.03.2023 – 26.03.2023
Lucia Scardia Heriot-Watt University 29.03.2023 – 06.04.2023
Anja Schlömerkemper University of Würzburg 08.03.2023 – 10.03.2023
Bernd Schmidt Universität Augsburg 08.01.2023 – 13.01.2023
Bernd Schmidt Universität Augsburg 20.02.2023 – 24.02.2023
Bernd Schmidt Universität Augsburg 19.03.2023 – 26.03.2023
Akram Sharif TU Dresden 19.02.2023 – 25.03.2023
Theresa Simon University of Münster 08.01.2023 – 21.01.2023
Theresa Simon University of Münster 02.04.2023 – 07.04.2023
Bianca Stroffolini University of Naples Federico II 08.01.2023 – 14.01.2023
Bianca Stroffolini University of Naples Federico II 28.03.2023 – 13.04.2023
William Sumners Heriot-Watt University 28.03.2023 – 10.04.2023
Riccardo Tione Max Planck Institute for Mathematics in the Sciences 15.01.2023 – 21.01.2023
Riccardo Tione Max Planck Institute for Mathematics in the Sciences 05.03.2023 – 11.03.2023
Camillo Tissot Universität Heidelberg 19.02.2023 – 15.03.2023
Antonio Tribuzio Universität Heidelberg 19.02.2023 – 22.03.2023
Juan José Velázquez Lopez Universität Bonn
Stephen Watson University of Glasgow 18.02.2023 – 09.04.2023
Yong Yu Department of Mathematics, The Chinese University of Hong Kong 08.01.2023 – 14.01.2023
Arghir Dani Zarnescu Basque Center for Applied Mathematics, Spain 03.01.2023 – 31.03.2023
Konstantinos Zemas University of Münster 26.02.2023 – 24.03.2023
Ruming Zhang Karlsruhe Institute of Technology 19.02.2023 – 04.03.2023
Christian Zillinger Karlsruher Institut für Technlogie 06.03.2023 – 10.03.2023
Christian Zillinger Karlsruher Institut für Technlogie 03.04.2023 – 14.04.2023
Barbara Zwicknagl Humboldt-Universität zu Berlin 08.03.2023 – 01.04.2023
PERSON
AFFILIATION
PERIOD OF STAY
Amit Acharya Carnegie Mellon University 08.01.2023 – 14.01.2023
Annika Bach Sapienza University of Rome 08.01.2023 – 13.01.2023
Anne Bernand-Mantel CNRS-LPCNO 08.01.2023 – 14.01.2023
Giacomo Canevari Dipartimento di Informatica, Università di Verona 08.01.2023 – 14.01.2023
Razvan-Dumitru Ceuca Basque Center for Applied Mathematics (BCAM) 07.01.2023 – 04.02.2023
Xian Chen (Sherry) Hong Kong University of Science and Technology 09.01.2023 – 14.01.2023
Giovanni Di Fratta Università degli Studi di Napoli 08.01.2023 – 13.01.2023
Federico Luigi Dipasquale Università degli Studi di Napoli 08.01.2023 – 14.01.2023
Irene Fonseca Carnegie Mellon University 08.01.2023 – 10.01.2023
Martino Fortuna La Sapienza università di Roma 08.01.2023 – 04.02.2023
Likhit Ganedi RWTH Aachen University 08.01.2023 – 14.01.2023
Adriana Garroni Sapienza, Università di Roma 08.01.2023 – 14.01.2023
Zhiyuan Geng BCAM- Basque Center for Applied Mathematics 08.01.2023 – 15.02.2023
Rossella Giorgio Technische Universität Wien 09.01.2023 – 13.01.2023
Dmitry Golovaty University of Akron 08.01.2023 – 31.01.2023
Leon Happ Technische Universität Wien 08.01.2023 – 13.01.2023
Davit Harutyunyan University of California Santa Barbara 05.01.2023 – 14.01.2023
Radu Ignat Institut de Mathématiques de Toulouse 06.01.2023 – 14.04.2023
Xavier Lamy Université Paul Sabatier 09.01.2023 – 15.04.2023
Xingyu Li Toulouse Mathematics Institute 09.01.2023 – 13.01.2023
Massimiliano Morini Università di Parma 08.01.2023 – 14.01.2023
Cyrill Muratov Università di Pisa 08.01.2023 – 14.01.2023
Felix Otto Max Planck Institute for Mathematics in the Sciences 08.01.2023 – 14.01.2023
Anastasija Pesic Humboldt-Universitaet zu Berlin 08.01.2023 – 14.01.2023
Bogdan Raita Scuola Normale Superiore di Pisa
Miha Ravnik University of Ljubljana 12.01.2023 – 14.01.2023
Tobias Ried Max Planck Institute for Mathematics in the Sciences 08.01.2023 – 21.01.2023
Michele Ruggeri University of Strathclyde 08.01.2023 – 13.01.2023
Angkana Rüland Ruprecht-Karls-Universität Heidelberg 05.01.2023 – 10.01.2023
Bernd Schmidt Universität Augsburg 08.01.2023 – 13.01.2023
Theresa Simon University of Münster 08.01.2023 – 21.01.2023
Valeriy Slastikov University of Bristol
Ivan Smalyukh University of Colorado at Boulder 08.01.2023 – 14.01.2023
Bianca Stroffolini University of Naples Federico II 08.01.2023 – 14.01.2023
Yong Yu Department of Mathematics, The Chinese University of Hong Kong 08.01.2023 – 14.01.2023
Arghir Dani Zarnescu Basque Center for Applied Mathematics, Spain 03.01.2023 – 31.03.2023
Caterina Ida Zeppieri University of Muenster 08.01.2023 – 13.01.2023
PERSON
AFFILIATION
PERIOD OF STAY
Amit Acharya Carnegie Mellon University 01.02.2023 – 28.02.2023
Giacomo Canevari Dipartimento di Informatica, Università di Verona 12.02.2023 – 27.02.2023
Georg Dolzmann Universität Regensburg 19.02.2023 – 31.03.2023
Jonathan Fabiszisky University of Münster 20.02.2023 – 25.02.2023
Maria Stella Gelli Università di Pisa 20.02.2023 – 25.02.2023
Janusz Ginster Humboldt-Universität zu Berlin 19.02.2023 – 03.03.2023
Radu Ignat Institut de Mathématiques de Toulouse 06.01.2023 – 14.04.2023
Dorothee Knees University of Kassel 20.02.2023 – 03.03.2023
Xavier Lamy Université Paul Sabatier 09.01.2023 – 15.04.2023
Marta Lewicka University of Pittsburgh 17.01.2023 – 31.03.2023
Peter Lewintan University of Duisburg-Essen 19.02.2023 – 18.03.2023
Cy Maor Hebrew University of Jerusalem 19.02.2023 – 25.02.2023
Alice Marveggio Institute of Science and Technology Austria (ISTA) 02.02.2023 – 29.03.2023
Alexander Mielke WIAS 20.02.2023 – 03.03.2023
Maria-Giovanna Mora Università di Pavia 19.02.2023 – 25.02.2023
Gokul Gopan Nair Cornell University 01.02.2023 – 31.03.2023
Filip Rindler University of Warwick 20.02.2023 – 24.02.2023
Angkana Rüland Ruprecht-Karls-Universität Heidelberg 13.02.2023 – 14.04.2023
Mohammad Sarhil Institut für Mechanik, Universität Duisburg-Essen 21.02.2023 – 25.02.2023
Bernd Schmidt Universität Augsburg 20.02.2023 – 24.02.2023
Jörg Schröder Universität Duisburg-Essen 20.02.2023 – 23.02.2023
Akram Sharif TU Dresden 19.02.2023 – 25.03.2023
Camillo Tissot Universität Heidelberg 19.02.2023 – 15.03.2023
Antonio Tribuzio Universität Heidelberg 19.02.2023 – 22.03.2023
Philipp Tscherner Albert-Ludwigs-University Freiburg 20.02.2023 – 24.02.2023
Stephen Watson University of Glasgow 18.02.2023 – 09.04.2023
David Wiedemann University of Augsburg 20.02.2023 – 25.02.2023
Piotr Wozniak University of Münster 20.02.2023 – 25.02.2023
Arghir Dani Zarnescu Basque Center for Applied Mathematics, Spain 03.01.2023 – 31.03.2023
Ruming Zhang Karlsruhe Institute of Technology 19.02.2023 – 04.03.2023
PERSON
AFFILIATION
PERIOD OF STAY
Hendrik Baers Universität Heidelberg 01.03.2023 – 14.04.2023
Anna Kh. Balci Bielefeld University 20.03.2023 – 25.03.2023
Valeria Banica Sorbonne Université 20.03.2023 – 24.03.2023
Daniel Castro Weizmann Institute of Science 19.03.2023 – 25.03.2023
Andrea Chiesa University of Vienna 19.03.2023 – 24.03.2023
Antoine Detaille Université Claude Bernard Lyon 1 19.03.2023 – 25.03.2023
Jakob Deutsch TU Wien 19.03.2023 – 24.03.2023
Giovanni Di Fratta Università degli Studi di Napoli 02.03.2023 – 22.03.2023
Federico Luigi Dipasquale Università degli Studi di Napoli 12.03.2023 – 01.04.2023
Georg Dolzmann Universität Regensburg 19.02.2023 – 31.03.2023
Shilpa Dutta Julius-Maximilians-Universität Würzburg 19.03.2023 – 25.03.2023
Jonathan Fabiszisky University of Münster 20.03.2023 – 01.04.2023
Gabriele Fissore Radboud Universiteit 19.03.2023 – 24.03.2023
Maria Stella Gelli Università di Pisa 06.03.2023 – 14.04.2023
Rossella Giorgio Technische Universität Wien 19.03.2023 – 24.03.2023
Andreea Grecu “Gheorghe Mihoc – Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy 19.03.2023 – 01.04.2023
Leon Happ Technische Universität Wien 19.03.2023 – 24.03.2023
Radu Ignat Institut de Mathématiques de Toulouse 06.01.2023 – 14.04.2023
Richard D. James University of Minnesota 19.03.2023 – 25.03.2023
Thibault Lacombe UT3 Paul Sabatier 13.03.2023 – 01.04.2023
Xavier Lamy Université Paul Sabatier 09.01.2023 – 15.04.2023
Marta Lewicka University of Pittsburgh 17.01.2023 – 31.03.2023
Dragos Manea the Romanian Academy 19.03.2023 – 25.03.2023
Alice Marveggio Institute of Science and Technology Austria (ISTA) 02.02.2023 – 29.03.2023
Sulemana Musah University for Development Studies 19.03.2023 – 25.03.2023
Mickaël Nahon Max Planck Institute for Mathematics in the Sciences 19.03.2023 – 25.03.2023
Gokul Gopan Nair Cornell University 01.02.2023 – 31.03.2023
Isaac Newell University of Oxford 19.03.2023 – 01.04.2023
Luc Nguyen University of Oxford 13.03.2023 – 14.04.2023
Hywel Normington University of Strathclyde 19.03.2023 – 25.03.2023
PERSON
AFFILIATION
PERIOD OF STAY
 
 
 
 
 
 
 
 
 

Trimester Seminar Series

January 17, 2023 (CEST)

3:15 - 4:00pm Tim Laux (University of Bonn)

Title: Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow

Abstract: Anisotropic mean curvature flow is a simple geometric evolution equation that models microstructure in complex materials. In this talk, I will show how it arises as the sharp-interface limit of the anisotropic Allen-Cahn equation. The proof relies on distributional solution concepts for both the diffuse and sharp interface models, and a suitable relative energy. With the same relative energy, one can prove a weak-strong uniqueness result, which relies on the construction of gradient flow calibrations for the anisotropic energy functionals. If time permits, I will also mention a few open problems. This is joint work with Kerrek Stinson and Clemens Ullrich.

January 24, 2023 (CEST)

3:30 - 4:30pm John Ball  (Heriot-Watt University and Maxwell Institute for Mathematical Sciences, Edinburgh)

Title: Monodromy and approach to equilibrium for viscoelastic models allowing microstructure

Abstract: For certain models of one-dimensional viscoelasticity, there are infinitely many equilibria representing phase mixtures. In order to prove convergence as time tends to infinity of solutions to a single equilibrium, it seems necessary to impose a nondegeneracy condition on the constitutive equation for the stress. The talk will explain this, and show how in some cases the nondegeneracy condition can be proved using the monodromy group of a holomorphic function. This is joint work with Inna Capdeboscq and Yasemin  Şengül.

January 31, 2023 (CEST)

3:00 - 4:00pm Elio Marconi (Università di Padova)

Title: Stability of the vortex in line-energy models

February 7, 2023 (CEST)

15:00 - 16:00 Marta Lewicka (University of Pittsburgh)

Title: The Monge-Ampere system: convex integration in arbitrary dimension and codimension

February 14, 2023 (CEST)

15:00 - 16:00 Mickaël Nahon (MPI Leipzig)

Title: A free discontinuity approach to optimal profiles in Stokes flows

Abstract: We consider an incompressible Stokes fluid contained in a box B

that flows around an obstacle KB with a Navier boundary condition on K. I will present existence and partial regularity results for the minimization of the drag of K among all profiles with certain constraints on the measure and perimeter of K, based on techniques that were developed for Griffith's fracture model in brittle materials. This is a joint work with Dorin Bucur, Antonin Chambolle and Alessandro Giacomini.

February 28, 2023 (CEST)

15:00 - 16:00  Roberta Marziani (TU Dortmund)

Title: 3D variational models for dislocations

Abstract: In this talk we give a brief introduction on theory of dislocations in the context of continuum elasticity. Afterwards we will introduce a 3D variational model for dislocations. We then show that the asymptotics via Gamma convergence is independent of the specific choice of the energy and of the regularization procedure.
This result is based on a joint work with Sergio Conti and Adriana Garroni.

March 7, 2023 (CEST)

3:00 - 4:0pm André Guerra (ETH Zürich)

Title: Quasiconvexity and nonlinear Elasticity

Abstract: Quasiconvexity is the fundamental existence condition for variational problems, yet it is poorly understood. Two outstanding problems remain:

  • 1) does rank-one convexity, a simple necessary condition, imply quasiconvexity in two dimensions?
  • 2) can one prove existence theorems for quasiconvex energies in the context of nonlinear Elasticity?

In this talk we show that both problems have a positive answer in a special class of isotropic energies. Our proof combines complex analysis with the theory of gradient Young measures. On the way to the main result, we establish quasiconvexity inequalities for the Burkholder function which yield, in particular, many sharp higher integrability results.
The talk is based on joint work with Kari Astala, Daniel Faraco, Aleksis Koski and Jan Kristensen.

4:30 - 5:30pm Antonio Tribuzio (Uni Heidelberg)

Title: Energy scaling of singular-perturbation models involving higher-order laminates

Abstract: Motivated by the appearance of complex microstructures in the modelling of shape-memory alloys, we study the energy scaling behaviour of some N-well problems with surface energy given by a singular higher-order term. In the case of absence of gauge invariances (e.g. with respect to the action of SO(n) or Skew(n)), we provide an ansatz-free lower bound which relies on a bootstrap argument in Fourier space and gives evidence of the higher order of lamination involved. The upper bound is provided by iterated branching constructions.
In the end, we show how a similar approach can be used in the determination of a lower bound for a more realistic model, namely the geometrically linearized cubic-to-tetragonal phase transition, in which a second order lamination is forced by the presence of affine boundary conditions. This is a joint work with Angkana Rüland.

March 8, 2023 (CEST)

3:00 - 4:00pm Illya M. Karabash (IAM, the University of Bonn)

Title: Composite structures with defects in the spectral optimization of leaky optical microresonators

Abstract: The optical engineering fabrication and numerical experiments for high-Q cavities led to a series of new analytical and computational problems related to optimization of resonances. The talk is devoted to the problem how to design an open  resonator that has a dissipation eigenvalue as close as possible to the real line under certain fabrication constraints. It is planned to explain the rigorous analytical background for such problems and, in particular, why the Pareto optimization settings are natural. Then we concentrate on the recent optimal control reformulation developed jointly with Herbert Koch and Ievgen Verbytskyi, as well as on resulting Hamilton-Jacobi-Bellman PDEs and extremal synthesis.

March 14, 2023 (CEST)

3:00 - 4:00pm Kostantinos Zemas (Universität Münster)

Title: Homogenization of nonlinear randomly perforated materials under minimal assumptions on the geometry

Abstract: In this work we combine and generalize earlier works of Giunti-Höfer-Velazquez (on the homogenization of the Poisson equation in random critically perforated domains) and Ansini-Braides (on a variational approach for the more general nonlinear vectorial problem in the periodic setting), each one in the direction of the other.
Namely, we show that under similar general assumptions on the geometry of the random perforations as the ones posed in the work of Giunti, Höfer and Velazquez, the stochastic analogue of the result of Ansini-Braides holds true, with an average deterministic nonlinear capacitary-term appearing in the Γ-limit.
This is joint work with Caterina Zeppieri and Lucia Scardia.

March 15, 2023 (CEST)

3:00 - 4:00pm Maria Carme Calderer (University of Minnesota)

Title: Mathematical Problems at the Interface of Materials Sciences and Biology

Abstract: It is well known in liquid crystal research that nuclei of ordered materials emerging from the isotropic state usually show a shape topologically equivalent to a sphere, such as in the case of nematic liquid crystal droplets. In this presentation, we analyze a new type of free boundary shapes, in the form of tori, that consist of chromonic liquid crystals in the hexagonal phase. We show that such shapes are minimizers of a multi-constraint liquid crystal bulk energy plus an anisotropic surface contribution, the latter being responsible for the faceted shapes observed in the experiments. Let us recall that chromonic liquid crystals consist of flat, plank-like molecules found, for instance, in food dies and antiasthmatic drugs that form liquid crystal phases when dissolved in water. Due to, both, the hydrophilic and hydrophobic groups present in such molecules, they form columnar stacks that tend to align themselves in a parallel fashion, forming increasingly ordered liquid crystal phases with rising concentration. From a different point of view, condensed DNA also forms chromonic liquid crystal phases, with the same optical properties as the die and drug compounds. In vitro DNA, in a gel with condensing agents, also forms toroidal droplets but with a typical size of about one-millionth that of its chromonic counterparts. In vivo, such ordered arrangements are encountered in the quiescent state of encapsidated, double stranded-DNA viruses that infect bacteria, known as bacteriophages, the liquid crystal organization being a key part of their biological function to ensure an optimal infection. Mathematically, we represent a virus as a vector field-line pair that minimize an energy, the sum of the bending and twist components of the DNA center curve plus its electrostatic energy and that of the environmental ions. We conclude with some remarks on the dynamics of the packaging and infection processes.

4:30 - 5:30pm Douglas Arnold (University of Minnesota)

Title: Wave localization and its landscape

Abstract: The puzzling phenomenon of wave localization refers to unexpected confinement of waves triggered by disorder in the propagating media.  Localization arises in many physical and mathematical systems and has many important implications and applications.  A particularly important case is the Schrödinger equation of quantum mechanics, for which the localization behavior is crucial to the electrical properties of materials.  Mathematically it is tied to exponential decay of eigenfunctions of operators instead of their expected extension throughout the domain.  Although localization has been studied by physicists and mathematicians for the better part of a century, many aspects remain mysterious.  In particular, the sort of deterministic quantitative results needed to predict, control, and exploit localization have remained elusive.  This talk will focus on major strides made in recent years based on the introduction of the landscape function and its partner, the effective potential.  We will describe these developments from the viewpoint of a computational mathematician who sees the landscape theory as a completely unorthodox sort of a numerical method for computing spectra.


Publications

No.
Author(s)
Title
Preprint
Publication
2023a01 Davoli, E.; Di Fratta, G.; Fiorenza, A.; Happ, L. A modular Poincaré-Wirtinger type inequality on Lipschitz domains for Sobolev spaces with variable exponents 2304.13132
2023a02 Ignat, R.; Rus, M. Vortex sheet solutions for the Ginzburg-Landau system in cylinders: symmetry and global minimality 2301.11430
2023a03 Guerra, A.; Xavier Lamy, X.; Zemas, K. Optimal quantitative stability of the Möbius group of the sphere in all dimensions 2401.06593
 
2023a04 Contreras, A.; Lamy, X. A symmetry breaking phenomenon for anisotropic harmonic maps from a 2D annulus into 𝕊1 2311.15758
2023a05 Guerra, A.; Lamy, X.; Zemas, K. Sharp quantitative stability of the Möbius group among sphere-valued maps in arbitrary dimension 2305.19886
2023a06 Raiţă, B.; Rüland, A.; Tissot, C.; Tribuzio, A. On Scaling Properties for a Class of Two-Well Problems for Higher Order Homogeneous Linear Differential Operators 2306.14660
2023a07 Rüland, A.; Tribuzio, A. On the Scaling of the Cubic-to-Tetragonal Phase Transformation with Displacement Boundary Conditions 2306.05740
2023a08 Dipasquale, F.L.; Stroffolini, B. Manifold-constrained free discontinuity problems and Sobolev approximation 2307.02265
2023a09 De Philippis, G.; Guerra, A.; Tione, R. Unique continuation for differential inclusions 2312.05022
2023a10 Geng, Z.; Roy, A.; Zarnescu, A. Global existence of Weak Solutions for a model of nematic liquid crystal-colloidal interactions 2310.16245
2023a11 Kouskiya, U.; Acharya, A. Hidden convexity in the heat, linear transport, and Euler's rigid body equations: A computational approach 2304.09418

to appear in Quarterly of Applied Mathematics, 2023
2023a12 Acharya, A. A Hidden Convexity in Continuum Mechanics, with application to classical, continuous-time, rate-(in)dependent plasticity 2310.03201
2023a13 Singh, S.; Ginster, J.; Acharya, A. A Hidden Convexity of Nonlinear Elasticity 2401.08538
 
2023a14 Kouskiya, U.; Acharya, A. Inviscid Burgers as a degenerate elliptic problem 2401.08814
2023a15 Canevari, G.; Dipasquale, F.L.; Orlandi, G. The Yang-Mills-Higgs functional on complex line bundles: asymptotics for critical points 2304.11346
 
2023a16 Dipasquale, F.L.; Stroffolini, B. Manifold-constrained free discontinuity problems and Sobolev approximation

2307.02265

2023a17 Conti, S.; Dolzmann, D.; Müller, S. Optimal rigidity estimates for maps of a compact Riemannian manifold to itself

2402.06448

2023a18 Ried, T.; Román, C. Domain branching in micromagnetism: scaling law for the global and local energies

2308.07239

2023a19 Normington, H.; Ruggeri, M. Convergent finite element methods for antiferromagnetic and ferrimagnetic materials

2312.04939

2023a20 Tribuzio, A.; Zemas, K. Energy barriers for boundary nucleation in a two-well model without gauge invariance

2403.04567

2023a21 Ignat, R.; Nahon, M.; Nguyen, L. Minimality of vortex solutions to Ginzburg-Landau type systems for gradient fields in the unit ball in dimension

2310.11384
 

2023a22 Eller, M.; Karabash, I.M. Homogenization and nonselfadjoint spectral optimization for dissipative Maxwell eigenproblems

2401.01049

2023a23 Ginster, J.; Rüland, A.; Tribuzio, A.; Zwicknagl, B. On the Effect of Geometry on Scaling Laws for a Class of Martensitic Phase Transformations

2405.05927


Workshop: "Current challenges in complex materials: modelling and analysis"

January 9 - 13, 2023

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Irene Fonseca (Carnegie Mellon), Valeriy Slastikov (Bristol), Arghir Zarnescu (BCAM)

Description: Many recent and spectacular technological advances are driven by the evelopments of novel complex materials with extraordinary and unique features. The adequate mathematical models are essential for the discovery and systematical study of the properties of these complex materials. There exists a number of well-accepted models for complex materials with well-understood mathematical challenges, for instance Oseen-Frank and Landau-de Gennes models for liquid crystals, Landau-Lifschitz and Brown models for magnetic materials, to name just a few. However, contemporary active investigations in physics, for instance, focus on heterogeneous or layered materials where multiple components with different properties are combined at appropriate scales. The main aim of this workshop is to bring together mathematicians and scientists working in various areas of materials science and applied mathematics in order to identify the main challenges posed by the modelling and analysis of complex materials.


Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.


"SPP meets TP" Workshop: Variational methods for complex phenomena in solids

February 21 - 24, 2023

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Georg Dolzmann (Regensburg), Xavier Lamy (Toulouse), Angkana Rüland (Heidelberg)

Description: In the past years, the interplay between the mathematical analysis and engineering of solids has lead to the emergence of exciting new and complex materials with exceptional properties. In all of these, multiple scales are present which in turn provide new formidable mathematical challenges. Important progress has, in particular, been obtained through variational methods including the derivation of effective models through Γ-convergence, variational evolution problems or relaxation methods. Yet major questions remain unsolved. It is the purpose of this workshop is to bring together experts working in this field and to provide a platform enhancing the interaction between the researchers from the Germany-based Priority Programme 2256 and the trimester programme.


Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.


 


Spring School "Recent trends in the mathematics of complex materials"

March 20 - 24, 2023

Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)

Organizers: Arghir Zarnescu (BCAM), Xavier Lamy (Toulouse)

Lecturers:

  • Valeria Banica (Sorbonne University)
  • Radu Ignat (Université Toulouse 3)
  • Richard James (University of Minnesota)
  • Lucia Scardia (Heriot-Watt University)
  • Arghir Zarnescu (BCAM)
     

Description: The school will feature four courses aiming to provide an entry point into recent advances in mathematical techniques relevant to the study of complex materials models. It should be of interest both to graduate students aiming to get an education in the mathematics of complex materials as well as for more advanced researchers aiming to enter a new field of study. 

The application for the spring school has been closed.


Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.


Workshop: "Topological and geometrical aspects in complex materials"

March 27 - 31, 2023

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Valeria Banica (Sorbonne), Radu Ignat (Toulouse), Luc Nguyen (Oxford)

Description: The main focus of the workshop is the analysis of topological and geometrical singularities in PDE problems arising in complex materials. These singularities typically exhibit themselves in the form of microstructures or defects of different types (points, lines, interfaces…). The associated models often have a variational formulation and deep analysis techniques are needed to describe the geometric structure, symmetry, stability and dynamics of these singularities. This workshop will bring together specialists in Calculus of Variations and PDEs working on singular phenomena that could give new insights into the physics of complex materials.


Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.


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