Welcome
I am a post-doc at the Weierstraß Institute for Applied Analysis and Stochastics, Berlin, and member of the research group Partial Differential Equations of Alexander Mielke.
I am also a member of the Berlin Mathematical School (BMS) in the Postdoctoral Faculty.
Together with Annegret Glitzky I am head of the MATH+ project AA2-1 Hybrid models for the electrothermal behavior of organic semiconductor devices.
I have been awarded the ISIMM Junior Prize 2018 at STAMM conference "Mathematics & Mechanics: Natural Philosophy in the 21st Century" in Oxford.
Contact| Matthias.Liero@wias-berlin.de (Public Key) | |
| Phone | +49 (0) 30 20372 542 |
| Fax | +49 (0) 30 20372 311 |
Teaching
In the summer term SS2018 I am giving a lecture on Mehrdimensionale Variationsrechnung at Humboldt Universität zu Berlin, Tuesdays from 1pm and Thursdays from 9am. The tutorial is on Tuesday from 3pm.
In the winter term WS2017/18 I was giving a lecture on Optimal transport and Wasserstein gradient flows at Humboldt Universität zu Berlin, Tuesdays from 9am.
Research interests
My mathematical expertise is in the field of nonlinear partial differential equations. In particular, the rigorous derivation of new effective models in various problems in natural sciences using novel mathematical techniques is one of my major interests. In my diploma I gave a rigorous justification of an evolutionary elastoplastic plate model for continuum mechanics using the notion of Gamma-convergence. In a joint work with U. Stefanelli (Vienna), we extended the Weighted-Energy-Dissipation principle from parabolic to hyperbolic equations to make them accessible to variational methods.
In the recent years, the mathematical modeling, analysis, and simulation of optoelectronic devices, such as solar cells and organic light-emitting diodes, has become an essential application for me. I work closely with my colleagues Annegret Glitzky, Thomas Koprucki, Jürgen Fuhrmann, and Duy-Hai Doan from WIAS on organic devices. In a joint work with the Dresden Integrated Center for Applied Physics and Photonic Materials, in particular with Axel Fischer, Reinhard Scholz and Sebastian Reineke, we derived a novel PDE model, involving the p(x)-Laplacian with discontinuous p(x), to describe the current and heat flow in organic light-emitting diodes. This was the first model to correctly predict S-shaped current-voltage characteristics with regions of negative differential resistance as observed in measurements.
Moreover, with Michael Sawatzki and Hans Kleemann from IAPP we investigate the behavior and new concepts of organic transistors.
However, also the more abstract theory behind partial differential equations is in the focus of my current work. One particular highlight of a recent joint work with Alexander Mielke (WIAS Berlin) and Giuseppe Savaré (Pavia) was the derivation and characterization of the so-called Hellinger-Kantorovich distance, which can be seen as a generalization of the famous Wasserstein distance to arbitrary measures.
In general, my scientific work is guided by the aim to strengthen the cooperation between analysis and its applications by inventing and further developing the mathematical foundations and techniques to make them applicable for practical questions in other sciences.
Projects
I have been involved in the following projects:- MATHEON project SE18 (2017—2018): Models for heat and charge-carrier flow in organic electronics
- MATHEON project SE2 (2014—2017): Electrothermal modeling of large-area OLEDs.
- MATHEON project D22 (2010—2014): Modeling of Electronic Properties of Interfaces in Solar Cells
Publications
- , Experimental proof of Joule heating-induced switched-back regions in OLEDs, accepted in Light: Science & Applications, , , 2020.
- , Instationary drift-diffusion problems with Gauss–Fermi statistics and field-dependent mobility for organic semiconductor devices, Comm. Math. Sci., 17, 33–59, 2019.
- , An existence result for a class of electrothermal drift-diffusion models with Gauss–Fermi statistics for organic semiconductor devices, WIAS-Preprint, 2593, 2019.
- , Analysis of a drift-diffusion model for organic semiconductor devices, Z. Angew. Math. Phys., 70, 55, 2019.
- , The weighted energy-dissipation principle and evolutionary Γ-convergence for doubly nonlinear problems, ESAIM Control Optim. Calc. Var., 25, 36, 2019. (Link)
- , Introducing pinMOS Memory: A Novel, Nonvolatile Organic Memory Device, Advanced Functional Materials, n/a, 1907119, 2019. (Link)
- , Analysis of a hybrid model for the electro-thermal behavior of semiconductor heterostructures, WIAS-Preprint, 2636, 2019.
- , Drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices, WIAS-Preprint, 2630, 2019.
- , Effective diffusion in thin structures via generalized gradient systems and EDP-convergence, WIAS-Preprint, 2601, 2019.
- , Evolutionary Γ-convergence of gradient systems modeling slow and fast chemical reactions, Nonlinearity, 31, 3689–3706, 2018. (Link)
- , Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures, Inventiones mathematicae, 211, 969–1117, 2018. (Link)
- , Balance of Horizontal and Vertical Charge Transport in Organic Field-Effect Transistors, Phys. Rev. Applied, 10, 034069, 2018. (Link)
- , Full Electrothermal OLED Model Including Nonlinear Self-heating Effects, Phys. Rev. Applied, 10, 014023, 2018. (Link)
- , Homogenization of Cahn–Hilliard-type equations via evolutionary Γ-convergence, Nonlinear Differential Equations and Applications NoDEA, 25, 6, 2018. (Link)
- , Hybrid Finite-Volume/Finite-Element Schemes for p(x)-Laplace Thermistor Models, In: Clément Cancès, Pascal Omnes (eds.) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, 397–405, 2017.
- , 3D electrothermal simulations of organic LEDs showing negative differential resistance, Opt. Quantum Electron., 49, 330/1–330/8, 2017.
- , Thermistor systems of p(x)-Laplace-type with discontinuous exponents via entropy solutions, Discr. Cont. Dynam. Systems Ser.~S, 10, 697–713, 2017.
- , On microscopic origins of generalized gradient structures, Discr. Cont. Dynam. Systems Ser.~S, 10, 1, 2017. (Link)
- , Analysis of p(x)-Laplace thermistor models describing the electrothermal behavior of organic semiconductor devices, Nonlinear Analysis: Real World Applications, 34, 536–562, 2017. (Link)
- , A PDE Model for Electrothermal Feedback in Organic Semiconductor Devices, Progress in Industrial Mathematics at ECMI 2016, 99–106, 2017.
- , Modeling and Simulation of Electrothermal Feedback in Large-area Organic LEDs, Proceedings of the 17th International Conference on Numerical Simulation of Optoelectronic Devices, NUSOD 2017, 105–106, 2017.
- , The Hellinger-Kantorovich distance as a generalization of optimal-transport distances to scalar reaction-diffusion problems, Oberwolfach Rep. 14, 47–50, 2017.
- , Systems describing electrothermal effects with p(x)-Laplace like structure for discontinuous variable exponents, SIAM J. Math. Analysis, 48, 3496–3514, 2016.
- , Point contacts at the copper-indium-gallium-selenide interface–A theoretical outlook, Journal of Applied Physics, 119, 155304, 2016. (Link)
- , Optimal Transport in Competition with Reaction: The Hellinger–Kantorovich Distance and Geodesic Curves, SIAM Journal on Mathematical Analysis, 48, 2869–2911, 2016. (Link)
- , p-Laplace thermistor modeling of electrothermal feedback in organic semiconductor devices, Z. Angew. Math. Phys., 66, 2957–2977, 2015.
- , On gradient structures for Markov chains and the passage to Wasserstein gradient flows, Networks & Heterogeneous Media, 10, 233–253, 2015. (Link)
- , Gradient structures and geodesic convexity for reaction-diffusion systems, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371, 20120346, 2013. (Link)
- , Passing from bulk to bulk-surface evolution in the Allen–Cahn equation, Nonlinear Differential Equations and Applications NoDEA, 20, 919–942, 2013. (Link)
- , A new minimum principle for Lagrangian mechanics, J. Nonlinear Sci., 23, 179–204, 2013.
- , Weighted inertia-dissipation-energy functionals for semilinear equations, Boll. Unione Mat. Ital. (9), 6, 1–27, 2013.
- , Rigorous derivation of a plate theory in linear elastoplasticity via Γ-convergence, Nonlinear Differential Equations and Applications NoDEA, 19, 437–457, 2012. (Link)
- , An evolutionary elastoplastic plate model derived via Γ-convergence, Math. Models Meth. Appl. Sci. (M$^3$AS), 21, 1961–1986, 2011.
- , Rate independent Kurzweil processes, Applications of Mathematics, 54, 117–145, 2009. (Link)
- , Testing the Acceleration Function in Lifetime Models, In: Filia Vonta, Mikhail Nikulin, Nikolaos Limnios, Catherine Huber-Carol (eds.) Statistical Models and Methods for Biomedical and Technical Systems, 225–239, 2008. (Link)
Short CV
| 1982 | Born in Berlin, Germany |
| 2002 | Abitur, Carl-von-Ossietzky Gymnasium, Berlin |
| 2002 -- 2003 | Civilian service, Charité Berlin |
| 2003 -- 2008 | Study of Mathematics (minor in Physics) at Humboldt-Universität zu Berlin, Diploma Thesis: Herleitung eines elastoplastischen Plattenmodells mit Methoden der Γ-Konvergenz (supervisor: Prof. Dr. Alexander Mielke) |
| 2006 -- 2007 | Student assistant at WIAS Berlin, Research Group Thermodynamic Modeling and Analysis of Phase Transitions |
| 2008 -- 2010 | PhD student in DFG Research Training Group 1128 Analysis, Numerics, and Optimization of Multiphase Problems |
| Feb 2010 -- Jul 2010 | Research period at I.M.A.T.I. Pavia, funded by BioSMA research programme (supervisor: Prof. Dr. Ulisse Stefanelli) |
| Aug 2010 -- Dec 2012 | PhD student at WIAS Berlin, MATHEON project D22: Modeling of Electronic Properties of Interfaces in Solar Cells |
| Dec 2012 | Defense of PhD thesis at Humboldt-Universität zu Berlin: Variational Methods in Evolution (Supervisors: Prof. Dr. Alexander Mielke, Prof. Dr. Ulisse Stefanelli) |
Miscellaneous
Together with Maciek Korzec from TU Berlin I organized a BMS Intensive Course on Evolution Equations and their Applications from November 27-29, 2013. For details see the website or the poster (PDF).
- Local organizer of Workshop Mathematics for Semiconductor Heterostructures, September 2012
- Organizer of Workshop Applied Mathematics and Simulation for Semiconductors, March 2015
Self-heating in 2.54mm x 2.54mm OLED sample on glass substrate. The interplay between temperature activated hopping transport and Joule heating leads to complicated electrothermal feedback, leading to S-shaped current-voltage characteristics with rewgions of negative differential resistance. This behavior was studied in Matheon project SE2 in cooperation with the Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP).
Hole density, hole current density and electrostatic potential in Vertical Organic Field-Effect Transistor for applied drain voltage and opening of gate. This behavior was studied in Matheon project SE18 in cooperation with the Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP).