Veranstaltungen
- Donnerstag, 05.09.2024, 12:00 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Martijn Gösgens, TU Eindhoven, NL:
The Erdős-Rényi Random Graph Conditioned on Every Component Being a Clique
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
We consider an Erdős-Rényi random graph, conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques. Hence, this conditional distribution defines a distribution over partitions. The motivation for this model comes from community detection, where one wishes to partition graph vertices into groups that are better connected internally than externally. Using tools from analytic combinatorics, we prove limit theorems for several graph observables of this conditional distribution: the number of cliques; the number of edges; and the degree distribution. We consider several regimes of the connection probability $p$ as the number of vertices n diverges. For $p=frac12$, the conditioning yields the uniform distribution over set partitions, which is well-studied, but has not been studied as a graph distribution before. For $p<\frac{1}{2}$, we show that the number of cliques is of the order $n/\sqrt{\log n}$, while for $p>frac12$, we prove that the graph consists of a single clique with high probability. This shows that there is a phase transition at $p=frac12$. We additionally study the near-critical regime $pdownarrowfrac12$, as well as the sparse regime $pdownarrow 0$.
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Seminar Interacting Random Systems (Hybrid Event)
Veranstalter
WIAS Berlin
- Donnerstag, 05.09.2024, 15:00 Uhr (WIAS-406)
- Seminar Materialmodellierung
Prof. Dr. Georgy Kitavtsev, Middle East Technical University, Nothern Cyprus Campus:
Composite solutions to a liquid bilayer model
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Veranstalter
WIAS Berlin
- 10. September 2024 (HU Berlin HVP)
- Workshop/Konferenz: AMaSiS 2024 : Tutorials
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Humboldt-Universität zu Berlin, Hausvogteiplatz 5-7, R. 0007
Abstrakt
Tutorial 1 by Jesús Carrete Montaña, U Zaragoza:
Thermal conductivity calculations with the Boltzmann transport equation and machine-learning force fields
Solutions of the Boltzmann transport equation (BTE) for phonons with inputs from density-functional-theory (DFT) calculations have been successful at providing predictive, parameter-free estimates of the thermal conductivity of many pristine and defect-laden semiconductors, albeit at very significant computational cost. Machine-learning force fields, through their ability to provide results with DFT-like quality in a small fraction of the time, can revolutionize that situation. This tutorial will first guide the audience through all the steps of a conventional DFT+BTE calculation, followed by the active learning of a descriptor-based neural-network potential. That force field will then be validated by reproducing the ab-initio results.
Tutorial 2 by Michele Simoncelli, U Cambridge:
From density-functional theory to dual wave-particle transport and device simulation
Quantitative theoretical predictions for charge and heat transport phenomena in semiconductors are crucial to design devices for energy conversion or management. We present recent advances in Quantum ESPRESSO, an open-source density-functional-theory (DFT) software, that allows us to simulate from first principles the thermoelectric properties of semiconductors. After discussing how to compute the band structure of electrons and phonons, we introduce the framework needed to quantify their interactions. We discuss how these quantitites enter into the microscopic Wigner formulation for transport in solids, which enables us to predict the transport coefficients in materials ranging from crystals to glasses and with variable level of doping. Finally, we show that microscopic transport equations for electron and phonon transport can be coarse-grained into mesoscopic viscous equations useful to design devices. These are partial differential equations that generalize Ohm's or Fourier's laws describing not only diffusive transport but also fluid-like phenomena measured in recent, pioneering experiments.
Veranstalter
Einstein Foundation Berlin
WIAS Berlin
- Dienstag, 10.09.2024, 10:30 Uhr (WIAS-HVP-3.13)
- Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Aaron Sander, Technische Universität München:
Verifying the equivalence or non-equivalence of quantum circuits with tensor networks
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Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13
Abstrakt
The development of quantum computers and algorithms is currently rapidly accelerating and will likely continue to do so in the next few years and even decades. As these systems continue to increase in size and complexity, there is an increasing need for methods to aid in their design. In particular, there is a need for debugging tools at each level of the quantum computing stack, specifically in the compilation and optimization of quantum circuits. In this work, we bridge the gap between quantum many-body physics and computer science by using tensor network techniques to verify the equivalence or non-equivalence of quantum circuits in order to detect errors that may occur during the many steps of this process.
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Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations
Veranstalter
WIAS Berlin
- 11. – 13. September 2024 (LG)
- Workshop/Konferenz: AMaSiS 2024: Applied Mathematics and Simulation for Semiconductor Devices
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Haus der Leibniz-Gemeinschaft, Chausseestr. 111, 10115 Berlin
Abstrakt
AMaSiS 2024 is an interdisciplinary workshop dedicated to the mathematical modeling and numerical simulation of semiconductor devices. AMaSiS 2024 aims at bringing together experts from mathematics, physics, engineering, and materials science for discussions on computational materials science and electronic structure theory, quantum and semiclassical transport, simulation of semiconductor devices, and upscaling from quantum mechanics and particle systems to continuum scale models.
Veranstalter
WIAS Berlin
Einstein Foundation Berlin
- Dienstag, 17.09.2024, 10:15 Uhr (WIAS-406)
- Seminar Nichtlineare Optimierung und Inverse Probleme
Prof. Dr. Masahiro Yamamoto, University of Tokyo, Japan:
Inverse problems for time-fractional diffusion-wave equations
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)
Veranstalter
WIAS Berlin
- Mittwoch, 18.09.2024, 10:00 Uhr (WIAS-405-406)
- Seminar Numerische Mathematik
Albert J. Pool, Deutsches Zentrum für Luft- und Raumfahrt e.V.:
Nonlinear dynamics as a ground-state solution on quantum computers
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation. We describe a general procedure to construct efficient quantum circuits for the cost function evaluation required by VQAs. To mitigate the barren plateau problem during the optimization, we propose an adaptive multigrid strategy. The approach is illustrated for the nonlinear Burgers equation. We classically optimize quantum circuits to represent the desired ground-state solutions, run them on IBM Q System One and Quantinuum System Model H1, and demonstrate that current quantum computers are capable of accurately reproducing the exact results.
Veranstalter
WIAS Berlin
- Mittwoch, 09.10.2024, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Christopher Renaud Chan, Université Grenoble Alpes:
tba
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Weitere Informationen
Seminar Interacting Random Systems (Hybrid Event)
Veranstalter
WIAS Berlin