| 2023Marina Ferreira, Eugenia Franco, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Coagulation equations with source leading to anomalous self-similarity
2023
https://arxiv.org/abs/2305.16921
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| Fabian Hoppe, Hannes Meinlschmidt and Ira Neitzel
Global-in-time solutions for quasilinear parabolic PDEs with mixed boundary conditions in the Bessel dual scale
2023
https://arxiv.org/abs/2303.04659
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| 2022Marina A. Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Non-power law constant flux solutions for the Smoluchowski coagulation equation
2022
https://arxiv.org/abs/2207.09518
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| Marina A. Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Asymptotic localization in multicomponent mass conserving coagulation equations
2022
https://arxiv.org/abs/2203.08076
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| Fabian Hoppe and Ira Neitzel
Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization
2022
https://ins.uni-bonn.de/media/public/publication-media/2201.pdf?pk=1589
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| 2021Barbara Niethammer, Robert L. Pego, André Schlichting and Juan J. L. Velázquez
Oscillations in a Becker-Döring model with injection and depletion
2021
https://ui.adsabs.harvard.edu/abs/2021arXiv210206751N
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| 2020A. Bufetov and P. Nejjar
Shock fluctuations in TASEP under a variety of time scalings
arXiv:2003.12414 2020
https://arxiv.org/abs/2003.12414
Abstract: We consider the totally asymmetric simple exclusion process (TASEP) with two different initial conditions with shock discontinuities, made by block of fully packed particles. Initially a second class particle is at the left of a shock discontinuity. Using multicolored TASEP we derive an exact formulas for the distribution of the second class particle and colored height functions. These are given in terms of the height function at different positions of a single TASEP configuration. We study the limiting distributions of second class particles (and colored height functions). The result depends on how the width blocks of particles scale with the observation time; we study a variety of such scalings. |
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| Fabian Hoppe and Ira Neitzel
Optimal control of quasilinear parabolic PDEs with state constraints
2020
https://ins.uni-bonn.de/media/public/publication-media/INSPreprint2004.pdf
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| Fabian Hoppe and Ira Neitzel
A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE
2020
https://ins.uni-bonn.de/media/public/publication-media/INSPreprint2005.pdf
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| Richard D. James and Alessia Nota
Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case
Nonlinearity, 33(8): 3781--3815 2020
10.1088/1361-6544/ab853f
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| P. Nejjar
KPZ statistics of second class particles in ASEP via mixing
Commun. Math. Phys., 378: 601--623 2020
https://doi.org/10.1007/s00220-020-03782-5
Abstract: We consider the asymmetric simple exclusion process on Z with a single second class particle initially at the origin. The first class particles form two rarefaction fans which come together at the origin, where the large time density jumps from 0 to 1. We are interested in X(t), the position of the second class particle at time t. We show that, under the KPZ 1/3 scaling, X(t) is asymptotically distributed as the difference of two independent, GUE-distributed random variables.The key part of the proof is to show that X(t) equals, up to a negligible term, the difference of a random number of holes and particles, with the randomness built up by ASEP itself. This provides a KPZ analogue to the 1994 result of Ferrari and Fontes, where this randomness comes from the initial data and leads to Gaussian limit laws. |
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| Alessia Nota, Juan J. L. Velázquez and Raphael Winter
On the theory of kinetic equations for interacting particle systems with long range interactions
arXiv e-prints: arXiv:2003.11605 2020
https://ui.adsabs.harvard.edu/abs/2020arXiv200311605N
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| 2019Alexander Effland, Sebastian Neumayer and Martin Rumpf
Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds
2019
https://arxiv.org/abs/1902.10930
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| Alexander Effland, Erich Kobler, Anne Brandenburg, Teresa Klatzer, Leonie Neuhäuser, Michael Hölzel, Jennifer Landsberg, Thomas Pock and Martin Rumpf
Joint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data
International Journal of Computer Assisted Radiology and Surgery, 14(4): 587--599 2019
https://dx.doi.org/10.1007/s11548-019-01919-z
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| Patrik L. Ferrari and Peter Nejjar
Statistics of TASEP with three merging characteristics
preprint: arXiv:1910.14083 2019
https://arxiv.org/abs/1910.14083
Abstract: In this paper we consider the totally asymmetric simple exclusion process, with non-random initial condition having three regions of constant densities of particles. From left to right, the densities of the three regions are increasing. Consequently, there are three characteristics which meet, i.e., two shocks merge. We study the particle fluctuations at this merging point and show that they are given by a product of three (properly scaled) GOE Tracy-Widom distribution functions. We work directly in TASEP without relying on the connection to last passage percolation. |
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| Marina Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Stationary non-equilibrium solutions for coagulation systems
arXiv e-prints: arXiv:1909.10608 2019
https://ui.adsabs.harvard.edu/abs/2019arXiv190910608F
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| Fabian Hoppe and Ira Neitzel
Convergence of the SQP Method for Quasilinear Parabolic Optimal Control Problems
2019
https://ins.uni-bonn.de/media/public/publication-media/INSPreprint1907.pdf
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| Richard D. James, Alessia Nota and J. J. L. Velázquez
Long-time asymptotics for homoenergetic solutions of the Boltzmann equation: Collision-dominated case
Journal of Nonlinear Science, 3: 1-31 2019
https://link.springer.com/article/10.1007/s00332-019-09535-6
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| Jian-Guo Liu, B. Niethammer and Robert L. Pego
Self-similar Spreading in a Merging-Splitting Model of Animal Group Size
Journal of Statistical Physics: 102 2019
10.1007/s10955-019-02280-w
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| Bertrand Lods, Alessia Nota and Federica Pezzotti
A Kac model for kinetic annihilation
arXiv e-prints: arXiv:1904.03447 2019
https://ui.adsabs.harvard.edu/abs/2019arXiv190403447L
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