Preprints - IAM Publications


	2022 A. Nota J.W. Jang B. Kepka and J.J.L. Velázquez Vanishing angular singularity limit to the hard-sphere Boltzmann equation 2022 https://arxiv.org/abs/2209.14075

	2021 Jin Woo Jang and Robert M. Strain Frequency multiplier estimates for the linearized relativistic Boltzmann operator without angular cutoff 2021 https://arxiv.org/abs/2102.08846

	Jin Woo Jang and Juan J. L. Velázquez LTE and Non-LTE Solutions in Gases Interacting with Radiation 2021 https://arxiv.org/abs/2109.10071

	Hwijae Son, Jin Woo Jang, Woo Jin Han and Hyung Ju Hwang Sobolev Training for the Neural Network Solutions of PDEs 2021 https://arxiv.org/abs/2101.08932

	2020 James Chapman, Jin Woo Jang and Robert M. Strain On the Determinant Problem for the Relativistic Boltzmann Equation 2020 https://ui.adsabs.harvard.edu/abs/2020arXiv200602540C

	Margherita Disertori, Alessandro Giuliani and Ian Jauslin Plate-nematic phase in three dimensions Comm. Math. Phys., 373(1): 327--356 2020 10.1007/s00220-019-03543-z

	David Fajman, Gernot Heißel and Jin Woo Jang Averaging with a time-dependent perturbation parameter 2020 https://ui.adsabs.harvard.edu/abs/2020arXiv200612844F

	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

	Jin Woo Jang and Juan J. L. Velázquez Kinetic Models for Semiflexible Polymers in a Half-plane 2020 https://ui.adsabs.harvard.edu/abs/2020arXiv201101491J

	Jae Yong Lee, Jin Woo Jang and Hyung Ju Hwang The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach 2020 https://ui.adsabs.harvard.edu/abs/2020arXiv200913280L

	2019 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

	2018 Margherita Disertori, Alessandro Giuliani and Ian Jauslin Plate-nematic phase in three dimensions arXiv e-prints: arXiv:1805.05700 2018 https://ui.adsabs.harvard.edu/abs/2018arXiv180505700D

	Matthias Erbar and Nicolas Juillet Smoothing and non-smoothing via a flow tangent to the Ricci flow J. Math. Pures Appl. (9), 110: 123--154 2018 10.1016/j.matpur.2017.07.006

	R. D. James, A. Nota and JJL Velázquez Self-similar profiles for homoenergetic solutions of the Boltzmann equation: particle velocity distribution and entropy 2018 https://arxiv.org/abs/1710.03653

	2016 V. Beffara, S. Chhita and K. Johansson Airy point process at the liquid-gas boundary arXiv:1606.08653 2016 http://arxiv.org/abs/1606.08653 Abstract: {Domino tilings of the two-periodic Aztec diamond feature all of the three possible types of phases of random tiling models. These phases are determined by the decay of correlations between dominoes and are generally known as solid, liquid and gas. The liquid-solid boundary is easy to define microscopically and is known in many models to be described by the Airy process in the limit of a large random tiling. The liquid-gas boundary has no obvious microscopic description. Using the height function we define a random measure in the two-periodic Aztec diamond designed to detect the long range correlations visible at the liquid-gas boundary. We prove that this random measure converges to the extended Airy point process. This indicates that, in a sense, the liquid-gas boundary should also be described by the Airy process.}

	2015 Juhi Jang, Juan J. L. Velázquez and Hyung Ju Hwang On the structure of the singular set for the kinetic Fokker-Planck equations in domains with boundaries 2015 http://arxiv.org/abs/1509.03366

	2014 Sunil Chhita and Kurt Johansson Domino statistics of the two-periodic Aztec diamond arXiv e-prints 2014 http://arxiv.org/abs/1410.2385 Abstract: Random domino tilings of the Aztec diamond shape exhibit interesting features and some of the statistical properties seen in random matrix theory. As a statistical mechanical model it can be thought of as a dimer model or as a certain random surface. We consider the Aztec diamond with a two-periodic weighting which exhibits all three possible phases that occur in these types of models, often referred to as solid, liquid and gas. To analyze this model, we use entries of the inverse Kasteleyn matrix which give the probability of any configuration of dominoes. A formula for these entries, for this particular model, was derived by Chhita and Young (2014). In this paper, we find a major simplication of this formula expressing entries of the inverse Kasteleyn matrix by double contour integrals which makes it possible to investigate their asymptotics. In a part of the Aztec diamond we use this formula to show that the entries of the inverse Kasteleyn matrix converge to the known entries of the full-plane inverse Kasteleyn matrices for the different phases. We also study the detailed asymptotics of the covariance between dominoes at both the 'solid-liquid' and 'liquid-gas' boundaries. Finally we provide a potential candidate for a combinatorial description of the liquid-gas boundary.

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