Research

Research interests

Kinetic Theory, Statistical mechanics, Analysis of PDEs, Quantum Mechanics.

Scientific Publications


Published Papers


  1. A. Nota, C. Saffirio, S. Simonella, Derivation of the generalized linear Boltzmann equation for magnetotransport. To appear in Ann. Inst. H. Poincaré Probab. Statist. (arXiv:1910.12983)

  2. M.A. Ferreira, J. Lukkarinen, A. Nota, J.J.L. Velázquez, Localization in stationary non-equilibrium solutions for multicomponent coagulation systems. To appear in Commun. Math. Phys. (arXiv:2006.14840)

  3. A. Nota, J.J.L. Velázquez, R. Winter, Interacting particle systems with long range interactions: scaling limits and kinetic equations. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. Vol. 32 , Issue 2, 335–377 (2021) DOI 10.4171/rlm/939

  4. M.A. Ferreira, J. Lukkarinen, A. Nota, J.J.L. Velázquez, Stationary non-equilibrium solutions for coagulation systems. Arch. Rational Mech. Anal. (2021) https://doi.org/10.1007/s00205-021-01623-w

  5. A. Bobylev, A. Nota, J.J.L. Velázquez, Self-similar asymptotics for a modified Maxwell-Boltzmann equation in systems subject to deformations. Commun. Math. Phys. Vol. 380, 409-448 (2020)[article]

  6. R.D. James, A. Nota, J.J.L. Velázquez, Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Hyperbolic-dominated case. Nonlinearity Vol. 33, Issue 8, 3781-3815 (2020) [article]

  7. B. Lods, A. Nota, F, Pezzotti, A Kac model for annihilation of particles, J. Nonlinear Sci. (2020) [article]

  8. B. Lods, A. Nota, R. Winter, Kinetic description of a Rayleigh Gas with annihilation, J. Stat. Phys. Vol. 176, Issue 6, 1434–1462 (2019) [article]

  9. R.D. James, A. Nota, J.J.L. Velázquez, Long time asymptotics for homoenergetic solutions of the Boltzmann equation. Collision-dominated case, J. Nonlinear Sci. https://doi.org/10.1007/s00332-019-09535-6 (2019) [article]

  10. B. Niethammer, A. Nota, S. Throm, J.J.L. Velázquez, Self-similar asymptotic behavior for the solutions of a linear coagulation equation, J. Differential Equations Vol. 266, Issue 1, pp. 653-715 (2019) [article]

  11. R.D. James, A. Nota, J.J.L. Velázquez, Self-similar profiles for homoenergetic solutions of the Boltzmann equation: particle velocity distribution and entropy, Arch. Rational Mech. Anal. Vol. 231, Issue 2, pp. 787-843 (2019) [article]

  12. J. Lukkarinen, M. Marcozzi and A. Nota, Summability of connected correlation functions of coupled lattice fields, J. Stat. Phys. Vol. 171, Issue 2, pp. 189-206 (2018) [article]

  13. A. Nota, S. Simonella, J.J.L. Velázquez, On the theory of Lorentz gases with long range interactions, Rev. Math. Phys. Vol. 30, No. 3, 1850007 (2018) [article]

  14. A. Nota, J.J.L. Velázquez, On the growth of a particle coalescing in a Poisson distribution of obstacles, Commun. Math. Phys. Vol. 354, Issue 3, pp. 957-1013 (2017) [article]

  15. J. Lukkarinen, M. Marcozzi and A. Nota, Harmonic chain with velocity flips: thermalization and kinetic theory, J. Stat. Phys. Vol. 165, Issue 5, pp. 809-844 (2016) [article]

  16. M. Marcozzi and A. Nota, Derivation of the linear Landau equation and linear Boltzmann equation from the Lorentz model with magnetic field, J. Stat. Phys. Vol.162, Issue 6, pp. 1539-1565 (2016) [article]

  17. G. Basile, A. Nota, F. Pezzotti and M. Pulvirenti, Derivation of the Fick's Law for the Lorentz Model in a low density regime, Commun. Math. Phys. Vol. 336, Issue 3, pp. 1607-1636 (2015) [article]

  18. A. Nota, Diffusive limit for the random Lorentz gas, From Particle Systems to Partial Di erential Equations II, Springer Proceedings in Mathematics & Statistics, Vol. 129, pp. 273-292 (2015) [article]

  19. G. Basile, A. Nota and M. Pulvirenti, A Diffusion Limit for a Test Particle in a Random Distribution of Scatterers, J. Stat. Phys. Vol. 155, Issue 6, pp. 1087-1111 (2014) [article]


Conference Proceedings

  1. A. Nota, C. Saffirio, J.L.L. Velázquez, Mini-Workshop: Lorentz Gas Dynamics: particle systems and scaling limits. Oberwolfach Rep. 16 (2019), no. 1, 617-661, DOI:10.4171/OWR/2019/10

  2. A. Nota, On the derivation of linear kinetic equations from a Lorentz Gas with long-range interactions, Oberwolfach Reports, Large Scale Stochastic Dynamics, Report No. 42/2019, DOI: 10.4171/OWR/2019/42

  3. A. Nota, Kinetic description for the Lorentz Gas with long-range interactions, Oberwolfach Reports, Classical and Quantum Mechanical Models of Many-Particle Systems, Report No. 56/2017, DOI: 10.4171/OWR/2017/56


Preprints

  1. A. Nota, J.J.L. Velázquez, R. Winter, Interacting particle systems with long range interactions: approximation by tagged particles in random fields. arXiv:2103.09740 (2021)

  2. M.A. Ferreira, J. Lukkarinen, A. Nota, J.J.L. Velázquez, Multicomponent coagulation systems: existence and non-existence of stationary non-equilibrium solutions. (2021)


Notes

A. Nota, Fick's Law for the Lorentz Model in a weak coupling regime arXiv:1411.6474 [preprint]


Ph.D. Thesis

From microscopic dynamics to macroscopic equations: scaling limits for the Lorentz gas, Alessia Nota (2014)