# Research

## Research interests

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

## Scientific Publications

### Published Papers

A. Nota, J.J.L. Velázquez, Homoenergetic solutions of the Boltzmann equation : the case of simple-shear deformations. To appear in

*Mathematics in Engineering*(2021)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). To appear in

*Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.*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)M.A. Ferreira, J. Lukkarinen, A. Nota, J.J.L. Velázquez, Localization in stationary non-equilibrium solutions for multicomponent coagulation systems.

*Commun. Math. Phys.*Vol. 388, Issue 1, 479-506 (2021)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/939M.A. Ferreira, J. Lukkarinen, A. Nota, J.J.L. Velázquez, Stationary non-equilibrium solutions for coagulation systems.

*Arch. Rational Mech. Anal.*Vol. 240, 809-875 (2021) https://doi.org/10.1007/s00205-021-01623-wA. 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**]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**]B. Lods, A. Nota, F, Pezzotti, A Kac model for annihilation of particles,

*J. Nonlinear Sci.*(2020) [**article**]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**]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]**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**]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**]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**]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**]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**]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**]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**]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**]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**]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

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/2019/10A. 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/2019/42A. 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

M.A. Ferreira, J. Lukkarinen, A. Nota, J.J.L. Velázquez, Multicomponent coagulation systems: existence and non-existence of stationary non-equilibrium solutions. arXiv:2103.12763 (2021)

M.A. Ferreira, J. Lukkarinen, A. Nota, J.J.L. Velázquez, Asymptotic localization in multicomponent mass conserving coagulation equations. arXiv:2203.08076 (2022)

### 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)