Room 108 (first floor)

Instituto Nacional de Matemática Pura e Aplicada - IMPA

Estrada Dona Castorina 110, Rio de Janeiro 22460-320 Brazil

Tel.: +55 21 2529 5070

Fax: +55 21 2529 5075

Homepage: http://fluid.impa.br

Brazilian Chapter of InterPore

The International Society for Porous Media

**Ph.D. Student:** Ciro Sobrinho Campolina Martins

**Ph.D. Advisor:** Alexei A. Mailybaev

**Thesis:** Fluid Flows and Boundaries on Logarithmic Lattices

**Abstract:** Several open problems in fluid dynamics are related to the multi-scale nature of turbulence and the effects of boundary conditions. To overcome the limited resolution of direct numerical simulations, simplified toy-models are commonly employed in the study of large spatial range flows. In the construction of such models, one modifies equations of motion, preserving only certain parts believed to be important. In this thesis, we propose a different approach. Instead of simplifying equations, one introduces a simplified configuration space: we define velocity fields and boundary effects on multi-dimensional logarithmic lattices in Fourier space. Operations upon these variables are provided in a rigorous mathematical framework, so equations of motion are written in their exact original form. As a consequence, the resulting models preserve the same symmetry groups, inviscid invariants and regularity properties. The strong reduction in degrees of freedom allows computational simulations of incredibly large spatial ranges. Using the new simplified models, we address two important open problems: the finite time singularities in ideal flow and the vanishing viscosity limit in the presence of solid boundaries. We observe strong robustness of the chaotic blowup scenario in the three-dimensional incompressible Euler equations and promising results towards the investigation of potentially singular behavior close to solid boundaries.

**Wednesday, Nov. 30, 2022 at 10:00 AM (RJ) **

**News:** https://impa.br/noticias/pos-doutor-do-impa-participa-de-seminario-em-cartagena/

A matemática aplicada no cálculo da trajetória de foguetes, no comportamento e evolução de tumores de mama, no resfriamento do vidro e na construção de redes neurais para desenvolvimento de inteligência artificial. São exemplos como esse, da ciência utilizada no setor produtivo e na sociedade, que Marlon López, pós-doutor no laboratório de Dinâmica dos Fluidos do IMPA, levará para o 4º Encontro Matemático do Caribe, que acontece de 29 de novembro a 2 de dezembro, em Cartagena, na Colômbia.

López apresentará a palestra “A importância da modelação matemática no desenvolvimento tecnológico” na conferência de abertura do evento. O fórum será realizado no Parque Industrial e Tecnológico Carlos Vélez Pombo. Também haverá transmissão online do encontro.

Fluid Flows and Boundaries on Logarithmic Lattices

Qui 24 nov 2022, 13:30 - SALA 224

**Resumo: **Several open problems in fluid dynamics are related to the multi-scale nature of turbulence and the effects of boundary conditions. To overcome the limited resolution of direct numerical simulations, simplified toy-models are commonly employed in the study of large spatial range flows. In the construction of such models, one modifies equations of motion, preserving only certain parts believed to be important. In this thesis, we propose a different approach. Instead of simplifying equations, one introduces a simplified configuration space: we define velocity fields and boundary effects on multi-dimensional logarithmic lattices in Fourier space. Operations upon these variables are provided in a rigorous mathematical framework, so equations of motion are written in their exact original form. As a consequence, the resulting models preserve the same symmetry groups, inviscid invariants and regularity properties. The strong reduction in degrees of freedom allows computational simulations of incredibly large spatial ranges. Using the new simplified models, we address two important open problems: the finite time singularities in ideal flow and the vanishing viscosity limit in the presence of solid boundaries. We observe strong robustness of the chaotic blowup scenario in the three-dimensional incompressible Euler equations and promising results towards the investigation of potentially singular behavior close to solid boundaries. These are results of my PhD research under the supervision of Prof. Alexei Mailybaev.

Webpage: https://impa.br/seminarios

**Ph.D. Student:** Júlia Domingues Lemos

**Ph.D. Advisor:** Alexei A. Mailybaev

**Thesis:** Data-based approach for time-correlated closures of turbulence models

**Friday Oct. 14, 2022 10:00 AM (RJ) **

Depinning asymptotics in ergodic media

Qui 08 set 2022, 13:30 - SALA 224 **Seminário de Matemática Aplicada e Computacional**

**Resumo: **We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymptotics for the speed, with exponent depending a local dimension of the ergodic measure near extremal values. We also show that our conceptual assumptions are satisfied in a context of weak inhomogeneity of the medium and almost balanced kinetics.

The talk is based on a joint work with A. Scheel

Webpage: https://impa.br/seminarios

Spontaneous stochasticity in experimental turbulence : from thermal noise to irreversibility

Qui 01 set 2022, 13:30 - SALA 224 **Seminário de Matemática Aplicada e Computacional**

**Resumo: **This talk aims at introducing some general ideas to find experimental evidence of spontaneous stochasticity in turbulence.

Some recent theories reconsidered thermal noise when it comes to correctly modeling small scales of turbulence; noise that might also be at the origin of spontaneous stochasticity. The first part of this talk will be dedicated on introducing the experiment and discussing the use of hot-wires to try to observe those weakly energetic random fluctuations.

The study of relation between spontaneous stochasticity and irreversibility will be presented in a second part. We will be especially discussing the use of tools from differential geometry and phase transition theory to enlighten experimental data analysis.

Webpage: https://impa.br/seminarios

Spontaneous Stochasticity in the Kraichnan Model of Turbulence

Qui 18 ago 2022, 13:30 - SALA 224** **

**Resumo: **In this talk we discuss the Kraichnan model of passive scalar advection, which can be used to model turbulent dispersion of particles. We give a brief introduction of the main concepts related to the model and proceed to show how the phenomenon of spontaneous stochasticity takes place in the framework of Gaussian velocity (random) fields. Possible extension to non-Gaussian (intermittent) velocity fields are also discussed.

Webpage: https://impa.br/seminarios

Wave-particle dynamics in hydrodynamic quantum analogues

Qui 04 ago 2022, 13:30 - SALA 224

**Resumo: **The groundbreaking discovery by Yves Couder and Emmanuel Fort (Paris, 2005) led to many works on pilot-wave hydrodynamics. Pilot-wave hydrodynamics originates from bouncing droplets of silicon oil that can levitate over a vibrating bath of the same fluid and be self-propelled by the Faraday waves it generates. Following Couder and Fort, these walking droplets are viewed as a hydrodynamic quantum analogue (HQA) of a wave-particle system. We have deduced the first wave-droplet dynamical system which, through scientific computing, has revealed several new dynamical properties not imagined possible for a classical mechanical system. A series of new articles have originated recently from Nachbin (Chaos 2018) where it was shown for the first time that two oscillators can be correlated at a distance, without any explicit coupling between them. An overview of these recents results will be presented, including those of a recent Nature Comm. Physics paper (June 2022) where we show the cooperative tunneling of two particles.

Webpage: https://impa.br/seminarios

The 5th-Interpore conference of the Brazilian chapter, will be held from **1 to 2 August 2022** in a fully virtual format with scientific program focusing on advances in the research, methods, and theory of Porous Media in close connection to the topics: **Green World**, **Smart Materials**, **Oil Science** and **Synchrotron light, Biosciences, Biorenewables, Nanotechnology**.

Webpage: https://interpore2022br.ufrn.br/

**Ph.D. Student:** José Manuel Escorcia Tafur

**Thesis:** Post-Blowup Dynamics for the Nonlinear Schrödinger Equation

José Manuel has been working during his doctoral studies under the supervision of Professor Alexei A. Mailybaev.

https://impa.br/noticias/pesquisando-escorcia-aprendeu-linguagem-universal-da-ciencia/

**Monday Nov. 29, 2021 12:30 PM (RJ) **

of the course "**An Introduction to Stochastic Differential Equations with applications to Fluid Dynamics**" by Theodore Drivas and Simon Thalabard.

January-February 2019:

**Mon, Wed, Fri 10-12 a.m. at room 345**

Webpage: http://www.interpore2019br.lncc.br/

**06/aug, 13:00, room 228**: Group meeting: talks by Ciro Campolina and Vitor Sudbrack.

**Thesis Defense of Luis Fernando Lozano**: "Diffusive effects in Riemann solutions for three phase flow in porous media".

**27/07/2018 - 13:30 at room 228.**

**Seminar (11/07):** Marco Martins Afonso (Centro de Matemática da Universidade do Porto) "Renormalized transport of inertial particles", 11:00, room 228.

**Seminar (26/06):** Luis Fernando Lozano Guerrero (IMPA) "Estudo do efeito de difusão (simplificada) em sistemas não estritamente hiperbólicos de leis de conservação", 13:30 at room 347.

Lectures at IMPA by Prof. Uriel Frisch, May 11-17.

**Seminar (26/03)**: John Bush (MIT - Dep. of Mathematics)

"Hydrodynamic quantum analogs", 11:00 at room 228.

The paper by Prof. Mailybaev showing that light stops at exceptional points is featured in newspapers and science news articles: Newsweek, The Independent, Daily Mail, Phys.org, ScienceAlert.

IMPA's press release (portuguese) may be read here.

Group meeting: Hugo Saraiva, Turbulence reading course

- 20/fev, 10:30, room 224

- 06/feb, 10:30, room 224

- 30/jan, 10:30, room 224

- 23/jan, 10:30, room 224

Seminar: Vikas Krishnamurthy (UFPe), Complex analysis for compressible vortex dynamics (16/jan, 15:30, room 333)

Group meeting: Hugo Saraiva, Turbulence reading course (09/jan, 10:30, room 345)

(12/2017) Tribute to Clarice Lispector and Leopoldo Nachbin

Group meeting: Hugo Saraiva, Theory for Lattice-Boltzmann Method for two-phase flows - part 2 (07/dec, 13:30, room 333)

Group meeting: Hugo Saraiva, Theory for Lattice-Boltzmann Method for two-phase flows - part 1 (30/nov, 13:30, room 333)

(09/2017) Article about the career and life of professor Dan Marchesin, our Laboratory's Head and founder (English / Portuguese)

Videos: talks of the Workshop on Conservation Laws and Applications, celebrating the 70th birthday of Dan Marchesin

70^{th} birthday of Dan Marchesin

Seminar: Wanderson Lambert, Teoria matemática de fluxo bifásico em meios porosos com diversos componentes químicos (24/mar, 10:30, room 236)

Group meeting: Hugo Saraiva, Entropy (24/mar, 13:30, room 236)

Group meeting: Hugo Saraiva, Boltzmann equation (9/mar, 13:30, room 345)

Interview for Galileu (03/2017).

Videos: IMPA-Bath Workshop in Mathematics

Videos: Workshop on Turbulent Dissipation, Mixing and Predictability. January 9 - 13, 2017, IPAM, Los Angeles

Videos: 2nd IMPA-InterPore Conference on Porous Media