# Home - Research

# Juan F. Marín

Physicist

Departamento de Física - Universidad Tecnológica Metropolitana.

Santiago, Chile.

j.marinm@utem.cl

I'm a physicist, deeply passionate about the nonlinearity of nature.

My research interests are broad, from Josephson junctions, polymer chains, infectious diseases, and fluid mechanics to the cosmos. Currently, I am applying the theory of nonlinear physics to studying fluids, turbulence, and hydrodynamic instabilities.

## Areas of interest

Nonlinear models of turbulence.

Applications of nonlinear dynamical systems to the modelling of infectious diseases.

Faraday instabilities and pattern formation in hydrodynamical, optical and granular systems.

Gravity waves and Rogue Waves in hydrodynamics.

Dynamics of solitons in Josephson junctions and DNA chains.

Nonlinear wave propagation in random media

# Research team

Joaquín Morales Palominos, thesis student in biomathematics (Master) UTEM.

Project: "Active Brownian particles with memory"Lucas Carreño Maldonado, thesis student in mechanical engineering (Undergraduate) UTEM.

Project: "Autoresonance in water channels"Felipe Solorza Muñoz, thesis student in mechanical engineering (Undergraduate) UTEM.

Project: "Blood flow turbulence around aortic valve implants"

# Past students

Alicia Castro Montés, Magister in Physical Sciences (Co-mentored).

Now PhD student at Universidad de Santiago de Chile.

Thesis: "Dynamics of fluxon-bubbles under spatiotemporal driving forces",

Pontificia Universidad Católica de Valparaíso, 2021.

Teaching

During the second semester of 2024, I'm teaching:

1) "Complexity and emergent computational methods" for the PhD program in Applied Informatics in Health and the Environment (DIASMA).

2) "Linear and nonlinear Fockker-Planck equations" for the Magister program in Biomathematics.In previous terms, I've taught:

1) "Complexity and emergent computational methods" for the PhD program in Applied Informatics in Health and the Environment (2nd term 2023).

2) "Stochastic methods and diffusive processes" for the Magister program in Biomathematics. 1st term (2024)

2) "Laboratory of Classical Mechanics" for Engineering Sciences. 1st term (2024)

2) "Laboratory of Optics and Waves" for Engineering Sciences: 1st term (2024) and 2nd term (2023).

# RESEARCH PROJECTS

## Rogue waves driven by underwater forcing in channels

Rogue waves are large-amplitude waves suddenly appearing on the surface of the ocean, in basins of arbitrary depth with and without strong currents. Many linear, nonlinear and probabilistic theories have emerged since the first confirmation of their existence. However, the physical mechanisms that give rise to such events are still controversial. Understanding the phenomenon of rogue waves would be very useful to forecast, implementing protocols and selecting areas with a higher risk of rogue wave occurrence based on the oceanographic and meteorological conditions of the zones. I am currently interested in the phenomenon of rogue wave generation in annular water channels by a random underwater forcing. The main goal of this project is to shed light on the real mechanism of rogue wave formation and to elucidate the true role of randomness, dispersion, resonance, and nonlinearity.

In collaboration with:

Isis Vivanco & Leonardo Gordillo (Universidad de Santiago, Chile) 🇨🇱

Bruce Cartwright (Pacific Engineering Systems International, Australia) 🇦🇺

### References

[1] Vivanco, Cartwright, Ledesma , Gordillo, and Marín. Fluids 6, 6:222, 2021

[2] Marín, Egli, Vivanco, Cartwright, and Gordillo. Arxiv preprint 2209.00748, 2022

[3] Vivanco, Egli, Cartwright, Marín, and Gordillo. Arxiv preprint 2406.00264, 2024

## Localised Faraday patterns induced by heterogeneous parametric drive

When a fluid is subjected to vertical vibrations, a pattern can be generated on the surface if the amplitude of the oscillations is above a certain threshold. This is the Faraday instability, where waves oscillate at half the forcing frequency. Although these patterns have been widely investigated in the past, the case of heterogeneous drive has been considered only recently [1]. Motivated by systems in which uniform drive is not plausible, we are investigating theoretically, numerically and experimentally the generation of localised Faraday patterns induced by a localised parametric drive. Using a heterogeneous parametrically driven nonlinear Schrödinger equation as a model, we are performing a complete nonlinear analysis of the system to understand theoretically nonlinear saturation phenomena.

In collaboration with:

Saliya Coulibaly & Majid Taki (Université de Lille, France) 🇫🇷

Mónica García-Ñustes & Rafael Riveros Ávila

(Pontificia Universidad Católica de Valparaíso, Chile) 🇨🇱Leonardo Gordillo (Universidad de Santiago, Chile) 🇨🇱

### References

[1] Urra, Marín, Páez-Silva, Taki, Coulibaly, Gordillo, and García-Ñustes. Physical Review E 99 (3) 033115, 2019

[2] Marín, Riveros-Ávila, Coulibaly, Taki, Gordillo, and García-Ñustes. Communications Physics 6, 63, 2023

## Capillary retraction of liquid filaments

When a liquid filament is left free in the air, it begins to retract by the action of surface tension to minimize its area. For instance, when we pull out honey with a stick and we cut the honey thread, it retracts with a certain speed (the Taylor-Culick speed). The initially cylindrical filament tries to minimise its energy by forming a big drop at the free end. This phenomenon, as a predecessor of drop formation by the breaking of liquid threads (Rayleigh-Plateau instability), has important applications in ink-printing technologies. We are using a lubrication model based on the three-dimensional axisymmetric Navier-Stokes equations to investigate the system. We have derived a long-time asymptotic-state expansion for the filament profile, obtaining good agreement with numerical simulations [1]. We prove that below a critical Ohnesorge number, liquid filaments naturally develop travelling capillary waves along their surface and a neck behind the drop where pinch-off might occur through a dynamic instability [1]. In this project, we are obtaining a full picture of the recoiling process going beyond the classic results of the velocity of retraction found by Taylor and Culick.

In collaboration with:

Francesco Paolo Contò (University of Cambridge, UK) 🇬🇧

J. Rafael Castrejón-Pita (University College London, UK) 🇬🇧

Arnaud Antkowiak (Sorbonne Université, Paris, France) 🇫🇷

Leonardo Gordillo (Universidad de Santiago, Chile) 🇨🇱

### References

[1] Contò, Marín, Antkowiak, Castrejón-Pita, and Gordillo. Scientific Reports 9(1), 15488, 2019

## Dynamics of soliton-bubbles in Josephson junctions

The transmission, reflection, and annihilation of waves that go from one medium to another, or that collide with a localised defect, is a widespread problem in physics. Such a problem appears in many situations, from quantum mechanical to electrodynamical phenomena. A crucial point to consider is that when such waves are nonlinear, more complicated and fascinating phenomena can occur! When such waves have an internal structure, such as in the case of sine-Gordon solitons, the presence of localised but not point-like heterogeneities can cause the destabilisation of internal modes, producing bubble-like and drop-like structures that are sustained by the same heterogeneities that create them. We are investigating the formation, stability and controlled transport of these kind of localised structures in Josephson junctions.

In collaboration with:

Mónica García-Ñustes (Pontificia Universidad Católica de Valparaíso, Chile) 🇨🇱

Jorge A. González (Florida International University, United States) 🇺🇸

### References

[1] García-Ñustes, González and Marín. Physical Review E 95 (3) 032222, 2017

[2] Marín. Journal of Physics: Conference Series 1043, 012001, 2018

[3] Castro-Montes, Marín, Teca-Wellmann, González and García-Ñustes. Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 6:063132, 2020

Generation of a soliton bubble in a sine-Gordon system, from Ref. [1].

Stability of bubble-like fluxons. Supplemental material from Ref. [3].

## Dynamics of kinks and true-vacuum bubbles in nonlinear field theories

First-order phase transitions in nonlinear field theories are important problems in particle physics and cosmology. The underlying phenomenon is that of bubble nucleation, which can be triggered by a nonlinear instability that is energetically above a nucleation barrier. Such nucleation usually occurs around an impurity, such as tiny black holes, and has important implications in vacuum stability, quark confinement, and cosmological models. I study the dynamics of soliton bubbles in nonlinear Klein-Gordon systems using Higgs-like potentials that are relevant in vacuum decay problems. I'm interested in phenomena such as vacuum decay seeded by small heterogeneities and anomalous effects due to infinite-action instantons.

In collaboration with:

Jorge A. González (Florida International University, United States) 🇺🇸

Luis Emilio Guerrero (Universidad Simón Bolívar, Venezuela) 🇻🇪

Alberto Bellorín (Universidad Central de Venezuela, Venezuela) 🇻🇪

Mónica García-Ñustes (Pontificia Universidad Católica de Valparaíso, Chile) 🇨🇱

Luis Vázquez (Universidad Complutense de Madrid, Spain) 🇪🇸

Salvador Jiménez (Universidad Politécnica de Madrid, Spain) 🇪🇸

### References

[1] González, Bellorín, García-Ñustes, Guerrero, Jimenez, Marín and Vazquez. Journal of Cosmology and Astroparticle Physics (06)033, 2018

[2] González, Bellorín, Guerrero, Jiménez, Marín, and Vázquez. Brazilian Journal of Physics, 50: 759-770, 2020

[3] Marín, Journal of High Energy Physics 02, 198, 2021