A one-dimensional three-state run-and-tumble model with a ‘cell cycle’ published in EPJE

Graphical abstract of the publication. (Image from the article.)
A one-dimensional three-state run-and-tumble model with a ‘cell cycle’
Davide Breoni, Fabian Schwarzendahl, Ralf Blossey, Hartmut Löwen
The European Physics Journal E 45, 83 (2022)
arXiv: 2206.00992

We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferating mobile phases and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their number densities, where mobility is allowed with different running speeds in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean and squared-displacements for the distribution of all cells, as well as for the number density of settled cells. The latter displays a surprising super-ballistic scaling t^3 at early times. Including repulsive and attractive interactions between the mobile cell populations and the settled cells, we explore the stability of the system and employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a non-equilibrium state diagram.

Poster by Davide at the Active Matter and Active Media Summer School 2022, Cargèse, France

Davide presents his poster on the 7th of October in the Institut d’Études Scientifiques of Cargèse. (Photo by Stefania Ketzetzi.)
Davide presented his work at the Active Matter and Active Media Summer School 2022 in Cargèse, France. His poster “A one-dimensional three-state run-and-tumble model with a ‘cell cycle’“, focuses on the modelling of the dynamics and life cycle of the Caulobacter crescentus with Fokker-Planck equations.

Brownian particles driven by spatially periodic noise published in EPJE

Brownian particles driven by spatially periodic noise
Davide Breoni, Ralf Blossey, Hartmut Löwen
The European Physical Journal E 45, 18 (2022)
arXiv: 2111.10220

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular we find a very slow dynamics for the mean displacement, scaling as t^(-1/2) with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker-Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient.

Round Table Discussion on Fluids and Active Matter

A screenshot taken during the round table discussion of 13 September 2021.

In our third round table we had the pleasure of Gareth Alexander, Ignacio Pagonabarraga and Julia Yeomans as our guest panellists. This time the overall theme was “Fluids and Active Matter” and hosted by Chun-Jen Chen, Davide Breoni, Danne van Roon, Audrey Nsamela, Dana Hassan and Sandrine Heijnen. 

It started out with an interesting discussion regarding the motivation to get in and what amazes them the most in the field of active matter. Here it became clear that active systems can have their passive counterparts, and works for easy transitions from active to passive systems, but at the same time, such active systems still have the potential to answer many fundamental questions. From this topic, one of the key takeaways was that the project that you are currently working on should be the subject that amazes you the most. 

The next topic that stood as the centre of the discussion was turbulence. Turbulence is an interesting phenomenon where a lot of things are still unknown. The intriguing concept here was that real, or fluid-dynamical, turbulence is different from active turbulence. As a clarification, Julia Yeomans introduced the following comparison. Real turbulence is observed in a waterfall where the energy follows the Kolmogorov cascade. In active turbulence, the energy originates from the individual particles moving and does not follow the same energy trend  as real turbulence. 

As one of the final topics, we were wondering what are the main takeaways regarding active nematics, especially if it’s not your field. We got it set for you in four points. One, it is fundamentally unstable and therefore creates flows. Point number two, motile topological effects. Number three, the potential connection it has to biological systems and the ability to explain similar processes. Finally, number four, the fact that we are looking at non-equilibrium systems.

Round Table Discussion on Introduction to Theoretical Active Matter

A screenshot taken during the round table discussion of 7 September 20201.

The first round table in the theoretical training gave a chance to start an interesting discussion which will continue in the following meetings.

The organizing ESRs were Ayten Gülce Bayram, Laura Natali, Liam Ruske, Jérémie Bertrand, Davide Breoni and Audrey Nsamela. They welcomed and introduced the three guests of the session: Nuno Araújo from the University of Lisbon, Jan Wehr from the University of Arizona and Denis Bartolo from École normale supérieure de Lyon.

The round table started with a personal question to the speakers about their interests and motivations for working in theoretical active matter. Having different backgrounds, the answers were very different, Nuno was attracted by non-intuitive behaviors observed in active matter experiments, while Jan started from a purely mathematical point of view and then moved towards physics of active systems. Denis provided another motivation, being head of a lab that deals with both theory and experiments.

The following discussion focused on the interaction and hierarchy between theory, simulations, and experiments. They all agree that establishing a constructive collaboration with experimental groups is not easy, but at the same time, it can have many benefits for both sides. However, none of the three elements is necessary for the others: a good paper can be presenting a theory not connected with experiments, even if its possible applications are not foreseeable yet. Denis firmly pointed out the difference between the observations and the tools (theoretical, numerical, and experimental) employed to explain it.

We also had a few more specific questions for the speakers, such as the distinctions in thinking between mathematicians and theoretical physicists, the possible applications to financial markets, and the differences in modeling artificial flocks and human crowds, which are often controlled by non-hydrodynamic variables.

We concluded the meeting by asking every one of our guests their tips for communicating the theory of active matter to a larger public. Here the answers were more relaxed and can be summed up as: trying to avoid technical and mathematical details while explaining the importance of the research problems, also using more familiar examples such as simulations employed in animation movies.

The Active Matter network has a new logo !

New ActiveMatter logos: color and BW version. (Image by ActiveMatter ESRs)
With a joint effort of the ESR students, a new logo for the ActiveMatter website was designed. The idea started as a handdrawing on a piece of paper and was quickly adapted to a better version with drawing softwares. More than 15 logos were suggested and submitted to a vote. The competition was fierce but we all came to agree on one of them and we are happy to present you the new official logo of the ITN ActiveMatter !

Round Table Discussion on: Collective Behavior

The fourth roundtable was an opportunity for all students to discuss the topic “Collective Behavior” on Zoom with a panel of guests: Clemens Bechinger from the University of Konstanz, Ivo Buttinoni from Heinrich Heine University in Dusseldorf and Caroline Beck Adiels from Gothenburg University. The event was organized by Daniela Pérez, Danne van Roon, Davide Breoni, Jérémie Bertrand, Laura Natali and Liam Ruske on March 24th.

Although the guests had different background they seemed to agree on the fact that complex behavior can emerge from an ensemble of entities that obey a small number of simple rules. Indeed, minimalistic models such as the Vicsek model account for phase transition from a disordered motion to large scale motion and more; phenomena that appear to be universal.

A question on the role of intelligence and communication in collective behavior started the discussion. Although some animals or colony of bacteria may seem intelligent (e.g. escaping from a predator in a clever way or making long-lasting symbiotic microfilms), we must bear in mind that collective behavior is… collective, and rarely arises from decisions made individually. It may be said that in the animal kingdom, the need for survival requires a need to adapt and therefore to be intelligent, but this need for intelligence can be outsourced and solved at the level of the group rather than hardwired in the physical brain of each animal (or human).

It is also conceivable that one of the entities acts as a leader and ignites a collective behavior. Giovanni Volpe made an interesting remark, stating that a leader is the one who defines the objective function to be optimized by the group. The idea of leadership in collective behavior of microscopic systems remain largely unexplored by physicists.

After one hour of fruitful discussion and back and forth between the students and the guests, the session was finished and we resumed our activities with a better understanding of collective behavior. We thank the panelists for their inputs and attendance!

Round Table Discussion on: Machine Learning

The third round table session of the experimental training was about machine learning and its role in science, in particular physics and active matter. The panelists invited to the discussion were Carlo Manzo from Vic University, Benjamin Midtvedt and Saga Helgadottir from Gothenburg University, Onofrio Maragò and Alessandro Magazzù from CNR ICPF-Messina. The discussion was organized and lead by Jesus M. A. Dominguez, Davide Breoni, Liam Ruske, Chun-Jen Chen and Alireza Khoshzaban, who are students attending the training.

The discussion touched topics like the applications of machine learning in fields like optics, biophysics, medical research, the potentialities and the reliability of the method. Questions on when a machine learning approach is advisable and how cautious one must be when applying machine learning were also addressed. Current important logical and practical aspects of the method were also discussed, together with the need of testing machine learning applications against more classical ones. The panelists also stated the importance of reliably checking the results obtained to avoid biases that can lead to false conclusions.

After one hour of fruitful discussion we gained a broader perspective and a deeper understanding of machine learning.

Active noise-driven particles under space-dependent friction in one dimension on arXiv

Sketch of the confining potential U(x) = κ|x|, a linear friction gradient γ(x) = γ0+γ1|x| in arbitrary units. The particle, shown by a blue dot on the x-axis, is activated by noise (indicated in red), under the influence of the potential and the friction gradient. Image by D. Breoni.
Active noise-driven particles under space-dependent friction in one dimension

Davide Breoni, Ralf Blossey, Hartmut Löwen
arxiv: 2102.09944

Abstract: We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate x, which is simultaneously exposed to a space-dependent friction coefficient γ (x), a confining potential U(x) and non-equilibrium (i.e., active) noise. Specically, we consider frictions γ (x) = γ0 + γ1|x|p and potentials U(x) ∝ |x|p with exponents p = 1; 2 and n = 0; 1; 2. We provide analytical and numerical results for the particle dynamics for short times and the stationary
probability density functions (PDFs) for long times. The short-time behaviour displays diffusive and ballistic regimes while the stationary PDFs display unique characteristic features depending on the exponent values (p; n). The PDFs interpolate between Laplacian, Gaussian and bimodal distributions, whereby a change between these different behaviours can be achieved by a tuning of the friction strengths ratio
γ0 / γ1. Our model is relevant for molecular motors moving on a
one-dimensional track and can also be realized for confined self-propelled colloidal particles.

Active Brownian and inertial particles in disordered environments: short-time expansion of the mean-square displacement on ArXiv

Active Brownian and inertial particles in disordered environments: short-time expansion of the mean-square displacement
Davide Breoni, Michael Schmiedeberg, Hartmut Löwen
arXiv: 2010.11076

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square-displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behaviour adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is α = 3 and α = 4. We confirm our theoretical predictions by computer simulations. Moreover they are verifiable in experiments on self-propelled colloids in random environments.