東京大学 竹内研究室 公式ウェブページ

We will discuss new methods to, in principle, obtain all cumulants of von Neumann entropy over different models of random states. The new methods uncover the structures of cumulants in terms of lower-order joint cumulants involving families of ancillary linear statistics. Importantly, the new methods avoid the tedious tasks of simplifying nested summations that prevent existing methods in the literature to obtain higher-order cumulants. This talk is based on an ongoing joint work with Youyi Huang.

A fingering pattern is observed when a less viscous fluid displaces another less viscous fluid in a small space such as porous media or Hele-Shaw cells. This phenomenon is called Saffman-Taylor instability or viscous fingering(VF). Such study is important for several fields such as energy, biological and environmental fields. The VF studies have been categorized into miscible and immiscible systems. The miscible system has infinite mutual solubility like glycerol and water case, whereas the immiscible system has no mutual solubility like oil and water case. However, the presenter and colleagues have suggested the third category, namely, a partially miscible system, which has finite mutual solubility, and have found that the VF in the partially miscible system shows droplet pattern instead of fingering pattern. This is due to the coupling of hydrodynamic (VF) with chemical thermodynamics (phase separation and Korteweg force). In the lecture, the presenter will show several patterns created in the partially miscible system in experiments, and the numerical simulation.

Bacteria encounter and exert mechanical forces, although this physical dimension has been less studied compared to their eukaryotic cell counterparts. Neisseria meningitidis, or meningococcus, is a bacterial pathogen responsible for human septicaemia and meningitis. Infection caused by this bacterium and its interaction with the human host is largely determined by mechanical forces at several levels. Bacterial adhesion to the endothelium is mediated by a filamentous structure called the type IV pilus, which can generate piconewton traction forces. Bacteria form aggregates inside the vessel lumen that have viscous fluid properties. Once the lumen is filled, the bacteria proliferate in a spatially confined environment. The biological and mechanical processes that occur during these sequential host-pathogen interactions will be described and their implications during the infection process discussed.

We have investigated how one can manipulate the shape of a small cluster of colloids (or nano-particles) using an external field in the presence of thermal fluctuations. This problem can be formulated as a minimization of first passage times in configuration space. We obtain the optimal solution using Dynamic Programming. We then show how the efficiency in Reinforcement-Learning approaches vanish at the nanoscale due to thermal fluctuations.

References:
[1] Reinforcement Learning with thermal fluctuations at the nano-scale. F Boccardo, O Pierre-Louis, arXiv preprint arXiv:2311.17519 2024
[2] Temperature transitions and degeneracy in the control of small clusters with a macroscopic field. F Boccardo, O Pierre-Louis 2022, Journal of Statistical Mechanics: Theory and Experiment (10), 103205 2022
[3] Equilibrium return times of small fluctuating clusters and vacancies. F Boccardo, Y Benamara, O Pierre-Louis,　Physical Review E 106, 024120 2022
[4] Controlling the shape of small clusters with and without macroscopic fields. F Boccardo, O Pierre-Louis, Physical Review Letters 128, 256102 2022

Many synthetic, biological, or bio-inspired fluids show orientational order of the building blocks, and can also be intrinsically active or driven out of equilibrium. Disclination lines are string-like singularities within the orientational field and can show intricate non-equilibrium dynamics. I will present the formalism of describing and modelling disclinations through tensorial order parameter field and the velocity field. I will focus on selected problems, for example, how to determine the stability of a disclination loop with a zero topological charge for different flow profiles, and show the role of disclination dynamics in the context of logic operations, microrobotics, nematic microfluidics, and active nematic fluids.

In an unshaken liquid culture, aerobic bacteria easily evolve to construct cellular mats at the air-liquid interface (ALI), a unique habitat with high oxygen access. Adaptive mutants typically overproduce extracellular matrices to form robust mat structures but grow slower than the ancestor. The genetic basis of mat formation in a model organism, Pseudomonas fluorescens, has been the subject of intensive investigation; however, little is known about the mechanical aspects that affect the emergence and maintenance of slow-growing mat formers. In this work, we revealed the diminished ALI colonization of the adaptive mutants due to the general trade-off between motility and matrix production. The deficiency in colonization and growth was overcome by in-situ mutations and low dispersal from the ALI. These findings proposed a novel evolutionary scenario in which adaptive mutants occupied a spatial niche not by migration but by in-situ mutations, highlighting the importance of pre-colonization by the ancestor and the population size. Given the ubiquity of the trade-off between motility and matrix production across bacteria, the mechanism revealed here is expected to be applicable to numerous environments, such as those affecting the adaptive evolution of crypt-colonizing bacteria in an animal gut.

Active matter denotes systems with self-propulsion and arises in biological, soft, robotic, and social settings [1]. Here, we outline some of our group's recent efforts in active systems,including active matter interacting with ordered and disordered substrates, where various kinds of active clogging and commensuration effects can occur that have connections with frustrated systems and Mott physics. We also discuss chiral active systems with a Magnus force, where we find edge currents similar to those found for topological systems or charged particles in magnetic fields. In the presence of quenched disorder, the chiral active system also shows side jump effects with an active matter Hall angle. Finally, we discuss coupled active matter swarmulators where, in addition to activity, the particles have an internal degree of freedom that can become synchronized or antisynchronized. This system shows a variety of new kinds of motility-induced phase-separated states, including active matter stripes, frustrated states, gels, cluster fluids, and glassy states.

[1] Active Brownian particles in complex and crowded environments, Clemens Bechinger, Roberto Di Leonardo, Hartmut Lowen, Charles Reichhardt Giorgio Volpe, and Giovanni Volpe, Reviews of Modern Physics 88 045006 (2016).

Filamentous cyanobacteria can show fascinating patterns of self-organization, which however are not well-understood from a physical perspective. We investigate the motility and collective organization of colonies of these simple multicellular lifeforms. As their area density increases, linear chains of cells gliding on a substrate show a transition from an isotropic distribution to bundles of filaments arranged in a reticulate pattern. Based on our experimental observations of individual behavior and pairwise interactions, we introduce a model accounting for the filaments' large aspect ratio, fluctuations in curvature, motility, and nematic interactions. This minimal model of active filaments recapitulates the observations, and rationalizes the appearance of a characteristic lengthscale in the system, based on the Peclet number of the cyanobacteria filaments.

Key question addressed in this seminar: importance of two-fluid effects on macroscopic and mesoscopic scales in complex fluids. Topics of central importance are immiscibility and velocity differences. Two-fluid hydrodynamics can be applied to materials with two subsystems, which can move relative to each other. The additional macroscopic variables always include the concentration of one component and the relative velocity. The three specific systems covered here are:
1) Smectic clusters in nematic phases: breakdown of flow alignment and sign change of the anisotropy of electric conductivity [1].
2) Clusters above the glass transition in polymeric and low molecular weight materials [2].
3) Magnetorheological fluids (MRFs): onset of column formation in magnetic fields [3].

[1] H.R. Brand and H. Pleiner, Phys. Rev. E 103, 012705 (2021).
[2] H. Pleiner and H.R. Brand, Rheol. Acta 60, 675 (2021).
[3] H. Pleiner, D. Svensek, T. Potisk, and H.R. Brand, Phys. Rev. E 101, 032601 (2020).

We investigate the scaling behavior of Nambu-Goldstone (NG) modes in the ordered phase of the Vicsek model, introducing a phenomenological equation of motion (EOM) incorporating a previously overlooked non-linear term. This term arises from the interaction between velocity fields and density fluctuations, leading to new scaling behaviors. We derive exact scaling exponents in two dimensions, which reproduce the isotropic scaling behavior reported in a prior numerical simulation.