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These lecture notes describe a basic theory of chemically active droplets, which are droplets kept away from equilibrium by driven chemical reactions. The notes assume a basic familiarity with equilibrium thermodynamics of phase separation,…

Soft Condensed Matter · Physics 2024-07-16 David Zwicker

We study the structure and dynamics of a transient network composed of droplets of microemulsion connected by telechelic polymers. The polymer induces a bridging attraction between droplets without changing their shape. A viscoelastic…

Soft Condensed Matter · Physics 2009-10-31 F. Molino , J. Appell , M. Filali , E. Michel , G. Porte , S. Mora , E. Sunyer

Active emulsions and liquid crystalline shells are intriguing and experimentally realisable types of topological matter. Here we numerically study the morphology and spatiotemporal dynamics of a double emulsion, where one or two passive…

The phase behaviour of amphiphilic multiblock copolymers with a large number of blocks in semidilute solutions is studied by lattice Monte Carlo simulations. The influence on the resulting structures of the concentration, the solvent…

Soft Condensed Matter · Physics 2016-08-18 Virginie Hugouvieux , Monique A. V. Axelos , Max Kolb

We have recently developed a simulation approach to calculate the equilibrium phase diagram of particle-based microphase formers. Here, this approach is used to calculate the phase behavior of the square-well linear model for different…

Soft Condensed Matter · Physics 2016-08-02 Yuan Zhuang , Patrick Charbonneau

It is increasingly being realized that liquid-crystalline features can play an important role in the properties and dynamics of cell monolayers. Here, we present a cell-based model of cell layers, based on the phase-field formulation, that…

Soft Condensed Matter · Physics 2022-04-28 Aleksandra Ardaševa , Romain Mueller , Amin Doostmohammadi

Biomolecular condensates are essential for cellular organization and result from phase separation in systems far from thermodynamic equilibrium. Among various models, chemically active droplets play a significant role, consisting of…

Soft Condensed Matter · Physics 2025-05-19 Jacques Fries , Roxanne Berthin , Chengjie Luo , Marie Jardat , David Zwicker , Vincent Dahirel , Pierre Illien

Biomolecular phase separation is typically attributed to the polymer physics of long, disordered chains. However, the underlying chemical grammar, i.e. the specific interactions between protein and RNA building blocks, remains poorly…

Biological Physics · Physics 2026-04-21 Greta Grassmann , Giancarlo Ruocco , Mattia Miotto

Droplet formation has emerged as an essential concept for the spatiotemporal organisation of biomolecules in cells. However, classical descriptions of droplet dynamics based on passive liquid-liquid phase separation cannot capture the…

Biological Physics · Physics 2025-11-14 David Zwicker , Oliver W. Paulin , Cathelijne ter Burg

A simple model of an active colloid consisting of dumbbell-shaped particles that cyclically change their length without propelling themselves is proposed and analyzed. At nanoscales, it represents an idealization for bacterial cytoplasm or…

Adaptation and Self-Organizing Systems · Physics 2020-01-28 Yuki Koyano , Hiroyuki Kitahata , Alexander S. Mikhailov

Models of adhesion of extended particles on linear and planar substrates are of interest in interpreting surface deposition in colloid, polymer, and certain biological systems. An introduction is presented to recent theoretical advances in…

Condensed Matter · Physics 2016-11-03 Vladimir Privman

A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium…

Soft Condensed Matter · Physics 2021-12-21 Marco Baiesi , Stefano Iubini , Enzo Orlandini

Whereas entropy can induce phase behavior that is as rich as seen in energetic systems, microphase separation remains a very rare phenomenon in entropic systems. In this paper, we present a density functional approach to study the…

Soft Condensed Matter · Physics 2009-11-10 Paul P. F. Wessels , Bela M. Mulder

Proteins and nucleic acids can spontaneously self-assemble into membraneless droplet-like compartments, both in vitro and in vivo. A key component of these droplets are multi-valent proteins that possess several adhesive domains with…

Biomolecules · Quantitative Biology 2020-01-10 Srivastav Ranganathan , Eugene Shakhnovich

Mixtures of microtubules and molecular motors form active materials with diverse dynamical behaviors that vary based on their constituents' molecular properties. We map the non-equilibrium phase diagram of microtubules and tip-accumulating…

Soft Condensed Matter · Physics 2021-08-04 Bezia Lemma , Noah P. Mitchell , Radhika Subramanian , Daniel J. Needleman , Zvonimir Dogic

We show that a viscoelastic thin sheet driven out of equilibrium by active structural remodelling develops a rich variety of shapes as a result of a competition between viscous relaxation and activity. In the regime where active processes…

Soft Condensed Matter · Physics 2020-02-26 D. A. Matoz-Fernandez , Fordyce A. Davidson , Nicola R. Stanley-Wall , Rastko Sknepnek

We have constructed a model for the kinetics of rupture of membranes under tension, applying physical principles relevant to lipid bilayers held together by hydrophobic interactions. The membrane is characterized by the bulk compressibility…

Biological Physics · Physics 2009-11-07 Luc Fournier , Bela Joos

Phase separation routinely occurs in both living and synthetic systems. These phases are often complex and distinguished by features including crystallinity, nematic order, and a host of other nonconserved order parameters. For systems at…

Statistical Mechanics · Physics 2025-12-08 Daniel Evans , Ahmad K. Omar

In living cells, cycles of formation and dissolution of liquid droplets can mediate biological functions such as DNA repair. However, the minimal physicochemical prerequisite for such droplet oscillations remains elusive. Here, we present a…

Soft Condensed Matter · Physics 2025-03-17 Ivar S. Haugerud , Hidde D. Vuijk , Job Boekhoven , Christoph A. Weber

Active glasses refer to a class of driven non-equilibrium systems that share remarkably similar dynamical behavior as conventional glass-formers in equilibrium. Glass-like dynamical characteristics have been observed in various biological…

Soft Condensed Matter · Physics 2024-12-24 Subhodeep Dey , Smarajit Karmakar