arXiv subjects

Ludwig A. Hoffmann

Publications and source records attributed to Ludwig A. Hoffmann.

8 recordsLinked to original sources

arXiv2026

Posture selection in active elastic filaments

Posture control in slender bodies such as snakes and eels arises from the interplay between passive deformation, active internal actuation, and task-level constraints. We formulate a general framework for the selection of stable postures in active elastic filaments subject to distributed forcing from gravity and fluid drag, by combining the constraints of mechanical equilibrium with optimal control theory. Our theory leads to a minimal description in terms of parameters governing the competition between hydrodynamic and gravitational loading, elasticity, and activity. We show that posture selection reflects a trade-off between control cost, function and dynamical stability, leading to the coexistence of distinct solution branches and abrupt transitions between them. Applying the theory to sessile eels in flow, we recover the experimentally observed transition from upright to reclining postures and predict scaling laws for body shape and exposed length. More generally, our results provide a unified perspective on how active filaments can regulate geometry to maintain function in external fields, with implications for biological and artificial systems.

cond-mat.soft↗

arXiv2026

How to grow a straight filament

How can a growing biological filament remain straight despite stochastic fluctuations in growth? Motivated by filamentary structures that develop reproducibly across biological systems, we study the stability of a noisy, growing elastic filament regulated by feedback. We formulate a minimal model in which growth responds to the filament's strain, curvature, and orientation through local or nonlocal spatiotemporal feedback laws. Linear stability analysis identifies the conditions under which these feedback mechanisms stabilize a straight configuration. In the presence of noise, we show that purely local feedback requires orientation sensing to suppress long-wavelength instabilities, whereas nonlocal feedback allows stabilization through proprioceptive (curvature) sensing alone. Coupling to an elastic substrate further suppresses large-scale fluctuations. Our results establish minimal control strategies that ensure robust straight growth and suggest experimental signatures for identifying the feedback mechanisms underlying morphogenesis.

cond-mat.soft↗

arXiv2023

Designing highly efficient lock-and-key interactions in anisotropic active particles

Cluster formation of microscopic swimmers is key to the formation of biofilms and colonies, efficient motion and nutrient uptake, but, in the absence of other interactions, requires high swimmer concentrations to occur. Here we experimentally and numerically show that cluster formation can be dramatically enhanced by an anisotropic swimmer shape. We analyze a class of model microswimmers with a shape that can be continuously tuned from spherical to bent and straight rods. In all cases, clustering can be described by Michaelis-Menten kinetics governed by a single scaling parameter that depends on particle density and shape only. We rationalize these shape-dependent dynamics from the interplay between interlocking probability and cluster stability. The bent rod shape promotes assembly even at vanishingly low particle densities and we identify the most efficient shape to be a semicircle. Our work provides key insights into how shape can be used to rationally design out-of-equilibrium self-organization, key to creating active functional materials and designing targeted two-component drug delivery.

cond-mat.soft↗

arXiv2023

Theory of cellular homochirality and trait evolution in flocking systems

Chirality is a feature of many biological systems and much research has been focused on understanding the origin and implications of this property. Famously, sugars and amino acids found in nature are homochiral, i.e., chiral symmetry is broken and only one of the two possible chiral states is ever observed. Certain types of cells show chiral behavior, too. Understanding the origin of cellular chirality and its effect on tissues and cellular dynamics is still an open problem and subject to much (recent) research, e.g., in the context of drosophila morphogenesis. Here, we develop a simple model to describe the possible origin of homochirality in cells. Combining the Vicsek model for collective behavior with the model of Jafarpour et al., developed to describe the emergence of molecular homochirality, we investigate how a homochiral state might have evolved in cells from an initially symmetric state without any mechanisms that explicitly break chiral symmetry. We investigate the transition to homochirality and show how the "openness" of the system as well as noise determine if and when a globally homochiral state is reached. We discuss how our model can be applied to the evolution of traits in flocking systems in general, or to study systems consisting of multiple interacting species.

q-bio.CB↗

arXiv2023

Tuneable defect-curvature coupling and topological transitions in active shells

Recent experimental observations have suggested that topological defects can facilitate the creation of sharp features in developing embryos. Whereas these observations echo established knowledge about the interplay between geometry and topology in two-dimensional passive liquid crystals, the role of activity has mostly remained unexplored. In this article we focus on deformable shells consisting of either polar or nematic active liquid crystals and demonstrate that activity renders the mechanical coupling between defects and curvature much more involved and versatile than previously thought. Using a combination of linear stability analysis and three-dimensional computational fluid dynamics, we demonstrate that such a coupling can in fact be tuned, depending on the type of liquid crystal order, the specific structure of the defect (i.e. asters or vortices) and the nature of the active forces. In polar systems, this can drive a spectacular transition from spherical to toroidal topology, in the presence of large extensile activity. Our analysis strengthens the idea that defects could serve as topological morphogens and provides a number of predictions that could be tested in in vitro studies, for instance in the context of organoids.

cond-mat.soft↗

arXiv2022

Theory of defect-mediated morphogenesis

Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable active polar liquid crystals. Using a combination of linear stability analysis and computational fluid dynamics, we demonstrate that active layers, such as confined cell monolayers, are unstable to the formation of protrusions in the presence of disclinations. The instability originates from an interplay between the focusing of the elastic forces, mediated by defects, and the renormalization of the system's surface tension by the active flow. The posttransitional regime is also characterized by several complex morphodynamical processes, such as oscillatory deformations, droplet nucleation, and active turbulence. Our findings offer an explanation of recent observations on tissue morphogenesis and shed light on the dynamics of active surfaces in general.

cond-mat.soft↗

arXiv2021

Topology-driven ordering of flocking matter

When interacting motile units self-organize into flocks, they realize one of the most robust ordered state found in nature. However, after twenty five years of intense research, the very mechanism controlling the ordering dynamics of both living and artificial flocks has remained unsettled. Here, combining active-colloid experiments, numerical simulations and analytical work, we explain how flocking liquids heal their spontaneous flows initially plagued by collections of topological defects to achieve long-ranged polar order even in two dimensions. We demonstrate that the self-similar ordering of flocking matter is ruled by a living network of domain walls linking all $\pm 1$ vortices, and guiding their annihilation dynamics. Crucially, this singular orientational structure echoes the formation of extended density patterns in the shape of interconnected bow ties. We establish that this double structure emerges from the interplay between self-advection and density gradients dressing each $-1$ topological charges with four orientation walls. We then explain how active Magnus forces link all topological charges with extended domain walls, while elastic interactions drive their attraction along the resulting filamentous network of polarization singularities. Taken together our experimental, numerical and analytical results illuminate the suppression of all flow singularities, and the emergence of pristine unidirectional order in flocking matter.

cond-mat.soft↗

arXiv2020

Chiral stresses in nematic cell monolayers

Recent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are well described by active nematic hydrodynamics. While recovering some of the hallmark predictions of this framework, however, these experiments have also revealed a number of unexpected features that could be ascribed to the existence of chirality over length scales larger than the typical size of a cell. In this article we elaborate on the microscopic origin of chiral stresses in nematic cell monolayers and investigate how chirality affects the motion of topological defects, as well as the collective motion in stripe-shaped domains. We find that chirality introduces a characteristic asymmetry in the collective cellular flow, from which the ratio between chiral and non-chiral active stresses can be inferred by particle-image-velocimetry measurements. Furthermore, we find that chirality changes the nature of the spontaneous flow transition under confinement and that, for specific anchoring conditions, the latter has the structure of an imperfect pitchfork bifurcation.

cond-mat.soft↗