arXiv subjects

Jörn Dunkel

Publications and source records attributed to Jörn Dunkel.

At least 55 records · Page 3Linked to original sources

arXiv2018

Stokes' second problem and reduction of inertia in active fluids

We study a generalized Navier-Stokes model describing the thin-film flows in non-dilute suspensions of ATP-driven microtubules or swimming bacteria that are enclosed by a moving ring-shaped container. Considering Stokes' second problem, which concerns the motion of an oscillating boundary, our numerical analysis predicts that a periodically rotating ring will oscillate at a higher frequency in an active fluid than in a passive fluid, due to an activity-induced reduction of the fluid inertia. In the case of a freely suspended fluid-container system that is isolated from external forces or torques, active fluid stresses can induce large fluctuations in the container's angular momentum if the confinement radius matches certain multiples of the intrinsic vortex size of the active suspension. This effect could be utilized to transform collective microscopic swimmer activity into macroscopic motion in optimally tuned geometries.

cond-mat.soft↗

arXiv2018

Information transmission and signal permutation in active flow networks

Recent experiments show that both natural and artificial microswimmers in narrow channel-like geometries will self-organise to form steady, directed flows. This suggests that networks of flowing active matter could function as novel autonomous microfluidic devices. However, little is known about how information propagates through these far-from-equilibrium systems. Through a mathematical analogy with spin-ice vertex models, we investigate here the input-output characteristics of generic incompressible active flow networks (AFNs). Our analysis shows that information transport through an AFN is inherently different from conventional pressure or voltage driven networks. Active flows on hexagonal arrays preserve input information over longer distances than their passive counterparts and are highly sensitive to bulk topological defects, whose presence can be inferred from marginal input-output distributions alone. This sensitivity further allows controlled permutations on parallel inputs, revealing an unexpected link between active matter and group theory that can guide new microfluidic mixing strategies facilitated by active matter and aid the design of generic autonomous information transport networks.

physics.bio-ph↗

arXiv2018

Geometry of wave propagation on active deformable surfaces

Fundamental biological and biomimetic processes, from tissue morphogenesis to soft robotics, rely on the propagation of chemical and mechanical surface waves to signal and coordinate active force generation. The complex interplay between surface geometry and contraction wave dynamics remains poorly understood, but will be essential for the future design of chemically-driven soft robots and active materials. Here, we couple prototypical chemical wave and reaction-diffusion models to non-Euclidean shell mechanics to identify and characterize generic features of chemo-mechanical wave propagation on active deformable surfaces. Our theoretical framework is validated against recent data from contractile wave measurements on ascidian and starfish oocytes, producing good quantitative agreement in both cases. The theory is then applied to illustrate how geometry and preexisting discrete symmetries can be utilized to focus active elastic surface waves. We highlight the practical potential of chemo-mechanical coupling by demonstrating spontaneous wave-induced locomotion of elastic shells of various geometries. Altogether, our results show how geometry, elasticity and chemical signaling can be harnessed to construct dynamically adaptable, autonomously moving mechanical surface wave guides.

cond-mat.soft↗

arXiv2018

Controlling fracture cascades through twisting and quenching

Fracture limits the structural stability of macroscopic and microscopic materials, from beams and bones to microtubules and nanotubes. Despite recent progress, fracture control continues to present profound practical and theoretical challenges. A famous longstanding problem posed by Feynman asks why brittle elastic rods appear almost always to fragment into at least three pieces when placed under large bending stresses. Feynman's observation raises fundamental questions about the existence of protocols that can robustly induce binary fracture in brittle materials. Using experiments, simulations and analytical scaling arguments, we demonstrate controlled binary fracture of brittle elastic rods for two distinct protocols based on twisting and nonadiabatic quenching. Our experimental data for twist-controlled fracture agree quantitatively with a theoretically predicted phase diagram. Furthermore, we establish novel asymptotic scaling relations for quenched fracture. Due to their general character, these results are expected to apply to torsional and kinetic fracture processes in a wide range of systems.

cond-mat.soft↗

arXiv2018

Functional control of network dynamics using designed Laplacian spectra

Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such systems, the spectrum of the underlying graph Laplacian plays a key role in controlling the matter or information flow. Spectral graph theory has traditionally prioritized unweighted networks. Here, we introduce a complementary framework, providing a mathematically rigorous weighted graph construction that exactly realizes any desired spectrum. We illustrate the broad applicability of this approach by showing how designer spectra can be used to control the dynamics of various archetypal physical systems. Specifically, we demonstrate that a strategically placed gap induces chimera states in Kuramoto-type oscillator networks, completely suppresses pattern formation in a generic Swift-Hohenberg model, and leads to persistent localization in a discrete Gross-Pitaevskii quantum network. Our approach can be generalized to design continuous band gaps through periodic extensions of finite networks.

physics.soc-ph↗

arXiv2017

Anomalous chained turbulence in actively driven flows on spheres

Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for non-equilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in non-planar geometries. The analytical tractability of the theory is demonstrated through exact stationary solutions for the case of a spherical bubble geometry. Direct numerical simulations reveal a curvature-induced transition from a burst phase to an anomalous turbulent phase that differs distinctly from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of anti-ferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network. The coherent motion of the vortex chain network provides an efficient mechanism for upward energy transfer from smaller to larger scales, presenting an alternative to the conventional energy cascade in classical 2D turbulence.

physics.flu-dyn↗

arXiv2017

The nature of triad interactions in active turbulence

Generalized Navier-Stokes (GNS) equations describing three-dimensional (3D) active fluids with flow-dependent spectral forcing have been shown to possess numerical solutions that can sustain significant energy transfer to larger scales by realising chiral Beltrami-type chaotic flows. To rationalise these findings, we study here the triad truncations of polynomial and Gaussian GNS models focusing on modes lying in the energy injection range. Identifying a previously unknown cubic invariant, we show that the asymptotic triad dynamics reduces to that of a forced rigid body coupled to a particle moving in a magnetic field. This analogy allows us to classify triadic interactions by their asymptotic stability: unstable triads correspond to rigid-body forcing along the largest and smallest principal axes, whereas stable triads arise from forcing along the middle axis. Analysis of the polynomial GNS model reveals that unstable triads induce exponential growth of energy and helicity, whereas stable triads develop a limit cycle of bounded energy and helicity. This suggests that the unstable triads dominate the initial relaxation stage of the full hydrodynamic equations, whereas the stable triads determine the statistically stationary state. To test this hypothesis, we introduce and investigate the Gaussian active turbulence model, which develops a Kolmogorov-type $-5/3$ energy spectrum at large wavelengths. Similar to the polynomial case, the steady-state chaotic flows spontaneously accumulate non-zero mean helicity while exhibiting Beltrami statistics and upward energy transport. Our results suggest that self-sustained Beltrami-type flows and an inverse energy cascade may be generic features of 3D active turbulence models with flow-dependent spectral forcing.

physics.flu-dyn↗

arXiv2017

Mode selection in compressible active flow networks

Coherent, large scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by small-scale local energy input. Here, we introduce and explore an analytically tractable nonlinear model for compressible active flow networks. In contrast to thermally-driven systems, we find that active friction selects discrete states with a limited number of oscillation modes activated at distinct fixed amplitudes. Using perturbation theory, we systematically predict the stationary states of noisy networks and find good agreement with a Bayesian state estimation based on a hidden Markov model applied to simulated time series data. Our results suggest that the macroscopic response of active network structures, from actomyosin force networks to cytoplasmic flows, can be dominated by a significantly reduced number of modes, in contrast to energy equipartition in thermal equilibrium. The model is also well-suited to study topological sound modes and spectral band gaps in active matter.

physics.bio-ph↗

arXiv2017

Active matter logic for autonomous microfluidics

Chemically or optically powered active matter plays an increasingly important role in materials design but its computational potential has yet to be explored systematically. The competition between energy consumption and dissipation imposes stringent physical constraints on the information transport in active flow networks, facilitating global optimization strategies that are not well understood. Here, we combine insights from recent microbial experiments with concepts from lattice-field theory and non-equilibrium statistical mechanics to introduce a generic theoretical framework for active matter logic (AML). Highlighting conceptual differences with classical and quantum computation, we demonstrate how the inherent non-locality of incompressible active flow networks can be utilized to construct universal logical operations, Fredkin gates and memory storage in SR latches through the synchronized self-organization of many individual network components. Our work lays the conceptual foundation for developing autonomous microfluidic transport devices driven by bacterial fluids, active liquid crystals or chemically engineered motile colloids.

physics.bio-ph↗

arXiv2017

Kibble-Zurek mechanism in curved elastic surface crystals

Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals, to domain structures formed in the early universe. The Kibble-Zurek (KZ) mechanism describes the topological defect formation in continuous non-equilibrium phase transitions with a constant finite quench rate. Universal KZ scaling laws have been verified experimentally and numerically for second-order transitions in planar Euclidean geometries, but their validity for discontinuous first-order transitions in curved and topologically nontrivial systems still poses an open question. Here, we use recent experimentally confirmed theory to investigate topological defect formation in curved elastic surface crystals formed by stress-quenching a bilayer material. Studying both spherical and toroidal crystals, we find that the defect densities follow KZ-type power laws independent of surface geometry and topology. Moreover, the nucleation sequences agree with recent experimental observations for spherical colloidal crystals. These results suggest that KZ scaling laws hold for a much broader class of dynamical phase transitions than previously thought, including non-thermal first-order transitions in non-planar geometries.

cond-mat.soft↗

arXiv2017

Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break mirror symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls mirror-symmetry breaking and the emergence of a 3D inverse cascade.

physics.flu-dyn↗

arXiv2016

Antipolar ordering of topological defects in active liquid crystals

ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional active liquid crystals (ALCs) that exhibit a rich creation and annihilation dynamics of topological defects, reminiscent of particle-pair production processes in quantum systems. This recent discovery has sparked considerable interest but a quantitative theoretical description is still lacking. We present and validate a minimal continuum theory for this new class of active matter systems by generalizing the classical Landau-de Gennes free-energy to account for the experimentally observed spontaneous buckling of motor-driven extensile microtubule bundles. The resulting model agrees with recently published data and predicts a regime of antipolar order. Our analysis implies that ALCs are governed by the same generic ordering principles that determine the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer materials. Moreover, the theory manifests an energetic analogy with strongly interacting quantum gases. Generally, our results suggest that complex non-equilibrium pattern-formation phenomena might be predictable from a few fundamental symmetry-breaking and scale-selection principles.

cond-mat.soft↗

arXiv2016

Geometry-dependent viscosity reduction in sheared active fluids

We investigate flow pattern formation and viscosity reduction mechanisms in active fluids by studying a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present exact analytical solutions including stress-free vortex lattices and introduce a computational framework that allows the efficient treatment of previously intractable higher-order shear boundary conditions. Large-scale parameter scans identify the conditions for spontaneous flow symmetry breaking, geometry-dependent viscosity reduction and negative-viscosity states amenable to energy harvesting in confined suspensions. The theory uses only generic assumptions about the symmetries and long-wavelength structure of active stress tensors, suggesting that inviscid phases may be achievable in a broad class of non-equilibrium fluids by tuning confinement geometry and pattern scale selection.

physics.flu-dyn↗

arXiv2016

Stochastic cycle selection in active flow networks

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such non-equilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of non-biological far-from-equilibrium networks, including actively controlled information flows, and establishes a new correspondence between active flow networks and generalized ice-type models.

physics.bio-ph↗

arXiv2015

Ferromagnetic and antiferromagnetic order in bacterial vortex lattices

Despite their inherent non-equilibrium nature, living systems can self-organize in highly ordered collective states that share striking similarities with the thermodynamic equilibrium phases of conventional condensed matter and fluid systems. Examples range from the liquid-crystal-like arrangements of bacterial colonies, microbial suspensions and tissues to the coherent macro-scale dynamics in schools of fish and flocks of birds. Yet, the generic mathematical principles that govern the emergence of structure in such artificial and biological systems are elusive. It is not clear when, or even whether, well-established theoretical concepts describing universal thermostatistics of equilibrium systems can capture and classify ordered states of living matter. Here, we connect these two previously disparate regimes: Through microfluidic experiments and mathematical modelling, we demonstrate that lattices of hydrodynamically coupled bacterial vortices can spontaneously organize into distinct phases of ferro- and antiferromagnetic order. The preferred phase can be controlled by tuning the vortex coupling through changes of the inter-cavity gap widths. The emergence of opposing order regimes is tightly linked to the existence of geometry-induced edge currents, reminiscent of those in quantum systems. Our experimental observations can be rationalized in terms of a generic lattice field theory, suggesting that bacterial spin networks belong to the same universality class as a wide range of equilibrium systems.

cond-mat.soft↗

arXiv2015

Hydrodynamic length-scale selection and effective viscosity in microswimmer suspensions

A universal characteristic of mesoscale turbulence in active suspensions is the emergence of a typical vortex length scale, distinctly different from the scale-invariance of turbulent high-Reynolds number flows. Collective length-scale selection has been observed in bacterial fluids, endothelial tissue and active colloides, yet the physical origins of this phenomenon remain elusive. Here, we systematically derive an effective fourth-order field theory from a generic microscopic model that allows us to predict the typical vortex size in microswimmer suspensions. Building on a self-consistent closure condition, the derivation shows that the vortex length scale is determined by the competition between local alignment forces and intermediate-range hydrodynamic interactions. Vortex structures found in simulations of the theory agree with recent measurements in Bacillus subtilis suspensions. Moreover, our approach correctly predicts an effective viscosity enhancement (reduction), as reported experimentally for puller (pusher) microorganisms.

cond-mat.soft↗

arXiv2015

Cortical microtubule nucleation can organise the cytoskeleton of $Drosophila$ oocytes to define the anteroposterior axis

Many cells contain non-centrosomal arrays of microtubules (MT), but the assembly, organisation and function of these arrays are poorly understood. We present the first theoretical model for the non-centrosomal MT cytoskeleton in $Drosophila$ oocytes, in which $bicoid$ and $oskar$ mRNAs become localised to establish the anterior-posterior body axis. Constrained by experimental measurements, the model shows that a simple gradient of cortical MT nucleation is sufficient to reproduce the observed MT distribution, cytoplasmic flow patterns and localisation of $oskar$ and naive $bicoid$ mRNAs. Our simulations exclude a major role for cytoplasmic flows in localisation and reveal an organisation of the MT cytoskeleton that is more ordered than previously thought. Furthermore, modulating cortical MT nucleation induces a bifurcation in cytoskeletal organisation that accounts for the phenotypes of polarity mutants. Thus, our three-dimensional model explains many features of the MT network and highlights the importance of differential cortical MT nucleation for axis formation.

q-bio.SC↗

arXiv2015

Curvature-controlled defect localization in crystalline wrinkling patterns

We investigate the influence of curvature and topology on crystalline wrinkling patterns in generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elastic materials, thus promising improved control over hierarchical bending, buckling or folding processes. Generally, this study suggests that bilayer systems provide an inexpensive yet valuable experimental test-bed for exploring the effects of geometrically induced forces on assemblies of topological charges.

cond-mat.soft↗