arXiv subjects

Francis G. Woodhouse

Publications and source records attributed to Francis G. Woodhouse.

15 recordsLinked to original sources

arXiv2021

Crowded transport within networked representations of complex geometries

Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport phenomena. However, in general, the interplay between crowding and geometry in complex real-life environments is poorly understood. Existing analytical methodologies are not always readily extendable to heterogeneous environments: in these situations predictions of crowded transport behaviour within heterogeneous environments rely on computationally intensive mesh-based approaches. Here, we take a different approach by employing networked representations of complex environments to provide an efficient framework within which the interactions between networked geometry and crowding can be explored. We demonstrate how the framework can be used to: extract detailed information at the level of the whole population or an individual within it; identify the topological features of environments that enable accurate prediction of transport phenomena; and, provide insights into the design of optimal environments.

physics.soc-ph↗

arXiv2019

Displacement of transport processes on networked topologies

Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a definition fails to incorporate information of the actual path the particle traversed. In this work we consider another definition for the displacement of a particle on networked topologies. Using this definition, which we term the winding distance, we demonstrate that for Brownian particles, confinement to a network can induce a transition in the mean squared displacement from diffusive to ballistic behaviour, $\langle x^2(t) \rangle \propto t^2$ for long times. A multiple scales approach is used to derive a macroscopic evolution equation for the displacement of a particle and uncover a topological condition for whether this transition in the mean squared displacement will occur. Furthermore, for networks satisfying this topological condition, we identify a prediction of the timescale upon which the displacement transitions to long-time behaviour. Finally, we extend the investigation of displacement on networks to a class of anomalously diffusive transport processes, where we find that the mean squared displacement at long times is affected by both network topology and the character of the transport process.

cond-mat.stat-mech↗

arXiv2018

Autonomous actuation of zero modes in mechanical networks far from equilibrium

A zero mode, or floppy mode, is a non-trivial coupling of mechanical components yielding a degree of freedom with no resistance to deformation. Engineered zero modes have the potential to act as microscopic motors or memory devices, but this requires an internal actuation mechanism that can overcome unwanted fluctuations in other modes and the dissipation inherent in real systems. In this work, we show theoretically and experimentally that complex zero modes in mechanical networks can be selectively mobilized by non-equilibrium activity. We find that a correlated active bath actuates an infinitesimal zero mode while simultaneously suppressing fluctuations in higher modes compared to thermal fluctuations, which we experimentally mimic by high frequency shaking of a physical network. Furthermore, self-propulsive dynamics spontaneously mobilise finite mechanisms as exemplified by a self-propelled topological soliton. Non-equilibrium activity thus enables autonomous actuation of coordinated mechanisms engineered through network topology.

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

Topology-dependent density optima for efficient simultaneous network exploration

A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimise this process: how many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric exclusion process is optimised at a searcher density that is well predicted by the spectral gap. Furthermore, we find that non-equilibrium processes, realised through the addition of bias, can support significantly increased density optima. Our results suggest novel hybrid strategies of serial and parallel search for efficient information gathering in social interaction and biological transport networks.

math.OC↗

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

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↗

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↗

arXiv2013

Cytoplasmic Streaming in Plant Cells Emerges Naturally by Microfilament Self-Organization

Many cells exhibit large-scale active circulation of their entire fluid contents, a process termed cytoplasmic streaming. This phenomenon is particularly prevalent in plant cells, often presenting strikingly regimented flow patterns. The driving mechanism in such cells is known: myosin-coated organelles entrain cytoplasm as they process along actin filament bundles fixed at the periphery. Still unknown, however, is the developmental process which constructs the well-ordered actin configurations required for coherent cell-scale flow. Previous experimental works on streaming regeneration in cells of Characean algae, whose longitudinal flow is perhaps the most regimented of all, hint at an autonomous process of microfilament self-organization driving the formation of streaming patterns during morphogenesis. Working from first principles, we propose a robust model of streaming emergence that combines motor dynamics with both micro- and macroscopic hydrodynamics to explain how several independent processes, each ineffectual on its own, can reinforce to ultimately develop the patterns of streaming observed in the Characeae and other streaming species.

cond-mat.soft↗

arXiv2013

Membrane Viscosity Determined from Shear-Driven Flow in Giant Vesicles

The viscosity of lipid bilayer membranes plays an important role in determining the diffusion constant of embedded proteins and the dynamics of membrane deformations, yet it has historically proven very difficult to measure. Here we introduce a new method based on quantification of the large-scale circulation patterns induced inside vesicles adhered to a solid surface and subjected to simple shear flow in a microfluidic device. Particle Image Velocimetry based on spinning disk confocal imaging of tracer particles inside and outside of the vesicle, and tracking of phase-separated membrane domains are used to reconstruct the full three-dimensional flow pattern induced by the shear. These measurements show excellent agreement with the predictions of a recent theoretical analysis, and allow direct determination of the membrane viscosity.

cond-mat.soft↗

arXiv2013

Confinement Stabilizes a Bacterial Suspension into a Spiral Vortex

Confining surfaces play crucial roles in dynamics, transport and order in many physical systems, but their effects on active matter, a broad class of dynamically self-organizing systems, are poorly understood. We investigate here the influence of global confinement and surface curvature on collective motion by studying the flow and orientational order within small droplets of a dense bacterial suspension. The competition between radial confinement, self-propulsion, steric interactions and hydrodynamics robustly induces an intriguing steady single-vortex state, in which cells align in inwardly-spiralling patterns accompanied by a thin counterrotating boundary layer. A minimal continuum model is shown to be in good agreement with these observations.

cond-mat.soft↗

arXiv2013

Spontaneous Circulation of Confined Active Suspensions

Many active fluid systems encountered in biology are set in total geometric confinement. Cytoplasmic streaming in plant cells is a prominent and ubiquitous example, in which cargo-carrying molecular motors move along polymer filaments and generate coherent cell-scale flow. When filaments are not fixed to the cell periphery, a situation found both in vivo and in vitro, we observe that the basic dynamics of streaming are closely related to those of a non-motile stresslet suspension. Under this model, it is demonstrated that confinement makes possible a stable circulating state; a linear stability analysis reveals an activity threshold for spontaneous auto-circulation. Numerical analysis of the long-time behavior reveals a phenomenon akin to defect separation in nematic liquid crystals, and a high-activity bifurcation to an oscillatory regime.

cond-mat.soft↗

arXiv2012

Shear-Driven Circulation Patterns in Lipid Membrane Vesicles

Recent experiments have shown that when a near-hemispherical lipid vesicle attached to a solid surface is subjected to a simple shear flow it exhibits a pattern of membrane circulation much like a dipole vortex. This is in marked contrast to the toroidal circulation that would occur in the related problem of a drop of immiscible fluid attached to a surface and subjected to shear. This profound difference in flow patterns arises from the lateral incompressibility of the membrane, which restricts the observable flows to those in which the velocity field in the membrane is two-dimensionally divergence free. Here we study these circulation patterns within the simplest model of membrane fluid dynamics. A systematic expansion of the flow field based on Papkovich--Neuber potentials is developed for general viscosity ratios between the membrane and the surrounding fluids. Comparison with experimental results [C. Vézy, G. Massiera, and A. Viallat, Soft Matter 3, 844 (2007)] is made, and it is shown how such studies could allow measurements of the membrane viscosity. Issues of symmetry-breaking and pattern selection are discussed.

physics.flu-dyn↗