arXiv subjects

Matthew S. Turner

Publications and source records attributed to Matthew S. Turner.

At least 19 recordsLinked to original sources

arXiv2024

Membrane tubes with active pumping: water transport, vacuole formation and osmoregulation

The need for organisms to regulate their volume and osmolarity when surrounded by freshwater is a basic physical challenge for many bacteria, protists and algae. Taking inspiration from the contractile vacuole complex found in many protists, we discuss how simple models of active membrane tubes can give insights into the fluid and active ionic transport properties of such systems. We show that a simple membrane tube with unidirectional ion pumps, and passive ion and water channels, forms a large vacuole due to osmotically-driven water flow and that this can be used to actively pump water out of the cell interior. We discuss the use of this system as a possible minimal method for osmoregulation.

physics.bio-ph↗

arXiv2024

Nash epidemics

Faced with a dangerous epidemic humans will spontaneously social distance to reduce their risk of infection at a socio-economic cost. Compartmentalised epidemic models have been extended to include this endogenous decision making: Individuals choose their behaviour to optimise a utility function, self-consistently giving rise to population behaviour. Here we study the properties of the resulting Nash equilibria, in which no member of the population can gain an advantage by unilaterally adopting different behaviour. We leverage a new analytic solution to obtain, (1) a simple relationship between rational social distancing behaviour and the current number of infections; (2) new scaling results for how the infection peak and number of total cases depend on the cost of contracting the disease; (3) characteristic infection costs that divide regimes of strong and weak behavioural response and depend only on the basic reproduction number of the disease; (4) a closed form expression for the value of the utility. We discuss how these analytic results provide a deep and intuitive understanding into the disease dynamics, useful for both individuals and policymakers. In particular the relationship between social distancing and infections represents a heuristic that could be communicated to the population to encourage, or "bootstrap", rational behaviour.

econ.TH↗

arXiv2024

Rational social distancing policy during epidemics with limited healthcare capacity

Epidemics of infectious diseases posing a serious risk to human health have occurred throughout history. During recent epidemics there has been much debate about policy, including how and when to impose restrictions on behaviour. Policymakers must balance a complex spectrum of objectives, suggesting a need for quantitative tools. Whether health services might be `overwhelmed' has emerged as a key consideration. Here we show how costly interventions, such as taxes or subsidies on behaviour, can be used to exactly align individuals' decision making with government preferences even when these are not aligned. In order to achieve this, we develop a nested optimisation algorithm of both the government intervention strategy and the resulting equilibrium behaviour of individuals. We focus on a situation in which the capacity of the healthcare system to treat patients is limited and identify conditions under which the disease dynamics respect the capacity limit. We find an extremely sharp drop in peak infections at a critical maximum infection cost in the government's objective function. This is in marked contrast to the gradual reduction of infections if individuals make decisions without government intervention. We find optimal interventions vary less strongly in time when interventions are costly to the government and that the critical cost of the policy switch depends on how costly interventions are.

econ.TH↗

arXiv2024

Rational social distancing in epidemics with uncertain vaccination timing

During epidemics people may reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision-making depends on information about vaccination timing in a differential game in which individual decision-making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We predict stronger social distancing the earlier the vaccination is expected and also the more sharply peaked its probability distribution. In particular, equilibrium social distancing only meaningfully deviates from the no-vaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting.

econ.TH↗

arXiv2023

Environmental path-entropy and collective motion

Inspired by the swarming or flocking of animal systems we study groups of agents moving in unbounded 2D space. Individual trajectories derive from a ``bottom-up'' principle: individuals reorient to maximise their future path entropy over environmental states. This can be seen as a proxy for keeping options open, a principle that may confer evolutionary fitness in an uncertain world. We find an ordered (co-aligned) state naturally emerges, as well as disordered states or rotating clusters; similar phenotypes are observed in birds, insects and fish, respectively. The ordered state exhibits an order-disorder transition under two forms of noise: (i) standard additive orientational noise, applied to the post-decision orientations (ii) ``cognitive'' noise, overlaid onto each individual's model of the future paths of other agents. Unusually, the order increases at low noise, before later decreasing through the order-disorder transition as the noise increases further.

cond-mat.stat-mech↗

arXiv2022

Learning to swim efficiently in a nonuniform flow field

Microswimmers can acquire information on the surrounding fluid by sensing mechanical queues. They can then navigate in response to these signals. We analyse this navigation by combining deep reinforcement learning with direct numerical simulations to resolve the hydrodynamics. We study how local and non-local information can be used to train a swimmer to achieve particular swimming tasks in a non-uniform flow field, in particular a zig-zag shear flow. The swimming tasks are (1) learning how to swim in the vorticity direction, (2) the shear-gradient direction, and (3) the shear flow direction. We find that access to lab frame information on the swimmer's instantaneous orientation is all that is required in order to reach the optimal policy for (1,2). However, information on both the translational and rotational velocities seem to be required to achieve (3). Inspired by biological microorganisms we also consider the case where the swimmers sense local information, i.e. surface hydrodynamic forces, together with a signal direction. This might correspond to gravity or, for micro-organisms with light sensors, a light source. In this case, we show that the swimmer can reach a comparable level of performance as a swimmer with access to lab frame variables. We also analyse the role of different swimming modes, i.e. pusher, puller, and neutral swimmers.

physics.flu-dyn↗

arXiv2022

Dynamics of microswimmers near a liquid-liquid interface with viscosity difference

Transport of material across liquid interfaces is ubiquitous for living cells and is also a crucial step in drug delivery and in many industrial processes. The fluids that are present on either side of the interfaces will usually have different viscosities. We present a physical model for the dynamics of microswimmers near a soft and penetrable interface that we solve using computer simulations of Navier-Stokes flows. The literature contains studies of similar isoviscous fluid systems, where the two fluids have the same viscosity. Here we extend this to the more general case where they have different viscosities. We investigate the effect of the fluid viscosity ratio on the movement patterns of microswimmers. We find that swimmers systematically reorientate towards the region containing the lower viscosity fluid. Ultimately this is expected to drive the swimmers to behave as if they are more inclined to swim in low viscosity fluids. Furthermore, in addition to the types of swimming already reported in the isoviscous system, i.e. bouncing, sliding and penetrating, we observed a hovering motion, in which strong pullers swim parallel to the interface with a certain distance, which is consistent with the dynamics of such swimmers near the solid wall.

cond-mat.soft↗

arXiv2022

Dynamics of microswimmers near a soft penetrable interface

Few simulations exist for microswimmers near deformable interfaces. Here, we present numerical simulations of the hydrodynamic flows associated with a single microswimmer embedded in a binary fluid mixture. The two fluids demix, separated by a penetrable and deformable interface that we assume to be initially prepared in its planar ground-state. We find that the microswimmer can either penetrate the interface, move parallel to it or bounce back off it. We analyze how the trajectory depends on the swimmer type (pusher/puller) and the angle of incidence with respect to the interface. Our simulations are performed in a system with periodic boundary conditions, corresponding to an infinite array of fluid interfaces. A puller reaches a steady state in which it either swims parallel to the interface or selects a perpendicular orientation, repeatedly penetrating through the interface. In contrast, a pusher follows a bouncing trajectory between two interfaces. We discuss several examples in biology in which swimmers penetrate soft interfaces. Our work can be seen as a highly simplified model of such processes.

cond-mat.soft↗

arXiv2022

Collective Motion of Quincke Rollers with Fully Resolved Hydrodynamics

A Quincke roller is a unique active particle that can run and tumble freely on a flat plate due to the torque generated by a uniform DC electric field applied perpendicular to the plate. A system involving many such particles exhibits a variety of collective dynamics, such as the disordered gas, polar liquid, and active crystal states. We performed direct numerical simulations of a three-dimensional system containing many self-rotating particles to explicitly resolve the hydrodynamic interactions among rotating particles. The collective motion depends on the magnitude of the dipole moments induced on the dielectric particles, the area fraction of particles, and the strength of interparticle attraction. We find that the highly ordered polar liquid state is destabilized by the hydrodynamic interaction between rotating particles at high densities: the near-field lubrication interaction becomes dominant over far-field effects as the interparticle separation becomes shorter.

cond-mat.soft↗

arXiv2022

Nash Neural Networks : Inferring Utilities from Optimal Behaviour

We propose Nash Neural Networks ($N^3$) as a new type of Physics Informed Neural Network that is able to infer the underlying utility from observations of how rational individuals behave in a differential game with a Nash equilibrium. We assume that the dynamics for both the population and the individual are known, but not the payoff function, which specifies the cost per unit time of being in any particular state. We construct our network in such a way that the Euler-Lagrange equations of the corresponding optimal control problem are satisfied and the optimal control is self-consistently determined. In this way, we are able to learn the unknown payoff function in an unsupervised manner. We have applied the $N^3$ to study the optimal behaviour during epidemics, in which individuals can choose to socially distance depending on the state of the pandemic and the cost of being infected. Training our network against synthetic data for a simple SIR model, we showed that it is possible to accurately reproduce the hidden payoff function, in such a way that the game dynamics are respected. Our approach will have far-reaching applications, as it allows one to infer utilities from behavioural data, and can thus be applied to study a wide array of problems in science, engineering, economics and government planning.

cs.LG↗

arXiv2021

The role of the cell cycle in collective cell dynamics

Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network controlling growth and division, and couple this to the physical forces arising within the cell collective. We analyse this model using both particle-based computer simulations and a continuum theory. We focus on 2D colonies confined in a channel. These develop moving growth fronts of dividing cells with quiescent cells in the interior. The profile and speed of these fronts are non-trivially related to the substrate friction and the cell cycle parameters, providing a possible approach to measure such parameters in experiments.

physics.bio-ph↗

arXiv2021

Whirligig Beetles as Corralled Active Brownian Particles

We study the collective dynamics of groups of whirligig beetles Dineutus discolor (Coleoptera: Gyrinidae) swimming freely on the surface of water. We extract individual trajectories for each beetle, including positions and orientations, and use this to discover (i) a density dependent speed scaling like $v\simρ^{-ν}$ with $ν\approx0.4$ over two orders of magnitude in density (ii) an inertial delay for velocity alignment of $\sim 13$ ms and (iii) coexisting high and low density phases, consistent with motility induced phase separation (MIPS). We modify a standard active brownian particle (ABP) model to a Corralled ABP (CABP) model that functions in open space by incorporating a density-dependent reorientation of the beetles, towards the cluster. We use our new model to test our hypothesis that a MIPS (or a MIPS like effect) can explain the co-occurrence of high and low density phases we see in our data. The fitted model then successfully recovers a MIPS-like condensed phase for $N=200$ and the absence of such a phase for smaller group sizes $N=50,100$.

q-bio.QM↗

arXiv2020

Measuring Gaussian rigidity using curved substrates

The Gaussian (saddle splay) rigidity of fluid membranes controls their equilibrium topology but is notoriously difficult to measure. In lipid mixtures, typical of living cells, linear interfaces separate liquid ordered (LO) from liquid disordered (LD) bilayer phases at subcritical temperatures. Here we consider such membranes supported by curved supports that thereby control the membrane curvatures. We show how spectral analysis of the fluctuations of the LO-LD interface provides a novel way of measuring the difference in Gaussian rigidity between the two phases. We provide a number of conditions for such interface fluctuations to be both experimentally measurable and sufficiently sensitive to the value of the Gaussian rigidity, whilst remaining in the perturbative regime of our analysis.

cond-mat.soft↗

arXiv2020

Dynamics of passive and active membrane tubes

Utilising Onsager's variational formulation, we derive dynamical equations for the relaxation of a fluid membrane tube in the limit of small deformation, allowing for a contrast of solvent viscosity across the membrane and variations in surface tension due to membrane incompressibility. We compute the relaxation rates, recovering known results in the case of purely axis-symmetric perturbations and making new predictions for higher order (azimuthal) $m$-modes. We analyse the long and short wavelength limits of these modes by making use of various asymptotic arguments. We incorporate stochastic terms to our dynamical equations suitable to describe both passive thermal forces and non-equilibrium active forces. We derive expressions for the fluctuation amplitudes, an effective temperature associated with active fluctuations, and the power spectral density for both the thermal and active fluctuations. We discuss an experimental assay that might enable measurement of these fluctuations to infer the properties of the active noise. Finally we discuss our results in the context of active membranes more generally and give an overview of some open questions in the field.

cond-mat.soft↗

arXiv2020

Shear-driven instabilities of membrane tubes and dynamin-induced scission

Motivated by the mechanics of dynamin-mediated membrane tube fission we analyse the stability of fluid membrane tubes subjected to shear flow in azimuthal direction. We find a novel helical instability driven by the membrane shear flow which results in a non-equilibrium steady state for the tube fluctuations. This instability has its onset at shear rates that may be physiologically accessible under the action of dynamin and could also be probed using in-vitro experiments on membrane nanotubes, e.g. using magnetic tweezers. We discuss how such an instability may play a role in the mechanism for dynamin-mediated membrane tube fission.

physics.bio-ph↗

arXiv2019

Intrinsically motivated collective motion

Collective motion is found in various animal systems, active suspensions and robotic or virtual agents. This is often understood using high level models that directly encode selected empirical features, such as co-alignment and cohesion. Can these features be shown to emerge from an underlying, low-level principle? We find that they emerge naturally under Future State Maximisation (FSM). Here agents perceive a visual representation of the world around them, such as might be recorded on a simple retina, and then move to maximise the number of different visual environments that they expect to be able to access in the future. Such a control principle may confer evolutionary fitness in an uncertain world by enabling agents to deal with a wide variety of future scenarios. The collective dynamics that spontaneously emerge under FSM resemble animal systems in several qualitative aspects, including cohesion, co-alignment and collision suppression, none of which are explicitly encoded in the model. A multi-layered neural network trained on simulated trajectories is shown to represent a heuristic mimicking FSM. Similar levels of reasoning would seem to be accessible under animal cognition, demonstrating a possible route to the emergence of collective motion in social animals directly from the control principle underlying FSM. Such models may also be good candidates for encoding into possible future realisations of artificial "intelligent" matter, able to sense light, process information and move.

physics.bio-ph↗

arXiv2019

Density distributions and depth in flocks

Recent experimental evidence suggests that interactions in flocks of birds do not involve a characteristic length scale. Bird flocks have also been revealed to have an inhomogeneous density distribution, with the density of birds near the border greater than near the centre. We introduce a strictly metric-free model for collective behaviour that incorporates a distributed motional bias, providing control of the density distribution. A simple version of this model is then able to provide a good fit to published data for the density variation across flocks of Starlings. We find that it is necessary for individuals on the edge of the flock to have an inward motional bias but that birds in the interior of the flock instead must have an outward bias. We discuss the ability of individuals to determine their depth within a flock and show how this might be achieved by relatively simple analysis of their visual environment.

q-bio.QM↗

arXiv2018

Hydro-osmotic instabilities in active membrane tubes

We study a membrane tube with unidirectional ion pumps driving an osmotic pressure difference. A pressure driven peristaltic instability is identified, qualitatively distinct from similar tension-driven Rayleigh type instabilities on membrane tubes. We discuss how this instability could be related to the function and biogenesis of membrane bound organelles, in particular the contractile vacuole complex. The unusually long natural wavelength of this instability is in agreement with that observed in cells.

physics.bio-ph↗