arXiv subjects

D. A. Head

Publications and source records attributed to D. A. Head.

At least 19 recordsLinked to original sources

arXiv2025

Predicting rigidity and connectivity percolation in disordered particulate networks using graph neural networks

Graph neural networks can accurately predict the chemical properties of many molecular systems, but their suitability for large, macromolecular assemblies such as gels is unknown. Here, graph neural networks were trained and optimised for two large-scale classification problems: the rigidity of a molecular network, and the connectivity percolation status which is non-trivial to determine for systems with periodic boundaries. Models trained on lattice systems were found to achieve accuracies >95% for rigidity classification, with slightly lower scores for connectivity percolation due to the inherent class imbalance in the data. Dynamically generated off-lattice networks achieved consistently lower accuracies overall due to the correlated nature of the network geometry that was absent in the lattices. An open source tool is provided allowing usage of the highest-scoring trained models, and directions for future improved tools to surmount the challenges limiting accuracy in certain situations are discussed.

physics.comp-ph↗

arXiv2015

Importance of non-affine viscoelastic response in disordered fibre networks

Disordered fibre networks are ubiquitous in nature and have a wide range of industrial applications as novel biomaterials. Predicting their viscoelastic response is straightforward for affine deformations that are uniform over all length scales, but when affinity fails, as has been observed experimentally, modelling becomes challenging. Here we introduce a numerical methodology to predict the steady-state viscoelastic spectra and degree of affinity for disordered fibre networks driven at arbitrary frequencies. Applying this method to a peptide gel model reveals a monotonic increase of the shear modulus as the soft, non-affine normal modes are successively suppressed as the driving frequency increases. In addition to being dominated by fibril bending, these low frequency network modes are also shown to be delocalised. The presented methodology provides insights into the importance of non-affinity in the viscoelastic response of peptide gels, and is easily extendible to all types of fibre networks.

cond-mat.soft↗

arXiv2014

Non-equilibrium structure and dynamics in a microscopic model of thin film active gels

In the presence of ATP, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modelling can help to quantify the relationship between individual motors plus filaments to organisation and dynamics on molecular and supra-molecular length scales. Here we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment and detachment, including a differential detachment rate from filament ends, reveals a range of non-equilibrium behaviour. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles or layers, whose stability depends on motor speed and differential end-detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit super-diffusive mass transport, where filament translocation scales with lag time with non-unique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end-detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modelling in the field of active gels.

physics.bio-ph↗

arXiv2013

Local mechanical response in semiflexible polymer networks subjected to an axisymmetric prestress

Analytical and numerical calculations are presented for the mechanical response of fiber networks in a state of axisymmetric prestress, in the limit where geometric non-linearities such as fiber rotation are negligible. This allows us to focus on the anisotropy deriving purely from the non-linear force-extension curves of individual fibers. The number of independent elastic coefficients for isotropic, axisymmetric and fully anisotropic networks are enumerated, before deriving expressions for the response to a locally applied force that can be tested against e.g. microrheology experiments. Localised forces can generate anisotropy away from the point of application, so numerical integration of non-linear continuum equations is employed to determine the stress field, and induced mechanical anisotropy, at points located directly behind and in front of a force monopole. Results are presented for the wormlike chain model in normalised forms, allowing them to be easily mapped to a range of systems. Finally, the relevance of these findings to naturally occurring systems and directions for future investigation are discussed.

physics.bio-ph↗

arXiv2013

Linear surface roughness growth and flow smoothening in a three-dimensional biofilm model

The sessile microbial communities known as biofilms exhibit varying architectures as environmental factors are varied, which for immersed biofilms includes the shear rate of the surrounding flow. Here we modify an established agent-based biofilm model to include affine flow, and employ it to analyse the growth of surface roughness of single-species, three-dimensional biofilms. We find linear growth laws for surface geometry in both horizontal and vertical directions, and measure the thickness of the active surface layer, which is shown to anti-correlate with roughness. Flow is shown to monotonically reduce surface roughness without affecting the thickness of the active layer. We argue that the rapid roughening is due to non-local surface interactions mediated by the nutrient field, which are curtailed when advection competes with diffusion. We further argue the need for simplified models to elucidate the underlying mechanisms coupling flow to growth.

physics.bio-ph↗

arXiv2010

Non-local fluctuation correlations in active gels

Many active materials and biological systems are driven far from equilibrium by embedded agents that spontaneously generate forces and distort the surrounding material. Probing and characterizing these athermal fluctuations is essential for understanding the properties and behaviors of such systems. Here we present a mathematical procedure to estimate the local action of force-generating agents from the observed fluctuating displacement fields. The active agents are modeled as oriented force dipoles or isotropic compression foci, and the matrix on which they act is assumed to be either a compressible elastic continuum or a coupled network-solvent system. Correlations at a single point and between points separated by an arbitrary distance are obtained, giving a total of three independent fluctuation modes that can be tested with microrheology experiments. Since oriented dipoles and isotropic compression foci give different contributions to these fluctuation modes, ratiometric analysis allows us characterize the force generators. We also predict and experimentally find a high-frequency ballistic regime, arising from individual force generating events in the form of the slow build-up of stress followed by rapid but finite decay. Finally, we provide a quantitative statistical model to estimate the mean filament tension from these athermal fluctuations, which leads to stiffening of active networks.

cond-mat.mtrl-sci↗

arXiv2009

Critical scaling and aging in cooling systems near the jamming transition

We conduct athermal simulations of freely-cooling, viscous soft spheres around the jamming transition density ϕ_{J}, and find evidence for a growing length ξ(t) that governs relaxation to mechanical equilibrium. ξ(t) is manifest in both the velocity correlation function, and the spatial correlations in a scalar measure of local force balance which we define. Data for different densities ϕcan be collapsed onto two master curves by scaling ξ(t) and t by powers of |ϕ-ϕ_{J}|, indicative of critical scaling. Furthermore, particle transport for ϕ>ϕ_{J} exhibits aging and superdiffusion similar to a range of soft matter experiments, suggesting a common origin. Finally, we explain how ξ(t) at late times maps onto known behavior away from ϕ_{J}.

cond-mat.soft↗

arXiv2007

Well defined transition to gel-like aggregates of attractive athermal particles

In an attempt to extend the range of model jamming transitions, we simulate systems of athermal particles which attract when slightly overlapping. Following from recent work on purely repulsive systems, dynamics are neglected and relaxation performed via a potential energy minimisation algorithm. Our central finding is of a transition to a low-density tensile solid which is sharp in the limit of infinite system size. The critical density depends on the range of the attractive regime in the pair-potential. Furthermore, solidity is shown to be related to the coordination number of the packing according to the approximate constraint-counting scheme known as Maxwell counting, although more corrections need to be considered than with the repulsive-only case, as explained. We finish by discussing how the numerical difficulties encountered in this work could be overcome in future studies.

cond-mat.soft↗

arXiv2006

Volume-controlled buckling of thin elastic shells: Application to crusts formed on evaporating partially-wetted droplets

Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and the substrate. This volume constraint mimics the incompressibility of the unevaporated solvent. Discontinuous buckling is found to occur for sufficiently thin and/or large contact angle shells, and robustly takes the form of a single circular region near the boundary that `snaps' to an inverted shape, in contrast to externally pressurised shells. Scaling theory for shallow shells is shown to well approximate the critical buckling volume, the subsequent enlargement of the inverted region and the contact line force.

cond-mat.mtrl-sci↗

arXiv2006

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapour interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by non-linear quasi-static simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a non-uniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find data collapse onto a master curve for both buckling pressure and deformation mode, thus allowing us to predict when the deformed shape is a dimple, mexican hat, and so on. This master curve is parameterised by a dimensionless measure of the non-uniformity of the shell. We also speculate on how overlapping timescales for gelation and deformation may alter our findings.

cond-mat.mtrl-sci↗

arXiv2005

The mechanical response of semiflexible networks to localized perturbations

Previous research on semiflexible polymers including cytoskeletal networks in cells has suggested the existence of distinct regimes of elastic response, in which the strain field is either uniform (affine) or non-uniform (non-affine) under external stress. Associated with these regimes, it has been further suggested that a new fundamental length scale emerges, which characterizes the scale for the crossover from non-affine to affine deformations. Here, we extend these studies by probing the response to localized forces and force dipoles. We show that the previously identified nonaffinity length [D.A. Head et al. PRE 68, 061907 (2003).] controls the mesoscopic response to point forces and the crossover to continuum elastic behavior at large distances.

cond-mat.soft↗

arXiv2005

A mean field description of jamming in non-cohesive frictionless particulate systems

A theory for kinetic arrest in isotropic systems of repulsive, radially-interacting particles is presented that predicts exponents for the scaling of various macroscopic quantities near the rigidity transition that are in agreement with simulations, including the non-trivial shear exponent. Both statics and dynamics are treated in a simplified, one-particle level description, and coupled via the assumption that kinetic arrest occurs on the boundary between mechanically stable and unstable regions of the static parameter diagram. This suggests the arrested states observed in simulations are at (or near) an elastic buckling transition. Some additional numerical evidence to confirm the scaling of microscopic quantities is also provided.

cond-mat.mtrl-sci↗

arXiv2005

First order rigidity transition and multiple stability regimes for random networks with internal stresses

By applying effective medium-style calculations to random spring networks, we demonstrate that internal stresses fundamentally alter the nature of the rigidity transition in disordered materials, changing it from continuous to first-order and increasing the mean coordination number z at which rigidity first occurs. Furthermore, we predict the existence of a novel stability regime at low z when the distribution of stresses is asymmetric. Means of verifying these predictions are suggested.

cond-mat.mtrl-sci↗

arXiv2003

Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks

Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominantly affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.

cond-mat.soft↗

arXiv2003

Non-universality of elastic exponents in random bond-bending networks

We numerically investigate the rigidity percolation transition in two-dimensional flexible, random rod networks with freely rotating cross-links. Near the transition, networks are dominated by bending modes and the elastic modulii vanish with an exponent f=3.0\pm0.2, in contrast with central force percolation which shares the same geometric exponents. This indicates that universality for geometric quantities does not imply universality for elastic ones. The implications of this result for actin-fiber networks is discussed.

cond-mat.stat-mech↗

arXiv2003

Deformation of crosslinked semiflexible polymer networks

Networks of filamentous proteins play a crucial role in cell mechanics. These cytoskeletal networks, together with various crosslinking and other associated proteins largely determine the (visco)elastic response of cells. In this letter we study a model system of crosslinked, stiff filaments in order to explore the connection between the microstructure under strain and the macroscopic response of cytoskeletal networks. We find two distinct regimes as a function primarily of crosslink density and filament rigidity: one characterized by affine deformation and one by non-affine deformation. We characterize the crossover between these two.

cond-mat.dis-nn↗

arXiv2003

Anomalous force diffusion in nearly-ordered packings of frictionless discs

We derive analytic expressions for force propagation in packings of frictionless discs with a narrow distribution of disc sizes, by expanding to first order about the known ordered solution. The distribution of contact forces P(f) is found to be narrow at the upper surface, and broaden at a rate that varies with depth, being superdiffusive near the surface until crossing over to a subdiffusive regime near the fixed base. Furthermore, the response to an isolated load propagates along the edge of a `cone,' as in the ordered case, but fluctuates under ensemble averaging by an amount that depends purely on height, not on the lateral position. Finally, we comment on ways in which the analytical framework presented here could be extended to a wider range of granular packings.

cond-mat.dis-nn↗

arXiv2002

Rheological Chaos in a Scalar Shear-Thickening Model

We study a simple scalar constitutive equation for a shear-thickening material at zero Reynolds number, in which the shear stress σis driven at a constant shear rate \dotγand relaxes by two parallel decay processes: a nonlinear decay at a nonmonotonic rate R(σ_1) and a linear decay at rate λσ_2. Here σ_{1,2}(t) = τ_{1,2}^{-1}\int_0^tσ(t')\exp[-(t-t')/τ_{1,2}] {\rm d}t' are two retarded stresses. For suitable parameters, the steady state flow curve is monotonic but unstable; this arises when τ_2>τ_1 and 0>R'(σ)>-λso that monotonicity is restored only through the strongly retarded term (which might model a slow evolution of material structure under stress). Within the unstable region we find a period-doubling sequence leading to chaos. Instability, but not chaos, persists even for the case τ_1\to 0. A similar generic mechanism might also arise in shear thinning systems and in some banded flows.

cond-mat.soft↗