arXiv subjects

Joshua F. Robinson

Publications and source records attributed to Joshua F. Robinson.

14 recordsLinked to original sources

arXiv2026

Approximate additivity in the solvent-mediated potential of mean force for ultrasoft particle systems

Recently an approximate additivity principle has been successfully applied to molecular chemical potentials in ultrasoft particle systems [R. L. Hendrikse, C. Amador and M. R. Wilson, Phys. Chem. Chem. Phys. 27, 1554 (2025)]. We articulate this additivity principle as one of two ansätze and apply these to dimers in the infinite dilution limit. In this limit, we show that the solvent-mediated potential of mean force (PMF) between solutes, extracted from the hypernetted-chain (HNC) closure of the Ornstein-Zernike equations, can be expressed as a convolution between solute-specific generalised excluded volume functions. In the limit of a structureless solvent of point particles and hard core solutes, this recovers the exact Asakura-Oosawa depletion potential as the overlap between excluded volume spheres. The theory extends to the opposite limit of ultrasoft particle solvents and solutes, such as those encountered in dissipative particle dynamics (DPD), where the solvent-mediated PMF can be recovered with considerable accuracy. These results confirm that in coarse-grained molecular DPD simulations the parametrisation of the solute-solvent interactions is sensitive to the intramolecular bond lengths if they are smaller than the range of the solvent-solvent interaction potential, due to the overlap of the soft excluded volume functions.

cond-mat.soft↗

arXiv2025

Statistics and morphologies of stable droplets in scalar active fluids

Conventional phase segregation is controlled by a positive interfacial tension, which implies that the system relaxes towards a state in which the interfacial area (or length) is minimized, typically manifesting as a single droplet that grows with the system size. Intriguingly, the extension of the underlying Model B paradigm by two non-potential terms (Active Model B+) is able to describe the stable coexistence of many finite droplets. Here we numerical study Active Model B+ in the vicinity of the transition between a single droplet (macrophase segregation) and multiple droplets (microphase segregation). Our results show that, although noise shifts transitions, the overall agreement with the mean-field theoretical predictions is very good. We find a strong correlation of droplet properties with a single parameter that determines the number, density, and the fractal dimension of droplets. Deeper inside the droplet phase we observe another transition to a hexagonal lattice of regular droplets.

cond-mat.soft↗

arXiv2025

Universal limiting behaviour of reaction-diffusion systems with conservation laws

Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely studied as two separate paradigms. Here we show that in reaction-diffusion systems composed of many species, the presence of a conservation law constrains the evolution of the conserved quantity to be governed by a Cahn-Hilliard-like equation. This establishes a direct link with the paradigm of coexistence and recent "active" field theories. Hence, even for complex many-species systems a dramatically simplified but accurate description emerges over coarse spatio-temporal scales. Using the nullcline (the line of homogeneous steady states) as the central motif, we develop a geometrical framework which endows chemical space with a basis and suitable coordinates. This framework allows us to capture and understand the effect of eliminating fast non-conserved degrees of freedom, and to explicitly construct coefficients of the coarse field theory. We expect that the theory we develop here will be particularly relevant to advance our understanding of biomolecular condensates.

cond-mat.soft↗

arXiv2025

Critical inertia for particle capture is determined by surface geometry at forward stagnation point

Aerosols are ubiquitous, and particle capture from particle-laden air as it flows past an obstacle is of widespread practical importance. Neglecting diffusion, previous work has shown that for a smooth curved surface in both Stokes flow and inviscid flow, only particles with inertia above a threshold value (quantified by the nondimensional Stokes number) collide with the surface. Here we show that the critical Stokes number decreases with increasing Reynolds number of the air flow, and the mechanism behind this threshold is the same at all finite Reynolds numbers but becomes qualitatively different in the limit of infinite Reynolds number (inviscid flow). In addition we show that in the latter case (inviscid flow) the threshold is set solely by the flow near the stagnation point, whereas at finite Reynolds numbers the threshold also depends on the flow far from the stagnation point. The threshold also depends on obstacle geometry and we show that fibers whose cross section is flattened along the flow direction have greater size selectivity than fibers with a circular cross section.

physics.flu-dyn↗

arXiv2024

Renormalisation group theory applied to $\ddot{x}+\dot{x}+x^2=0$

The titular ordinary differential equation (ODE) is encountered in the theory of on-axis inertial particle capture by a blunt stationary collector at a viscous-flow stagnation point. Phase space for the ODE divides into two attractor basins, representing particle trajectories which do or do not collide with the collector in a finite time. Written as $\ddot{x} + \dot{x} + εx^2 = 0$, we formulate the renormalisation group (RG) amplitude equations for this problem and argue that the critical trajectory which separates the attractor basins corresponds to a trivial but exact solution of these, and can therefore be extracted as a power series in $ε$. We show how this can be used to find the cross-over between capture and non-capture as a function of distance from the stagnation point, for a particle released into the flow with no initial acceleration. This cross-over, previously only computable by numerical integration of the ODE, can therefore be expressed as a (numerically) convergent series with rational terms.

math-ph↗

arXiv2024

Thermodynamics of active matter: Tracking dissipation across scales

The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how local dissipation due to effective chemical events manifests on large scales in active matter. We start from a microscopic model for a single catalytic particle involving explicit solute molecules and show that it undergoes directed motion. Leveraging stochastic thermodynamics, we calculate the average entropy production rate for interacting particles. We then show how the model of active Brownian particles emerges in a certain limit and we determine the entropy production rate on the level of the hydrodynamic equations. Our results augment the model of active Brownian particles with rigorous expressions for the dissipation that cannot be inferred from their equations of motion, and we illustrate consequences for wall aggregation and motility-induced phase separation. Notably, our bottom-up approach reveals that a naive application of the Onsager currents yields an incorrect expression for the local dissipation.

cond-mat.soft↗

arXiv2022

Many-body correlations are non-negligible in both fragile and strong glassformers

It is widely believed that the emergence of slow glassy dynamics is encoded in a material's microstructure. First-principles theory [mode-coupling theory (MCT)] is able to predict the dramatic slowdown of the dynamics from only static two-point correlations as input, yet it cannot capture all of the observed dynamical behavior. Here we go beyond two-point spatial correlation functions by extending MCT systematically to include higher-order static and dynamic correlations. We demonstrate that only adding the static triplet direct correlations already qualitatively changes the predicted glass-transition diagram of binary hard spheres and silica. Moreover, we find a non-trivial competition between static triplet correlations that work to stabilize the glass state, and dynamic higher-order correlations which destabilize it for both materials. We conclude that the conventionally neglected static triplet direct correlations as well as higher-order dynamic correlations are in fact non-negligible in both fragile and strong glassformers.

cond-mat.soft↗

arXiv2022

Modelling the filtration efficiency of a woven fabric: The role of multiple lengthscales

During the COVID-19 pandemic, many millions have worn masks made of woven fabric, to reduce the risk of transmission of COVID-19. Masks are essentially air filters worn on the face, that should filter out as many of the dangerous particles as possible. Here the dangerous particles are the droplets containing virus that are exhaled by an infected person. Woven fabric is unlike the material used in standard air filters. Woven fabric consists of fibres twisted together into yarns that are then woven into fabric. There are therefore two lengthscales: the diameters of: (i) the fibre and (ii) the yarn. Standard air filters have only (i). To understand how woven fabrics filter, we have used confocal microscopy to take three dimensional images of woven fabric. We then used the image to perform Lattice Boltzmann simulations of the air flow through fabric. With this flow field we calculated the filtration efficiency for particles a micrometre and larger in diameter. In agreement with experimental measurements by others, we find that for particles in this size range, filtration efficiency is low. For particles with a diameter of 1.5 micrometres our estimated efficiency is in the range 2.5 to 10%. The low efficiency is due to most of the air flow being channelled through relatively large (tens of micrometres across) inter-yarn pores. So we conclude that fabric is expected to filter poorly due to the hierarchical structure of woven fabrics.

physics.flu-dyn↗

arXiv2022

How effective are face coverings in reducing transmission of COVID-19?

In the COVID-19 pandemic, billions are wearing face masks, in both health care settings and in public. Which type of mask we should wear in what situation, is therefore important. There are three basic types: cotton, surgical, and respirators (e.g. FFP2, N95 and similar). All are essentially air filters worn on the face. Air filtration is relatively well understood, however, we have almost no direct evidence on the relative role played by aerosol particles of differing sizes in disease transmission. But if the virus concentration is assumed independent of aerosol particle size, then most virus will be in particles > 1 $μ$m. We develop a model that predicts surgical masks are effective at reducing the risk of airborne transmission because the filtering material most surgical masks use is highly effective at filtering particles with diameters > 1 $μ$m. However, surgical masks are significantly less effective than masks of FFP2, N95 and similar standards, mostly due to the poor fit of surgical masks. Earlier work found that ~30% of the air bypasses a surgical mask and is not filtered. This highlights the fact that standards for surgical masks do not specify how well the mask should fit, and so are not adequate for protection against COVID-19.

cond-mat.soft↗

arXiv2021

Efficacy of face coverings in reducing transmission of COVID-19: calculations based on models of droplet capture

In the COVID--19 pandemic, among the more controversial issues is the use of masks and face coverings. Much of the concern boils down to the question -- just how effective are face coverings? One means to address this question is to review our understanding of the physical mechanisms by which masks and coverings operate -- steric interception, inertial impaction, diffusion and electrostatic capture. We enquire as to what extent these can be used to predict the efficacy of coverings. We combine the predictions of the models of these mechanisms which exist in the filtration literature and compare the predictions with recent experiments and lattice Boltzmann simulations, and find reasonable agreement with the former and good agreement with the latter. Building on these results, we explore the parameter space for woven cotton fabrics to show that three-layered cloth masks can be constructed with comparable filtration performance to surgical masks under ideal conditions. Reusable cloth masks thus present an environmentally friendly alternative to surgical masks so long as the face seal is adequate enough to minimise leakage.

cond-mat.soft↗

arXiv2019

Nucleation kinetics in drying sodium nitrate aerosols

A quantitative understanding of the evaporative drying kinetics and nucleation rates of aqueous based aerosol droplets is important for a wide range of applications, from atmospheric aerosols to industrial processes such as spray drying. Here, we introduce a numerical model for interpreting measurements of the evaporation rate and phase change of drying free droplets made using a single particle approach. We explore the evaporation of aqueous sodium chloride and sodium nitrate solution droplets. Although the chloride salt is observed to reproducibly crystallise at all drying rates, the nitrate salt solution can lose virtually all of its water content without crystallising. The latter phenomenon has implications for our understanding of the competition between the drying rate and nucleation kinetics in these two systems. The nucleation model is used in combination with the measurements of crystallisation events to infer nucleation rates at varying equilibrium state points, showing that classical nucleation theory provides a good description of the crystallisation of the chloride salt but not the nitrate salt solution droplets. The reasons for this difference are considered.

cond-mat.soft↗

arXiv2019

Morphological thermodynamics for hard bodies from a controlled expansion

The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive (classical) density functional theory approaches. Despite this, fundamental questions remain over why it is accurate and how one might include higher-order terms to improve accuracy. We derive the morphometric approach as the exact resummation of terms in the virial series, providing further justification of the approach. The resulting theory is less accurate than previous morphometric theories, but provides fundamental insights into the inclusion of higher-order terms and to extensions to mixtures of convex bodies of arbitrary shape.

cond-mat.stat-mech↗

arXiv2019

Many-body correlations from integral geometry

In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was the morphometric approach, a synthesis of integral geometry and liquid state theory, which has traditionally been derived from fundamental measure theory. We present the morphometric approach in a new context as a generalisation of scaled particle theory, and derive several morphometric theories for hard spheres of fundamental and practical interest. Our central result is a new theory which is particularly suited to the treatment of many-body correlation functions in the hard sphere liquid, which we demonstrate by numerical tests against simulation.

cond-mat.stat-mech↗

arXiv2019

Morphometric approach to many-body correlations in hard spheres

We model the thermodynamics of local structures within the hard sphere liquid at arbitrary volume fractions through the \textit{morphometric} calculation of $n$-body correlations. We calculate absolute free energies of local geometric motifs in excellent quantitative agreement with molecular dynamics simulations across the liquid and supercooled liquid regimes. We find a bimodality in the density library of states where five-fold symmetric structures appear lower in free energy than four-fold symmetric structures, and from a single reaction path predict a relaxation barrier which scales linearly in the compressibility factor. The method provides a new route to assess changes in the free energy landscape at volume fractions dynamically inaccessible to conventional techniques.

cond-mat.stat-mech↗