arXiv subjects

Richard G. Morris

Publications and source records attributed to Richard G. Morris.

At least 19 recordsLinked to original sources

arXiv2026

Defect Kinematics in 2D Nematics: Contributions from Surface Topology, Intrinsic and Extrinsic Geometry, Solitons, Defect Orientations, and Elastic Anisotropy

We characterise the particlelike kinematics of charge-carrying topological defects in nematic media via a geometric field theory. This differs from the theory of electromagnetism, with which it is often compared, due to the absence of gauge-invariance. In both approaches, basic defect interactions are governed by a propagator, which depends upon the global topology and/or intrinsic geometry of the surface. For nematic materials, however, the minimisation of the free energy is sensitive to constraints that a gauge invariant theory would otherwise be indifferent to. Hodge theory is used to capture these as `harmonic' excitations, unifying two factors known to additionally affect the kinematics of defects in nematics: relative defect orientations and topological solitons. Perturbations to the form of the energy are also permitted in nematic materials due to gauge \emph{non}invariance. Those that introduce non-linearities in the corresponding Euler--Lagrange equations are shown to result in defect interactions that go beyond pairwise despite the otherwise abelian nature of the underlying U(1) symmetry. We show how this type of induced many-body effect manifests in the cases of non-zero extrinsic curvature and/or elastic anisotropy.

cond-mat.soft↗

arXiv2026

Nonreciprocal buckling makes active filaments polyfunctional

Active filaments are a workhorse for propulsion and actuation across biology, soft robotics and mechanical metamaterials. However, artificial active rods suffer from limited robustness and adaptivity because they rely on external control, or are tethered to a substrate. Here we bypass these constraints by demonstrating that non-reciprocal interactions lead to large-scale unidirectional dynamics in free-standing slender structures. By coupling the bending modes of a buckled beam anti-symmetrically, we transform the multistable dynamics of elastic snap-through into persistent cycles of shape change. In contrast to the critical point underpinning beam buckling, this transition to self-snapping is mediated by a critical exceptional point, at which bending modes simultaneously become unstable and degenerate. Upon environmental perturbation, our active filaments exploit self-snapping for a range of functionality including crawling, digging and walking. Our work advances critical exceptional physics as a guiding principle for programming instabilities into functional active materials.

cond-mat.soft↗

arXiv2025

Capillarity Reveals the Role of Capsid Geometry in HIV Nuclear Translocation

The protective capsid encasing the genetic material of Human Immunodeficiency Virus (HIV) has been shown to traverse the nuclear pore complex (NPC) intact, despite exceeding the passive diffusion threshold by over three orders of magnitude. This remarkable feat is attributed to the properties of the capsid surface, which confer solubility within the NPC's phase-separated, condensate-like barrier. In this context, we apply the classical framework of wetting and capillarity -- integrating analytical methods with sharp- and diffuse-interface numerical simulations -- to elucidate the physical underpinnings of HIV nuclear entry. Our analysis captures several key phenomena: the reorientation of incoming capsids due to torques arising from asymmetric capillary forces; the role of confinement in limiting capsid penetration depths; the classification of translocation mechanics according to changes in topology and interfacial area; and the influence of (spontaneous) rotational symmetry-breaking on energetics. These effects are all shown to depend critically on capsid geometry, arguing for a physical basis for HIV's characteristic capsid shape.

physics.bio-ph↗

arXiv2025

Stochastic Multistability of Clonallike States in the Eigen Model: a Fidelity Catastrophe

The Eigen model is a prototypical toy model of evolution that is synonymous with the so-called error catastrophe: when mutation rates are sufficiently high, the genetic variant with the largest replication rate does not occupy the largest fraction of the total population because it acts as a source for the other variants. Here we show that, in the stochastic version of the Eigen model, there is also a fidelity catastrophe. This arises due to the state-dependence of fluctuations and occurs when rates of mutation fall beneath a certain threshold, which we calculate. The result is a type of noise-induced multistability whereupon the system stochastically switches between short-lived regimes of effectively clonal behavior by different genetic variants. Most notably, when the number of possible variants -- typically $\sim4^L$, with $L\gg 1$ the length of the genome -- is significantly larger than the population size, there is only a vanishingly small interval of mutation rates for which the Eigen model is neither in the fidelity- nor error-catastrophe regimes, seemingly subverting traditional expectations for evolutionary systems.

q-bio.PE↗

arXiv2025

Stochastically bistable growth and decay in the Togashi-Kaneko model

The two-state Togashi-Kaneko model demonstrates how, at finite system sizes, autocatalysis can lead to noise-induced bistability between the cellular concentrations of different molecular species. Here, we show that, in the biologically relevant scenario of species-dependent export rates, the nascent stochastic switching between molecular species also drives a concomitant switching between periods of growth or decay in the total population size. We demonstrate this behavior using stochastic simulations as well as the numerical integration of a Fokker-Planck equation that approximates the finite system-size limit. By combining piecewise-deterministic-Markov and linear-noise approximations, we further find analytic expressions for the stationary distributions of the different molecular species when stochastic switching is faster than the dynamics in the total population size. We envisage that other models in the voter class -- including spin systems, flocking and opinion dynamics -- may also exhibit aperiodic growth and decay in population size, as well as be amenable to similar techniques.

cond-mat.stat-mech↗

arXiv2025

Non-Stationary Critical Phenomena: Expanding The Critical Point

A prototypical model of symmetry-broken active matter -- biased quorum-sensing active particles (bQSAPs) -- is used to extend notions of dynamic critical phenomena to the paradigmatic setting of driven transport, where characteristic behaviours are nonstationary and involve persistent fluxes. To do so, we construct an effective field theory with a single order-parameter -- a nonstationary analogue of active Model B -- that reflects the fact that different properties of bQSAPs can only be interpreted in terms of passive thermodynamics in appropriately chosen inertial frames. This codifies the movement of phase boundaries due to nonequilibrium fluxes between coexisting bulk phases in terms of a difference in effective chemical potentials and therefore an {\it unequal} tangent construction on a bulk free energy density. The result is both an anomalous form of coarsening and, more generally, an exotic phase structure; binodals are permitted to cross spinodal lines so that criticality is no longer constrained to a single point. Instead, criticality, with exponents that are seemingly unchanged from symmetric QSAPs, is shown to exist along a line that marks the entry to an otherwise forbidden region of phase space. The interior of this region is not critical in the conventional sense, but retains certain features of criticality, which we term pseudo-critical. Whilst an inability to satisfy a Ginzburg criterion implies that fluctuations remain relevant at macroscopic scales, finite-wavenumber fluctuations grow at finite rates and exhibit non-trivial dispersion relations. The interplay between the growth of fluctuations and the speed at which they move relative to the bulk results in distinct regimes of micro- and meso-phase separation.

cond-mat.stat-mech↗

arXiv2025

Geometric Frustration in Twist-Bend Nematic Droplets

Liquid crystals formed of bent-core molecules are exotic materials that exhibit the twist-bend nematic phase. This arises when an energetic preference for nonzero local bend distortion is accommodated via twist in the texture, resulting in properties synonymous with both smectics and cholesterics. Here we describe how the frustration inherent to the twist-bend phase can be exacerbated by confinement and boundary anchoring. Using a combination of numerical simulations, topological and geometric analysis, we catalogue the equilibrium textures that arise in spherical twist-bend droplets with a radial anchoring as the two key parameters -- the molecular cone angle and the ratio between the pitch length and droplet radius -- are varied. This form of confinement is known to produce a wide variety of topologically and geometrically complex metastable states in cholesterics. We find that twist-bend nematic droplets are no different, exhibiting a variety of complex layered states, defect constellations, and Hopfions. However, whilst many of the structures and defect configurations that we observe are equivalent to their cholesteric counterparts, they are geometrically very distinct, in part due to the absence of chirality.

cond-mat.soft↗

arXiv2025

A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise

We derive a stochastic partial differential equation that describes the fluctuating behaviour of reaction-diffusion systems of N particles, undergoing Markovian, unary reactions. This generalises the work of Dean [J. Phys. A: Math. and Gen., 29 (24), L613, (1996)] through the inclusion of random Poisson fields. Our approach is based on weak interactions, which has the dual benefit that the resulting equations asymptotically converge (in the N to infinity limit) on a variation of a McKean- Vlasov diffusion, whilst still being related to the case of Dean-like strong interactions via a trivial rescaling. Various examples are presented, alongside a discussion of possible extensions to more complicated reaction schemes.

cond-mat.stat-mech↗

arXiv2024

Defect Dynamics in Cholesterics: Beyond the Peach-Koehler Force

The Peach-Koehler force between disclination lines was originally formulated in the study of crystalline solids, and has since been adopted to provide a notion of interactions between disclination lines in nematic liquid crystals. Here, we argue that the standard formulation of this interaction force seemingly fails for materials where there is a symmetry-broken ground state, and suggest that this is due to the interaction between disclination lines and merons: non-singular yet non-trivial topological solitons. We examine this in the context of chiral nematic (cholesteric) liquid crystals, which provide a natural setting for studying these interactions due to their energetic preference for meron tubes in the form of double-twist cylinders. Through a combination of theory and simulation we demonstrate that, for sufficiently strong chirality, defects of $+1/2$ winding will change their winding through the emission of a meron line, and that interactions between the merons and defects dominate over defect-defect interactions. Instead of Peach-Koehler framework, we employ a method based on contact topology - the Gray stability theorem - to directly calculate the velocity field of the material. We apply our framework to point defects as well as disclination lines. Our results have implications not just for chiral materials, but also for other phases with modulated ground states, such as the twist-bend and splay-bend nematics.

cond-mat.soft↗

arXiv2024

More ATP Does Not Equal More Contractility: Power And Remodelling In Reconstituted Actomyosin

The cytoskeletal component actomyosin is a canonical example of active matter since the powerstroke cycle locally converts chemical energy in the form of adenoside triphosphate (ATP) into mechanical work for remodelling. Observing myosin II minifilaments as they remodel actin {\it in vitro}, we now report that: at high concentrations of ATP, myosin minifilaments form metastable swirling patterns that are characterised by recurrent vortex and spiral-like motifs, whereas; at low concentrations of ATP, such structures give way to aster-like patterns. To explain this, we construct the (quasi-)steady states of a polar active hydrodynamic theory of actomyosin whose ATP-scaling is obtained from a microscopic, stochastic description for the ATP-dependent binding of the heads of single myosin II minifilaments. The latter codifies the heuristic that, since the powerstroke cycle involves the unbinding of myosin II heads from actin, increases in the concentration of ATP reduce the likelihood that a given myosin II minifilament has more than one head bound simultaneously, reducing its ability to generate contractile forces and increasing the relative likelihood of processive motion. This reproduces several qualitative and some quantitative aspects of experiments, providing evidence for the central phenomenon of the theory: an ATP-dependent active contractile instability. ATP therefore controls not only the rate at which work is done -- \textit{i.e.,} the power -- but also the mode by which this occurs.

physics.bio-ph↗

arXiv2024

Active morphodynamics of intracellular organelles in the trafficking pathway

From the Golgi apparatus to endosomes, organelles in the endomembrane system exhibit complex and varied morphologies that are often related to their function. Such membrane-bound organelles operate far from equilibrium due to directed fluxes of smaller trafficking vesicles; the physical principles governing the emergence and maintenance of these structures have thus remained elusive. By understanding individual fission and fusion events in terms of active mechano-chemical cycles, we show how such trafficking manifests at the hydrodynamic scale, resulting not only in fluxes of material -- such as membrane area and encapsulated volume -- but also in active stresses that drive momentum transfer between an organelle and its cytosolic environment. Due to the fluid and deformable nature of the bounding membrane, this gives rise to novel physics, coupling nonequilibrium forces to organelle composition, morphology and hydrodynamic flows. We demonstrate how both stable compartment drift and ramified sac-like morphologies, each reminiscent of Golgi-cisternae, emerge naturally from the same underlying nonequilibrium dynamics of fission and fusion.

cond-mat.soft↗

arXiv2024

Morse Theory and Meron Mediated Interactions Between Disclination Lines in Nematics

The topological understanding of nematic liquid crystals is traditionally centered on singularities, or defects, and their classification via homotopy theory. However, this approach has ultimately proved insufficient to properly capture a range of complex behaviours that have been reported in three dimensions. To address this, we argue that a finer understanding of topology is required, in which non-singular but non-trivial topological solitons - so-called merons - play a central role in mediating interactions between disclination lines. We present a comprehensive framework for capturing such behaviour that draws heavily on aspects of Morse theory; the key notion being that merons appear singular under projection onto a two-dimensional surface. This permits the use of singularity theory and dividing curves to characterise nematic textures via tomography, as well as an understanding of topological transitions via surgery theory. We use our ideas to understand and classify complex three-dimensional behaviours, such as the linking, rewiring and crossing of disclination lines, as well as to provide a new perspective on defect charge.

cond-mat.soft↗

arXiv2024

Gauge Freedom and Objective Rates in the Morphodynamics of Fluid Deformable Surfaces: the Jaumann Rate vs. the Material Derivative

Morphodynamic descriptions of fluid deformable surfaces are relevant for a range of biological and soft matter phenomena, spanning materials that can be passive or active, as well as ordered or topological. However, a principled, geometric formulation of the correct hydrodynamic equations has remained opaque, with objective rates proving a central, contentious issue. We argue that this is due to a conflation of several important notions that must be disambiguated when describing fluid deformable surfaces. These are the Eulerian and Lagrangian perspectives on fluid motion, and three different types of gauge freedom: in the ambient space; in the parameterisation of the surface, and; in the choice of frame field on the surface. We clarify these ideas, and show that objective rates in fluid deformable surfaces are time derivatives that are invariant under the first of these gauge freedoms, and which also preserve the structure of the ambient metric. The latter condition reduces a potentially infinite number of possible objective rates to only two: the material derivative and the Jaumann rate. The material derivative is invariant under the Galilean group, and therefore applies to velocities, whose rate captures the conservation of momentum. The Jaumann derivative is invariant under all time-dependent isometries, and therefore applies to local order parameters, or symmetry-broken variables, such as the nematic $Q$-tensor. We provide examples of material and Jaumann rates in two different frame fields that are pertinent to the current applications of the fluid mechanics of deformable surfaces.

physics.flu-dyn↗

arXiv2024

Advecting Scaffolds: Controlling The Remodelling Of Actomyosin With Anillin

We propose and analyse an active hydrodynamic theory that characterises the effects of the scaffold protein anillin. Anillin is found at major sites of cortical activity, such as adherens junctions and the cytokinetic furrow, where the canonical regulator of actomyosin remodelling is the small GTPase, RhoA. RhoA acts via intermediary 'effectors' to increase both the rates of activation of myosin motors and the polymerisation of actin filaments. Anillin has been shown to scaffold this action of RhoA - improving critical rates in the signalling pathway without altering the essential biochemistry - but its contribution to the wider spatio-temporal organisation of the cortical cytoskeleton remains poorly understood. Here, we combine analytics and numerics to show how anillin can non-trivially regulate the cytoskeleton at hydrodynamic scales. At short times, anillin can amplify or dampen existing contractile instabilities, as well as alter the parameter ranges over which they occur. At long times, it can change both the size and speed of steady-state travelling pulses. The primary mechanism that underpins these behaviours is established to be the advection of anillin by myosin II motors, with the specifics relying on the values of two coupling parameters. These codify anillin's effect on local signalling kinetics and can be traced back to its interaction with the acidic phospholipid phosphatidylinositol 4,5-bisphosphate (PIP2), thereby establishing a putative connection between actomyosin remodelling and membrane composition.

q-bio.SC↗

arXiv2023

Morphodynamics of Active Nematic Fluid Surfaces

Morphodynamic equations governing the behaviour of active nematic fluids on deformable curved surfaces are constructed in the large deformation limit. Emphasis is placed on the formulation of objective rates that account for normal deformations whilst ensuring that tangential flows are Eulerian, and the use of the surface derivative (rather than the covariant derivative) in the nematic free energy, which elastically couples local order to out-of-plane bending of the surface. Focusing on surface geometry and its dynamical interplay with the hydrodynamics, several illustrative instabilities are then characterised. These include cases where the role of the Scriven-Love number and its nematic analogue are non-negligible, and where the active nematic forcing can be characterised by an analogue of the Föppl-von-Kármán number. For the former, flows and changes to the nematic texture are coupled to surface geometry by viscous dissipation. This is shown to result in non-trivial relaxation dynamics for a nematic tube. For the latter, the nematic active forcing couples to the surface bending terms of the nematic free energy, resulting in extensile (active ruffling) and contractile (active pearling) instabilities in the tube shape, as well as active bend instabilities in the nematic texture. In comparison to the flat case, such bend instabilities now have a threshold set by the extrinsic curvature of the tube. Finally, we examine a topological defect located on an almost flat surface and show that there exists a steady state where a combination of defect elasticity, activity and non-negligible spin-connection drive a shape change in the surface.

cond-mat.soft↗

arXiv2022

Dynamical phases in growing populations: understanding recovery from bottlenecks

Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given population bottleneck remain poorly understood. In this context, we show that long-term post-bottleneck outcomes can depend crucially on the rate at which a diminished population grows whilst recovering. That is, two otherwise identical populations, each having undergone the same bottleneck, can fixate on dramatically different demographics due to different rates of post-bottleneck growth. This behaviour is moreover shown to change non-trivially with different levels of mutation. The underlying mechanism can be traced to intrinsic fluctuations whose standard deviation decreases in time with the inverse square root of the growing population size. Crucially, such decreasing fluctuations couple to the underlying dynamics and result in distinct regimes of (non-equilibrium) demographic behaviour, delimited by abrupt transitions at critical population sizes. Seen through this lens, growth and mutation alter evolutionary outcomes by changing the duration and character of dynamical phases; a feature that we speculate may be of generic importance across many systems.

q-bio.PE↗

arXiv2022

Bivalent Kinetics: Insights from Many Body Physics

Bivalency confers several concentration-dependent phenomena, including avidity, competitive exchange and multi-site competitive exchange. Since these concepts are crucial for a wide variety of topics in cell and molecular biology, their extension, modification and/or re-purposing is also increasingly important for the design and construction of de-novo synthetic systems at the nanoscale. In this context, we draw upon classical techniques of statistical physics to revisit bivalency, highlighting that receptor site geometry offers a design modality independent of the chemistry of the individual binding interfaces themselves. Recasting the problem in terms of many-body coordination, we explore extended, translationally-invariant chains and lattices of receptor sites. This not only brings clarity to behaviours associated with simpler motifs, but also enables us to distil core principles for the rational design of concentration-dependent kinetics in synthetic soft-systems, which centre on the notion of geometric frustration. In doing so, we also reveal the possibility of other tunable spatio-temporal features, such as correlation lengths, mean-squared displacements and percolation-like transitions.

cond-mat.stat-mech↗

arXiv2021

Active Flows and Deformable Surfaces in Development

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients -- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

physics.bio-ph↗