Stokes traction on an active particle.

The mechanics and statistical mechanics of a suspension of active particles are determined by the traction (force per unit area) on their surfaces. Here we present an exact solution of the direct boundary integral equation for the traction on a spherical active particle in an imposed slow viscous flow. Both single- and double-layer integral operators can be simultaneously diagonalized in a basis of irreducible tensorial spherical harmonics and the solution, thus, can be presented as an infinite number of linear relations between the harmonic coefficients of the traction and the velocity at the boundary of the particle. These generalize Stokes laws for the force and torque. Using these relations we obtain simple expressions for physically relevant quantities such as the symmetric-irreducible dipole acting on, or the power dissipated by, an active particle in an arbitrary imposed flow. We further present an explicit expression for the variance of the Brownian contributions to the traction on an active colloid in a thermally fluctuating fluid.

Measurement of irreversibility and entropy production via the tubular ensemble.

The appealing theoretical measure of irreversibility in a stochastic process, as the ratio of the probabilities of a trajectory and its time reversal, cannot be accessed directly in experiments since the probability of a single trajectory is zero. We regularize this definition by considering, instead, the limiting ratio of probabilities for trajectories to remain in the tubular neighborhood of a smooth path and its time reversal. The resulting pathwise medium entropy production agrees with the formal expression from stochastic thermodynamics and can be obtained from measurable tube probabilities. Estimating the latter from numerically sampled trajectories for Langevin dynamics yields excellent agreement with theory. By combining our measurement of pathwise entropy production with a Markov chain Monte Carlo algorithm, we infer the entropy-production distribution for a transition path ensemble directly from short recorded trajectories. Our work enables the measurement of irreversibility along individual paths and path ensembles in a model-free manner.

Bayesian inference across multiple models suggests a strong increase in lethality of COVID-19 in late 2020 in the UK.

We apply Bayesian inference methods to a suite of distinct compartmental models of generalised SEIR type, in which diagnosis and quarantine are included via extra compartments. We investigate the evidence for a change in lethality of COVID-19 in late autumn 2020 in the UK, using age-structured, weekly national aggregate data for cases and mortalities. Models that allow a (step-like or graded) change in infection fatality rate (IFR) have consistently higher model evidence than those without. Moreover, they all infer a close to two-fold increase in IFR. This value lies well above most previously available estimates. However, the same models consistently infer that, most probably, the increase in IFR preceded the time window during which variant B.1.1.7 (alpha) became the dominant strain in the UK. Therefore, according to our models, the caseload and mortality data do not offer unequivocal evidence for higher lethality of a new variant. We compare these results for the UK with similar models for Germany and France, which also show increases in inferred IFR during the same period, despite the even later arrival of new variants in those countries. We argue that while the new variant(s) may be one contributing cause of a large increase in IFR in the UK in autumn 2020, other factors, such as seasonality, or pressure on health services, are likely to also have contributed.

Efficient and flexible methods for simulating models of time since infection.

Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models that are more faithful to the microscopic details of disease transmission can offer more reliable projections, which in turn can lead to more reliable control strategies. For example, many epidemic models describe disease progression via a series of artificial stages or compartments (e.g., exposed, activated, infectious, etc.) but an epidemic model that explicitly tracks time since infection (TSI) can provide a more precise description. At present, epidemic models with compartments are more common than TSI models, largely due to the higher computational cost and complexity typically associated with TSI models. Here, however, we show that with the right discretization scheme a TSI model is not much more difficult to solve than a compartment model with three or four stages for the infected class. We also provide a perspective for adding stages to a TSI model in a way that decouples the disease transmission dynamics from the residence time distributions at each stage. These results are also generalized for age-structured TSI models in an Appendix. Finally, as proof of principle for the efficiency of the proposed numerical methods, we provide calculations for optimal epidemic control by nonpharmaceutical intervention. Many of the tools described in this paper are available through the software package pyross.

Erratum: Periodic Orbits of Active Particles Induced by Hydrodynamic Monopoles [Phys. Rev. Lett. 124, 088003 (2020)].

This corrects the article DOI: 10.1103/PhysRevLett.124.088003.

Internal friction controls active ciliary oscillations near the instability threshold.

Ciliary oscillations driven by molecular motors cause fluid motion at micron scale. Stable oscillations require a substantial source of dissipation to balance the energy input of motors. Conventionally, it stems from external fluid. We show, in contrast, that external fluid friction is negligible compared to internal elastic stress through a simultaneous measurement of motion and flow field of an isolated and active Chlamydomonas cilium beating near the instability threshold. Consequently, internal friction emerges as the sole source of dissipation for ciliary oscillations. We combine these experimental insights with theoretical modeling of active filaments to show that an instability to oscillations takes place when active stresses are strain softening and shear thinning. Together, our results reveal a counterintuitive mechanism of ciliary beating and provide a general experimental and theoretical methodology to analyze other active filaments, both biological and synthetic ones.

Flow-induced phase separation of active particles is controlled by boundary conditions.

Active particles, including swimming microorganisms, autophoretic colloids, and droplets, are known to self-organize into ordered structures at fluid-solid boundaries. The entrainment of particles in the attractive parts of their spontaneous flows has been postulated as a possible mechanism underlying this phenomenon. Here, combining experiments, theory, and numerical simulations, we demonstrate the validity of this flow-induced ordering mechanism in a suspension of active emulsion droplets. We show that the mechanism can be controlled, with a variety of resultant ordered structures, by simply altering hydrodynamic boundary conditions. Thus, for flow in Hele-Shaw cells, metastable lines or stable traveling bands can be obtained by varying the cell height. Similarly, for flow bounded by a plane, dynamic crystallites are formed. At a no-slip wall, the crystallites are characterized by a continuous out-of-plane flux of particles that circulate and re-enter at the crystallite edges, thereby stabilizing them. At an interface where the tangential stress vanishes, the crystallites are strictly 2D, with no out-of-plane flux. We rationalize these experimental results by calculating, in each case, the slow viscous flow produced by the droplets and the long-ranged, many-body active forces and torques between them. The results of numerical simulations of motion under the action of the active forces and torques are in excellent agreement with experiments. Our work elucidates the mechanism of flow-induced phase separation in active fluids, particularly active colloidal suspensions, and demonstrates its control by boundaries, suggesting routes to geometric and topological phenomena in an active matter.

Linking Catalyst-Coated Isotropic Colloids into "Active" Flexible Chains Enhances Their Diffusivity.

Active colloids are not constrained by equilibrium: ballistic propulsion, superdiffusive behavior, or enhanced diffusivities have been reported for active Janus particles. At high concentrations, interactions between active colloids give rise to complex emergent behavior. Their collective dynamics result in the formation of several hundred particle-strong flocks or swarms. Here, we demonstrate significant diffusivity enhancement for colloidal objects that neither have a Janus architecture nor are at high concentrations. We employ uniformly catalyst-coated, viz. chemo-mechanically, isotropic colloids and link them into a chain to enforce proximity. Activity arises from hydrodynamic interactions between enchained colloidal beads due to reaction-induced phoretic flows catalyzed by platinum nanoparticles on the colloid surface. This results in diffusivity enhancements of up to 60% for individual chains in dilute solution. Chains with increasing flexibility exhibit higher diffusivities. Simulations accounting for hydrodynamic interactions between enchained colloids due to active phoretic flows accurately capture the experimental diffusivity. These simulations reveal that the enhancement in diffusivity can be attributed to the interplay between chain conformational fluctuations and activity. Our results show that activity can be used to systematically modulate the mobility of soft slender bodies.

Universal evolution of a viscous-capillary spreading drop.

The rate of spreading or retraction of a drop on a flat substrate is determined through a balance of surface tension and hydrodynamic flow. While asymptotic regimes are known, no general rate equation has hitherto been available. Here, we revisit this classic problem, in a regime governed by capillary and viscous forces, by performing an exhaustive numerical study of drop evolution as a function of the contact angle with the substrate. Our study reveals a universal evolution of the drop radius parameterised only by the substrate wettability. Two limits of this evolution recover the familiar exponential and algebraic regimes. Our results show quantitative comparison with the evolution derived from lubrication theory, indicating that dissipation at the contact line is the key determinant in drop evolution. Our work, both numerical and theoretical, provides a foundation for studying the full temporal dynamics of droplet evolution under the influence of external fields and thermal fluctuations, which are of importance in nanofluidics.

Do liquid drops roll or slide on inclined surfaces?

We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analyzed by decomposing the gradient of the velocity inside the droplet into a shear and a residual flow. This decomposition helps in distinguishing sliding versus rolling motion of the drop. Our detailed study confirms intuition, in that rolling motion dominates as the droplet shape approaches a circle, and the viscosity contrast between the droplet and the ambient fluid becomes large. As a consequence of kinematics, the amount of rotation in a general droplet shape follows a universal curve characterized by geometry, and independent of Bond number, surface inclination and equilibrium contact angle, but determined by the slip length and viscosity contrast. Our results open the way toward a rational design of droplet-surface properties, both when rolling motion is desirable (as in self-cleaning hydrophobic droplets) and when it must be prevented (as in insecticide sprays on leaves).

Fluvial landscapes of the Harappan civilization.

The collapse of the Bronze Age Harappan, one of the earliest urban civilizations, remains an enigma. Urbanism flourished in the western region of the Indo-Gangetic Plain for approximately 600 y, but since approximately 3,900 y ago, the total settled area and settlement sizes declined, many sites were abandoned, and a significant shift in site numbers and density towards the east is recorded. We report morphologic and chronologic evidence indicating that fluvial landscapes in Harappan territory became remarkably stable during the late Holocene as aridification intensified in the region after approximately 5,000 BP. Upstream on the alluvial plain, the large Himalayan rivers in Punjab stopped incising, while downstream, sedimentation slowed on the distinctive mega-fluvial ridge, which the Indus built in Sindh. This fluvial quiescence suggests a gradual decrease in flood intensity that probably stimulated intensive agriculture initially and encouraged urbanization around 4,500 BP. However, further decline in monsoon precipitation led to conditions adverse to both inundation- and rain-based farming. Contrary to earlier assumptions that a large glacier-fed Himalayan river, identified by some with the mythical Sarasvati, watered the Harappan heartland on the interfluve between the Indus and Ganges basins, we show that only monsoonal-fed rivers were active there during the Holocene. As the monsoon weakened, monsoonal rivers gradually dried or became seasonal, affecting habitability along their courses. Hydroclimatic stress increased the vulnerability of agricultural production supporting Harappan urbanism, leading to settlement downsizing, diversification of crops, and a drastic increase in settlements in the moister monsoon regions of the upper Punjab, Haryana, and Uttar Pradesh.

Statistical analysis of the Indus script using n-grams.

The Indus script is one of the major undeciphered scripts of the ancient world. The small size of the corpus, the absence of bilingual texts, and the lack of definite knowledge of the underlying language has frustrated efforts at decipherment since the discovery of the remains of the Indus civilization. Building on previous statistical approaches, we apply the tools of statistical language processing, specifically n-gram Markov chains, to analyze the syntax of the Indus script. We find that unigrams follow a Zipf-Mandelbrot distribution. Text beginner and ender distributions are unequal, providing internal evidence for syntax. We see clear evidence of strong bigram correlations and extract significant pairs and triplets using a log-likelihood measure of association. Highly frequent pairs and triplets are not always highly significant. The model performance is evaluated using information-theoretic measures and cross-validation. The model can restore doubtfully read texts with an accuracy of about 75%. We find that a quadrigram Markov chain saturates information theoretic measures against a held-out corpus. Our work forms the basis for the development of a stochastic grammar which may be used to explore the syntax of the Indus script in greater detail.