Self-Ordering of Buckling, Bending, and Bumping Beams.

A collection of thin structures buckle, bend, and bump into each other when confined. This contact can lead to the formation of patterns: hair will self-organize in curls; DNA strands will layer into cell nuclei; paper, when crumpled, will fold in on itself, forming a maze of interleaved sheets. This pattern formation changes how densely the structures can pack, as well as the mechanical properties of the system. How and when these patterns form, as well as the force required to pack these structures is not currently understood. Here we study the emergence of order in a canonical example of packing in slender structures, i.e., a system of parallel confined elastic beams. Using tabletop experiments, simulations, and standard theory from statistical mechanics, we predict the amount of confinement (growth or compression) of the beams that will guarantee a global system order, which depends only on the initial geometry of the system. Furthermore, we find that the compressive stiffness and stored bending energy of this metamaterial are directly proportional to the number of beams that are geometrically frustrated at any given point. We expect these results to elucidate the mechanisms leading to pattern formation in these kinds of systems and to provide a new mechanical metamaterial, with a tunable resistance to compressive force.

Rapid Characterization of Multiple-Contact Miscibility: Toward a Slim-Tube on a Chip.

Carbon dioxide enhanced oil recovery (CO2-EOR) has been widely used to improve production from mature oil fields around the world. To be effective, the injected gas and reservoir oil must develop miscibility, which generally requires prolonged contact between the two phases while in relative motion. Thus, identifying whether miscibility is possible is crucial for determining the feasibility of such EOR projects. The current industry-standard method of characterization, the slim-tube, requires weeks of analysis, while alternative methods are unable to infer all routes to miscibility, producing significant overestimates in required pressures. Microfluidic devices have the potential to simplify and speed up the analysis by offering high levels of fluid control and excellent visualization. Recently, high-pressure microfluidic devices etched into glass and exploiting crude oil's natural fluorescence have been successfully demonstrated. Here we focus on designing a microfluidic channel for identifying the development of miscibility. We prove its accuracy for a known ternary fluid system that mimics the true oil-gas system and can be manipulated at room temperature and pressure. Our chip consists of a single channel with several inline pocket structures. The chip is initially flooded with one phase before a second phase is injected via a flow-rate-controlled pump. The first phase is then rapidly displaced in the primary channel, but small samples are retained within the pockets. Over time, these trapped droplets can be observed as they interact with the continuously flowing second phase. When the fluid concentrations meet the conditions for development of miscibility, a dramatic and visually observable change in behavior occurs, allowing for characterization within 2 h.

Superwalking Droplets.

A walker is a droplet of liquid that self-propels on the free surface of an oscillating bath of the same liquid through feedback between the droplet and its wave field. We have studied walking droplets in the presence of two driving frequencies and have observed a new class of walking droplets, which we coin superwalkers. Superwalkers may be more than double the size of the largest walkers, may travel at more than triple the speed of the fastest ones, and enable a plethora of novel multidroplet behaviors.

Pilot-wave dynamics of two identical, in-phase bouncing droplets.

A droplet bouncing on the surface of a vibrating liquid bath can move horizontally guided by the wave it produces on impacting the bath. The wave itself is modified by the environment, and thus, the interactions of the moving droplet with the surroundings are mediated through the wave. This forms an example of a pilot-wave system. Taking the Oza-Rosales-Bush description for walking droplets as a theoretical pilot-wave model, we investigate the dynamics of two interacting identical, in-phase bouncing droplets theoretically and numerically. A remarkably rich range of behaviors is encountered as a function of the two system parameters, the ratio of inertia to drag, κ , and the ratio of wave forcing to drag, ß . The droplets typically travel together in a tightly bound pair, although they unbind when the wave forcing is large and inertia is small or inertia is moderately large and wave forcing is moderately small. Bound pairs can exhibit a range of trajectories depending on parameter values, including straight lines, sub-diffusive random walks, and closed loops. The droplets themselves may maintain their relative positions, oscillate toward and away from one another, or interchange positions regularly or chaotically as they travel. We explore these regimes and others and the bifurcations between them through analytic and numerical linear stability analyses and through fully nonlinear numerical simulation.

Hong-Ou-Mandel-like two-droplet correlations.

We present a numerical study of two-droplet pair correlations for in-phase droplets walking on a vibrating bath. Two such walkers are launched toward a common point of intersection. As they approach, their carrier waves may overlap and the droplets have a non-zero probability of forming a two-droplet bound state. The likelihood of such pairing is quantified by measuring the probability of finding the droplets in a bound state at late times. Three generic types of two-droplet correlations are observed: promenading, orbiting, and chasing pair of walkers. For certain parameters, the droplets may become correlated for certain initial path differences and remain uncorrelated for others, while in other cases, the droplets may never produce droplet pairs. These observations pave the way for further studies of strongly correlated many-droplet behaviors in the hydrodynamical quantum analogs of bouncing and walking droplets.

Quantifying the impact of individual and collective compliance with infection control measures for ethical public health policy.

Infectious disease control measures often require collective compliance of large numbers of individuals to benefit public health. This raises ethical questions regarding the value of the public health benefit created by individual and collective compliance. Answering these requires estimating the extent to which individual actions prevent infection of others. We develop mathematical techniques enabling quantification of the impacts of individuals or groups complying with three public health measures: border quarantine, isolation of infected individuals, and prevention via vaccination/prophylaxis. The results suggest that (i) these interventions exhibit synergy: They become more effective on a per-individual basis as compliance increases, and (ii) there is often substantial "overdetermination" of transmission. If a susceptible person contacts multiple infectious individuals, an intervention preventing one transmission may not change the ultimate outcome (thus, risk imposed by some individuals may erode the benefits of others' compliance). These results have implications for public health policy during epidemics.

Stop-and-go locomotion of superwalking droplets.

Vertically vibrating a liquid bath at two frequencies, f and f/2, having a constant relative phase difference can give rise to self-propelled superwalking droplets on the liquid surface. We have numerically investigated such superwalking droplets in the regime where the phase difference varies slowly with time. We predict the emergence of stop-and-go motion of droplets, consistent with experimental observations [Valani et al. Phys. Rev. Lett. 123, 024503 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.024503]. Our simulations in the parameter space spanned by the droplet size and the rate of traversal of the phase difference uncover three different types of droplet motion: back-and-forth, forth-and-forth, and irregular stop-and-go motion, which we explore in detail. Our findings lay a foundation for further studies of dynamically driven droplets, whereby the droplet's motion may be guided by engineering arbitrary time-dependent phase difference functions.

Unsteady dynamics of a classical particle-wave entity.

A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by the waves it generates on each impact. This results in a self-propelled classical particle-wave entity. By using a one-dimensional theoretical pilot-wave model with a generalized wave form, we investigate the dynamics of this particle-wave entity. We employ different spatial wave forms to understand the role played by both wave oscillations and spatial wave decay in the walking dynamics. We observe steady walking motion as well as unsteady motions such as oscillating walking, self-trapped oscillations, and irregular walking. We explore the dynamical and statistical aspects of irregular walking and show an equivalence between the droplet dynamics and the Lorenz system, as well as making connections with the Langevin equation and deterministic diffusion.

Epidemics with general generation interval distributions.

We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic effects dominate and show that epidemics tend to happen faster than deterministic calculations predict. If an outbreak is sufficiently large, stochastic effects are negligible and we modify the standard ordinary differential equation (ODE) model to accommodate age-of-infection effects. We avoid the use of partial differential equations which typically appear in related models. We introduce a "memoryless" ODE system which approximates the true solutions. Finally, we analyze the transition from the stochastic to the deterministic phase.

Pore-scale multiple-contact miscibility measurements in a microfluidic chip.

Carbon dioxide enhanced oil recovery is an interim solution as the world transitions to a cleaner energy future, extending oil production from existing fields whilst also sequestering carbon dioxide. To make this process efficient, the gas and oil need to develop miscibility over a period of time through the exchange of chemical components between the two phases, termed multiple-contact miscibility. Currently, measurements to infer the development of multiple-contact miscibility are limited to macroscopic visualization. We present a "rock-on-a-chip" measurement system that offers several potential measurements for different wetting conditions to infer the onset of multiple-contact miscibility. Here, a two-dimensional microfluidic porous medium with a stochastic distribution of pillars was created, and an analogue ternary system was used to mimic the real oil and gas multiple-contact miscibility process. Experiments were performed in two directions, imbibition and drainage, permitting study of different wetting properties of the host rock. The distinct behavior of trapped non-wetting ganglia during imbibition and the evolution of phase interfaces during drainage were observed and analyzed as the system developed miscibility. We show how these observations can be converted into rapid measurements for identifying the development of miscibility.

Saturation effects and the concurrency hypothesis: Insights from an analytic model.

Sexual partnerships that overlap in time (concurrent relationships) may play a significant role in the HIV epidemic, but the precise effect is unclear. We derive edge-based compartmental models of disease spread in idealized dynamic populations with and without concurrency to allow for an investigation of its effects. Our models assume that partnerships change in time and individuals enter and leave the at-risk population. Infected individuals transmit at a constant per-partnership rate to their susceptible partners. In our idealized populations we find regions of parameter space where the existence of concurrent partnerships leads to substantially faster growth and higher equilibrium levels, but also regions in which the existence of concurrent partnerships has very little impact on the growth or the equilibrium. Additionally we find mixed regimes in which concurrency significantly increases the early growth, but has little effect on the ultimate equilibrium level. Guided by model predictions, we discuss general conditions under which concurrent relationships would be expected to have large or small effects in real-world settings. Our observation that the impact of concurrency saturates suggests that concurrency-reducing interventions may be most effective in populations with low to moderate concurrency.

Edge-based compartmental modelling for infectious disease spread.

The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action susceptible-infected-recovered model of Kermack & McKendrick. Its usefulness derives largely from its conceptual and mathematical simplicity; however, it incorrectly assumes that all individuals have the same contact rate and partnerships are fleeting. In this study, we introduce edge-based compartmental modelling, a technique eliminating these assumptions. We derive simple ordinary differential equation models capturing social heterogeneity (heterogeneous contact rates) while explicitly considering the impact of partnership duration. We introduce a graphical interpretation allowing for easy derivation and communication of the model and focus on applying the technique under different assumptions about how contact rates are distributed and how long partnerships last.