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 mathematical simplicity; however, it incorrectly assumes that all individuals have same contact rate partnerships are fleeting. In this study, we introduce edge-based compartmental modelling , a technique eliminating these assumptions. We derive simple ordinary...

Abstract We numerically characterize the temporal regimes for solutal convection from almost first contact to high dissolved solute concentration in a two-dimensional ideal porous layer Rayleigh numbers $\mathcal{R}$ between $100$ and $5\times 10^4$ . The lower boundary is impenetrable. upper saturated with either impermeable or partially permeable fluid flow. In case, initially there pure diffusion of away boundary, followed by birth growth convective fingers. Eventually fingers interact...

Motivated by convection in the context of geological carbon-dioxide (CO2) storage, we present an experimental study dissolution-driven a Hele–Shaw cell for Rayleigh numbers \documentclass[12pt]{minimal}\begin{document}$\mathcal {R}$\end{document}R range \documentclass[12pt]{minimal}\begin{document}$100 < \mathcal {R}< 1700$\end{document}100<R<1700. We use potassium permanganate (KMnO4) water as analog CO2 brine and infer concentration profiles at high spatial...

Motivated by convection in the context of geological carbon dioxide sequestration, we present conditions for free, dissolution-driven a horizontal, ideal porous layer from time-dependent, pure-diffusion base state. We assume that solute as separate phase is instantaneously placed pores above given horizontal level at time zero, and gradually diffuses into underlying liquid. As concentration dissolved liquid increases, its density increases system may eventually become gravitationally...

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

A collection of thin structures buckle, bend, and bump into each other when confined. This contact can lead to the formation patterns: hair will self-organize in curls; DNA strands layer cell nuclei; paper, crumpled, fold on itself, forming a maze interleaved sheets. pattern changes how densely pack, as well mechanical properties system. How these patterns form, force required pack is not currently understood. Here we study emergence order canonical example packing slender structures, i.e.,...

Volcanic eruptions commonly produce buoyant ash-laden plumes that rise through the stratified atmosphere. On reaching their level of neutral buoyancy, these cease rising and transition to horizontally spreading intrusions. Such intrusions occur widely in density-stratified fluid environments, this paper we develop a shallow-layer model governs motion. We couple dynamical for particle transport sedimentation, predict both time-dependent distribution ash within volcanic flux falls towards...

A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by waves it generates each impact. This results in self-propelled classical particle-wave entity. By using one-dimensional theoretical pilot-wave model with generalized wave form, we investigate dynamics this We employ different spatial forms to understand role played both oscillations and decay walking dynamics. observe steady motion as well unsteady motions such oscillating walking,...

Abstract We investigate the conditions under which saucer‐shaped sills form and segment in upper crust. performed a series of scaled laboratory experiments that employ visco‐elastic‐plastic Laponite RD® (LRD) gels to model crustal rocks, Newtonian paraffin oil as magma analog. Saucer‐shaped always formed with two‐layer These show sharp transitions from an inner flat sill outer inclined sheets, are characterized by non‐planar margins. The results that: (a) transition sheet occurs when radius...

Rhythmic patterns are widespread in geological materials. A particularly striking, macroscale example is zebra rock from the East Kimberley region of northwestern Australia. The famous for its distinctive, rhythmically ordered, iron-oxide pattern, which transforms an Ediacaran-aged siltstone into attractive semi-precious gemstone. Several different formation mechanisms this pattern have been proposed previous studies, with two most prominent being redoximorphic banding acid-sulfate soils and...

Abstract We analyse the buckling stability of a thin, viscous sheet when subject to simple shear, providing conditions for onset dominant out-of-plane modes using two models: (i) an asymptotic theory dynamics plate, and (ii) full Stokes equations. In either case, plate is stabilized by combination resistance, surface tension buoyancy relative underlying denser fluid. limit vanishing thickness, plates buckle at shear rate $\gamma / (\ensuremath{\mu} d)$ independent buoyancy, where $2d$ $...

A new class of self-propelled droplets, coined superwalkers, has been shown to emerge when a bath silicone oil is vibrated simultaneously at given frequency and its subharmonic tone with relative phase difference between them (Valani et al. 2019). To understand the emergence superwalking we explore their vertical horizontal dynamics by extending previously established theoretical models for walkers driven single superwalkers two frequencies. Here show that driving frequencies an appropriate...

A droplet bouncing on the surface of a vibrating liquid bath can move horizontally guided by wave it produces impacting bath. The itself is modified environment, and thus, interactions moving with surroundings are mediated through wave. This forms an example pilot-wave system. Taking Oza–Rosales–Bush description for walking droplets as theoretical model, we investigate dynamics two interacting identical, in-phase theoretically numerically. remarkably rich range behaviors encountered function...

Infectious disease control measures often require collective compliance of large numbers individuals to benefit public health. This raises ethical questions regarding the value health created by individual and compliance. Answering these requires estimating extent which actions prevent infection others. We develop mathematical techniques enabling quantification impacts or groups complying with three measures: border quarantine, isolation infected individuals, prevention via...

We present a numerical study of two-droplet pair correlations for in-phase droplets walking on vibrating bath. Two such walkers are launched toward common point intersection. As they approach, their carrier waves may overlap and the have non-zero probability forming bound state. The likelihood pairing is quantified by measuring finding in state at late times. Three generic types observed: promenading, orbiting, chasing walkers. For certain parameters, become correlated initial path...

Carbon dioxide enhanced oil recovery is an interim solution as the world transitions to a cleaner energy future, extending production from existing fields whilst also sequestering carbon dioxide. To make this process efficient, gas and need develop miscibility over period of time through exchange chemical components between two phases, termed multiple-contact miscibility. Currently, measurements infer development are limited macroscopic visualization. We present "rock-on-a-chip" measurement...

Sexual partnerships that overlap in time (concurrent relationships) may play a significant role the HIV epidemic, but precise effect is unclear. We derive edge-based compartmental models of disease spread idealized dynamic populations with and without concurrency to allow for an investigation its effects. Our assume change individuals enter leave at-risk population. Infected transmit at constant per-partnership rate their susceptible partners. In our we find regions parameter space where...

Carbon dioxide enhanced oil recovery (CO2-EOR) has been widely used to improve production from mature fields around the world. To be effective, injected gas and reservoir must develop miscibility, which generally requires prolonged contact between two phases while in relative motion. Thus, identifying whether miscibility is possible crucial for determining feasibility of such EOR projects. The current industry-standard method characterization, slim-tube, weeks analysis, alternative methods...

A phase-plane approach is used to determine similarity solutions of the axisymmetric shallow-water equations which represent inwardly propagating, inviscid gravity currents. Froude number condition characterizes movement front. The unique exponent found numerically as a function frontal and height velocity profiles are presented for three different numbers. fluid speed seen increase monotonically towards front except very close where decreases. maxima in both increases, reflecting change...