116 citations · 406 across the 19 of their papers we have counts for
20 papers
The Onset Acceleration for Surfactant Covered Faraday Waves
Stephen L. Strickland, Karen E. Daniels, Michael Shearer
Faraday waves are gravity-capillary waves that emerge on the surface of a vertically vibrated fluid when the energy injected via vibration exceeds the energy lost due to viscous di…
The Kawahara Equation: Traveling Wave Solutions Joining Periodic Waves
Patrick Sprenger, Thomas J. Bridges, Michael Shearer
The Kawahara equation is a weakly nonlinear long-wave model of dispersive waves that emerges when leading order dispersive effects are in balance with the next order correction. Tr…
Dispersive Riemann problem for the Benjamin-Bona-Mahony equation
T. Congy, G. A. El, M. A. Hoefer +1
Long time dynamics of the smoothed step initial value problem or dispersive Riemann problem for the Benjamin-Bona-Mahony (BBM) equation are studied using asy…
Distinguishing deformation mechanisms in elastocapillary experiments
Shih-Yuan Chen, Aaron Bardall, Michael Shearer +1
Soft materials are known to deform due to a variety of mechanisms, including capillarity, buoyancy, and swelling. In this paper, we present experiments on polyvinylsiloxane gel thr…
Gradient Induced Droplet Motion Over Soft Solids
Aaron Bardall, Shih-Yuan Chen, Karen E. Daniels +1
Fluid droplets can be induced to move over rigid or flexible surfaces under external or body forces. We describe the effect of variations in material properties of a flexible subst…
Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure
T. Congy, G. A. El, M. A. Hoefer +1
The nonlinear Schrödinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-fre…
A Scalar Conservation Law for Plume Migration in Carbon Sequestration
Elisabeth Brown, Michael Shearer
A quasi-linear hyperbolic partial differential equation with a discontinuous flux models geologic carbon dioxide migration and storage. Dual flux curves characterize the model, giv…
Stationary Expansion Shocks for a Regularized Boussinesq System
G. A. El, M. A. Hoefer, M. Shearer
Stationary expansion shocks have been recently identified as a new type of solution to hyperbolic conservation laws regularized by non-local dispersive terms that naturally arise i…
Well-posed continuum equations for granular flow with compressibility and -rheology
T. Barker, D. G. Schaeffer, M. Shearer +1
Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb…
Deformation of an Elastic Substrate Due to a Resting Sessile Droplet
Aaron Bardall, Karen E. Daniels, Michael Shearer
On a sufficiently-soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at th…
Expansion shock waves in regularised shallow water theory
Gennady A. El, Mark A. Hoefer, Michael Shearer
We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularised shallow water equations that include the Benjamin-Bona-Mahoney…
Wetting dynamics of a collapsing fluid hole
Joshua Bostwick, Joshua Dijksman, Michael Shearer
The collapse dynamics of an axisymmetric fluid cavity that wets the bottom of a rotating bucket bound by vertical sidewalls are studied. Lubrication theory is applied to the govern…
Spatiotemporal measurement of surfactant distribution on gravity-capillary waves
Stephen L Strickland, Michael Shearer, Karen E Daniels
Materials adsorbed to the surface of a fluid -- for instance, crude oil, biogenic slicks, or industrial/medical surfactants -- will move in response to surface waves. Due to the di…
Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws
G. A. El, M. A. Hoefer, M. Shearer
We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and d…
Traveling Waves for Conservation Laws with Cubic Nonlinearity and BBM Type Dispersion
Michael Shearer, Kimberly R. Spayd, Ellen R. Swanson
Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of…
Elastocapillary deformations on partially-wetting substrates: rival contact-line models
Joshua B. Bostwick, Michael Shearer, Karen E. Daniels
A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting fo…
Surfactant Spreading on a Thin Liquid Film: Reconciling Models and Experiments
Ellen R. Swanson, Stephen L. Strickland, Michael Shearer +1
The spreading dynamics of surfactant molecules on a thin fluid layer is of both fundamental and practical interest. A mathematical model formulated by Gaver and Grotberg 1990 descr…
The Buckley-Leverett Equation with Dynamic Capillary Pressure
K. Spayd, M. Shearer
The Buckley-Leverett equation for two phase flow in a porous medium is modified by including a dependence of capillary pressure on the rate of change of saturation. This model, due…
Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow
Lindsay B. H. May, Michael Shearer, Karen E. Daniels
Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled…
Shear-driven size segregation of granular materials: modeling and experiment
Lindsay B. H. May, Laura A. Golick, Katherine C. Phillips +2
Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of…