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The linear stability of a shear layer in a highly diffusive stably stratified atmosphere has been investigated. This study completes and extends previous works by Dudis (1974) and Jones (1977). We show that: (i) an asymptotic regime is…
A disordered solid, such as an athermal jammed packing of soft spheres, exists in a rugged potential-energy landscape in which there are a myriad of stable configurations that defy easy enumeration and characterization. Nevertheless, in…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
The proliferation of turbulence in subcritical wall-bounded shear flows involves spatially localised coherent structures. Turbulent spots correspond to finite-time nonlinear responses to pointwise disturbances and are regarded as seeds of…
Consider a sequence of masses $m_0,m_1,...$ arriving uniformly at random at some points $u_0,u_1,...$ on the unit circle $\mathbb{R}/\mathbb{Z}$ (or on $\mathbb{Z}/n\mathbb{Z}$, in the discrete version). Upon arrival, each mass undergoes a…
This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…
The stability of optimal transport maps with respect to perturbations of the marginals is a question of interest for several reasons, ranging from the justification of the linearized optimal transport framework to numerical analysis and…
Dissipation is a common occurrence in real-world systems and is generally considered to be detrimental to transport. In this study, we examine the transport properties of a narrow quantum anomalous Hall system with dissipation applied on…
The transport and dispersion of multiple species of charged ions are central to many biological and physical processes, including electrokinetic ion separation. However, most theoretical studies of dispersion in channels have focused on…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…
Stably placing an object in a multi-object scene is a fundamental challenge in robotic manipulation, as placements must be penetration-free, establish precise surface contact, and result in a force equilibrium. To assess stability, existing…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
Computer simulation of the hopping charge transport in disordered organic materials has been carried out explicitly taking into account charge-charge interactions. This approach provides a possibility to take into account dynamic…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
When a mixture of two kinds of grains differing in size and shape is poured in a vertical two-dimensional cell, the mixture spontaneously stratifies in alternating layers of small and large grains, whenever the large grains are more faceted…
I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
When polydisperse granular systems are sheared, the transverse dynamics is characterized by the interplay of size segregation and diffusion. Segregation in nonuniform and confined shearing flows is studied using annular shear cell…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
Many key environmental, industrial, and energy processes rely on controlling fluid transport within subsurface porous media. These media are typically structurally heterogeneous, often with vertically-layered strata of distinct…