Related papers: Surface Shape of Two-Dimensional Granular Piles
We theoretically and numerically investigate the steady flow of two-dimensional granular materials in a rotating drum using the discrete element method and a continuum model with the $\mu(I)$-rheology. The velocity fields obtained from both…
Considering recent results revealing the existence of multi-scale rigid clusters of grains embedded in granular surface flows, i.e. flows down an erodible bed, we describe here the surface flows rheology through a non-local constitutive…
With a toppling rule which generates metastable sites, we explore the properties of a gradient-driven sandpile that is minimally perturbed at one boundary. In two dimensions we find that the transport of grains takes place along deep…
On one hand, we study the class of graphs on surfaces, satisfying tessellation properties, with positive Forman curvature on each edge. Via medial graphs, we provide a new proof for the finiteness of the class, and give a complete…
In continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral.…
Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady…
A simple solid-on-solid model, proposed earlier to describe overlayer-induced faceting of bcc(111) surface, is applied to faceting of spherical surfaces covered by adsorbate monolayer. Monte Carlo simulation results show that morphology of…
A deposition process with particles having realistic intermediate stickiness is studied in 2+1 dimensions. At each stage of the deposition process, for any given configuration, a newly depositing particle gives rise to allowed set of…
The correspondence between 2-parameter families of oriented lines in ${\Bbb{R}}^3$ and surfaces in $T{\Bbb{P}}^1$ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences…
This paper is concerned with the application of finite element methods to obtain solutions for steady fully developed second-grade flows in a curved pipe of circular cross-section and arbitrary curvature ratio, under a given axial pressure…
The pore-surface and surface-surface correlation functions are structural characteristics that play an important role in theoretical materials science and in small-angle scattering theory. Exact analytical expressions for the surface…
Granular flow down an inclined plane is ubiquitous in geophysical and industrial applications. On rough inclines, the flow exhibits Bagnold's velocity profile and follows the so-called $\mu(I)$ local rheology. On insufficiently rough or…
We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify…
We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via appropriate statistical approaches. Different random substrate families are represented as stationary random functions.…
We study the transition between steady flows of non-cohesive granular materials in quasi-2D bounded heaps by suddenly changing the feed rate. In both experiments and simulations, the primary feature of the transition is a wedge of flowing…
Motivated by a number of recent investigations, we define and investigate the various properties of the ruled surfaces depend on three dimensional Lie groups with a bi-variant metric. We give useful results involving the characterizations…
We formulate a continuum model for aeolian sand ripples consisting of two species of grains: a lower layer of relatively immobile clusters, with an upper layer of highly mobile grains moving on top. We predict analytically the ripple…
We consider steady gravity-driven flow of a thin layer of viscous fluid over a curved substrate. The substrate has topographical variations (`bumps') on a large scale compared to the layer thickness. Using lubrication theory, we find the…
During drying of colloidal suspensions, colloidal particles can form concentrated particle layers beneath the receding free surface. The drying rate can gradually decrease with the growth of the particle layers. We construct a model to…
We present a scaled particle density functional study of two-dimensional binary mixtures of hard convex particles with one or both species being ellipses. In particular, we divide our study into two parts. The first part is devoted to the…