Related papers: Closed, Two Dimensional Surface Dynamics
We show that a complex normal surface singularity admitting a contracting automorphism is necessarily quasihomogeneous. We also describe the geometry of a compact complex surface arising as the orbit space of such a contracting…
Two-dimensional potential flows of an ideal fluid with a free surface are considered in situations when shape of the bottom depends on time due to external reasons. Exact nonlinear equations describing surface waves in terms of the so…
The fact that minimal surfaces in the four-dimensional Euclidean space admit natural parameters implies that any minimal surface is determined uniquely up to a motion by two curvature functions, satisfying a system of two PDE's (the system…
We study the Dirichlet problem associated to the equation for self-similar surfaces for graphs over the Euclidean plane with a disk removed. We show the existence of a solution provided the boundary conditions on the boundary circle are…
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions.…
We study the dynamics of circular active particles (AP) on a two dimensional periodic undulated surface. Each particle has an internal energy mechanism which is modeled by an active friction force and it is controlled by an activity…
Deformations can induce rotation with zero angular momentum where dissipation is a natural ``cost function''. This gives rise to an optimization problem of finding the most effective rotation with zero angular momentum. For certain plastic…
In this article we investigated surface of nanocrystals (NC) of uranium dioxide (UO2) using molecular dynamics (MD) under isolated (non-periodic) boundary conditions with the approximation of pair potentials and rigid ions. It is shown that…
In the present work we study the behavior of sequences of smooth global isothermic immersions of a given closed surface and having a uniformly bounded total curvature. We prove that, if the conformal class of this sequence is bounded in the…
Curvature plays a central role in the proper function of many biological processes. With active matter being a standard framework for understanding many aspects of the physics of life, it is natural to ask what effect curvature has on the…
We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the…
We explain the linear growth of smooth solid helium facets by the presence of lattice point defects. To implement this task, the framework of very general two-velocity elasticity theory equations is developed. Boundary conditions for these…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
Two-dimensional Molecular Dynamics simulations are used to model the free surface flow of spheres falling down an inclined chute. The interaction between the particles in our model is assumed to be subjected to the Hertzian contact force…
There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…
We suggest kinetic models of dissipation for an ensemble of interacting oriented particles, for example, moving magnetized particles. This is achieved by introducing a double bracket dissipation in kinetic equations using an oriented…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
Using agent-based simulations of self-propelled particles subject to short-range repulsion and nematic alignment we explore the dynamical phases of a dense active material confined to the surface of a sphere. We map the dynamical phase…
We study the geometry of the mean fitness surface of replicator systems and its relationship to evolutionary trajectory dynamics. Using the symmetric--antisymmetric decomposition of the fitness landscape matrix, we derive an explicit…
In homogenous space Sol we study compact surfaces with constant mean curvature and with non-empty boundary. We ask how the geometry of the boundary curve imposes restrictions over all possible configurations that the surface can adopt. We…