Related papers: Fourth-order flows in surface modelling
In this report, I summarize the experimental results on {\bf bulk properties and flow} presented at Quark Matter 2004. It is organized in four sections: 1) Initial condition and stopping; 2) Particle spectra and freeze-outs; 3) Anisotropic…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
We describe convex quadric surfaces in n dimensions and characterize them as convex surfaces with quadric sections by a continuous family of hyperplanes.
Studies of granular materials, both theoretical and experimental, are often restricted to convex grain shapes. We demonstrate that a non-convex grain shape can lead to a qualitatively novel macroscopic dynamics. Spatial crosses (hexapods)…
In this work we present a new conceptual model to describe fluid flow in a porous media system in presence of a large fault. Geological faults are often modeled simply as interfaces in the rock matrix, but they are complex structure where…
We establish a curvature estimate for classical minimal surfaces with total boundary curvature less than 4\pi. The main application is a bound on the genus of these surfaces depending solely on the geometry of the boundary curve. We also…
The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on…
A heat flow method is used to deform convex hypersurfaces in a ring domain to a hypersurface whose harmonic mean curvature is a prescribed function.
Normalizing flows have arisen as a tool to accelerate Monte Carlo sampling for lattice field theories. This work reviews recent progress in applying normalizing flows to 4-dimensional nonabelian gauge theories, focusing on two advancements:…
Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous application focused on two-dimensional homogeneous fluid, this study examines the geometric…
We discuss the scaling laws for the flow generated in a viscous fluid by a wave propagating along a solid boundary. This has applications to the displacement of tiny objects on solids, under the effect of progressive surface waves and for…
We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for…
The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to…
We consider a class of anisotropic curvature flows called a crystalline curvature flow. We present a survey on this class of flows with special emphasis on the well-posedness of its initial value problem.
We develop a continuum description of partially fluidized granular flows. Our theory is based on the hydrodynamic equation for the flow coupled with the order parameter equation which describes the transition between flowing and static…
We investigate geometric invariants of cuspidal edges on focal surfaces of regular surface. In particular, we shall clarify the sign of the singular curvature at a cuspidal edge on a focal surface using singularities of parallel surface of…
Caroline Series' [{\em The modular surface and continued fractions}, J. Lond. Math. Soc. (2), {\bf 31}, no.~1, (1985), 69--80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular…
This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle it is a flow like method in…
In [5], S\'aez and Schn\"urer studied the graphical mean curvature flow of complete hypersurfaces defined on subsets of Euclidean space. They obtained long time existence. Moreover, they provided a new interpretation of weak mean curvature…
In this second part of our overview of the different metric curvatures and their various applications, we concentrate on the Ricci curvature and flow for polyhedral surfaces and higher dimensional manifolds, and we largely review our…