Related papers: Notes on Smooth and Singular Volumetric Growth

Mixing, and coherence are fundamental issues at the heart of understanding transport in fluid dynamics and other non-autonomous dynamical systems. Recently, the notion of coherence has come to a more rigorous footing, and particularly…

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting…

We study a variational problem for piecewise-smooth hypersurfaces in the (n+1)-dimensional Euclidean space with an anisotropic energy. An anisotropic energy is the integral of an energy density that depends on the normal at each point over…

Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…

In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…

We consider the volume preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long time asymptotics…

The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…

A finite volume symplectic manifold is said to have "packing stability" if the only obstruction to symplectically embedding sufficiently small balls is the volume obstruction. Packing stability has been shown in a variety of cases and it…

We will show that the cotangent bundle of a manifold whose free loopspace homology grows exponentially is not symplectomorphic to any smooth affine variety. We will also show that the unit cotangent bundle of such a manifold is not Stein…

In this paper we would like give a short review of our recent works and current investigation in modeling of solid film surfaces growth based on computer Monte Carlo simulations. We also discuss effect of some simplification in growth rules…

This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension…

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…

We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…

We investigate numerically the influence of an homogeneous shear flow on the spinodal decomposition of a binary mixture by solving the Cahn-Hilliard equation in a two-dimensional geometry. Several aspects of this much studied problem are…

Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of…

Modern astronomical observations in cosmology provide increasingly strong evidence that the expansion of the Universe is accelerating. Explanations of the cosmic acceleration within the framework of general relativity use the hypothesis…

This continuum mechanical theory aims at detailing the underlying rational mechanics of dynamic boundary conditions proposed by Fischer, Maass, & Dieterich [1], Goldstein, Miranville, & Schimperna [2], and Knopf, Lam, Liu & Metzger, [3]. As…

Processes are often viewed as coalgebras, with the structure maps specifying the state transitions. In the simplest case, the state spaces are discrete, and the structure map simply takes each state to the next states. But the coalgebraic…

Three-dimensional central symmetric bodies different from spheres that can float in all orientations are considered. For relative density rho=1/2 there are solutions, if holes in the body are allowed. For rho different from 1/2 the body is…

In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the…