Related papers: Notes on Smooth and Singular Volumetric Growth
This paper examines the mechanisms of coherent structure interactions in spatially evolving turbulent free shear layers at different values of the velocity ratio parameter {\lambda}=$(U_1-U_2)/(U_1+U_2)$, where $U_1$ and $U_2 (\leq U_1)$…
This paper gives some examples of hypersurfaces $\phi_t(M^n)$ evolving in time with speed determined by functions of the normal curvatures in an $(n+1)$-dimensional hyperbolic manifold; we emphasize the case of flow by harmonic mean…
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
We study the motion of smooth, strictly convex bodies in $\mathbb{R}^n$ expanding in the direction of their normal vector field with speed depending on Gauss curvature and support function.
We study the possibility that the universe is subjected to a deformation, besides its expansion described by Friedmann's equations. The concept of smooth deformation of a riemannian manifolds associated with the extrinsic curvature is…
The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded…
In this paper we investigate the flow of surfaces by a class of symmetric functions of the principal curvatures with a mixed volume constraint. We consider compact surfaces without boundary that can be written as a graph over a sphere. The…
The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity…
In the material science literature we find two continuum models for crystalline defects: (i) A body with (finite) isolated defects is typically modeled as a Riemannian manifold with singularities, and (ii) a body with continuously…
We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…
Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…
The two-fold singularity has played a significant role in our understanding of uniqueness and stability in piecewise smooth dynamical systems. When a vector field is discontinuous at some hypersurface, it can become tangent to that surface…
Computer simulations and scaling theory are used to investigate the damping of oscillations during epitaxial growth on high-symmetry surfaces. The crossover from smooth to rough growth takes place after the deposition of (D/F)^\delta…
In this article we consider the general problem of translating definitions and results from the category of discrete-time dynamical systems to the category of flows. We consider the dynamics of homeomorphisms and flows on compact metric…
We use the Dynamic Density-Functional Formalism and the Fundamental Measure Theory as applied to a fluid of parallel hard squares to study the dynamics of heterogeneous growth of non-uniform phases with columnar and crystalline symmetries.…
A systematic investigation of the phase separation dynamics in self-assembled multi-component bilayer fluid vesicles and open membranes is presented. We use large-scale dissipative particle dynamics to explicitly account for solvent,…
We consider the local kinematics at fluid interfaces in two-phase flows within the sharp interface framework. In the considered case with phase change and slip at the interface, the governing velocity field is discontinuous at the phase…
A mechanism is proposed for the growth of vesicles dispersed in a liquid solvent and a size distribution function is obtained for the vesicles, both from the first principles calculations. This distribution function is shown to be…
The relationship between the volume and surface energy coefficients in the liquid drop A^{-1/3} expansion of nuclear masses is discussed. The volume and surface coefficients in the liquid drop expansion share the same physical origin and…
In this paper, we derive curvature estimates for strongly stable hypersurfaces with constant mean curvature immersed in $\mathbb{R}^{n+1}$, which show that the locally controlled volume growth yields a globally controlled volume growth if…