Remodelling of biological tissue, due to changes in microstructure, is treated in the continuum mechanical setting. Microstructural change is expressed as an evolution of the reference configuration. This evolution is expressed as a point-to-point map from the reference configuration to a remodelled configuration. A “preferred” change in configuration is considered in the form of a globally inc...

Let T be a discrete subgroup of automorphisms of H", with fundamental polyhedron of finite volume, finite number of sides, and N cusps. Denote by Ar the Laplace-Beltrami operator acting on functions automorphic with respect to T. We give a new short proof of the fact that Ar has absolutely continuous spectrum of uniform multiplicity N on (-00,«11 l)/2)2), plus a standard discrete spectrum. We s...

We propose a covariant definition of the fractional Klein-Gordon equation with long-range interactions independent metric underlying manifold. As an example we consider on AdS$_{2+1}$, computing explicit kernel representation Laplace-Beltrami operator as well two-point propagator equation. Our results suggest that only exists if mass is small compared to inverse AdS radius, presumably because s...

<p style='text-indent:20px;'>In this paper, we introduce a rigorous computational approach to prove existence of rotation invariant patterns for nonlinear Laplace-Beltrami equation posed on the 2-sphere. After changing spherical coordinates, problem becomes singular second order boundary value (BVP) interval <inline-formula><tex-math id="M1">\begin{document}$ (0,\frac{\pi}{2}]...

First, we prove that the BMO condition by John–Nirenberg leads in natural way to asymptotic homogeneity at origin of regular homeomorphic solutions degenerate Beltrami equations. Then, on this basis establish a series criteria for existence equations whole complex plane with infinity. These results can be applied fluid mechanics strongly anisotropic and inhomogeneous media because equation is f...

We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as models the same electrical conduction phenomenon in heterogeneous media, neglecting magnetic field. One of problems is concentration limit other one, when thickness dielectric inclusions goes to zero. The concentrated problem involves transmission condition through interfaces, mediated by suitable Laplace-B...

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansi...

This study is concerned with the investigation of the associated properties of subcell discretisations for viscoelastic flows, where aspects of compatibility of solution function spaces are paramount. We introduce one new scheme, through a subcell finite element approximation fe(sc), and compare and contrast this against two precursor schemes – one with finite element discretisation in common, ...

Beltrami states for compressible barotropic flows are deduced by minimizing the total kinetic energy while keeping the total helicity constant. A Hamiltonian basis for these Beltrami states is also sketched.