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Minimizers of a weighted maximum of the Gauss curvature
On a Riemann surface [`(S)] with smooth boundary, we consider Riemannian metrics conformal to a given background metric. Let κ be a smooth, positive function on [`(S)]. If K denotes the Gauss curvature, then the L ∞-norm of K/κ...
Travelling waves for a Frenkel-Kontorova chain
In this article, the Frenkel–Kontorova model for dislocation dynamics is considered, where the on-site potential consists of quadratic wells joined by small arcs, which can be spinodal (concave) as commonly assumed in physics....
Nonexistence of slow heteroclinic travelling waves for a bistable Hamiltonian lattice model
The nonexistence of heteroclinic travelling waves in an atomistic model for martensitic phase transitions is the focus of this study. The elastic energy is assumed to be piecewise quadratic, with two wells representing two...
Kinetic relations for a lattice model of phase transitions
The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi-Pasta-Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large...
Minimizers of a weighted maximum of the Gauss curvature
On a Riemann surface [`(S)] with smooth boundary, we consider Riemannian metrics conformal to a given background metric. Let κ be a smooth, positive function on [`(S)]. If K denotes the Gauss curvature, then the L ∞-norm of K/κ...
Calculation of long time classical trajectories
We study the problem of finding a path that joins a given initial state with a final one, where the evolution is governed by classical (Hamiltonian) dynamics. A new algorithm for the computation of long time transition...
Kinetic relations for a lattice model of phase transitions
The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi-Pasta-Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large...
Travelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potential
The Frenkel–Kontorova model for dislocation dynamics from 1938 is given by a chain of atoms, where neighbouring atoms interact through a linear spring and are exposed to a smooth periodic on-site potential. A dislocation moving...
On selection criteria for problems with moving inhomogeneities
We study mechanical problems with multiple solutions and introduce a thermodynamic framework to formulate two different selection criteria in terms of macroscopic energy productions and fluxes. Simple examples for lattice motion...
Calculation of long time classical trajectories
We study the problem of finding a path that joins a given initial state with a final one, where the evolution is governed by classical (Hamiltonian) dynamics. A new algorithm for the computation of long time transition...
Travelling heteroclinic waves in a Frenkel-Kontorova chain with anharmonic on-site potential
The Frenkel–Kontorova model for dislocation dynamics from 1938 is given by a chain of atoms, where neighbouring atoms interact through a linear spring and are exposed to a smooth periodic on-site potential. A dislocation moving...
Travelling waves for a Frenkel-Kontorova chain
In this article, the Frenkel–Kontorova model for dislocation dynamics is considered, where the on-site potential consists of quadratic wells joined by small arcs, which can be spinodal (concave) as commonly assumed in physics....
AN ELASTIC FLOW FOR NONLINEAR SPLINE INTERPOLATIONS IN ℝ<sup>n</sup>
In this paper we use the method of geometric flow on the problem of nonlinear spline interpolations for non-closed curves in n-dimensional Euclidean spaces. The method applies theory of fourth-order parabolic PDEs to each...
Nonexistence of slow heteroclinic travelling waves for a bistable Hamiltonian lattice model
The nonexistence of heteroclinic travelling waves in an atomistic model for martensitic phase transitions is the focus of this study. The elastic energy is assumed to be piecewise quadratic, with two wells representing two...
On selection criteria for problems with moving inhomogeneities
We study mechanical problems with multiple solutions and introduce a thermodynamic framework to formulate two different selection criteria in terms of macroscopic energy productions and fluxes. Simple examples for lattice motion...
AN ELASTIC FLOW FOR NONLINEAR SPLINE INTERPOLATIONS IN ℝ<sup>n</sup>
In this paper we use the method of geometric flow on the problem of nonlinear spline interpolations for non-closed curves in n-dimensional Euclidean spaces. The method applies theory of fourth-order parabolic PDEs to each...
A systems biology approach uncovers the core gene regulatory network governing iridophore fate choice from the neural crest.
Kleio Petratou, Tatiana Subkhankulova, James A Lister, Andrea Rocco, Hartmut Schwetlick, Robert N Kelsh
Dec 13, 2018
Multipotent neural crest (NC) progenitors generate an astonishing array of derivatives, including neuronal, skeletal components and pigment cells (chromatophores), but the molecular mechanisms allowing balanced selection of each...
On the Γ-limit for a non-uniformly bounded sequence of two-phase metric functionals
We consider the Γ-limit of a highly oscillatory Riemannian metric length functional as its period tends to 0. The metric coefficient takes values in either {1, ∞} or {1, βε-g} where β, ε > 0 and p ∈ (0, ∞). We...
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