Geometrical models for grain dynamics

Geometrical Models for Grain Dynamics

General Geometrical Models of Grain Boundaries

Geonetric models of grain boundaries have been extensively studied following Bollmann's original ideas. 1hese models apply only for symmorphic structures with one atom per primitive unit cell. These restrictions may be easily avoided by introducing some elementary concepts of crystallography which lead to an unified description of homophase interfaces. Ihe notion of symmetry dictated extrema is...

Geometrical Models for Substitutions

We consider a substitutive version of the Arnoux-Yoccoz Interval Exchange Transformation (IET) related to the Tribonacci substitution. We construct the so-called stepped lines associated to the fixed points of the substitution in the Abelianisation (symbolic) space. We analyse various projections of the stepped line recovering the Rauzy Fractal, a Peano Curve related to the work of Arnoux [1], ...

Geometrical Models of the Phase Space Structures Governing Reaction Dynamics

Hamiltonian dynamical systems possessing equilibria of saddle × centre × · · · × centre stability type display reaction-type dynamics for energies close to the energy of such equilibria; entrance and exit from certain regions of the phase space is only possible via narrow bottlenecks created by the influence of the equilibrium points. In this paper we provide a thorough pedagogical description ...

Understanding Neuronal Dynamics by Geometrical Dissection of Minimal Models

Contents 1. Introduction 5 1.1. Nonlinear behaviors, time scales, our approach 5 1.2. Electrical activity of cells 6 2. Revisiting the Hodgkin-Huxley equations 10 2.1. Background and formulation 10 2.2. Hodgkin-Huxley gating equations as idealized kinetic models 12 2.3. Dissection of the action potential 13 2.3.1. Current-voltage relations 13 2.3.2. Qualitative view of fast-slow dissection 15 2...