Lagrangian geometrical models in physics

A stochastic Lagrangian approach for geometrical uncertainties in electrostatics

This work proposes a general framework to quantify uncertainty arising from geometrical variations in the electrostatic analysis. The uncertainty associated with geometry is modeled as a random field which is first expanded using either polynomial chaos or Karhunen–Loève expansion in terms of independent random variables. The random field is then treated as a random displacement applied to the ...

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 for Grain Dynamics

A closer look at rock physics models and their assisted interpretation in seismic exploration

Subsurface rocks and their fluid content along with their architecture affect reflected seismic waves through variations in their travel time, reflection amplitude, and phase within the field of exploration seismology. The combined effects of these factors make subsurface interpretation by using reflection waves very difficult. Therefore, assistance from other subsurface disciplines is needed i...

Models in Physics

In its most common use, the term ‘model’ refers to a simplified and stylised version of the socalled target system, the part or aspect of the world that we are interested in. For instance, in order to determine the orbit of a planet moving around the sun we model the planet and the sun as perfect homogenous spheres that gravitationally interact with each other but nothing else in the universe, ...