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• 08:11, 9 September 2025 Rosso talk contribs created page TBan-IV (Created page with "== Bienaymé Galton Watson process== A time <math> t=0 </math> appears as infected individual which dies with a rate <math> a </math> and branches with a rate <math> b </math>. On average, each infection generates in average <math> R_0 = b/a </math> new ones. Real epidemics corresponds to <math> R_0>1 </math>. At time <math> t </math>, the infected population is <math> n(t) </math>, while the total infected population is <center> <math> N(t) = \int_0^t n(t') d t'...")
• 20:59, 8 September 2025 Rosso talk contribs created page LBan-V (Created page with "<Strong> Goal: </Strong> We solve the mean field version of the cellular automaton, derive its avalanche statistics and make a connection with the Bienaymé-Galton-Watson process used to describe an epidemic outbreak. = Fully connected (mean field) model for the cellular automaton= Let's study the mean field version of the cellular automata introduced in the previous lecture. We introduce two approximations: * Replace the Laplacian, which is short range, with a mea...")
• 17:31, 31 August 2025 Rosso talk contribs created page LBan-IV (Created page with "= Pinning and Depinning of a Disordered Material = In earlier lectures, we discussed how disordered systems can become trapped in deep energy states, forming a glass. Today, we will examine how such systems can also be ''pinned'' and resist external deformation. This behavior arises because disorder creates a complex energy landscape with numerous features, including minima (of varying depth), maxima, and saddle points. When an external force is applied, it tilts t...")
• 14:50, 31 August 2025 Rosso talk contribs created page TBan-III (Created page with "= Exercise 2: Edwards-Wilkinson Interface with Stationary Initial Condition (7.5 points) = Consider an Edwards-Wilkinson interface in 1+1 dimensions, at temperature <math>T</math>, and of length <math>L</math> with periodic boundary conditions: <center><math> \frac{\partial h(x,t)}{\partial t} = \nu \nabla^2 h(x,t) + \eta(x,t) </math></center> where <math>\eta(x,t)</math> is a Gaussian white noise with zero mean and variance: <center><math> \langle \eta(x,t) \eta(x',...")