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- 09:11, 9 September 2025 TBan-IV (hist | edit) [2,500 bytes] Rosso (talk | contribs) (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'...")
- 21:59, 8 September 2025 LBan-V (hist | edit) [12,523 bytes] Rosso (talk | contribs) (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...")
- 18:31, 31 August 2025 LBan-IV (hist | edit) [12,925 bytes] Rosso (talk | contribs) (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...")
- 15:50, 31 August 2025 TBan-III (hist | edit) [8,882 bytes] Rosso (talk | contribs) (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',...")
- 20:26, 30 August 2025 TBan-II (hist | edit) [2,705 bytes] Rosso (talk | contribs) (Created page with "==Dijkstra Algorithm and transfer matrix== thumb|left|Sketch of the discrete Directed Polymer model. At each time the polymer grows either one step left either one step right. A random energy <math> V(\tau,x)</math> is associated at each node and the total energy is simply <math> E[x(\tau)] =\sum_{\tau=0}^t V(\tau,x)</math>. We introduce a lattice model for the directed polymer (see figure). In a companion notebook we provide the implementa...")
- 19:10, 27 August 2025 LBan-III (hist | edit) [939 bytes] Rosso (talk | contribs) (Created page with "= Goal = The goal of this lecture is to present the final lecture on KPZ and directed polymers in finite dimension. We show that for <math>d>2</math>, a "glass transition" occurs. = KPZ: from 1D to the Cayley tree = Much is known about KPZ, but several aspects remain elusive: In <math>d=1</math>, we have <math>\theta=1/3</math> and a glassy regime present at all temperatures. The stationary solution of the KPZ equation describes, at long times, the fluctuations of qu...")
- 21:06, 6 August 2025 LBan-II (hist | edit) [10,511 bytes] Rosso (talk | contribs) (Created page with "=Edwards Wilkinson: an interface with thermal fluctuations: = Consider domain wall <math> h(r,t)</math> fluctuating at equilibrium at the temparature <math> T</math>. Here <math> t</math> is time, <math> r </math> defines the d-dimensional coordinate of the interface and <math> h</math> is the scalar height field. Hence, the domain wall separating two phases in a film has <math> d=1, r \in \cal{R}</math>, in a solid instead <math> d=2, r \in \cal{R}^2</math>. Two...")
- 16:23, 6 August 2025 TBan-I (hist | edit) [5,126 bytes] Rosso (talk | contribs) (Created page with "ciao")
- 16:18, 31 July 2025 LBan-1 (hist | edit) [14,079 bytes] Rosso (talk | contribs) (Created page with "aaa")
- 12:25, 31 July 2025 ICTS (hist | edit) [1,283 bytes] Rosso (talk | contribs) (Created page with "== Course description == This course deals with systems in which the presence of impurities or amorphous structures (in other words, of disorder) influences radically the physics, generating novel phenomena. These phenomena involve the properties of the system at equilibrium (freezing transitions, glassy phase and glassy system), as well as their dynamical evolution out-of-equilibrium (pinning, avalanches). * The simplest spin-glass: solution of the Random Energy Mode...")
![thumb|left|Sketch of the discrete Directed Polymer model. At each time the polymer grows either one step left either one step right. A random energy <math> V(\tau,x)</math> is associated at each node and the total energy is simply <math> E[x(\tau)] =\sum_{\tau=0}^t V(\tau,x)</math>.](/wikids/index.php/File:SketchDPRM.png){kind=link}