Semestre | Oblig. | Option | Filières |
BA4 | x |
Cours | 1 hebdo |
Exercices | 1 hebdo |
TP | 2 hebdo |
Plan d'étude | Semestre | Oblig. | Option | Filières |
Physique 2020-21 | BA4 | x |
Cursus | Sem. | Type |
---|---|---|
Physique | BA4 | Obl. |
Suite du cours de Physique numérique I. Résolution de roblèmes avec conditions aux limites et aux valeurs initiales décrits par des équations aux dérivées partielles.
Equation de Poisson. Equation de la chaleur. Cas uni- et bi-dimensionnels. Schémas de différences finies et d’éléments finis. Méthodes itératives : Gauss-Seidel, surrelaxation.
Advection-Diffusion. Schéma explicite, différences finies. Analyse de stabilité de Von Neuman. Condition de stabilité CFL (Courant-Friedrichs-Lewy). Diffusion et marche aléatoire : approche Monte Carlo.
Propagation d’ondes. Conditions initiales et aux limites. Modes propres, fréquences propres. Analyse de stabilité. Ondes en milieu inhomogène.
Mécanique quantique. Equation de Schrödinger dépendante du temps. Schéma semi-implicite unitaire de Crank-Nicolson. Particule libre, étalement du paquet d’onde. Barrières de potentiel, effet tunnel. Oscillateur harmonique, limite semi-classique. Etats propres, équation de Schrödinger stationnaire. Puits de potentiel, états liés. Particule dans un potentiel périodique, bandes d’énergies interdites.
S’il reste du temps: Mécanique statistique, modèle d’Ising, approche Monte Carlo, algorithme de Metropolis..
Plusieurs applications seront faites en exercice et en pratique, avec évaluation des rapports rendus.
Cours de 1e année (Physique avancée I-II, Programmation, Informatique, Analyse avancée I-II, Algèbre linéaire avancée I-II)
Physique numérique I
Présentations ex cathedra, exercices et applications pratiques dirigés
Participation au cours. Résolution de projets impliquant la formulation analytique, les méthodes numériques et leur implémentation dans un code de calcul. Production et analyse des résultats. Soumission des rapports.
Contrôle continu
Notes de cours
N.J. Giordano, Computational Physics, Pearson Prentice Hall 2006
F.J. Vesely, Computational Physics, an Introduction, Kluwer Academic Plenum 2001
Disponible sur le site web du cours.
obligatoire
obligatoire
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
TP
Practical work
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Pendant le semestre
During the semester
Session été
Session summer
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CODE56074095
BOOLEAN_Symbol
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BOOLEAN_Symbol
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