Euler-Lagrange Equation

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Page 3 of 4

Covers constraints, Lagrange equations, generalized coordinates, cyclic coordinates, conservation laws, and Hamilton formalism.

Optimal Transport: Gradient Flows in Rd

Explores optimal transport and gradient flows in Rd, emphasizing convergence and the role of Lipschitz and Picard-Lindelöf theorems.

Hamiltonian Formulation and Equivalence with Euler-Lagrange

Explores Hamiltonian formulation and its equivalence with Euler-Lagrange equations, illustrated through examples.

Optimal Transport: Rockafellar Theorem

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Approximation in Sobolev Spaces

Covers the approximation of functions in Sobolev spaces using smooth functions.

Optimization with Lagrange Multipliers

Covers advanced optimization techniques using Lagrange multipliers to find extrema of functions subject to constraints.

Maximum Entropy Principle: Stochastic Differential Equations

Explores the application of randomness in physical models, focusing on Brownian motion and diffusion.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Molecular Dynamics Simulations: Basics and Algorithms

Covers the basics of molecular dynamics simulations, ensemble properties, classical mechanics formulations, numerical integration, energy conservation, and constraint algorithms.

Stellar Orbits: Lagrange Points

Explores stellar orbits in rotating potentials, focusing on surfaces of section, integrals of motion, and stability around Lagrange points.