Lectures related to Brownian Motion: From Molecules to Cells

Maximum Entropy Principle: Stochastic Differential Equations

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

Brownian Motion: Molecular Nature Revealed

Explores the history, mathematical models, and experimental techniques of Brownian Motion, revealing its molecular nature and significance in cell biology.

Stochastic Processes: Brownian Motion

Explores Brownian motion, Langevin equations, and stochastic processes in physics.

Fourier Transform and Spectral Densities

Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.

Diffusion in Fluids: Understanding Mass Transport

Covers diffusion, focusing on mass transport in fluids and its mathematical formulation.

Brownian Motion: Theory and Applications

Covers the theory of Brownian motion, diffusion, and random walks, with a focus on Einstein's theory for one-dimensional motion.

Brownian Motion: Einstein Derivation

Covers the derivation of Brownian motion by Einstein and Langevin equations, including the Chapman Kolmogorov equation.

White Noise Form of the Langevin Equation

Covers the white noise form of the Langevin equation and its applications.

Stochastic Differential Equations

Covers Stochastic Differential Equations, Wiener increment, Ito's lemma, and white noise integration in financial modeling.

Langevin dynamics: Path Integral Methods

Covers Langevin dynamics, Fokker-Planck equation, solving the Langevin equation, and efficiency of Langevin sampling in molecular dynamics.

Diffusion Coefficients: Understanding Molecular Movement

Covers diffusion coefficients, self-diffusion, and the Stokes-Einstein relation in fluids.

Fokker-Planck Equations

Explores Fokker-Planck equations, escape rates, and first passage time analysis in statistical physics.

Martingales and Brownian Motion Construction

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

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Diffusion in Cells

Explores diffusion in cells, focusing on molecular movement and the impact of size and environment.

Brownian Motion: Fundamentals and Applications

Covers the fundamentals of Brownian motion and its applications in various fields.

Stochastic Calculus: Itô's Formula

Covers Stochastic Calculus, focusing on Itô's Formula, Stochastic Differential Equations, martingale properties, and option pricing.

Stochastic Calculus: Brownian Motion

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.

Membrane Dynamics: Pores and Aggregates

Discusses self-assembly dynamics in oil and lipid systems, focusing on aggregate growth and pore formation in lipid bilayers.

Stochastic Calculus: Integrals and Processes

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.