History of Brownian Motion in a Nutshell
The Random Elevator Game
Solution of the Diffusion Equation in Free Space
One-Dimensional Semi-infinite Systems Solutions
Diffusion Between Two Targets
Diffusion in the Presence of a Force Field
Trapping Particles Influenced by External Forces
Splitting and Breaking Brownian Pathways: Conditional Processes
Diffusion with Stochastic Resetting
Langevin Equation and Brownian Dynamics Simulations
Numerical Solutions of the Diffusion Equation
Two-Dimensional Systems
Reaction-Diffusion Equations
Three-Dimensional Systems

This book offers the reader a journey through the counterintuitive nature of Brownian motion under confinement. Diffusion is a universal phenomenon that controls a wide range of physical, chemical, and biological processes. The transport of spatially-constrained molecules and small particles is ubiquitous in nature and technology and plays an essential role in different processes. Understanding the physics of diffusion under conditions of confinement is essential for a number of biological phenomena and potential technological applications in micro- and nanofluidics, among others.



Studies on diffusion under confinement are typically difficult to understand for young scientists and students because of the extensive background on diffusion processes, physics, and mathematics that is required. All of this information is provided in this book, which is essentially self-contained as a result of the authors’ efforts to make it accessible to an audience of students from avariety of different backgrounds. The book also provides the necessary mathematical details so students can follow the technical process required to solve each problem. Readers will also find detailed explanations of the main results based on the last 30 years of research devoted to studying diffusion under confinement. The authors approach the physical problem from various angles and discuss the role of geometries and boundary conditions in diffusion.