Anomalous diffusion describes a deviation from the classical Brownian motion, where the mean squared displacement of particles is not linear with time, indicating either subdiffusive or superdiffusive behavior. This phenomenon is crucial in understanding complex systems such as biological environments, disordered media, and financial markets, where traditional diffusion models fail to capture the intricacies of particle movement.

Anomalous Diffusion

Anomalous diffusion

classical Brownian motion

Mean Squared Displacement (MSD) is a measure of the average squared distance traveled by particles over time, typically used to analyze diffusion and random motion in physical systems. It provides insight into the mobility and dynamic behavior of particles, with applications in fields such as physics, chemistry, and biology.

mean squared displacement

Subdiffusive behavior

superdiffusive behavior

Complex systems are characterized by intricate interactions and interdependencies among their components, leading to emergent behavior that cannot be easily predicted from the properties of individual parts. These systems are often adaptive, dynamic, and exhibit non-linear behaviors, making them challenging to analyze and manage.

complex systems

biological environments

disordered media

Financial markets are platforms where individuals and institutions can trade financial securities, commodities, and other fungible items at prices that reflect supply and demand. They play a crucial role in the economy by facilitating liquidity, price discovery, and the efficient allocation of resources.

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