Anomalous diffusion refers to a type of random motion or dispersal process that deviates from the typical behavior observed in normal or classical diffusion. It is characterized by irregular, non-Gaussian, or non-linear patterns that do not conform to the assumptions of traditional diffusion models.
In classical diffusion, the movement of particles or substances is governed by rules such as Fick's laws, which assume a constant and symmetric spreading pattern over time. However, in anomalous diffusion, the spreading of particles or substances exhibits characteristics that deviate from these assumptions. This can manifest as non-uniform spreading, uneven rates of diffusion, or different scaling behaviors.
Anomalous diffusion can be observed in various phenomena and diverse systems, such as fluid dynamics, random walks, biological processes, and financial markets. It has significant implications across multiple fields of science, including physics, chemistry, biology, and economics.
The causes of anomalous diffusion can be diverse, ranging from heterogeneous environments, complex interactions, external forces, or memory effects. Such processes may exhibit characteristics such as long-range correlations, power-law behaviors, or fractal structures.
Understanding and quantifying anomalous diffusion is crucial for accurately modeling and predicting various natural and artificial processes. It requires advanced mathematical and statistical techniques, such as fractional calculus, random walks, or continuous-time random processes.
Overall, anomalous diffusion represents a departure from the standard assumptions of classical diffusion, characterized by irregular, non-linear, and non-Gaussian spreading patterns that occur in a wide range of natural and man-made systems.
