This review examines intermittent target search strategies, which combine phases of slow
motion, allowing the searcher to detect the target, and phases of fast motion during which …

We review the general problem of random searches in the context of biological encounters.
We analyze deterministic and stochastic aspects of searching in general and address the …

We propose here a motivation for a mixed local/nonlocal problem with a new type of
Neumann condition. Our description is based on formal expansions and approximations. In …

Cell movement—for example, during embryogenesis or tumor metastasis—is a complex
dynamical process resulting from an intricate interplay of multiple components of the cellular …

Intermittent search processes switch between local Brownian search events and ballistic
relocation phases. We demonstrate analytically and numerically in one dimension that when …

Random walk methods and diffusion theory pervaded ecological sciences as methods to
analyze and describe animal movement. Consequently, statistical physics was mostly seen …

The hypothesis that the optimal search strategy is a Lévy walk (LW) or Lévy flight, originally
suggested in 1995, has generated an explosion of interest and controversy. Long-standing …

The movement ecology framework depicts animal movement as the result of the combined
effects of internal and external constraints on animal navigation and motion capacities …

The origin of fractal patterns is a fundamental problem in many areas of science. In
ecological systems, fractal patterns show up in many subtle ways and have been interpreted …

The Lévy hypothesis states that inverse square Lévy walks are optimal search strategies
because they maximize the encounter rate with sparse, randomly distributed, replenishable …