Related papers: Scaling Mobility Patterns and Collective Movements…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…
We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…
In this paper, we conduct a literature review of laws of motion based on stochastic search strategies which are mainly focused on exploring highly dynamic environments. In this regard, stochastic search strategies represent an interesting…
Collective behavior in animals has long been modeled through self-propelled particle models, which reproduce striking group-level phenomena through abstract interaction forces. Yet these models are fundamentally descriptive: they leave open…
Thanks to recent technological advances, it is now possible to track with an unprecedented precision and for long periods of time the movement patterns of many living organisms in their habitat. The increasing amount of data available on…
Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…
The study of animal movement is challenging because it is a process modulated by many factors acting at different spatial and temporal scales. Several models have been proposed which differ primarily in the temporal conceptualization,…
We perform a numerical analysis of a recent introduced model for describing collective movement in alarmed animals groups. This model, derived from a position-based interaction and a limited attention field, displays a non-equilibrium phase…
Scale-invariant spatial or temporal patterns and L\'evy flight motion have been observed in a large variety of biological systems. It has been argued that animals in general might perform L\'evy flight motion with power law distribution of…
Lattice-based random walk models are widely used to study populations of migrating cells with motility bias and proliferation. Crowding is typically represented by volume exclusion, where each lattice site can be occupied by at most one…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
We study the limiting behaviors of a generalized elephant random walk on the integer lattice. This random walk is defined by using two sequences of parameters expressing the memory at each step from the whole past and the drift of each step…
The solvability of the three-dimensional O($N$) scalar field theory in the large $N$ limit makes it an ideal toy model exhibiting "walking" behavior, expected in some SU($N$) gauge theories with a large number of fermion flavors. We study…
Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale…
Principles of self-organization play an increasingly central role in models of human activity. Notably, individual human displacements exhibit strongly recurrent patterns that are characterized by scaling laws and can be mechanistically…