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Locomotion is essential for living cells. It enables bacteria and algae to explore space for food, cancer to spread, and immune system to fight infections. Motile cells display trajectories of intriguing complexity, from regular (e.g.…
One thing that discriminates living things from inanimate matter is their ability to generate similarly complex or non-random architectures in a large abundance. From DNA sequences to folded protein structures, living cells, microbial…
In this review we summarize theoretical progress in the field of active matter, placing it in the context of recent experiments. Our approach offers a unified framework for the mechanical and statistical properties of living matter:…
Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired…
Brownian motion provides a bedrock for the understanding of soft condensed matter and, therefore, of the physical description of the microscopic biological world. Inspired by this domain, and combining softness with hydrodynamic energy…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale…
Animals locomote for various reasons: to search for food, find suitable habitat, pursue prey, escape from predators, or seek a mate. The grand scale of biodiversity contributes to the great locomotory design and mode diversity. Various…
Trajectory prediction is a fundamental and challenging task for numerous applications, such as autonomous driving and intelligent robots. Currently, most of existing work treat the pedestrian trajectory as a series of fixed two-dimensional…
A human is a thing that moves in space. Like all things that move in space, we can in principle use differential equations to describe their motion as a set of functions that maps time to position (and velocity, acceleration, and so on).…
One of the most efficient ways of generating goal-directed walking motions is synthesising the final motion based on footprints. Nevertheless, current implementations have not examined the generation of continuous motion based on…
A new hidden variable theory is proposed, according to which particles follows definite trajectories, as in Bohmian Mechanics or Nelson's stochastic mechanics; in the new theory, however, the trajectories are classical, i.e. Newtonian. This…
Understanding protein dynamics are essential for deciphering protein functional mechanisms and developing molecular therapies. However, the complex high-dimensional dynamics and interatomic interactions of biological processes pose…
The movement of organisms is subject to a multitude of influences of widely varying character: from the bio-mechanics of the individual, over the interaction with the complex environment many animals live in, to evolutionary pressure and…
The cells and tissues that make up our body juggle contradictory mechanical demands. It is crucial for their survival to be able to withstand large mechanical loads, but it is equally crucial for them to produce forces and actively change…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
The multifarious internal workings of organisms are difficult to reconcile with a single feature defining a state of being alive. Indeed, definitions of life rely on emergent properties (growth, capacity to evolve, agency) only symptomatic…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
Randomly moving active particles can be herded into directed motion by asymmetric geometric structures. Although such a rectification process has been extensively studied due to its fundamental, biological, and technological relevance, a…
The ability of many living systems to actively self-propel underlies critical biomedical, environmental, and industrial processes. While such active transport is well-studied in uniform settings, environmental complexities such as geometric…