Related papers: Molecular Spiders on the Plane
Diffusion of tracer particles in the cytoplasm of mammalian cells is often anomalous with a marked heterogeneity even within individual particle trajectories. Despite considerable efforts, the mechanisms behind these observations have…
We consider a discrete time particle model for kinetic transport on the two dimensional integer lattice. The particle can move due to advection in the $x$-direction and due to dispersion. This happens when the particle is free, but it can…
We prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping…
The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on a hyper-cubic lattice and study ordering probabilities associated with these…
Random walks of particles on a lattice are a classical paradigm for the microscopic mechanism underlying diffusive processes. In deterministic walks, the role of space and time can be reversed, and the microscopic dynamics can produce quite…
Little research into tactile feet has been done for walking robots despite the benefits such feedback could give when walking on uneven terrain. This paper describes the development of a simple, robust and inexpensive tactile foot for…
In human crowds, interactions among individuals give rise to a variety of self-organized collective motions that help the group to effectively solve the problem of coordination. However, it is still not known exactly how humans adjust their…
We study chemically driven running droplets on a partially wetting solid substrate by means of coupled evolution equations for the thickness profile of the droplets and the density profile of an adsorbate layer. Two models are introduced…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
Single molecule DNA experiments often generate data from force versus extension measurements involving the tethering of a microsphere to one end of a single DNA molecule while the other is attached to a substrate. We show that the…
In probability theory, reinforced walks are random walks on a lattice (or more generally a graph) that preferentially revisit neighboring `locations' (sites or bonds) that have been visited before. In this paper, we consider walks with…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
The motility of eukaryotic cells is strongly influenced by their environment, with confined cells often developing qualitatively different motility patterns from those migrating on simple two-dimensional substrates. Recent experiments,…
In some physical and biological swarms, agents effectively move and interact along curved surfaces. The associated constraints and symmetries can affect collective-motion patterns, but little is known about pattern stability in the presence…
Enzymes have been shown to diffuse faster in the presence of their reactants. Recently, we revealed new insights into this process of enhanced diffusion using single-particle tracking (SPT) with total internal reflection fluorescence (TIRF)…
Snakes and their bio-inspired robot counterparts have demonstrated locomotion on a wide range of terrains. However, dynamic vertical climbing is one locomotion strategy that has received little attention in the existing snake robotics…
In this paper, a new method to efficiently simulate diffusion controlled second order chemical reactions is derived and applied to site-specific DNA-binding proteins. The protein enters a spherical cell and propagates via two competing…
We study the path behavior of the symmetric walk on some special comb-type subsets of ${\mathbb Z}^2$ which are obtained from ${\mathbb Z}^2$ by generalizing the comb having finitely many horizontal lines instead of one.
Topologically nontrivial adiabatic loops of the orientation of a homogeneous external magnetic field drive the walking of paramagnetic colloidal bipeds above a deformed quasi-periodic magnetic square pattern. Depending on the topological…
Crawling cell motility is vital to many biological processes such as wound healing and the immune response. Using a minimal model we investigate the effects of patterned substrate adhesiveness and biophysical cell parameters on the…