Related papers: Molecular Spiders on the Plane
Synthetic bio-molecular spiders with "legs" made of single-stranded segments of DNA can move on a surface which is also covered by single-stranded segments of DNA complementary to the leg DNA. In experimental realizations, when a leg…
Molecular spiders are synthetic bio-molecular systems which have "legs" made of short single-stranded segments of DNA. Spiders move on a surface covered with single-stranded DNA segments complementary to legs. Different mappings are…
Molecular spiders are synthetic molecular motors based on DNA nanotechnology. While natural molecular motors have evolved towards very high efficiency, it remains a major challenge to develop efficient designs for man-made molecular motors.…
We study the motion of random walkers with residence time bias between first and subsequent visits to a site, as a model for synthetic molecular walkers composed of coupled DNAzyme legs known as molecular spiders. The mechanism of the…
Molecular spiders are synthetic catalytic DNA-based nanoscale walkers. We study the mean first passage time for abstract models of spiders moving on a finite two-dimensional lattice with various boundary conditions, and compare it with the…
A simple symmetric random walk is considered on a spider that is a collection of half lines (we call them legs) joined at the origin. We establish a strong approximation of this random walk by the so-called Brownian spider. Transition…
Spider walks are systems of interacting particles. The particles move independently as long as their movement do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized.…
Understanding the motion of particles with ligand-receptors is important for biomedical applications and material design. Yet, even among a single design, the prototypical DNA-coated colloids, seemingly similar micrometric particles hop or…
Particles with ligand-receptor contacts bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such "nanoscale caterpillars" is a challenge, since binding events often…
We consider a simple symmetric random walk on a spider, that is a collection of half lines (we call them legs) joined at the origin. Our main question is the following: if the walker makes $n$ steps how high can he go up on all legs. This…
Self-repelling two-leg (biped) spider walk is considered where the local stochastic movements are governed by two independent control parameters $ \beta_d$ and $ \beta_h $, so that the former controls the distance ($ d $) between the legs…
A spider consists of several, say $N$, particles. Particles can jump independently according to a random walk if the movement does not violate some given restriction rules. If the movement violates a rule it is not carried out. We consider…
Orb-weaving spiders detect prey on a web using vibration sensors at leg joints. They often dynamically crouch their legs during prey sensing, likely an active sensing strategy. However, how leg crouching enhances sensing is poorly…
A simple random walk and a Brownian motion are considered on a spider that is a collection of half lines (we call them legs) joined in the origin. We give a strong approximation of these two objects and their local times. For fixed number…
We introduce a model for translational molecular motors to demonstrate that a multivalent catalytic walker with flexible, uncoordinated legs can transform the free energy of surface-bound substrate sites into mechanical work and undergo…
Artificial nanowalkers are inspired by biomolecular counterparts from living cells, but remain far from comparable to the latter in design principles. The walkers reported to date mostly rely on chemical mechanisms to gain a direction; they…
Colloidal particles with DNA `legs' that can bind reversibly to receptors on a surface can be made to `walk' if there is a gradient in receptor concentration. We use a combination of theory and Monte Carlo simulations to explore how…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
While most insect-inspired robots come with a simple tarsus such as a hemispherical foot tip, insect legs have complex tarsal structures and claws, which enable them to walk on complex terrain. Their sharp claws can smoothly attach and…
Recent demonstrations indicate that silicon-spin QPUs will be able to shuttle physical qubits rapidly and with high fidelity - a desirable feature for maximising logical connectivity, supporting new codes, and routing around damage. However…