Related papers: A simple self-avoiding walking process as a reason…

A contact map is a simple representation of the structure of proteins and other chain-like macromolecules. This representation is quite amenable to numerical studies of folding. We show that the number of contact maps corresponding to the…

We analyze the strengths and limitations of steered discrete time quantum walks in generating quantum states of bipartite quantum systems comprising of a qubit coupled to a qudit system. We demonstrate that not all quantum states in the…

Mechanisms of locomotion in microscopic systems are of great interest not only for technological applications, but also for the sake of understanding, and potentially harnessing, processes far from thermal equilibrium. Down-scaling is a…

We analyze the equlibrium statistics of a long linear homo-polymer chain confined in between two flat geometrical constraints under good solvent condition. The chain is ocupying two dimensional space and geometrical constraints are two…

We investigate self-avoiding walk models of linear block copolymers adsorbed at a surface and desorbed by the action of a force. We rigorously establish the dependence of the free energy on the adsorption and force parameters, and the form…

Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…

We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…

Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently, a two-dimensional model (triangular…

We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…

In this chapter we will highlight our experimental studies on natural human walking analysis and introduce a biologically inspired design for simple bipedal locomotion system of humanoid robots. Inspiration comes directly from human walking…

Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the…

Random walks with a general, nonlinear barrier have found recent applications ranging from reionization topology to refinements in the excursion set theory of halos. Here, we derive the first-crossing distribution of random walks with a…

We develop a path-based approach to continuous-time random walks on networks with arbitrarily weighted edges. We describe an efficient numerical algorithm for calculating statistical properties of the stochastic path ensemble. After…

We consider the biased random walk on a tree constructed from the set of finite self-avoiding walks on a lattice, and use it to construct probability measures on infinite self-avoiding walks. The limit measure (if it exists) obtained when…

We investigate the dynamic scaling properties of stochastic particle systems on a non-deterministic scale-free network. It has been known that the dynamic scaling behavior depends on the degree distribution exponent of the underlying…

Predicting the macroscopic mechanical behavior of polymeric materials from the micro-structural features has remained a challenge for decades. Existing theoretical models often fail to accurately capture the experimental data, due to…

We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation…

Interacting Growth Walks is a recently proposed stochastic model for studying the coil-globule transition of linear polymers. We propose a flat energy histogram version for Interacting Growth Walk. We demonstrate the algorithm on two…

Random walks find extensive application across various complex network domains, including embedding generation and link prediction. Despite the widespread utilization of random walks, the precise impact of distinct biases on embedding…

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in $d$ dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when…