Related papers: Theoretical estimate of the probability for macrom…
A particular class of random walks with a spin factor on a three dimensional cubic lattice is studied. This three dimensional random walk model is a simple generalization of random walk for the two dimensional Ising model. All critical…
A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied by a mesoscopic theory and by MC simulations. We assume hard-cores of the same size for both components, short-range attraction long-range…
In this paper I describe the computer simulations that I have performed to critically examine the Lauritzen-Hoffman and the Sadler-Gilmer theories of polymer crystallization. In particular, I have computed the free energy profile for…
A microscopic model is proposed for the interactions between sickle hemoglobin molecules based on information from the protein data bank. A Monte Carlo simulation of a simplified two patch model is carried out, with the goal of…
A simple recursion procedure was devised to generate lattice configurations with probability distributions given by simple approximate Yang-Mills vacuum wavefunctionals. A few quantities determined in ensembles of these configurations are…
Theoretical models are vital for exploring the galaxy merger process, which plays a crucial role in the evolution of galaxies. Recent advances in modelling have placed tight constraints on the buildup of stellar material in galaxies across…
We introduce a Markov Chain Monte Carlo (MCMC) algorithm to generate samples from probability distributions supported on a $d$-dimensional lattice $\Lambda = \mathbf{B}\mathbb{Z}^d$, where $\mathbf{B}$ is a full-rank matrix. Specifically,…
An important goal of self-assembly is to achieve a preprogrammed structure with high fidelity. Here, we control the valence of DNA-functionalized emulsions to make linear and branched model polymers, or `colloidomers'. The distribution of…
We present the results of analytic calculations and numerical simulations of the behaviour of a new class of chain molecules which we call thick polymers. The concept of the thickness of such a polymer, viewed as a tube, is encapsulated by…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…
A simple model for the formation of the polymer-enzyme conjugates has been proposed and described using corresponding extension of the Wertheim's first-order thermodynamic perturbation theory (TPT1) for the system of associating chain…
In this note, we compute the probability that a two-dimensional symmetric random walk visits more vertices than expected, for deviations on scales between the mean behavior and linear growth.
In this work we developed a theoretical model to describe the polymerization of very long macromolecules with simultaneous precipitation. As a reference system for our model we consider UHMWPE polymerization process, via homogeneous…
Collapse of the polymer chain upon the sharp decrease of solvent quality is studied. During collapse, any pair of polymer units appearing in a sufficiently close vicinity in space has the possibility with a certain probability to form an…
A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads…
We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
How do we estimate the probability of an abundant objects' formation, with minimal context or assumption about is origin? To explore this we have previously introduced the concept of pathway assembly (as pathway complexity), in a graph…
We study stability of a growth process generated by sequential adsorption of particles on a one-dimensional lattice torus, that is, the process formed by the numbers of adsorbed particles at lattice sites, called heights. Here the stability…