Related papers: Theoretical estimate of the probability for macrom…
Random heteropolymers are a minimal description of biopolymers and can provide a theoretical framework to the investigate the formation of loops in biophysical experiments. A two--state model provides a consistent and robust way to study…
Computer modeling of formation of the one-dimensional and three-dimensional monatomic nanostructures by the method of atom-atom potentials was done. The arrangement of atoms was defined on the basis of the energy minimum. Our calculations…
In this thesis the formation and properties of a polymer gel on and at a surface are investigated. The gel under investigation is defined as a three-dimensional network of "phantom" macromolecules that form permanent links with one another…
We develop a statistical model for a confined chain molecule based on a monomer grand canonical ensemble. The molecule is subject to an external chemical potential, a backbone interaction, and an attractive interaction between all monomers.…
Molecular process of polymer collapse was reproduced by isothermal molecular dynamics simulation. The initial polymer chains were obtained by mean of random walks in continuum space. Two potential models were considered to represent short…
A lattice model is presented for the simulation of dynamics in polymeric systems. Each polymer is represented as a chain of monomers, residing on a sequence of nearest-neighbor sites of a face-centered-cubic lattice. The polymers are self-…
The shape of a polymer plays an important role in determining its interactions with other molecules and with the environment, and is in turn affected by both of them. As a consequence, in the literature the shape properties of a chain in…
Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
We study reversible polymerization of rings. In this stochastic process, two monomers bond and as a consequence, two disjoint rings may merge into a compound ring, or, a single ring may split into two fragment rings. This…
We study the influence of structural obstacles in a disordered environment on the size and shape characteristics of long flexible polymer macromolecules. We use the model of self-avoiding random walks on diluted regular lattices at the…
We use a recently developed lattice model to study the percolation of particles of different sizes and shapes in the presence of a polymer matrix. The polymer is modeled as an infinitely long semiflexible chain. We study the effects of the…
We study the conformational properties of complex polymer macromolecules, consisting in general of $n$ subsequently connected chains (blocks) of different lengths and distinct chemical structure. Depending on the solvent conditions, the…
Molecular motors interacting with cytoskeletal filaments undergo peculiar random walks consisting of alternating sequences of directed movements along the filaments and diffusive motion in the surrounding solution. An ensemble of motors is…
The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different vertices. The sequence of degree bounds acts…
The formation of chain-folded structures from the melt is observed in molecular dynamics simulations resembling the lamellae of polymer crystals. Crystallization and subsequent melting temperatures are related linearly to the inverse…
We study a single flexible chain molecule grafted to a membrane which has pores of size slightly larger than the monomer size. On both sides of the membrane there is the same solvent. When this solvent is good, i.e. when the polymer is…
Polymer fibers consist of macromolecules oriented along the fiber axis. Better alignment of chains leads to an increased strength of the fiber. It is believed that the key factor preventing formation of a perfectly oriented fiber is…
We analyze the statistics of loops formation in $f$-branched star polymers in an environment with structural defects, correlated at large distances $r$ according to a power law $\sim r^{-a}$. Applying the direct polymer renormalization…
We compute the uniform probability that finitely many polynomials over a finite field are pairwise coprime and compare the result with the formula one gets using the natural density as probability measure. It will turn out that the formulas…