Related papers: Branched Polymers with Excluded Volume Effects/ Re…
We investigate the nodal volume of random hyperspherical harmonics $\lbrace T_{\ell;d}\rbrace_{\ell\in \mathbb N}$ on the $d$-dimensional unit sphere ($d\ge 2$). We exploit an orthogonal expansion in terms of Laguerre polynomials; this…
In this paper the excluded volume of binary similar hyperparticles with small size difference in D-dimensional Euclidean spaces R2, R3, and R4 is studied using two different statistical geometry approaches. These geometric approaches,…
Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representation for intrinsic and dual volumes of convex polynomial…
The tethered-particle method is a single-molecule technique that has been used to explore the dynamics of a variety of macromolecules of biological interest. We give a theoretical analysis of the particle motions in such experiments. Our…
Two-dimensional semiflexible polymer rings are studied both by imaging circular DNA adsorbed on a mica surface and by Monte Carlo simulations of phantom polymers as well as of polymers with finite thickness. Comparison of size and shape of…
The inter-molecular structure of semidilute polymer solutions is studied theoretically. The low density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the…
The statistical mechanics of a treelike polymer in a confining volume is relevant to the packaging of the genome in RNA viruses. Making use of the mapping of the grand partition function of this system onto the statistical mechanics of a…
The aim of this paper is twofold: - To give an elementary and self-contained proof of an explicit formula for the free energy for a general class of polymer chains interacting with an environment through periodic potentials. This…
Single partially confined collapsed polymers are studied in two dimensions. They are described by self-avoiding random walks with nearest-neighbour attractions below the $\Theta$-point, on the surface of an infinitely long cylinder. For the…
Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice ($d=3$ dimensions) and square lattice ($d=2$ dimensions), varying chain stiffness by an energy…
We show that correlation functions for branched polymers correspond to those for $\phi^3$ theory with a single mass insertion, not those for the $\phi^3$ theory themselves, as has been widely believed. In particular, the two-point function…
In this review we provide an organized summary of the theoretical and computational results which are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide…
We investigate the motion of two overlapping polymers with self-avoidance confined in a narrow 2d box. A statistical model is constructed using blob free-energy arguments. We find spontaneous segregation under the condition: $L > R_{//}$,…
In this work we present scattering functions of conjugates consisting of a colloid particle and a self-avoiding polymer chain. This model is directly derived from the two point correlation function with the inclusion of excluded volume…
In the family of unit balls with constant volume we look at the ones whose algebraic representation has some extremal property. We consider the family of nonnegative homogeneous polynomials of even degree $d$ whose sublevel set $\G=\{\x:…
We explore semi-dilute and concentrated oligomers and polymers in a broad range of polymerization indices N ranging from 1 to a 100 and in a range of monomer number densities $\phi$ from 0.1 to 0.8 via molecular dynamics simulations and…
We prove that for any partition $(\lambda_1,...,\lambda_{d^2})$ of size $\ell d$ there exists $k\ge 1$ such that the tensor square of the irreducible representation of the symmetric group $S_{k\ell d}$ with respect to the rectangular…
The relation among the volume coefficient $K$(=incompressibility of the nuclear matter), the Coulomb coefficient $K_c$, and the volume-symmetry coefficient $K_{vs}$ of the nucleus incompressibility are studied in the framework of the…
We apply results derived in other contexts for the spectrum of the Laplace operator in curved geometries to the study of an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D and conclude that the free energy…
In this article we study some optimal design problems related to nonstandard growth eigenvalues ruled by the $g-$Laplacian operator. More precisely, given $\Omega\subset \R^n$ and $\alpha,c>0$ we consider the optimization problem $\inf \{…