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We derive the linear force-extension relation for a wormlike chain of arbitrary stiffness including entropy elasticity, bending and thermodynamic buckling. From this we infer the plateau modulus $G^0$ of an isotropic entangled solution of…
The usual strategy for deducing the $\pi\mbox{--}\pi^\ast$ electronic energy (or optical bandgap) in a molecule with an "infinite" number of conjugated double bonds consists in fitting a function with some adjustable parameters to the…
A {\it new} formula for the force vs extension relation is derived from the discrete version of the so called {\it worm like chain} model. This formula correctly fits some recent experimental data on polymer stretching and some numerical…
The relation between force and stretch in the worm-like chain model of entropic elasticity is examined. Although no closed-form expression is valid for all values of forcing, solutions in the form of asymptotic series can be obtained under…
Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the…
In this paper we compare two polymer stretching experiments. The outcome of both experiments is a force-extension relation. We use a one-dimensional model to show that in general the two quantities are not equal. In certain limits, however,…
A quantitative theory of the buckling of a worm like chain based on a semi-classical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows to go beyond the…
The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different…
Although the stretching of polymers and biomolecules is important in numerous settings, their response when confined to two-dimensions is relatively poorly-studied. In this paper, we derive closed-form analytical expressions for the…
We present exact closed-form expressions and complete asymptotic expansions for the electrostatic force between two charged conducting spheres of arbitrary sizes. Using asymptotic expansions of the force we confirm that even like-charged…
For many physical quantities, theory supplies weak- and strong-coupling expansions of the types $\sum a_n \alpha ^n$ and $ \alpha ^p\sum b_n (\alpha^{-2/q) ^n$, respectively. Either or both of these may have a zero radius of convergence. We…
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
We investigate in some detail an alternative simulation strategy for lattice field theory based on the so-called worm algorithm introduced by Prokof'ev and Svistunov in 2001. It amounts to stochastically simulating the strong coupling…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1% relative…
We derive exact and closed-form expressions for a large class of two-point and three-point inflation correlators with the tree-level exchange of a single massive particle. The intermediate massive particle is allowed to have arbitrary mass,…
The finite-lattice method of series expansions has been combined with a new extrapolation procedure to extend the low-temperature series for the specific heat, spontaneous magnetisation and susceptibility of the spin-1 Ising model on the…
In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…
Quite recently, Izmailian and Hu [Phys. Rev. Lett. 86, 5160 (2001)] studied the finite-size correction terms for the free energy per spin and the inverse correlation length of the critical two-dimensional Ising model. They obtained the…