Related papers: On hereditary models of polymers
An evolution operator L_n with n arbitrary, typical of several models, is analyzed. When n= 1, the operator characterizes the standard linear solid of viscoelasticity, whose properties are already established in previous papers. The…
Linear polymers are represented as chains of hopping reptons and their motion is described as a stochastic process on a lattice. This admittedly crude approximation still catches essential physics of polymer motion, i.e. the universal…
Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary…
We introduce a new model of random layered media, extending the Matheron-de Marsily model: Here we allow for the flows to change in time. For such layered structures, we solve exactly the equations of motion for single particles, and also…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
We derive the general conditions for fully-nonlinear symmetry-integrable second-order evolution equations and their first-order recursion operators. We then apply the established Propositions to find links between a class of fully-nonlinear…
We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…
The cage model for polymer reptation, proposed by Evans and Edwards, and its recent extension to model DNA electrophoresis, are studied by numerically exact computation of the drift velocities for polymers with a length L of up to 15…
A general form of the fifth-order nonlinear evolution equation is considered. Helmholtz solution of the inverse variational problem is used to derive conditions under which this equation admits an analytic representation. A Lennard type…
We present a model for semiflexible polymers in Hamiltonian formulation which interpolates between a Rouse chain and worm-like chain. Both models are realized as limits for the parameters. The model parameters can also be chosen to match…
A mechanism deriving new well-posed evolutionary equations from given ones is inspected. It turns out that there is one particular spatial operator from which many of the standard evolutionary problems of mathematical physics can be…
The operational calculus associated with Hermite numbers has been shown to be an effective tool for simplifying the study of special functions. Within this context, Hermite polynomials have been viewed as Newton binomials, with the…
We extend the Rouse model of polymer dynamics to situations of non-stationary chain growth. For a dragged polymer chain of length $N(t) = t^\alpha$, we find two transitions in conformational dynamics. At $\alpha= 1/2$, the propagation of…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…
We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same property. The construction of the correspond- ing family of matrix…
A simple one-dimensional model is constructed for polymer motion. It exhibits the crossover from reptation to Rouse dynamics through gradually allowing hernia creation and annihilation. The model is treated by the density matrix technique…
The competition between reptation and Rouse Dynamics is incorporated in the Rubinstein-Duke model for polymer motion by extending it with sideways motions, which cross barriers and create or annihilate hernias. Using the Density-Matrix…
This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…
An efficient numerical framework is presented for modeling viscoelasticity and permanent set of polymers. It is based on the hereditary integral form of transient network theory, in which polymer chains belong to distinct networks each with…
The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…