Related papers: A generalized conservation law for main-chain poly…
We present and analyze correlation functions of a main-chain polymer nematic in a continuum worm-like chain description for two types of constraints formalized by the tensorial and vectorial conservation laws, both originating in the…
We derive the "conservation law" for nematic polymers in tensorial form valid for quadrupolar orientational order in contradistinction to the conservation law in the case of polar orientational order. Due to microscopic differences in the…
Linear polymers and other connected "line liquids" exhibit a coupling between density and equilibrium nematic order on the macroscopic level that gives rise to a Meyer-de Gennes vectorial conservation law. Nevertheless, isotropic linear…
Using molecular dynamics simulations, we provide chain-level insights into the dissimilarities in rearrangements of polymers under uniaxial tensile and compressive deformation in glassy and semicrystalline samples of varying chain lengths.…
Conformations of a single semiflexible polymer chain dissolved in a low molecular weight liquid crystalline solvents (nematogens) are examined by using a mean field theory. We takes into account a stiffness and partial orientational…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
The main purpose of this article is to disseminate among a wide audience of physicists a known result, which is available since a couple of years to the \emph{cognoscenti} of differential forms on manifolds; namely, that charge conservation…
We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer {\sl via} the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the…
A statistical mechanical description of flexible and semi-flexible polymer chains in a poor solvent is developed in the constant force and constant distance ensembles. We predict the existence of many intermediate states at low temperatures…
The critical incompatibility of polymers with different compositions scales inversely with their length. For instance, a mixture of A and B homopolymers of length $N$ segregates at $\chi_{AB}^{cr} = 2/N$. But what if the difference between…
The consequences of rotational invariance in a recent theory of fluctuations in dilute polymer nematics are explored. A correct rotationally invariant free energy insures that anomalous couplings are not generated in a one-loop…
A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second law of thermodynamics. This observation easily generalizes to…
The work in this article is inspired by a classical problem: the statistical physical properties of a closed polymer loop that is wound around a rod. Historically the preserved topology of this system has been addressed through…
We study two cross-linked polymer systems in the strong stretching regime. The first consists of two polymers sharing one endpoint, with the other two endpoints coupled by a harmonic potential. Within the weakly bending approximation, we…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
In this paper, we present a theory to efficiently deal with mechanical properties of heterogeneous polymer chain in free space and the central problem is to evaluate the diffusion equation and orientation-orientation correlation function,…
Despite the large number of publications on symmetry analysis of the geopotential forecast equation, its group foliations laws have not been considered previously. The present publication aims to address this shortcoming. First, group…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…