Related papers: Tensorial conservation law for nematic polymers
We explore the implications of the conservation law(s) and the corresponding "continuity equation(s)", resulting from the coupling between the positional and the orientational order in main-chain polymer nematics, by showing that the…
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…
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…
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…
In order to address the selection mechanism that is responsible for the unique lamellar orientation observed in block copolymers under oscillatory shears, we use a constitutive law for the dissipative part of the stress tensor that respects…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
Despite their considerable practical and biological applications, the link between molecular properties, assembly conditions and self-organized structure in confined polymer solutions remains elusive. Here, we explore the lyotropic nematic…
We study the nonlinear wave equation for arbitrary function with fourth order dissipation. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth…
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.…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
A complete and explicit classification of all independent local conservation laws of Maxwell's equations in four dimensional Minkowski space is given. Besides the elementary linear conservation laws, and the well-known quadratic…
In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the…
We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another…
Polymers are a primary building block in many biomaterials, often interacting with anisotropic backgrounds. While previous studies have considered polymer dynamics within nematic solvents, rarely are the the effects of anisotropic viscosity…
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…
Conservation laws are one of the most generic and useful concepts in physics. In nonlinear optical parametric processes, conservation of photonic energy, momenta and parity often lead to selection rules, restricting the allowed polarization…
Within the framework of continuum theory, we draw a parallel between ferromagnetic materials and nematic liquid crystals confined on curved surfaces, which are both characterized by local interaction and anchoring potentials. We show that…
Using a manifestly invariant Lagrangian density based on Clebsch fields and suitable for geophysical fluid dynamics, the conservation of mass, entropy, momentum and energy, and the associated symmetries are investigated. In contrast, it is…