Generalized conservation law for main-chain polymer nematics

Generalized conservation law for main-chain polymer nematics.

We explore the implications of the conservation law(s) and the corresponding so-called continuity equation(s), resulting from the coupling between the positional and the orientational order in main-chain polymer nematics, by showing that the vectorial and tensorial forms of these equations are in general not equivalent and cannot be reduced to one another, but neither are they disjoint alternat...

Correlation functions of main-chain polymer nematics constrained by tensorial and vectorial conservation laws.

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 microscopic chain integrity, i.e., the connectivity of the polymer chains. In particular, our aim is to identify the features of the correlation functions that are...

A hybrid model for molecular-dynamics simulations of semiflexible main-chain liquid-crystalline polymer melts.

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The Conservation Law

Markov chain network training and conservation law approximations: Linking microscopic and macroscopic models for evolution

In this paper, a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of Markov chains and the approximation of conservation law equations is proposed. This framework allows us to demonstrate an intrinsic link between microscopic and macroscopic models for evolution via the concept of perturbed generalized dynamic systems. The ma...