Multiscaling for Systems with a Broad Continuum of Characteristic Lengths and Times: Structural Transitions in Nanocomposites - Physics > Biological PhysicsReport as inadecuate




Multiscaling for Systems with a Broad Continuum of Characteristic Lengths and Times: Structural Transitions in Nanocomposites - Physics > Biological Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: The multiscale approach to N-body systems is generalized to address the broadcontinuum of long time and length scales associated with collective behaviors.A technique is developed based on the concept of an uncountable set of timevariables and of order parameters OPs specifying major features of thesystem. We adopt this perspective as a natural extension of the commonly useddiscrete set of timescales and OPs which is practical when only a few,widely-separated scales exist. The existence of a gap in the spectrum oftimescales for such a system under quasiequilibrium conditions is used tointroduce a continuous scaling and perform a multiscale analysis of theLiouville equation. A functional-differential Smoluchowski equation is derivedfor the stochastic dynamics of the continuum of Fourier component orderparameters. A continuum of spatially non-local Langevin equations for the OPsis also derived. The theory is demonstrated via the analysis of structuraltransitions in a composite material, as occurs for viral capsids and molecularcircuits.



Author: Stephen Pankavich, Peter Ortoleva

Source: https://arxiv.org/







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