# Coarse graining, dynamic renormalization and the kinetic theory of shock clustering

Source: [Coarse graining, dynamic renormalization and the kinetic theory of shock clustering](<https://www.sota2.com/research/paper/68fa2dd61e209131ce85cf43>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T16:31:31.017Z

Authors: Xingjie Li, Matthew O. Williams, Ioannis G. Kevrekidis, Govind Menon

Published: 2014-11-02T17:36:14.000Z

## Abstract

We demonstrate the utility of the equation free methodology developed by one of the authors (I.G.K) for the study of scalar conservation laws with disordered initial conditions. The numerical scheme is benchmarked on exact solutions in Burgers turbulence corresponding to Levy process initial data. For these initial data, the kinetics of shock clustering is described by Smoluchowski's coagulation equation with additive kernel. The equation free methodology is used to develop a particle scheme that computes self-similar solutions to the coagulation equation, including those with fat tails.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1411.0284>)

[PDF](<https://arxiv.org/pdf/1411.0284.pdf>)