KTH Matematik  

Matematisk Statistik

Tid: 20 december 2017 kl 15.00-15.35.

Seminarierummet F11, Institutionen för matematik, KTH, Lindstedtsvägen 22.

Föredragshållare: Markus Meder

Title: A continuum approximation of the Fermi-Pasta-Ulam-Tsingou model with Langevin dynamics

Abstract: In continuum mechanics, the conservation laws for mass, momentum and energy coupled with the constitutive relations of the stress and heat flux could be a powerful solution method for continuum systems. However, it is required that the equations form a closed system, i.e. that the stress and heat flux are formulated as functions of the conserved variables.

This thesis studies the constitutive relations of the stress and heat flux in the Fermi-Pasta-Ulam- Tsingou model with Langevin dynamics, by the means of molecular dynamics simulations. In essence, the model consists of a many particle system in the presence of a heat bath, where each particle is chained to its two neighbors by a nonlinear quadratic spring force.

A numerical method is implemented to propagate the particle dynamics. Following Hardy [7], formulas relating the macroscopic entities to the particle dynamics are employed in order to study the behavior of the stress and heat flux in relation to the mass, momentum and energy. In fact, the numerical result show that the stress appears as a linear function of the energy.

The full report (pdf)

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Sidansvarig: Jimmy Olsson
Uppdaterad: 13/12-2017