Spectral properties of dissipation

TL;DR

This paper introduces spectral diffusivity to analyze dissipation in continua, separating dissipative components into noninteracting modes that serve as effective diffusivities or conductivities.

Contribution

It presents a novel spectral approach to dissipation analysis, enabling mode-based characterization of dissipative properties in linear systems.

Findings

Spectral diffusivity effectively characterizes dissipation.

Dissipative components are separated into noninteracting modes.

Modes serve as effective diffusivities or conductivities.

Abstract

The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is similar to mode analysis in wave propagation. The new modal quantities characterise dissipation and best interpreted as effective diffusivities, or, in case of heat conduction, as effective heat conductivities of the material.