Date:

Wed, 20/01/2021 - 12:00 to 13:30

See also: Nonlinear Seminar

**O.V.Gendelman, Faculty of Mechanical engineering, Technion – Israel Institute of Technology**

*Lecturer:*Abstract:

It is commonly accepted today, that one-dimenisonal lattice models can belong to three

universality classes with respect to the bulk heat conduction. The first class (e.g. lattices with

linear interactions) is characterized by heat flux that is proportional to temperature difference

rather than to the temperature gradient. The second class includes models with size-dependent heat conduction coefficient (e.g. Fermi-Pasta-Ulam model and similar nonlinear

chains with conserved momentum). The third class includes the chains that can be

characterized by well-defined convergent heat conduction coefficient in the thermodynamic

limit (e.g. Frenkel – Kontorova model or chain of rotators). There exist some quarrels and

contradictions on classification of various exotic chain models, but the universality classes

seem well-established.

The talk will address, in a sense, the opposite limit case with respect to a transport in the

homogeneous bulk – Kapitza, or boundary, thermal resistance (KR). This phenomenon (sharp

step in the temperature profile) readily reveals itself if one considers either isolated isotopic

or link defect in the homogeneous chain, or interface between two chain fragments with

different characteristics. Linear chain model with isolated defect allows exact analytic solution

for the KR – so, contrary to the bulk conductivity, the resistance has well-defined value also in

the linear chain. However, the result strongly depends on the model of thermostat –

therefore, the anomaly still is well articulated.

Account of nonlinearity demonstrates that the KR properties are related to the universality

class with respect to the heat conduction, to which the considered chain model belongs. In

linear chains, the KR does not depend on the chain length in the thermodynamic limit, but

substantially depends on the characteristics of thermostats used in the simulations. In the

models with size-dependent heat conduction coefficient, the KR also is substantially size-dependent, despite strong localization of the Kapitza step. Finally, in the models with normal

heat conductivity the KR is also normal, i.e. size- and thermostat-independent in the

thermodynamical limit.