Applied nonequilibrium statistical mechanics - Dr. Astrid S. de Wijn

Theory and modelling - tribology, surface science, transport properties, nonlinear dynamics, condensed matter

Our aim is to develop new, general, models for transport of matter, energy, and momentum, and relate it to microscopic nonlinear dynamics. We currently focus on two types of systems:

We employ computational as well as analytical methods to solve applied and fundamental problems. We collaborate with experimental as well as theoretical researchers from a wide variety of fields, ranging from chemical engineering to mathematical physics. More details below.

This research subgroup is part of the Materials group at the Department of Mechanical and Industrial Engineering at the Norwegian University of Science and Technology (NTNU)

People


List of publications.

A list of some available topics for Master-level projects.


Links and associated activities


Research topics

Transport properties in general, but friction in particular, are challenging theoretically, because there is no general formalism to describe them. To understand transport, we must link microscopic dynamics of particles to macroscopic averages. For equilibrium systems, such as a liquid that is completely stationary, the powerful formalisms of equilibrium statistical mechanics provide a framework for this. For systems with transport, which are out of equilibrium, we are stuck using ad-hoc approaches that are only valid in particular cases, and often we are forced to resort to numerical simulations.

Fundamental tribology theory

Friction is so ubiquitous in everyday life that we often don't even think about it. In industrialid societies, a great deal of energy and material is lost due to friction, and friction and wear are extremely important in the operation of all devices with moving parts Humans have been dealing with friction since prehistoric times, and we have developed phenomenological laws to describe it. Nevertheless, we still do not fully understand these laws and their coefficients. As a result, attempts to engineer low-friction surfaces or effective lubricants are often based on trial and error.

One of the main reasons why friction is such a challenging subject, is because many different effects occur at different scales. While two sliding surfaces appear flat on macroscopic scales, they are in fact almost never truly flat (see figure). On smaller scales, the roughness of the surfaces means that the actual contact area is small compared to the apparent contact area. The actual contacts are of the order of micrometer in size. Energy is dissipated in a variety of ways at these contacts by atomic interaction that occur on the scale of a nanometer. To understand friction on large, macroscopic scales, we must first understand friction on micro and nanometer scales. (The study of friction on very small scales is called nanotribology.) During the last few decades, there have been enormous developments in experimental techniques for probing friction on small scales, such as the atomic force microscope (AFM), but theoretical understanding is lagging behind. Theoretical techniques have also undergone developments: the mathematical understanding of dynamical systems as well as the massive increases in computing power have handed us the tools we need to finally understand friction. In our group, we study and model friction on this basic level.

Nonlinear dynamics of nanosystems on surfaces and simple models

Nanoscale systems are becoming more and more experimentally accessible, due to advances in microscopic manipulation and measurement techniques. Nano-scale friction experiments, using Atomic Force Microscopes for example, provide an especially useful window into transport of mass, energy, and momentum in nanoscale systems. Theoretical approaches to these systems, however, are often restricted to numerical simulations. Dynamical systems theory, which also forms the foundations of statistical mechanics, therefore is the most promising basis for understanding the mechanics of nanosystems. Deeper qualitative understanding of the role of nonlinear dynamics in nanoscale systems provides insight into experimental results as well as ways to control the motion (friction or diffusion) of nanosystems on surfaces. Our focus here is on fundamental (qualitative, general) understanding and relatively simple models that contain the essential dynamics.

Applied kinetic theory

Accurate values for transport coefficients such as the viscosity of complex gases and liquids are needed in many practical applications. The viscosity of a lubricant, for example, is crucial for its effectiveness. Kinetic theory is the only instrument at our disposal for turning detailed knowledge of the interactions between molecules into predictions for transport coefficients. Nevertheless, it is notoriously difficult to obtain accurate results for transport coefficients of any but the simplest systems. Our objective is to develop new kinetic approaches to transport coefficients such as viscosity and diffusion of liquids and gases.

Dynamical properties of many-particle systems

Dynamical properties such as ergodicity, chaos, and integrability play an essential role in the foundations of both equilibrium and nonequilibrium statistical physics. In systems consisting of many particles, these properties behave differently from how they behave in systems with small numbers of degrees of freedom, where they are typically studied. Consequently, little is known about the universality of the dynamical properties of many-particle systems.

Miscelaneous

We sometimes stray into other fields, such as strongly-correlated electron systems, glasses, and biophysics.