Microscopic Laws vs. Macroscopic Laws: Perspectives from Kinetic Theory and Hydrodynamics

SBMLsqueezer: Kinetic Laws

Hydrodynamics and growth laws in lamellar ordering

Ordering of lamellar phases described by a free-energy functional with short-range interactions is numerically investigated in two dimensions by means of a pseudo-spectral method. The ordering process is found to depend on the fluid viscosity: it is arrested for large viscosity values and proceeds as a power law for small ones, with a crossover regime for intermediate values. At varying the fre...

Simple Microscopic Theory of Amontons’ Laws for Static Friction

A microscopic theory for the ubiquitous phenomenon of static friction is presented. Interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load, in accordance with Amontons’ laws. However the friction coefficient between bare surfaces vanishes as the area of individual c...

Simple microscopic theory of Amontons's laws for static friction.

A microscopic theory for the ubiquitous phenomenon of static friction is presented. Interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load, in accordance with Amontons's laws. However, the friction coefficient between bare surfaces vanishes as the area of individual...

A kinetic theory of shock clustering in scalar conservation laws

We describe a kinetic theory for shock clustering in scalar conservation laws with random initial data. Our main discovery is that for a natural class of random data the shock clustering is described by a completely integrable Hamiltonian system. Thus, the problem is in a precise sense exactly solvable. Our results have implications in other areas: mathematical physics (limits of shell models o...