We're happy to welcome:
Tanja Schilling (Universität Freiburg)
How to make noise
In physics, we hardly ever describe a system in terms of all of its microscopic degrees of freedom. We usually resort to effective coarse-grained models, which predict the behaviour of "relevant" system properties. One widely used effective equation of motion for coarse-grained variables is the Langevin equation, a stochastic differential equation, in which the effect of the neglected degrees of freedom is encoded in friction terms and stochastic noise.
In this seminar we will review the steps of derivation and approximation that are required to obtain the Langevin equation from a system's microscopic description. We will discuss the interplay between the potential of mean force and the memory kernel, the range of validity of the second fluctuation dissipation theorem, and the stochastic interpretation of the fluctuating force, i.e. the noise.
Oliver Bühler (New York University)
A drunkard’s view of dual cascades in wave turbulence
Spectral cascades in 3d and 2d hydrodynamic turbulence are reasonably well understood and served as a role model for subsequent studies of analogous cascades in wave turbulence. In particular, the workings of the famous dual cascade in 2d turbulence became the paradigm for wave turbulence systems based on four-wave resonances (e.g. surface waves, or the nonlinear Schrödinger equation with cubic nonlinearity). However, it can be argued that the familiarity of dual cascades masks profound differences between the 2d hydrodynamic case and its wave turbulence counterpart, and that these differences can strongly affect detailed turbulence measurements in numerical models or experiments. In this elementary talk, I will introduce the various cascade pictures at a simple level and then illustrate the peculiarities of the wave turbulence dual cascade based on recent high-resolution simulations. I will also present a new semi-empiric toy model of dual cascades in wave turbulence that is surprisingly accurate in explaining the peculiar results of the numerical simulations.
Adrian Muntean (Karlstad University)
Mathematics of phase separation in interacting ternary mixtures under evaporation: The unexpected story of a non-local evolution system
Inspired by experimental evidence collected when processing thin films from ternary solutions made of two solutes, typically polymers, and one solvent, we study computationally the morphology formation of domains obtained in three-state systems using both a lattice (microscopic) model and a continuum (macroscopic) counterpart.
The lattice-based approach relies on the Blume-Capel nearest neighbor model with bulk conservative Kawasaki dynamics, whereas as continuum system we consider a coupled system of evolution equations (with nonlinear nonlocal drifts) that is derived as hydrodynamic limit when replacing the nearest neighbor interaction in the lattice case by a suitable Kac potential. We explore how the obtained morphology depends on the solvent content in the mixture. In particular, we study how these scenarios change when the solvent is allowed to evaporate. Essentially, we illustrate how the evaporation process affects the shape and connectivity of the evolving-in-time morphologies. As a final note, we give a statement about the well-posedness of the continuum model, sketch its proof, and then point out how well our finite volumes schemes are able to construct approximations of the wanted weak solution.
This is a report on recent joint work with Rainey Lyons (University of Colorado Boulder, USA), Andrea Muntean (Karlstad University, Sweden), and Emilio N.M. Cirillo (La Sapienza University, Rome, Italy).