Applied Mathematics Research Centre

The AMRC hosts a series of seminars on subjects in statistical physics and fluid dynamics.

**Linear stability of a Stewartson shear layer induced by differential rotation**

Shear layers in rotating flows are abundant in nature, occurring in atmospheric storms, hurricanes, and polar vortices on planets with atmospheres. In 1957, Stewartson developed theoretical expressions relating the thickness of a shear layer between concentric cylinders of fluid rotating at slightly different rates to the Ekman number, and later works have yielded insight into the stability of these shearing flows to azimuthal disturbances. Renewed interest in these flows has been motivated by their possible connection with the polygonal distortion of polar vortices on several planets. We use numerical simulation to determine the axisymmetric flow solutions for these flows across a wide range of Ekman and Rossby numbers, and employ a linear stability analysis to describe the stability of these flows to infinitesimal azimuthal disturbances. The theoretical scaling of shear layer thickness with Ekman number is found to closely follow theory across much of the Ekman-Rossby number parameter space, and we further propose relationships for the preferred azimuthal instability wavelengths as functions of Rossby and Ekman numbers.

**Can a spin glass phase survive in an external magnetic field?**

The existence of a spin glass phase below the upper critical dimension (6 dimensions) in presence of a magnetic field is still a long-standing and controversial issue. We will review the basics facts of spin glasses and the two main (and competing) theoretical approaches: the Droplet and the Replica Symmetry Breaking theories. Nextly we will describe our numerical simulations (using the Janus dedicated supercomputer) in four dimensions and in presence of a magnetic field which clearly show up the existence of the De Almeida-Thouless line. Following, we will describe numerical simulations in the one dimensional diluted long range model in field which also shows the existence of a spin glass phase in field below the upper critical dimension. Finally we will present new results obtained by the Janus collaboration in three dimensions in a field using out-of-equilibrium methods.

**The statistical physics of loops on lattices***Wednesday June 19, 2013, 15:00 h, DH Seminar room*

I will give an overview of recent work on the statistical physics of lattice models of close-packed loops. The models have two phases -- one in which all loops are finite, and another in which some loops are extended -- and the interest is in universal features of these phases and the transitions between them. The models describe a number of problems in classical statistical physics -- where, for example, the loops may be vortex lines in a three-dimensional random field -- and also many-body quantum systems -- where the loops are world-lines of particles.

**Random Planar Curves and 2d Critical Behaviour***Wednesday June 5, 2013, 16:00 h, DH Seminar room*

TBA

**Non-linear models for complex healthcare datasets***Friday May 10, 2013, 15:00 h, DH Seminar room*

TBA