Applied Mathematics Research Centre

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

**Diffusion of the dead***Wednesday February 25, 2015, 14:00 h, DH Seminar Room*

Knowing how long we have before we interact with a zombie could mean the difference between life, death and zombification. Here, we apply the same mathematical models to zombies that you would use to describe flu, or measles. We use this model to derive exact and approximate interaction times and use these to develop strategies which allow the human race to survive impending doom.

**Entropy production at criticality for nonequilibrium lattice models**

An out of equilibrium Glauber-Ising model, ruled by irreversible and stochastic Markovian dynamics, is dealt with in an attempt to improve our comprehension concerning the critical behavior and phase transitions in nonequilibrium systems. Therefore, an Ising model, governed by the competition between Glauber dynamics acting in interlaced square lattices, is proposed. Previous results have shown how the derivative of the rate of entropy generation, presenting a scalable divergent behavior at the critical point, may elucidate aspects of irreversibility and criticality of these systems. The comprehension of this phenomenon can be used to gain a wider perspective of universality classes. The model was analyzed by means of mean-field approximations and Monte Carlo simulations. The results show a second order phase transition, reflected in a logarithmic divergence of the entropy production’s derivative, suggesting a shared universality class with the Ising model.

**Parameterization of Electrostatic Interaction in Computer Simulation Thermostable Polyimides***Wednesday February 11, 16:30 h, DH Seminar Room*

TBA

**Stability and transition of the boundary-layer flow over rotating cone***Wednesday February 11, 15:00 h, DH Seminar Room*

Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as Görtler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode.

**Absolute and convective instabilities in eccentric Taylor-Couette-Poiseuille flow***Wednesday February 4, 15:00 h, DH Seminar Room*

After more than a century of research and well over 1500 bibliographical references (Tagg, 1992), the Taylor–Couette flow is certainly one of the most studied flows in hydrodynamic instability theory. The effects of a pressure-driven axial flow or eccentricity of the cylinders on the stability properties have also been studied separately. However, little is known about the combination of these two effects, despite its high relevance to the oil industry.

Indeed, this configuration can be used to model the drilling of an oil-well. In practice, mud is injected through the rotating drillstring and flows back to the surface through the annular gap (between the drillstring and the rock face), carrying the rock cuttings out of the well. Eccentricity is caused by unavoidable bending of the long drillstring along its axis. Transition to complex hydrodynamic regimes or turbulence is obviously detrimental to the drilling process (pressure losses, resonance, etc.).

A comprehensive stability analysis of this flow has been carried out, using numerical methods. It was found that eccentricity invariably reduces the temporal growth rate, for any fixed axial Reynolds number. However, the effect of eccentricity on the spatio-temporal dynamics of the flow is more complex: depending on the regime, eccentricity can either increase or decrease the absolute growth rate, enhancing or hindering absolute instability. This study paves the way for higher-fidelity modelling of drilling flows, including nonlinear or non-Newtonian effects.

**Computational investigation of polymers***Wednesday February 4, 14:30 h, DH Seminar Room*

In this talk I like to give an overview over some computational methods which were used or developed during my time as a PhD student. One point of the talk will be the microcanonical ensemble and the comparison of MD and MC simulations. Other topics will be the multicanonical NPT simulations as well as exact enumerations on multiple GPUs.

**Dependence of fluid flows in an evaporating sessile droplet on the characteristics of the substrate***Wednesday February 4, 14:00 h, DH Seminar Room*

Temperature distributions and the corresponding vortex structures in an evaporating sessile droplet are obtained by performing detailed numerical calculations. A Marangoni convection induced by thermal conduction in the drop and the substrate is demonstrated to be able to result not only in a single vortex, but also in two or three vortices, depending on the ratio of substrate to fluid thermal conductivities, on the substrate thickness and the contact angle. The ``phase diagrams'' containing information on the number, orientation and spatial location of the vortices for quasistationary fluid flows are presented and analysed. The results obtained demonstrate that the fluid flow structure in evaporating droplets can be influenced in a controlled manner by selecting substrates with appropriate properties.

**Why we need expert leaders in universities, hospitals & other setting***Wednesday January 28, 15:00 h, DH Seminar Room*

My research is on leadership and organizational performance. My central argument is that leaders should have a deep understanding of the core business of the organizations they are to lead. Being a good manager alone is not a sufficient condition. Evidence for ‘expert leadership’ began with a focus on university leadership (‘Socrates in the Boardroom: Why Research Universities Should be Led by Top Scholars’, Princeton University Press, 2009). Later studies have looked at hospital CEOs, and leaders in highly competitive fields such as Formula 1 Championships. Recent work has gone inside universities to ask who should lead academic departments, and a new Leverhulme study will try to understand how scientists’ productivity and job satisfaction are influenced by their leaders’ characteristics.

**A turbulent phase transition for self-organised flows in tokamak plasmas***Wednesday January 14, 15:00 h, DH Seminar Room*

Tokamak plasma turbulence is qualitatively quite different to neutral fluid turbulence: strong linear kinetic damping, for example, leads to the absence of an inertial range. On long wavelength and timescales, only certain highly symmetric modes, which are free from kinetic damping, have substantial amplitudes. One of these modes captures the rotation profile of the tokamak. We show that for a certain range of parameters, the dynamics of the rotation profile of the tokamak transitions from diffusive to antidiffusive at short wavelength. This leads to increasing fluctuation levels followed by a breakup into zones of opposite vorticity. We show that the Cahn-Hilliard equation provides a useful model for the qualitative dynamics that result.