Imperial College London

Ultracold atomic gases have recently proven to be enormously rich

systems from the perspective of a condensed matter physicist. With

the advent of optical lattices, such systems can now realise idealised

model Hamiltonians used to investigate strongly correlated materials.

Conversely, ultracold atomic gases can exhibit quantum phases and

dynamics with no counterpart in the solid state due to their extra

degrees of freedom and unique environments virtually free of

dissipation. In this talk, I will discuss examples of such behaviour

arising from spinor degrees of freedom on which my recent research has

focused. Examples will include bosons with artificially induced

spin-orbit coupling and the non-equilibrium dynamics of spinor

condensates.

Some striking, and potentially useful, effects in electrokinetics occur for

bipolar membranes: applications are in medical diagnostics amongst other areas.

The purpose of this talk is to describe the experiments, the dominant features observed

and then model the phenomena: This uncovers the physics that control this process.

Time-periodic reverse voltage bias

across a bipolar membrane is shown to exhibit transient hysteresis.

This is due to the incomplete depletion of mobile ions, at the junction

between the membranes, within two adjoining polarized layers; the layer thickness depends on

the applied voltage and the surface charge densities. Experiments

show that the hysteresis consists of an Ohmic linear rise in the

total current with respect to the voltage, followed by a

decay of the current. A limiting current is established for a long

period when all the mobile ions are depleted from the polarized layer.

If the resulting high field within the two polarized layers is

sufficiently large, water dissociation occurs to produce proton and

hydroxyl travelling wave fronts which contribute to another large jump

in the current. We use numerical simulation and asymptotic analysis

to interpret the experimental results and

to estimate the amplitude of the transient hysteresis and the

water-dissociation current.

 Abstract:  In this talk we will introduce a new particle approximation scheme to solve the stochastic filtering problem. This new scheme makes use of the Kusuoka-Lyons-Victoir (KLV) method to approximate the dynamics of the signal. In order to control the computational cost, a partial sampling procedure based on the tree based branching algorithm (TBBA) is performed. The novelty of the method lies in the fact that the weights used in the TBBA are computed combining the cubature weights and the filtering weights. In this way, we can avoid the sample degeneracy problem inherent to particle filters. We will also present some simulations showing the performance of the method.

The AdS/CFT correspondence is a powerful tool to analyse strongly coupled quantum field

theories. Over the past few years there has been a surge of activity aimed at finding

possible applications to condensed matter systems. One focus has been to holographically

realise various kinds of phases via the construction of fascinating new classes of black

hole solutions. In this framework, I will discuss the possibility of describing finite

temperature phase transitions leading to spontaneous breaking of translational invariance of

the dual field theory at strong coupling. Along with the general setup I will also discuss

specific string/M theory embeddings of the corresponding symmetry breaking modes leading to

the description of such phases.

Through the advent of enhanced medical imaging computational modelling can now be applied to anatomically correct arterial geometries. However many flow feautures under physiological and pathological flow paraemeters, even in idealised problems, are relatively poorly understood. A commonly studied idealisation of an arterial blockage or stenosis, potentially generated by atherosclerosis, is a sinusoidally varying constricted tube. Although most physiological flow conditions are typically laminar, in this configuration turbulent flow states can arise due to the local increase in sectional Reynolds number. To examine the onset of turbulence in this geometry, under a simple non-reversing pulsatile flows, we have applied Floquet stability analysis and direct
numerical simulation.
As illustrated in the above figure, a period-doubling absolute instability mode associated with alternating tilting of the vortex rings that are ejected out of the stenosis/constriction during each pulse. This primary instability occurs for relatively large reduced velocities associated with long pulse periods (or low Womersley numbers). For lower reduced velocities the primary instability typically manifests itself as azimuthal waves (Widnall instability modes) of low wavenumber that grow on each vortex ring. We have also observed the shear layer of the steady axisymmetric flow is convectively unstable at still shorter temporal periods.
In this presentation we shall outline the challenges of modelling vascular flow problems with a particular focus on idealised stenotic flow. After briefly outlining the numerical analysis methods we shall discuss the flow investigations outlined above and their relation to more classical vortex instabilities.

In this talk we show that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave.

The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain.

The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions

Voltammetry is a powerful method for interrogating electrochemical systems. A voltage is applied to an electrode and the resulting current response analysed to determine features of the system under investigation, such as concentrations, diffusion coefficients, rate constants and thermodynamic potentials. Here we will focus on ac voltammetry, where the voltage signal consists of a high frequency sine-wave superimposed on a linear ramp. Using multiple scales analysis, we find analytical solutions for the harmonics of the current response and show how they can be used to determine the system parameters. We also include the effects of capacitance due to the double-layer at the electrode surface and show that even in the presence of large capacitance, the harmonics of the current response can still be isolated using the FFT and the Hanning window.