DH 1st floor SR

In my talk I will introduce the concept of spectral discrete solitons

(SDSs): solutions of nonlinear Schroedinger type equations, which are localized on a regular grid in frequency space. In time domain such solitons correspond to periodic trains of pulses. SDSs play important role in cascaded four-wave-mixing processes (frequency comb generation) in optical fibres, where initial excitation by a two-frequency pump leads to the generation of multiple side-bands. When free space diffraction is taken into consideration, a non-trivial generalization of 1D SDSs will be discussed, in which every individual harmonic is an optical vortex with its own topological charge. Such excitations correspond to spatio-temporal helical beams.

A kinetic theory for swarming systems of interacting individuals will be described with and without noise. Starting from the the particle model \cite{DCBC}, one can construct solutions to a kinetic equation for the single particle probability distribution function using distances between measures \cite{dobru}. Analogously, we will discuss the mean-field limit for these problems with noise.

We will also present and analys the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale The large-time behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. It will be shown that the solutions concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution.

The presence of additives, which may or may not be surface-active, can have a dramatic influence on interfacial flows. The presence of surfactants alters the interfacial tension and drives Marangoni flow that leads to fingering instabilities in drops spreading on ultra-thin films. Surfactants also play a major role in coating flows, foam drainage, jet breakup and may be responsible for the so-called ``super-spreading" of drops on hydrophobic substrates. The addition of surface-inactive nano-particles to thin films and drops also influences the interfacial dynamics and has recently been shown to accelerate spreading and to modify the boiling characteristics of nanofluids. These findings have been attributed to the structural component of the disjoining pressure resulting from the ordered layering of nanoparticles in the region near the contact line. In this talk, we present a collection of results which demonstrate that the above-mentioned effects of surfactants and nano-particles can be captured using long-wave models.

Many growing plant cells undergo rapid axial elongation with negligible radial expansion. Growth is driven by high internal turgor pressure causing viscous stretching of the cell wall, with embedded cellulose microfibrils providing the wall with strongly anisotropic properties. We present a theoretical model of a growing cell, representing the primary cell wall as a thin axisymmetric fibre-reinforced viscous sheet supported between rigid end plates. Asymptotic reduction of the governing equations, under simple sets of assumptions about the fibre and wall properties, yields variants of the traditional Lockhart equation, which relates the axial cell growth rate to the internal pressure. The model provides insights into the geometric and biomechanical parameters underlying bulk quantities such as wall extensibility and shows how either dynamical changes in wall material properties or passive fibre reorientation may suppress cell elongation. We then investigate how the action of enzymes on the cell wall microstructure can lead to the required dynamic changes in macroscale wall material properties, and thus demonstrate a mechanism by which hormones may regulate plant growth.

Whenever we say the words "fluid flows" or "shape changes" we enter the realm of infinite-dimensional geometric mechanics. Water, for example, flows. In fact, Euler's equations tell us that water flows a particular way. Namely, it flows to get out of its own way as adroitly as possible. The shape of water changes by smooth invertible maps called diffeos (short for diffeomorphisms). The flow responsible for this optimal change of shape follows the path of shortest length, the geodesic, defined by the metric of kinetic energy. Not just the flow of water, but the optimal morphing of any shape into another follows one of these optimal paths.

The lecture will be about the commonalities between fluid dynamics and shape changes and will be discussed in the language most suited to fundamental understanding -- the language of geometric mechanics. A common theme will be the use of momentum maps and geometric control for steering along the optimal paths using emergent singular solutions of the initial value problem for a nonlinear partial differential equation called EPDiff, that governs metamorphosis along the geodesic flow of the diffeos. The main application will be in the registration and comparison of Magnetic Resonance Images for clinical diagnosis and medical procedures.

Colorectal cancer (CRC) is one of the leading causes of cancer-related death worldwide, demanding a response from scientists and clinicians to understand its aetiology and develop effective treatment. CRC is thought to originate via genetic alterations that cause disruption to the cellular dynamics of the crypts of Lieberkűhn, test-tube shaped glands located in both the small and large intestine, which are lined with a monolayer of epithelial cells. It is believed that during colorectal carcinogenesis, dysplastic crypts accumulate mutations that destabilise cell-cell contacts, resulting in crypt buckling and fission. Once weakened, the corrupted structure allows mutated cells to migrate to neighbouring crypts, to break through to the underlying tissue and so aid the growth and malignancy of a tumour. To provide further insight into the tissue-level effects of these genetic mutations, a multi-scale model of the crypt with a realistic, deformable geometry is required. This talk concerns the progress and development of such a model, and its usefulness as a predictive tool to further the understanding of interactions across spatial scales within the context of colorectal cancer.

Graphics processing units (GPU) are well suited to decrease the

computational in-

tensity of stochastic simulation of chemical reaction systems. We

compare Gillespie’s

Direct Method and Gibson-Bruck’s Next Reaction Method on GPUs. The gain

of the

GPU implementation of these algorithms is approximately 120 times faster

than on a

CPU. Furthermore our implementation is integrated into the Systems

Biology Toolbox

for Matlab and acts as a direct replacement of its Matlab based

implementation.

A behavioral mean-variance portfolio selection problem in continuous time is formulated and studied. Based on the standard mean-variance portfolio selection problem, the cumulative distribution function of the cash flow is distorted by a probability distortion function. Then the problem is no longer a convex optimization problem. This feature distinguishes it from the conventional linear-quadratic (LQ) problems.

The stochastic optimal LQ control theory no longer applies. We take the quantile function of the terminal cash flow as the decision variable.

The corresponding optimal terminal cash flow can be recovered by the optimal quantile function. Then the efficient strategy is the hedging strategy of the optimal terminal cash flow.

The talk concerns experiments that study strategic thinking by eliciting subjects’ initial responses to series of different but related games, while monitoring and analyzing the patterns of subjects’ searches for hidden but freely accessible payoff information along with their decisions.

Using a large panel data set of Swedish pension savers (75,000 investors, daily portfolios 2000-2008) we show that active investors outperform inactive investors and that there is a causal effect of fund switches on performance. The higher performance is earned not by market timing, but by dynamic fund picking (within the same asset class). While activity is positive for the individual investor, there are indications that it generates costs for other investors.