To forgive and to forget: racial memory in South Africa and the US

Paper presented at the Wits History Workshop: The TRC; Commissioning the Past, 11-14 June, 199

Quantitative Rates of Convergence to Equilibrium for the Degenerate Linear Boltzmann equation on the Torus

We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In \cite{BS13} Bernard and Salvarani showed that this equation converges exponentially fast to equilibrium if and only if the jump rate satisfies the geometric control condition of Bardos, Lebeau and Rauch \cite{BLR91}. In \cite{HL15} Han-Kwan and L\'{e}autaud showed a more general result for linear Boltzmann equations under the action of potentials in different geometric contexts, including the case of unbounded velocities. In this paper we obtain quantitative rates of convergence to equilibrium when the geometric control condition is satisfied, using a probabilistic approach based on Doeblin's theorem from Markov chains.Comment: 22 page

Bounds on Wahl singularities from symplectic topology

A complex surface is said to have general type if its canonical bundle is big. The moduli space of surfaces of general type with fixed characteristic numbers $K^2$ and $\chi$ admits a compactification, constructed by Kolla ́r and Shepherd-Barron, whose boundary points correspond to surfaces with semi-log-canonical (slc) singularities, in much the way that the boundary points of Deligne-Mumford space correspond to nodal curves

Driven Tracers in a One-Dimensional Periodic Hard-Core Lattice Gas

Totally asymmetric tracer particles in an environment of symmetric hard-core particles on a ring are studied. Stationary state properties, including the environment density profile and tracer velocity are derived explicitly for a single tracer. Systems with more than one tracer are shown to factorise into single-tracer subsystems, allowing the single tracer results to be extended to an arbitrary number of tracers. We demonstrate the existence of a cooperative effect, where many tracers move with a higher velocity than a single tracer in an environment of the same size and density. Analytic calculations are verified by simulations. Results are compared to established results in related systems.Comment: Added reference. Corrected typo in section 3.

Integrability of two-species partially asymmetric exclusion processes

We work towards the classification of all one-dimensional exclusion processes with two species of particles that can be solved by a nested coordinate Bethe Ansatz. Using the Yang-Baxter equations, we obtain conditions on the model parameters that ensure that the underlying system is integrable. Three classes of integrable models are thus found. Of these, two classes are well known in literature, but the third has not been studied until recently, and never in the context of the Bethe ansatz. The Bethe equations are derived for the latter model as well as for the associated dynamics encoding the large deviation of the currents.Comment: 15 pages, 2 figure

Matrix product solution for a partially asymmetric 1D lattice gas with a free defect

A one-dimensional, driven lattice gas with a freely moving, driven defect particle is studied. Although the dynamics of the defect are simply biased diffusion, it disrupts the local density of the gas, creating nontrivial nonequilibrium steady states. The phase diagram is derived using mean field theory and comprises three phases. In two phases, the defect causes small localized perturbations in the density profile. In the third, it creates a shock, with two regions at different bulk densities. When the hopping rates satisfy a particular condition (that the products of the rates of the gas and defect are equal), it is found that the steady state can be solved exactly using a two-dimensional matrix product ansatz. This is used to derive the phase diagram for that case exactly and obtain exact asymptotic and finite size expressions for the density profiles and currents in all phases. In particular, the front width in the shock phase on a system of size $L$ is found to scale as $L^{1/2}$, which is not predicted by mean field theory. The results are found to agree well with Monte Carlo simulations.Comment: 20 pages, 5 figure

Current fluctuations in a partially asymmetric simple exclusion process with a defect particle

We study an exclusion process on a ring comprising a free defect particle in a bath of normal particles. The model is one of the few integrable cases in which the bath particles are partially asymmetric. The presence of the free defect creates localized or shock phases according to parameter values. We use a functional approach to Bethe equations resulting from a nested Bethe ansatz to calculate exactly the mean currents and diffusion constants. The results agree very well with Monte-Carlo simulations and reveal the main modes of fluctuation in the different phases of the steady state.Comment: 17 pages, 4 figure

The influence of task difficulty, social tolerance and model success on social learning in Barbary macaques

Despite playing a pivotal role in the inception of animal culture studies, macaque social learning is surprisingly understudied. Social learning is important to survival and influenced by dominance and affiliation in social animals. Individuals generally rely on social learning when individual learning is costly, and selectively use social learning strategies influencing what is learned and from whom. Here, we combined social learning experiments, using extractive foraging tasks, with network-based diffusion analysis (using various social relationships) to investigate the transmission of social information in free-ranging Barbary macaques. We also investigated the influence of task difficulty on reliance on social information and evidence for social learning strategies. Social learning was detected for the most difficult tasks only, with huddling relations outside task introductions, and observation networks during task introductions, predicting social transmission. For the most difficult task only, individuals appeared to employ a social learning strategy of copying the most successful demonstrator observed. Results indicate that high social tolerance represents social learning opportunities and influences social learning processes. The reliance of Barbary macaques on social learning, and cues of model-success supports the costly information hypothesis. Our study provides more statistical evidence to the previous claims indicative of culture in macaques

Nonlinearities and all-optical switching in semiconductor laser amplifiers

The nonlinear properties of semiconductor laser amplifiers have been investigated, particularly at the transparency bias point, in the InGaAsP/InP and GaAs/AlGaAs material systems. An all-solid-state F-centre laser system has been developed. It consisted of a diode-pumped Nd:YLF laser mode-locked at 77 MHz repetition rate, producing pulse durations of 6-20 ps with an average power of 2.2 W. The Nd:YLF laser synchronously pumps the F-centre laser producing pulse widths as short as 4ps with average powers of 200 mW. The available wavelength tuning range was from 1.45 mum to 1.55 mum. The Nd:YLF pump laser, although not designed to do so, Kerr lensed mode-locked. The reason for this unexpected behaviour was investigated and was shown to be due to the unusual laser cavity design. Thermal lensing is shown have a significant impact on the cavity stability and is believed to degrade the laser performance. The nonlinear coefficient, n2, has been measured by self-phase-modulation, for pulses of picosecond duration in a 5QW InGaAsP laser amplifier at a wavelength of 1.5 mum. Subsequently a pump-probe study, showed the likely origin of this nonlinearity was carrier heating. The pump-probe studies have also shown that this nonlinearity saturates for mW power levels at the pulse durations used. The gain saturation caused by carrier heating is modelled and the calculated saturation powers relate well to the pump-probe data. The mechanism that causes the effective saturation of the nonlinearity is therefore attributed to carrier heating induced gain saturation. For the first time an integrated active asymmetric Mach-Zehnder interferometer laser amplifier has been fabricated in the AlGaAs/GaAs material system. This structure has been characterised as a laser and tested as an all-optical switch at the transparency bias point. The Mach-Zehnder was switched with pulses of 100 fs duration corresponding to a pulse energy of 3pJ. The device shows inferior performance to passive waveguide and fibre all-optical switches, in the area of switching contrast. Similar active amplifier switches in the nonlinear directional coupler configuration also show better characteristics. The poor performance of the Mach-Zehnder used here is believed to be due to arm asymmetries caused by gain saturation or fabrication variations. A detailed model of the switching characteristics is presented. However it was not possible to use the model to deduce key material parameters because the model provided a good fit to the experimental data across a wide matrix of parameters, up to 100% variation in n2, alpha and beta