We discussed in a comprehensive fashion the classical algebraic theory of anyons both in terms of fusion theory and the category formalism. We first introduced the motivation of studying anyons and the notions to be used in fusion theory. We then talked about the motivation of fusion theory and we introduced fusion theory in detail. We also showed some important identities before we gave a few examples of the usage of fusion theory and how it could be used to help simplify our problem. We then related anyons with fusion theory by introducing braiding and topological spin. We had some detailed discussion about the topological spin and justified their relationship with the wave-function when identical anyons were swapped. We gave a very brief introduction about category theory and we also talked about a few easy understanding examples. We then talked about how fusion theory and category theory could be related.

The use of scanning near field optical microscopy (SNOM), as a mean of breaking the far-field diffraction limit, has been widely applied to the study of surface polaritons and photoluminescence of two dimensional materials. There are, however, wide-spread obstacles which lower the resolution of the microscopy and the overall image quality. One of them is the residue attached to the surface arisen from the annealing process and another factor is the strong background field due to the Atomic Force Microscopy (AFM) tip structure. We have investigated the optimal condition for annealing Polypropylene Carbonate (PPC), which is the main source of the residue on the material surface. We have drawn the conclusion that annealing at 600 ℃ for its maximum temperature and an ultraslow heating and cooling process gives the lowest residue. Alternative devices that eliminate the necessity of the annealing of PPC were also considered. We also did simulations to find the optimal material configuration for the back-ground-free campanile SNOM tip. The result shows that using silver as the material with an aluminum cover gives the best efficiency of coupling between near-field and far-field signals.

Shaking of an optical lattice allows to engineer new effective Hamiltonian and create novel many-body states of fermions in this artificial lattice. A piezo-driven translatable mirror is capable of driving at frequencies up to tens to a hundred of kilohertz with excellent pointing stability. The aim of this project is to characterize piezoelectric actuators with different shapes and in various configurations. Tested characteristics are frequency response, maximal expansion, static steering error and micro-motion. This simple design should be useful for a broad set of optical applications where tilt-free displacements are required.

An important feature of strongly correlated electron systems is the tuning between interesting ground states such as unconventional superconductivity and exotic magnetism. Pressure is a clean, continuous and systematic tuning parameter. However, due to the restricted accessibility introduced by high-pressure devices, compatible magnetic field sensors with sufficient sensitivity are rare. This greatly limits the detections and detailed studies of pressure-induced phenomena. Here, we utilize nitrogen vacancy (NV) centers in diamond as a powerful, spatially-resolved vector field sensor for material research under pressure at cryogenic temperatures. Using a single crystal of BaFe2(As0.59P0.41)2 as an example, we extract the superconducting transition temperature (Tc), the local magnetic field profile in the Meissner state and the critical fields (Hc1 and Hc2). The method developed in this work will become a unique tool for tuning, probing and understanding quantum many body systems.

In quantum field theory, the vacuum state is not truly empty, but is rather filled with tiny fluctuations and dependent on system parameters. By changing the system parameters in time, these field fluctuations can be amplified into observable radiation in a process called dynamical Casimir effect(DCE), which has recently been experimentally seen in superconducting circuits. Traditionally, studies of DCE focused on modulating macroscopic objects in time, such as moving conducting plates and dielectric materials with time dependent permittivity to produce photons. However, little has been done to understand DCE on the microscopic level. In this presentation, I will introduce the effects of individual atoms on the vacuum, and how varying them in time in different manners, including changing its internal state by scattering a single photon, by resonant laser driving; as well as moving the atom in different trajectories, leads to emission of pairs of photons. Interesting properties in the emitted photons’ spectra, directionality and polarization entanglement will also be discussed.

Twente Mass and Heat Transfer Water Tunnel (MHT) was designed for research in shear-induced turbulent multiphase channel flow heated inhomogeneously. Investigation of such a complex system remains insufficient in spite of huge effort having spent on it in the recent years. Our objective is to provide a comprehensive study of the statistical properties the single-phase turbulent flow of MHT through various approaches of statistical analysis, namely probability distribution, energy spectra, structure function and scaling exponent. These results could help the further study of this system in the future.

Multidimensional Lotka-Volterra model is primarily used to explain the dynamics of competition among different species in a biological community such as bacteria community. Previous research have used random matrix with a given mean and standard deviation to represent the competitive term in the Lotka-Volterra model(Bunin), but they are very complex to analyse. We used a simple matrix with two alternating parameters to represent one community, and then set up multiple identical communities between which species can migrate with a certain speed. We find that by controlling the migration and competition parameter, we can identify four phases of the system. Our research examines the dynamics and equilibrium of these four phases — Coexistence Phase, Homogeneous Bistability Phase, Heterogeneous Bistability Phase, Unbounded Growth Phase.

Silicon surface is one of the most studied surfaces in surface science. Here we present a computational approach using a hybrid scheme of Particle Swarm Optimization (PSO) to search silicon (001) surface reconstruction. Using Tersoff pseudopotential instead of ab initio method as cost function, we have developed a systematic way to obtain the correct surface reconstruction with a high accuracy.

Oil spill and explosion accidents become increasingly common, bringing about billion-dollar costs and incalculable environmental damages. As cement encasement defects are named as one of the major reasons, there exists a need in a viable solution for testing the wellbore integrity; a collaboration of research groups in Brown university and KAUST is working in developing a spintronics device to detect the cracks; the magnetic tunneling junction sensor used presents an advantageous combination of high sensitivity, low power consumption, small physical size and low cost.

Terrestrial ecosystems, with a large portion as forests, are known to be an important component shaping regional climate. Terrestrial ecosystems modulate climate by two major pathways: biogeochemically fixing atmospheric carbon (mainly CO2) and biogeophysically controlling the surface energy balance. Studies show that different biogeophysical impacts may compensate each other since forests can reduce albedo and increase net radiation, but promote evapotranspiration and cool down the surface. In this presentation, we will look into how these effects are modelled in land surface model. Since we have limited information about the environment (both spatial and temporal) and limited computational resources, instead of solving fundamental equations, there are alternative ways for modelling a mean profile for the energy flux terms. It illustrates the complexity of the Earth system and shows how Earth system scientists attempt to tackle the limitations. Also, we have performed model experiments using our in-house ecophysiological model, Terrestrial Ecosystem Model in R (TEMIR), with a biogeophysics module that simulate the surface energy budget. By quantifying the two compensating biogeophysical effects, we conclude that forests could regulate the warming climate only in lower latitude but potentially enhance warming in the higher latitude regions that may offset larger-scale biogeochemical cooling.

Why are a few drugs with properties beyond the rule of 5 (bRo5) absorbed across the intestinal mucosa while most other bRo5 compounds are not? Are such exceptional bRo5 compounds exclusively taken up by carrier-mediated transport or are they able to permeate the lipid bilayer (passive lipoidal diffusion)? Our experimental data with liposomes indicate that tetracycline, which violates one rule of the Ro5, and rifampicin, violating three of the rules, significantly permeate a phospholipid bilayer with kinetics similar to labetalol and metoprolol, respectively. Published data from experimental work and molecular dynamics simulations suggest that the formation of intramolecular H-bonds and the possibility to adopt an elongated shape besides the presence of a significant fraction of net neutral species facilitate lipid bilayer permeation. As an alternative to lipid bilayer permeation, carrier proteins can be targeted to improve absorption, with the potential drawbacks of drug–drug interactions and non-linear pharmacokinetics.