The threshold for integer homology in random d-complexes

Let Y ~ Y_d(n,p) denote the Bernoulli random d-dimensional simplicial complex. We answer a question of Linial and Meshulam from 2003, showing that the threshold for vanishing of homology H_{d-1}(Y; Z) is less than 80d log n / n. This bound is tight, up to a constant factor.Comment: 12 pages, updated to include an additional torsion group boun

Accurate and efficient calculation of response times for groundwater flow

We study measures of the amount of time required for transient flow in heterogeneous porous media to effectively reach steady state, also known as the response time. Here, we develop a new approach that extends the concept of mean action time. Previous applications of the theory of mean action time to estimate the response time use the first two central moments of the probability density function associated with the transition from the initial condition, at $t=0$, to the steady state condition that arises in the long time limit, as $t \to \infty$. This previous approach leads to a computationally convenient estimation of the response time, but the accuracy can be poor. Here, we outline a powerful extension using the first $k$ raw moments, showing how to produce an extremely accurate estimate by making use of asymptotic properties of the cumulative distribution function. Results are validated using an existing laboratory-scale data set describing flow in a homogeneous porous medium. In addition, we demonstrate how the results also apply to flow in heterogeneous porous media. Overall, the new method is: (i) extremely accurate; and (ii) computationally inexpensive. In fact, the computational cost of the new method is orders of magnitude less than the computational effort required to study the response time by solving the transient flow equation. Furthermore, the approach provides a rigorous mathematical connection with the heuristic argument that the response time for flow in a homogeneous porous medium is proportional to $L^2/D$, where $L$ is a relevant length scale, and $D$ is the aquifer diffusivity. Here, we extend such heuristic arguments by providing a clear mathematical definition of the proportionality constant.Comment: 22 pages, 3 figures, accepted version of paper published in Journal of Hydrolog

New homogenization approaches for stochastic transport through heterogeneous media

The diffusion of molecules in complex intracellular environments can be strongly influenced by spatial heterogeneity and stochasticity. A key challenge when modelling such processes using stochastic random walk frameworks is that negative jump coefficients can arise when transport operators are discretized on heterogeneous domains. Often this is dealt with through homogenization approximations by replacing the heterogeneous medium with an $\textit{effective}$ homogeneous medium. In this work, we present a new class of homogenization approximations by considering a stochastic diffusive transport model on a one-dimensional domain containing an arbitrary number of layers with different jump rates. We derive closed form solutions for the $k$th moment of particle lifetime, carefully explaining how to deal with the internal interfaces between layers. These general tools allow us to derive simple formulae for the effective transport coefficients, leading to significant generalisations of previous homogenization approaches. Here, we find that different jump rates in the layers gives rise to a net bias, leading to a non-zero advection, for the entire homogenized system. Example calculations show that our generalized approach can lead to very different outcomes than traditional approaches, thereby having the potential to significantly affect simulation studies that use homogenization approximations.Comment: 9 pages, 2 figures, accepted version of paper published in The Journal of Chemical Physic

Dynamic decoherence control of a solid-state nuclear-quadrupole qubit

We report on the application of a dynamic decoherence control pulse sequence on a nuclear-quadrupole transition in Pr3+∶Y2SiO5. Process tomography is used to analyze the effect of the pulse sequence. The pulse sequence was found to increase the decoherence time of the transition to over 30 seconds. Although the decoherence time was significantly increased, the population terms were found to rapidly decay on the application of the pulse sequence. The increase of this decay rate is attributed to inhomogeneity in the ensemble. Methods to circumvent this limit are discussed

Impacts of Operating Parameters on Extracellular Polymeric Substances Production in a High Rate Activated Sludge System with Low Solids Retention Times

The Adsorption/Bio-oxidation (A/B) process accomplishes carbon capture via bio-flocculation in the adsorption stage (A-stage) to maximize energy recovery while simultaneously providing an optimal carbon to nitrogen (C/N) ratio for denitrification in the Bio-oxidation stage (B-Stage). The present study evaluated the influence of the solids retention time (SRT), dissolved oxygen (DO) concentration, and production of extracellular polymeric substances (EPS) on bio-flocculation and subsequent carbon capture using a pilot-scale A-stage process. A mixed liquor suspended solids (MLSS)-based control strategy was implemented to manage carbon capture by maintaining a constant MLSS concentration of 3,000 mg/L in response to diurnal variations in organic loading. Bio-flocculation, in terms of colloidal organic matter removal and concentration of effluent suspended solids, was enhanced by operating at a 0.56 day SRT compared to a 0.26 day SRT regardless of the DO concentration. Increasing the DO concentration from 0.5 to 1.0 mg/L at a longer SRT resulted in maximum bio-flocculation and carbon capture without significantly increasing the amount of COD lost to mineralization. These operating conditions coincided with a large reduction in loosely bound EPS (LB-EPS) and slight reduction in tightly bound EPS (TB-EPS) leading to the lowest LB-EPS to TB-EPS (LB/TB) ratio. Further increasing the DO concentration to 1.5 mg/L did not enhance bio-flocculation or carbon capture. Although EPS may have contributed to enhancing bio-flocculation, correlations found between EPS production and bio-flocculation were not as strong compared to operating conditions such as the SRT, DO concentration, MLSS concentration and influent wastewater characteristics. On the other hand, EPS production showed strong correlations for suspended solids removal and subsequent carbon capture in the A-stage pilot, especially when operated at a longer SRT

Baby Skyrmions in AdS

We study the baby Skyrme model in a pure AdS background without a mass term. The tail decays and scalings of massless radial solutions are demonstrated to take a similar form to those of the massive flat space model, with the AdS curvature playing a similar role to the flat space pion mass. We also numerically find minimal energy solutions for a range of higher topological charges and find that they form concentric ring-like solutions. Popcorn transitions (named in analogy with studies of toy models of holographic QCD) from an n layer to an n + 1-layer configuration are observed at topological charges 9 and 27 and further popcorn transitions for higher charges are predicted. Finally, a pointparticle approximation for the model is derived and used to successfully predict the ring structures and popcorn transitions for higher charge solitons

Baryons, salt and popcorn in holographic QCD

The Sakai-Sugimoto model is the leading model of holographic QCD. It has an effective five-dimensional description in which baryons correspond to the bulk topological solitons of a Yang-Mills-Chern-Simons theory. However, the large dimensionality of the model means studying soliton solutions either analytically or numerically is difficult. Sakai-Sugimoto solitons in the high density limit should provide an analogue of cold, dense QCD. Two competing theories for high-density solutions are the dyon salt model, in which the appropriate crystal is a salt-like arrangement of dyons, and the baryonic popcorn model in which a series of transitions occurs where the three-dimensional soliton crystal develops extra layers in the holographic direction. In this thesis we consider a range of low-dimensional analogues and approximations to the Sakai-Sugimoto model. We first investigate an O(3) sigma model stabilised by vector mesons, and a baby Skyrme model in pure AdS spacetime, before moving on to consider homogeneous ansätze in both the holographic baby Skyrme and full Sakai- Sugimoto models. In each case we look for analogues of the dyon salt and baryonic popcorn configurations, and find evidence for new features in the high-density regime of holographic QCD

Development, trials and testing of an innovative method to improve strength characteristics of hollow cable bolts

The 70 t Sumo is a resin point-anchored, pre-tensioned, post-grouted hollow cable bolt for tunnel roof support, particularly in poor ground conditions. An innovative ancillary product to the 70 t Sumo is the Booster cable, which is designed to reinforce the Sumo and enhance the systems shear and tensile performance. The Booster cable is an 11 mm 7-wire PC strand with a nominal breaking load of 15 tonnes, which is inserted into the hollow centre tube of the 70 t Sumo after grouting, while the grout is still pliable. Theoretically, the Booster can increase the tensile and shear capacity of the 70 t Sumo by up to 20%. The Booster reinforced 70 t Sumo is useful in high demand conditions where additional support strength is required without the need to install new support. This paper will present results from laboratory tests undertaken to quantify the tensile and shear characteristics of the 70 t Sumo reinforced with the Booster cable. A case study of a support trial using Booster reinforced 70 t Sumo cable bolts at a Dendrobium is also presented in this paper. The Booster cable successfully reduced 70 t Sumo cable bolt densities by 25%, from four cables per meter to three