Graph limits of random graphs from a subset of connected kk-trees

For any set $\Omega$ of non-negative integers such that $\{0,1\}\subseteq \Omega$ and $\{0,1\}\ne \Omega$, we consider a random $\Omega$-$k$-tree ${\sf G}_{n,k}$ that is uniformly selected from all connected $k$-trees of $(n+k)$ vertices where the number of $(k+1)$-cliques that contain any fixed $k$-clique belongs to $\Omega$. We prove that ${\sf G}_{n,k}$, scaled by $(kH_{k}\sigma_{\Omega})/(2\sqrt{n})$ where $H_{k}$ is the $k$-th Harmonic number and $\sigma_{\Omega}>0$, converges to the Continuum Random Tree $\mathcal{T}_{{\sf e}}$. Furthermore, we prove the local convergence of the rooted random $\Omega$-$k$-tree ${\sf G}_{n,k}^{\circ}$ to an infinite but locally finite random $\Omega$-$k$-tree ${\sf G}_{\infty,k}$.Comment: 21 pages, 6 figure

Real-time terahertz imaging with a single-pixel detector

Terahertz (THz) radiation is poised to have an essential role in many imaging applications, from industrial inspections to medical diagnosis. However, commercialization is prevented by impractical and expensive THz instrumentation. Single-pixel cameras have emerged as alternatives to multi-pixel cameras due to reduced costs and superior durability. Here, by optimizing the modulation geometry and post-processing algorithms, we demonstrate the acquisition of a THz-video (32 × 32 pixels at 6 frames-per-second), shown in real-time, using a single-pixel fiber-coupled photoconductive THz detector. A laser diode with a digital micromirror device shining visible light onto silicon acts as the spatial THz modulator. We mathematically account for the temporal response of the system, reduce noise with a lock-in free carrier-wave modulation and realize quick, noise-robust image undersampling. Since our modifications do not impose intricate manufacturing, require long post-processing, nor sacrifice the time-resolving capabilities of THz-spectrometers, their greatest asset, this work has the potential to serve as a foundation for all future single-pixel THz imaging systems

Imaging Fines Migration Induced by Salinity Changes

This project aims at confirming positive LS-EOR (low salinity enhanced oil recovery) effects with fluorescent microscopy, an unprecedented approach. The fluorescent microscopy employed in this project used a confocal microscope and total internal reflection fluorescence (TIRF); these allowed the acquisition of 3D images using a non-destructive procedure. For the first part of the project, confocal microscopy was utilised to test the average fluorescent intensity and the scope of 8 different types of clay minerals. Comparing fluorescent features of high and low defect kaolinite, also 3 types of LDH Mg/Al and another 3 types of LDH Mg/Fe were included in this study. Moreover, SEM was applied to analyse the structure of clay minerals, and XRD was applied to determine the impurities within the clay samples. The sample which determined that clay minerals fluoresce on a consistent basis were aged with formation brine and either polar crude oil or non-polar crude oil, these aged clay samples were utilised for the second part of the project, which was aimed at observing any movement of clay by lowering the salinity. AFM and TIRF were employed for the latter section. Based upon the attained results, the following is notable: firstly, that the presence of iron in clay minerals diminishes the fluorescent intensity, also high defect clay minerals do not exhibit a steady fluorescence intensity. Secondly, testing with SEM and XRD revealed that KGa-1b might be the only clay sample that has the potential of autofluorescence, since the percentage of fluoresced pixels was more than the percentage of impure minerals that would fluoresce at the applied wavelength. Finally, AFM and TIRF confirmed LS-EOR effects even without the presence of polar components in the system, especially after fourfold dilution from the initial ionic concentration caused the clay minerals to move more vigorously; significant clay swelling at the salinity level was also witnessed. In summary, the novel approach of TIRF is deemed well suited in terms of its technique for the study of fines migration. Four-fold dilution of high salinity brine initiated clay swelling and dispersion, still salinity higher than generally accepted as the LS-EOR optimal salinity level was given. It can be interpreted that fines dispersion and migration could be initiated at a higher salinity, while the emulsion phase form and the oil molecule surface release may require a much lower ionic concentration in order to enable residual oil recovery. LS-EOR effects observed under the TIRF and AFM, arising due to the weaker electrostatic forces developed by lowering the system's salinity hence, the generally accepted importance of polar oil components for LS-EOR effects does not hold in these experiments. Positive LS- EOR effects revealed by TIRF, AFM, and FFM consequently concluded that electrical double layer expansion would be the most dominant attribution for LS-EOR