A local lattice Boltzmann method for multiple immiscible fluids and dense suspensions of drops

The lattice Boltzmann method (LBM) for computational fluid dynamics benefits from a simple, explicit, completely local computational algorithm making it highly efficient. We extend LBM to recover hydrodynamics of multi-component immiscible fluids, whilst retaining a completely local, explicit and simple algorithm. Hence, no computationally expensive lattice gradients, interaction potentials or curvatures, that use information from neighbouring lattice sites, need be calculated, which makes the method highly scalable and suitable for high performance parallel computing. The method is analytic and is shown to recover correct continuum hydrodynamic equations of motion and interfacial boundary conditions. This LBM may be further extended to situations containing a high number (O(100)) of individually immiscible drops. We make comparisons of the emergent non-Newtonian behaviour with a power-law fluid model. We anticipate our method will have a range applications in engineering, industrial and biological sciences

Synthetic, sterochemical, and electronic studies of organophosphorous ligands and their transition metal complexes

The synthesis of a variety of 2-coordinate aminophosphorus cationic compounds has been previously achieved by several experimental techniques. In this work, the preparation of analogous oxygen substituted species was investigated and the (\u2731)P NMR data presented. The reaction of the potent metal nucleophile, Fe((eta)(\u275)-Cp)(CO)(,2)(\u27-), with a wide variety of compounds of the type Cl-P(ER)(,2) (E = O, S, NR) produced a number of interesting complexes including the cis and trans-Fe((eta)(\u275)-Cp)(CO)(P(ER)(,2))(,2) complexes. (\u271)H, (\u2713)C, and (\u2731)P NMR spectral data for these compounds are presented. Linear correlations between (\u2731)P NMR and infrared (nu)(,CO) parameters were observed for the first time and are rationalized in terms of the expected bonding within the complex;An X-ray crystallographic study of the cis and trans isomers of Fe((eta)(\u275)-Cp)(CO)((mu)-P(OCH(,2)C(Me)(,2)CH(,2)O))(,2)(\u27 )was completed and confirmed the predicted structures. Several interesting structural features are presented and discussed in terms of bonding considerations;From the reaction of the Fe((eta)(\u275)-Cp)(CO)(,2)(\u27-) anion with ClP(OC(Me)(,2)C(Me)(,2)O),(\u27 )the unique (eta)(\u274)-cyclopentadiene complex, Fe((eta)(\u274)-C(,5)H(,6))(CO)(L)(OC)(,3)Fe, was obtained in addition to the cis and trans isomers mentioned above. An X-ray crystallographic investigation of this complex was undertaken and is reported here. The structure confirmed the predicted composition, based upon spectral data, and showed a number of very interesting features including very short P-Fe and very long Fe-Fe and P-P bond distances and large Fe-P-Fe and flap angles. These are rationalized in terms of isovalent hybridization and molecular orbital theories;Synthetic procedures for the preparation, isolation, and purification of chiral trivalent phosphites with the primary chiral site at phosphorus were developed. Three methods for the optical resolution of these complexes were investigated. The first successful separation into enantiomers of a trivalent phosphite was achieved using diastereomeric platinum(II) complexes. These complexes were separated chromatographically followed by the destruction of the complex with cyanide. The free, resolved enantiomers were obtained in purified form by chromatography

Introduction to Advances in Teaching and Learning Technologies Minitrack

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PPP Loans - Small Business Vaccine and Corporate Sting

As a result of the COVID-19 Pandemic, the U.S. Government passed the CARES Act. One key aspect of the Act was the Paycheck Protection Program (PPP), whose primary purpose was to provide relief to struggling small businesses and retain employment levels through the use of forgivable loans. According to the U.S. Small Business Administration, in 2020, over 383,000 PPP loans totaling just under $42.5 Million went to the Accommodation and Food Services industry. As intended, most loans went to small businesses; however, a few large public corporations faced severe public backlash after applying to and accepting PPP loans. A legislative loophole allowed individual restaurants to qualify, even if their parent corporation did not. We analyzed quarterly financial statements from March 2019 through December 2020 of 23 public companies in the restaurant industry, including eight that accepted PPP payments. We noted whether any subsidiary or franchisee applied for, received, or returned a PPP loan. We present an analysis of key metrics from the quarterly financial statements

Topological generation of simple algebraic groups

Let $G$ be a simple algebraic group over an algebraically closed field and let $X$ be an irreducible subvariety of $G^r$ with $r \geqslant 2$. In this paper, we consider the general problem of determining if there exists a tuple $(x_1, \ldots, x_r) \in X$ such that $\langle x_1, \ldots, x_r \rangle$ is Zariski dense in $G$. We are primarily interested in the case where $X = C_1 \times \cdots \times C_r$ and each $C_i$ is a conjugacy class of $G$ comprising elements of prime order modulo the center of $G$. In this setting, our main theorem gives a complete solution to the problem when $G$ is a symplectic or orthogonal group. By combining our results with earlier work on linear and exceptional groups, this gives a complete solution for all simple algebraic groups. We also present several applications. For example, we use our main theorem to show that many faithful representations of symplectic and orthogonal groups are generically free. We also establish new asymptotic results on the probabilistic generation of finite simple groups by pairs of prime order elements, completing a line of research initiated by Liebeck and Shalev over 25 years ago.Comment: 69 pages; to appear in J. Eur. Math. Soc. (JEMS

Hydrologic controls on seasonal and inter-annual variability of Congo River particulate organic matter source and reservoir age

We present dissolved organic carbon (DOC) concentrations, particulate organic matter (POM) composition (δ13C, δ15N, ∆14C, N/C), and particulate glycerol dialkyl glycerol tetraether (GDGT) distributions from a 34-month time-series near the mouth of the Congo River. An end-member mixing model using δ13C and N/C indicates that exported POM is consistently dominated by C3 rainforest soil sources, with increasing contribution from C3 vegetation and decreasing contribution from phytoplankton at high discharge. Large C4 inputs are never observed despite covering ≈ 13% of the catchment. Low and variable ∆14C values during 2011 [annual mean = (− 148 ± 82) ‰], when discharge from left-bank tributaries located in the southern hemisphere reached record lows, likely reflect a bias toward pre-aged POM derived from the Cuvette Congolaise swamp forest. In contrast, ∆14C values were stable near − 50‰ between January and June 2013, when left-bank discharge was highest. We suggest that headwater POM is replaced and/or diluted by C3 vegetation and pre-aged soils during transit through the Cuvette Congolaise, whereas left-bank tributaries export significantly less pre-aged material. GDGT distributions provide further evidence for seasonal and inter-annual variability in soil provenance. The cyclization of branched tetraethers and the GDGT-0 to crenarchaeol ratio are positively correlated with discharge (r ≥ 0.70; p-value ≤ 4.3 × 10− 5) due to the incorporation of swamp-forest soils when discharge from right-bank tributaries located in the northern hemisphere is high. Both metrics reach record lows during 2013, supporting our interpretation of increased left-bank contribution at this time. We conclude that hydrologic variability is a major control of POM provenance in the Congo River Basin and that tropical wetlands can be a significant POM source despite their small geographic coverage

Expression profiling of snoRNAs in normal hematopoiesis and AML

Key Points A subset of snoRNAs is expressed in a developmental- and lineage-specific manner during human hematopoiesis. Neither host gene expression nor alternative splicing accounted for the observed differential expression of snoRNAs in a subset of AML.</jats:p

Abnormal rib count in scoliosis surgery: impact on the reporting of spinal fusion levels

Purpose Variation in rib numbering has been noted in adolescent idiopathic scoliosis (AIS), but its effect on the reporting of fusion levels has not been studied. We hypothesized that vertebral numbering variations can lead to differing documentation of fusion levels. Methods: We examined the radiographs of 161 surgical AIS patients and 179 control patients without scoliosis. For AIS patients, the operative report of fusion levels was compared to conventional vertebral labeling from the first thoracic level and proceeding caudal. We defined normal counts as 12 thoracic (rib-bearing) and five lumbar (non-rib-bearing) vertebrae. We compared our counts with data from 181 anatomic specimens. Results: Among AIS patients, 22 (14 %) had an abnormal number of ribs and 29 (18 %) had either abnormal rib or lumbar count. In 12/29 (41 %) patients, the operative report differed from conventional labeling by one level, versus 3/132 (2 %) patients with normal numbering (p < 0.001). However, there were no cases seen of wrong fusion levels based on curve pattern. Among controls, 11 % had abnormal rib count (p = 0.41) compared to the rate in AIS. Anatomic specimen data did not differ in abnormal rib count (p = 1.0) or thoracolumbar pattern (p = 0.59). Conclusions: The rate of numerical variations in the thoracolumbar vertebrae of AIS patients is equivalent to that in the general population. When variations in rib count are present, differences in numbering levels can occur. In the treatment of scoliosis, no wrong fusion levels were noted. However, for both scoliosis patients and the general population, we suggest adherence to conventional labeling to enhance clarity