Scale-dependent Macroscopic Balance Equations Governing Transport Through Porous Media: Theory and Observations

A theory is developed providing a rational framework for spatial scale- dependent fluid’s flow and heat transfer, and mass of a component migrating with it through porous media. Introducing the assumption of a non-Brownian type motion and referring to asymptotic expansion in powers of a small defined parameter, we develop a novel approach associated with macroscopic balance equations obtained by averaging over a Representative Elementary Volume (REV). We prove that these equations can be decomposed into a primary part that refers to the REV length scale and a secondary part valid at a length scale smaller than that of the corresponding REV length. Further to our previous development, we obtain two general forms of the primary and secondary macroscopic balance equations. One is based on the assumption that the advective flux of the extensive quantity is dominant over that of the dispersive flux, whereas the other disregards this assumption. Moreover we also introduce the primary and secondary macroscopic forms for the fluid heat- transfer equation. Considering a Newtonian fluid, the resulting primary Navier–Stokes equation can vary from a nonlinear wave equation to a drag-dominant equation at the fluid–solid interface (Darcy’s law). The secondary momentum balance equation describes a wave equation governing the concurrent propagation of the intensive momentum and the dispersive momentum flux, deviating from their corresponding average terms. The primary macroscopic fluid heat-transfer equation accounts for advective and dispersive heat fluxes and the secondary macroscopic heat-transfer equation involves the simultaneous advection of heat deviating from its corresponding intensive average quantity. The primary macroscopic solute mass balance equation accounts for advection and hydrodynamic dispersion. The secondary macroscopic component mass balance equation is in the form of pure advection governing migration of the deviation from the average component concentration. At this stage, we focus on establishing the viability of the developed theory. We do this by arguing that field observations of motion at small spatial scales are coherent with the hyperbolic characteristics of the secondary balance equations. Field observations under natural gradient flow conditions show excessive high concentration (average of 50 mg/L) of colloids under land irrigated by sewage effluents. We argue that this displacement of condensed colloidal parcels manifests the theoretical findings for the smaller spatial scale. Further evidence show the accumulation of particles moving behind the front of an emitted shockwave. We consider this as an experimental proof reinforcing the argument that colloidal migration is subject to the action of a shockwave in the fluid and pure advection transport, governed by the respective suggested hyperbolic macroscopic balance equations of fluid momentum and component mass at the smaller spatial scale.     

Applications of bulk queues to group testing models with incomplete identification

A population of items is said to be “group-testable”, (i) if the items can be classified as “good” and “bad”, and (ii) if it is possible to carry out a simultaneous test on a batch of items with two possible outcomes: “Success” (indicating that all items in the batch are good) or “failure” (indicating a contaminated batch). In this paper, we assume that the items to be tested arrive at the group-testing centre according to a Poisson process and are served (i.e., group-tested) in batches by one server. The service time distribution is general but it depends on the batch size being tested. These assumptions give rise to the bulk queueing model M/G^(m,M)/1, where m and M(>m) are the decision variables where each batch size can be between m and M. We develop the generating function for the steady-state probabilities of the embedded Markov chain. We then consider a more realistic finite state version of the problem where the testing centre has a finite capacity and present an expected profit objective function. We compute the optimal values of the decision variables (m, M) that maximize the expected profit. For a special case of the problem, we determine the optimal decision explicitly in terms of the Lambert function.     

First total synthesis of murisolin

The first and concise total synthesis of murisolin (1) was accomplished using asymmetric alkynylation and Sonogashira coupling as the key steps. The threo/trans/threo-type THF ring moiety was constructed with excellent stereoselectivity by asymmetric alkynylation of 1,6-heptadiyne to alpha-tetrahydrofuranic aldehyde, which was also prepared via the asymmetric alkynylation.     

A pure-dephasing model for overtone lineshapes

A model is developed for calculatinq the pure-dephasing (T₂) contribution to overtone lineshapes in isolated molecules. The linewidth is attributed to time-dependent fluctuations in the frequency of the overtone transition, resulting from the vibrational motions in the molecule, and no transfer of energy (intramolecular vibrational distribution) occurs in this picture. Numerical calculations for 2,3,5,6-paradeuterobenzene are presented.     

Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree-Fock and density functional theory

An efficient and accurate analytic gradient method is presented for Hartree-Fock and density functional calculations using multiresolution analysis in multiwavelet bases. The derivative is efficiently computed as an inner product between compressed forms of the density and the differentiated nuclear potential through the Hellmann-Feynman theorem. A smoothed nuclear potential is directly differentiated, and the smoothing parameter required for a given accuracy is empirically determined from calculations on six homonuclear diatomic molecules. The derivatives of N2 molecule are shown using multiresolution calculation for various accuracies with comparison to correlation consistent Gaussian-type basis sets. The optimized geometries of several molecules are presented using Hartree-Fock and density functional theory. A highly precise Hartree-Fock optimization for the H2O molecule produced six digits for the geometric parameters.     

Total synthesis of murisolins and evaluation of tumor-growth inhibitory activity

Convergent total syntheses of murisolin (1), natural 16,19-cis-murisolin 2, and unnatural 16,19-cis-murisolin 3 were accomplished by asymmetric alkynylation of alpha-tetrahydrofuranic aldehyde with a diyne and Sonogashira coupling with a gamma-lactone segment as the key steps. Stereoisomers of alpha-tetrahydrofuranic aldehyde were synthesized with high optical purity and the asymmetric alkynylation of these with 1,6-heptadiyne proceeded in good yield and with high diastereoselectivity. The cell-growth inhibition profile and COMPARE analysis of the synthetic compounds 1-3 were also investigated.     

Regioselective Synthesis of 4-Aryl-1,3-dihydroxy-2-naphthoates through 1,2-Aryl-Migrative Ring Rearrangement Reaction and their Photoluminescence Properties

4-Aryl-1,3-dihydroxy-2-naphthoates having the less accessible 1,2,3,4-tetrasubstituted naphthalene scaffold and that show photoluminescence emission from solid state as well as in solutions, were selectively synthesized from brominated lactol silyl ethers through the 1,2-aryl-migrative ring rearrangement reaction.