Modeling Chemotactic Waves in Saturated Porous Media using Adaptive Mesh Refinement

Bacterial transport is heavily influenced by chemical gradients and interfaces that exist in the subsurface. The main aim of this article is to describe a method of simulating the propagation of a traveling bacterial wave in a contaminated region and the resulting degradation of the contaminant. The presence of the chemotactic term and the relatively small bacterial diffusion means that the wave contains a very sharp wavefront. We, therefore, use an upwind conservative numerical scheme to obtain accurate and numerically stable solutions. The accuracy of the method is verified by comparisons with an exact one-dimensional solution of a simplified problem to give the same wavespeed. The method is then used to simulate the propagation of a realistic chemotactic wave in one dimension. We then use adaptive mesh refinement (AMR) to compute the propagation of chemotactic waves in two dimensions using the simplified model calibrated to give the same wavespeed as the full model.     

Rogue wave early warning through spectral measurements?

We study the spectra of the Peregrine soliton and higher-order rational solutions of the nonlinear Schrödinger equation (NLSE), which we use as a model of the rogue waves in optics and in the deep ocean. We show that these solutions have specific triangular spectra that are certainly easily measurable in optical systems and which may be amenable to characterisation in ocean environments. As the triangular feature of the solutions appears at an early stage of their evolution, this raises the possibility of early detection and possible localized warning of the appearance of rogue waves. We anticipate that studying the characteristics of “early warning spectra” of rogue waves may become an important future field of research.     

The Mathematical Basis of Population Genetics∗

In this paper the topic known to biologists as population genetics is presented in terms of the Cartesian product. The gene, being a set of an ordered pair of elements (alleles), provides an example of a lattice in which the axes represent the composition of the gene in respective parents, and shows as co‐ordinates the possible genetic composition of individuals of the next generation with respect to that gene. When the axes are made to represent, respectively, the set of male and female parents of a population as a whole then it is the next generation as a whole that is represented by the co‐ordinates.

Population genetics is also shown to provide an example of the binomial expansion (p+q)ⁿ in which n is 2, while on those occasions when the gene can be composed of any two of a number of elements (alleles) it expands to (p+q + r+ ... + w)² with p,q,r.....w, each representing the frequencies of an allele of the gene in the population.

It is upon these mathematical models that the study of population genetics depends and the incidence of alleles in any population is established.

     

In-source CID of guanosine: Gas phase ion-molecule reactions

In-source collision induced dissociation was applied to access second generation ions of protonated guanosine. The in-source gas-phase behavior of [BH2]+-NH3 (m/z 135, C5H3N4O+) was investigated. Adduct formation and reactions with available solvent molecules (H2O and CH3OH) were demonstrated. Several addition/elimination sequences were observed for this particular ion and solvent molecules. Dissociation pathways for the newly formed ions were developed using a QqTOF mass spectrometer, permitting the assignment of elemental compositions of all product ions produced. Reaction schemes were suggested arising from the ring-opened intermediate of the protonated base moiety [BH2]+, obtained from fragmentation of guanosine. The mass spectral data revealed that the in-source CH3OH-reaction product underwent more complex fragmentations than the comparable ion following reaction with H2O. A rearrangement and a parallel radical dissociation pathway were discerned. Apart from the mass spectrometric evidence, the fragmentation schemes are supported by density functional theory calculations, in which the reaction of the ring-opened protonated guanine intermediate with CH3OH and a number of subsequent fragmentations were elaborated. Additionally, an in-source transition from the ring-opened intermediate of protonated guanine to the ring-opened intermediate of protonated xanthine was suggested. For comparison, a low-energy collision induced dissociation study of xanthosine was performed. Its dissociation pathways agreed with our assumption.     

Mix-and-heat benzylation of alcohols using a bench-stable pyridinium salt

2-Benzyloxy-1-methylpyridinium triflate (1) is a stable, neutral organic salt that converts alcohols into benzyl ethers upon warming. The synthesis and reactivity of 1 are described herein. Benzylation of a wide range of alcohols occurs in good to excellent yield.     

Strain-promoted azide-alkyne cycloadditions of benzocyclononynes

Preliminary studies related to the design and development of new cycloalkyne reagents for metal-free click coupling are reported. Cyclononynes are more stable than cyclooctynes, and the robust benzocyclononyne platform offers spontaneous reactivity toward azides at rates competitive with other azidophiles that have been employed for metal-free click coupling. Benzocyclononynes (e.g., 1) provide valuable insight into the design of new cycloalkynes for strain-promoted azide-alkyne cycloaddition (SPAAC) couplings for applications in which side reactions and decomposition of the reagent must be kept to a minimum.     

Balls in Rk do not cut all subsets of k + 2 points

For any set E cf k + 2 points in $\text{k}$^k, k = 1, 2,…, not all subsets of E are of the form B ∩ E where E is a ball.     

Studies of potassium ferrite K1+xFe11O17. I. Electronic conductivity and defect structure

The electronic conductivity of the nonstoichiometric potassium ferrite phase (with the β-alumina structure) has been measured as a function of temperature and potassium ion concentration. The latter was varied by coulometric titration using the cell: K_11q/K-β-alumina/K_1+xFe₁₁O₁₇. At 523°K the conductivity increased nearly linearly as x was increased from 0.09 to 0.65 while the activation energy for conduction decreased from 0.1 to 0.07 eV. The cell emf was completely reversible. The results are consistent with the view that the excess potassium ions are charge compensated by reduction of Fe³⁺ to Fe²⁺, and a comparison with results in the literature for some ironcontaining spinels suggests that a similar small polaron electron hopping mechanism operates.