Asymptotics of a small liquid drop on a cone and plate rheometer

A cone and a plate rheometer is a laboratory apparatus used to measure the viscosity and other related parameters of a non-Newtonian liquid subject to an applied force. A small drop, of order millimetres, of the liquid is located between the horizontal plate and the shallow cone of the rheometer. Rotation of the cone ensues, the liquid begins to flow and the plate starts to rotate. Liquid parameters are inferred based on the difference in the applied rotational force and the resulting rotational force of the plate. To describe the flow of the drop, the initial drop configuration, before rotation commences, must be determined. The equilibrium drop profile is given by the solution to the well-known nonlinear Young-Laplace equation. We formulate asymptotic solutions for the drop profile based on the small Bond number. The modelling of the drop exhibits a rich asymptotic structure consisting of five distinct scalings which are resolved via the method matched asymptotics

The shape of a small liquid drop on a cone and plate rheometer

We construct asymptotic solutions for the shape of a small liquid sessile drop in a cone and plate rheometer. The approximation is based on small Bond number or, equivalently, on a characteristic length scale which is much smaller than the capillary length. The drop has a complicated asymptotic structure, consisting of five separate scalings, which is resolved using the method of matched asymptotic expansions. We find that the presence of a substrate above (and below) the drop gives rise to qualitatively new drop configurations

Particle size segregation in granular flow in silos

Segregation and layering of alumina in storage silos are investigated, with a view to predicting output quality versus time, given known variations in input quality on emplacement. A variety of experiments were conducted, existing relevant publications were reviewed, and the basis for an algorithm for predicting the effect of withdrawing from a central flowing region, in combination with variations in quality due to geometric, layering and segregation effects, is described in this report

Generalized Sagnac Effect

Experiments were conducted to study light propagation in a light waveguide loop consisting of linearly and circularly moving segments. We found that any segment of the loop contributes to the total phase difference between two counterpropagating light beams in the loop. The contribution is proportional to a product of the moving velocity v and the projection of the segment length Deltal on the moving direction, Deltaphi=4pivDeltal/clambda. It is independent of the type of motion and the refractive index of waveguides. The finding includes the Sagnac effect of rotation as a special case and suggests a new fiber optic sensor for measuring linear motion with nanoscale sensitivity.Comment: 3 pages (including 3 figures

Nanomatemàtiques: modelització matemàtica a la nanoescala

En aquest article exposem tres problemes estudiats recentment al grup de Matemàtica Industrial del Centre de Recerca Matemàtica, en els quals l'aproximació del continu resulta vàlida per a descriure fenòmens a la nanoescala: 1. Transferència de calor en nanofluids: els resultats experimentals que confirmen l'increment de la capacitat de transferir calor dels nanofluids respecte dels fluids estàndard són sovint contradictoris. Mitjançant una anàlisi de capa límit mostrarem com el model matemàtic utilitzat en nombroses ocasions per justificar l'increment en la transferència de calor dels nanofluids preveu, de fet, una disminució d'aquesta propietat. 2. Fusió de nanopartícules: les nanopartícules mostren un increment abrupte de la velocitat de transició de fase a mesura que el seu radi decreix. Presentarem un model matemàtic que descriu aquest fenomen. El model preveu temps totals de transició sòlid-líquid que concorden amb les observacions experimentals. 3. Increment del flux d'un fluid en nanotubs de carboni (CNT): mostrarem que els resultats experimentals sobre l'increment de flux en nanotubs de carboni es poden explicar mitjançant les equacions estàndard de la dinàmica de fluids amb la incorporació d'una capa d'extinció (depletion layer) a la interfície entre el fluid i el sòlid.Postprint (published version

QTL for seed protein and amino acids in the Benning × Danbaekkong soybean population

Soybean, rather than nitrogen-containing forages, is the primary source of quality protein in feed formulations for domestic swine, poultry, and dairy industries. As a sole dietary source of protein, soybean is deficient in the amino acids lysine (Lys), threonine (Thr), methionine (Met), and cysteine (Cys). Increasing these amino acids would benefit the feed industry. The objective of the present study was to identify quantitative trait loci (QTL) associated with crude protein (cp) and amino acids in the ‘Benning’ × ‘Danbaekkong’ population. The population was grown in five southern USA environments. Amino acid concentrations as a fraction of cp (Lys/cp, Thr/cp, Met/cp, Cys/cp, and Met + Cys/cp) were determined by near-infrared reflectance spectroscopy. Four QTL associated with the variation in crude protein were detected on chromosomes (Chr) 14, 15, 17, and 20, of which, a QTL on Chr 20 explained 55 % of the phenotypic variation. In the same chromosomal region, QTL for Lys/cp, Thr/cp, Met/cp, Cys/cp and Met + Cys/cp were detected. At these QTL, the Danbaekkong allele resulted in reduced levels of these amino acids and increased protein concentration. Two additional QTL for Lys/cp were detected on Chr 08 and 20, and three QTL for Thr/cp on Chr 01, 09, and 17. Three QTL were identified on Chr 06, 09 and 10 for Met/cp, and one QTL was found for Cys/cp on Chr 10. The study provides information concerning the relationship between crude protein and levels of essential amino acids and may allow for the improvement of these traits in soybean using marker-assisted selection

High-throughput SNP discovery and assay development in common bean

<p>Abstract</p> <p>Background</p> <p>Next generation sequencing has significantly increased the speed at which single nucleotide polymorphisms (SNPs) can be discovered and subsequently used as molecular markers for research. Unfortunately, for species such as common bean (<it>Phaseolus vulgaris </it>L.) which do not have a whole genome sequence available, the use of next generation sequencing for SNP discovery is much more difficult and costly. To this end we developed a method which couples sequences obtained from the Roche 454-FLX system (454) with the Illumina Genome Analyzer (GA) for high-throughput SNP discovery.</p> <p>Results</p> <p>Using a multi-tier reduced representation library we discovered a total of 3,487 SNPs of which 2,795 contained sufficient flanking genomic sequence for SNP assay development. Using Sanger sequencing to determine the validation rate of these SNPs, we found that 86% are likely to be true SNPs. Furthermore, we designed a GoldenGate assay which contained 1,050 of the 3,487 predicted SNPs. A total of 827 of the 1,050 SNPs produced a working GoldenGate assay (79%).</p> <p>Conclusions</p> <p>Through combining two next generation sequencing techniques we have developed a method that allows high-throughput SNP discovery in any diploid organism without the need of a whole genome sequence or the creation of normalized cDNA libraries. The need to only perform one 454 run and one GA sequencer run allows high-throughput SNP discovery with sufficient sequence for assay development to be performed in organisms, such as common bean, which have limited genomic resources.</p

Parametric localized modes in quadratic nonlinear photonic structures

We analyze two-color spatially localized modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi-2) nonlinear interfaces embedded into a linear layered structure --- a quasi-one-dimensional quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi-2 equations), and find, numerically and analytically, the spatially localized solutions --- discrete gap solitons. For a single nonlinear interface in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities and differences with quadratic solitons in homogeneous media.Comment: 9 pages, 8 figure