Solution of a hydrodynamic lubrication problem with Maple

A set of partial differential equations, arising in a calculation of hydrodynamic lubricationeffects, was solved using a perturbation technique. All of the algebraic manipulations required to find the solution were performed using Maple. The main challenge was the efficient handling and simplification of very long expression, which was met by the power of Maple's built-in procedures and by algebraic transformations suggested by the solution to the lowest-order approximation. As a result, the solution was obtained to a higher order, with greater reliability, than would otherwise have been possible

The impact of the grazing animal on phosphorus, nitrogen, potassium and suspended solids loss from grazed pastures, Part A

Teagasc wishes to acknowledge the support of the Environmental Research Technological Development and Innovation (ERTDI) Programme under the Productive Sector Operational Programme which was financed by the Irish Government under the National Development Plan 2000-2006.End of project reportIn Ireland 90% of the 4.2 million ha of farmland is grassland. Phosphorus deficiency limited grassland production in Ireland and this was corrected by chemical fertiliser use in the 1960s and 1970s. The increased inputs of fertilisers led to increased intensification of grassland with a doubling of grass yield and of grazing animal numbers, from about 3 million to over 6 million livestock units. There is little information on relative contribution of increased chemical fertiliser use compared to increased grazing animal numbers on phosphorus loss to water. The main objective of this study was to obtain information on nutrient loss, particularly phosphorus, in overland flow from cut and grazed grassland plots, with a range of soil test phosphorus levels over three years and implications.Environmental Protection Agenc

The effect of grain size on magnetic properties in Sm\u3csub\u3e2\u3c/sub\u3eFe\u3csub\u3e17\u3c/sub\u3eN\u3csub\u3ex\u3c/sub\u3e

The microstructures of melt spun Sm11Fe89 and (Sm11Fe89)94Ti3C3 have been investigated under different solidification conditions. The magnetic properties of the nitrided materials have been related to the observed microstructures. Melt spinning of the Sm11Fe89 alloys resulted in grain sizes at or above the single domain limit. The addition of Ti and C resulted in an order of magnitude refinement in the microstructural scale. The magnetic properties of the samples with grain sizes below the single domain limit decreased with decreasing grain size due to increased intergranular exchange coupling

Lattice Boltzmann for Binary Fluids with Suspended Colloids

A new description of the binary fluid problem via the lattice Boltzmann method is presented which highlights the use of the moments in constructing two equilibrium distribution functions. This offers a number of benefits, including better isotropy, and a more natural route to the inclusion of multiple relaxation times for the binary fluid problem. In addition, the implementation of solid colloidal particles suspended in the binary mixture is addressed, which extends the solid-fluid boundary conditions for mass and momentum to include a single conserved compositional order parameter. A number of simple benchmark problems involving a single particle at or near a fluid-fluid interface are undertaken and show good agreement with available theoretical or numerical results.Comment: 10 pages, 4 figures, ICMMES 200

Detection of noncyling cows by heatmount decectors and ultrasound before treatment with progesterone

Our objective was to determine accuracy of identifying anovulatory lactating dairy cows before the application of a timed AI protocol [with or without progesterone supplementation via a controlled internal drug release (CIDR) insert and 2 different timings of AI] by using heatmount detectors and a single ovarian ultrasound examination. At 6 Midwest locations, 1,072 cows were enrolled in a Presynch protocol (2 injections of prostaglandin F2α(PGF2α) 14 days apart) with the second injection administered 14 days before initiating the Ovsynch protocol (injection of gonadotropin releasing hormone (GnRH) 7 days before and 48 hours after PGF2αinjection, with timed AI at 0 or 24 hours after the second GnRH injection). Heatmount detectors were applied to cows at the time of the first Presynch injection, assessed 14 days later at the second Presynch injection and again at initiation of the Ovsynch protocol, and ovaries were examined for presence of a visible corpus luteum (CL) by ultrasound before initiation of treatment. Treatments were assigned to cows based on presence or absence of a visible CL: 1) anovulatory (no CL + CIDR insert for 7 d); 2) anovulatory (no CL + no CIDR); and 3) cycling (CL present). Further, every other cow in the 3 treatments was assigned to be inseminated concurrent with the second GnRH injection of Ovsynch (0 hour) or 24 hours later. Pregnancy was diagnosed at 33 and 61 days after the second GnRH injection. Heatmount detectors and a single ultrasound examination both underestimated proportions of cows classified as anovulatory or having no prior luteal activity compared with those classifications determined by concentrations of progesterone in blood serum. Overall accuracy of heatmount detectors and ultrasound was 71 and 84%, respectively. Application of progesterone to cows without a CL at the time of the first injection of GnRH reduced incidence of ovulation but improved pregnancy rates at day 33 or 61 compared with nontreated cows without a CL at the onset of the Ovsynch protocol. Pregnancy rates and pregnancy survival did not differ for cows having a CL before treatment compared with those not having a CL but treated with progesterone. Pregnancy rates were 1.5-fold greater for cows ovulating in response to the first GnRH injection. Timing of AI at 0 or 24 hours after the second GnRH injection did not alter pregnancy rates, but cows having prior luteal activity before treatment had improved pregnancy rates compared with anovulatory cows. We conclude that identifying anovulatory cows by ultrasound was more accurate than by heatmount detectors. Subsequent treatment of potential anovulatory cows with progesterone failed to improve fertility but had benefit for cows with prior estrous cycles at the onset of the timed AI (TAI) protocol, regardless of luteal status before the final luteolytic injection of PGF2α.; Dairy Day, 2007, Kansas State University, Manhattan, KS, 2007; Dairy Research, 2007 is known as Dairy Day, 200

Localization for Yang-Mills Theory on the Fuzzy Sphere

We present a new model for Yang-Mills theory on the fuzzy sphere in which the configuration space of gauge fields is given by a coadjoint orbit. In the classical limit it reduces to ordinary Yang-Mills theory on the sphere. We find all classical solutions of the gauge theory and use nonabelian localization techniques to write the partition function entirely as a sum over local contributions from critical points of the action, which are evaluated explicitly. The partition function of ordinary Yang-Mills theory on the sphere is recovered in the classical limit as a sum over instantons. We also apply abelian localization techniques and the geometry of symmetric spaces to derive an explicit combinatorial expression for the partition function, and compare the two approaches. These extend the standard techniques for solving gauge theory on the sphere to the fuzzy case in a rigorous framework.Comment: 55 pages. V2: references added; V3: minor corrections, reference added; Final version to be published in Communications in Mathematical Physic

Defect configurations and dynamical behavior in a Gay-Berne nematic emulsion

To model a nematic emulsion consisting of a surfactant-coated water droplet dispersed in a nematic host, we performed a molecular dynamics simulation of a droplet immersed in a system of 2048 Gay-Berne ellipsoids in a nematic phase. Strong radial anchoring at the surface of the droplet induced a Saturn ring defect configuration, consistent with theoretical predictions for very small droplets. A surface ring configuration was observed for lower radial anchoring strengths, and a pair of point defects was found near the poles of the droplet for tangential anchoring. We also simulated the falling ball experiment and measured the drag force anisotropy, in the presence of strong radial anchoring as well as zero anchoring strength.Comment: 17 pages, 15 figure

Automated Generation of User Guidance by Combining Computation and Deduction

Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an emerging generation of educational mathematics assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction, is the most reliable technology used to check user input. However ATP is inherently weak in automatically generating solutions for arbitrary problems in applied mathematics. This weakness is crucial for EMAs: when ATP checks user input as incorrect and the learner gets stuck then the system should be able to suggest possible next steps. The key idea of Lucas Interpretation is to compute the steps of a calculation following a program written in a novel CTP-based programming language, i.e. computation provides the next steps. User guidance is generated by combining deduction and computation: the latter is performed by a specific language interpreter, which works like a debugger and hands over control to the learner at breakpoints, i.e. tactics generating the steps of calculation. The interpreter also builds up logical contexts providing ATP with the data required for checking user input, thus combining computation and deduction. The paper describes the concepts underlying Lucas Interpretation so that open questions can adequately be addressed, and prerequisites for further work are provided.Comment: In Proceedings THedu'11, arXiv:1202.453

Anomalous scaling and Lee-Yang zeroes in Self-Organized Criticality

We show that the generating functions of avalanche observables in SOC models exhibits a Lee-Yang phenomenon. This establishes a new link between the classical theory of critical phenomena and SOC. A scaling theory of the Lee-Yang zeroes is proposed including finite sampling effects.Comment: 33 pages, 19 figures, submitte