Application of partition method to vibration problems of plates

The “partition method” or “sub-domain method” consists of expressing the solution of a governing differential equation, partial or ordinary, in terms of functions which satisfy the boundary conditions and setting to zero the error in the differential equation integrated over each of the sub-domains into which the given domain is partitioned. In this paper, the use of this method in eigenvalue problems with particular reference to vibration of plates is investigated. The deflection of the plate is expressed in terms of polynomials satisfying the boundary conditions completely. Setting the integrated error in each of the subdomains to zero results in a set of simultaneous, linear, homogeneous, algebraic equations in the undetermined coefficients of the deflection series. The algebraic eigenvalue problem is then solved for eigenvalues and eigenvectors. Convergence is examined in a few typical cases and is found to be satisfactory. The results obtained are compared with existing results based on other methods and are found to be in very good agreement.

Variation in water extraction with maize plant density and its impact on model application

The use of maize simulation models to determine the optimum plant population for rainfed environments allows the evaluation of plant populations over multiple years and locations at a lower cost than traditional field experimentation. However the APSIM maize model that has been used to conduct some of these 'virtual' experiments assumes that the maximum rate of soil water extraction by the crop root system is constant across plant populations. This untested assumption may cause grain yield to be overestimated in lower plant populations. A field experiment was conducted to determine whether maximum rates of water extraction vary with plant population, and the maximum rate of soil water extraction was estimated for three plant populations (2.4, 3.5 and 5.5 plants m(-2)) under water limited conditions. Maximum soil water extraction rates in the field experiment decreased linearly with plant population, and no difference was detected between plant populations for the crop lower limit of soil water extraction. Re-analysis of previous maize simulation experiments demonstrated that the use of inappropriately high extraction-rate parameters at low plant populations inflated predictions of grain yield, and could cause erroneous recommendations to be made for plant population. The results demonstrate the importance of validating crop simulation models across the range of intended treatments. (C) 2013 Elsevier E.V. All rights reserved.

Evaluating and validating abundance monitoring methods in the absence of populations of known size: review and application to a passive tracking index

Rarely is it possible to obtain absolute numbers in free-ranging populations and although various direct and indirect methods are used to estimate abundance, few are validated against populations of known size. In this paper, we apply grounding, calibration and verification methods, used to validate mathematical models, to methods of estimating relative abundance. To illustrate how this might be done, we consider and evaluate the widely applied passive tracking index (PTI) methodology. Using published data, we examine the rationality of PTI methodology, how conceptually animal activity and abundance are related and how alternative methods are subject to similar biases or produce similar abundance estimates and trends. We then attune the method against populations representing a range of densities likely to be encountered in the field. Finally, we compare PTI trends against a prediction that adjacent populations of the same species will have similar abundance values and trends in activity. We show that while PTI abundance estimates are subject to environmental and behavioural stochasticity peculiar to each species, the PTI method and associated variance estimate showed high probability of detection, high precision of abundance values and, generally, low variability between surveys, and suggest that the PTI method applied using this procedure and for these species provides a sensitive and credible index of abundance. This same or similar validation approach can and should be applied to alternative relative abundance methods in order to demonstrate their credibility and justify their use.

Immunologic studies on nucleic acids and their components II. Reversible inhibition of anti-nucleoside antibodies in aqueous pyridine and its application in antibody

The effect of aqueous pyridine on a hapten—antihapten system was investigated by the quantitative precipitin reaction and by the membrane filtration method. It was found that dilute solutions of pyridine inhibited the reaction between isopentenyladenosine and its antiserum. Other solvents examined were less effective. The effect of pyridine was reversible at concentrations where complete inhibition occurred, thus indicating its use for the dissociation of antigen—antibody complexes. The inhibitory effect of pyridine was exploited in a single-step purification method for anti—isopentenyladenosine and antideoxy-adenylate antibodies. In addition, generally applicable methods for linking nucleosides and nucleotides to aminoethyl-Sepharose are described.

A note on the application of a radiation condition for a source in a rotating stratified fluid

The motion due to an oscillatory point source in a rotating stratified fluid has been studied by Sarma & Naidu (1972) by using threefold Fourier transforms. The solution obtained by them in the hyperbolic case is wrong since they did not make use of any radiation condition, which is always necessary to get the correct solution. Whenever the motion is created by a source, the condition of radiation is that the sources must remain sources, not sinks of energy and no energy may be radiated from infinity into the prescribed singularities of the field. The purpose of the present note is to explain how Lighthill's (1960) radiation condition can be applied in the hyperbolic case to pick the correct solution. Further, the solution thus obtained is reiterated by an alternative procedure using Sommerfeld's (1964) radiation condition.

Unusual effects of anisotropic bonding in Cu(II) and Ni(II) oxides with K2NiF4 structure

Geometric constraints present in A2BO4 compounds with the tetragonal-T structure of K2NiF4 impose a strong pressure on the B---OII---B bonds and a stretching of the A---OI---A bonds in the basal planes if the tolerance factor is t congruent with RAO/√2 RBO < 1, where RAO and RBO are the sums of the A---O and B---O ionic radii. The tetragonal-T phase of La2NiO4 becomes monoclinic for Pr2NiO4, orthorhombic for La2CuO4, and tetragonal-T′ for Pr2CuO4. The atomic displacements in these distorted phases are discussed and rationalized in terms of the chemistry of the various compounds. The strong pressure on the B---OII---B bonds produces itinerant σ*x2−y2 bands and a relative stabilization of localized dz2 orbitals. Magnetic susceptibility and transport data reveal an intersection of the Fermi energy with the d2z2 levels for half the copper ions in La2CuO4; this intersection is responsible for an intrinsic localized moment associated with a configuration fluctuation; below 200 K the localized moment smoothly vanishes with decreasing temperature as the d2z2 level becomes filled. In La2NiO4, the localized moments for half-filled dz2 orbitals induce strong correlations among the σ*x2−y2 electrons above Td reverse similar, equals 200 K; at lower temperatures the σ*x2−y2 electrons appear to contribute nothing to the magnetic susceptibility, which obeys a Curie-Weiss law giving a μeff corresponding to S = 1/2, but shows no magnetic order to lowest temperatures. These surprising results are verified by comparison with the mixed systems La2Ni1−xCuxO4 and La2−2xSr2xNi1−xTixO4. The onset of a charge-density wave below 200 K is proposed for both La2CuO4 and La2NiO4, but the atomic displacements would be short-range cooperative in mixed systems. The semiconductor-metallic transitions observed in several systems are found in many cases to obey the relation Ea reverse similar, equals kTmin, where varrho = varrho0exp(−Ea/kT) and Tmin is the temperature of minimum resistivity varrho. This relation is interpreted in terms of a diffusive charge-carrier mobility with Ea reverse similar, equals ΔHm reverse similar, equals kT at T = Tmin.

Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.

Immunologic studies on nucleic acids and their components II. Reversible inhibition of anti-nucleoside antibodies in aqueous pyridine and its application in antibody purification

The effect of aqueous pyridine on a hapten—antihapten system was investigated by the quantitative precipitin reaction and by the membrane filtration method. It was found that dilute solutions of pyridine inhibited the reaction between isopentenyladenosine and its antiserum. Other solvents examined were less effective. The effect of pyridine was reversible at concentrations where complete inhibition occurred, thus indicating its use for the dissociation of antigen—antibody complexes. The inhibitory effect of pyridine was exploited in a single-step purification method for anti—isopentenyladenosine and antideoxy-adenylate antibodies. In addition, generally applicable methods for linking nucleosides and nucleotides to aminoethyl-Sepharose are described.

Methods to improve gene signal: Application to cDNA microarrays

Microarrays are high throughput biological assays that allow the screening of thousands of genes for their expression. The main idea behind microarrays is to compute for each gene a unique signal that is directly proportional to the quantity of mRNA that was hybridized on the chip. A large number of steps and errors associated with each step make the generated expression signal noisy. As a result, microarray data need to be carefully pre-processed before their analysis can be assumed to lead to reliable and biologically relevant conclusions. This thesis focuses on developing methods for improving gene signal and further utilizing this improved signal for higher level analysis. To achieve this, first, approaches for designing microarray experiments using various optimality criteria, considering both biological and technical replicates, are described. A carefully designed experiment leads to signal with low noise, as the effect of unwanted variations is minimized and the precision of the estimates of the parameters of interest are maximized. Second, a system for improving the gene signal by using three scans at varying scanner sensitivities is developed. A novel Bayesian latent intensity model is then applied on these three sets of expression values, corresponding to the three scans, to estimate the suitably calibrated true signal of genes. Third, a novel image segmentation approach that segregates the fluorescent signal from the undesired noise is developed using an additional dye, SYBR green RNA II. This technique helped in identifying signal only with respect to the hybridized DNA, and signal corresponding to dust, scratch, spilling of dye, and other noises, are avoided. Fourth, an integrated statistical model is developed, where signal correction, systematic array effects, dye effects, and differential expression, are modelled jointly as opposed to a sequential application of several methods of analysis. The methods described in here have been tested only for cDNA microarrays, but can also, with some modifications, be applied to other high-throughput technologies. Keywords: High-throughput technology, microarray, cDNA, multiple scans, Bayesian hierarchical models, image analysis, experimental design, MCMC, WinBUGS.