On a linear steady-state system of equations in microcontinuum fluid mechanics

Galerkin representations and integral representations are obtained for the linearized system of coupled differential equations governing steady incompressible flow of a micropolar fluid. The special case of 2-dimensional Stokes flows is then examined and further representation formulae as well as asymptotic expressions, are generated for both the microrotation and velocity vectors. With the aid of these formulae, the Stokes Paradox for micropolar fluids is established.

A linear root water uptake model

A model of root water extraction is proposed, in which a linear variation of extraction rate with depth is assumed. Five crops are chosen for simulation studies of the model, and soil moisture depletion under optimal conditions from different layers for each crop is calculated. Similar calculations are also made using the constant extraction rate model. Rooting depth is assumed to vary linearly with potential evapotranspiration for each crop during the vegetative phase. The calculated depletion patterns are compared with measured mean depletion patterns for each crop. It is shown that the constant extraction rate model results in large errors in the prediction of soil moisture depletion, while the proposed linear extraction rate model gives satisfactory results. Hypothetical depletion patterns predicted by the model in combination with a moisture tension-dependent sink term developed elsewhere are indicated.

Unsteady three-dimensional boundary layer flow over a flat plate with attached cylinder

The unsteady laminar incompressible three-dimensional boundary layer flow and heat transfer on a flat plate with an attached cylinder have been studied when the free stream velocity components and wall temperature vary inversely as linear and quadratic functions of time, respectively. The governing semisimilar partial differential equations with three independent variables have been solved numerically using a quasilinear finite-difference scheme. The results indicate that the skin friction increases with parameter λ which characterizes the unsteadiness in the free stream velocity and the streamwise distance Image , but the heat transfer decreases. However, the skin friction and heat transfer are found to change little along Image . The effect of the Prandtl number on the heat transfer is found to be more pronounced when λ is small, whereas the effect of the dissipation parameter is more pronounced when λ is comparatively large.

CSSI-PRO: a method for secondary structure type editing, assignment and estimation in proteins using linear combination of backbone chemical shifts

Estimation of secondary structure in polypeptides is important for studying their structure, folding and dynamics. In NMR spectroscopy, such information is generally obtained after sequence specific resonance assignments are completed. We present here a new methodology for assignment of secondary structure type to spin systems in proteins directly from NMR spectra, without prior knowledge of resonance assignments. The methodology, named Combination of Shifts for Secondary Structure Identification in Proteins (CSSI-PRO), involves detection of specific linear combination of backbone H-1(alpha) and C-13' chemical shifts in a two-dimensional (2D) NMR experiment based on G-matrix Fourier transform (GFT) NMR spectroscopy. Such linear combinations of shifts facilitate editing of residues belonging to alpha-helical/beta-strand regions into distinct spectral regions nearly independent of the amino acid type, thereby allowing the estimation of overall secondary structure content of the protein. Comparison of the predicted secondary structure content with those estimated based on their respective 3D structures and/or the method of Chemical Shift Index for 237 proteins gives a correlation of more than 90% and an overall rmsd of 7.0%, which is comparable to other biophysical techniques used for structural characterization of proteins. Taken together, this methodology has a wide range of applications in NMR spectroscopy such as rapid protein structure determination, monitoring conformational changes in protein-folding/ligand-binding studies and automated resonance assignment.

A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements. the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.

Non-linear flapping vibrations of rotating blades

The non-linear equations of motion of a rotating blade undergoing extensional and flapwise bending vibration are derived, including non-linearities up to O (ε3). The strain-displacement relationship derived is compared with expressions derived by earlier investigators and the errors and the approximations made in some of those are brought out. The equations of motion are solved under the inextensionality condition to obtain the influence of the amplitude on the fundamental flapwise natural frequency of the rotating blade. It is found that large finite amplitudes have a softening effect on the flapwise frequency and that this influence becomes stronger at higher speeds of rotation.

Characterization of protoporphyrin as the physiological regulator of delta-aminolevulinate dehydratase in Neurospora crassa

In Neurospora crassa, the activity of δ-aminolevulinate dehydratase, the second and rate-limiting enzyme of the heme-biosynthetic pathway, is low in normal cells compared to the activity detected in plants, animals and bacteria. The activity is almost undetectable when Neurospora crassa is grown under iron-deficient conditions. The enzyme activity increases strikingly on addition of iron to iron-deficient cultures. This increase can be blocked by the addition of protoporphyrin, the penultimate product of the heme-biosynthetic pathway, to the cultures. The question whether iron directly acts at the genetic level or acts merely by removing protoporphyrin, converting the latter into heme prosthetic groups of hemoproteins, has been investigated by studying the effect of inhibition of heme synthesis on the induction of δ-aminolevulinate dehydratase. It has been found that treatments with levulinic acid or cyanide which inhibit the formation of the porphyrin moiety, induce δ-aminolevulinate dehydratase, whereas treatments which inhibit at a step after protoporphyrin formation (iron-deficiency and cobalt treatment) repress the enzyme. The endogenous levels of protoporphyrin are strictly controlled: a decrease below the optimum level causing induction and an increase above the optimum level leading to repression of δ-aminolevulinate dehydratase. Levulinic acid and cyanide can induce the enzyme in iron-deficient cultures in the absence of added iron, indicating that the metal iron acts only by converting protoporphyrin to heme fixed in hemoproteins in Neurospora crassa. Therefore it is suggested that protoporphyrin is the physiological regulator of δ-aminolevulinate dehydratase in Neurospora crassa.

A linear ramp control circuit using two LM 556 dual timers

A simple linear ramp control circuit, suitable for use with force-commutated thyrister circuits is discussed here. The circuit is based on only two IM 558 dual timer iCs, operating from a single 15 V supply. The reset terminals facilitate inhibition of the output of any stage. The use of this circuit in a thyristor chopper operating at 400 Hz 13 described.

A Branch and Bound Algorithm for a Transportation Type Problem with Piecewise Linear Convex Objective Function

A branch and bound type algorithm is presented in this paper to the problem of finding a transportation schedule which minimises the total transportation cost, where the transportation cost over each route is assumed to be a piecewice linear continuous convex function with increasing slopes. The algorithm is an extension of the work done by Balachandran and Perry, in which the transportation cost over each route is assumed to beapiecewise linear discontinuous function with decreasing slopes. A numerical example is solved illustrating the algorithm.

A Gaussian quadrature analysis of linear sweep voltammetry

The application of Gaussian Quadrature (GQ) procedures to the evaluation of i—E curves in linear sweep voltammetry is advocated. It is shown that a high degree of precision is achieved with these methods and the values obtained through GQ are in good agreement with (and even better than) the values reported in literature by Nicholson-Shain, for example. Another welcome feature with GQ is its ability to be interpreted as an elegant, efficient analytic approximation scheme too. A comparison of the values obtained by this approach and by a recent scheme based on series approximation proposed by Oldham is made and excellent agreement is shown to exist.

Self-tuning control of a class of multivariable non-linear systems

Self-tuning is applied to the minimum variance control of non-linear multivariable systems which can be characterized by a ' multivariable Hammerstein model '. It is also shown that such systems are not amenable to self-tuning control if control costing is to be included in the performance criterion.

Observers for linear systems with unknown inputs

This paper presents a constructive solution to the problem of designing a reduced-order Luenberger observer for linear systems subject to arbitrary unknown inputs.

A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

Approximate analysis of coupled non-linear non-conservative systems subjected to step-function excitation

The paper deals with the approximate analysis of non-linear non-conservative systems oftwo degrees of freedom subjected to step-function excitation. The method of averaging of Krylov and Bogoliubov is used to arrive at the approximate equations for amplitude and phase. An example of a spring-mass-damper system is presented to illustrate the method and a comparison with numerical results brings out the validity of the approach.