Study of a class of non-linear systems reducible to equivalent linear systems

In this paper, a method of arriving at transformations which convert a class of non-linear systems into equivalent linear systems, has been presented along with suitable examples, which illustrate its application.

Comparative study of some constitutive equations characterising non-Newtonian fluids

This paper compares, in a general way, the predictions of the constitutive equations given by Rivlin and Ericksen, Oldroyd, and Walters. Whether we consider the rotational problems in cylindrical co-ordinates or in spherical polar co-ordinates, the effect of the non-Newtonicity on the secondary flows is collected in a single parameterα which can be explicitly expressed in terms of the non-Newtonian parameters that occur in each of the above-mentioned constitutive equations. Thus, for a given value ofα, all the three fluids will have identical secondary flows. It is only through the study of appropriate normal stresses that a Rivlin-Ericksen fluid can be distinguished from the other two fluids which are indistinguishable as long as this non-Newtonian parameter has the same value.

Solvolytic disproportionation of non-stoichiometric oxides of praseodymium and terbiumstar, open

The solvolytic disproportionation of non-stoichiometric PrOχ and TbOχ in acid solutions to produce higher oxides has been investigated. Some new non-stoichiometric phases have been reported. A number of interesting features of the non-stoichiometric rare earth oxides have been discussed and the need for a satisfactory structural model has been pointed out.

Evolution of the Neckeraceae (Bryophyta): resolving the backbone phylogeny

Earlier phylogenetic studies, including species belonging to the Neckeraceae, have indicated that this pleurocarpous moss family shares a strongly supported sister group relationship with the Lembophyllaceae, but the family delimitation of the former needs adjustment. To test the monophyly of the Neckeraceae, as well as to redefine the family circumscription and to pinpoint its phylogenetic position in a larger context, a phylogenetic study based on molecular data was carried out. Sequence data were compiled, combining data from all three genomes: nuclear ITS1 and 2, plastid trnS-rps4-trnT-trnL-trnF and rpl16, and mitochondrial nad5 intron. The Neckeraceae have sometimes been divided into the two families, Neckeraceae and Thamnobryaceae, a division rejected here. Both parsimony and Bayesian analyses of molecular data revealed that the family concept of the Neckeraceae needs several further adjustments, such as the exclusion of some individual species and smaller genera as well as the inclusion of the Leptodontaceae. Within the family three well-supported clades (A, B and C) can be distinguished. Members of clade A are mainly non-Asiatic and nontropical. Most species have a weak costa and immersed capsules with reduced peristomes (mainly Neckera spp.) and the teeth at the leaf margins are usually unicellular. Clade B members are also mainly non-Asiatic. They are typically fairly robust, distinctly stipilate, having a single, at least relatively strong costa, long setae (capsules exserted), and the peristomes are well developed or only somewhat reduced. Members of clade C are essentially Asiatic and tropical. The species of this clade usually have a strong costa and a long seta, the seta often being mammillose in its upper part. The peristome types in this clade are mixed, since both reduced and unreduced types are found. Several neckeraceous genera that were recognised on a morphological basis are polyphyletic (e.g. Neckera, Homalia, Thamnobryum, Porotrichum). Ancestral state reconstructions revealed that currently used diagnostic traits, such as the leaf asymmetry and costa strength are highly homoplastic. Similarly, the reconstructions revealed that the 'reduced' sporophyte features have evolved independently in each of the three clades.

Functional role of the Mso1p-Sec1p complex in membrane fusion regulation

Sec1/Munc18 (SM) protein family members are evolutionary conserved proteins. They perform an essential, albeit poorly understood function in SNARE complex formation in membrane fusion. In addition to the SNARE complex components, only a few SM protein binding proteins are known. Typically, their binding modes to SM proteins and their contribution to the membrane fusion regulation is poorly characterised. We identified Mso1p as a novel Sec1p interacting partner. It was shown that Mso1p and Sec1p interact at sites of polarised secretion and that this localisation is dependent on the Rab GTPase Sec4p and its GEF Sec2p. Using targeted mutagenesis and N- and C-terminal deletants, it was discovered that the interaction between an N-terminal peptide of Mso1p and the putative Syntaxin N-peptide binding area in Sec1p domain 1 is important for membrane fusion regulation. The yeast Syntaxin homologues Sso1p and Sso2p lack the N-terminal peptide. Our results show that in addition to binding to the putative N-peptide binding area in Sec1p, Mso1p can interact with Sso1p and Sso2p. This result suggests that Mso1p can mimic the N-peptide binding to facilitate membrane fusion. In addition to Mso1p, a novel role in membrane fusion regulation was revealed for the Sec1p C-terminal tail, which is missing in its mammalian homologues. Deletion of the Sec1p-tail results in temperature sensitive growth and reduced sporulation. Using in vivo and in vitro experiments, it was shown that the Sec1p-tail mediates SNARE complex binding and assembly. These results propose a regulatory role for the Sec1p-tail in SNARE complex formation. Furthermore, two novel interaction partners for Mso1p, the Rab GTPase Sec4p and plasma membrane phospholipids, were identified. The Sec4p link was identified using Bimolecular Fluorescence Complementation assays with Mso1p and the non-SNARE binding Sec1p(1-657). The assay revealed that Mso1p can target Sec1p(1-657) to sites of secretion. This effect is mediated via the Mso1p C-terminus, which previously has been genetically linked to Sec4p. These results and in vitro binding experiments suggest that Mso1p acts in cooperation with the GTP-bound form of Sec4p on vesicle-like structures prior to membrane fusion. Mso1p shares homology with the PIP2 binding domain of the mammalian Munc18 binding Mint proteins. It was shown both in vivo and in vitro that Mso1p is a phospholipid inserting protein and that this insertion is mediated by the conserved Mso1p amino terminus. In vivo, the Mso1p phospholipid binding is needed for sporulation and Mso1p-Sec1p localisation at the sites of secretion at the plasma membrane. The results reveal a novel layer of membrane fusion regulation in exocytosis and propose a coordinating role for Mso1p in connection with membrane lipids, Sec1p, Sec4p and SNARE complexes in this process.

Slow rotation of a sphere in a non-Newtonian fluid with or without suction or injection

The flow generated by the rotation of a sphere in an infinitely extending fluid has recently been studied by Goldshtik. The corresponding problem for non-Newtonian Reiner-Rivlin fluids has been studied by Datta. Bhatnagar and Rajeswari have studied the secondary flow between two concentric spheres rotating about an axis in the non-Newtonian fluids. This last investigation was further generalised by Rajeswari to include the effects of small radial suction or injection. In Part A of the present investigation, we have studied the secondary flow generated by the slow rotation of a single sphere in non-Newtonian fluid obeying the Rivlin-Ericksen constitutive equation. In Part B, the effects of small suction or injection have been studied which is applied in an arbitrary direction at the surface of the sphere. In the absence of suction or injection, the secondary flow for small values of the visco-elastic parameter is similar to that of Newtonian fluids with inclusion of inertia terms in the Oseen approximation. If this parameter exceeds Kc = 18R/219, whereR is the Reynolds number, the breaking of the flow field takes place into two domains, in one of which the stream lines form closed loops. For still higher values of this parameter, the complete reversal of the sense of the flow takes place. When suction or injection is included, the breaking of the flow persists under certain condition investigated in this paper. When this condition is broken, the breaking of the flow is obliterated.

Flow of an electrically conducting non-newtonian fluid between two rotating coaxial cones in the presence of external magnetic field due to an axial current

Bhatnagar and Rathna (Quar. Journ. Mech. Appl. Maths., 1963,16, 329) investigated the flows of Newtonian, Reiner-Rivlin and Rivlin-Ericksen fluids between two rotating coaxial cones. In case of the last two types of fluids, they predicted the breaking of secondary flow field in any meridian plane. We find that such breaking is avoided by the application of a sufficiently strong azimuthal magnetic field arising from a line current along the axis of the cones.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Cerimetry in non-aqueous media - Oxidation of oxalic acid through the intermediate formation of ceric oxalate

It was found that ceric oxalate is an intermediate product in the oxidation of oxalic acid by ammonium hexanitrato cerate in solvents such as acetonitrile, and a mixture of acetonitrile and glacial acetic acid. Conditions for the formation of ceric oxalate and its decomposition into carbon dioxide and cerous oxalate have been studied. An analytical method for the estimation of oxalic acid in non-aqueous media has been evolved based on this reaction.

Searching the inclusive ℓγE̸T+b-quark signature for radiative top quark decay and non-standard-model processes

In a search for new phenomena in a signature suppressed in the standard model of elementary particles (SM), we compare the inclusive production of events containing a lepton, a photon, significant transverse momentum imbalance (MET), and a jet identified as containing a b-quark, to SM predictions. The search uses data produced in proton-antiproton collisions at 1.96 TeV corresponding to 1.9 fb-1 of integrated luminosity taken with the CDF detector at the Fermilab Tevatron. We find 28 lepton+photon+MET+b events versus an expectation of 31.0+4.1/-3.5 events. If we further require events to contain at least three jets and large total transverse energy, simulations predict that the largest SM source is top-quark pair production with an additional radiated photon, ttbar+photon. In the data we observe 16 ttbar+photon candidate events versus an expectation from SM sources of 11.2+2.3/-2.1. Assuming the difference between the observed number and the predicted non-top-quark total is due to SM top quark production, we estimate the ttg cross section to be 0.15 +- 0.08 pb.