Non-Fermi liquid theory of quantum hall effects

Within the Grassmannian U(2N)/U(N) x U(N) nonlinear sigma-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping. (C) 2005 Pleiades Publishing, Inc.

Non-Protein Amino Acids in the Design of Secondary Structure Scaffolds

The use of stereochemically constrained amino acids permits the design of short peptides as models for protein secondary structures. Amino acid residues that are restrained to a limited range of backbone torsion angles (ϕ-ψ) may be used as folding nuclei in the design of helices and β-hairpins. α-Amino-isobutyric acid (Aib) and related Cαα dialkylated residues are strong promoters of helix formation, as exemplified by a large body of experimentally determined structures of helical peptides. DPro-Xxx sequences strongly favor type II’ turn conformations, which serve to nucleate registered β-hairpin formation. Appropriately positioned DPro-Xxx segments may be used to nucleate the formation of multistranded antiparallel β-sheet structures. Mixed (α/β) secondary structures can be generated by linking rigid modules of helices and β-hairpins. The approach of using stereochemically constrained residues promotes folding by limiting the local structural space at specific residues. Several aspects of secondary structure design are outlined in this chapter, along with commonly used methods of spectroscopic characterization.

Approximate methods for step function response of undamped non-linear spring mass systems with arbitrary hardening type spring characteristic

The possibility of applying two approximate methods for determining the salient features of response of undamped non-linear spring mass systems subjected to a step input, is examined. The results obtained on the basis of these approximate methods are compared with the exact results that are available for some particular types of spring characteristics. The extension of the approximate methods for non-linear systems with general polynomial restoring force characteristics is indicated.

Effect of static deflection on natural frequency of non-linear spring mass system by direct linearization method

An exact expression for the frequency of a non-linear cubic spring mass system is obtained considering the effect of static deflection. An alternative expression for the approximate frequency is also obtained by the direct linearization procedure; it is shown that this is very accurate as compared with the exact method. This approximate frequency equation is used to explain a “dual behaviour” of the frequency amplitude curves.

The oscillation of a spheroid along its axis in a non-Newtonian fluid

The present paper investigates the nature of the fluid flow when a spheroid is suspended in an infinitely extending elastico-viscous fluid defined by the constitutive equations given by Oldroyd or Rivlin and Ericksen, and is made to perform small amplitude oscillations along its axis. The solution of the vector wave equation is expressed in terms of the solution of the corresponding scalar wave equation, without the use of Heine's function or spheroidal wave functions. Two special cases (i) a sphere and (ii) a spheroid of small ellipticity, are studied in detail.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.

Response spectrum of non-linear spring mass system subjected to transient disturbances

The transient response spectrum of a cubic spring mass system subjected to a step function input is obtained. An approximate method is adopted where non-linear restoring force characteristic is replaced by two linear segments, so that the mean square error between them is a minimum. The effect of viscous damping on the peak response is also discussed for various values of the damping constant and the non-linearity restoring force parameter.

Non-Linear vibration of an elastic string

Equations proposed in previous work on the non-linear motion of a string show a basic disagreement, which is here traced to an assumption about the longitudinal displacement u. It is shown that it is neither necessary nor justifiable to assume that u is zero; and also that the velocity of propagation of u disturbances in a string is different from that in an infinite medium, although this difference is usually negligible. After formulating the exact equations of motion for the string, a systematic procedure is described for obtaining approximations to these equations to any order, making only the assumption that the strain in the material of the string is small. The lowest order equations in this scheme are non-linear, and are used to describe the response of a string near resonance. Finally, it is shown that in the absence of damping, planar motion of a string is always unstable at sufficiently high amplitudes, the critical amplitude falling to zero at the natural frequency and its subharmonics. The effect of slight damping on this instability is also discussed.

A new approach to the study of non-linear non-autonomous systems

In this paper, a new approach to the study of non-linear, non-autonomous systems is presented. The method outlined is based on the idea of solving the governing differential equations of order n by a process of successive reduction of their order. This is achieved by the use of “differential transformation functions”. The value of the technique presented in the study of problems arising in the field of non-linear mechanics and the like, is illustrated by means of suitable examples drawn from different fields such as vibrations, rigid body dynamics, etc.

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.

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.