The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems

Use of some new planes such as the R-x, R2-x (where R represents in the n-dimensional phase space, the radius vector from the origin to any point on the trajectory described by the system) is suggested for analysis of nonlinear systems of any kind. The stability conditions in these planes are given. For easy understanding of the method, the transformation from the phase plane to the R-x, R2-x planes is brought out for second-order systems. In general, while these planes serve as useful as the phase plane, they have proved to be simpler in determining quickly the general behavior of certain classes of second-order nonlinear systems. A chart and a simple formula are suggested to evaluate time easily from the R-x and R2-x trajectories, respectively. A means of solving higher-order nonlinear systems is also illustrated. Finally, a comparative study of the trajectories near singular points on the phase plane and on the new planes is made.

Stabilization of the collagen structure by hydroxyproline residues

The molecular structure of collagen is now accepted to be based on a triple-stranded coiled-coil, in which the three strands are held together predominantly by hydrogen bonds. Recent experimental evidence has shown that the presence of hydroxyproline residues in the third position of the repeating tripeptide unit lends additional stability to the collagen structure. In this paper, we report a model structure, which is supported by these observations. In a model structure proposed earlier, there are two hydrogen bonds per tripeptide unit, one of which is a direct interchain hydrogen bond, while the second hydrogen bond can be formedvia a water molecule. It has now been shown that the same water molecule can also form a hydrogen bond with the oxygen of theγ-hydroxyl group of hydroxyproline in the third position in the sequence (Gly-R2-R3). This hydroxyl group can also take part in an inter-triple-helix hydrogen bond. Our studies thus show the role played by hydroxyproline residues in the structure and stability of collagen.

Stereochemical restrictions on the occurrence of amino acid residues in the collagen structure

The primary structure of collagen is characterized by the repeating tripeptide sequence (Gly-R2-R3)n. The results of theoretical studies, carried out using contact criteria to compute the stereochemically allowed orientations for various side chains at locations 2 and 3, are reported here. It is found that side chains with only γ-atoms, as in valine, serine and threonine, or with only one δ-methyl group, as in isoleucine, can occur equally well at locations 2 and 3, as is actually the case in collagen. Side chains with two Cδ-atoms, as in leucine and phenyl-alanine, can also be accommodated at both positions. However, if they occur as R3 their freedom of orientation is severely restricted in the presence of a proline residue as R2 in a neighbouring chain. If water molecules bound to the chains of the triple helix are assumed to be present, then location 3 is virtually impossible for leucine and phenylalanine residues. Location 2 is, however, unaffected, and their presence as R2 can help to shield the water molecules from disturbance by the solvent medium. This may be the reason for the preferential occurrence of Leu and Phe residues in location 2 in the collagen triplets, although the polypeptides (Gly-Pro-Leu)n and (Gly-Pro-Phe)n form collagen-like structures.

Cytotoxicity of half sandwich ruthenium(II) complexes with strong hydrogen bond acceptor ligands and their mechanism of action

Neutral and cationic organometallic ruthenium(II) piano stool complexes of the type [(eta(6)-cymene)R-uCl(X)(Y)] (complexes R1-R8) has been synthesized and characterized. In cationic complexes, X, Y is either a eta(2) phosphorus ligand such as 1,1-bis(diphenylphosphino)methane (DPPM) and 1,2-bis(diphenylphosphino)ethane (DPPE) or partially oxidized ligands such as 1,2-bis(diphenylphosphino)methane monooxide (DPPMO) and 1,2-bis(diphenylphosphino)ethane monooxide (DPPEO) which are strong hydrogen bond acceptors. In neutral complexes. X is chloride and Y is a monodentate phosphorous donor. Complexes with DPPM and DPPMO ligands ([(eta(6)-cymene)Ru(eta(2)-DPPM)Cl]PF6 (R2), [(eta(6)-cymene)Ru(eta(2)-DPPMO)Cl]PF6 (R3), [(eta(6)-cymene)Ru(eta(1)-DPPM)Cl-2] (R5) and [(eta(6)-cymene)Ru(eta(1)-DPPMO)Cl-2] (R6) show good cytotoxicity. Growth inhibition study of several human cancer cell lines by these complexes has been carried out. Mechanistic studies for R5 and R6 show that inhibition of cancer cell growth involves both cell cycle arrest and apoptosis induction. Using an apoptosis PCR array, we identified the sets of antiapoptotic genes that were down regulated and pro-apoptotic genes that were up regulated. These complexes were also found to be potent metastasis inhibitors as they prevented cell invasion through matrigel. The complexes were shown to bind DNA in a non intercalative fashion and cause unwinding of plasmid DNA in cell-free medium by competitive ethidium bromide binding, viscosity measurements, thermal denaturation and gel mobility shift assays.

Mapping of Average Shear Wave Velocity for Bangalore Region: A Case Study

Mapping the shear wave velocity profile is an important part in seismic hazard and microzonation studies. The shear wave velocity of soil in the city of Bangalore was mapped using the Multichannel Analysis of Surface Wave (MASW) technique. An empirical relationship was found between the Standard Penetration Test (SPT) corrected N value ((N1)60cs) and measured shear wave velocity (Vs). The survey points were selected in such a way that the results represent the entire Bangalore region, covering an area of 220 km2. Fifty-eight 1-D and 20 2-D MASW surveys were performed and their velocity profiles determined. The average shear wave velocity of Bangalore soils was evaluated for depths of 5 m, 10 m, 15 m, 20 m, 25 m and 30 m. The sub-soil classification was made for seismic local site effect evaluation based on average shear wave velocity of 30-m depth (Vs30) of sites using the National Earthquake Hazards Reduction Program (NEHRP) and International Building Code (IBC) classification. Mapping clearly indicates that the depth of soil obtained from MASW closely matches with the soil layers identified in SPT bore holes. Estimation of local site effects for an earthquake requires knowledge of the dynamic properties of soil, which is usually expressed in terms of shear wave velocity. Hence, to make use of abundant SPT data available on many geotechnical projects in Bangalore, an attempt was made to develop a relationship between Vs (m/s) and (N1)60cs. The measured shear wave velocity at 38 locations close to SPT boreholes was used to generate the correlation between the corrected N values and shear wave velocity. A power fit model correlation was developed with a regression coefficient (R2) of 0.84. This relationship between shear wave velocity and corrected SPT N values correlates well with the Japan Road Association equations.

The effect of viscosity and surface tension on the Taylor instability of the surface of a cavitation bubble*

This paper is devoted to a consideration of the following problem: A spherical mass of fluid of density varrho1, viscosity μ1 and external radius R is surrounded by a fluid of density varrho2 and viscosity μ2.The fluids are immiscible and incompressible. The interface is accelerated radially by g1: to study the effect of viscosity and surface tension on the stability of the interface. By analyzing the problem in spherical harmonics the mathematical problem is reduced to one of solution of the characteristic determinant equation. The particular case of a cavity bubble, where the viscosity μ1 of the fluid inside the bubble is negligible in comparison with the viscosity μ2 of the fluid outside the bubble, is considered in some detail. It is shown that viscosity has a stabilizing role on the interface; and when g1 > T(n − 1) (n + 2)/R2(varrho2 − varrho1) the stabilizing role of both viscosity and surface tension is more pronounced than would result when either of them is taken individually.

The 31p nmr Spectra of Isomeric Diaminohexa-hlorocyclotetraphosphazatetraenes; Examples of a2b2 and aa'bb' spin Systems

The 31P nmr spectra of 2,4- and 2,6-diamino-derivatives of octachlorocyclotetraphosphazatetraene, N4P4Cl6(NR1R2)2 (R1 = H, R2 = But; R1 = H, R2 = CH2Ph; R1 = Me, R2 = Ph), have been measured. The 2,4- and 2,6-isomers were analysed as AA'BB' and A2B2 spin systems respectively. In the 2,4-isomers the spin-spin couplings 2J(PNP) and 4J(PNPNP) were of opposite sign.

Polypeptide models of collagen. II. Solution properties of (Pro-Gly-Phe)n

The conformation of (Pro-Gly-Phe)n in trifluoroethanol was investigated using CD, nmr and ir techniques. After making appropriate correction for the contribution of the phenylalanine chromophore to the observed CD spectra of the polytripeptide at several temperatures, it is found that (Pro-Gly-Phe)n can exist in a partially triple-helical conformation in this solvent a t low temperatures. The nmr and ir data support this conclusion. In conjunction with recent theoretical sutdies, our data offer an explanation for the preferential occurrence of the Phe residue in position 2 of the tripeptide sequence Gly-R2-R3, in collagen.

Electromagnetic wave propagation at the interface between two polar semiconductors

The interface between two polar semiconductors can support three types of phonon-plasmon-polariton modes propagating in three well-defined frequency windows ??1?[min(?1,?3),?R1], ??2?[max(?2,?4),?R2], and ??3?[min(?2,?4),?R3]. The limiting frequencies ?1,2,3,4 are defined by ?1(?)=0, ?2(?)=0, and ?R1,2,3 by ?1(?)+?2(?)=0, where ?i(?) are dielectric functions of the two media with i=1,2. The dispersion, decay distances, and polarization of the three modes are discussed. The variation of the limiting frequencies with the interface plasma parameter ???p22/?p12 reveals an interesting feature in the dispersion characteristics of these modes. For the interfaces for which the bulk coupled phonon-plasmon frequencies of medium 1 are greater than the LO frequency or are less than the TO frequency of medium 2, there exist two values of ?=?1 and ?2(

MNDO study of coupled strained hydrocarbons: Additivity of exocyclic C---C bond contraction induced by different ring systems

MNDO geometry optimizations were carried out on a series of symmetrically and unsymmetrically coupled strained ring hydrocarbons, R1-R1 and R1–R2 (R1=methyl, cyclopropyl, 1-bicyclo[1.1.0]butyl, 1-bicyclo[1.1.1]pentyl, prismyl, cubyl, 6-tricyclo [3.1.1.03,6]heptyl, and tetrahedryl groups; R2=methyl and cyclopropyl). The remarkable contraction of the C---C bond connecting the strained rings found experimentally in a few cases was reproduced correctly by the calculations. A linear correlation was found between the bond length shortening and the bond angle widening at the corresponding carbon atoms for all the structures considered. The reduction in C---C bond lengths due to various ring systems is additive. The additivity indicates that inter-ring interactions which effect the central bond length are absent and confirms the common electronic origin of bond contraction in these systems, viz. enhanced s-character in the exocyclic bonds of strained rings.

Synthesis, spectral characterisation and single-crystal structure of a bicyclic tetraphosphapentazane tetraoxide, N5P4ET5O4(OC6H3Me2-2,6)2

Reaction of the bicyclic phosphazane N5P4Et5Cl2 with 2,6-dimethylphenol and subsequent oxidation of the product by aqueous hydrogen peroxide yields N5P4Et5O4(OC6H3Me2-2,6)2 in 85% yield. Its structure has been established by NMR spectroscopy and single-crystal X-ray diffraction. The compound crystallises in the monoclinic space group C2/c with a= 21.245(5), b= 10.879(2), c= 16.450(6)Å, ?= 123.94(2)°, Z= 4, R= 0.066. The structural features are compared with those of bicyclic ?5-phosphazenes of type N5P4R3(NR1R2)5(NHR3)(R1,R3= Me or Et, R2= H or Me). The observed conformation of the N3P3 rings in the present compound is mainly dictated by the maximisation of the stabilising influence of �negative hyperconjugative interactions� between the nitrogen lone pairs and the adjacent P�X ?* orbitals.

Effect of Speed and Pressure on Dry Sliding Interactions of Alumina against Steel

Sliding of alumina (87%) pins against a hardened steel disk over a range of pressures (3.3-30.0 MPa) and speeds (0.1-12.0 ms(-1)) has been studied. Four different regions (R1, R2, R3, and R4) of friction as a function of speed have been identified. R1 and RS exhibit single-valued friction while in R2 and R4 the friction exhibits dual behavior. The speed range over which these regions prevail is sensitive to the pressure. R1 and R2 are low-speed and low-temperature regions, and in both, metal transfer and formation and compaction of gamma-Fe2O3 occur. R3 and R4 are associated with high speeds and high interface temperatures. Formation of FeO, FeAl2O4, and FeAlO3 has been observed. The implications of the tribochemical interactions on friction and wear characteristics are discussed.

Volume Change behaviour in Calcitic Soil influenced with Sulphuric Acid using Artificial Neural Networks

This paper elucidates the methodology of applying artificial neural network model (ANNM) to predict the percent swell of calcitic soil in sulphuric acid solutions, a complex phenomenon involving many parameters. Swell data required for modelling is experimentally obtained using conventional oedometer tests under nominal surcharge. The phases in ANN include optimal design of architecture, operation and training of architecture. The designed optimal neural model (3-5-1) is a fully connected three layer feed forward network with symmetric sigmoid activation function and trained by the back propagation algorithm to minimize a quadratic error criterion.The used model requires parameters such as duration of interaction, calcite mineral content and acid concentration for prediction of swell. The observed strong correlation coefficient (R2 = 0.9979) between the values determined by the experiment and predicted using the developed model demonstrates that the network can provide answers to complex problems in geotechnical engineering.

Electrical Breakdown of Gases Between Coaxial Cylindrical Electrodes in Crossed Electric and Magnetic Fields

Sparking potentials have been measured in nitrogen and dry air between coaxial cylindrical electrodes for values of n = R2/R1 = approximately 1 to 30 (R1 = inner electrode radius, R2 = outer electrode radius) in the presence of crossed uniform magnetic fields. The magnetic flux density was varied from 0 to 3000 Gauss. It has been shown that the minimum sparking potentials in the presence of the crossed magnetic field can be evaluated on the basis of the equivalent pressure concept when the secondary ionization coefficient does not vary appreciably with B/p (B = magnetic flux density, p = gas pressure). The values of secondary ionization coefficients �¿B in nitrogen in crossed fields calculated from measured values of sparking potentials and Townsend ionization coefficients taken from the literature, have been reported. The calculated values of collision frequencies in nitrogen from minimum sparking potentials in crossed fields are found to increase with increasing B/p at constant E/pe (pe = equivalent pressure). Studies on the similarity relationship in crossed fields has shown that the similarity theorem is obeyed in dry air for both polarities of the central electrode in crossed fields.

Tar characterisation in new generation agro-residue gasifiers - Cyclone and downdraft open top twin air entry systems

This paper deals with the characterisation of tar from two configurations of bioresidue thermochemical conversion reactors designed for producer gas based power generation systems. The pulverised fuel reactor is a cyclone system (R1) and the solid bioresidue reactor (denoted R2) is an open top twin air entry system both at 75-90 kg/h capacity (to generate electricity similar to 100 kVA). The reactor, R2, has undergone rigorous test in a major Indo-Swiss programme for the tar quantity at various conditions. The former is a recent technology development. Tars collected from these systems by a standard tar collection apparatus at the laboratory at Indian Institute of Science have been analysed at the Royal Institute of Technology (KTH), Sweden. The results of these analyses show that these thermochemical conversion reactors behave differently from the earlier reactors reported in literature in so far as tar generation is concerned. The extent of tar in hot gas is about 700-800 ppm for R1 and 70-100 ppm for R2. The amounts of the major compounds - naphthalene and phenol-are much lower that what is generally understood to happen in the gasifiers in Europe. It is suggested that the longer residence times at high temperatures allowed for in these reactors is responsible for this behavior. It is concluded the new generation reactor concepts extensively tried out at lower power levels hold promise for high power atmospheric gasification systems for woody as well as pulverisable bioresidues.