ESR studies of phase transitions in double propionates

Detailed ESR investigations of Mn2+ substituting for Ca2+ in Ca2Sr(C2H5COO)6 (DSP), Ca2Pb(C2H5COO)6 (DLP) and Ca2Ba(C2H5COO)6 (DBP), in single crystals and powders, over the temperature range from 200°C to -180°C have been carried out to study the successive phase transitions in these compounds. (DSP: [Tetragonal] ← 8.5°C → [tetragonal, ferroelectric] [tetragonal] ← -169°C → [monoclinic, ferroelectric]; DLP : [tetragonal] ← 60°C → [tetragonal, ferroelectric] ← -71.5°C → [monoclinic, ferroelectric]; [Cubic] ← -6°C → [orthorhombic] ← -75°C → [?]). Spectra have been analysed in terms of axial spin Hamiltonians and the temperature dependences of the parameters studied. In DSP and DLP across the I ↔ II transition, new physically and chemically inequivalent sites appear indicating the disappearance of the diad axes on which the propionate groups are located, bringing out the connection between the motional states of the propionate groups and the occurence of ferroelectricity. The II ↔ III transition also causes chemically inequivalent sites to develop, indicating that the transitions may not be isomorphous as believed previously. In DBP, the -6°C transition leads to (i) a doubling of both physically and chemically inequivalent sites (ii) a small (150 G at -6°C to 170 G at -8°C), but abrupt change in the magnitude of the zero-field splitting tensor D, and (iii) displacements of the orientations of the D tensors. Results are interpreted in terms of alternate rotations of the oxygen octahedra, showing participation of the carboxyl oxygens in the transition. No drastic changes in the parameters occur across the -75°C transition consistent with its second order nature. Similarities and dissimilarities of the ESR spectra of the three compounds in relation to the phase transitions, are discussed.

Isoperimetric Problem and Meta-fibonacci Sequences

Let G = (V,E) be a simple, finite, undirected graph. For S ⊆ V, let $\delta(S,G) = \{ (u,v) \in E : u \in S \mbox { and } v \in V-S \}$ and $\phi(S,G) = \{ v \in V -S: \exists u \in S$ , such that (u,v) ∈ E} be the edge and vertex boundary of S, respectively. Given an integer i, 1 ≤ i ≤ ∣ V ∣, the edge and vertex isoperimetric value at i is defined as b e (i,G) =  min S ⊆ V; |S| = i |δ(S,G)| and b v (i,G) =  min S ⊆ V; |S| = i |φ(S,G)|, respectively. The edge (vertex) isoperimetric problem is to determine the value of b e (i, G) (b v (i, G)) for each i, 1 ≤ i ≤ |V|. If we have the further restriction that the set S should induce a connected subgraph of G, then the corresponding variation of the isoperimetric problem is known as the connected isoperimetric problem. The connected edge (vertex) isoperimetric values are defined in a corresponding way. It turns out that the connected edge isoperimetric and the connected vertex isoperimetric values are equal at each i, 1 ≤ i ≤ |V|, if G is a tree. Therefore we use the notation b c (i, T) to denote the connected edge (vertex) isoperimetric value of T at i. Hofstadter had introduced the interesting concept of meta-fibonacci sequences in his famous book “Gödel, Escher, Bach. An Eternal Golden Braid”. The sequence he introduced is known as the Hofstadter sequences and most of the problems he raised regarding this sequence is still open. Since then mathematicians studied many other closely related meta-fibonacci sequences such as Tanny sequences, Conway sequences, Conolly sequences etc. Let T 2 be an infinite complete binary tree. In this paper we related the connected isoperimetric problem on T 2 with the Tanny sequences which is defined by the recurrence relation a(i) = a(i − 1 − a(i − 1)) + a(i − 2 − a(i − 2)), a(0) = a(1) = a(2) = 1. In particular, we show that b c (i, T 2) = i + 2 − 2a(i), for each i ≥ 1. We also propose efficient polynomial time algorithms to find vertex isoperimetric values at i of bounded pathwidth and bounded treewidth graphs.

Seismic Microzonation: Principles,Practices and Experiments

This paper presents an overview of the seismic microzonation and the grade/level based study along with methods used for estimating hazard. The principles of seismic microzonation along with some current practices are discussed. Summary of seismic microzonation experiments carried out in India is presented. A detailed work of seismic microzonation of Bangalore has been presented as a case study. In this case study, a seismotectonic map for microzonation area has been developed covering 350 km radius around Bangalore, India using seismicity and seismotectonic parameters of the region. For seismic microzonation Bangalore Mahanagar Palike (BMP) area of 220 km2 has been selected as the study area. Seismic hazard analysis has been carried out using deterministic as well as probabilistic approaches. Synthetic ground motion at 653 locations, recurrence relation and peak ground acceleration maps at rock level have been generated. A detailed site characterization has been carried out using borehole with standard penetration test (SPT) ―N‖ values and geophysical data. The base map and 3-dimensional sub surface borehole model has been generated for study area using geographical information system (GIS). Multichannel analysis of surface wave (MASW)method has been used to generate one-dimensional shear wave velocity profile at 58 locations and two- dimensional profile at 20 locations. These shear wave velocities are used to estimate equivalent shear wave velocity in the study area at every 5m intervals up to a depth of 30m. Because of wider variation in the rock depth, equivalent shear for the soil overburden thickness alone has been estimated and mapped using ArcGIS 9.2. Based on equivalent shear wave velocity of soil overburden thickness, the study area is classified as ―site class D‖. Site response study has been carried out using geotechnical properties and synthetic ground motions with program SHAKE2000.The soil in the study area is classified as soil with moderate amplification potential. Site response results obtained using standard penetration test (SPT) ―N‖ values and shear wave velocity are compared, it is found that the results based on shear wave velocity is lower than the results based on SPT ―N‖ values. Further, predominant frequency of soil column has been estimated based on ambient noise survey measurements using instruments of L4-3D short period sensors equipped with Reftek 24 bit digital acquisition systems. Predominant frequency obtained from site response study is compared with ambient noise survey. In general, predominant frequencies in the study area vary from 3Hz to 12Hz. Due to flat terrain in the study area, the induced effect of land slide possibility is considered to be remote. However, induced effect of liquefaction hazard has been estimated and mapped. Finally, by integrating the above hazard parameters two hazard index maps have been developed using Analytic Hierarchy Process (AHP) on GIS platform. One map is based on deterministic hazard analysis and other map is based on probabilistic hazard analysis. Finally, a general guideline is proposed by bringing out the advantages and disadvantages of different approaches.

Seismic Microzonation of Bangalore - Preliminary Maps

This paper presents an overview of the seismic microzonation and the grade/level based study along with methods used for estimating hazard. The principles of seismic microzonation along with some current practices are discussed. Summary of seismic microzonation experiments carried out in India is presented. A detailed work of seismic microzonation of Bangalore has been presented as a case study. In this case study, a seismotectonic map for microzonation area has been developed covering 350 km radius around Bangalore, India using seismicity and seismotectonic parameters of the region. For seismic microzonation Bangalore Mahanagar Palike (BMP) area of 220 km2 has been selected as the study area. Seismic hazard analysis has been carried out using deterministic as well as probabilistic approaches. Synthetic ground motion at 653 locations, recurrence relation and peak ground acceleration maps at rock level have been generated. A detailed site characterization has been carried out using borehole with standard penetration test (SPT) ―N‖ values and geophysical data. The base map and 3-dimensional sub surface borehole model has been generated for study area using geographical information system (GIS). Multichannel analysis of surface wave (MASW)method has been used to generate one-dimensional shear wave velocity profile at 58 locations and two- dimensional profile at 20 locations. These shear wave velocities are used to estimate equivalent shear wave velocity in the study area at every 5m intervals up to a depth of 30m. Because of wider variation in the rock depth, equivalent shear for the soil overburden thickness alone has been estimated and mapped using ArcGIS 9.2. Based on equivalent shear wave velocity of soil overburden thickness, the study area is classified as ―site class D‖. Site response study has been carried out using geotechnical properties and synthetic ground motions with program SHAKE2000.The soil in the study area is classified as soil with moderate amplification potential. Site response results obtained using standard penetration test (SPT) ―N‖ values and shear wave velocity are compared, it is found that the results based on shear wave velocity is lower than the results based on SPT ―N‖ values. Further, predominant frequency of soil column has been estimated based on ambient noise survey measurements using instruments of L4-3D short period sensors equipped with Reftek 24 bit digital acquisition systems. Predominant frequency obtained from site response study is compared with ambient noise survey. In general, predominant frequencies in the study area vary from 3Hz to 12Hz. Due to flat terrain in the study area, the induced effect of land slide possibility is considered to be remote. However, induced effect of liquefaction hazard has been estimated and mapped. Finally, by integrating the above hazard parameters two hazard index maps have been developed using Analytic Hierarchy Process (AHP) on GIS platform. One map is based on deterministic hazard analysis and other map is based on probabilistic hazard analysis. Finally, a general guideline is proposed by bringing out the advantages and disadvantages of different approaches.

Adam-Gibbs Relation for Glass-Forming Liquids in Two, Three, and Four Dimensions

The Adam-Gibbs relation between relaxation times and the configurational entropy has been tested extensively for glass formers using experimental data and computer simulation results. Although the form of the relation contains no dependence on the spatial dimensionality in the original formulation, subsequent derivations of the Adam-Gibbs relation allow for such a possibility. We test the Adam-Gibbs relation in two, three, and four spatial dimensions using computer simulations of model glass formers. We find that the relation is valid in three and four dimensions. But in two dimensions, the relation does not hold, and interestingly, no single alternate relation describes the results for the different model systems we study.

Breakdown of the Stokes-Einstein relation in two, three, and four dimensions

The breakdown of the Stokes-Einstein (SE) relation between diffusivity and viscosity at low temperatures is considered to be one of the hallmarks of glassy dynamics in liquids. Theoretical analyses relate this breakdown with the presence of heterogeneous dynamics, and by extension, with the fragility of glass formers. We perform an investigation of the breakdown of the SE relation in 2, 3, and 4 dimensions in order to understand these interrelations. Results from simulations of model glass formers show that the degree of the breakdown of the SE relation decreases with increasing spatial dimensionality. The breakdown itself can be rationalized via the difference between the activation free energies for diffusivity and viscosity (or relaxation times) in the Adam-Gibbs relation in three and four dimensions. The behavior in two dimensions also can be understood in terms of a generalized Adam-Gibbs relation that is observed in previous work. We calculate various measures of heterogeneity of dynamics and find that the degree of the SE breakdown and measures of heterogeneity of dynamics are generally well correlated but with some exceptions. The two-dimensional systems we study show deviations from the pattern of behavior of the three-and four-dimensional systems both at high and low temperatures. The fragility of the studied liquids is found to increase with spatial dimensionality, contrary to the expectation based on the association of fragility with heterogeneous dynamics.

Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

We investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs2, Cd3As2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y lattices matched to InP, CdS, PbTe, PbSnTe and Pb1−xSnxSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices.

Matrices of finite Lorentz transformations in a noncompact basis. III. Completeness relation for O(2, 1)

A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.

Three-User Cognitive Channels with Cumulative Message Sharing: An Achievable Rate Region

In this paper, an achievable rate region for the three-user discrete memoryless interference channel with asymmetric transmitter cooperation is derived. The three-user channel facilitates different ways of message sharing between the transmitters. We introduce a manner of noncausal (genie aided) unidirectional message-sharing, which we term cumulative message sharing. We consider receivers with predetermined decoding capabilities, and define a cognitive interference channel. We then derive an achievable rate region for this channel by employing a coding scheme which is a combination of superposition and Gel'fand-Pinsker coding techniques.

Metal-spinel-corundum three phase equilibria in the system Ni-Cr-Al-O at 1373 K

The tie-lines representing the inter-crystalline ion exchange equilibria between the NiCr2O4-NiAl2O4 spinet solid solution and Cr2O3-Al2O3 corundum solid solution are determined by electron microprobe andEDAX pointcountanalysis of the oxide phases equilibrated with metallic Ni at 1373 K. The component activities in the spinet solid solution are derived from the tie-lines and thermodynamic data for Cr2O3-Al2O3 solid solution available in the literature. The Gibbs energy of mixing of the spinet solid solution calculated from the experimental data is discussed in relation to the values derived from the cation distribution models which assume random mixing of cations on both tetrahedral and octahedral sites. Positive deviation from the models is observed indicating significant positive enthalpy contribution arising form the size mismatch between Al+3 and Ni+2 ions on the tetrahedral site and Al+3, Ni+2 and Cr+3 on the octahedral site. Variation of the oxygen potential for threephase equilibrium involving metallic nickel, spinet solid solution and corundum solid solution is computed as a function of composition of the solid solutions at 1373 K. The oxygen potential exhibits a minimum at aluminum cationic fraction eta(Al)/(eta(Al) + eta(Cr)) = 0.524 in the oxide solid solutions.

Conformationally restricted formyl methionyl tripeptide chemoattractants: a three-dimensional structure-activity study of analogs incorporating a C alpha,alpha-dialkylated glycine at position 2

The conformationally restricted CHO-L-Met-Xxx-L-Phe-OY (where Xxx = Aib, Ac3c, Ac5c, Ac6c, and Ac7c; Y = H, Me) tripeptides, analogs of the chemoattractant CHO-L-Met-L-Leu-L-Phe-OH, have been synthesized in solution by classical methods and fully characterized. Compounds were compared to determine the combined effect of backbone conformational preferences and side-chain bulkiness on the relation of three-dimensional structure to biological activity. Each peptide was tested for its ability to induce granule enzyme secretion from rabbit peritoneal polymorphonuclear leukocytes. In parallel, a conformational analysis on the CHO-blocked peptide and their tertbutyloxycarbonylated synthetic precursors was performed in the crystal state and in solution using X-ray diffraction, infrared absorption, and 1H nuclear magnetic resonance. The biological and conformational data are discussed in relation to the proposed model of the chemotactic peptide receptor of rabbit neutrophils.

Laminar compressible boundary layer flow at a three-dimensional stagnation point with vectored mass transfer

The effect of surface mass transfer velocities having normal, principal and transverse direction components (�vectored� suction and injection) on the steady, laminar, compressible boundary layer at a three-dimensional stagnation point has been investigated both for nodal and saddle points of attachment. The similarity solutions of the boundary layer equations were obtained numerically by the method of parametric differentiation. The principal and transverse direction surface mass transfer velocities significantly affect the skin friction (both in the principal and transverse directions) and the heat transfer. Also the inadequacy of assuming a linear viscosity-temperature relation at low-wall temperatures is shown.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Strongly magnetized cold degenerate electron gas: Mass-radius relation of the magnetized white dwarf

We consider a relativistic, degenerate electron gas at zero temperature under the influence of a strong, uniform, static magnetic field, neglecting any form of interactions. Since the density of states for the electrons changes due to the presence of the magnetic field (which gives rise to Landau quantization), the corresponding equation of state also gets modified. In order to investigate the effect of very strong magnetic field, we focus only on systems in which a maximum of either one, two, or three Landau level(s) is/are occupied. This is important since, if a very large number of Landau levels are filled, it implies a very low magnetic field strength which yields back Chandrasekhar's celebrated nonmagnetic results. The maximum number of occupied Landau levels is fixed by the correct choice of two parameters, namely, the magnetic field strength and the maximum Fermi energy of the system. We study the equations of state of these one-level, two-level, and three-level systems and compare them by taking three different maximum Fermi energies. We also find the effect of the strong magnetic field on the mass-radius relation of the underlying star composed of the gas stated above. We obtain an exciting result that it is possible to have an electron-degenerate static star, namely, magnetized white dwarfs, with a mass significantly greater than the Chandrasekhar limit in the range 2.3-2.6M(circle dot), provided it has an appropriate magnetic field strength and central density. In fact, recent observations of peculiar type Ia supernovae-SN 2006gz, SN 2007if, SN 2009dc, SN 2003fg-seem to suggest super-Chandrasekhar-mass white dwarfs with masses up to 2.4-2.8M(circle dot) as their most likely progenitors. Interestingly, our results seem to lie within these observational limits.

On the recurrence of great subduction zone earthquakes

The last decade has witnessed two unusually large tsunamigenic earthquakes. The devastation from the 2004 Sumatra Andaman and the 2011 Tohoku-Oki earthquakes (both of moment magnitude >= 9.0) and their ensuing tsunamis comes as a harsh reminder on the need to assess and mitigate coastal hazards due to earthquakes and tsunamis worldwide. Along any given subduction zone, megathrust tsunamigenic earthquakes occur over intervals considerably longer than their documented histories and thus, 2004-type events may appear totally `out of the blue'. In order to understand and assess the risk from tsunamis, we need to know their long-term frequency and magnitude, going beyond documented history, to recent geological records. The ability to do this depends on our knowledge of the processes that govern subduction zones, their responses to interseismic and coseismic deformation, and on our expertise to identify and relate tsunami deposits to earthquake sources. In this article, we review the current state of understanding on the recurrence of great thrust earthquakes along global subduction zones.