Quantum Phase Diagram of One-Dimensional Spin and Hubbard Models with Transitions to Bond Order Wave Phases

Similar quantum phase diagrams and transitions are found for three classes of one-dimensional models with equally spaced sites, singlet ground states (GS), inversion symmetry at sites and a bond order wave (BOW) phase in some sectors. The models are frustrated spin-1/2 chains with variable range exchange, half-filled Hubbard models with spin-independent interactions and modified Hubbard models with site energies for describing organic charge transfer salts. In some range of parameters, the models have a first order quantum transition at which the GS expectation value of the sublattice spin < S-A(2)> of odd or even-numbered sites is discontinuous. There is an intermediate BOW phase for other model parameters that lead to two continuous quantum transitions with continuous < S-A(2)>. Exact diagonalization of finite systems and symmetry arguments provide a unified picture of familiar 1D models that have appeared separately in widely different contexts.

Quantum Phase Diagram of One-Dimensional Spin and Hubbard Models with Transitions to Bond Order Wave Phases

Similar quantum phase diagrams and transitions are found for three classes of one-dimensional models with equally spaced sites, singlet ground states (GS), inversion symmetry at sites and a bond order wave (BOW) phase in some sectors. The models are frustrated spin-1/2 chains with variable range exchange, half-filled Hubbard models with spin-independent interactions and modified Hubbard models with site energies for describing organic charge transfer salts. In some range of parameters, the models have a first order quantum transition at which the GS expectation value of the sublattice spin < S-A(2)> of odd or even-numbered sites is discontinuous. There is an intermediate BOW phase for other model parameters that lead to two continuous quantum transitions with continuous < S-A(2)>. Exact diagonalization of finite systems and symmetry arguments provide a unified picture of familiar 1D models that have appeared separately in widely different contexts.

Dynamic Site Characterization and Correlation of Shear Wave Velocity with Standard Penetration Test `N' Values for the City of Agartala, Tripura State, India

Seismic site characterization is the basic requirement for seismic microzonation and site response studies of an area. Site characterization helps to gauge the average dynamic properties of soil deposits and thus helps to evaluate the surface level response. This paper presents a seismic site characterization of Agartala city, the capital of Tripura state, in the northeast of India. Seismically, Agartala city is situated in the Bengal Basin zone which is classified as a highly active seismic zone, assigned by Indian seismic code BIS-1893, Indian Standard Criteria for Earthquake Resistant Design of Structures, Part-1 General Provisions and Buildings. According to the Bureau of Indian Standards, New Delhi (2002), it is the highest seismic level (zone-V) in the country. The city is very close to the Sylhet fault (Bangladesh) where two major earthquakes (M (w) > 7) have occurred in the past and affected severely this city and the whole of northeast India. In order to perform site response evaluation, a series of geophysical tests at 27 locations were conducted using the multichannel analysis of surface waves (MASW) technique, which is an advanced method for obtaining shear wave velocity (V (s)) profiles from in situ measurements. Similarly, standard penetration test (SPT-N) bore log data sets have been obtained from the Urban Development Department, Govt. of Tripura. In the collected data sets, out of 50 bore logs, 27 were selected which are close to the MASW test locations and used for further study. Both the data sets (V (s) profiles with depth and SPT-N bore log profiles) have been used to calculate the average shear wave velocity (V (s)30) and average SPT-N values for the upper 30 m depth of the subsurface soil profiles. These were used for site classification of the study area recommended by the National Earthquake Hazard Reduction Program (NEHRP) manual. The average V (s)30 and SPT-N classified the study area as seismic site class D and E categories, indicating that the city is susceptible to site effects and liquefaction. Further, the different data set combinations between V (s) and SPT-N (corrected and uncorrected) values have been used to develop site-specific correlation equations by statistical regression, as `V (s)' is a function of SPT-N value (corrected and uncorrected), considered with or without depth. However, after considering the data set pairs, a probabilistic approach has also been presented to develop a correlation using a quantile-quantile (Q-Q) plot. A comparison has also been made with the well known published correlations (for all soils) available in the literature. The present correlations closely agree with the other equations, but, comparatively, the correlation of shear wave velocity with the variation of depth and uncorrected SPT-N values provides a more suitable predicting model. Also the Q-Q plot agrees with all the other equations. In the absence of in situ measurements, the present correlations could be used to measure V (s) profiles of the study area for site response studies.

Molecular Cage Impregnated Palladium Nanoparticles: Efficient, Additive-Free Heterogeneous Catalysts for Cyanation of Aryl Halides

Two shape-persistent covalent cages (CC1(r) and CC2(r)) have been devised from triphenyl amine-based trialdehydes and cyclohexane diamine building blocks utilizing the dynamic imine chemistry followed by imine bond reduction. The cage compounds have been characterized by several spectroscopic techniques which suggest that CC1(r) and CC2(r) are 2+3] and 8+12] self-assembled architectures, respectively. These state-of-the-art molecules have a porous interior and stable aromatic backbone with multiple palladium binding sites to engineer the controlled synthesis and stabilization of ultrafine palladium nanoparticles (PdNPs). As-synthesized cage-embedded PdNPs have been characterized by transmission electron microscopy (TEM), scanning electron microscopy (SEM), and powder X-ray diffraction (PXRD). Inductively coupled plasma optical emission spectrometry reveals that Pd@CC1(r) and Pd@CC2(r) have 40 and 25 wt% palladium loading, respectively. On the basis of TEM analysis, it has been estimated that as small as similar to 1.8 nm PdNPs could be stabilized inside the CC1(r), while larger CC2(r) could stabilize similar to 3.7 nm NPs. In contrast, reduction of palladium salts in the absence of the cages form structure less agglomerates. The well-dispersed cage-embedded NPs exhibit efficient catalytic performance in the cyanation of aryl halides under heterogeneous, additive-free condition. Moreover, these materials have excellent stability and recyclability without any agglomeration of PdNPs after several cycles.

Cl-35 NQR study of cation polarizability in metal salts of monochloro acetic acid

Various metal salts (Na, K, Rb, and NH4) of monochloro acetic acid were prepared and the Cl-35 nuclear quadrupole resonance frequencies were measured at room temperature. A comparative study of nuclear quadrupole resonance frequencies of monochloro acetic acid and its metal salts is carried out. The frequency shifts obtained in the respective metal chloroacetates are used to estimate the changes in the ionicity of C-Cl bond. Further, the changes in the ionicity of C-Cl bond were used to estimate the percentage of intra-molecular charge transfer between respective cation-anion of the metal salts of chloro acetic acid. The nuclear quadrupole resonance frequency is found to decrease with increasing ionicity of the alkali metal ion.

Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach

In this paper an approach for obtaining depth and section modulus of the cantilever sheet pile wall using inverse reliability method is described. The proposed procedure employs inverse first order reliability method to obtain the design penetration depth and section modulus of the steel sheet pile wall in order that the reliability of the wall against failure modes must meet a desired level of safety. Sensitivity analysis is conducted to assess the effect of uncertainties in design parameters on the reliability of cantilever sheet pile walls. The analysis is performed by treating back fill soil properties, depth of the water table from the top of the sheet pile wall, yield strength of steel and section modulus of steel pile as random variables. Two limit states, viz., rotational and flexural failure of sheet pile wall are considered. The results using this approach are used to develop a set of reliability based design charts for different coefficients of variation of friction angle of the backfill (5%, 10% and 15%). System reliability considerations in terms of series and parallel systems are also studied.

Seismic passive earth pressures in soils

Seismic passive earth pressure coefficients were computed by the method of limit equilibrium using a pseudostatic approach for seismic forces. Composite curved rupture surfaces were considered in the analysis. While earlier studies using this type of analysis were mainly for sands, seismic passive earth pressure coefficients were obtained in the present study considering the effects of cohesion, surcharge, and own weight. The minimum seismic passive force was obtained by adding the individual minimum values of these components and the validity of the principle of superposition was examined. Other parameters considered in the analysis were wall batter angle, ground surface slope, soil friction angle, wall friction angle, wall adhesion to soil cohesion ratio, and horizontal and vertical seismic accelerations. The seismic earth pressure coefficients were found to be highly sensitive to the seismic acceleration coefficients both in the horizontal and vertical directions. Results of the study are presented in the form of figures and tables. Comparisons of the proposed method with available theories in the seismic case are also presented.

Seismic passive resistance in soils for negative wall friction

: In the presence of pseudo-static seismic forces, passive earth pressure coefficients behind retaining walls were generated using the limit equilibrium method of analysis for the negative wall friction angle case (i.e., the wall moves upwards relative to the backfill) with logarithmic spirals as rupture surfaces. Individual density, surcharge, and cohesion components were computed to obtain the total minimum seismic passive resistance in soils by adding together the individual minimum components. The effect of variation in wall batter angle, ground slope, wall friction angle, soil friction angle, and horizontal and vertical seismic accelerations on seismic passive earth pressures are considered in the analysis. The seismic passive earth pressure coefficients are found to be highly sensitive to the seismic acceleration coefficients both in the horizontal and the vertical directions. The results are presented in graphical and tabular formats.

A Reliable method of obtaining Breakthrough Curves of ions in Soils using Transport Equation

Molecular diffusion plays a dominant role in transport of contaminants through fine-grained soils with low hydraulic conductivity. Attenuation processes occur while contaminants travel through the soils. Effective diffusion coefficient (De) is expected to take into consideration various attenuation processes. Effective diffusion coefficient has been considered to develop a general approach for modelling of contaminant transport in soils.The effective diffusion coefficient of sodium in presence of sulphate has been obtained using the column test.The reliability of De, has been checked by comparing theoretical breakthrough curves of sodium ion in soils obtained using advection diffusion equation with the experimental curve.

Impact of Sulphate counter ion in the migration of sodium ion through soils

Laboratory advection-diffusion tests are performed on two regional soils-Brown Earth and Red Earth-in order to assess their capacity to control contaminant migration with synthetic contaminant solution of sodium sulphate with sodium concentration of 1000 mg/L. The test was designed to study the transport/attenuation behaviour of sodium in the presence of sulphate. Effective diffusion coefficient (De) that takes into consideration of attenuation processes is used. Cation exchange capacity is an important factor for the attenuation of cationic species. Monovalent sodium ion cannot usually replace other cations and the retention of sodium ion is very less. This is particularly true when chloride is anion is solution. However, sulphate is likely to play a role in the attenuation of sodium. Cation exchange capacity and type of exchangeable ions of soils are likely to play an important role. The effect of sulphate ions on the effective diffusion coefficient of sodium, in two different types of soils, of different cation exchange capacity has been studied. The effective diffusion coefficients of sodium ion for both the soils were calculated using Ogata Bank’s equation. It was shown that effective diffusion coefficient of sodium in the presence of sulphate is lower for Brown Earth than for Red Earth due to exchange of sodium with calcium ions from the exchangeable complex of clay. The soil with the higher cation exchange retained more sodium. Consequently, the breakthrough times and the number of pore volumes of sodium ion increase with the cation exchange capacity of soil.

Variation of diffusivity with the cation radii in molten salts of superionic conductors containing iodine anion: A molecular dynamics study

A molecular dynamics study of the dependence of diffusivity of the cation on ionic radii in molten AgI is reported. We have employed modified Parinello-Rahman-Vashistha interionic pair potential proposed by Shimojo and Kobayashi.(1) Our results suggest that the diffusivity of the cation exhibits an increase followed by a decrease as the ionic radius is increased. Several structural and dynamical properties are reported.

Polymorphs, Salts, and Cocrystals: What's in a Name?

The December 2011 release of a draft United States Food and Drug Administration (FDA) guidance concerning regulatory classification of pharmaceutical cocrystals of active pharmaceutical ingredients (APIs) addressed two matters of topical interest to the crystal engineering and pharmaceutical science communities: (1) a proposed definition of cocrystals; (2) a proposed classification of pharmaceutical cocrystals as dissociable ``API-excipient'' molecular complexes. The Indo U.S. Bilateral Meeting sponsored by the Indo-U.S. Science and Technology Forum titled The Evolving Role of Solid State Chemistry in Pharmaceutical Science was held in Manesar near Delhi, India, from February 2-4, 2012. A session of the meeting was devoted to discussion of the FDA guidance draft. The debate generated strong consensus on the need to define cocrystals more broadly and to classify them like salts. It was also concluded that the diversity of API crystal forms makes it difficult to classify solid forms into three categories that are mutually exclusive. This perspective summarizes the discussion in the Indo-U.S. Bilateral Meeting and includes contributions from researchers who were not participants in the meeting.