An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.     

Alcohols as Fluoroalkyl Synthons: Ni-catalyzed Dehydrogenative Approach to Access Polyfluoroalkyl Bis-indoles

An acceptorless dehydrogenative strategy for the synthesis of polyfluoroalkylated bis-indoles is described by employing an earth-abundant nickel-based catalytic system under air. The notable feature of the present transformation is the use of bench stable and easily affordable polyfluorinated alcohols without any pre-functionalization for the introduction of precious polyfluoroalkyl groups. The developed straightforward protocol accomplished biologically relevant fluoroalkyl bis-indoles in a sustainable fashion. Extensive DFT study predicts the unique role of indole molecules which stabilizes the transition states during the dehydrogenation process of polyfluorinated alcohols, presumably through non-covalent π⋅⋅⋅π and H-bonding interactions.     

An alternative route to tethered Ru(II) transfer hydrogenation catalysts

A new route towards a series of tethered η⁶-arene/Ru(II) catalysts for use in the transfer and pressure hydrogenation of ketones and aldehydes to alcohols is reported. The route proceeds through the formation of an amide from the diamine precursor, followed by reduction, rather than the direct alkylation of the diamine. This has the advantage that dialkylation of the amine is avoided during the synthesis. Through this new route, both racemic and enantiomerically-pure η⁶-arene/Ru(II) tethered catalysts can be prepared in high yield.     

An AFM Dynamic Contact Model with Finite Thickness Correction to Study Micro-Rheology of Biological Cells

Experimental Techniques - One of the major sources of error in Atomic Force Microscopy based Force Spectroscopic studies is bottom substrate effect, which comes due to assumption of infinite sample...     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Distribution of Shower Particles as Obtained in the Analysis of a 10 + 13p Shower Event

We present here the analysis of an accelerator produced 10 + 13p shower event observed in nuclear emulsion. The DULLER -WALKER method is applied to obtain the distribution of secondary shower particles, and the particles having the closest log₁₀ tan θ_L values are taken to form a cluster. This cluster formation is also confirmed by the target diagram method. If this cluster is conceived to be a high spin resonance and the secondary pions to be the decay products of this resonance, then the azimuthal integral distribution curve fits fairly well with our experimental data.     

Two storage inventory model with fuzzy deterioration over a random planning horizon

An inventory model for a deteriorating item with stock dependent demand is developed under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. For crisp deterioration rate, the expected profit is derived and maximized via genetic algorithm (GA). On the other hand, when deterioration rate is imprecise then optimistic/pessimistic equivalent of fuzzy objective function is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to maximize the optimistic/pessimistic return and finally fuzzy simulation-based GA is developed to solve the model. The models are illustrated with some numerical data. Sensitivity analyses on expected profit function with respect to distribution parameter λ and confidence levels α₁ and α₂ are also presented.