Extensivity of entropy and modern form of Gibbs paradox

The extensivity property of entropy is clarified in the light of a critical examination of the entropy formula based on quantum statistics and the relevant thermodynamic requirement. The modern form of the Gibbs paradox, related to the discontinuous jump in entropy due to identity or non-identity of particles, is critically investigated. Qualitative framework of a new resolution of this paradox, which analyses the general effect of distinction mark on the Hamiltonian of a system of identical particles, is outlined.     

A modified Ashcroft pseudopotential: application to aluminium

Unified study of the different properties of metals clearly reveals the inadequacy of the empty-core Ashcroft pseudopotential even in the case of simple metals. In the present paper we propose a modification of the one-parameter Ashcroft pseudopotential by assuming the parameterr _c to be wave vector-dependent. This introduces a simple modification of the electron-ion pseudopotential in the reciprocal space. The corresponding potential in the configuration space shows that the abrupt change in the Coulomb potential atr=r _c is replaced by a continuous change spread over a small region near the core boundary. The present model has been used to make a unified study of Al and is found to be a significant improvement over the simple Ashcroft model. The agreement between the calculated and experimental values is found to be quite satisfactory.     

Bell's inequality and non-contextual dispersion-free states

With a view to exploring the possibility of wider implication of Bell's theorem, we argue that Bell's inequality is derivable as a general consequence of non-contextual hidden-variable theories. We formulate a new type of gedanken example indicating incompatibility of Bell's inequality with quantum mechanical predictions concerning simultaneous measurement of commuting observables associated with a system having no spatially separated components, where the locality condition is not at issue. Significance of this example is pointed out.     

Optimal time advancing dispersion relation preserving schemes

In this paper we examine the constrained optimization of explicit Runge–Kutta (RK) schemes coupled with central spatial discretization schemes to solve the one-dimensional convection equation. The constraints are defined with respect to the correct error propagation equation which goes beyond the traditional von Neumann analysis   developed in Sengupta et al. [T.K. Sengupta, A. Dipankar, P. Sagaut, Error dynamics: beyond von Neumann analysis, J. Comput. Phys. 226 (2007) 1211–1218]. The efficiency of these optimal schemes is demonstrated for the one-dimensional convection problem and also by solving the Navier–Stokes equations for a two-dimensional lid-driven cavity (LDC) problem. For the LDC problem, results for Re=1000$\mathit{Re}=1000$ are compared with results using spectral methods in Botella and Peyret [O. Botella, R. Peyret, Benchmark spectral results on the lid-driven cavity flow, Comput. Fluids 27 (1998) 421–433] to calibrate the method in solving the steady state problem. We also report the results of the same flow at Re=10,000$\mathit{Re}=10\text{,}000$ and compare them with some recent results to establish the correctness and accuracy of the scheme for solving unsteady flow problems. Finally, we also compare our results for a wave-packet propagation problem with another method developed for computational aeroacoustics.     

On Spliced Sequences and the Density of Points with Respect to a Matrix Constructed by using a Weight Function

Ukrainian Mathematical Journal - Following the line of investigation in [Linear Algebra Appl., 487, 22–42 (2015)], for y ∈ ? and a sequence...     

Defect production in nonlinear quench across a quantum critical point

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.     

Segmented conjugated macromolecules containing silicon and boron: ADMET synthesis and luminescent properties

Boron‐ and silicon‐containing conjugated homo‐ and copolymers could be synthesized using acyclic diene metathesis (ADMET) condensation of bis‐styryl monomers. Both, tri‐and tetra‐coordinated boron monomers were successfully polymerized forming homopolymers, or random copolymers (if polymerized together with a silicon containing co‐monomer). Polymer molecular weights M_n were measured at ～6000 to 15,000 g/mol (NMR end group analysis) with molecular weight distributions M_w/M_n ～1.8 to 2.2. The polymers absorbed at λ_max ～317 to 406 nm and emitted at λ_max ～370 to 494 nm with fluorescent quantum efficiencies ～24 to 48%. The copolymer with tri‐coordinate boron showed highly efficient fluorescence quenching in the presence of fluoride ions at ratios boron/fluoride ～5/1, demonstrating its potential as anion sensor. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1707–1718     

2-Isopropylbenzimidazole and 2-methylbenzimidazole as bulky proton sources: Stereoselective protonation and application to the synthesis of γ- and δ-lactones

2-Isopropylbenzimidazole and 2-methylbenzimidazole have been found to be effective bulky proton sources for stereoselective protonation of chiral enolate anions. 2-Isopropylbenzimidazole worked in the stereoselective protonation of the Birch reduction of chiral α,β-unsaturated imides. On the other hand, 2-methylbenzimidazole was found to be the best protonation reagent in the isomerization reaction of α,β-unsaturated imide into β,γ-unsaturated imide. The Birch reduction using 2-isopropylbenzimidazole realized a concise and stereoselective synthesis of δ-lactone 14, a sex pheromone of Macrocentrus grandii, while the isomerization reaction using 2-methylbenzimidazole was employed in the highly stereoselective synthesis of the γ-lactone intermediate in the synthesis of depsipeptide antibiotics. These bulky proton sources would be powerful tools to achieve a concise synthesis of natural products.     

Structural features and dye-sensitized solar cell performance of chemically synthesized F doped ZnO particles

Journal of Solid State Electrochemistry - In dye-sensitized solar cell (DSSC) application, the particulate morphologies of photo-anode facilitate efficient dye loading and thus lead to better...