Stability of Charged Thin-Shell Wormholes in (2+1) Dimensions

In this paper we construct charged thin-shell wormholes in (2+1)-dimensions applying the cut-and-paste technique implemented by Visser, from a BTZ black hole which was discovered by Bañados, Teitelboim and Zanelli (Phys. Rev. Lett. 69:1849, 1992), and the surface stress are determined using the Darmois-Israel formalism at the wormhole throat. We analyzed the stability of the shell considering phantom-energy or generalised Chaplygin gas equation of state for the exotic matter at the throat. We also discussed the linearized stability of charged thin-shell wormholes around the static solution.     

Middle school students’ proportional reasoning in real life contexts in the domain of geometry and measurement

The purpose of this study was to examine middle school students’ proportional reasoning, solution strategies and difficulties in real life contexts in the domain of geometry and measurement. The underlying reasons of the difficulties were investigated as well. Mixed research design was adopted for the aims of the study by collecting data through an achievement test from 935 sixth, seventh and eighth grade students. The achievement test included real life problems that required proportional reasoning, and were related to the measurement of length, perimeter, area and volume concepts. In addition, task-based interviews were conducted on 12 of these students to collect more comprehensive data and to support the findings of the achievement test. Findings revealed that although students were mostly successful in giving correct answers, their reasoning lacked a clear argument of the direct and indirect proportional relationships between the variables and that they approached the problems by superficial characteristics of the problems.     

Branching random walks,stable point processes and regular variation

Using the theory of regular variation, we give a sufficient condition for a point process to be in the superposition domain of attraction of a strictly stable point process. This sufficient condition is used to obtain the weak limit of a sequence of point processes induced by a branching random walk with jointly regularly varying displacements. Because of heavy tails of the step size distribution, we can invoke a one large jump principle at the level of point processes to give an explicit representation of the limiting point process. As a consequence, we extend the main result of Durrett (1983) and verify that two related predictions of Brunet and Derrida (2011) remain valid for this model.     

Deflection of light by black holes and massless wormholes in massive gravity

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass M and an extra parameter S namely ‘scalar charge’. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter \(\lambda \) in the metric characterizes so-called ‘hair’. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter \(\lambda \). Then, by introducing a simple coordinate transformation \(r^\lambda =S+v^2\) into the black hole metric, we were able to find a massless wormhole solution of Einstein–Rosen (ER) (Einstein and Rosen, Phys Rev 43:73, 1935) type with scalar charge S. The programme is then repeated in terms of the Gauss–Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter \(\lambda \). In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.     

Microstructural characterization of ultrafine-grain interstitial-free steel by X-ray diffraction line profile analysis

This paper highlights the microstructural features of commercially available interstitial free (IF) steel specimens deformed by equal channel angular pressing (ECAP) up to four passes following the route A. The microstructure of the samples was studied by different techniques of X-ray diffraction peak profile analysis as a function of strain (ε). It was found that the crystallite size is reduced substantially already at ε=2.3 and it does not change significantly during further deformation. At the same time, the dislocation density increases gradually up to ε=4.6. The dislocation densities estimated from X-ray diffraction study are found to correlate very well with the experimentally obtained yield strength of the samples.     

Stereoelectronic and dynamical effects dictate nitrogen inversion during valence isomerism in benzene imine

Benzene imine (1) ⇌ 1H-azepine (2) isomerization occurs through sequential valence and endo–exo isomerism. Quantum chemical and quasiclassical trajectory (QCT) simulations reveal the coupled reaction pathway – ring-expansion followed by N-inversion to the most stable isomer, exo-1H-azepine (Exo-2). Direct-dynamics produce a mixture of endo- and exo-1H-azepine stereoisomers and govern the endo-1H-azepine (Endo-2) ⇌ exo-1H-azepine (Exo-2) ratio. Exo-2 is computationally identified as the most stable product while Endo-2 is fleetingly stable with a survival time (S_T) ∼50 fs. N-Methyl substitution exclusively results in an exo-1-methyl-1H-azepine isomer. F-substitution at the N-site increases the barrier for N-inversion and alters the preference by stabilizing Endo-2. Interestingly, the exo-1-fluoro-1H-azepine (minor product) is formed through bifurcation via non-statistical dynamics. A highly concaved Arrhenius plot for 1a → 2a highlights the influence of heavy-atom tunneling on valence isomerism, particularly at low temperatures. Heavy-atom tunneling also results in a normal N–H(D) secondary KIE above 100 K even though the increase in hybridization from sp² to sp³ at nitrogen should cause an inverse KIE classically.

Non-classical processes such as heavy-atom tunneling and post transition-state dynamics govern stereoselectivity for benzene imine ⇌ 1H-azepine.     

Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint

Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters—i.e., the efficiency and work done—is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamic variables (on which the efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of the sum uncertainty relation of position and momentum operators with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through the uncertainty relation.     

Construction of unsymmetrical bis-urea macrocyclic host for neutral molecule and chloride-ion binding

Construction of synthetic macrocyclic host that can bind with neutral molecules and anions has potential applications in supramolecular chemistry. Herein, we have designed and synthesized blue light emitting an unsymmetrical neutral bis-urea macrocyclic host. This macrocycle can bind with neutral DMF molecule (1:1) as well as Cl⁻ ion (1:1) through noncovalent interactions. X-Ray crystal structure, ¹H NMR titrations with Job's Plot, HRMS with isotropic distribution pattern, FT-IR, and density functional theory analysis revealed the binding of bis-urea macrocyclic host with the guest molecule.