From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel–Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag–Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.     

Synthesis and Evaluation of a Schiff-Based Fluorescent Chemosensors for the Selective and Sensitive Detection of Cu<Superscript>2+</Superscript> in Aqueous Media with Fluorescence Off-On Responses

Copper being an essential nutrient; also pose a risk for human health in excessive amount. A simple and convenient method for the detection of trace amount of copper was employed using an optical probe R1 based on Schiff base. The probe was synthesized by Schiff base condensation of benzyl amine and 2-hydroxy-1-napthaldehyde and characterized by single X-ray diffraction, ¹H NMR and FTIR. By screening its fluorescence response in a mixture of DMSO and H₂O (20:80, v/v) R1 displayed a pronounced enhancement in fluorescence only upon treatment with copper. Other examined metal ions such as alkali, alkaline and transition had no influence. Within a wide pH range 5–12 R1 could selectively detect copper by interrupting ICT mechanism that results in CHEF. From Job’s plot analysis a 2:1 binding stoichiometry was revealed. The fluorescence response was linear in the range 1–10?×?10^?9 M with detection limit 30?×?10^?9 M. Association constant was determined as 1?×?10¹¹ M^?2 by Benesi-Hilderbrand plot. As a fast responsive probe it possesses good reproducibility and was employed for detection of copper in different water samples.     

Evidence of short-range screening in shock-compressed aluminum plasma

We have investigated the angular variation in elastic x-ray scattering from a dense, laser-shock-compressed aluminum foil. A comparison of the experiment with simulations using an embedded atom potential in a molecular dynamics simulation shows a significantly better agreement than simulations based on an unscreened one-component plasma model. These data illustrate, experimentally, the importance of screening for the dense plasma static structure factor.     

Local Approximation Properties of Modified Baskakov Operators

In this paper, we introduce a general modification of the classical Baskakov operators which do not need to preserve the test function x ². Then, we study an approximation theorem, a Voronovskaya theorem, and various local approximation results for our modified Baskakov operators.     

Calorimetric investigations of the hydrolytic degradation for a series of β-sultams

The hydrolytic degradation of four β-sultams was investigated using isothermal microcalorimetry to determine kinetic and enthalpic data. Firstly, all four compounds were analysed in the solid-state at 310 K, with a significant substituent-based stabilising/destabilising effect being observed. Secondly, the four compounds were analysed in the presence of pH 4 acetate buffer, at three temperatures (298, 310 and 323 K). Under these conditions, the substituent choice affected the rate of hydrolysis and the associated change in enthalpy for each compound. Based on the calorimetric data presented in this work, no change in reaction mechanism for the hydrolytic degradation was observed over the temperature range considered.     

Conservation laws and conserved quantities for laminar two-dimensional and radial jets

A systematic way to derive the conserved quantities for the liquid jet, free jet and wall jet using conservation laws is presented. Both two-dimensional and radial jets are considered. The jet flows are described by Prandtl’s momentum boundary layer equation and the continuity equation. The multiplier approach (also know as variational derivative approach) is first applied to construct a basis of conserved vectors for the system. The basis consists of two conserved vectors. By integrating the corresponding conservation laws across the jet and imposing the boundary conditions, conserved quantities are derived for the liquid jet and the free jet. The multiplier approach is then applied to construct a basis of conserved vectors for the third-order partial differential equation for the stream function. The basis consists of two local conserved vectors one of which is a non-local conserved vector for the system. The conserved quantities for the free jet and the wall jet are derived from the corresponding conservation laws and boundary conditions. The approach gives a unified treatment to the derivation of conserved quantities for jet flows and may lead to a new classification of jets through conserved vectors and their multipliers.     

Room temperature charge-transfer phosphorescence from organic donor–acceptor Co-crystals

Engineering the electronic excited state manifolds of organic molecules can give rise to various functional outcomes, including ambient triplet harvesting, that has received prodigious attention in the recent past. Herein, we introduce a modular, non-covalent approach to bias the entire excited state landscape of an organic molecule using tunable ‘through-space charge-transfer’ interactions with appropriate donors. Although charge-transfer (CT) donor–acceptor complexes have been extensively explored as functional and supramolecular motifs in the realm of soft organic materials, they could not imprint their potentiality in the field of luminescent materials, and it still remains as a challenge. Thus, in the present study, we investigate the modulation of the excited state emission characteristics of a simple pyromellitic diimide derivative on complexation with appropriate donor molecules of varying electronic characteristics to demonstrate the selective harvesting of emission from its locally excited (LE) and CT singlet and triplet states. Remarkably, co-crystallization of the pyromellitic diimide with heavy-atom substituted and electron-rich aromatic donors leads to an unprecedented ambient CT phosphorescence with impressive efficiency and notable lifetime. Further, gradual minimizing of the electron-donating strength of the donors from 1,4-diiodo-2,3,5,6-tetramethylbenzene (or 1,2-diiodo-3,4,5,6-tetramethylbenzene) to 1,2-diiodo-4,5-dimethylbenzene and 1-bromo-4-iodobenzene modulates the source of ambient phosphorescence emission from the ³CT excited state to ³LE excited state. Through comprehensive spectroscopic, theoretical studies, and single-crystal analyses, we elucidate the unparalleled role of intermolecular donor–acceptor interactions to toggle between the emissive excited states and stabilize the triplet excitons. We envisage that the present study will be able to provide new and innovative dimensions to the existing molecular designs employed for triplet harvesting.

A modular, non-covalent donor–acceptor strategy is proposed to bias the excited-state manifold of organic systems and to realize unprecedented charge-transfer phosphorescence.     

Supercritical CO2 drying of pure silica aerogels: effect of drying time on textural properties of nanoporous silica aerogels

Journal of Sol-Gel Science and Technology - Aerogel technologies provide high-performance lightweight materials with unique textural characteristics such as high specific surface area and open...     

A numerical and analytical approach for exploration of entropy generation in Sisko nanofluid flow having swimming microorganisms

Journal of Thermal Analysis and Calorimetry - A new system of equations is developed using Galerkin finite element scheme for the investigation of the generation of entropy in viscoelastic Sisko...