Ultrafast Excited State Relaxation Dynamics of New Fuchsine- a Triphenylmethane Derivative Dye

An all-inclusive investigation of the ultrafast excited state relaxation dynamics of a triphenylmethane derivative molecule, New Fuchsine (NF), using a combined approach of density functional theory (DFT), femtosecond transient absorption spectroscopy (fs-TAS), and photoluminescence spectroscopy is presented in this work. The DFT calculations confirmed the formation of twisted molecular structure in the excited state of NF in ethanol solution with bond rotation of ≈86°. TAS measurements of NF solution exhibited ultrafast ground state-recovery pathway via a conical intersection confirming an ultrafast structural reorientation. On the contrary, TAS measurements of NF thin-film exhibited a longer excited-state lifetime suggesting a hindered molecular twisted state formed as an intermediate step. Photophysical kinetic models are proposed to globally fit the fs-TAS data establishing the twisted intramolecular charge transfer (TICT) state mediated ground state recovery for NF in solution and thin film, respectively. Temperature-dependent photoluminescence study of NF film provided a clear insight into the effect of rotational motion of phenyl rings in NF molecules over the TICT mediated emission.     

An Anthracene-Based Metal-Organic Framework for Selective Photo-Reduction of Carbon Dioxide to Formic Acid Coupled with Water Oxidation

A Zr-based metal-organic framework has been synthesized and employed as a catalyst for photochemical carbon dioxide reduction coupled with water oxidation. The catalyst shows significant carbon dioxide reduction property with concomitant water oxidation. The catalyst has broad visible light as well as UV light absorption property, which is further confirmed from electronic absorption spectroscopy. Formic acid was the only reduced product from carbon dioxide with a turn-over frequency (TOF) of 0.69 h⁻¹ in addition to oxygen, which was produced with a TOF of 0.54 h⁻¹. No external photosensitizer is used and the ligand itself acts as the light harvester. The efficient and selective photochemical carbon dioxide reduction to formic acid with concomitant water oxidation using Zr-based MOF as catalyst is thus demonstrated here.     

New Solutions for (1+1)-Dimensional and (2+1)-Dimensional Kaup–Kupershmidt Equations

In this paper, using the exp-function method we obtain some new exact solutions for (1+1)-dimensional and (2+1)-dimensional Kaup–Kupershmidt (KK) equations. We show figures of some of the new solutions obtained here. We conclude that the exp-function method presents a wider applicability for handling nonlinear partial differential equations.     

Optical solitons with time-dependent dispersion,nonlinearity and attenuation in a power-law media

This paper studies optical solitons in a power-law media with time-dependent coefficients of dispersion, nonlinearity and attenuation. The 1-soliton solution is obtained for the nonlinear Schrödinger’s equation with power-law nonlinearity. In addition, a relation between these coefficients is obtained for the solitons to exist. Finally, the velocity of the soliton is also obtained in terms of these coefficients.     

Analysis of flow in the plate‐spiral of a reaction turbine using a streamline upwind Petrov–Galerkin method

The prediction of the flow field in a novel spiral casing has been accomplished. Hydraulic turbine manufacturers are considering the potential of using a special type of spiral casing because of the easier manufacturing process involved in its fabrication. These special spiral casings are known as plate‐spirals. Numerical simulation of complex three‐dimensional flow through such spiral casings has been accomplished using a finite element method (FEM). An explicit Eulerian velocity correction scheme has been deployed to solve the Reynolds‐average Navier–Stokes equations. The simulation has been performed to describe the flow in high Reynolds number (10⁶) regimes. For spatial discretization, a streamline upwind Petrov–Galerkin (SUPG) technique has been used. The velocity field and the pressure distribution inside the spiral casing reveal meaningful results. Copyright © 2000 John Wiley & Sons, Ltd.     

Limit constructions over Riemann surfaces and their parameter spaces, and the commensurability group actions

To any compact hyperbolic Riemann surface X, we associate a new type of automorphism group — called its commensurability automorphism group, ComAut(X). The members of ComAut(X) arise from closed circuits, starting and ending at X, where the edges represent holomorphic covering maps amongst compact connected Riemann surfaces (and the vertices represent the covering surfaces). This group turns out to be the isotropy subgroup, at the point represented by X (in $ T_\infty $), for the action of the universal commensurability modular group on the universal direct limit of Teichmüller spaces, $ T_\infty $. Now, each point of $ T_\infty $ represents a complex structure on the universal hyperbolic solenoid. We notice that ComAut(X) acts by holomorphic automorphisms on that complex solenoid. Interestingly, this action turns out to be ergodic (with respect to the natural measure on the solenoid) if and only if the Fuchsian group uniformizing X is arithmetic. Furthermore, the action of the commensurability modular group, and of its isotropy subgroups, on some natural vector bundles over $ T_\infty $, are studied by us.