Time Evolution of Vibration-Induced Excited State Decay

A simple model consisting of two electronic levels and one vibrational mode (phonon) was theoretically studied. The electronic-vibrational interaction was linear in the vibrational displacement. The vibrational mode was taken in the harmonic approximation and was attached to the thermal bath formed by the ambient environment. The kinetic constants of the vibrational dissipation were of the second order in the vibrational-bath coupling and were taken in the Markovian limit. Although, depending on the parameters of the model, different curves of the non-radiative vibration-induced excited state decay were obtained, in general, three time intervals, corresponding to different physical behaviour, were found. In the short-time interval, small oscillations superimposed on the excited state decay were observed. They were determined by the vibrational frequency and influenced by electronic-vibrational coupling. In the middle-time interval, almost quasi-exponential decay was detected; its rate constant increased with stronger electronic-vibrational interaction and speed of vibrational relaxation. In the long-time interval, the decay was very slow and, under special conditions, even an asymptotic non-zero excited state population was observed. Its value increased with the strength of the off-diagonal electron-vibrational coupling. Links of the parameters of the model with quantum chemical terms were estimated.     

Combined intra-intermolecular criss-cross cycloaddition of a new fluorinated unsymmetrical allenylazine with alkynes

The reaction of a new fluorinated unsymmetrical allenylazine with dimethyl acetylenedicarboxylate and phenylacetylene affords the combined intra-intermolecular criss-cross cycloaddition products, 2,3-disubstituted-1,10-diazatricyclo[5.2.1.0^4,10]deca-2,6-diene derivatives. The products contain three fused five-membered rings with two nitrogen atoms within an unsaturated heterocyclic system. The structures were assigned using 2D NMR correlations and in the case of the phenylacetylene adduct by X-ray structure analysis.     

New intra-intermolecular criss-cross cycloaddition of unsymmetrical allenylazines with alkynes leading to three fused five-membered heterocycles

This report describes a new type of intra-intermolecular criss-cross cycloadditions. Thermal reactions of unsymmetrical allenylazines in the presence of alkynes led to three fused five-membered heterocycles in some cases. In the case of unsymmetrical substituted alkynes, a regioselectivity was observed. The molecular structures of all products are discussed. One X-ray crystal structure is also reported.     

Chromatic number of Hasse diagrams,eyebrows and dimension

We construct posets of dimension 2 with highly chromatic Hasse diagrams. This solves a previous problem by Nesetril and Trotter.     

The motion of a compressible viscous fluid around rotating body

We consider the motion of compressible viscous fluids around a rotating rigid obstacle when the velocity at infinity is non zero and parallel to the axis of rotation. We prove the existence of weak solution.     

A Photochemical/Thermal Switch Based on 4,4′-Bis(benzimidazolio)stilbene: Synthesis and Supramolecular Properties.

Stilbene derivatives are well-recognised substructures of molecular switches based on photochemically and/or thermally induced (E)/(Z) isomerisation. We combined a stilbene motif with two benzimidazolium arms to prepare new sorts of supramolecular building blocks and examined their binding properties towards cucurbit[n]urils (n=7, 8) and cyclodextrins (β-CD, γ-CD) in water. Based on the ¹H NMR data and molecular dynamics simulations, we found that two distinct complexes with different stoichiometry, i. e., guest@β-CD and guest@β-CD₂, coexist in equilibrium in a water solution of the (Z)-stilbene-based guests. We also demonstrated that the bis(benzimidazolio)stilbene guests can be transformed from the (E) into the (Z) form via UV irradiation and back via thermal treatment in DMSO.     

Space-charge limited currents in insulators with the Gaussian distribution of traps

A direct mathematical procedure is presented for obtaining the volt-ampere characteristic in an insulating material having Gaussian energy-distribution of traps, under the condition of space-charge-limited emission into the material. The current-voltage dependence is of the V ⁿ type; the exponent n depends on the temperature and the width of the Gaussian distribution. The current-voltage dependence derived for the Gaussian trap energy distribution is formally identical with the case of exponential distribution of the trap density in energy.     

Rough surface scattering simulations using graphics cards

In this article we present results of rough surface scattering calculations using a graphical processing unit implementation of the Finite Difference in Time Domain algorithm. Numerical results are compared to real measurements and computational performance is compared to computer processor implementation of the same algorithm. As a basis for computations, atomic force microscope measurements of surface morphology are used. It is shown that the graphical processing unit capabilities can be used to speedup presented computationally demanding algorithms without loss of precision.     

The stationary Oseen equations in an exterior domain: An approach in weighted Sobolev spaces

In this work, we study the linearized Navier–Stokes equations in an exterior domain of R³${\mathbb{R}}^3$ at the steady state, that is, the Oseen equations. We are interested in the existence and the uniqueness of weak, strong and very weak solutions in L^p$L^p$-theory which makes our work more difficult. Our analysis is based on the principle that linear exterior problems can be solved by combining their properties in the whole space R³${\mathbb{R}}^3$ and the properties in bounded domains. Our approach rests on the use of weighted Sobolev spaces.