Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

Cold compaction of ceramic powder: Computational analysis of the effect of pressing method and die shape

This paper deals with a computational analysis of the influence of the pressing method and part geometry on the final density distribution in the cold compaction process of ceramic alumina powders. The analysis is based on the explicit finite-element model proposed and validated in a previous study. The mechanical behavior of the processing material is described using a multisurface elastoplastic model, the modified Drucker-Prager/Cap model Published in Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 129–134, October 2007.     

BRST invariance and the conical pendulum

The Hamiltonian formulation of the BRST method for quantizing constrained systems developed recently by Nemeschanskyet al is applied to the well-known problem of the conical pendulum in classical mechanics. The similarity of the system to a gauge theory wherein the two constraints serve as generators of local Abelian gauge transformations is also pointed out. The definition of the physical states of the system as a gauge theory and also as a BRST invariant theory is then discussed in some detail.     

Forward and backward pericyclic photochemical reactions have intermediates in common, yet cyclobutenes break the rules.

Photochemical pericyclic reactions are believed to proceed via a so-called pericyclic minimum on the lowest excited potential surface (S(1)), which is common to both the forward and backward reactions. Such a common intermediate has never been directly detected. The photointerconversion of 1,3-butadiene and cyclobutene is the prevailing prototype for such reactions, yet only diene ring closure proceeds with the stereospecificity that the Woodward-Hoffmann rules predict. This contrast seems to exclude a common intermediate. Using ultrafast spectroscopy, we show that the excited states of two cyclobutene/diene isomeric pairs are linked by not one, but by two common minima, p* and ct*. Starting from the diene side (cyclohepta-1,3-diene and cycloocta-1,3-diene), electrocyclic ring closure passes via the pericyclic minimum p*, whereas ct* is mainly responsible for cis-trans isomerization. Starting from the corresponding cyclobutenes (bicyclo[3.2.0]heptene-6 and bicyclo[4.2.0]octene-7), the forbidden isomer is formed from ct*. The path branches at the first (S(2)/S(1)) conical intersection towards p* and ct*. The fact that the energetically unfavorable ct* path can compete is ascribed to a dynamic effect: the momentum in C=C twist direction, acquired--such as in other olefins--in the Franck-Condon region of the cyclobutenes.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Invariance of the cone algebra without asymptotics

Let B be a manifold with conical singularities, and denote by the smooth bounded manifold with cylindrical ends obtained by blowing up near the singularities.B.-W. Schulze has developed a framework for a pseudodifferential calculus on B by defining various classes of distribution spaces and operator algebras, working in fixed coordinates on the manifold . I am showing here that the Mellin Sobolev spaces without asymptotics, the cone algebra without asymptotics, and its ideal of smoothing operators are independent of the choice of coordinates and therefore may be considered intrinsic objects for manifolds with conical singularities.     

Influence of static and dynamical structural changes on ultrafast processes mediated by conical intersections

The technological needs imposed by the exponential miniaturization trend of conventional electronic devices has drawn attention towards the development of smaller and faster devices like ultrafast molecular switches. In recent years molecular switches emerge again in the focus of active and innovative research with state-of-the-art optical tools recording their dynamics in real time. Still many questions about the underlying microscopic mechanism are left open, including potential factors that effect the switching process in either way, improve or worsen it. Due to the complexity of such molecules it is difficult to obtain a global answer from experiment alone. On the other side molecular switches are generally too large for a complete quantum chemical and quantum dynamical calculation. In our group we therefore developed an ab initio based modular model to handle the laser induced quantum dynamics in molecular switches like fulgides. It enables us to study the effect of internal molecular coupling and of the molecular response to external fields. We can investigate the related wave packet dynamics, the switching efficiency and the controllability. Our results focus on the laser induced ring opening in fulgides, which equals one direction of the switching process. Presented are the influence of a conical intersection seam and of time-dependent potentials, mimicking the mean interaction with the environment. Furthermore the relation of controllability and the wave packet's momentum is studied and the influence of potential barriers on the switching dynamics is shown.     

A High Sensitivity Fluorescent Chemo-sensory System Based on β-Cyclodextrin Dimer Modified with Dansyl Moieties

-Cyclodextrin dimer linked with ethylenediamine at the upper rim of the cyclodextrin has been synthesized and then modified with two dansyl moieties inthe presence of N,N'-dicyclohexylcarbodiimide. The sensing ability and bindingproperty of the title compound were investigated for steroids and terpenoids. Thefluorescence intensity of this dimer was decreased when a host–guest complex was formed. The value I/I⁰, where I⁰ and I are fluorescence intensitiesin the absence and presence of a guest and I is I⁰- I, was used as a parameter of sensitivity. This host exhibited a much higher sensitivity and selective molecular recognition ability for bile acids such as ursodeoxycholic acid andchenodeoxycholic acid and terpenoids such as (-)-borneol than the dansyl-modifiedcyclodextrins reported previously including -cyclodextrin dimer. The behaviors of the appended moieties of the host during the formation of host–guest complexes were studied using induced circular dichroism (ICD) and fluorescence spectra. The ICD intensityof this dimer was decreased on accommodation of a guest and this spectral pattern of the title dimer was opposite to that of bis dansyl-modified -cyclodextrin monomer. Theguest-induced variations in the fluorescence and ICD intensities suggest that this dimer formed a 1 : 1 host–guest complex and the appended moieties act as a hydrophobic cap.     

Exploring Potential Energy Surfaces for Aggregation‐Induced Emission—From Solution to Crystal

Aggregation‐induced emission (AIE) is a phenomenon where non‐luminescent compounds in solution become strongly luminescent in aggregate and solid phase. It provides a fertile ground for luminescent applications that has rapidly developed in the last 15 years. In this review, we focus on the contributions of theory and computations to understanding the molecular mechanism behind it. Starting from initial models, such as restriction of intramolecular rotations (RIR), and the calculation of non‐radiative rates with Fermi's golden rule (FGR), we center on studies of the global excited‐state potential energy surfaces that have provided the basis for the restricted access to a conical intersection (RACI) model. In this model, which has been shown to apply for a diverse group of AIEgens, the lack of fluorescence in solution comes from radiationless decay at a CI in solution that is hindered in the aggregate state. We also highlight how intermolecular interactions modulate the photophysics in the aggregate phase, in terms of fluorescence quantum yield and emission color.     

Excited-state surfaces of ethylene from the B13 strong-correlation density functional

The energy surfaces of the ground and low-lying excited states of ethylene are challenging tests of multi-reference electronic structure methods. A variety of multi-reference wavefunction theories have been applied to this problem and the ensuing photochemistry has been well studied. Density-functional methods, however, have been less successful. In this work, the ‘B13’ strong-correlation density functional is used to generate multi-reference orbitals for the computation of the three lowest-lying singlet states. We explore the states and energies as a function of torsion angle, and as a function of the pyramidalisation angle with respect to the twisted orthogonal structure. The former features an avoided crossing at the orthogonal structure; the latter a C_s slice through a conical intersection. Both features are well reproduced by our B13 method.