A comparison of the Discontinuous-Galerkin- and Spectral-Difference-Method on triangulations using PKD polynomials

This paper gives a first numerical comparison of the Discontinuous-Galerkin-(DG) and Spectral-Difference-Method (SD) under almost equivalent conditions for smooth test cases.     

Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model

We study multi-fissuration and debonding phenomena of a thin film bonded to a stiff substrate using the variational approach to fracture mechanics. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g., thermal) strains in the film or imposed displacements of the substrate. Fracture phenomena are accounted for by adopting a Griffith model for debonding and transverse fracture. On the basis of energy minimization arguments, we recover the key qualitative properties of the experimental evidences, like the periodicity of transverse cracks and the peripheral debonding of each regular segment. Phase diagrams relate the maximum number of transverse cracks that may be created before debonding takes place, as a function of the material properties and the sample’s geometry. The theoretical results are illustrated with numerical simulations obtained through a finite element discretization and a regularized variational formulation of the Ambrosio–Tortorelli type, which is suited to further extensions in two-dimensional settings.     

Excited State Tuning of Bis(tridentate) Ruthenium(II) Polypyridine Chromophores by Push–Pull Effects and Bite Angle Optimization: A Comprehensive Experimental and Theoretical Study

The synergy of push–pull substitution and enlarged ligand bite angles has been used in functionalized heteroleptic bis(tridentate) polypyridine complexes of ruthenium(II) to shift the ¹MLCT absorption and the ³MLCT emission to lower energy, enhance the emission quantum yield, and to prolong the ³MLCT excited‐state lifetime. In these complexes, that is, [Ru(ddpd)(EtOOC‐tpy)][PF₆]₂, [Ru(ddpd‐NH₂)(EtOOC‐tpy)][PF₆]₂, [Ru(ddpd){(MeOOC)₃‐tpy}][PF₆]₂, and [Ru(ddpd‐NH₂){(EtOOC)₃‐tpy}][PF₆]₂ the combination of the electron‐accepting 2,2′;6′,2′′‐terpyridine (tpy) ligand equipped with one or three COOR substituents with the electron‐donating N,N′‐dimethyl‐N,N′‐dipyridin‐2‐ylpyridine‐2,6‐diamine (ddpd) ligand decorated with none or one NH₂ group enforces spatially separated and orthogonal frontier orbitals with a small HOMO–LUMO gap resulting in low‐energy ¹MLCT and ³MLCT states. The extended bite angle of the ddpd ligand increases the ligand field splitting and pushes the deactivating ³MC state to higher energy. The properties of the new isomerically pure mixed ligand complexes have been studied by using electrochemistry, UV/Vis absorption spectroscopy, static and time‐resolved luminescence spectroscopy, and transient absorption spectroscopy. The experimental data were rationalized by using density functional calculations on differently charged species (charge n=0–4) and on triplet excited states (³MLCT and ³MC) as well as by time‐dependent density functional calculations (excited singlet states).     

The interior proximal extragradient method for solving equilibrium problems

In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms.     

Luminescence Properties of New Fused Benzothiophene Derivatives and Their Conductive Oligomers Structural and Solvent Effects

The structural and solvent effects on the electronic absorption and fluorescence spectra, and fluorescence quantum yields, of four new fused benzothiophene derivatives, including benzothieno[3,2b]-thiophene (BTT), benzothieno[3,2-b]benzothiophene (BTBT), 6-methoxy[1]benzothieno[3,2b]-thiophene (MeOBTT), and benzothieno[3,2-b]indole (BTI) were investigated at 295 K. The luminescence properties of the corresponding conductive oligomers, poly(BTT) and poly (MeOBTT), electrosynthesized in acetonitrile, were also studied. Satisfactory McRae, Suppan, and Kawski-Chamma-Viallet solvatochromic correlations were established for the four monomers in most solvents. A weak negative solvatochromic behavior was found for these compounds, indicating that their dipole moments are slightly lower in the excited singlet state than in the ground state. Kamlet-Abboud-Taft multiparametric correlations were also obtained for absorption and fluorescence wave numbers and quantum yields, demonstrating the existence of specific solute-solvent interactions. In the case of the oligomers, important red-shifts of the fluorescence emission maxima ( 90–110 nm) relative to the corresponding monomers were observed, which shows the extent of conjugated segments in the oligomer chains.     

A facile synthesis of α-chloroboronic esters via the base induced reaction of α,α-dichloromethyl methyl ether with hindered borinic esters

Treatment of hindered borinic esters, R₂ BOR′; with an equimolar quantity of α,α-dichloromethyl methyl ether and lithium triethylcarboxide yields the α-chloroboronic esters, R₂ CHClB(OCH₃)OR′, in excellent yields. In cases where the steric requirements of R are not sufficient, the steric requirements of R′ can be increased to achieve the synthesis.