On the failure of hyperbolicity in elasticity

The failure of hyperbolicity leading to the instability as an ill-posedness of the Cauchy problem is investigated for elasticity. The criteria for that instability are derived in terms of the potential energy as a function of the strain invariants. The theory is illustrated by examples.     

A unified model description of mobile and localized adsorption: I. MFA with nonadditive lateral interactions — an application to disordered adsorbed monolayer on a structureless substrate

A simple model is used to treat mobile adsorption on a structureless substrate. The influence of temperature on the state of motion of adsorbed particles is described by means of an interpolation formula used earlier in the theory of hindered rotation, whereas the influence of the nearest-neighbour potential with varying degree of coverage is accounted for in terms of a “free area”, available for individual particle motion, for which a simple analytical expression, based on an harmonic oscillator approximation, is obtained. An irregularity in the long range order of the adsorbed monolayer is introduced in terms of “varying distances”, resp. of varying energy bonds between the particles in dependence of the number of nearest neighbours actually present in the first coordination sphere of each particle (nonadditivity of the bonds).     

A unified model description of mobile and localized adsorption: II. Adsorption on crystalline surfaces — a gradual transition between mobile and localized adsorption

The model used in Part I is now extended to account for the periodic potential of the substrate. The influence of the energetical structure of the substrate on the state of motion of a single particle is allowed for at varying degree of coverage so that the gradual transition from localized to mobile adsorption with growing temperature may be described. The impact of the energetical characteristics of adsorbate and adsorbent on the critical parameters of the adsorption isotherms is investigated. These parameters are also considerably influenced when non-additivity of the lateral bonds is taken into account. On a perfectly smooth substrate, as well as in the case of potential wells of the substrate coinciding in size with the diameter of the adatoms, the model predicts the impossibility of a first order phase transition between “additive” and “nonadditive” phases. The last result could be related to the problem of 2D melting, provided the degree of disorder in both adsorbate phases is adequately expressed in terms of varying nonadditivity of the energy bonds.     

Selective and efficient electrocatalytic way to spirobarbituric dihydrofurans

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Pseudo six-component stereoselective synthesis of 2,4,6-triaryl-3,3,5,5-tetracyanopiperidines

The Knövenagel–Michael–Mannich cascade reaction of aromatic aldehyde (3 equiv.), malononitrile (2 equiv.) and ammonium acetate or aqueous ammonia provides convenient stereoselective access tocis,cis-2,4,6-triaryl-3,3,5,5-tetracyanopiperidines in 62–94% yields. Six new bonds form as a result of the domino process, ammonium acetate serving as a nitrogen source.     

The first synthesis of spirocyclopentyl derivatives of lupane triterpenoids by radical nitrocyclization of C-2-diallyl substituted betulonates

Radical cyclization of the 1,6-hexadiene moiety in 2,2-diallyl substituted methyl or benzyl dihydrobetulonates initiated by Fe(NO₃)₃·9H₂O in the presence of FeCl₃ or LiCl gave hitherto unknown spirocyclic compounds in which ring A of the lupane triterpenoid at position C-2 is spiro coupled with a vicinally substituted nitromethyl- and chloromethylcyclopentane. Based on a quantum-chemical assessment of the energy characteristics of this reaction, the most probable configurations of the chiral atoms in the spirocyclopentane ring were determined for the major diastereomers isolated in individual form.     

A graph-theoretical kinetic Monte Carlo framework for on-lattice chemical kinetics

Existing kinetic Monte Carlo (KMC) frameworks for the simulation of adsorption, desorption, diffusion, and reaction on a lattice often assume that each participating species occupies a single site and represent elementary events involving a maximum of two sites. However, these assumptions may be inadequate, especially in the case of complex chemistries, involving multidentate species or complex coverage and neighboring patterns between several lattice sites. We have developed a novel approach that employs graph-theoretical ideas to overcome these challenges and treat easily complex chemistries. As a benchmark, the Ziff-Gulari-Barshad system is simulated and comparisons of the computational times of the graph-theoretical KMC and a simpler KMC approach are made. Further, to demonstrate the capabilities of our framework, the water-gas shift chemistry on Pt(111) is simulated.