On the probability of the outcomes in buckling of an elastic beam

A nonlinear time-varying one-degree-of-freedom system, which is used for the modelling of the buckling of a loaded beam in Euler??s problem, is considered. For a slowly changing load, the deterministic approach in this problem fails if the trajectories pass through the separatrix. An expression for the probability of possible outcomes of the evolution of the oscillations is obtained. The analytical and numerical results are compared.     

Coherent photogalvanic valley Hall effect

The theory of the coherent photogalvanic valley Hall effect in two-dimensional systems with the Dirac spectrum of charge carriers is formulated. The study deals with a two-dimensional sample irradiated by two electromagnetic waves, at the fundamental and doubled frequencies. Both frequencies exceed the band gap of the material, whereas the wave with the fundamental frequency having circular polarization and a high intensity is taken into account in a nonperturbative manner. The wave at the doubled frequency is linearly polarized and the electrical conductivity of the two-dimensional system is calculated with respect to it. The effect under study manifests itself as the dc Hall current in the direction orthogonal to the electric field of the weak electromagnetic wave. It is assumed that, in equilibrium, the sample is in the insulating state with the completely occupied valence band and empty conduction band. The strong electromagnetic wave induces a nonequilibrium filling of the bands and the system passes to a strongly nonequilibrium steady state. The behavior of the Hall current in the case of nonequilibrium distribution functions is analyzed both including and disregarding the intraband relaxation and interband recombination.     

Pyrrolidine-thioxotetrahydropyrimidinone as an efficient organocatalyst for the enantioselective Michael addition of cyclic ketones to nitrodienes

Among the various Michael additions, the enantioselective reaction between cyclic ketones and nitrodienes has received little attention in comparison to the corresponding reaction with nitroolefins. A bifunctional organocatalyst consisting of the pyrrolidine moiety and a thioxotetrahydropyrimidinone ring successfully catalyzed this asymmetric transformation. The products of the reaction between various ketones and nitrodienes were obtained in high yields (up to 96%) with excellent diastereo- (up to >98:2 dr) and enantioselectivities (up to 99:1% er).     

First mushroom-shaped adhesive microstructure: A review

This letter reviews the adhesive and frictional properties of the first mushroom-shaped adhesive microstructure (MSAMS), which has come a long way from inspiration by the attachment devices evolved in beetles to a large-scale industrial production. It was shown to have an that about twice higher pull-off force compared to a smooth control made from the same material measured on smooth substrates. Pull-off forces measured underwater are even higher than those in air. Moreover, it retained adhesive performance over thousands of attachment cycles and initial adhesive capability could be recovered by washing after being contaminated. In shearing, MSAMS exhibits reduced and stabilized friction in comparison with a smooth control, which demonstrated pronounced stick-slip motion, and shows zero pull-off force in a sheared state, allowing the adhesion to be switched on and off. The presence of a fluid in the contact zone showed adhesion enhancement on both smooth and rough substrates. All these features lead us to conclude that MSAMS may have practical potential in a variety of applications.     

Percolation Thresholds in Ternary Polymer Melt Blends with Separate Dispersions of the Inner Phases: Mathematical Model

A mathematical model based on a straightforward geometrical background is developed which enables predictions of a transition of one dispersed phase to a cocontinuous one (i.e., the percolation threshold) on addition of another dispersed phase during melt mixing in ternary polymer blends. The present work concerns only ternary blends with two separate dispersions of the inner phases in which no encapsulation takes place. In addition, in order to simplify the model, one of the inner phases was represented by hard, nondeformable microspheres The expression developed describes well an experimental relationship between the percolation threshold, the concentration above which the former dispersed phase transforms to a continuous one, and concentrations of both inner phases. The results agree well with the experimental data obtained in a previous work.