Hypersingular integral equation for multiple curved cracks problem in plane elasticity

The complex variable function method is used to formulate the multiple curved crack problems into hypersingular integral equations. These hypersingular integral equations are solved numerically for the unknown function, which are later used to find the stress intensity factor, SIF, for the problem considered. Numerical examples for double circular arc cracks are presented.     

Gasanalyse

Ohne Zusammenfassung     

Surface structural evolution during the thermal decomposition of a PdO(101) thin film

We used scanning tunneling microscopy (STM) to characterize PdO(101) thin films grown on Pd(111), and the structural changes that occur during isothermal decomposition. We find that the PdO(101) thin films have high-quality surface structures that are characterized by large, crystalline terraces with low concentrations of point defects. Small domains of single-layer oxide are also present on the top layer of relatively thick PdO(101) films grown at 500 K. The thinner PdO(101) films exhibit negligible quantities of such domains, apparently because new domains agglomerate rapidly as the film thickness decreases. We find that the isothermal decomposition rate of a PdO(101) film at 720 K exhibits an autocatalytic regime in which the rate of oxygen desorption increases as the oxide decomposes. Our STM results demonstrate that reduced sites created during oxide decomposition catalyze further PdO decomposition, and reveal strong kinetic anisotropies in the decomposition. The kinetic anisotropies produce one-dimensional reaction fronts that propagate preferentially along the atomic rows of the PdO(101) surface, resulting in the formation of long chains of reduced sites. We also find that reduced sites promote oxygen recombination in neighboring rows of the Pd(101) structure, causing loops and larger aggregates of reduced sites to form. The promotion of decomposition across the atomic rows can qualitatively explain the autocatalytic desorption kinetics. Finally, the STM images provide evidence that underlying PdO(101) layers transfer oxygen to reduced surface domains, thus producing large domains of PdO(101) islands that coexist with reduced domains as well as the larger PdO(101) terraces of the initial surface. Re-oxidation of the surface acts to sustain the autocatalytic decomposition kinetics, and provides a mechanism for oxygen atoms to ultimately evolve from the subsurface of the PdO(101) film.     

Subalgebras of FA-presentable algebras

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First, an example is given to show that the class of finitely generated FA-presentable algebras is not closed under forming finitely generated subalgebras, even within the class of algebras with only unary operations. In contrast, a finitely generated subalgebra of an FA-presentable algebra with a single unary operation is itself FA-presentable. Furthermore, it is proven that the class of unary FA-presentable algebras is closed under forming finitely generated subalgebras and that the membership problem for such subalgebras is decidable.     

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015