Phase transitions in graphs on orientable surfaces

Let be the orientable surface of genus and denote by the class of all graphs on vertex set with edges embeddable on . We prove that the component structure of a graph chosen uniformly at random from features two phase transitions. The first phase transition mirrors the classical phase transition in the Erd?s‐Rényi random graph chosen uniformly at random from all graphs with vertex set and edges. It takes place at , when the giant component emerges. The second phase transition occurs at , when the giant component covers almost all vertices of the graph. This kind of phenomenon is strikingly different from and has only been observed for graphs on surfaces.     

A simple microwave process for the preparation of cobalt oxide nanoparticles supported on carbon nanotubes for electrocatalytic applications

Journal of Solid State Electrochemistry - Cobalt oxide nanoparticles supported on multiwalled carbon nanotubes (CoOx/CNTs) were prepared by a facile and rapid solid-state synthesis using microwave...     

Congruences for overpartitions with restricted odd differences

The Ramanujan Journal - In a recent work, Bringmann, Dousse, Lovejoy, and Mahlburg defined the function $$\overline{t}(n)$$ to be the number of overpartitions of weight n where (i) the difference...     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Asymptotics in percolation on high‐girth expanders

We consider supercritical bond percolation on a family of high‐girth ‐regular expanders. The previous study of Alon, Benjamini and Stacey established that its critical probability for the appearance of a linear‐sized (“giant”) component is . Our main result recovers the sharp asymptotics of the size and degree distribution of the vertices in the giant and its 2‐core at any . It was further shown in the previous study that the second largest component, at any , has size at most for some . We show that, unlike the situation in the classical Erd?s‐Rényi random graph, the second largest component in bond percolation on a regular expander, even with an arbitrarily large girth, can have size for arbitrarily close to 1. Moreover, as a by‐product of that construction, we answer negatively a question of Benjamini on the relation between the diameter of a component in percolation on expanders and the existence of a giant component. Finally, we establish other typical features of the giant component, for example, the existence of a linear path.     

Theoretical investigation of the crystallographic structure,anisotropic elastic response,and electronic properties of the major borides in Ni-based superalloys

ABSTRACT

In Ni-based superalloys, it is usually found that borides can strengthen the grain boundaries, thereby resulting in an increase in mechanical strength and high-temperature creep properties. Due to their importance and prevalence in Ni-based superalloys, this study employs first-principles methods to investigate the crystallographic structure, anisotropic elastic response, and electronic properties of the major borides, such as M₂B, M₅B₃ and M₃B₂ (M: Cr, Mo, W), respectively, which is necessary for the assessment of complex mechanical responses of Ni-based superalloys. The results demonstrate that the studied borides are all thermodynamically and mechanically stable. Among the M _x B _y binary borides analysed, Cr _x B _y exhibits the largest shear modulus, Young’s modulus, and Vicker hardness values, and these properties increase with the increase of B contents. The studied borides display nearly isotropic elastic properties except for W₅B₃ and W₃B₂. The electronic structure analysis of M _x B _y shows that the strong hybridisation between M-d and B-p orbitals leads to these borides exhibiting higher theoretical hardness, and the overlapping peaks of M-d and B-p orbitals move to a lower energy area with the increase of B contents, which leads to the increase of shear and Young’s moduli of M _x B _y . Furthermore, for M₃B₂ borides, the Cr-B bonds and Cr–Cr bonds are much stronger than the W-B & Mo-B bonds, and W-W & Mo-Mo bonds, respectively, which leads to Cr _x B _y yielding the largest values of elastic moduli.     

Thermometric analysis of blood metabolites in ICU patients

Journal of Thermal Analysis and Calorimetry - Real-time monitoring of patient’s blood metabolites, such as glucose and lactate, could potentially improve surgery and recovery outcomes for...