Molecular dynamics study of cluster structure and rotational wave properties in solid-state nanostructures

Molecular dynamics simulation was performed to study the formation of cluster structure, interfaces, and surfaces with different curvature radii in a perfect nanocrystal passed through by a nonlinear wave. It is shown that this process is a type of nanostructure self-organization in response to an external energy flux with subsequent development of a strong rotational field.     

Differential Graded Bocses and A ∞ $A_{\infty }$ -Modules

Algebras and Representation Theory - We introduce and study the category of twisted modules over a triangular differential graded bocs. We show that in this category idempotents split, that it...     

Step cost functions in a fleet size and mix vehicle routing problem with time windows

Annals of Operations Research - The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several specificities...     

Mesoscopic Strain Fields Measurement During the Allotropic α − γ Transformation in High Purity Iron

The allotropic phase change from ferrite to austenite represents a moment of massive interplay between the microstructural and mechanical states of iron. The difference of compacity between the two phases induces a microplastic accommodation in the material at grain scale. However, mechanical heterogeneities resulting from the transformation process remain challenging to characterise due to the high temperature conditions it is associated with. We developed experimental equipment for in situ observation of α ? γ and γ ? α transformations. Images of the surface of an iron sample taken by an optical camera were used as input for a Digital Image Correlation (DIC) routine. Special care was taken to maximize image resolution to capture sub-grain phenomena. Observations show that, at the mesoscopic scale, shear strain fields exhibit strong localisations that are evidence of transformations that are occurring.

     

Structural verification of a tetrahydrotetrazole compound

Tetrahydrotetrazoles are five‐membered‐ring heterocycles containing four contiguous saturated nitrogen atoms. Very few examples of such compounds have been reported in the literature. Our previous attempt at the synthesis of a member of this class of compound suggested that the N—N bonds may be more labile than expected. This finding raised the question as to whether the structures of any of the previously reported tetrahydrotetrazoles had been properly assigned. We have reproduced the synthesis of a reported tetrahydrotetrazole, namely 1,2‐di‐tert‐butyl 3‐phenyl‐1H,2H,3H,10bH‐[1,2,3,4]tetrazolo[5,1‐a]isoquinoline‐1,2‐dicarboxylate, C₂₅H₃₀N₄O₄, and have now confidently confirmed its structure via X‐ray crystallography. However, while sufficiently stable in the crystal phase, we discovered that it remains very labile in solution (having a half‐life of only 15 min at 20 °C in CDCl₃). A tentative reaction pathway for its dissociation based on ¹H NMR spectral evidence is provided.     

Structure of Zinc Nanotubes

Crystallography Reports - The formation of Zn-based nanotubes by electrochemical synthesis in pores of template polymer matrices is considered. It is established that the number of defects in the...     

Three-weight linear codes from Weil sums

Journal of Algebraic Combinatorics - By appropriately choosing a defining set, we define a class of linear codes and establish their complete weight enumerators and weight enumerators using Weil...     

Formation and Characterization of Concentration Inhomogeneities in Melt-Grown Crystals

Crystallography Reports - The specific features of the formation of concentration inhomogeneities in crystals grown by the Czochralski method (GaSb:Te, Ge:Ga) and by the Bridgman method...     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.