New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd–Bullough–Mikhailov and Tzitzéica–Dodd–Bullough equations, are obtained using the exp_a function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.     

Structure–phase state of the surface layers in rails subjected to differential hardening

A layer-by-layer analysis of the structures, the phase compositions, and the defect substructures of differentially hardened rails has been carried by optical and transmission electron microscopy. It is found that the material volume of the rail head fillet is cooled faster than the volume located along the central axis.     

Molecular structure and granule morphology of native and heat‐moisture‐treated pinhão starch

Pinhão seed is an unconventional source of starch and the pines grow up in native forests of southern Latin America. In this study, pinhão starch was adjusted at 15, 20 and 25% moisture content and heated to 100, 110 and 120 °C for 1 h. A decrease in λ max (starch/iodine complex) was observed as a result of increase in temperature and moisture content of HMT. The ratio of crystalline to amorphous phase in pinhão starch was determined via Fourier transform infra red by taking 1045/1022 band ratio. A decrease in crystallinity occurred as a result of HMT. Polarised light microscopy indicated a loss of birefringence of starch granules under 120 °C at 25% moisture content. Granule size distribution was further confirmed via scanning electron microscopy which showed the HMT effects. These results increased the understanding on molecular and structural properties of HMT pinhão starch and broadened its food and nonfood industrial applications.     

Analysis of a two-dimensional symmetric problem on extension of an Al-polyimide-Cu layered structure with a model crack

To increase the efficiency of designing systems intended for monitoring surface cracks in aluminum structures during their working life, we have analyzed a two-dimensional symmetric problem on uniaxial extension of an Al-polyimide-Cu layered structure with ideal adhesion between layers and a model crack in the aluminum base. The problem has been first solved for a sample with the crack modeled by a zero-thickness notch using the ANSYS engineering simulation program package. It is shown that this setting of the problem can lead to inadequate results as manifested, in particular, by significantly overstated mechanical stresses in aluminum in the region of crack emergence on the surface. In order to eliminate this difficulty, we propose to use the structure with a model defect in the form of a notch of nonzero thickness in the initial unstressed state of the structure. Recommendations for selecting the thickness of a notch used in the model structure are given.