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.     

Robust optimisation of sustainable food grain transportation with uncertain supply and intentional disruptions

The proliferating need for sustainability intervention in food grain transportation planning is anchoring the attention of researchers in the interests of stakeholders and environment at large. Uncertainty associated with food grain supply further intensifies the problem steering the need for designing robust, cost-efficient and sustainable models. In line with this, this paper aims to develop a robust and sustainable intermodal transportation model to facilitate single type of food grain commodity shipments while considering procurement uncertainty, greenhouse gas emissions, and intentional hub disruption. The problem is designed as a mixed integer non-linear robust optimisation model on a hub and spoke network for evaluating near optimal shipment quantity, route selection and hub location decisions. The robust optimisation approach considers minimisation of total relative regret associated with total cost subject to several real-time constraints. A version of Particle Swarm Optimisation with Differential Evolution is proposed to tackle the resulting NP-hard problem. The model is tested with two other state-of the art meta-heuristics for small, medium, and large datasets subject to different procurement scenarios inspired from real time food grain operations in Indian context. Finally, the solution is evaluated with respect to total cost, model and solution robustness for all instances.     

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.