Investigation of tiny jet locations effect in a sudden expansion duct for high-speed flows control using experimental and optimization methods

Meccanica - The present research focuses on dynamic flow control management using tiny jets with three combinations; the first one located at 90° intervals of the base, the second one located...     

Error Estimates for a Class of Elliptic Optimal Control Problems

In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible control and the optimal control is introduced. This error quantity can be estimated from both sides using the estimates for the cost functional value. The theoretical results are confirmed by numerical tests.     

Thiacalixarene Appended Azo-based Supramolecular Systems: Self-assembly and Photo Tuning Reversible Liquid Crystalline Properties

Four new azo-based supramolecular materials containing thiacalixarene core substituted by variable alkoxy groups ( TFA₁ – TFA₄ ) have been designed and synthesized for the mesomorphic and photoswitching properties. The liquid crystalline behavior were accomplished by using DSC, POM, and XRD studies. All azo-based thiacalixarene based materials with short and higher chain length display columnar hexagonal mesophase with broad temperature range. The thermal behavior of all the materials was investigated by DSC and TGA study. The structural and conformational study of the lower rim functionalized materials was confirmed by using different techniques. These thiacalixarene moulded liquid crystalline compounds shows columnar self-assembly type behavior and higher thermal stability. The introduction of bi-substituted azo-ester network towards the lower rim of thiacalixarene core has impact on the electron delocalization and liquid crystalline properties. The photoswitching properties suggested cis and trans azo-isomerization under radiation of UV light and higher thermal back relaxation time. The mesogenic behaviour of compound TFA₂ and TFA₄ were demolished by the influence of cis and trans isomerization. The structure-property correlation is studied to understand the variation in mesogenic properties with the substitution of variable alkoxy side chain.     

Torands Revisited: Metal Sequestration and Self‐Assembly of Cyclo‐2,9‐tris‐1,10‐phenanthroline Hexaaza Macrocycles

A series of novel toroidal cyclo‐2,9‐tris‐1,10‐phenanthroline macrocycles with an unusual hexaaza cavity are reported. Nickel‐mediated Yamamoto aryl–aryl coupling was found to be a versatile tool for the cyclotrimerization of functionalized 1,10‐phenathroline precursors. Due to the now improved processability, both liquid‐crystalline behavior in the bulk phase and two‐dimensional self‐assembly at the molecular level could be studied, for the first time, for a torand system. The macrocycles exhibited a strong affinity for the complexation of different metal cations, as evidenced by MALDI‐TOF analysis and spectroscopic methods. Experimental results were correlated to an extensive computational study of the cyclo‐2,9‐tris‐1,10‐phenanthroline cavity and its binding mode for metal cations. Due to the combination of several interesting features, toroidal macrocycles may find future applications in the field of ion and charge transport through molecular channels, as well as for chemical sensing and molecular writing in surface‐confined monolayers under STM conditions.     

A steady-state moving crack of longitudinal shear with an infinitely narrow plastic zone

A simple model of longitudinal shear with a plastic zone at the tip of the crack is considered in the paper. The plasticity zone is assumed to be narrow, and fulfillment of the Mises condition is stipulated on its boundary. The crack moves with a constant velocity without change in the length.Translated from Zhurnal Prikladnoi Mekhaniki i Teknieheskoi Fiziki, No. 2, pp. 121–126, March–April, 1973.     

Investigation of the dynamics of the development of cracks by the method of photoelasticity

An experimental investigation was made of the process of the development of cracks in two materials: polymethyl methacrylate and a polymerized epoxy resin. For these materials, determinations were made of their optical and mechanical characteristics, such as density, the speed of sound, the critical value of the coefficient of singularity of the stress field at the tip of cracks. As the dynamic characteristic of the process of the development of cracks, an investigation is made of the dependences connecting the coefficient of the singularity of the stress field at the tip of a moving crack and the rate of development of the crack. The question of the interaction between two cracks moving in a previously elongated sample is discussed.     

Correlation between Quantum Entanglement and Quantum Coherence in the Case of XY Spin Chains with the Dzyaloshinskii–Moriya Interaction

Journal of Experimental and Theoretical Physics - Recently, there has been an increased interest in studying quantum entanglement and quantum coherence. Since both of these properties are...