Systems of quasi-variational relations with applications

In this paper, we introduce a system of quasi-variational relations (in short, SQVR) and present several examples which show that it is a very general and unified model of several problems. We establish the existence of solutions of SQVP, in general, and several other problems, in particular. As an application of our results, we derive maximal element theorems and a collectively fixed point theorem for a family of multivalued maps. As further applications, we study Ky Fan type inequality / inclusion problem for vector valued bifunctions which includes constrained Nash equilibrium problem as a special case. We also present a common fixed point theorem for a family of multivalued maps. The results of this paper improve and generalize several known results on (system of) quasi-equilibrium problems, (system of) quasi-variational inclusions, constrained Nash equilibrium problem, collectively fixed point theorem and KKM type theorems for a family of multivalued maps. Our results also contain several results which appeared in recent literature.     

Holographic Dark Energy in Higher Derivative Gravity with Varying Gravitational Constant

In this paper we investigate the holographic dark energy scenario in higher derivative gravity with a varying gravitational constant. We introduce a kind of energy density from higher derivative gravity which has role of the same as holographic dark energy. We obtain the exact differential equation , which determine the evolution of the dark energy density based on varying gravitational constant G. We also find out a cosmological application of our work by evaluating a relation for the equation of state of dark energy for low redshifts containing varying G correction.     

An Iterative method for nonlinear variational inequalities arising in elastoplasticity ∗

In this paper, we study an iterative method, which includes the Ka?anov method as a particular case, for solving nonlinear variational inequalities of the second kind. A convergence result is also proved under suitable assumptions. We apply our iterative method to solve an elastoplasticity problem.     

Insights into the binding mechanism of 2,5-substituted 4-pyrone derivatives as therapeutic agents for fused dimeric interactions: A computational study using QTAIM,dynamics and docking simulations of protein–ligand complexes

The study is focused on examining 2,5-Substituted 4-Pyrone based compounds through quantum chemical and topological analysis techniques, evaluating the properties of these compounds, including their geometrical structure, intermolecular interactions and assess their possible applications. Additionally, the molecular stability, charge delocalization and UV-Visible data was investigated and compared with the calculated energy and oscillator strength using the TD-DFT approach. The researchers observed that charge transfer occurred within the molecule, indicated by the HOMO and LUMO energies. It was also found that the compound exhibited planarity and higher chemical reactivity. The calculated Mulliken charges and molecular electrostatic potential were used to interpret the Fukui index data that help predict reactive sites and understand the reactivity patterns of specific atoms in a compound. The study is aimed to understand the role of NCI in the molecule under investigation using electron localization functions and localized orbit locator methods. Molecular docking and ADMET studies were conducting involving a detailed MD simulation of a protein-ligand complex using the OPLS3e force field and the SPC water model. These findings could prove to be beneficial in developing new therapeutic agents with various pharmacological effects and potential toxicities.     

Size-dependent buckling analysis of functionally graded third-order shear deformable microbeams including thermal environment effect

Presented herein is the prediction of buckling behavior of size-dependent microbeams made of functionally graded materials (FGMs) including thermal environment effect. To this purpose, strain gradient elasticity theory is incorporated into the classical third-order shear deformation beam theory to develop a non-classical beam model which contains three additional internal material length scale parameters to consider the effects of size dependencies. The higher-order governing differential equations are derived on the basis of Hamilton’s principle. Afterward, the size-dependent differential equations and related boundary conditions are discretized along with commonly used end supports by employing generalized differential quadrature (GDQ) method. A parametric study is carried out to demonstrate the influences of the dimensionless length scale parameter, material property gradient index, temperature change, length-to-thickness aspect ratio and end supports on the buckling characteristics of FGM microbeams. It is revealed that temperature change plays more important role in the buckling behavior of FGM microbeams with higher values of dimensionless length scale parameter.     

Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into the different types of plate theory namely as classical plate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT). An exact solution is conducted to obtain the critical biaxial buckling loads of simply-supported square and rectangular SLGSs with various values of side-length and nonlocal parameter corresponding to each type of nonlocal plate model. Then, molecular dynamics (MD) simulations are performed for a series of armchair and zigzag SLGSs with different side-lengths, the results of which are matched with those obtained by the nonlocal plate models to extract the appropriate values of nonlocal parameter relevant to each type of nonlocal elastic plate model and chirality. It is found that the present nonlocal plate models with their proposed proper values of nonlocal parameter have an excellent capability to predict the biaxial buckling response of SLGSs.     

Generalized vector variational-like inequalities and vector optimization in Asplund spaces

Some properties of pseudoinvex functions, defined by means of limiting subdifferential, are obtained. Furthermore, the equivalence between vector variational-like inequalities involving limiting subdifferential and vector optimization problems are studied under pseudoinvexity condition.     

Helicoidal Patterning of Nanorods with Polymer Ligands

Chiral packing of ligands on the surface of nanoparticles (NPs) is of fundamental and practical importance, as it determines how NPs interact with each other and with the molecular world. Herein, for gold nanorods (NRs) capped with end‐grafted nonchiral polymer ligands, we show a new mechanism of chiral surface patterning. Under poor solvency conditions, a smooth polymer layer segregates into helicoidally organized surface‐pinned micelles (patches). The helicoidal morphology is dictated by the polymer grafting density and the ratio of the polymer ligand length to nanorod radius. Outside this specific parameter space, a range of polymer surface structures was observed, including random, shish‐kebab, and hybrid patches, as well as a smooth polymer layer. We characterize polymer surface morphology by theoretical and experimental state diagrams. The helicoidally organized polymer patches on the NR surface can be used as a template for the helicoidal organization of other NPs, masked synthesis on the NR surface, as well as the exploration of new NP self‐assembly modes.     

Ion‐Specific Assembly of Strong,Tough, and Stiff Biofibers

Designing engineering materials with high stiffness and high toughness is challenging as stiff materials tend to be brittle. Many biological materials realize this objective through multiscale (i.e., atomic‐ to macroscale) mechanisms that are extremely difficult to replicate in synthetic materials. Inspired from the architecture of such biological structures, we here present flow‐assisted organization and assembly of renewable native cellulose nanofibrils (CNFs), which yields highly anisotropic biofibers characterized by a unique combination of high strength (1010 MPa), high toughness (62 MJ m^?3) and high stiffness (57 GPa). We observed that properties of the fibers are primarily governed by specific ion characteristics such as hydration enthalpy and polarizability. A fundamental facet of this study is thus to elucidate the role of specific anion binding following the Hofmeister series on the mechanical properties of wet fibrillar networks, and link this to the differences in properties of dry nanostructured fibers. This knowledge is useful for rational design of nanomaterials and is critical for validation of specific ion effect theories. The bioinspired assembly demonstrated here is relevant example for designing high‐performance materials with absolute structural control.