فهرست مطالب v. parvaneh

In this research, a multi-scale model was used to analyze the vibrational behavior of the atomic force microscope (AFM) on a graphene sheet sample. Cantilever and silicone tip base were simulated based on the continuum mechanics using finite element modeling and the tip apex were modeled based on the Tersoff potential by the structural mechanics modeling. The contact behavior between the tip and graphene was investigated using measuring friction force during the tip movement on the graphene layer, and its results were compared to the results obtained from molecular dynamics simulation and experimental test. The friction force between the tip and graphene increases by enhancing the tip radius and the contact surface between the tip and the sample. Moreover, the friction force dwindles by heightening the number of graphene layers as a result of sliding graphene layers on each other and diminishing the Poker effect (wrinkling). With the initial distance displacement of the tip from the sample, two curves of the tip vibration amplitude variations and the phase change between tip vibration and excitation vibration were plotted, and the effect of crack and its location in the cantilever was studied. The results showed that the crack in the cantilever can dramatically influence the tip vibration amplitude and the phase change between the tip vibration and the excitation signal.

A new and attractive metric space is a P-metric space which is a generalization of the concept of b-metric spaces. The generalization of the principle of Banach contraction has been carried out by many authors. Generalizations focus on the extension of metric spaces and the extension of contraction conditions. A few metrics, such as partial metrics, G-metrics, 2-metrics and Branciari metrics are some examples of metrics provided in this field. The aim of this paper is to present some common fixed point results for two mappings (one of them is weakly isotone increasing with respect to another) in the framework of ordered $p$-metric spaces. Our results are generalizations of the presented results in [H. K. Nashine, B. Samet and C. Vetro, Math. Comput. Modelling, 54 (2011) 712–720] and [ J.R. Roshana, V. Parvaneh and Z. Kadelburg, J.Nonlinear Sci. Appl., 7 (2014), 229--245]. An example is also provided to support our results.