Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part I: Theoretical formulations

The potential applications of nanoplates in energy storage, chemical and biological sensors, solar cells, field emission, and transporting of nanocars have been attracted the attentions of the nanotechnology community to them during recent years. Herein, the later application of nanoplates from nonlocal elastodynamic point of view is of interest. To this end, dynamic response of a nanoplate subjected to a moving nanoparticle is examined within the context of nonlocal continuum theory of Eringen. The fully simply supported nanoplate is modeled based on the nonlocal Kirchhoff, Mindlin, and higher-order plate theories. The non-dimensional equations of motion of the nonlocal plate models are established. The effects of moving nanoparticle's weight and existing friction between the surfaces of the moving nanoparticle and nanoplate on the in-plane and out-of-plane vibrations of the nanoplate are incorporated into the formulations of the proposed models. The eigen function expansion and the Laplace transform methods are employed for discretization of the governing equations in the spatial and the time domains, respectively. The analytical expressions of the dynamic deformation field associated with each nonlocal plate theory are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight path (an opened path) as well as an ellipse path (a closed path). The dynamic in-plane forces and moments of each nonlocal plate model are also derived. Furthermore, the critical velocity and the critical angular velocity of the moving nanoparticle for the proposed models are expressed analytically for the aforementioned paths. Part II of this work consists in a comprehensive parametric study where the effects of influential parameters on dynamic response of the proposed nonlocal plate models are scrutinized in some detail.     

Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part II: Parametric studies

The possible usage of nanoplates in transporting of nanovehicles encouraged the author to propose some nonlocal plate models in the companion paper where the nanovehicle (i.e., moving nanoparticle) was modeled by a moving point load by considering its friction with the upper surface of the nanoplate. In this paper, a comprehensive parametric study is carried out to study the effects of length to thickness ratio of the nanoplate, small-scale parameter, and velocity (or angular velocity) of the moving nanoparticle on dynamic response of nonlocal Kirchhoff, Mindlin, and higher-order plates subjected to a moving nanoparticle. Herein, dynamic response of the nanoplate covers both time histories and dynamic amplitude factors of the in- and out-of-plane displacements. The capabilities of various nonlocal plate models in predicting the displacement field caused by friction and mass weight of the moving nanoparticle are then explored through various numerical analyses for two cases: (i) the moving nanoparticle moves along a diagonal of the nanoplate; (ii) the moving nanoparticle orbits on an ellipse path whose center is coincident with the nanoplate's center. The obtained results indicate that due to the incorporation of small-scale effect into shear strain energy of the nanoplate, an appropriate nonlocal plate model should be used. The results show that the choice of the nanoplate model to use relies on the small-scale parameter, geometrical properties of the nanoplate, and velocity of the moving nanoparticle.     

Free and forced vibrations of graphene platelets reinforced composite laminated arches subjected to moving load

Meccanica - In the present investigation, free vibration and also forced vibration response of a graphene platelet reinforced composite (GPLRC) laminated curved beam is investigated. It is assumed...     

Rules for macropolyhedral boranes

Based on extensive computational studies, rules to derive the thermodynamically most stable macropolyhedral borane for any formula between B_nH_n−4 to B_nH_n+8 were identified. Formally, the macropolyhedral boranes may be obtained by condensing regular convex borane clusters where as many BH₃ moieties are eliminated as vertexes are shared in the macropolyhedral framework. Macropolyhedral boranes consisting of two cluster fragments may be classified according to their general formulae ranging from B_nH_n−4 to B_nH_n+8. For each of these formulae, various structure types are conceivable differing in the number of shared vertexes and in the types of combined cluster fragments. However, for each general formula, only one structure type is known experimentally and this one is also computationally found to be thermodynamically preferred! For each class of macropolyhedral B_nH_m boranes, a preferred number of shared vertexes is identified, and this determines the number of skeletal electron pairs. With this knowledge, the type of fused clusters, i.e. the most favourable framework, may be predicted. The concept of preferred fragments may be applied to even predict the distribution of vertexes among the fused fragments in the thermodynamically most stable isomers. When there is at least one closo fragment it has 12-vertexes. Without any closo fragment the most stable macropolyhedral borane has a nido 10-vertex cluster fragment.     

Synthesis of core–shell magnetic ion-imprinted polymer nanospheres for selective solid-phase extraction of Pb2+ from biological,food, and wastewater samples

Magnetic ion-imprinted polymer nanospheres, which have core–shell structures, have been synthesized as an adsorbent for extraction of Pb²⁺ from real samples prior to its flame atomic absorption spectrometric determination. The prepared adsorbent has been characterized using XRD, VSM, TEM, and FTIR measurements. The optimization results revealed that the adsorbent exhibited high selectivity toward Pb²⁺ over other cations such as Cu²⁺ and Zn²⁺. In addition, the removal efficiency of synthesized adsorbent was considerable (q_m?=?171.42?mg g^?1), its calibration curve was linear (0.5?850.0?ng mL^?1), and detection limit was 0.01?ng mL^?1. These results suggested that the prepared nanoadsorbent is an ideal candidate for solid-phase extraction of Pb²⁺ ions.     

A combined computational and experimental study of methane activation during oxidative coupling of methane (OCM) by surface metal oxide catalysts

The experimentally validated computational models developed herein, for the first time, show that Mn-promotion does not enhance the activity of the surface Na₂WO₄ catalytic active sites for CH₄ heterolytic dissociation during OCM. Contrary to previous understanding, it is demonstrated that Mn-promotion poisons the surface WO₄ catalytic active sites resulting in surface WO₅ sites with retarded kinetics for C–H scission. On the other hand, dimeric Mn₂O₅ surface sites, identified and studied via ab initio molecular dynamics and thermodynamics, were found to be more efficient in activating CH₄ than the poisoned surface WO₅ sites or the original WO₄ sites. However, the surface reaction intermediates formed from CH₄ activation over the Mn₂O₅ surface sites are more stable than those formed over the Na₂WO₄ surface sites. The higher stability of the surface intermediates makes their desorption unfavorable, increasing the likelihood of over-oxidation to CO_x, in agreement with the experimental findings in the literature on Mn-promoted catalysts. Consequently, the Mn-promoter does not appear to have an essential positive role in synergistically tuning the structure of the Na₂WO₄ surface sites towards CH₄ activation but can yield MnO_x surface sites that activate CH₄ faster than Na₂WO₄ surface sites, but unselectively.

The experimentally validated computational models developed herein, for the first time, show that Mn-promotion does not necessarily enhance the activity of the surface Na₂WO₄ catalytic active sites for CH₄ heterolytic dissociation during OCM.     

Commuting Graphs of Group Algebras

The commuting graph of a ring R, denoted by Γ(R), is a graph of all whose vertices are noncentral elements of R, and 2 distinct vertices x and y are adjacent if and only if xy = yx. In this article we investigate some graph-theoretic properties of Γ(kG), where G is a finite group, k is a field, and 0 ≠ |G| ∈k. Among other results it is shown that if G is a finite nonabelian group and k is an algebraically closed field, then Γ(kG) is not connected if and only if |G| = 6 or 8. For an arbitrary field k, we prove that Γ(kG) is connected if G is a nonabelian finite simple group or G′ ≠ G″ and G″ ≠ 1.     

Betti Numbers of Path Ideals of Trees

Let R = k[x₁,…, x_n], where k is a field. The path ideal (of length t) of a directed graph G is the monomial ideal, denoted by I_t(G), whose generators correspond to the directed paths of length t in G. We determine all the graded Betti numbers of the path ideal of a directed rooted tree with respect to some graphical terms.     

Finding common weights based on the DM's preference information

Data Envelopment Analysis (DEA) is basically a linear programming-based technique used for measuring the relative performance of organizational units, referred to as Decision Making Units (DMUs). The flexibility in selecting the weights in standard DEA models deters the comparison among DMUs on a common base. Moreover, these weights are not suitable to measure the preferences of a decision maker (DM). For dealing with the first difficulty, the concept of common weights was proposed in the DEA literature. But, none of the common weights approaches address the second difficulty. This paper proposes an alternative approach that we term as ‘preference common weights’, which is both practical and intellectually consistent with the DEA philosophy. To do this, we introduce a multiple objective linear programming model in which objective functions are input/output variables subject to the constraints similar to the equations that define production possibility set of standard DEA models. Then by using the Zionts–Wallenius method, we can generate common weights as the DM's underlying value structure about objective functions.