Sub-Angstrom oscillation amplitude non-contact atomic force microscopy for lateral force gradient measurement

We report the first results from novel sub-Angstrom oscillation amplitude non-contact atomic force microscopy developed for lateral force gradient measurements. Quantitative lateral force gradients between a tungsten tip and Si(1 1 1)-(7 × 7) surface can be measured using this microscope. Simultaneous lateral force gradient and scanning tunnelling microscope images of single and multi atomic steps are obtained. In our measurement, tunnel current is used as feedback. The lateral stiffness contrast has been observed to be 2.5 N/m at single atomic step, in contrast to 13 N/m at multi atomic step on Si(1 1 1) surface. We also carried out a series of lateral stiffness-distance spectroscopy. We observed lateral stiffness-distance curves exhibit sharp increase in the stiffness as the sample is approached towards the surface. We usually observed positive stiffness and sometimes going into slightly negative region.     

Lovelock tensor as generalized Einstein tensor

We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, with the aid of a generalized trace operator which we define, for any inhomogeneous Euler–Lagrange expression that can be spanned linearly in terms of homogeneous tensors. Then, through an application of this generalized trace operator, we demonstrate that the Lovelock tensor analogizes the mathematical form of the Einstein tensor, hence, it represents a generalized Einstein tensor. Finally, we apply this technique to the scalar Gauss–Bonnet gravity as an another version of string–inspired gravity. This work was partially supported by a grant from the MSRT/Iran.     

Computer simulation study of the Levy flight process

The random walk simulation of a Levy flight shows a linear relation between the mean square displacement 〈r²〉 and time. We have analyzed different aspects of this linearity. It is shown that the restriction of jump length to a maximum value (l_m) affects the diffusion coefficient, even though it remains constant for l_m greater than 1464. So, this factor has no effect on the linearity. In addition, it is shown that the number of samples does not affect the results. We have demonstrated that the relation between the mean square displacement and time remains linear in a continuous space, while continuous variables just reduce the diffusion coefficient. The results also imply that the movement of a Levy flight particle is similar to the case in which the particle moves in each time step with an average jump length 〈l〉. Finally, it is shown that the non-linear relation of the Levy flight will be satisfied if we use a time average instead of an ensemble average. The difference between the time average and ensemble average results shows that the Levy distribution may be a non-ergodic distribution.     

The effect of solute—membrane affinity on cyclic hydrocarbon—water transport in pressure-driven membrane separation processes

Experimental results for the pressure-driven membrane separation of cyclic hydrocarbons (1,3-cyclohexadiene, cyclohexene, and cyclohexane) from dilute binary aqueous solution using asymmetric cellulose acetate membranes are reported here. In these experiments, total solution fluxes are significantly lower than pure water fluxes at the same applied pressure; this flux reduction is attributed to strong solute—membrane affinity rather than to the osmotic pressure of either the bulk retentate or the boundary layer. An empirical parameter, Z, is used to describe flux reduction. A theoretically based friction parameter, B, is derived assuming the membrane can be represented as an ideal, finely porous membrane; this parameter indicates the influence of solute—membrane affinity on flow through the pores of the membrane. Both the empirical parameter Z and the theoretically based parameter B relate flux reduction to concentrations in the system. Both Z and B increase as solute—membrane affinity increases and decrease as membrane pore size increases. It is concluded that both the empirical flux reduction parameter, Z, and the theoretically based friction parameter, B, indicate the same system properties: solute—membrane affinity and membrane pore size.     

New concepts of regular and (highly) irregular vague graphs with applications

In this paper, some types of vague graphs are introdaced such as $d_m$-regular, $t{d}_m$-regular, $m$-highly irregular and $m$-highly totally irregular vague graphs are introduced and some properties of them are discussed. Comparative study between $d_m$-regular ($m$-highly irregular) vague graph and $t{d}_m$-regular ($m$-highly totally irregular) vague graph are done. In addition, $d_m$-regularity and $m$-highly irregularity on some vague graphs, which underlying crisp graphs are a cycle or a path is also studied. Finally, some applications of regular vague graphs are given for demonstration of fullerene molecules, road transport network and wireless multihop networks.     

The kinetic and thermodynamic study of the removal of Cr(VI) ion from aqueous solution by human hair waste

The removal of Cr(VI) ions from aqueous solution by human hair waste is investigated by using UV–Vis spectrophotometer technique. The morphological analysis of the human hair was also investigated by the scanning electron microscopy, Fourier transforms infrared spectroscopy and X-ray photoelectron spectroscopy. The influence of various physicochemical effective parameters such as pH, ionic strength, adsorbent amount, contact time, initial concentration of metal ion on removal of Cr(VI) ions by human hair process was also studied. The optimum conditions for this adsorption process were obtained at pH = 2 and contact time of 150 min while the highest Cr(VI) uptake is recorded for 0.5 g of the adsorbent per 100 ml of solution. Three isotherms models including Langmuir, Freundlich and Temkin were applied to describe the equilibrium data. It was found that the experimental data were well described by Freundlich isothermal model. The maximum adsorption capacity was found to be 11.64 mg g^?1.The thermodynamic study data showed that the adsorption process of Cr(VI) on human hair is an endothermic, spontaneous and physisorption reaction. The kinetics of the adsorption process was studied using three kinetics models including Lagergren-first-order, pseudo-second-order and Elovich model. The obtained data are indicated that the adsorption processes of Cr(VI) over human hair could be described by the pseudo-second-order kinetic model.     

Conservation laws and constitutive relations for density-gradient-dependent viscous fluids

Conservation laws and constitutive relations for a density-gradient-dependent viscous fluid as a multipolar continuum obeying an entropy inequality with generalized entropy flux and supply density are considered in this paper. A decomposition of the rate of work of dipolar stress, which reveals the contribution of various parts of this stress to the energy equation, is used to discuss the inconsistencies between the results obtained here and those obtained by Bluestein and Green [1] on the basis of the pioneering work of Green and Rivlin [8]. Furthermore, we discuss the connection between the model presented here and the materials of Korteweg type considered by Dunn and Serrin [6]. In particular, we relate the rate of work of dipolar stress and the interstitial working introduced by Dunn and Serrin [6].Received: 3 April 2004, Accepted: 6 December 2004, Published online: 4 March 2005 Correspondence to: M.M. Mehrabadi     

Material symmetry and the evolution of anisotropies in a simple material—II. The evolution of material symmetry

A proper evolutionary definition of material symmetry is presented. The evolution of a material's symmetries as the material undergoes a deformation history is followed, and a procedure for the identification of those changes which are common to all simple materials is provided. Explicit results are presented for initially isotropic, transversely isotropic, and orthotropic materials undergoing simple deformation histories.     

A new phosphorothioic triamide structure: P(S)[NHCH2C6H5]3

The structure of N,N′,N′′‐tribenzylphosphorothioic triamide, C₂₁H₂₄N₃PS, (I), and analysis of the bond‐angle sums at the N atoms for this compound, and for 74 structures with a P(S)[N]₃ skeleton and the N atom in a three‐coordinate geometry found in the Cambridge Structural Database [CSD; Groom & Allen (2014). Angew. Chem. Int. Ed. 53 , 662–671], are reported. For (I), the bond‐angle sum at one of the N atoms [359 (1)°] shows a nearly planar configuration, while the other two show a nonplanar geometry with bond‐angle sums of 342 (1) and 347 (1)°. The location of the atoms attached to the nonplanar N atoms suggests an anti orientation of the corresponding lone electron pairs (LEPs) on these N atoms with respect to the P=S group. For 74 structures with a P(S)[N]₃ skeleton and with the N atom in a three‐coordinate geometry, the bond‐angle sums at the N atoms were found to be in the range 293–360°. Among 307 such three‐coordinate N atoms, 39% (120 N atoms) have bond‐angle sums in the range 359–360°, in accordance with sp² hybridization, and 45% (138 N atoms) have bond‐angle sums in the range 352–359°, with hybridization close to sp². For the orientation of the LEP with respect to the P=S group, the anti orientation was found to be a general rule for N atoms, with the corresponding bond‐angle sums deviating by more than 8° from the planar value of 360°. In the title structure, the S atom takes part in intermolecular (N—H...)(N—H...)S hydrogen bonds, connecting the molecules into extended chains parallel to the b axis. The co‐operation of one N atom in an N—H...S hydrogen bond as an H‐atom donor, and in an N—H...N hydrogen bond as an acceptor, is a novel feature of the crystal structure.