The simple chaotic model of passive dynamic walking

Recent findings on the dynamical analysis of human locomotion characteristics such as stride length signal have shown that this process is intrinsically a chaotic behavior. The passive walking has been defined as walking down a shallow slope without using any muscular contraction as an active controller. Based on this definition, some knee-less models have been proposed to present the simplest possible models of human gait. To maintain stability, these simple passive models are compelled to show a wide range of different dynamics from order to chaos. Unfortunately, based on simplifications, for many years the cyclic period-one behavior of these models has been considered as the only stable response. This assumption is not in line with the findings about the nature of walking. Thus, this paper proposes a novel model to demonstrate that the knee-less passive dynamic models also have the ability to model the chaotic behavior of human locomotion with some modifications. The presented novel model can show chaotic behavior as a stable and acceptable answer using a chaotic function in heel-strike condition. The represented chaotic model is also able to simulate different types of motor deficits such as Parkinson’s disease only by manipulating the value of chaotic parameter. Our model has extensively examined in complexity and chaotic behavior using different analytical methods such as fractal dimension, bifurcation and largest Lyapunov exponent, and it was compared with conventional passive models and the stride signal of healthy subjects and Parkinson patients.     

Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams

This article deals with the wave propagation analysis of single/double layered functionally graded (FG) size-dependent nanobeams in elastic medium and subjected to a longitudinal magnetic field employing nonlocal elasticity theory. Material properties of nanobeam change gradually according to the sigmoid function. Applying an analytical solution, the acoustical and optical dispersion relations are explored for various wave number, nonlocality parameter, material composition, elastic foundation constants, and magnetic field intensity. It is found that frequency and phase velocity of waves propagating in S-FGM nanobeam are significantly affected by these parameters. Also, presence of cut-off and escape frequencies in wave propagation analysis of embedded S-FGM nanobeams is investigated.     

Motives and periods in Bianchi IX gravity models

We show that, when considering the anisotropic scaling factors and their derivatives as affine variables, the coefficients of the heat-kernel expansion of the Dirac–Laplacian on SU(2) Bianchi IX metrics are algebro-geometric periods of motives of complements in affine spaces of unions of quadrics and hyperplanes. We show that the motives are mixed Tate and we provide an explicit computation of their Grothendieck classes.     

Feasibility study on reducing lead and cadmium absorption by spinach (Spinacia oleracea L.) in a contaminated soil using nanoporous activated carbon

Activated carbons (AC) have been long recognized as prominent absorbents in industries and feature numerous applications in preventing or absorbing the harmful gases and liquids and could be employed for filtration and remediation or even reutilization of chemicals. In order to investigate the capacity of AC in reducing the absorption of heavy metals (HM) including lead (Pb) and cadmium (Cd) and dual complex (Pb?×?Cd) by spinach, a factorial experiment in a completely randomized design with three replications on a pot trial was conducted. Three factors including five levels of AC 0, 5000, 10000, 15000, 20000?mg/kg soil, one concentration level of Pb 4,000?mg/kg soil and one concentration level of cadmium Cd 8?mg/kg soil were tested. The index of heavy metal concentration was calculated in leaf, stem and root and their corresponding dry weights. Results illustrated that in contaminated soils, plants with AC exhibited a superior reduction of absorption of HM vis-à-vis the plants without AC. The foremost result regarding the impact of AC on reducing the concentration of Pb and Cd was observed in 20,000 level of AC. This reveals that AC declined the soil contamination and lessened the accumulation of HM into the shoots and roots. Results suggest that the application of AC may be an eligible solution for decreasing the translocation of HM into the plants.     

Development of data-based model-free representation of non-conservative dissipative systems

A general procedure is presented for developing data-based, non-parametric models of non-linear multi-degree-of-freedom, non-conservative, dissipative systems. Two broad classes of methods are discussed: one relying on the representation of the system restoring forces in a polynomial-basis format, and the other using artificial neural networks to map the complex transformations relating the system state variables to the needed system outputs. A non-linear two-degree-of-freedom system is used to formulate the approach under discussion and to generate synthetic data for calibrating the efficiency of the two methods in capturing complex non-linear phenomena (such as dry friction, hysteresis, dead-space non-linearities, and polynomial-type non-linearities) that are widely encountered in the applied mechanics field. Subsequently, a reconfigurable test apparatus was used to generate experimental measurements from a physical non-linear “joint” involving two-dimensional motion (translation and rotation) and complicated interaction forces between the different motion axes, among its internal elements. Both the polynomial-basis approach and the neural network method were used to develop high-fidelity, non-parametric models of the physical test article. The ability of the identified models to accurately “generalize” the essential features of the non-linear system was verified by comparing the predictions of the models with experimental measurements from data sets corresponding to different excitations than those used for identification purposes. It is shown that the identification techniques under discussion can be useful tools for developing accurate simulation models of complex multi-dimensional non-linear systems under broadband excitation.     

Synthesis and application of polythiophene-coated Fe3O4 nanoparticles for preconcentration of ultra-trace levels of cadmium in different real samples followed by electrothermal atomic absorption spectrometry

In this research, magnetic Fe₃O₄ nanoparticles were synthesised by co-precipitation method and modified with polythiophene (PT) to produce Fe₃O₄-PT nanoparticles for preconcentration and determination of cadmium (??) ion followed by electrothermal atomic absorption spectrometry. The results of FT-IR spectroscopy, EDX analysis and SEM images show that Fe₃O₄-PT nanoparticles were synthesised successfully. Different parameters such as sample pH, amounts of adsorbent, sample volume, extraction time, type and concentration of eluent and desorption time were completely investigated and optimum conditions were selected.

Under the optimum conditions, the calibration curve was linear in the range of 0.01–0.25 µg L^?1 of cadmium (??). The relative standard deviation was 4.7% (n = 7, 0.10 µg L^?1 Cd²⁺) and limit of detection was 3.30 ng L^?1. The accuracy of the proposed method was verified by the analysis of a certified reference material and spike method. Finally, the proposed method was applied for the determination of ultra-trace levels of cadmium (??) in different water and food samples.     

Fischer–Tropsch synthesis: evaluation of Gd and Ru promoters effect on Co/<Emphasis Type="Italic">γ</Emphasis>-Al<Subscript>2</Subscript>O<Subscript>3</Subscript> catalyst at different conditions

In this study, the effect of Ru and Gd promoters on 15Co/\(\gamma\)-Al₂O₃ catalyst in the Fischer–Tropsch synthesis is investigated. The catalysts were synthesized by dry impregnation method and characterized by XRD, adsorption/desorption of nitrogen, TPR, TEM, ICP and XPS analyses. Activity and selectivity of the catalysts were examined in a fixed bed reactor at 210–230 °C with a H₂/CO ratio of 2 and atmospheric pressure. The results showed that the Ru-promoted catalyst has the highest activity and methane selectivity which reduce the chain growth probability. The Gd-promoted catalyst was shown smaller particle size and higher dispersion of cobalt particles in compared with unpromoted catalyst. The smaller particles have more interaction and thus show the lower catalyst reducibility. The presence of Gd in the catalyst cause higher chain growth probability compared to the unpromoted one. The Ru–Gd-promoted catalysts were shown a synergic effect in the catalyst reducibility. Based on the screening of the catalysts in the atmospheric pressure; the unpromoted, 0.1Ru/15Co/Al₂O₃, and 0.1Ru1Gd/15Co/Al₂O₃ catalysts were selected to test at high pressure conditions, which the 0.1Ru1Gd/15Co catalyst showed the highest C₅ ⁺ selectivity (75%) compared with the 0.1Ru/15Co/Al₂O₃ and the unpromoted one.     

Photocatalytic Ring Opening of α-Epoxyketones: 1,3-Dioxolane Formation

 Photocatalytic ring opening of α-epoxyketones by 2,4,6-triphenylpyrylium tetrafluoroborate in acetone resulted in the formation of 1,3-dioxolanes as major products through C–O bond cleavage and the formation of alcoholic by-products through C–C bond cleavage. The type and nature of the substituent affects the rate of ring opening.     

The presentation of an approach for estimating the intramolecular hydrogen bond strength in conformational study of β-Aminoacrolein

All the plausible conformations of β-aminoacrolein (AMAC) have been investigated by the Bekes-Lee-Yang-Parr (B3LYP) nonlocal density functional with extended 6-311++G** basis set for studying the stability order of conformers and the various possibilities of intramolecular hydrogen bonding formation. In general the ketoamine (KA) conformers of AMAC, by mean average, are more stable than the corresponding enolimine (EI) and ketoimine (KI) analogues and this stability is mainly due to the π-electron resonance in these conformers that established by NH2 functional group. The contribution of resonance to the stability of chelated KA conformers is about 75.6 kJ/mol, which is greater than that of the hydrogen bond energy (E_HB=35.0 kJ/mol). The relative decreasing order of the various hydrogen bond energies was found to be: O–HN_imine(strong)>N_amine-HO_keto (normal)>N_imine-HO_hydroxyl (weak) > N_imine-HO_keto (weak). Hydrogen bond energies for all systems were obtained from the method that we called related rotamers method (RRM). The topological properties of the electron density contributions for various type of intramolecular hydrogen bond have been analyzed in term of the Bader theory of atoms in molecules (AIM). The results of these calculations support the previous calculations, which obtained by the related rotamer methods.