Solutions for the double Sine‐Gordon equation by Exp‐function,Tanh, and extended Tanh methods

In this work, we implement some analytical techniques such as the Exp‐function, Tanh, and extended Tanh methods for solving nonlinear partial differential equation, which contains sine terms, its name Double Sine‐Gordon equation. These methods obtain exact solutions of different types of differential equations in engineering mathematics. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

A Geometric Theory of Growth Mechanics

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. The time dependence of the metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and “shape”. We show that the time dependency of the material metric will affect the energy balance and the entropy production inequality; both the energy balance and the entropy production inequality have to be modified. We then obtain the governing equations covariantly by postulating invariance of energy balance under time-dependent spatial diffeomorphisms. We use the principle of maximum entropy production in deriving an evolution equation for the material metric. In the case of isotropic growth, we find those growth distributions that do not result in residual stresses. We then look at Lagrangian field theory of growing elastic solids. We will use the Lagrange–d’Alembert principle with Rayleigh’s dissipation functions to derive the governing equations. We make an explicit connection between our geometric theory and the conventional multiplicative decomposition of the deformation gradient, F=F _e F _g, into growth and elastic parts. We linearize the nonlinear theory and derive a linearized theory of growth mechanics. Finally, we obtain the stress-free growth distributions in the linearized theory.     

Nonlinear dynamics of tapping mode atomic force microscopy in the bistable phase

Nonlinear dynamics of amplitude modulation atomic force microscopy (AFM) is studied employing a reduced-order model based on a differential quadrature method (DQM). The AFM microcantilever is assumed to be operating in the dynamic contact or tapping mode while the microcantilever tip being initially located in the bistable region. We have found that the DQM is capable of precise prediction of the static bifurcation diagram and natural frequencies of the microcantilever. We have used the DQM to discretize the partial-differential equation governing the microcantilever motion and a finite difference method (FDM) to calculate limit-cycle responses of the AFM tip. It is shown that a combination of the DQM and FDM applied, respectively, to discretize the spatial and temporal derivatives provides an efficient, accurate procedure to address the complicated dynamic behavior exhibited by the AFM probe. The procedure was, therefore, utilized to study the response of the microcantilever to a base harmonic excitation through several numerical examples. We found that the dynamics of the AFM probe in the bistable region is totally different from those in the monostable region.     

The experimental/numerical investigation of variations in strip speed,water shower pattern and water temperature on high-temperature strip cooling rate in hot strip mill

Journal of Thermal Analysis and Calorimetry - Hot-rolled strips are cooled on the run-out table to achieve the customer-required mechanical properties. Cooling reduces the oxidation, which can...     

Potential energy and atomic stability of H2O/CuO nanoparticles flow and heat transfer in non-ideal microchannel via molecular dynamic approach: the Green–Kubo method

Journal of Thermal Analysis and Calorimetry - It is interesting to investigate the number of nanoparticle (NP) and temperature effects on H2O/CuO nanofluid thermal conductivity and the atomic...     

Free vibration and stability of an axially moving thin circular cylindrical shell using multiple scales method

This paper investigates the linear free vibration of axially moving simply supported thin circular cylindrical shells with constant and time-dependent velocity considering the effect of viscous structure damping. Classical shell theory is employed to express strain-displacement relation. Linear elasticity theory is used to write stress–strain relation considering Hook’s Law. Governing equations in cylindrical coordinates are derived using the Hamilton principle. Equilibrium equations are rewritten with the help of Donnell–Mushtari shell theory simplification assumptions. Motion equations for displacements in axial and circumferential directions are solved analytically concerning to displacement in the radial direction. As the displacement in the radial direction is the combination of driven and companion modes, the third motion equation is discretized using the Galerkin method. The set of ordinary differential equation obtained from the Galerkin method is solved using the steady-state method, which in practice leads to the prediction of the exact frequencies of vibration. By employing multiple scale method the critical speed values of a circular cylindrical shell and several types of instabilities are discussed. The numerical results show that by increasing the mean velocity, the system always loses stability by the divergence instability in different modes, and the critical speed values of lower modes are higher than those of higher modes. As well as the unstable regions for the resonances between velocity function fluctuation frequencies and the linear combination of natural frequencies is gained from the solvability condition of second order multiple scale method. The accuracy of the method is checked against the available data.

     

Distinguishing and quantification of the human visual pathways using high-spatial-resolution diffusion tensor tractography

Quantification of the living human visual system using MRI methods has been challenging, but several applications demand a reliable and time-efficient data acquisition protocol. In this study, we demonstrate the utility of high-spatial-resolution diffusion tensor fiber tractography (DTT) in reconstructing and quantifying the human visual pathways. Five healthy males, age range 24–37 years, were studied after approval of the institutional review board (IRB) at The University of Texas Health Science Center at Houston. We acquired diffusion tensor imaging (DTI) data with 1-mm slice thickness on a 3.0-Tesla clinical MRI scanner and analyzed the data using DTT with the fiber assignment by continuous tractography (FACT) algorithm. By utilizing the high-spatial-resolution DTI protocol with FACT algorithm, we were able to reconstruct and quantify bilateral optic pathways including the optic chiasm, optic tract, optic radiations free of contamination from neighboring white matter tracts.     

Energy and exergy analysis and optimization of a gas turbine cycle coupled by a bottoming organic Rankine cycle

Journal of Thermal Analysis and Calorimetry - In this study, the numerical analysis of energy and exergy has been performed for a gas turbine cycle coupled with an ORC cycle. Validation of current...     

Spatiotemporal patterns of stable isotopes and hydrochemistry in springs and river flow of the upper Karkheh River Basin,Iran

Karst springs of the Zagros Mountains contribute a significant amount to agricultural and human water demands of western and south-western Iran. For an adequate management of available water resources in semi-arid and arid regions, sufficient hydrological monitoring is needed, and hydro-chemical and isotope hydrological data provide important additional information. About 350 water samples were collected from precipitation, river water, and karst springs of the upper part of the Karkheh River Basin (20,895 km²) located between 33°35^′ and 34°55^′ North and 46°22^′ and 49°10^′ East with elevations ranging from 928 to 3563 m above sea level. Sampling was conducted in monthly time resolution from August 2011 to July 2012. All samples were analysed for hydro-chemical parameters (pH, electrical conductivity, and major ions) and stable isotopes (deuterium, oxygen-18). Isotope values of precipitation indicate a local meteoric water line (Zagros MWL δ²H=6.8 δ¹⁸O+10.1; R²=0.99) situated between the Mediterranean MWL and Global MWL. Spring and river water isotope values vary between?7.1 and?4.1 ‰, and?38 and?25 ‰ for δ¹⁸O and δ²H, respectively, responding to winter snowmelt and evaporation. This work implements stable isotopes and hydro-chemical information of springs and river water to understand hydrological and hydro-geological interrelations in karstic semi-arid areas and helps to improve the current water resources management practices of western Iran.     

Synthesis and characterization of copper(II) Schiff base complex supported on Fe3O4 magnetic nanoparticles: a recyclable catalyst for the one‐pot synthesis of 2,3‐dihydroquinazolin‐4(1H)‐ones

Fe₃O₄–Schiff base of Cu(II) is found to be a recyclable and heterogeneous catalyst for the rapid and efficient synthesis of various 2,3‐dihydroquinazolin‐4(1H)‐one derivatives from the two‐component condensation of 2‐aminobenzamide and an aldehyde. This reaction is simple, green and cost‐effective. Separation and recycling can also be easily done by magnetic decantation of the Fe₃O₄ nanoparticles with an external magnet. The prepared catalyst was characterized using thermogravimetry, Fourier transform infrared spectroscopy, vibrating sample magnetometry, inductively coupled plasma analysis, X‐ray diffraction and scanning electron microscopy. Copyright © 2015 John Wiley & Sons, Ltd.