Power-law Variation Research Articles

Fiber coupling efficiency for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

Nowadays it has been accepted that the Kolmogorov model is not the only possible turbulent one in the atmosphere, which has been confirmed by the increasing experimental evidence and some results of theoretical investigation. This has prompted the scientist community to study optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using the method of effective beam parameters and a non-Kolmogorov power spectrum which has a more general power law instead of standard Kolmogorov power law value 11/3 and a more general amplitude factor instead of constant value 0.033, the fiber coupling efficiency for a Gaussian-beam wave has been derived for a horizontal path in both weak and strong fluctuation regimes. And then the influence of spectral power law variations on the fiber coupling efficiency has been analyzed. It is anticipated that this work is helpful to the investigations of atmospheric turbulence and optical wave propagation in the atmospheric turbulence.

Magnetic properties of Fe3O4 nano-hollow spheres

We prepared magnetite nano-hollow spheres with diameter 100–725nm using solvothermal method. We studied the magnetic domain structures of the spheres and found them to vary from single domain for smaller diameter to multi-domain structure for the spheres of larger diameter. We also reported the frequency dependence of their magnetic properties and interestingly, found a systematic power law variation in coercivity and hysteresis loss with frequency, magnetic field strength and also with hollow sphere diameter. The results clearly represent that the domain wall width or the number of domains depends not only on the sphere diameter but also on the applied field frequency.

MAGNETIC AND ELECTRICAL PROPERTIES OF ELECTRON BEAM GUN DEPOSITED [Mn/Al] MULTILAYERED FILMS

By following electron beam gun evaporation technique, the magnetic multilayers in the configuration, [Mn(60nm)/Al(20nm)]n; n =1, 2 and 9 were deposited at 473K, under high vacuum conditions. From grazing incidence X- ray diffraction (GIXRD) studies, the grain sizes were determined and they were in the order of few nanometers. Atomic force microscope (AFM) were employed to study surface structure and grain sizes. The magnetization as a function of field at 150K and 200K have been measured using the MPMS SQUID - vibrating sample magnetometer (VSM). From the hysteresis loops, coercive field, saturation magnetization, remanent magnetization and antiferromagnetic coupling were determined. All the three films hinted at the existence of at antiferromagnetic interaction between Mn layers through Al layer. Electrical resistivity in the temperature range from 5K to 300K has been measured. Films exhibited semiconducting to metallic transition. The power law variation of resistivity with temperature was established for the metallic region. Conductivity data for semiconducting region of a film has been analysed using polaran hopping models, activation energy and density of states at Fermi level were established. This is for the first time that antiferromagnetic coupling between Mn layers through interfacer layer and semiconducting to metallic transition have been noticed in the present configuration of [Mn/Al] multilayers.

Scattering by circular cavity in radially inhomogeneous medium with wave velocity variation

Based on the theory of complex function and the principle of homogenization, harmonic dynamics stress of a radially infinite inhomogeneous medium with a circular cavity is investigated. Due to the symmetry, wave velocity is assumed to have power-law variation in the radial direction only, and the shear modulus is constant. The Helmholtz equation with a variable coefficient is equivalently transformed into a standard Helmholtz equation with a general conformal transformation method (GCTM). The displacements and stress fields are proposed. Numerical results show that the wave number and the inhomogeneity parameter of the medium have significant effects on the dynamic stress concentration around the circular cavity. The dynamic stress concentration factor (DSCF) becomes singular when the inhomogeneity parameter of medium is close to zero.

A general third-order theory of functionally graded plates with modified couple stress effect and the von Kármán nonlinearity: theory and finite element analysis

Finite element analysis of functionally graded plates based on a general third-order shear deformation plate theory with a modified couple stress effect and the von Karman nonlinearity is carried out to bring out the effects of couple stress, geometric nonlinearity and power-law variation of the material composition through the plate thickness on the bending deflections of plates. The theory requires no shear correction factors. The principle of virtual displacements is utilized to develop a nonlinear finite element model. The finite element model requires C1 continuity of all dependent variables. The microstructural effects are captured using a length scale parameter via the modified couple stress theory. The variation of two-constituent material is assumed through the thickness direction according to a power-law distribution. Numerical results are presented for static bending problems of rectangular plates with various boundary conditions to bring out the parametric effects of the power-law index and length scale parameter on the load–deflection characteristics of plates with various boundary conditions.

On measuring fracture toughness under load control in the presence of slow crack growth

The influence of slow crack growth in ceramics on the measurement of their fracture toughness under steadily increasing controlled load (as is generally practiced in microscale testing) is analyzed to identify conditions under which the phenomenon can cause error. The analysis considers the two regimes classically observed, namely a power-law variation of crack growth rate on the stress intensity factor K, and, at higher K values, a regime of fixed crack tip velocity up to rapid fracture at K=Kc. Results are presented for standard test specimens in a convenient graphical form and also in the form of upper bound expressions for loading rates above which measurements should be valid. It is shown that, when subcritical crack growth is present, chevron-notched samples present advantages over more conventional precracked specimens.

Nondiffracting chirped Bessel waves in optical antiguides

Chirped Bessel waves are introduced as stable (nondiffracting) solutions of the paraxial wave equation in optical antiguides with a power-law radial variation in their index of refraction. Through numerical simulations, we investigate the propagation of apodized (finite-energy) versions of such waves, with or without vorticity, in antiguides with practical parameters. The new waves exhibit a remarkable resistance against the defocusing effect of the unstable index potentials, outperforming standard Gaussians with the same full width at half-maximum. The chirped profile persists even under conditions of eccentric launching or antiguide bending and is also capable of self-healing like standard diffraction-free beams in free space.

Temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

In the past decades, both the increasing experimental evidence and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, based on the thin phase screen model and a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave is derived in the weak fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the influence of spectral power law variations on the temporal power spectrum of irradiance fluctuations.

Natural convection heat and mass transfer in MHD fluid flow past a moving vertical plate with variable surface temperature and concentration in a porous medium

A numerical investigation of two-dimensional steady laminar free convection flow with heat and mass transfer past a moving vertical plate in a porous medium subjected to a transverse magnetic field is carried out. The temperature and concentration level at the plate surface are assumed to follow a power-law type of distribution. The governing non-linear set of equations is solved numerically employing a fully implicit finite difference method. Results are presented to illustrate the influence of different parameters such as Grashof number (Gr), porosity parameter (Kp), magnetic field parameter (Mn) and exponents in the power law variation of the surface temperature and concentration, m and n. The dimensionless velocity, temperature and concentration profiles are analyzed and numerical data for the local Nusselt number and Sherwood number are presented. The study accentuates the significance of the relevant parameters.

Three-dimensional flow of nanofluid over a non-linearly stretching sheet: An application to solar energy

This work deals with the three-dimensional flow of nanofluid over an elastic sheet stretched non-linearly in two lateral directions. Suitable boundary conditions showing the power-law variation in the velocities are imposed. Further the recently suggested model for nanofluid is considered that requires nanoparticle volume fraction at the wall to be passively rather than actively controlled. A set of similarity transformations are introduced to convert the boundary layer equations into self-similar forms. The solutions have been obtained numerically through shooting method with fourth-fifth-order Runge–Kutta integration technique. The results reveal that penetration depths of temperature and nanoparticle volume fraction are decreasing functions of the power-law index. We notice that impact of Brownian motion in the temperature and heat transfer rate from the sheet is insignificant.

Analysis of nanoindentation of functionally graded layered bodies with surface elasticity

Due to the high surface to volume ratio of the nanoscale domain, the surface stress effect is a major concern in the analysis of mechanical response of the nanomaterials and nanostructures. This paper presents a nonlinear variational numerical model for the analysis of frictionless indentation of a functionally graded layered homogeneous elastic bodies considering surface/interface stress effect in the context of contact mechanics. To accommodate the influence of surface/interface energy, the complete constitutive relation of the Gurtin–Murdoch elasticity theory is adopted, while the bulk material follows the classical theory of linear elasticity. The graded, nonhomogeneous property of the nanolayer follows a power law variation of the shear modulus, while a constant Poisson׳s ratio is considered. Utilizing the generalized isoparametric formulation, the graded finite element method is utilized to incorporate the material property gradient at the element scale. Throughout the indentation interface, the Lagrange multiplier approach is adopted to exactly satisfy the inequality contact constraints, where the indentation forces and the displacement field are treated as independent variables. Three nanoindentation problems of different natures are analyzed using the developed variational-based finite element computational model. The achieved results show the significance of the surface/interface energy, size-dependency, and the material distribution of functionally graded layer on the mechanical response of indentation processes.

Two-Frequency Mutual Coherence Function of a Gaussian Beam Pulse Propagated Through Non-Kolmogorov Turbulent Atmosphere

Over the past half century, satellite-laser-communication technology has been the focus in many countries and areas due to its higher data transmission rates, smaller terminals, low probability of intercept, etc. Much manpower and material and financial resources have been put into the development of this technology. Usually, longer pulses can be modeled as if they were continuous-wave pulses during the time when the pulse is transmitted. However, this is not the case for ultrashort pulses that are usually used as a carrier in satellite-laser communication. For satellite-to-ground or ground-to-satellite links, the atmospheric effects are more deleterious to the laser pulse and their analysis is also more complicated. For a long time, laser pulse propagation in the turbulent atmosphere were studied based on the Kolmogorov model. However, increasing experimental evidence and theoretical investigations have shown that the Kolmogorov model is not the only possible turbulent one in the atmosphere, and there exists another turbulence, namely, the non-Kolmogorov turbulence. So it is necessary to perform the analysis of the laser-pulse propagation in the non-Kolmogorov turbulence. The two-frequency mutual coherence function (MCF) plays an important pole in determining the basic characteristics associated with the laser-pulse propagating in the atmospheric turbulence. In this paper, we consider a theoretical power spectrum of the refractive-index fluctuations with a generalized power law, derive the two-frequency MCFs of a Gaussian-beam pulse in weak turbulence for a horizontal path, and analyze the influence of spectral power-law variations on the two-frequency MCFs. We present an analytical expression for a collimated-beam pulse.

Dielectric and thermal response of poly[(vinylidene chloride)-co -acrylonitrile]/poly(methyl methacrylate) blend membranes

Poly(methyl methacrylate) was mixed with poly[(vinylidene chloride)-co-acrylonitrile] (Saran-F) and lithium perchlorate in tetrahydrofuran to make polymer blend systems. Solvent-free membranes with various blend ratios were prepared using a solution casting technique. Impedance analysis was used to study the electrical response of the polymer membranes, which shows that the 50:50 wt% blend ratio polymer membrane has a low bulk resistance and high dielectric constant at room temperature and hence high ionic conductivity. The dielectric behaviour was analysed using dielectric permittivity and electric modulus of the samples. The conductance spectra follow the universal power law variation. Structural analysis confirms the amorphous nature and functional group analysis confirms the miscibility. The decomposition temperature of the membranes was determined using thermogravimetric analysis. © 2014 Society of Chemical Industry

A coupled finite–hierarchic infinite element method for an inhomogeneous transversely isotropic soil layer under irregularly distributed strip load

In this paper, a coupled finite–hierarchic infinite element procedure is presented for an inhomogeneous transversely isotropic soil layer under irregularly distributed strip load. Elasticity and shear moduli follow a power law variation with depth. Quadratic quadrangular finite elements are coupled with a coordinate ascent hierarchic infinite element along the bounded edge using a least square approximation. The element mesh is fixed. Convergence is reached by increasing the polynomial degree. Novel results are presented for the vertical displacement and normal stress induced by uniform, parabolic, and triangular strip loads. The method is found to converge rapidly when the polynomial degree is increased. The calculated results for a homogeneous isotropic soil layer under a triangular strip load are compared with exact solutions and show excellent agreement. A parametric analysis reveals that inhomogeneity, transverse isotropy, layer depth, and form of strip load have an important effect on the soil layer physical behavior.

A Semi-Analytical Study of Geometrically Nonlinear Free Axisymmetric Vibrations of Thin Circular Functionally Graded Plates Using Iterative and Explicit Analytical Solution

. This paper deals with nonlinear free axisymmetric vibrations of functionally graded thin circular plates (FGCP) whose properties vary through its thickness. The inhomogeneity of the plate is characterized by a power law variation of the Young’s modulus and mass density of the material along the thickness direction, whereas Poisson’s ratio is assumed to be constant. The theoretical model is based on Hamilton’s principle and spectral analysis using a basis of admissible Bessel’s functions to yield the frequencies of the circular plates under clamped boundary conditions on the basis of the classical plate theory. The large vibration amplitudes problem, reduced to a set of non-linear algebraic equations, is solved numerically. The non-linear to linear frequency ratios are presented. Then, explicit analytical solutions are presented, based on the semi-analytical model previously developed by EL Kadiri et al. [1-2] for beams and rectangular plates, which allow direct and easy calculation for the first non-linear axisymmetric mode shape, with their associated non-linear frequencies of FG circular plates and which are expected to be very useful in engineering applications and in further analytical developments. An excellent agreement is found with the results obtained by the iterative method.

Cyclic Cohesive Zone Model for Simulation of Fatigue Failure Process in Adhesive Joints

Progressive failure process of adhesive joint under cyclic loading is of particular interest in this study. Such fatigue failure is described using damage mechanics with the assumed cohesive behaviour of the adhesive joint. Available cohesive zone model for monotonic loading is re-examined for extension to capture cyclic damage process of adhesive joints. Damage evolution in the adhesive joint is expressed in terms of cyclic degradation of interface strength and stiffness. Mixed-mode fatigue fracture of the joint is formulated based on relative displacements and strain energy release rate of the interface. A power-law type variation for each of these cohesive zone model parameters with accumulated load cycles is assumed in the presence of limited experimental data on cyclic interface fracture process. The cyclic cohesive zone model (CCZM) is implemented in commercial finite element analysis code and the model is validated using adhesively bonded 2024-T3 aluminium substrates with epoxy-based adhesive film (FM73M OST). The CCZM model is then examined for cyclic damage evolution characteristics of the adhesive lap joint subjected to cyclic displacement of Δδ = 0.1 mm, R=0 so as to induce shear-dominant fatigue failure. Results show that the cyclic interface damage started to initiate and propagate symmetrically from the both overlap edges and degradation of interface strength and stiffness started to accumulate after 0.5 cycles of displacement elapsed. The predicted results are consistent with the mechanics of relatively brittle interface failure process.

Vibro-acoustic response and sound transmission loss analysis of functionally graded plates

This paper presents analytical studies on the vibro-acoustic and sound transmission loss characteristics of functionally graded material (FGM) plates using a simple first-order shear deformation theory. The material properties of the plate are assumed to vary according to power law distribution of the constituent materials in terms of volume fraction. The sound radiation due to sinusoidally varying point load, uniformly distributed load and obliquely incident sound wave is computed by solving the Rayleigh integral with a primitive numerical scheme. Displacement, velocity, acceleration, radiated sound power level, radiated sound pressure level and radiation efficiency of FGM plate for varying power law index are examined. The sound transmission loss of the FGM plate for several incidence angles and varying power law index is studied in detail. It has been found that, for the plate being considered, the sound power level increases monotonically with increase in power law index at lower frequency range (0–500Hz) and a non-monotonic trend is appeared towards higher frequencies for both point and distributed force excitations. Increased vibration and acoustic response is observed for ceramic-rich FGM plate at higher frequency band; whereas a similar trend is seen for metal-rich FGM plate at lower frequency band. The dBA values are found to be decreasing with increase in power law index. The radiation efficiency of ceramic-rich FGM plate is noticed to be higher than that of metal and metal-rich FGM plates. The transmission loss below the first resonance frequency is high for ceramic-rich FGM plate and low for metal-rich FGM plate and further depends on the specific material property. The study has found that increased transmission loss can be achieved at higher frequencies with metal-rich FGM plates.

A mechanical picture of fractional-order Darcy equation

In this paper the authors show that fractional-order force-flux relations are obtained considering the flux of a viscous fluid across an elastic porous media. Indeed the one-dimensional fluid mass transport in an unbounded porous media with power-law variation of geometrical and physical properties yields a fractional-order relation among the ingoing flux and the applied pressure to the control section. As a power-law decay of the physical properties from the control section is considered, then the flux is related to a Caputo fractional derivative of the pressure of order 0⩽β≤1. If, instead, the physical properties of the media show a power-law increase from the control section, then flux is related to a fractional-order integral of order 0⩽β≤1. These two different behaviors may be related to different states of the mass flow across the porous media.

Free Convection Flow of Dissipative Fluid from Nonisothermal Vertical Cone

The effects of viscous dissipation with transient laminar free convection from a nonisothermal vertical cone at a wall surface temperature varying as a power function of the distance from the apex are considered. The fluid is assumed to be viscous and incompressible. The nondimensional governing equations of the flow are unsteady, coupled, and nonlinear partial differential equations, which are solved with the use of an efficient, accurate, and unconditionally stable finite difference scheme of the Crank–Nicolson type. The velocity and temperature profiles are obtained and analyzed to reveal the effect of viscous dissipation at various values of the Prandtl number and the exponent in the power law variation of the surface temperature. The local as well as average skin friction and Nusselt number are presented and analyzed. The present results are compared with available ones from the literature and are found to be in good agreement.

Wander of a Gaussian-Beam Wave Propagated Through a Non-Kolmogorov Turbulent Atmosphere

Both increasing experimental evidence and some results of theoretical investigation have shown that there exist two kinds of turbulence in the aerosphere, Kolmogorov and non-Kolmogorov turbulence. Thus, it is necessary to improve the theory of optical wave propagation through atmospheric turbulence, namely, study the laser-beam propagation in non-Kolmogorov turbulence, before analyzing the joint influence of the Kolmogorov turbulence and non-Kolmogorov one on satellite laser communication. The beam wander will lead to the performance degradation of satellite laser communication systems and exert an influence on the achievement and stability of its links. In this paper, we consider a theoretical power spectrum of refractive-index fluctuations with a generalized power law in order to derive the variance of Gaussian-beam wave wander in weak turbulence for a horizonal path and analyze the influence of spectral power-law variations on the beam wander. We show that the expression for the beam-wander variance is of concise closed form and independent of the optical wavelength.