Exponential Variation Research Articles

Dynamics of a polyelectrolyte through aerolysin channel as a function of applied voltage and concentration⋆.

We describe the behaviour of a polyelectrolyte in confined geometry. The transport of a polyelectrolyte, dextran sulfate, through a recombinant protein channel, aerolysin, inserted into a planar lipid bilayer is studied as a function of applied voltage and polyelectrolyte concentration and chain length. The aerolysin pore has a weak geometry asymmetry, a high number of charged residues and the polyelectrolyte is strongly negatively charged. The resulting current blockades were characterized by short and long dwelling times. Their frequency varies exponentially as a function of applied voltage and linearly as a function of polyelectrolyte concentration. The long blockade duration decreases exponentially when the electrical force increases. The ratio of the population of short events to the one of long events decreases when the applied voltage increases and displays an exponential variation. The long residence time increases with the polyelectrolyte chain length. We measure a reduction of the effective charge of the polyelectrolyte at the pore entry and inside the channel. For a fixed applied voltage, + / - 100 mV, at both sides of the protein pore entrance, the events frequency is similar as a function of dextran sulfate concentration. The mean blockade durations are independent of polyelectrolyte concentration and are similar for both entrances of the pore and remain constant as a function of the electrical force.

Distribution of cytochrome oxidase‐rich patches in human primary visual cortex

We studied the tangential distribution of cytochrome oxidase (CytOx)-rich patches (blobs) in the striate cortex (V1) of normally sighted Homo sapiens. We analyzed the spatial density and cross-sectional area of patches in CytOx-reacted tangential sections of flat-mounted preparations of V1 and surrounding areas. CytOx-rich patches were most clearly defined in the supragranular cortical layers of V1, particularly at middle levels of layer III. Variations in patch spatial density were subtle across different visual eccentricity representations. Within the binocular representation of V1, the average patch spatial density decreased slightly with increasing cortical eccentricity, from around 1.0 patch/mm2 in the foveal representation to 0.6 patch/mm2 at the representation of ∼60° eccentricity, but seemed to increase again at the representation of the monocular crescent. Across the entire sample, the cross-sectional area of patches (i.e., patch size) varied from approximately 0.2-0.8 mm2 , with a mean value of 0.32 mm2 . Notably, there was no significant variation in the mean patch size across eccentricity representations. Human patches are on average larger than those reported for nonhuman primate brains, and analysis of species with different brain sizes suggests an approximately linear relationship between V1 area and patch size. The relative constancy of patch metrics across eccentricities is in stark contrast with the exponential variation in V1 cortical magnification, suggesting a nearly invariant modular organization throughout human V1.

MEMS Micro-Sensor for Sensitive Low Power Methane Detection

This work, funded in part by the US EPA and NASA, is focused on creating a novel, ultra-low power and low cost microfabricated methane sensor. The focus of this work will develop a tiny low cost and low power platform sensor technology for identification of fugitive methane emissions, and subsequently serve the expanding methane/natural gas leak and safety market due to increased exploration, production and use of natural gas. Current work is dedicated to design, fabrication and testing of the detector system consisting of a unique MEMS sensor, discreet electronic components and proprietary “smart” algorithm. This program is important to overall greenhouse gas monitoring and contributing to the effort around the world to curb man-made contribution to climate change. Further, the sensor itself is “green” because it uses far less materials, and provides substantial power savings because it uses 10-100 times less power than current lowest power CH4 sensors. Because of the small size of the sensing element, it has a very low thermal mass and therefore improved sensitivity and a very fast response time measured in microseconds. Additional applications for this platform will be possible and extend the applications beyond methane to other atmospheric and fuel gases and vapors Micro-thermal conductivity detector (μTCD) gas sensors work by detecting changes in the thermal conductivity of the surrounding medium and are used as detectors in many applications such as gas chromatography systems, leak detectors, and pressure gauges. Conventional TCDs use steady-state resistance (i.e., temperature) measurements of a micro-heater. In this work, we are developing a new measurement method and hardware configuration based on the processing of the transient response of a low thermal mass TCD to an electric current step. The chip with three different design elements capable of 2 and 4 terminal measurements is illustrated at right. The method was implemented for a 100-μm-long and 1-μm-thick micro-fabricated bridge that consisted of doped polysilicon conductive film passivated with a 200-nm silicon nitride layer. Transient resistance variations of the μTCD in response to a square current pulse were studied in multiple mixtures of dilute gases in nitrogen. Simulations and experimental results are presented and compared for the time resolved and steady-state sensor response. Thermal analysis and simulation show that the sensor response is exponential in the transient state, that the time constant of this exponential variation was a linear function of the thermal conductivity of the gas ambient, and that the sensor was able to quantify the gas composition. The level of detection was estimated at 25 ppm for helium in N2 to 178 ppm carbon dioxide in N2. With this novel approach, the sensor requires approximately 3.6 nJ for a single measurement and needs only 300 μs of sampling time. This is significantly less than the energy and time required for steady-state DC measurements. Reference: US Patent 8,884,382: Stetter et al. Microfabricated Multi-dimensional Sensors and Sensing Systems Figure 1

A comparative analysis (real-time data and theoretical results) for propagation of SH waves in a viscoelastic model influenced by a point source

The propagation of SH waves in a heterogeneous viscoelastic layer lying over a heterogeneous viscoelastic half space from a point source is examined analytically. The significance of the heterogeneity of hyperbolic and exponential variations associated with rigidity, viscosity, and density is investigated mathematically. A dispersion equation and displacement components are computed in a compact form, considering the case that displacement and stress are continuous at the interface and stress vanishes on a free surface. The acquired dispersion equation signifies the relation between phase velocity and dimensionless wavenumber. The dispersion equation is highly influenced by heterogeneous parameters of both the layer and the half space. The dispersion equation is reduced to the classical equation of the Love wave after eliminating all the heterogeneous parameters, in agreement with pre-established results. The analysis uses the technique of Fourier transformation and Green’s function. The wavenumber is supposed to be complex, as the frequency is fixed in the viscoelastic model. Graphs are presented to demonstrate the effect of heterogeneous parameters on phase and damping velocity with respect to wavenumber.

Frictional receding contact problem for a graded bilayer system indented by a rigid punch

The frictional receding contact problem for two graded layers pressed by a rigid punch is considered in this paper. The punch is subjected to both normal and tangential loads thereby resulting in frictional contact with the upper layer. It is also assumed that the contact between the layers is frictional and the lower layer is fixed. It is further assumed that the gradation in the layers follows an exponential variation through the thickness with different profiles while Poissons ratios are taken as constants. Using standard Fourier transform, the contact problem is converted to a system of two singular integral equations in which the contact pressures and the contact widths are the unknowns. The integral equations are then solved numerically using Gauss–Jacobi integration formula. The Finite Element Method was additionally employed and both exponential and power law material gradation is used to solve the investigated problem and the obtained numerical and analytical results are in good agreement. The primary intention of this paper is to investigate the effect of material gradation, friction coefficients, layers thicknesses and material property mismatch at the interface between the layers on the contact pressures and contact widths.

Combined effect of Piezo-viscous dependency and non- Newtonian couple stresses in Annular Plates Squeeze-Film characteristics

In this article, the theoretical analysis of the combined study of non-Newtonian couple stresses with piezo-viscous dependency for annular plates squeeze film bearings have been carried out, with help of stokes micro continuum theory along with the exponential variation of viscosity with pressure. An approximate analytical solution is found using a small perturbation method. The solution for pressure and load capacity with distinct values of viscosity-pressure parameter are calculated and compared with iso-viscous couple stress and Newtonian lubricants and the results reveals that the effect of couple stresses and pressure-dependent viscosity variation enhances the load-carrying capacity and lengthens the squeeze film time.

Solar activity variations of equatorial spread F occurrence and sustenance during different seasons over Indian longitudes: Empirical model and causative mechanisms

A comprehensive analysis using nearly two decades of ionosonde data is carried out on the seasonal and solar cycle variations of Equatorial Spread F (ESF) irregularities over magnetic equatorial location Trivandrum (8.5°N, 77°E). The corresponding Rayleigh Taylor (RT) instability growth rates (γ) are also estimated. A seasonal pattern of ESF occurrence and the corresponding γ is established for low solar (LSA), medium solar (MSA) and high solar (HSA) activity periods. For LSA, it is seen that the γ maximizes during post sunset time with comparable magnitudes for autumnal equinox (AE), vernal equinox (VE) and winter solstice (WS), while for summer solstice (SS) it maximizes in the post-midnight period. Concurrent responses are seen in the ESF occurrence pattern. For MSA, γ maximizes during post-sunset for VE followed by WS and AE while SS maximises during post-midnight period. The ESF occurrence for MSA is highest for VE (80%), followed by AE (70%), WS (60%) and SS (50%). In case of HSA, maximum γ occurs for VE followed by AE, WS and SS. The concurrent ESF occurrence maximizes for VE and AE (90%), WS and SS at 70%.The solar cycle variation of γ is examined. γ shows a linear variation with F10.7 cm flux. Further, ESF percentage occurrence and duration show an exponential and linear variation respectively with γ. An empirical model on the solar activity dependence of ESF occurrence and sustenance time over Indian longitudes is arrived at using the database spanning two solar cycles for the first time.

Soret and Dufour effects on unsteady double diffusive natural convection in porous trapezoidal enclosures

This work examines the Soret and Dufour effects on the unsteady double-diffusive natural convection inside trapezoidal enclosures filled with isotropic porous medium with exponential variation of boundary conditions. The analysis uses a two-dimensional trapezoidal enclosure with the inclined walls being kept at constant cold temperature and concentration while the temperature and concentration vary exponentially on the bottom wall of the enclosure. The top wall of the trapezoidal is thermally insulated. The physical problems are represented by non-dimensional governing equations along with the corresponding boundary conditions are solved numerically by the finite difference method. The present results are validated by favorable comparisons with previously published results. Representative results depicting the effects the various parameters, namely, the buoyancy ratio parameter, and the Dufour and Soret numbers on the streamlines, isotherms, isoconcentration lines as well as the local Nusselt and Sherwood numbers are reported. In addition, numerical results for the average Nusselt and Sherwood numbers are presented in tabular forms for various parametric conditions and discussed.

Development of empirical model for predicting G∗/Sinδ and viscosity value for nanoclay and Carbon Nano Tube modified asphalt binder

The present research work was undertaken to develop a simple empirical model to evaluate superpave rutting factor (G∗/Sinδ) and viscosity value for Nano Clay (NC) and Carbon Nano Tube (CNT) modified asphalt binders. The amount of NC was varied as 0%, 2%, 4% and 6%, while CNT was varied as 0%, 0.4%, 0.75%, 1.5% and 2.25% by the weight of control binder. Nanomaterial factors (NCf for NC modified and CNTf for CNT modified asphalt binder) and temperature factors were evaluated to develop the final empirical model for G∗/Sinδ and viscosity. NC factor (NCf) as well as CNT factor (CNTf) were found to have exponential variation for viscosity model. In case of G∗/Sinδ model, CNTf found to have quadratic variation due to reduction in stiffness value at higher CNT doses, whereas, NCf showed exponential variation. Development of empirical model for evaluating G∗/Sinδ and viscosity value for NC and CNT modified asphalt binders has been successfully demonstrated in the present paper. Overall, it is expected that the proposed models may be helpful to practicing engineers for making judicious decision on selection of amount of NC or CNT to improve rutting and workability requirement of asphalt binder.

Analysis of surface wave behavior in corrugated piezomagnetic layer resting on inhomogeneous half-space

ABSTRACTThis paper deals with propagation of Love type waves in a Piezomagnetic layer with corrugated boundaries overlying an inhomogeneous half-space. Inhomogeneity of elastic half-space is caused due to exponential variations in elastic parameters. Dispersion relations are obtained for magnetically open and short cases. Prominent effects of inhomogeneity, layer's width and corrugation on the phase velocity of considered wave are illustrated through graphs. Some particular cases are derived and exhibited through graphs. Also the influence of undulation parameter, elastic parameter, and piezomagnetic coefficient on phase velocity of considered wave has been marked separately. The present study finds its applications in designing and optimization of Love wave sensors and Seismic Acoustic Wave (SAW) devices. Findings may also be used for analytical study of wave propagation in piezomagnetic coupled structures.

Buckling analysis of tapered BDFGM nano-beam under variable axial compression resting on elastic medium

The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

On the receding contact between a two-layer inhomogeneous laminate and a half-plane

This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.

Penetration of Nonstationary Ionospheric Electric Fields into Lower Atmospheric Layers in the Global Electric Circuit Model

The problem of the penetration of nonstationary ionospheric electric fields into the lower atmospheric layers is considered based on the model of the global electric circuit in the Earth’s atmosphere. For the equation of the electric field potential, a solution that takes into account exponential variation in the electrical conductivity with height has been obtained. Analysis of the solution made it possible to reveal three cases of the dependence of the solution on height. The first case (the case of high frequencies) corresponds to the Coulomb approximation, when the electrical conductivity of the atmosphere can be neglected. In the case of low frequencies (when the frequency of changes in the ionosphere potential is less than the quantity reciprocal to the time of electric relaxation of the atmosphere), a quasi-stationary regime, in which the variation in the electric potential of the atmosphere is determined by the electric conduction currents, occurs. In the third case, due to the increase in the electrical conductivity of the atmosphere, two spherical regions appear: with the Coulomb approximation in the lower region and conduction currents in the upper one. For these three cases, formulas for estimating the electric field strength near the Earth’s surface have been obtained.

Free vibration of square plate with temperature effect

In modern engineering, researchers/scientists are very keen to know first few modes of vibration because it provides how system/structure behaves under vibration. In this paper, author computed the natural vibration of non homogeneous tapered square plate. Here tapered means that plate’s thickness varies linearly along x-axis. Here non homogeneity arises in the plate’s material due to simultaneous variation in density (circular variation) and Poisson’s ratio (exponential variation). Temperature variation on the plate is viewed bi-parabolic along the axes. Rayleigh-Ritz technique is applied to obtain the frequency equation and vibrational frequency modes under different combination of parameters. The findings of the papers are presented in tabular form.

Impact of inhomogeneity on SH-type wave propagation in an initially stressed composite structure

The present analysis has been made on the influence of distinct form of inhomogeneity in a composite structure comprised of double superficial layers lying over a half-space, on the phase velocity of SH-type wave propagating through it. Propagation of SH-type wave in the said structure has been examined in four distinct cases of inhomogeneity viz. when inhomogeneity in double superficial layer is due to exponential variation in density only (Case I); when inhomogeneity in double superficial layers is due to exponential variation in rigidity only (Case II); when inhomogeneity in double superficial layer is due to exponential variation in rigidity, density and initial stress (Case III) and when inhomogeneity in double superficial layer is due to linear variation in rigidity, density and initial stress (Case IV). Closed-form expression of dispersion relation has been accomplished for all four aforementioned cases through extensive application of Debye asymptotic analysis. Deduced dispersion relations for all the cases are found in well-agreement to the classical Love-wave equation. Numerical computation has been carried out to graphically demonstrate the effect of inhomogeneity parameters, initial stress parameters as well as width ratio associated with double superficial layers in the composite structure for each of the four aforesaid cases on dispersion curve. Meticulous examination of distinct cases of inhomogeneity and initial stress in context of considered problem has been carried out with detailed analysis in a comparative approach.

Water movement through plant roots – exact solutions of the water flow equation in roots with linear or exponential piecewise hydraulic properties

Abstract. In 1978, Landsberg and Fowkes presented a solution of the water flow equation inside a root with uniform hydraulic properties. These properties are root radial conductivity and axial conductance, which control, respectively, the radial water flow between the root surface and xylem and the axial flow within the xylem. From the solution for the xylem water potential, functions that describe the radial and axial flow along the root axis were derived. These solutions can also be used to derive root macroscopic parameters that are potential input parameters of hydrological and crop models. In this paper, novel analytical solutions of the water flow equation are developed for roots whose hydraulic properties vary along their axis, which is the case for most plants. We derived solutions for single roots with linear or exponential variations of hydraulic properties with distance to root tip. These solutions were subsequently combined to construct single roots with complex hydraulic property profiles. The analytical solutions allow one to verify numerical solutions and to get a generalization of the hydric behaviour with the main influencing parameters of the solutions. The resulting flow distributions in heterogeneous roots differed from those in uniform roots and simulations led to more regular, less abrupt variations of xylem suction or radial flux along root axes. The model could successfully be applied to maize effective root conductance measurements to derive radial and axial hydraulic properties. We also show that very contrasted root water uptake patterns arise when using either uniform or heterogeneous root hydraulic properties in a soil–root model. The optimal root radius that maximizes water uptake under a carbon cost constraint was also studied. The optimal radius was shown to be highly dependent on the root hydraulic properties and close to observed properties in maize roots. We finally used the obtained functions for evaluating the impact of root maturation versus root growth on water uptake. Very diverse uptake strategies arise from the analysis. These solutions open new avenues to investigate for optimal genotype–environment–management interactions by optimization, for example, of plant-scale macroscopic hydraulic parameters used in ecohydrogolocial models.

Simulating energy cascade of shock wave formation process in a resonator by gas kinetic scheme

The temporal-spatial evolution of gas oscillation was simulated by gas kinetic scheme (GKS) in a cylindrical resonator, driven by a piston at one end and rigidly closed at the other end. Periodic shock waves propagating back and forth were observed in the resonator under finite amplitude of gas oscillation. The studied results demonstrated that the acoustic pressure is a saw-tooth waveform and the oscillatory velocity is a square waveform at the central position of the resonant tube. Moreover, it was found by harmonic analysis that there was no presence of obvious feature for pressure node in such a typical standing wave resonator, and the distribution of acoustic fields displayed a one-dimensional feature for the acoustic pressure while a quasi-one-dimensional form for oscillatory velocity, which demonstrated the nonlinear effects. The simulation results for axial distribution of acoustic intensity showed a good consistency with the published experimental data in the open literature domain, which provides a verification for the effectiveness of the GKS model proposed. The influence of displacement amplitude of the driving piston on the formation of shock wave was numerically investigated, and the simulated results revealed the cascade process of harmonic wave energy from the fundamental wave to higher harmonics. In addition, this study found that the acoustic intensity at the driving end of the resonant tube would increase linearly with the displacement amplitude of the piston due to nonlinear effects, rather than the exponential variation by linear theory. This research demonstrates that the GKS model is strongly capable of simulating nonlinear acoustic problems.

Fracture Analysis in an Imperfect FGM Orthotropic Strip Bonded Between Two Magneto-Electro-Elastic Layers

In this study, a functionally graded orthotropic layer sandwiched between two magneto-electro-elastic layers under anti-plane time-harmonic mechanic and in-plane electromagnetic loadings is studied. This paper examines the modeling of cracks by distribution of strain nuclei along crack lines. During this investigation, the Volterra-type screw dislocation is employed in the FGM orthotropic layer and the magneto-electro-elastic coating. The material properties of the strip are considered to obey exponential variations. To solve the dislocation problem, the complex Fourier transform is applied. One merit of this technique is the possibility of determination of the stress intensity factors for multiple smooth cracks. The system of equations is derived by considering the distribution of line dislocation on the crack. These equations are of Cauchy singular type in the location of dislocation, which can be solved numerically to obtain the dislocation density on the faces of the cracks. Various examples are solved, and the dynamic stress intensity factors are obtained. The effect of the cracks configuration, bonding constant, angular frequency and material properties on the mode III stress intensity factor is studied, and the validity of the analysis is checked.

English

English

Liouville-Green approximation: An analytical approach to study the elastic waves vibrations in composite structure of piezo material

This research article delves the study of surface waves in functionally graded piezoelectric material (FGPM) clubbed between two dissimilar piezomagnetic (PM) media. The transference of elastic waves in a composite structure is analyzed following the elastic wave theory of magneto-electro-elasticity. Liouville-Green’s (LG) approximation technique is used to solve the differential equation. The exponential variation is assumed in material gradients of FGPM stratum. It is noticed that the frequency of considered wave depends significantly on the material gradient coefficients, which may be a crucial factor to regulate the dispersion characteristics of functionally graded material (FGM) waveguides. Frequency equations have been obtained for electrically open and short cases in determinant form. The profound effect of parameters like material gradients (piezoelectric, dielectric and elastic) and width of the layers, on the phase velocity of Love type wave are presented graphically. Moreover, it is noticed that the material gradients also influences the electromechanical coupling factor. This influence has shown through the graph. Different parametric curves are merged into a single figure to increase the readability of the graphs. The magnetic potential function is derived analytically for all three gradient factors of FGPM plate. Obtained results are matched analytically and graphically with the established results.