Exponential Variation Research Articles

Dispersion of Love Wave in a Heterogeneous Orthotropic Layer Under Compressive Pre-Stress Lying Over an Isotropic Elastic Half-space With Rectangular Irregularity

This paper gives a theoretical take a look at on a dispersion of Love waves in a heterogeneous orthotropic layer under compressive pre-stress lying over an isotropic elastic half-space with rectangular irregularity. The heterogeneity within the layer is believed to get up due to exponential variation in shear moduli, pre-stress, and density. A closed-form solution has been gotten for the displacement within the assumed layer as well as infinite half-space. Numerical consequences are introduced for propagation characteristic within the terms of some of the dimensionless parameters and have been produced graphically.

Arrival Rate Functions

Asset price dynamics are taken to be accumulations of surprise jumps in the logarithm of prices. A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level. Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation. The motion is decomposed into a space dependent drift and a space dependent martingale component. Though there is some local mean reversion by and large the dynamics estimated is that of the momentum type. Risk compensation is seen by a linear relation between the exponential variation and measure distorted variations for the bid and ask prices of two price economies. Estimations are conducted for the S&P 500 index (SPX), the exchange traded fund for the financial sector (XLF), J. P. Morgan stock prices (JPM), the ratio of JPM to XLF and the ratio of XLF to SPX.

Risks and Their Rewards in Financial Markets: A Two Price Perspective

Prices in financial markets must move continuously and surprisingly to support their levels with returns. Consequently the function announcing the arrival rate of moves of different sizes becomes the equilibrium object, necessitating a reformulation of risk reward concepts in these terms. It is shown the exponential variation replaces the mean as a reward concept. Risk is measured by the shaves and add-ons implicit in the bid and ask prices of two price economies. An analysis of markets reveals that these two sided risk measures significantly impact rewards in the markets for stocks, stock spreads, and relative stock prices.

Influence of constraint effect of sidewall on maximum smoke temperature distribution under a tunnel ceiling

A sequence of tests and simulations with varying transverse fire locations were conducted in a full-scale tunnel to investigate the constraint effect of sidewall on the maximum smoke temperature distribution under a tunnel ceiling. Then, the simulated results were comprehensively compared with both those of the full-scale tests and the model-scale experiments from previous studies. The results of the full-scale experiment show that the longitudinal maximum smoke temperature rise distribution decreases can be approximated by a power function. However, the numerical simulation results indicate that an exponential distribution may be plausible. The normalized ceiling jet temperature rise at the impingement point displays an exponential variation with the distance between the fire source and the sidewall. Meanwhile, regression models taking the constraint effect of sidewall into account was developed to predict the ceiling jet impingement temperature in tunnel fires.

Heat convection and radiation in flighted rotary kilns: A minimal model

AbstractWe propose a minimal model aiming to describe heat transfer between particles (i.e. grains) and gases in a model of flighted rotary kilns. It considers a channel in which a convective gas interacts with a granular suspension and a granular bed. Despite its simplicity it captures the main experimental findings in the case of dilute suspension of heavy grains typical of what can be observed in many industrial rotary kilns. Energy balance between each phase takes into account the main heat transfer mechanisms between the transverse granular motion and the convective gas. In the absence of radiation heat transfer, the model predicts exponential variations of the temperatures characterized by a length which depends on the granular and gas heat flow rates as well as on the exchange areas. When radiation is taken into account, the model can be solved numerically. For this case, the temperature variations can be fitted by stretched exponentials whose parameters are found to be independent of the studied phases. Finally, an efficiency criterion is proposed to optimize the length of the system.

Shortcut to adiabaticity in spinor condensates

We devise a method to shortcut the adiabatic evolution of a spin-1 Bose gas with an external magnetic field as the control parameter. An initial many-body state with almost all bosons populating the Zeeman sublevel $m=0$, is evolved to a final state very close to a macroscopic spin-singlet condensate, a fragmented state with three macroscopically occupied Zeeman states. The shortcut protocol, obtained by an approximate mapping to a harmonic oscillator Hamiltonian, is compared to linear and exponential variations of the control parameter. We find a dramatic speedup of the dynamics when using the shortcut protocol.

A Modified Thermal Treatment Method for the Up-Scalable Synthesis of Size-Controlled Nanocrystalline Titania

Considering the increasing demand for titania nanoparticles with controlled quality for various applications, the present work reports the up-scalable synthesis of size-controlled titanium dioxide nanocrystals with a simple and convenient thermal treatment route. Titanium dioxide nanocrystals with tetragonal structure were synthesized directly from an aqueous solution containing titanium (IV) isopropoxide as the main reactant, polyvinyl pyrrolidone (PVP) as the capping agent, and deionized water as a solvent. With the elimination of the drying process in a thermal treatment method, an attempt was made to decrease the synthesis time. The mixture directly underwent calcination to form titanium dioxide (TiO2) nanocrystalline powder, which was confirmed by FT-IR, energy dispersive X-ray spectroscopy (EDX), and X-ray diffraction (XRD) analysis. The control over the size and optical properties of nanocrystals was achieved via variation in calcination temperatures. The obtained average sizes from XRD spectra and transmission electron microscopy (TEM) images showed exponential variation with increasing calcination temperature. The optical properties showed a decrease in the band gap energy with increasing calcination temperature due to the enlargement of the nanoparticle size. These results prove that direct calcination of reactant solution is a convenient thermal treatment route for the potential large-scale production of size-controlled Titania nanoparticles.

Shear wave propagation in viscoelastic heterogeneous layers lying over an initially stressed half-space

ABSTRACTThe role of the present article is to study the propagation of horizontally polarized shear waves in vertically heterogeneous viscoelastic double layers lying over a homogeneous half-space under initial stress. Both linear and exponential variations have been considered in the inhomogeneity associated to rigidity, internal friction, and density of the media. The dispersion equation of shear waves has been obtained in closed form. The dimensionless phase and damping velocities have been plotted against dimensionless wave number for different values of inhomogeneity parameters separately. Also, surface plots of phase velocity against dimensionless wave number and inhomogeneity parameters have been given.

Efficient simulations with electronic open boundaries

We present a reformulation of the hairy-probe method for introducing electronic open boundaries that is appropriate for steady-state calculations involving nonorthogonal atomic basis sets. As a check on the correctness of the method we investigate a perfect atomic wire of Cu atoms and a perfect nonorthogonal chain of H atoms. For both atom chains we find that the conductance has a value of exactly one quantum unit and that this is rather insensitive to the strength of coupling of the probes to the system, provided values of the coupling are of the same order as the mean interlevel spacing of the system without probes. For the Cu atom chain we find in addition that away from the regions with probes attached, the potential in the wire is uniform, while within them it follows a predicted exponential variation with position. We then apply the method to an initial investigation of the suitability of graphene as a contact material for molecular electronics. We perform calculations on a carbon nanoribbon to determine the correct coupling strength of the probes to the graphene and obtain a conductance of about two quantum units corresponding to two bands crossing the Fermi surface. We then compute the current through a benzene molecule attached to two graphene contacts and find only a very weak current because of the disruption of the $\ensuremath{\pi}$ conjugation by the covalent bond between the benzene and the graphene. In all cases we find that very strong or weak probe couplings suppress the current.

Instantaneous Portfolio Theory

Instantaneous risk is described by the arrival rate of jumps in log price relatives. Aggregate arrivals are infinite. There is then no concept of a mean return compensating risk exposure. The only risk-free instantaneous return is zero. All portfolios are subject to risk and there are only bad and better ways of holding risk. The univariate variance gamma model is extended to higher dimensions with an arrival rate function with full support in high dimensions and independent levels of skewness and excess kurtosis across assets. Concave bid price functionals are formulated as measure distorted variations. Specific measure distortions are calibrated to data on S&P 500 index options and the time series of the index. It is shown that univariate estimation by digital moments applied to uncentered data dominates the use of centered data. Measure distorted integrals are computed using Monte Carlo applied to gamma distributed elliptical radii with a low shape parameter. Risk reward frontiers exist between the finite exponential variation as the reward and measure distorted exponential variations as risk charges. For market portfolios on the efficient frontier as an optimal portfolio, differences in asset exponential variations are given by differences in exponential asset covariations with the risk charge differential of the market portfolio. Optimal portfolio exponential variations may be negative. Bid price maximizing portfolios are presented in two, six and twenty five dimensions with an efficient frontier between exponential variations illustrated in dimension six.

Tapering photonic crystal fibers for generating self-similar ultrashort pulses at 1550 nm

The generation of high-quality self-similar ultrashort pulses at 1550 nm by tapering the photonic crystal fibers (PCFs) is numerically demonstrated. We taper the PCF to achieve the exponentially decreasing dispersion and exponentially increasing nonlinearity profiles, which turn out to be the fundamental requirements for generating the chirped self-similar pulses. Further, we find that the chirped solitons could also be generated with the other three possible exponential variations. Thus, for the first time, we attempt tapering the PCFs for bringing in these exponentially varying dispersion and nonlinear profiles. We carry out the detailed pulse compression studies for various decay rates of the dispersion profiles as the decay rates of dispersion depend on the initial chirp and hence on compression factor, too. The unique feature of this pulse compressor lies in the fact that the required length of the tapered PCF is about 20 times less than that of the previously reported pulse compressor operating at 850 nm.

Generation of a train of ultrashort pulses using periodic waves in tapered photonic crystal fibres

We consider a light wave propagation in tapered photonic crystal fibres (PCFs) wherein the wave propagation is described by the variable coefficient nonlinear Schrödinger equation. We solve it directly by means of the theta function identities and Hirota bilinear method in order to obtain the exact periodic waves of sn, cn and dn types. These chirped period waves demand exponential variations in both dispersion and nonlinearity. Besides, we analytically demonstrate the generation of a train of ultrashort pulses using the periodic waves by exploiting the exponentially varying optical properties of the tapered PCFs. As a special case, we discuss the chirped solitary pulses under long wave limit of these periodic waves. In addition, we derive these types of periodic waves using the self-similar analysis and compare the results.

The Impact of the Wind Speed on the Dynamics of the Wind Energy System

Abstract The paper analyzes the operation of electric power subsystem consisting of the naval marine wind turbine, the synchronous generator and the electric accumulators at linear and exponential variations of wind speed. The management system is analyzed using various functions of wind speed variation. This subsystem requires to capture the wind energy with maximum efficiency, so a diesel engine and a synchronous generator subsystem can be used only as a complementary source of energy.

Electromagnetic wave propagation in time-dependent media with antisymmetric magnetoelectric coupling

This paper deals with electromagnetic wave propagation in time-dependent media with an antisymmetric magnetoelectric coupling and an isotropic time-dependent permittivity. We identify a new mechanism of linear birefringence, originated from the combined action of the time-dependent permittivity and the antisymmetric magnetoelectric coupling. Permittivity with linear and exponential temporal variations exemplifies the creation and control of these two distinct types of linear birefringent modes. As a novel nonlinear optical effect, a scheme utilizing optical Kerr effect in moving media is proposed for the realization of the predicted birefringence.

Effect of periodic corrugation, reinforcement, heterogeneity and initial stress on Love wave propagation

This paper investigates the impact of corrugated boundary surfaces, reinforcement on the propagation of Love-type wave in prestressed corrugated heterogeneous fiber-reinforced layer resting over a void pores half-space. The heterogeneity in the upper corrugated layer is caused due to exponential variation in the elastic constants with respect to the space variable pointing positively downwards. The dispersion equation in the complex form has been derived using method of separation of variables. The real and imaginary parts of the complex dispersion equation were separated and found in well agreement with the classical Love wave equation. Also, the attenuation of the Love waves has been discussed. The study reveals that such a medium transmits two fronts of Love waves. The first front depends upon the change in volume fraction of the pores and the second front depends upon the modulus of rigidity of the elastic matrix of the medium. The substantial influence of corrugation parameters, reinforcement, undulatory parameter, initial stress, heterogeneity parameter and position parameter on the phase velocity, and attenuation of Love-type wave have been observed and depicted by means of graph. It has been observed that the phase velocity decreases with the increase in initial stress parameters, heterogeneity, and reinforcement in upper layer.

Wave propagation in heterogeneous layers of the Earth

This paper represents the analytical and numerical study of the propagation of horizontally polarized shear wave in two inhomogeneous layers lying over an isotropic homogeneous semi-infinite elastic medium. The inhomogeneity of the upper layer is caused by the exponential variation of rigidity and density with the depth, whereas the second layer exhibits inhomogeneity due to quadratic variation in rigidity of the medium. The dispersion relation has been obtained in closed form using Debye asymptotic expansion which is the major highlight of this study. The comparative study and some important peculiarities have been revealed by means of graphical illustrations.

The Boussinesq–Mindlin problem for a non-homogeneous elastic halfspace

Boussinesq’s problem for the indentation of an isotropic, homogeneous elastic halfspace by a rigid circular punch constitutes a seminal problem in the theory of contact mechanics as does Mindlin’s problem for the action of a concentrated force at the interior of an isotropic, homogeneous elastic halfspace. The combined action of the surface indentation in the presence of the interior loading is referred to as the Boussinesq–Mindlin problem, which has important applications in the area of geomechanics. The Boussinesq–Mindlin problem, which represents a self-stressing loading configuration, serves as a useful model for interpreting the mechanics of indentation of geologic media for purposes of estimating their bulk elasticity properties. In this paper, the analysis of the problem is extended to include an exponential variation in the linear elastic shear modulus of the halfspace region.

Analysis of an arbitrarily oriented crack in a functionally graded plane using a non-local approach

This paper considers the problem of a mixed-mode crack embedded in an infinite graded medium in which the crack is arbitrarily oriented with respect to the material gradient. The material properties are assumed to have an exponential variation and the crack surfaces are subjected to both normal and tangential tractions which can be related to the external applied loads. Classical elasticity equations are reformulated to incorporate non-local effects by employing Eringen’s non-local theory resulting in a non-singular stress field. Using Fourier transform, two integral equations are derived where the unknowns are the jumps in displacements across the crack surfaces. These jumps are expanded in a series of Jacobi polynomials and then substituted into the integral equations which are solved using the so-called Schmidt method. In contrast with classical elasticity solutions, there are no stress singularities at the crack tips in this solution owing to the incorporation of non-local effects. Therefore, the use of non-local theory permits the use of maximum stress in conjunction with a brittle fracture criterion. The principal objective of this study is to investigate the effect of various parameters such as crack length, material gradient nonhomogeneity parameter, angular orientation of the crack and lattice parameter on the non-local stress field near the crack tips.

Impedance study of the influence of chromates on the properties of waterborne coatings deposited on 2024 aluminium alloy

Coatings formulated with either SrCrO4 or a mixture of Cr(VI)-free pigments were compared in an impedance study. In addition to classical EIS measurements carried out in the metal/coating/electrolyte configuration, the study involved measurement of the impedance of the coatings in the dry state, both before exposure to the electrolyte (0.5M NaCl solution) and after a 1-month exposure followed by a 12-month drying. The results were analysed with reference to models that assumed resistivity variations along the coating thickness. The resistivity-position dependence was close to a power law for dry coatings and close to exponential for wet coatings. In the latter, and for short immersion times, the exponential variation was located in the outer coating region, at shorter distances from the coating/solution interface, and then, for longer immersion times (>1 week), extended to the whole coating thickness. The effect of SrCrO4 leaching on the properties of the coating is discussed. For both coatings, the barrier effect remained high for a 1-month exposure.

The frictionless axial interaction of a rigid disk with a two-layered functionally graded transversely isotropic medium

A rigorous formulation is presented for the frictionless axisymmetric interaction of a rigid disk with a two-layered inhomogeneous medium. The materials are considered to be linearly elastic transversely isotropic materials and the exponential variation of properties along the depth of each layer is assumed in order to model the effect of inhomogeneity. The disk is considered to be at the top of the coating layer or embedded at the interface of the two media. By satisfying the boundary conditions, the problem leads to a dual integral equation and is reducible to a Fredholm integral equation of the second kind which is solved numerically. The numerical solutions survey the effect of material inhomogeneity through two special cases: a functionally graded coating on a homogeneous transversely isotropic half-space and a homogeneous transversely isotropic coating on an inhomogeneous half-space. The accuracy of the numerical solutions is verified by comparison with the corresponding solution for homogeneous material in the literature.