Exponential Density Distribution Research Articles

Crack problem in superconducting cylinder with exponential distribution of critical-current density

The general problem of a center crack in a long cylindrical superconductor with inhomogeneous critical-current distribution is studied based on the extended Bean model for zero-field cooling (ZFC) and field cooling (FC) magnetization processes, in which the inhomogeneous parameter η is introduced for characterizing the critical-current density distribution in inhomogeneous superconductor. The effect of the inhomogeneous parameter η on both the magnetic field distribution and the variations of the normalized stress intensity factors is also obtained based on the plane strain approach and J-integral theory. The numerical results indicate that the exponential distribution of critical-current density will lead a larger trapped field inside the inhomogeneous superconductor and cause the center of the cylinder to fracture more easily. In addition, it is worth pointing out that the nonlinear field distribution is unique to the Bean model by comparing the curve shapes of the magnetization loop with homogeneous and inhomogeneous critical-current distribution.

Surface Trap-Induced Conductivity Type Switching in Semiconductor Nanowires: Analytical and Numerical Analyses

Due to high surface-to-volume ratio, surface traps play crucial role in electronic properties of semiconductor nanowires and nanowire-based devices. Recently, it was experimentally demonstrated that surface traps even can induce conductivity type inversion in semiconductor nanowires. Here, we have performed theoretical and numerical analyses to investigate the influence of surface traps on semiconductor nanowire conductivity including possible inversion due to surface traps. The Poisson equation with consideration of both type of mobile charges and ionized donors was solved having surface trapped charges in Neumann boundary conditions. Different semiconductor materials and surface trap densities have been considered. Calculations were done considering single energy level of surface traps and then the results were generalized to exponential energetic distribution of surface states density. The effect of surface traps was analyzed both for low-doped and highly doped nanowires. It was shown that for moderate or lightly doped NWs, the conductivity type switching from n- to p-type can occur at small radii. The developed potential-based analytical model allows calculating the inversion charge raised due to surface traps. The accuracy of analytical calculations has been validated with TCAD simulations and qualitatively compared with published experimental data. This paper is useful for design optimization of nanowire-based photodetectors, sensors, and reconfigurable FETs.

Pilot-Scale Experimental Study and Mathematical Modeling of Buoyant Settling of Immiscible Heavy Fluid in Mud To Stop Annular-Gas Migration Above Leaking Cement

Summary Annular casing pressure (ACP) is defined as the accumulated pressure on the casing head. If pressure returns after bleed-down, then the casing annulus is said to be showing sustained casing pressure (SCP). SCP is caused by late gas migration in the annular-fluid column above the top of leaking cement and may result in atmospheric emissions or underground blowouts. Removal of SCP is required in places where SCP is regulated, particularly before the well-plugging and abandonment operations. Annular-intervention methods for SCP removal, which are less expensive than the conventional downhole-intervention methods, typically involve injecting heavy fluid into the affected annulus that would displace the annular fluid (AF), balance the pressure at the top of cement, and stop the gas leakage. Previous studies stated that the use of immiscible combinations of two fluids is more effective for the purpose; however, inattentive applications may result in excessive use of heavy fluid. In this study, a 20-ft carbon-steel pilot-well annulus was manufactured and used for displacement experiments with various water-based drilling muds and heavy fluids with different properties. Pressure-change data were collected from four different levels of the annulus, and volumes of fluids going in and out of the annulus were measured. Experiments indicated the formation of a mixture zone that would build bottoms up and expand during ongoing displacement. The proposed pressure-buildup model suggests an exponential distribution of density of this zone, and shows its high dependency on fluids’ properties and injection rate. The mathematical models were also converted into dimensionless process measures and proposed for use in real-well applications. The study demonstrates the viability and recommends the correct application of the method.

Vertical distribution and kinematics of protoplanetary nebulae in the galaxy

The catalogue of protoplanetary nebulae by Vickers et al. has been supplemented with the line-of-sight velocities and proper motions of their central stars from the literature. Based on an exponential density distribution, we have estimated the vertical scale height from objects with an age less than 3 Gyr belonging to the Galactic thin disk (luminosities higher than 5000 Lo) to be h=146+/-15 pc, while from a sample of older objects (luminosities lower than 5000 Lo) it is h=568+/-42 pc. We have produced a list of 147 nebulae in which there are only the line-of-sight velocities for 55 nebulae, only the proper motions for 25 nebulae, and both line-of-sight velocities and proper motions for 67 nebulae. Based on this kinematic sample, we have estimated the Galactic rotation parameters and the residual velocity dispersions of protoplanetary nebulae as a function of their age. We have established that there is a good correlation between the kinematic properties of nebulae and their separation in luminosity proposed by Vickers. Most of the nebulae are shown to be involved in the Galactic rotation, with the circular rotation velocity at the solar distance being V_0=227+/-23 km/s. The following principal semiaxes of the residual velocity dispersion ellipsoid have been found: (sigma1, sigma2, sigma3) = (47, 41, 29) km/s from a sample of young protoplanetary nebulae (with luminosities higher than 5000 Lo), (sigma1, sigma2, sigma3) = (50, 38, 28) km/s from a sample of older protoplanetary nebulae (with luminosities of 4000 Lo or 3500 Lo), and (sigma1, sigma_2, sigma3) = (91, 49, 36) km/s from a sample of halo nebulae (with luminosities of 1700 Lo).

Vertical distribution and kinematics of planetary nebulae in the milky way

Based on published data, we have produced a sample of planetary nebulae (PNe) that is complete within 2 kpc of the Sun. We have estimated the total number of PNe in the Galaxy from this sample to be 17000+/-3000 and determined the vertical scale height of the thin disk based on an exponential density distribution to be 197+/-10 pc. The next sample includes PNe from the Stanghellini-Haywood catalog with minor additions. For this purpose, we have used about 200 PNe with Peimbert's types I, II, and III. In this case, we have obtained a considerably higher value of the vertical scale height that increases noticeably with sample radius. We have experimentally found that it is necessary to reduce the distance scale of this catalog approximately by 20%. Then, for example, for PNe with heliocentric distances less than 4 kpc the vertical scale height is 256+/-12 kpc. A kinematic analysis has confirmed the necessity of such a reduction of the distance scale.

First-order analytic propagation of satellites in the exponential atmosphere of an oblate planet

The paper offers the fully analytic solution to the motion of a satellite orbiting under the influence of the two major perturbations, due to the oblateness and the atmospheric drag. The solution is presented in a time-explicit form, and takes into account an exponential distribution of the atmospheric density, an assumption that is reasonably close to reality. The approach involves two essential steps. The first one concerns a new approximate mathematical model that admits a closed-form solution with respect to a set of new variables. The second step is the determination of an infinitesimal contact transformation that allows to navigate between the new and the original variables. This contact transformation is obtained in exact form, and afterwards a Taylor series approximation is proposed in order to make all the computations explicit. The aforementioned transformation accommodates both perturbations, improving the accuracy of the orbit predictions by one order of magnitude with respect to the case when the atmospheric drag is absent from the transformation. Numerical simulations are performed for a low Earth orbit starting at an altitude of 350 km, and they show that the incorporation of drag terms into the contact transformation generates an error reduction by a factor of 7 in the position vector. The proposed method aims at improving the accuracy of analytic orbit propagation and transforming it into a viable alternative to the computationally intensive numerical methods.

Weighing the galactic disc using the Jeans equation: lessons from simulations

Using three-dimensional stellar kinematic data from simulated galaxies, we examine the efficacy of a Jeans equation analysis in reconstructing the total disk surface density, including the dark matter, at the "Solar" radius. Our simulation dataset includes galaxies formed in a cosmological context using state-of-the-art high resolution cosmological zoom simulations, and other idealised models. The cosmologically formed galaxies have been demonstrated to lie on many of the observed scaling relations for late-type spirals, and thus offer an interesting surrogate for real galaxies with the obvious advantage that all the kinematical data are known perfectly. We show that the vertical velocity dispersion is typically the dominant kinematic quantity in the analysis, and that the traditional method of using only the vertical force is reasonably effective at low heights above the disk plane. At higher heights the inclusion of the radial force becomes increasingly important. We also show that the method is sensitive to uncertainties in the measured disk parameters, particularly the scale lengths of the assumed double exponential density distribution, and the scale length of the radial velocity dispersion. In addition, we show that disk structure and low number statistics can lead to significant errors in the calculated surface densities. Finally we examine the implications of our results for previous studies of this sort, suggesting that more accurate measurements of the scale lengths may help reconcile conflicting estimates of the local dark matter density in the literature.

THE HYDRODYNAMICAL MODELS OF THE COMETARY COMPACT H ii REGION

We have developed a full numerical method to study the gas dynamics of cometary ultra-compact (UC) H II regions, and associated photodissociation regions (PDRs). The bow-shock and champagne-flow models with a $40.9/21.9 M_\odot$ star are simulated. In the bow-shock models, the massive star is assumed to move through dense ($n=8000~cm^{-3}$) molecular material with a stellar velocity of $15~km~s^{-1}$. In the champagne-flow models, an exponential distribution of density with a scale height of 0.2 pc is assumed. The profiles of the [Ne II] 12.81\mum and $H_2~S(2)$ lines from the ionized regions and PDRs are compared for two sets of models. In champagne-flow models, emission lines from the ionized gas clearly show the effect of acceleration along the direction toward the tail due to the density gradient. The kinematics of the molecular gas inside the dense shell is mainly due to the expansion of the H II region. However, in bow-shock models the ionized gas mainly moves in the same direction as the stellar motion. The kinematics of the molecular gas inside the dense shell simply reflects the motion of the dense shell with respect to the star. These differences can be used to distinguish two sets of models.

Hopping Transport of Charge Carriers in LEDs Based on Multiple InGaN/GaN Quantum Wells

The results of experimental studies of forward current–voltage characteristics of blue LEDs with an active region consisting of the multiple InGaN/GaN quantum wells are presented. A model explaining the limitation of the forward current at decreasing temperature is proposed. The model is based on the concept of current limited by the space charge and caused by hopping transport of electrons in the region of multiple quantum wells. It is shown that the most probable mechanism of charge accumulation is the electron capture by shallow traps. According to the results of different measurements, the activation energy of traps decreases with decreasing temperature, which is consistent with the concept of hopping conductance mechanism in materials with an exponential distribution of the defect state density in the band gap.

Potential of a Spheroid with Generalized Exponential Density Distribution

AbstractThe internal potential of an inhomogeneous layered spheroid with a small ellipticity and general exponential density distribution is derived in an analytical form. The results are presented in the form of standard Gauss hypergeometric function and validated numerically. The computing time when using this formula is noticeably smaller than the time required by numerical integration.

Compressibility effects on Rayleigh–Taylor instability in a vertical inhomogeneous rotating plasma

Compressibility effects on Rayleigh–Taylor instability in inhomogeneous plasma rotating uniformly in an external vertical magnetic field have been investigated. Using the exponential density distribution and in the presence of a fixed boundary condition, the linear growth rate is obtained for a finite compressible plasma layer. As well as the linear growth rate of a heavy compressible plasma layer supported by a lighter one is obtained. It is shown that, in the case of a finite compressible plasma layer and in the absence of an external magnetic field the system is always instable, while in the presence of an external magnetic field the system capitulates to the stability role that plays it. In the case of two compressible plasma layers, the compressibility (the ratio of specific heat values) has a stabilizing role that increases with the presence of an external vertical magnetic field. While the equilibrium pressure at the interface has an instability effect on the growth rates.

Rayleigh-Taylor Instability in Magnetized Plasma

The Rayleigh-Taylor instability in stratified plasma has been investigated in the presence of combined effect of horizontal and vertical magnetic field. The linear growth rate has been derived for the case where plasma with exponential density distribution is confined between two rigid planes by solving the linear MHD equations into normal mode. Some special cases have been particularized to explain the roles the variables of the problem play; numerical solutions have been made and some stability diagrams are plotted and discussed. The results show that, the growth rate depends on the horizontal and vertical components of magnetic field and also depends on the parameter λ*=λLD (λ is constant and LD is the density-scale length). The maximum instability happens at λ*=-0.5 and to get more stability model we select λ* such that it is different than λ*=-0.5. The vertical magnetic field component have a greater effect than the horizontal magnetic field component in the case of large wavelength, while in the case of short wavelength, the horizontal magnetic field components have greater effect than the vertical magnetic field component.

NUMERICAL INVESTIGATIONS OF STABILITY OF STRATIFIED VISCOELASTIC WALTERS' (MODEL B') FLUID/PLASMA IN THE PRESENCE OF QUANTUM PHYSICS SATURATING A POROUS MEDIUM

Quantum effects on the Rayleigh−Taylor instability in an inhomogeneous stratified incompressible, viscoelastic Walters' (model B') fluid/plasma through a porous medium are investigated. The linear growth rate is derived for the case where a plasma with exponential density, viscosity, viscoelasticity, and quantum parameter distribution is confined between two rigid planes at z = 0, z = h. The solution of the linearized equations of the system together with the boundary conditions leads to derive the dispersion relation (the relation between the normalized growth rate and square normalized behavior wave number) using the normal mode technique to explain the roles that the variables of the problem play. The behavior of growth rates with respect to the quantum effect and kinematic viscoelasticity are examined in the presence of porous medium, the medium permeability, and kinematic viscosity. The results show that the quantum effects bring about more stability for a certain wave number band on the growth rate of unstable configuration.

Superbubble evolution in disk galaxies

Galactic winds are a common phenomenon in starburst galaxies in the local universe as well as at higher redshifts. Their sources are superbubbles driven by sequential supernova explosions in star forming regions, which carve out large holes in the interstellar medium and eject hot, metal enriched gas into the halo and to the galactic neighborhood. We investigate the evolution of superbubbles in exponentially stratified disks. We present advanced analytical models for the expansion of such bubbles and calculate their evolution in space and time. With these models one can derive the energy input that is needed for blow-out of superbubbles into the halo and derive the break-up of the shell, since Rayleigh-Taylor instabilities develop soon after a bubble starts to accelerate into the halo. The approximation of Kompaneets is modified in order to calculate velocity and acceleration of a bubble analytically. Our new model differs from earlier ones, because it presents for the first time an analytical calculation for the expansion of superbubbles in an exponential density distribution driven by a time-dependent energy input rate. The time-sequence of supernova explosions of OB-stars is modeled using their main sequence lifetime and an initial mass function. We calculate the morphology and kinematics of superbubbles powered by three different kinds of energy input and we derive the energy input required for blow-out as a function of the density and the scale height of the ambient interstellar medium. The Rayleigh-Taylor instability timescale in the shell is calculated in order to estimate when the shell starts to fragment and finally breaks up. Analytical models are a very efficient tool for comparison to observations, like e.g. the Local Bubble and the W4 bubble discussed in this paper, and also give insight into the dynamics of superbubble evolution.

Arc Tan- Exponential Type Distribution Induced By Stereographic Projection / Bilinear Transformation On Modified Wrapped Exponential Distribution

Abstract In this paper we make an attempt to construct a new three parameter linear model, we call this new model as Arc Tan-Exponential Type distribution, by applying Stereographic Projection or equivalently Bilinear transformation on Wrapped Exponential distribution, Probability density and cumulative distribution functions of this new model are presented and their graphs are plotted for various values of parameters.

Fractal-based exponential distribution of urban density and self-affine fractal forms of cities

Urban population density always follows the exponential distribution and can be described with Clark’s model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark’s model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark’s model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.

Terahertz tomography of a photo-induced carrier based on pump-probe spectroscopy using counterpropagation geometry

A novel technique for the terahertz (THz) tomography of a photo-induced carrier that is based on optical-pump THz-probe time-resolved reflection spectroscopy using counterpropagation geometry of the pump and probe pulses has been proposed. Transient reflection due to the photo-induced carrier provides information about the physical properties and spatial distribution separately. We have experimentally demonstrated this method using a silicon wafer. The obtained complex reflection can be reproduced by the exact solution of Maxwell's equations, assuming an exponential distribution of the photo-induced carrier density.

External Magnetic Field Effects on the Rayleigh-Taylor Instability in an Inhomogeneous Rotating Quantum Plasma

The effects of external magnetic field effects on the Rayleigh-Taylor instability in an inhomogeneous stratified quantum plasma rotating uniformly are investigated. The external magnetic field is considered in both horizontal and vertical direction. The linear growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes at z=0 and z=h, by solving the linear QMHD equations into normal mode. Some special cases are particularized to explain the roles that play the variables of the problem. The results show that, the presence of both external horizontal and vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration. The maximum stability will happen in the case of wave number parallels to or in the same direction of external horizontal magnetic field.

THE STEADY-STATE WIND MODEL FOR YOUNG STELLAR CLUSTERS WITH AN EXPONENTIAL STELLAR DENSITY DISTRIBUTION

A hydrodynamic model for steady state, spherically-symmetric winds driven by young stellar clusters with an exponential stellar density distribution is presented. Unlike in most previous calculations, the position of the singular point R_sp, which separates the inner subsonic zone from the outer supersonic flow, is not associated with the star cluster edge, but calculated self-consistently. When the radiative losses of energy are negligible, the transition from the subsonic to the supersonic flow occurs always at R_sp ~ 4 R_c, where R_c is the characteristic scale for the stellar density distribution, irrespective of other star cluster parameters. This is not the case in the catastrophic cooling regime, when the temperature drops abruptly at a short distance from the star cluster center and the transition from the subsonic to the supersonic regime occurs at a much smaller distance from the star cluster center. The impact from the major star cluster parameters to the wind inner structure is thoroughly discussed. Particular attention is paid to the effects which radiative cooling provides to the flow. The results of the calculations for a set of input parameters, which lead to different hydrodynamic regimes, are presented and compared to the results from non-radiative 1D numerical simulations and to those from calculations with a homogeneous stellar mass distribution.

Rayleigh-Taylor instability in quantum magnetized viscous plasma

Quantum effects on Rayleigh-Taylor instability of stratified viscous plasmas layer under the influence of vertical magnetic field are investigated. By linearly solving the viscous QMHD equations into normal mode, a forth-order ordinary differential equation is obtained to describe the velocity perturbation. Then the growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes. The results show that, the presence of vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration for viscous plasma, which is greater than that of inviscous plasma.