Exponential Function Of Depth Research Articles

Experimental and theoretical research on the debrining process in sediments for a gas storage salt cavern

The sediments account for a large part of the total mined volume of the cavern in high impurity salt mines. This paper was aimed at the scientific problem of gas storage in the pore space of the sediments, and expanded the storage capacity of salt cavern in high impurity salt mines. Debrining in the mined space of salt caverns (contained sediments) is a vital step to complete the gas storage. To experimentally observe the debrining process, debrining experiments are carried out using a self-developed experimental device. The debrining process can be divided into four typical stages, e.g., rapid increase of injection gas pressure, discharging the upper brine, i.e. the brine free of sediments, discharging the brine in sediments, and rapid decrease of injection gas pressure. A mathematical model is proposed for calculating debrining parameters of a salt cavern including sediments based on the pressure equilibrium principle at the gas-brine interface. A numerical method is established for calculating the total debrining time of irregular salt caverns including sediments. The effective cross-sectional area of debrining process is calculated by using the porosity of the sediments. A linear function of the porosity of the transition zone of the sediment surface is put forward. Therefore, the porosity of the upper brine space can gradually transition to the sediments, avoiding the error of sudden increase of the gas-brine interface and debrining rate, which is consistent with the practical debrining process. The porosity of sediments is considered to be a decaying exponential function of depth based on the accumulation of sediment particles. The cross-sectional area at any depth can be obtained through the interpolation of the sonar scanning data. The Jianghan salt cavern is selected for the applications of the proposed model, and the descending speed and depth of the gas-brine interface, and injection gas pressure with debrining time are analyzed. Results show that the greater the debrining rate, the shorter the time to reach the final sediment surface. The descending speed of the gas-brine interface shows a U-shaped curve, which is significantly affected by the cavern shape and porosity of sediments. The increment of the debrining rate has little effect on the ultimate injection gas pressure but has a significant effect on the increasing rate of injection gas pressure. These results can provide a reference for enhancing gas storage by using the sediment pore space of the mined volume and thereby expanding the effective gas storage volume of salt caverns.

Effect of Initial Stress on an SH Wave in a Monoclinic Layer over a Heterogeneous Monoclinic Half-Space

Considering the propagation of an SH wave at a corrugated interface between a monoclinic layer and heterogeneous half-space in the presence of initial stress. The inhomogeneity in the half-space is the causation of an exponential function of depth. Whittaker’s function is employed to find the half-space solution. The dispersion relation has been established in closed form. The special cases are discussed, and the classical Love wave equation is one of the special cases. The influence of nonhomogeneity parameter, coupling parameter, and depth of irregularity on the phase velocity was studied.

Influence of irregular geologies and inhomogeneity on SH-wave propagation

In the present paper, a study is performed in an irregular earth crust, layered over a semi-infinite half-space under the effect of gravity. The irregularities at the interface are possible combinations of geometric shapes such as rectangular, paraboic and triangular notches. The aim of the study is to come up with the influence of these irregularities on the phase velocity of shear horizontal waves. The current work also explores how inhomogeneities affect SH-wave propagation. The medium is assumed to exhibit inhomogeneities as a function of depth. These functions are the product of a linear algebraic function and an exponential function of depth. By means of separation of variables and the substitution method, the equation of motion is reduced to the hypergeometric equation. Suitable boundary conditions are employed to derive a closed form of the dispersion equation. Numerical computations are performed to visualize the impact of irregularity and inhomogeneity. It is observed that the irregular interfaces and the inhomogeneity involved in the medium have a significant effect on SH-wave propagation.

The Nonlinear Effective Attenuation Coefficient of Spaceborne Oceanic Lidar Signal

Multiple scattering is an inevitable effect in spaceborne oceanic lidar because of the large footprint size and the high optical density of seawater. The effective attenuation coefficient klidar in oceanic lidar equation, which indicates the influence of the multiple scattering effect on the formation of lidar returns, is an important parameter in the retrieval of inherent optical properties (IOPs) of seawater. In this paper, the nonlinearity of klidar and the relationships between klidar and the IOPs of seawater are investigated by solving the radiative transfer equation with an improved semianalytic Monte Carlo model. klidar is found to decrease exponentially with the increase of depth in homogeneous waters. klidar is given as an exponential function of depth and IOPs of seawater. The results in this paper can help to have a better understanding of the multiple scattering effect of spaceborne lidar and improve the retrieval accuracy of the IOPs of seawater using spaceborne lidar.

Torsional wave frequency in heterogeneous earth crust lying over dry sandy semi-infinite substratum

The present study is carried out to investigate the transference of torsional surface waves in a heterogeneous anisotropic crust lying over a dry sandy half-space. The rigidities and densities as well as the initial stress are assumed varying as a function of depth in both the media. These variations are the product of the polynomial function of depth in degree n (n ∈ ℝ) and the exponential function of depth. Following the theory of elastic waves, the mathematical model is established. Separation of variables is used to obtain the displacement in the layer and the half-space. Intrinsic boundary conditions are imposed to derive the dispersion equation. The inhomogeneity parameters associated with the rigidity, the density, and the initial stress of the medium are found to have substantial influence on the phase velocity of the torsional surface wave. The graphical presentations are drawn to exhibit the findings. The results thus obtained are significant for the investigation and characterization of torsional surface wave in the heterogeneous anisotropic layer.

The Molecular Basis for Understanding the Impacts of Ocean Warming

AbstractA grand challenge for ocean chemists in the years ahead lies in the need to tackle the chemical consequences of ocean warming with the same rigor and intensity that has been brought to bear on the physical chemistry of ocean acidification. For over 50 years ocean chemistry has been dominated by the study of pH‐dependent processes, but to address the biogeochemical impacts of ocean warming, we will need to rapidly advance the discipline of ocean chemical physics where temperature is the master variable and the basic unit is the Joule. Just as it would be impossible to understand the ocean CO2 system without awareness of the essential pH‐dependent CO2‐HCO3‐CO3 equilibria, so too is it impossible to describe ocean chemical physics without knowledge of the bimolecular structure of water. Water, and water in sea water, is composed of a complex of dominant hydrogen bonded forms, and the singlet molecular H2O species, in temperature‐controlled equilibrium and the ratio of these forms, can now be precisely determined. The physical properties of sea water are traditionally described by fitting an ad hoc collection of coefficients to experimental data. They are more accurately described as temperature and pressure perturbations of the underlying molecular equilibrium state. Ocean oxygen consumption rates are accurately described as an Arrhenius function, and not as an exponential function of depth as has been the tradition for over 50 years. We do not now have good correlation between ocean models and observed warming and oxygen declines, and full anoxia with the emergence of hydrogen sulfide over large regions of the ocean is possible. The parallel ocean invasions of heat and fossil fuel CO2 must be combined to estimate their full impact.

Relationship between the effective attenuation coefficient of spaceborne lidar signal and the IOPs of seawater.

Multiple scattering is an inevitable effect in spaceborne oceanic lidar because of the large footprint size and the high optical density of seawater. The effective attenuation coefficient klidar in the oceanic lidar equation, which indicates the influence of the multiple scattering effect on the formation of lidar returns, is an important parameter in the retrieval of inherent optical properties (IOPs) of seawater. In this paper, the relationships between klidar of the spaceborne lidar signal and the IOPs of seawater are investigated by solving the radiative transfer equation with an improved semianalytic Monte Carlo model. Apart from the geometric loss factors, klidar is found to decrease exponentially with the increase of depth in homogeneous waters. klidar is given as an exponential function of depth and IOPs of seawater. The mean percentage errors between klidar calculated by the exponential function and the simulated ones in three typical stratified waters are within 0.5%, proving the effectiveness and applicability of this klidar-IOPs function. The results in this paper can help researchers have a better understanding of the multiple scattering effect of spaceborne lidar and improve the retrieval accuracy of the IOPs and the chlorophyll concentration of case 1 water from spaceborne lidar measurements.

Study of Heat Source Calibration and Modelling for Laser Welding Process

Heat source model is an important part when carrying out simulations of welding processes. The calibration process involves a great amount of numerical simulations or theoretical deductions with many simplifications. In this paper, an interaction finite element and optimization algorithm package is programmed to automatically calibrate heat source models. The results are then used to establish mathematical relationships between parameters of heat source and welding process variables. The models show that the absorption efficiency and depth of heat source are exponential functions of depth of focus and laser power, respectively while radius of heat source is determined by depth of focus quadratically.

Dispersion study of SH-wave propagation in an irregular magneto-elastic anisotropic crustal layer over an irregular heterogeneous half-space

This study investigates the effect of various parameters on the propagation of seismic SH-waves in a magneto-elastic anisotropic crustal layer with corrugated boundary surfaces, lying over a heterogeneous half-space. The shear elastic modulus and mass density of half-space are the exponential functions of depth. Inclusion of the concept of corrugated irregularity with magneto-elasticity in the anisotropic (Monoclinic) medium and heterogeneity in the half-space medium brings a novelty to the existing literature related to the study of SH-wave. The expression of general dispersion relation has been established in closed form by using suitable boundary conditions. The effects of magneto-elastic coupling, heterogeneity, corrugation, undulatory and position parameters on the phase velocity of SH-wave have been computed numerically and demonstrated graphically. Moreover, different cases of free and common surface corrugations are studied which serve as a focal theme of the study.

Vertical and horizontal distributions of microbial abundances and enzymatic activities in propylene-glycol-affected soils

The natural microbial activity in the unsaturated soil is vital for protecting groundwater in areas where high loads of biodegradable contaminants are supplied to the surface, which usually is the case for airports using aircraft de-icing fluids (ADF) in the cold season. Horizontal and vertical distributions of microbial abundance were assessed along the western runway of Oslo Airport (Gardermoen, Norway) to monitor the effect of ADF dispersion with special reference to the component with the highest chemical oxygen demand (COD), propylene glycol (PG). Microbial abundance was evaluated by several biondicators: colony-forming units (CFU) of some physiological groups (aerobic and anaerobic heterotrophs and microscopic fungi), most probable numbers (MPN) of PG degraders, selected catabolic enzymatic activities (fluorescein diacetate (FDA) hydrolase, dehydrogenase, and β-glucosidase). High correlations were found between the enzymatic activities and microbial counts in vertical soil profiles. All microbial abundance indicators showed a steep drop in the first meter of soil depth. The vertical distribution of microbial abundance can be correlated by a decreasing exponential function of depth. The horizontal trend of microbial abundance (evaluated as total aerobic CFU, MPN of PG-degraders, and FDA hydrolase activity) assessed in the surface soil at an increasing distance from the runway is correlated negatively with the PG and COD loads, suggesting the relevance of other chemicals in the modulation of microbial growth. The possible role of potassium formate, component of runway de-icers, has been tested in the laboratory by using mixed cultures of Pseudomonas spp., obtained by enrichment with a selective PG medium from soil samples taken at the most contaminated area near the runway. The inhibitory effect of formate on the growth of PG degraders is proven by the reduction of biomass yield on PG in the presence of formate.

PENDEKATAN BARU PEMETAAN BATHIMETRIC MENGGUNAKAN DATA PENGINDERAAN JAUH SPOT STUDI KASUS: TELUK PERIGI DAN TELUK POPOH (THE NEW APPROACH TO MAPPING BATHIMETRIC USING SPOT REMOTE SENSING DATA CASE STUDY: THE BAY AND POPOH GULF)

Bathymetric mapping derived from remote sensing have been carried out researchers, in order to determine the depth of the shallow waters especially sallow water depth. Bathymetric relief map shows the earth/terrain depicted by contour lines is called the isobath. Usually bathymetric determination using exponential function of depth. While in this paper described a new approach to calculate the depth of seawater derived from SPOT-4 satellite data using empirical formulas functions of logarithmic or quadratic equation built through correlasi the depth map obtained from DIHIDROS (Navy) with Digital Number or the reflectance values of SPOT band-1. This experience has been tested at Perigi bay in Trenggalek district and Popoh bay in Tulung Agung district. Based on the calculations, the spread of sallow water depth on Perigi and popoh bay about 5 – 70 meters
 Key words: Bathymetric, SPOT, Isobaths, Shallow water depth. correlation

Fractal behavior in continental crustal heat production

Abstract. The distribution of crustal heat production, which is the most important component in the elucidation of continental thermal structure, still remains a theoretical assumption. In general the heat production values must decrease with depth, but the form of decrease of heat production in the crust is not well understood. The commonly used heat production models are: "block model", in which heat production is constant from the surface to a given depth and the "exponential model", in which heat production diminishes as an exponential function of depth. The exponential model is more widely used wherein sources of the errors are heterogeneity of rock and long wavelength changes due to changes in lithology and tectonic elements, and as such exponential distribution does not work satisfactorily for the entire crust. In the present study, we analyze for the first time, deep crustal heat production data of six global areas namely Dharwar craton (India), Kaapvaal craton (South Africa), Baltic shield (Kola, Russia), Hidaka metamorphic belt (Japan), Nissho pluton (Japan) and Continental Deep Drilling site (KTB, Germany). The power spectrum of all the studied data sets exhibits power law behaviour. This would mean slower decay of heat production with depth, which conforms to the known geologic composition of the crust. Minimum value of the scaling exponent has been found for the KTB borehole, which is apparently related to higher heat production of gneisses, however for other study areas, scaling exponent is almost similar. We also found that the lower values of scaling exponents are related to higher heat production in the crust as is the case in KTB. Present finding has a direct relevance in computation of temperature-depth profiles in continental regions.

Scalar Conservation Laws with Nonconstant Coefficients with Application to Particle Size Segregation in Granular Flow

Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is nonstandard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case.

Role of epidermis in the optics and thermal physics of human skin

Some engineering approaches to the problems of optics and thermophysics of biological tissues have been developed. The light fields both within and beyond biological medium have been studied. The role of the epidermis in the formation of these fields is revealed. It is shown that in the general case epidermis cannot be considered as a spectral filter that only absorbs and does not scatter light. A convenient approximation of the fluence rate in a two-layer (epidermis and dermis) tissue is proposed, which is the sum of two exponential functions of depth in the epidermis. This approximation made it possible to obtain an analytical solution to the problem of heating biological tissues by an external narrow light beam. It is found that epidermis only slightly affects the temperature fields under blue light irradiation. However, when an external source of red light is used, the epidermis works as a heater and can increase several times the dermis temperature in comparison with a single-layer tissue. The reasons for these heating features are discussed. Examples of corresponding calculations are given.

Distributed and integrated response of a geographic information system‐based hydrologic model in the eastern Palouse region, Idaho

AbstractVerification of distributed hydrologic models is rare owing to the lack of spatially detailed field measurements and a common mismatch between the scale at which soil hydraulic properties are measured and the scale of a single modelling unit. In this study, two of the most commonly calibrated parameters, i.e. soil depth and the vertical distribution of lateral saturated hydraulic conductivity Ks, were eliminated by a spatially detailed soil characterization and results of a hillslope‐scale field experiment. The soil moisture routing (SMR) model, a geographic information system‐based hydrologic model, was modified to represent the dominant hydrologic processes for the Palouse region of northern Idaho. Modifications included Ks as a double exponential function of depth in a single soil layer, a snow accumulation and melt algorithm, and a simple relationship between storage and perched water depth (PWD) using the drainable porosity. The model was applied to a 2 ha catchment without calibration to measured data. Distributed responses were compared with observed PWD over a 3‐year period on a 10 m × 15 m grid. Integrated responses were compared with observed surface runoff at the catchment outlet. The modified SMR model simulated the PWD fluctuations remarkably well, especially considering the shallow soils in this catchment: a 0·20 m error in PWD is equivalent to only a 1·6% error in predicted soil moisture content. Simulations also captured PWD fluctuations during a year with high spatial variability of snow accumulation and snowmelt rates at upslope, mid‐slope, and toe slope positions with errors as low as 0·09 m, 0·12 m, and 0·12 m respectively. Errors in distributed and integrated model simulations were attributed mostly to misrepresentation of rain events and snowmelt timing problems. In one location in the catchment, simulated PWD was consistently greater than observed PWD, indicating a localized recharge zone, which was not identified by the soil morphological survey. Copyright © 2006 John Wiley & Sons, Ltd.

Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy

Most models of light propagation through tissue assume that the scattering properties of various tissue layers are the same. We present evidence that the scattering coefficient of cervical epithelium varies by a factor of 3 within the epithelium owing to variations in nuclear density and to the presence of keratin. We estimated the scattering coefficient from regions of normal and precancerous cervical epithelium by fitting reflectance measurements from confocal images to an exponential function of depth based on Beer's law of attenuation. The results suggest that the normal cervix is characterized by highly variable scattering in the superficial epithelium, low scattering in the intermediate epithelium, and high scattering in the basal and stromal regions. In high-grade dysplasia, high scattering from high-density nuclei is observed throughout the entire epithelium.

Formation of Nanocrystalline Structure at the Surface of Drill Hole in Steel

Microstructure of martensite steel near drill hole surface was investigated. The microstructure of drill hole surface can be divided into 3 layers with depth. From top surface, nanocrystalline layer, equiaxed submicron grain layer and deformed martensite structure layer. Nanograined layers have extremely high hardness, similar to those observed in the specimens treated by shot peening, ball milling, ball drop and particle impact deformation. The measured amount of shear strain produced by drilling was found to be an exponential function of depth from the hole surface. The amount of true strain at the hole surface region was estimated to exceed 7 which is considered to be the necessary amount of strain to produce nanocrystalline structure.

Vertical Nutrient Distributions in the Western North Pacific Ocean: Simple Model for Estimating Nutrient Upwelling, Export Flux and Consumption Rates

A one-dimensional, steady-state model has been developed to understand the factors controlling vertical distributions of nutrients such as nitrate and phosphate in the western North Pacific water columns. The model includes simple physics and some biogeochemical processes. Nutrients are supplied by upwelling of nutrient-rich deep waters with a constant upwelling velocity and nutrient regeneration due to decomposition of sinking particulate matter; the latter is expressed by an exponential-type export flux. Nutrients are consumed in the water column due to uptake by marine organisms, represented by a first-order substrate kinetics. The consumption rate constant is given as an exponential function of depth. The model has been applied to a data set of WOCE (World Ocean Circulation Experiment) P9 one-time measurements observed in the western North Pacific. The calculated curves fit well to observed vertical nutrient profiles from 100 m depth to over 2,500 m depth at 35 stations from 19°N to 33°30′ N along 137°E with correlation factors of greater than 0.998. A modified model, including a correction term representing a depth-dependent upwelling velocity, can reproduce observed vertical nutrient profiles at 32 stations from 5°N to 18°30′ N along 137°E with correlation factors greater than 0.993. The results support the hypothesis that most of the vertical nutrient profiles in the western North Pacific are controlled by particle export flux, consumption rate, remineralization rate and upwelling velocity.

Dating buried sediments using radioactive decay and muogenic production of 26Al and 10Be

Cosmogenic [ 26Al] and [ 10Be] depth profiles can be used to date river terrace sediments over million-year timescales, provided that production rates are well constrained with depth. Production by nucleon spallation, negative muon capture, and fast muon reactions can be approximated as exponential functions of depth, up to ∼5000 g cm −2. These production rates are used to date a ∼10 m profile of eroded terrace sediments to 1.50 +0.32/ −0.25 Ma. The measured [ 10Be] profile and the terrace age agree well with expectations, demonstrating feasibility of the technique.

Laser induced heating and emission of electrons from metallic targets

A high power laser incident on a metallic target heats the electrons in the skin layer within a few ps. For a specific dependence of electron–phonon collision frequency on electron temperature, ν∝Te1/2, the steady state electron temperature profile turns out to be an exponential function of depth. The heated electrons raise the rate of thermionic emission. When the laser is significantly converted into a surface plasma wave the rate of heating and emission is considerably enhanced.