Push Force Analysis of Anchor Block of the Oil and Gas Pipeline in a Single-Slope Tunnel Based on the Energy Balance Method

In this paper, a single-slope tunnel pipeline was analysed considering the effects of vertical earth pressure, horizontal soil pressure, inner pressure, thermal expansion force and pipeline—soil friction. The concept of stagnation point for the pipeline was proposed. Considering the deformation compatibility condition of the pipeline elbow, the push force of anchor blocks of a single-slope tunnel pipeline was derived based on an energy method. Then, the theoretical formula for this force is thus generated. Using the analytical equation, the push force of the anchor block of an X80 large-diameter pipeline from the West—East Gas Transmission Project was determined. Meanwhile, to verify the results of the analytical method, and the finite element method, four categories of finite element codes were introduced to calculate the push force, including CAESARII, ANSYS, AutoPIPE and ALGOR. The results show that the analytical results agree well with the numerical results, and the maximum relative error is only 4.1%. Therefore, the results obtained with the analytical method can satisfy engineering requirements.     

Localised impact of Sitka spruce (Picea sitchensis (Bong.) Carr.) on soil permeability

A typical upland soil catena afforested with Sitka spruce (Picea sitchensis (Bong.) Carr.) was chosen to examine the localised effect of trees on soil permeability. A borehole permeameter was used to measure soil permeability at 0.2 m and approximately 2 m distance from the stem of 20 trees at a fixed measurement depth of 0.25 to 0.45 m. In the case of the near-tree measurements, this corresponded to soil beneath the main root plate of each conifer. Two principal elements of the soil catena: the ferric podzol of the mid-slope and histosol soil of the foot-slope were investigated.The preliminary data set shows that within the ferric podzol element, the permeability of the soil beneath individual conifers was a factor of 5.4 less than that of the adjacent soil. In contrast, within the histosol sub-tree permeabilities could not be distinguished from those of soil 2 m away from each tree. The decrease in sub-tree permeability within the podzol may be caused by sensitivity of the Bsl horizon to consolidation by tree weight or by enhanced illuviation resulting from changes in local soil chemistry. The histosol may be less sensitive to such processes. The results of a consolidation test applied to the Rawls and Brakensiek model of soil permeability supported the possible role of consolidation in the reduction of soil permeability beneath conifers in podzolic soil. Additional data on soil bulk density, porosity and texture are required to corroborate either the consolidation or illuviation hypotheses. As the Bsl horizon of ferric podzol soil is typically slowly permeable, a further decline may (i) restrict root development and thus, increase windthrow hazard, and (ii) increase the lateral flow of water within podzolic Eag horizons and thus affect stream acidification. Deep ploughing of a site prior to afforestation may mitigate such impacts.     

Flow-induced permeation of non-occlusive blood clots: an MRI study and modelling

The success of clot thrombolysis very much depends on efficient clot permeation with blood plasma carrying the thrombolytic agent. In this paper clot permeation was studied by dynamic magnetic resonance imaging (MRI) on artificial non-occlusive blood clots inserted in an artificial circulation system filled with blood plasma to which an MRI contrast agent was added. The MRI results revealed that clot permeation is much faster and more efficient at the entrance of the flow channel across the clot. Clot permeation with fluid was simulated numerically as well. The simulation was based on numerical solution of Navier-Stokes equations for the flow in the channel and within the clot. The clot was considered as a porous material with known permeability and porosity. Based on the calculated velocity profiles, concentration profiles of fluid in the clot were modelled. These agreed well with the MRI results. The presented model of clot permeation with fluid may also serve as a useful extension to numerical modelling of dissolution of non-occlusive blood clots during thrombolytic therapy.     

The distribution of ammonium ion from a localized source into the soil

The distribution of ammoniun ions from a concentrated source in the soil is calculated with a computed model based on chromatographic theory. The analytical solution for the chromatographic equation with convective transport in a pistonlike flow, for a non linear adsorption isotherm, is compared with computer simulation model results and actual experimental data from soil solumns.Adsorption isotherms for the exchange of Ca⁺⁺ by NH₄ ⁺ ions in the range of 0.01 to 6 eq NH₄/I were obtained. The isotherm are described by a modification of Freundlich's isotherm.Ammonium displacement is a frontal movement. The resulting concentration profile is a uniform zone of influence within which ammonium concentration is close to 2/3 of the soil C.E.C. A relatively narrow transition zone exists between the zone of influence and the bulk soil.Good correlation was obtained between experimental and computed ammonium concentration distribution along the soil profile after leaching.The results presented in this work indicate that a quantitative estimation of the extent to which ammonium ions are transported from application site, and the processes following this transport, can be obtained.Present address of the first author: Universidad Catolica de Chile, Dept. of Soils, Chile.     

Comparison of analytically and numerically derived hydrogen exchange-rate distribution functions

Hydrogen exchange-rate probability density functions for lysozyme have been derived by numerical Laplace inversion with the computer program CONTIN. The resulting solution set includes a smooth bimodal solution in agreement with previous analytical results together with a smooth three-peak solution. Numerical analysis of lysozyme hydrogen-exchange data in glycerol/water cosolvent mixtures confirms the previous assignment of the slow-exchange peak to an exchange mechanism involving reversible unfolding. Physicochemical constrations that can reduce the size of the solution set are described. The results are compared with those obtained from previous analytical methods and the limitations of the discrete class and analytical appraches are discussed.     

Vacuum‐enhanced recovery of water and NAPL: Concept and field test

Many hydrocarbon‐contaminated soils contain nonaqueous phase liquid (NAPL) following releases from facilities such as underground storage tanks and pipelines. The recovery of free product by pumping from extraction wells or trenches is often an essential prerequisite step prior to further remedial actions. Vacuum‐enhanced NAPL recovery (sometimes referred to as dual‐phase extraction or bioslurping) has attracted recent attention because it offers a means to increase NAPL recovery rates compared with conventional methods, and to accomplish dewatering, while also facilitating vapor‐based unsaturated zone cleanup. A conceptual model is presented that recognizes the effects that vacuum‐enhanced recovery has on soil water and NAPL, with a focus on liquid residing at negative gage pressures and therefore lacking sufficient potential energy to flow into a conventional recovery well or trench. The imposition during vacuum‐enhanced recovery of subatmospheric pressures within the subsurface can reduce the required potential energy (i.e., the entry suction), allowing liquid to be extracted that hitherto had not been able to flow into the well; moreover, it induces both pneumatic and hydraulic gradients toward the vacuum source that increase the rate of water and NAPL recovery. This conceptual model was tested during a 3‐week‐long pilot study at a South Carolina industrial site at which diesel fuel had been discovered in a saprolite formation. During Phase 1 of the pilot study, conventional recovery (liquid only) was carried out from a well screened at the water table, while during Phase 2 dual‐phase extraction was performed at the same well. The application of 27 kPa vacuum resulted in an increase in NAPL recovery from negligible (Phase 1) to approximately 6.6 l/d (Phase 2), with a concurrent increase in water recovery from approximately 190 to 760 l/ d. Neutron moisture probe observations revealed that vadose‐zone liquids underwent redistribution toward the extraction well in response to the onset of Phase 2, also in accordance with the conceptual model. An understanding of soil physical relationships is crucial to the successful application of these and other in situ soil remediation technologies.     

Effect of macroscale formation of intraluminal thrombus on blood flow in abdominal aortic aneurysms

A mathematical approach of blood flow within an abdominal aortic aneurysm (AAA) with intraluminal thrombus (ILT) is presented. The macroscale formation of ILT is modeled as a growing porous medium with variable porosity and permeability according to values proposed in the literature. The model outlines the effect of a porous ILT on blood flow in AAAs. The numerical solution is obtained by employing a structured computational mesh of an idealized fusiform AAA geometry and applying the Galerkin weighted residual method in generalized curvilinear coordinates. Results on velocity and pressure fields of independent cases with and without ILT are presented and discussed. The vortices that develop within the aneurysmal cavity are studied and visualized as ILT becomes more condensed. From a mechanistic point of view, the reduction of bulge pressure, as ILT is thickening, supports the observation that ILT could protect the AAA from a possible rupture. The model also predicts a relocation of the maximum pressure region toward the zone proximal to the neck of the aneurysm. However, other mechanisms, such as the gradual wall weakening that usually accompany AAA and ILT formation, which are not included in this study, may offset this effect.     

Electrostatic potential and Born energy of charged molecules interacting with phospholipid membranes: calculation via 3-D numerical solution of the full Poisson equation.

Understanding the physicochemical basis of the interaction of molecules with lipid bilayers is fundamental to membrane biology. In this study, a new, three-dimensional numerical solution of the full Poisson equation including local dielectric variation is developed using finite difference techniques in order to model electrostatic interactions of charged molecules with a non-uniform dielectric. This solution is used to describe the electric field and electrostatic potential profile of a charged molecule interacting with a phospholipid bilayer in a manner consistent with the known composition and structure of the membrane. Furthermore, the Born interaction energy is then calculated by appropriate integration of the electric field over whole space. Numerical computations indicate that the electrostatic potential profile surrounding a charge molecule and its resultant Born interaction energy are a function of molecular position within the membrane and change most significantly within the polar region of the bilayer. The maximum interaction energy is observed when the charge is placed at the center of the hydrophobic core of the membrane and is strongly dependent on the size of the charge and on the thickness of the hydrocarbon core of the bilayer. The numerical results of this continuum model are compared with various analytical approximations for the Born energy including models established for discontinuous slab dielectrics. The calculated energies agree with the well-known Born analytical expression only when the charge is located near the center of a hydrocarbon core of greater than 60 A in thickness. The Born-image model shows excellent agreement with the numerical results only when modified to include an appropriate effective thickness of the low dielectric region. In addition, a newly derived approximation which considers the local mean dielectric provides a simple and continuous solution that also agrees well with the numerical results.     

Constitutive model of brain tissue suitable for finite element analysis of surgical procedures.

Realistic finite element modelling and simulation of neurosurgical procedures present a formidable challenge. Appropriate, finite deformation, constitutive model of brain tissue is a prerequisite for such development. In this paper, a large deformation, linear, viscoelastic model, suitable for direct use with commercially available finite element software packages such as ABAQUS is constructed. The proposed constitutive equation is of polynomial form with time-dependent coefficients. The model requires four material constants to be identified. The material constants were evaluated based on unconfined compression experiment results. The analytical as well as numerical solutions to the unconfined compression problem are presented. The agreement between the proposed theoretical model and the experiment is good for compression levels reaching 30% and for loading velocities varying over five orders of magnitude. The numerical solution using the finite element method matched the analytical solution very closely.     

A closed‐form solution for steady‐state coupled phloem/xylem flow using the Lambert‐W function

A closed‐form solution for steady‐state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert‐W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time‐dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed‐form solution, and is expected to be useful as a component part of larger numerical models of entire plants.     

A supramodal number representation in human intraparietal cortex

The triple-code theory of numerical processing postulates an abstract-semantic "number sense." Neuropsychology points to intraparietal cortex as a potential substrate, but previous functional neuroimaging studies did not dissociate the representation of numerical magnitude from task-driven effects on intraparietal activation. In an event-related fMRI study, we presented numbers, letters, and colors in the visual and auditory modality, asking subjects to respond to target items within each category. In the absence of explicit magnitude processing, numbers compared with letters and colors across modalities activated a bilateral region in the horizontal intraparietal sulcus. This stimulus-driven number-specific intraparietal response supports the idea of a supramodal number representation that is automatically accessed by presentation of numbers and may code magnitude information.     

Spectrum of the nonstationary electromyographic signal modelled with integral pulse frequency modulation and its application to estimating neural drive information

The spectrum of nonstationary electromyographic signal (EMG) is investigated, from which the error for neural drive information estimation from nonstationary EMG is studied in terms of signal-to-noise ratio (SNR), in analytical, numerical simulation, and experimental work. The signal refers to the neural drive information embedded within the nonstationary EMG, and noise refers to other portions of EMG that induce error in the estimation. The analytical expressions for the SNRs of force-modulated EMG with both single and multiple motor units (MU) are derived based on a sinusoidal integral pulse frequency modulation (IPFM) model. It is shown that the previously developed SNR expressions for stationary (unmodulated) EMG are special cases of the formulas presented here. The SNR results obtained from numerical simulated EMG agree very well with the analytical result. Results from nonstationary (modulated) surface EMG obtained from seven subjects also match the analytical and simulation results reasonably well. The results obtained from this work establish an analytical framework in studying and estimating the neural drive information contained in the EMG in the context of anisotonic and isometric contractions. Through the analytical study, the effects of different physiological parameters are identified, thus providing theoretical guidelines for developing advanced signal processing methods for nonstationary EMG in applications such as prosthesis control.     

Parametric studies on bioengineering effects of tree root-based suction on ground behaviour

Using native vegetation to improve soil stiffness, stabilise slopes and control erosion is a rapidly evolving process. A theoretical model previously developed by the authors for the rate of tree root water uptake together with an associated numerical simulation is used to study the effects of a wide range of soil, tree, and atmospheric parameters on partially saturated ground. The influence of different parameters on the maximum initial rate of root water uptake is investigated through parametric and sensitivity analyses. Field measurements taken from previously published literature are compared with numerical predictions for validation. The rate of selected parameters such as potential transpiration and its distribution, suction at wilting point, the coefficient of permeability and the distribution of root length density are studied in detail. The analysis shows that the rate of potential transpiration increases the soil matric suction and ground settlement, while the potential transpiration rate has an insignificant effect on the distribution of soil suction. Root density distribution factors affect the size of the influence zone. Suction at the wilting point increases the soil matric suction and ground settlement, whereas the saturation permeability decreases the maximum soil matric suction generated. The analysis confirms that the most sensitive parameters, including the coefficients of the tree root system, the transpiration rate, the permeability of the soil and its suction at the wilting point should be measured or estimated accurately for an acceptable prediction of ground conditions in the vicinity of trees.     

On the time for gene silencing at duplicate Loci

A simple approximate formula is found for the mean time for mutant genes to first fix at one or another of two duplicate loci. The fixation is a result of one-way mutation from the wild-type to the mutant alleles, but is retarded by strong selection against the doubly homozygous mutants. The two-dimensional diffusion that models the evolution of the mutant allele frequencies at the two loci is studied by means of a transformation to two univariate diffusions having different time scales. Most of the results, but not all, agree well with the numerical studies by previous authors. Some new simulation results are presented, which agree well with the analytical results and, therefore, cast doubt on some previous simulations.     

Restricted diffusion of molecules in porous affinity chromatography adsorbents.

A restricted diffusion model is constructed and solved in order to study the permeability of large adsorbate molecules in the pores of affinity chromatography media, when the adsorbate molecules are adsorbed onto immobilized ligands. The combined effects of steric hindrance at the entrance to the pores and frictional resistance within the pores, as well as the effects of pore size distribution, pore connectivity of the adsorbent, molecular size of adsorbate and ligand, and the fractional saturation of adsorption sites (ligands), are considered. Affinity adsorbents with dilute and high ligand concentrations are examined, and the permeability of the adsorbate in porous networks of connectivity nT is studied by means of effective medium approximation (EMA) numerical solutions. As expected, the permeability of the adsorbate decreases as the size of the adsorbate and/or ligand molecule increases. The permeability also decreases when the fractional saturation of the ligands increases, as well as when the pore connectivity of the network decreases. The dependence of the permeability on the pore connectivity tends to be less marked in adsorbents with concentrated ligand than in porous media with dilute ligand concentration. The conditions are also presented for which the percolation threshold is attained in a number of different systems. The restricted diffusion model and results of this work may be of importance in studies involving the modeling, prediction of the dynamic behavior, design, and control of affinity chromatography (biospecific adsorption) systems employing porous adsorbents. The theoretical results may also have important implications in the selection of a ligand as well as in the selection and construction of an affinity porous matrix, so that the adsorbate of interest can be efficiently separated from a given solution. Furthermore, with appropriate modifications this restricted diffusion model may be used in studies involving the immobilization of ligands or enzymes in porous solids.     

The effects of axial diffusion and permeability barriers on the transient response of tissue cylinders. I. Solution in transform space

Transient mass transfer in a Krogh tissue cylinder is described by a model taking into account axial diffusion in both blood and tissue, a localized permeability barrier at the capillary membrane and a diffusion barrier on the outer surface and at the ends of the cylinder. Radial diffusion in both blood and tissue is assumed to be infinitely fast. In contrast to previous work, which has usually relied on numerical methods for solving the equations, an exact solution is presented here in Laplace transform space. This allows calculation of the moments of the concentration at any point in the cylinder. Numerical results indicate that the moments of the residence time distribution are affected by the boundary conditions used, and that the discrepancies between the predictions using different conditions may be large in some physiological situations. Order-of-magnitude calculations are used to estimate when the use of simpler models may be feasible. The transform space solution may also be useful for parameter estimation, but it seems preferable to extend the present results to a time-domain solution for this purpose.     

A compact model to predict quantized sub-band energy levels and inversion layer centroids of MOSFETs with a parabolic potential well approximation

A compact model to predict sub-band energy levels and inversion charge centroids in the MOSFET surface inversion layer has been presented in this paper for parabolic potential well approximation. Based on a coupled solution of the Schrödinger equation and the Poisson equation following the WKB method, one transcendental equation of the sub-band energy level has been rigorously derived and then the approximate analytical solutions for the sub-band energy levels and the inversion charge centroids have been obtained. The analytical results are compared with the numerical data and a good agreement between the analytical and numerical is found.     

Coupled water transport in standing gradient models of the lateral intercellular space.

A standing gradient model of the lateral intercellular space is presented which includes a basement membrane of finite solute permeability. The solution to the model equations is estimated analytically using the "isotonic convection approximation" of Segel. In the case of solute pumps uniformly distributed along the length of the channel, the achievement of isotonic transport depends only on the water permeability of the cell membranes. The ability of the model to transport water against an adverse osmotic gradient is the sum of two terms: The first term is simply that for a well-stirred compartment model and reflects basement membrane solute permeability. The second term measures the added strength due to diffusion limitation within the interspace. It is observed, however, that the ability for uphill water transport due to diffusion limitation is diminished by high cell membrane water permeability. For physiologically relevant parameters, it appears that the high water permeability required for isotonic transport renders the contribution of the standing gradient relatively ineffective in transport against an osmotic gradient. Finally, when the model transports both isotonically and against a gradient, it is shown that substantial intraepithelial solute polarization effects are unavoidable. Thus, the measured epithelial water permeability will grossly underestimate the water permeability of the cell membranes. The accuracy of the analytic approximation is demonstrated by numerical solution of the complete model equations.     

Uncertainty in Predicting the Rate of Mass Removal Created by Soil Vapor Extraction Systems

Recently, several soil gas flow and vapor transport numerical models have been developed for use in designing soil vapor extraction (SVE) systems. This article examines how uncertainties in soil properties, specifically permeability, corresponds to uncertainties in the prediction of mass removal rates by numerical models. Scaling equations were first derived for both relevant geometric and nongeometric modeling parameters to enable the examination of the impact of uncertainties associated with spatial variations in soil properties on the prediction of mass removal rates in a somewhat general manner. Monte Carlo analyses of volatile organic compound removal from a hypothetical contaminated soil by SVE were then used to investigate the effect of system operation time and permeability variance on the uncertainty in mass removal rates as predicted by a numerical model. Results showed that uncertainty in the predicted mass removal rate increases as both mass removal increases and as the assumed permeability variance increases. These results indicate that the design of SVE system using deterministic modeling methods may not always correlate to an effective SVE system.