Computational Investigation on the Dispersive Transport of Angiographic Contrast Injected Antegradely Into Flow in a Tube

2007 ◽  
Author(s):  
Qing Hao ◽  
Baruch B. Lieber
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Single Molecule ◽  
Molecular Diffusion ◽  
Local Concentration ◽  
Dispersive Transport ◽  
Cross Sectional ◽  
Advection Dispersion ◽  
The Cross ◽  
The Difference

When a solute such as angiographic contrast is introduced into a solvent such as blood analog fluid flowing in a straight circular tube, it spreads under the combined action of molecule diffusion and the variation of velocity over the cross-section [8]. If two molecules are being carried in the flow, for example, one in the center and one near the wall, the rate of separation caused by the difference in bulk velocity will greatly exceed that caused by molecule motion. Given enough time, any single molecule would wander randomly throughout the cross section of the pipe because of molecular diffusion, and would sample at random all the advective velocities [4]. Therefore, Taylor [8] adopted the Lagrangian approach to the problem, casting the equations in a coordinate system that moves with the average velocity of the flow and replacing the molecular diffusion coefficient with a dispersion coefficient, and the local concentration with the cross sectional mean concentration. Recasting Taylor’s equation in an inertial coordinate system one obtained the so called advection-dispersion equation.

Automated Diagonal Slice and View Solution for 3D Device Structure Analysis

2018 ◽  
Author(s):  
Sang Hoon Lee ◽  
Jeff Blackwood ◽  
Stacey Stone ◽  
Michael Schmidt ◽  
Mark Williamson ◽  
...  
Keyword(s):  
Cross Section ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Image Data ◽  
Planar Surface ◽  
Device Structure ◽  
Cross Sectional ◽  
Device Structures ◽  
The Cross ◽  
Planar Analysis

Abstract The cross-sectional and planar analysis of current generation 3D device structures can be analyzed using a single Focused Ion Beam (FIB) mill. This is achieved using a diagonal milling technique that exposes a multilayer planar surface as well as the cross-section. this provides image data allowing for an efficient method to monitor the fabrication process and find device design errors. This process saves tremendous sample-to-data time, decreasing it from days to hours while still providing precise defect and structure data.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

The Cross Section of Expected Returns with MIDAS Betas

2011 ◽  
Vol 47 (1) ◽  
pp. 115-135 ◽  
Author(s):  
Mariano González ◽  
Juan Nave ◽  
Gonzalo Rubio
Keyword(s):  
Cross Section ◽  
Risk Premium ◽  
Market Risk ◽  
Ordinary Least Squares ◽  
Mixed Data ◽  
Expected Returns ◽  
Data Sampling ◽  
Cross Sectional ◽  
Market Risk Premium ◽  
The Cross

AbstractThis paper explores the cross-sectional variation of expected returns for a large cross section of industry and size/book-to-market portfolios. We employ mixed data sampling (MIDAS) to estimate a portfolio’s conditional beta with the market and with alternative risk factors and innovations to well-known macroeconomic variables. The market risk premium is positive and significant, and the result is robust to alternative asset pricing specifications and model misspecification. However, the traditional 2-pass ordinary least squares (OLS) cross-sectional regressions produce an estimate of the market risk premium that is negative, and significantly different from 0. Using alternative procedures, we compare both beta estimators. We conclude that beta estimates under MIDAS present lower mean absolute forecasting errors and generate better out-of-sample performance of the optimized portfolios relative to OLS betas.

An Analytical Method of Analyzing the Heat Conduction for the Unequal Cross-Section Straight Fin

2013 ◽  
Vol 365-366 ◽  
pp. 1211-1216
Author(s):  
Fan Zhang ◽  
Peng Yun Song
Keyword(s):  
Heat Conduction ◽  
Cross Section ◽  
Analytical Method ◽  
Thermal Analyses ◽  
Cross Sectional ◽  
Cross Section Area ◽  
Section Area ◽  
Calculation Results ◽  
The Cross ◽  
Analytical Expressions

The cross-section area of straight fin is often considered to be equal in the thermal analyses of straight fin, but sometimes it is unequalin actual situation. Taking a straight fin with two unequal cross-sectional areas as an example,an analytical method of heat conduction for unequal section straight fin is presented. The analytical expressions of temperature field and heat dissipating capacity about the fin,which has a smaller cross-section area near the fin base and a larger one, is obtained respectively. The calculation results of the unequal cross-section are fully consistent with the equal area one, so the method is proved right. The results show that the larger the cross section areanear the base,the better is the heat transfer, and the temperature at the base with larger cross-section area is lower than that with smaller cross-section area when the amount of heat is fixed.

scholarly journals Changes in Cross-sectional Areas of Posterior Extensor Muscles in Thoracic Spine: A 10-year Longitudinal MRI Study

2021 ◽  
Author(s):  
Hitoshi Umezawa ◽  
Kenshi Daimon ◽  
Hirokazu Fujiwara ◽  
Yuji Nishiwaki ◽  
Takehiro Michikawa ◽  
...  
Keyword(s):  
Cross Section ◽  
Disc Degeneration ◽  
Thoracic Spine ◽  
Erector Spinae ◽  
Related Factors ◽  
Cross Sectional ◽  
Fat Infiltration ◽  
Extensor Muscles ◽  
The Cross ◽  
Muscle Fat Infiltration

Abstract This study aimed to examine changes in the cross-sectional areas (CSAs) of posterior extensor muscles in the thoracic spine over 10 years and identify related factors. The subjects of this study were 85 volunteers (mean age: 44.8 ± 11.5) and the average follow-up period was about 10 years. The CSAs of the transversospinalis muscles, erector spinae muscles, and total CSAs of the extensor muscles from T1/2 to T11/12 were measured on MRI. The extent of muscle fat infiltration was assessed by the signal intensity (luminance) of the extensor muscles’ total cross section compared to a section of pure muscle. Associations of age, sex, body mass index, lifestyle, back pain, neck pain, neck stiffness, and intervertebral disc degeneration with the 10-year CSAs changes and muscle fat infiltration were examined by Poisson regression analysis. The mean CSAs of all index muscles increased significantly. Exercise habit was associated with increased CSAs of the erector spinae muscles and the total area of the extensor muscles. The cross-section mean luminance increased significantly from baseline, indicating a significant increase of fat infiltration in the posterior extensor muscles. Progression of disc degeneration was negatively associated with the increase of fat infiltration in the total extensor muscles.

scholarly journals Supplemental Material: Plate boundary trench retreat and dextral shear drive intracontinental fault-slip histories: Neogene dextral faulting across the Gabbs Valley and Gillis Ranges, Central Walker Lane, Nevada

2020 ◽  
Author(s):  
J. Lee ◽  
et al.
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Plate Boundary ◽  
Fault Slip ◽  
Cross Sectional ◽  
Walker Lane ◽  
Dextral Shear ◽  
The Cross

<div>Figure 6. Interpretative cross sections illustrating the cross-sectional geometry of several paleovalleys. See Figure 3 for location of all cross sections and Figure 8 for location of cross section CCʹ. Cross sections AAʹ and BBʹ are plotted at the same scale, and cross section CCʹ is plotted at a smaller scale. Figure 6 is intended to be viewed at a width of 45.1 cm.</div>

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

scholarly journals Influence of Geometric Parameters on Aerodynamic and Acoustic Performances of Bladeless Fans

2019 ◽  
Author(s):  
Ang Li ◽  
Jun Chen ◽  
Yangfan Liu ◽  
Stuart Bolton ◽  
Patricia Davies
Keyword(s):  
Cross Section ◽  
Fluid Dynamic ◽  
Geometric Parameters ◽  
Design Stage ◽  
Air Velocity ◽  
Cross Sectional ◽  
Future Design ◽  
Cross Sectional Profile ◽  
The Cross ◽  
Sectional Profile

Abstract In recent years, the bladeless fan that does not have visible impellers have been widely applied in household appliances. Since the customers are particularly sensitive to noise and the strength of wind generated by the fan, the aerodynamic and acoustic performances of the fan need to be accurately characterized in the design stage. In this study, computational fluid dynamic (CFD) and computational aeroacoustics (CAA) are applied to investigate the performances of different designs of a bladeless fan model. The influence of four parameters, namely the airfoil selection for cross-section of the wind channel, the slit width, the height of cross-section and the location of the slit, is investigated. The results indicate the streamwise air velocity increases significantly by narrowing the outlet, but the noise level increases simultaneously. In addition, the generated noise increases while the height of fan cross-section increases, and a 4mm height of the cross section is optimal for aerodynamic performance. When the slit is closer to the location of maximum thickness, the performances of the bladeless fan increases. Moreover, the performance is not changed significantly by changing the cross-sectional profile. Finally, the optimal geometric parameters are identified to guide the future design of the bladeless fan.

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