Geometric Scale Factor Research Articles

Steady unsaturated flow in two-dimensional scale-heterogeneous porous media

Unsaturated flow in scale heterogeneous porous media is described by a class of nonlinear partial differential equations involving three general coefficient functions. It is shown that among these, there is a large class of integrable models, being transformable to linear equations even when the spatially varying geometric dilation scale factor is an arbitrary twice differentiable function. Explicit solutions are constructed for basic boundary value problems that relate to field and laboratory measurements. In one of these solutions, the flow pattern is unaffected by the heterogeneity even though the water concentration is modified. From another solution, we predict the bulk conductivity of a heterogeneous soil sample with a constant hydraulic potential difference maintained between the ends.

Nucleate pool boiling from coated surfaces in saturated R-134a and R-407c

Pool nucleate boiling heat transfer experiments from coated surfaces immersed in saturated R-134a and R-407c with porous aluminum, copper, molybdenum, and pitted coating on a copper surface were conducted. The influence of coating thickness and porosity on heat transfer and boiling hysteresis were studied. The enhanced surface heat transfer coefficients are 2.5 times higher than those of the smooth surface. Furthermore, the effects of refrigerant thermophysical properties are also presented and discussed. The experimental data for plasma and flame spray coating surfaces were correlated in terms of the Reynolds number based on a mean pore diameter and porosity, Jakob number, constant heat flux number and geometric scale factor to provide a thermal design basis for engineering application.

Quantitative Evaluation of Effect of Gravity on Small-Scale Modeling

In many cases, small-scale modeling requires the scaling up of the gravitational acceleration. Yet this requirement sets a technical problem, and unless the use of a centrifuge is available, it is not fulfilled. Consequently there is a distortion in the extrapolated results of the small-scale model, which lacks scaling of gravity. So far, the extent of the effect of gravity scaling on the extrapolated results has been speculated. A quantitative way to evaluate this effect is suggested here. An expression for the distortion in the extrapolation of a measured model variable is developed, based on similitude requirements. This expression depends on the geometrical scaling factor, and on the ratio of a variable measured model value to the value of its gravitational component. It shows that for geometrical scaling factors of 10 and 50, the distortion is less than 10% when the gravitational component of the variable is less than 1% and ∼0.2%, respectively.

Compliant model tests with the Great Belt West Bridge piers in ice part i: Test methods and key results

A model test series has been performed to investigate the dynamic ice loads on a bridge pier of the Great Belt Link, Denmark. Two models were constructed at a geometric scale factor of 30. Each model consisted of a bridge pier with two separate bridge shafts. The ice loads were measured on the shafts as a function of interaction rate and ice attack direction for three different values of foundation stiffness: rigid in both horizontal directions, rigid in one horizontal direction but flexible in the other, and flexible in both horizontal directions. The experimental techniques and results of the test series are discussed and presented in tabular form.

Curvature, heat flow and normal stresses in two-dimensional models of mantle convection

Predictions of surface heat flow and normal stresses at the boundaries from two-dimensional finite-difference models of mantle convection in curvilinear coordinates are compared with similar predictions from plane layer models. Curvature effects are parametrized in terms of f, the ratio of the radii, or f a, the ratio of the areas, of the inner and outer bounding surfaces of the model solutions. Suites of numerical solutions with values of f ranging from 0.1 to 1.0 are presented for both cylindrical shell and axisymmetric spherical shell geometry. For either shell geometry it is shown that heat flow decreases with decreasing f according to a simple geometrical scaling factor which depends only on the ratio f. Results from the two shell geometries agree for common values of f a. In cylindrical geometry it is shown that decreasing f leads to an asymmetry in the distribution of normal stresses (which produce topography) at the upper surface relative to the lower surface. In the constant-viscosity models studied here, this asymmetry results in a maximum normal stress at the lower boundary which exceeds that at the upper boundary by about 60% for values of f appropriate to the whole mantle. Thus, curvature alone contributes to producing differences in the magnitude of stresses at the two bounding surfaces, although this contribution may be small compared with those of varying material properties, such as viscosity.

Similarity considerations in the physical modelling of steel making tundish systems

To assess and quantify the relative importance of Reynolds and Froude numbers in reduced scale model studies (these cannot be simultaneously respected when the scale factor is less than unity), aqueous model investigations were carried out on three different laboratory scale tundish models. The experimental tundish systems included two strand, five strand skewed delta shaped and six strand rectangular shaped vessels. Experimental observations show that the depth of liquid in the model would only correspond to that in the full scale system, provided the model flow rate is scaled in accordance with the relationship: Q m = λ 5/2 Q f.s , in which, λ is the geometrical scaling factor. Furthermore, on the basis of residence time distribution measurements in two different configurations of the five strand tundish, it was demonstrated explicitly that flow phenomena in tundish systems are largely dominated by inertial forces and are therefore, essentially Froude dominated

Stabilization-oriented preformulation study of photolabile menatetrenone (vitamin K 2)

The photostability of menatetrenone in rape seed oil as a solvent was investigated under irradiation with a fluorescent lamp to obtain basic information on encapsulation of the drug. The drug was susceptible to degradation by visible light below 480 nm and was most strongly degraded at around 430 nm, showing wavelength dependency. The degradation followed apparently first-order kinetics for a given initial concentration and exhibited a concentration dependency. The greater the initial concentration, the smaller was the degradation rate constant. Semilogarithmic plots of the apparent degradation rate constant against the reciprocal of illuminance demonstrated a linear relationship similar to that of Arrhenius-type behavior, and prediction of photostability under ordinary illumination conditions was suggested to be possible from the data obtained under conditions of accelerated illumination. Geometrical scale factors relating to the dosage form were also investigated, and it was found that round capsules were the most favorable shape from the viewpoint of stability.

Effects of variance in the size of the scatterer on its radar cross section

AbstractFor scale‐model measurement of the RCS of a lossy target, it is difficult to meet all the requirements of physical similarity [1], especially in the constitutive parameters of the absorbent materials because of their frequency dependence. One often avoids this problem by keeping the wavelength of incident radiation fixed with the sizes of the target scaled down. In this case, the scale factor to evaluate the RCS of prototype from that of a scale model must be found. This article gives brief expressions of the RCS and the scale factors for simply shaped scatterers by means of a PO approximation and the method of stationary phase. It is found that the physical scale factor q2 is not always proportional to the geometrical scale factor p2, but to p to the powers of 2‐4 for a variety of shaped scatterers, respectively, provided their characteristic dimensions are much greater than the working wavelength. © 1993 John Wiley & sons, Inc.

Quantification and modeling of macropore drainage

A series of experiments on undisturbed soil columns, followed by interpretation using simulation modeling, were conducted to estimate the influence of soil structure upon macroporosity and water flow. Four large soil columns taken from Niagara silt loam and Rhinebeck silty clay loam profiles were placed on a grid sampler to obtain 25 subsample outflow measurements per column. Columns were saturated from the bottom and saturated hydraulic conductivity was measured under shallow ponding. Columns were then gravity drained while outflow was collected. Saturated hydraulic conductivity and drainage volume were lognormally distributed over the column bottom area. Drainage volumes were not significantly different among columns or soils, at the 5% level. Analysis of the drainage rates of the columns indicated that soil texture influenced macropore geometry by controlling soil structure and plant rooting. Geometric scaling factors from the distribution of saturated hydraulic conductivity, applied to conductivity and potential in simulations of column drainage, did not reproduce the observed distribution of drainage volume. When additional normally-distributed coefficients were applied to porosity, the simulated drainage distributions were not significantly different from observed drainage distributions, at the 5% level.

Model tests of dynamic ice loading on the Chinese JZ-20-2 jacket platform

A model test program has been performed to study the dynamic ice loads on a jacket platform used in Bohai Bay, China. The tests were performed at a geometric scale factor of 1:26. The prototype structure/foundation compliance was modelled and the structure was subjected to scaled ice sheets corresponding to the ice conditions in the Bohai Bay. The loads, moments, displacements, and accelerations of the structure were measured. The test variables include the ice thickness, ice speed, elevation of ice cover, and structure orientation with respect to the ice motion. An analysis of the data shows good agreement with measured full-scale information. Key words: ice, loads, dynamic, vibration, jacket structure, foundation, China.

A computer program for electron gun design using second-order finite elements

A computer program has been developed for the analysis and design of electron guns. The program uses second-order, curved, isoparametric finite elements to obtain very accurate potential and field computation. Special features of the program include fast solution of the second-order finite element equations with a specially written incomplete Choleski conjugate gradient (ICCG) algorithm, accurate field computation using biquartic interpolation, and direct ray tracing with a third-order power series method. Space charge effects are taken into account, with an iterative solution of Poisson’s equation. The brightness is also computed. The second-order finite elements permit accurate simulation of curved cathodes and very large changes in geometrical scale factor. This allows the program to handle all types of electron guns, ranging from field emission guns with submicron radius cathodes, to high current Pierce-type guns. The computational techniques used are described and illustrated with typical examples.

Nuclear magnetic resonance microscopy with 4-microns resolution: theoretical study and experimental results.

Nuclear magnetic resonance (NMR) microscopy with 4-microns resolution, a step closer to the 1-micron resolution with which in vivo cellular imaging would be possible is described. An analysis of the ultimate resolution and voxel size dependent signal-to-noise ratio (SNR) in NMR microscopy is presented and experimentally verified. For microscopic scale objects (less than 1-mm diameter), the SNR based on the geometrical scale factor(s) is found to be proportional to sn where n less than 2, rather than n = 3 as previously supposed. This comes about because of a drastic reduction in sample noise coupled with a significant sensitivity gain realized in small diameter radiofrequency coils. A new pulse sequence which reduces both diffusion dependent resolution degradation and signal attenuation is presented. The selection of optimal bandwidth and acquisition time for maximal SNR is discussed. Experimental results obtained on both a 2.0-T whole-body system and a 7.0-T small bore system adapted for microscopy indicate the potentials of 4-microns resolution microscopy with the existing magnets.

Dependence of the round-off error in the solution of boundary integral equations on a geometrical scale factor

In the numerical treatment of certain boundary integral equations with logarithmically diverging kernels the sensitivity to round-off errors depends on a geometrical scale factor and is extremely large if the factor assumes a certain critical value. Christiansen has theoretically investigated the sensitivity on the basis of condition numbers [1]. In this paper the round-off error is actually determined and presented in dependence on the scale factor by plots.

Using color to separate reflection components

AbstractIn computer vision, the goal of which is to identify objects and their positions by examining images, one of the key steps is computing the surface normal of the visible surface at each point (“pixel”) in the image. Many sources of information are studied, such as outlines ofsuifaces, intensity gradients, object motion, and color. This article presents a method for analyzing a standard color image to determine the amount of interface (“specular”) and body (“diffuse”) reflection at each pixel. The interface reflection represents the highlights from the original image, and the body reflection represents the original image with highlights removed. Such intrinsic images are of interest because the geometric properties of each type of reflection are simpler than the geometric properties of intensity in a black‐and‐white image. The method is based upon a physical model of reflection which states that two distinct types of reflection–interface and body reflection–occur, and that each type can be decomposed into a relative spectral distribution and a geometric scale factor. This model is far more general than typical models used in computer vision and computer graphics, and includes most such models as special cases. In addition, the model does not assume a point light source or uniform illumination distribution over the scene. The properties of tristimulus integration are used to derive a new model of pixel‐value color distribution, and this model is exploited in an algorithm to derive the desired quantities. Suggestions are provided for extending the model to deal with diffuse illumination and for analyzing the two components of reflection.

A Mathematical Model for the Transport and Fate of Organic Chemicals in Unsaturated/Saturated Soils

A mathematical model, simulating the transport and fate of nonionizable organic compounds in unsaturated/saturated porous media (soils) in a terrestrial microcosm has been developed. Using the principles of water mass, momentum, heat energy and chemical mass balance, the three fields: moisture, temperature, and liquid phase chemical concentration are solved for simultaneously by coupling the soil slab to an environmentally realistic air-soil interface (a dynamic free boundary) conditions and a prescribed height water table. The environmental conditions at the soil surface-air chamber interface are easily changed, via geometric scaling factors, to simulate either an open agricultural field or a landfill type of situation. Illustrative simulation runs examine the effects of different soil-chemical characteristics on hydrological and chemical concentration profiles.

A mathematical model for the transport and fate of organic chemicals in unsaturated/saturated soils.

A mathematical model, simulating the transport and fate of nonionizable organic compounds in unsaturated/saturated porous media (soils) in a terrestrial microcosm has been developed. Using the principles of water mass, momentum, heat energy and chemical mass balance, the three fields: moisture, temperature, and liquid phase chemical concentration are solved for simultaneously by coupling the soil slab to an environmentally realistic air-soil interface (a dynamic free boundary) conditions and a prescribed height water table. The environmental conditions at the soil surface-air chamber interface are easily changed, via geometric scaling factors, to simulate either an open agricultural field or a landfill type of situation. Illustrative simulation runs examine the effects of different soil-chemical characteristics on hydrological and chemical concentration profiles.

Magnetotelluric Responses of Three-Dimensional Bodies in Layered Earths

The electromagnetic fields scattered by a three-dimensional (3-D) inhomogeneity in the earth are affected strongly by boundary charges. Boundary charges cause normalized electric field magnitudes, and thus tensor magnetotelluric (MT) apparent resistivities, to remain anomalous as frequency approaches zero. However, these E-field distortions below certain frequencies are essentially in-phase with the incident electric field. Moreover, normalized secondary magnetic field amplitudes over a body ultimately decline in proportion to the plane-wave impedance of the layered host. It follows that tipper element magnitudes and all MT function phases become minimally affected at low frequencies by an inhomogeneity. Resistivity structure in nature is a collection of inhomogeneities of various scales, and the small structures in this collection can have MT responses as strong locally as those of the large structures. Hence, any telluric distortion in overlying small-scale extraneous structure can be superimposed to arbitrarily low frequencies upon the apparent resistivities of buried targets. On the other hand, the MT responses of small and large bodies have frequency dependencies that are separated approximately as the square of the geometric scale factor distinguishing the different bodies. Therefore, tipper element magnitudes as well as the phase of all MT functions due to small-scale extraneous structure will be limited to high frequencies, so that one may 'see through' such structure with these functions to target responses occurring at lower frequencies. About a 3-D conductive body near the surface, interpretation using 1-D or 2-D TE modeling routines of the apparent resistivity and impedance phase identified as transverse electric (TE) can imply false low resistivities at depth. This is because these routines do not account for the effects of boundary charges. Furthermore, 3-D bodies in typical layered hosts, with layer resistivities that increase with depth in the upper several kilometres, are even less amenable to 2-D TE interpretation than are similar 3-D bodies in uniform half-spaces. However, centrally located profiles across geometrically regular, elongate 3-D prisms may be modeled accurately with a 2-D transverse magnetic (TM) algorithm, which implicitly includes boundary charges in its formulation. In defining apparent resistivity and impedance phase for TM modeling of such bodies, we recommend a fixed coordinate system derived using tipper-strike, calculated at the frequency for which tipper magnitude due to the inhomogeneity of interest is large relative to that due to any nearby extraneous structure.

Magnetotelluric responses of three‐dimensional bodies in layered earths

The electromagnetic fields scattered by a three‐dimensional (3-D) inhomogeneity in the earth are affected strongly by boundary charges. Boundary charges cause normalized electric field magnitudes, and thus tensor magnetotelluric (MT) apparent resistivities, to remain anomalous as frequency approaches zero. However, these E‐field distortions below certain frequencies are essentially in‐phase with the incident electric field. Moreover, normalized secondary magnetic field amplitudes over a body ultimately decline in proportion to the plane‐wave impedance of the layered host. It follows that tipper element magnitudes and all MT function phases become minimally affected at low frequencies by an inhomogeneity. Resistivity structure in nature is a collection of inhomogeneities of various scales, and the small structures in this collection can have MT responses as strong locally as those of the large structures. Hence, any telluric distortion in overlying small‐scale extraneous structure can be superimposed to arbitrarily low frequencies upon the apparent resistivities of buried targets. On the other hand, the MT responses of small and large bodies have frequency dependencies that are separated approximately as the square of the geometric scale factor distinguishing the different bodies. Therefore, tipper element magnitudes as well as the phases of all MT functions due to small‐scale extraneous structure will be limited to high frequencies, so that one may “see through” such structure with these functions to target responses occurring at lower frequencies. About a 3-D conductive body near the surface, interpretation using 1-D or 2-D TE modeling routines of the apparent resistivity and impedance phase identified as transverse electric (TE) can imply false low resistivities at depth. This is because these routines do not account for the effects of boundary charges. Furthermore, 3-D bodies in typical layered hosts, with layer resistivities that increase with depth in the upper several kilometers, are even less amenable to 2-D TE interpretation than are similar 3-D bodies in uniform half‐spaces. However, centrally located profiles across geometrically regular, elongate 3-D prisms may be modeled accurately with a 2-D transverse magnetic (TM) algorithm, which implicitly includes boundary charges in its formulation. In defining apparent resistivity and impedance phase for TM modeling of such bodies, we recommend a fixed coordinate system derived using tipper‐strike, calculated at the frequency for which tipper magnitude due to the inhomogeneity of interest is large relative to that due to any nearby extraneous structure.

Further improvements in vibrating sample magnetometer sensitivity

Improvements in sensitivity of a vibrating sample magnetometer (VSM) are presented. General geometric scaling factors for VSM detection coils also are discussed. The scaling factors show why such increased sensitivity is achieved. For small detection coils and efficient coupling with the sample, noise levels correspond to a change in magnetic moment of 3×10−9 emu at 50 kOe and 1×10−9 emu at 10 kOe. This corresponds to a change in susceptibility Δχ?10−13 emu/g-Oe for a 1-g sample at 10 kOe.

Printed Low Velocity Delay Lines for Cathode Readout of Proportional Chambers

A new type of flat delay line was developed which has a low propagation velocity and very good delay to rise time ratio. It can be constructed by printed circuit techniques without crossovers. The magnetic loops of a shifted periodic structure yield high inductance per unit length. Geometric scaling factors are shown. This line, forming the cathode plane of a proportional chamber, allows simultaneously, a satisfactory induced signal and the readout of the second coordinate by time delay without disturbing the electric field configuration around the anode. Optimization of position resolution vs. noise is discussed. Experimental results are shown. Other properties of such delay lines are discussed.