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Frequency-dependent viscous flow in channels with fractal rough surfaces

Description: The viscous dynamic permeability of some fractal-like channels is studied. For our particular class of geometries, the ratio of the pore surface area-to-volume tends to {infinity} (but has a finite cutoff), and the universal scaling of the dynamic permeability, k({omega}), needs modification. We performed accurate numerical computations of k({omega}) for channels characterized by deterministic fractal wall surfaces, for a broad range of fractal dimensions. The pertinent scaling model for k({omega}) introduces explicitly the fractal dimension of the wall surface for a range of frequencies across the transition between viscous and inertia dominated regimes. The new model provides excellent agreement with our numerical simulations.
Date: May 1, 2010
Creator: Cortis, A. & Berryman, J.G.
Partner: UNT Libraries Government Documents Department

Characterizing soil preferential flow using iodine--starch staining experiments and the active region model

Description: Thirteen iodine-starch staining experiments with different boundary conditions and measurement scales were conducted at two sites to study preferential flow processes in natural unsaturated soils. Digital imaging analyses were implemented to obtain the corresponding preferential flow patterns. The test results are used to evaluate a recently proposed active region model in terms of its usefulness and robustness for characterizing unsaturated flow processes at field scale. Test results provide useful insights into flow patterns in unsaturated soils. They show that flow pattern depends on the top boundary condition. As the total infiltrating-water depth increased form 20 mm to 80 mm for the 100 x 100 cm{sup 2} plots, the corresponding flow pattern changed from few preferential flow paths associated with a relatively small degree of stained coverage and a small infiltration depth, to a pattern characterized by a higher stained coverage and a larger infiltration depth, and to (finally) a relatively homogeneous flow pattern with few unstained area and a much larger infiltration depth. Test results also show that the preferential flow pattern became generally more heterogeneous and complex for a larger measurement scale (or size of infiltration plot). These observations support the general idea behind the active region model that preferential flow pattern in unsaturated soils are dynamic and depend on water flow conditions. Further analyses of the test results indicate that the active-region model is able to capture the major features of the observed flow pattern at the scale of interest, and the determined parameter values do not significantly depend on the test conditions (initial water content and total amount of infiltrating water) for a given test site. This supports the validity of the active region model that considers that parameter to be a property of the corresponding unsaturated soil. Results also show that some intrinsic relation seems to ...
Date: March 1, 2009
Creator: Sheng, Feng; Wang, Kang; Zhang, Renduo & Liu, Hui-Hai
Partner: UNT Libraries Government Documents Department

Quantitative Methods for Reservoir Characterization and Improved Recovery: Application to Heavy Oil Sands

Description: The first twelve months of the project focused on collecting data for characterization and modeling. In addition, data from Coalinga Field was analyzed to define the fractal structure present in the data set. The following sections of the report parallel the first four subtasks of the investigation were: (1) Collect and Load Property Data from Temblor Outcrops in California, (2) Collect and Load Property Data from Temblor Reservoir Sands, West Coalinga Field, California, (3) Collect and Load Property Data from Continuous Upper Cretaceous Outcrops in Utah, and (4) Define Fractal Structure in the Data Sets and Apply to Generating Property Representations.
Date: November 29, 2001
Creator: Castle, James W. & Molz, Fred J.
Partner: UNT Libraries Government Documents Department

Dimensions in Random Constructions.

Description: We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.
Date: May 2002
Creator: Berlinkov, Artemi
Partner: UNT Libraries

Quantization Dimension for Probability Definitions

Description: The term quantization refers to the process of estimating a given probability by a discrete probability supported on a finite set. The quantization dimension Dr of a probability is related to the asymptotic rate at which the expected distance (raised to the rth power) to the support of the quantized version of the probability goes to zero as the size of the support is allowed to go to infinity. This assumes that the quantized versions are in some sense ``optimal'' in that the expected distances have been minimized. In this dissertation we give a short history of quantization as well as some basic facts. We develop a generalized framework for the quantization dimension which extends the current theory to include a wider range of probability measures. This framework uses the theory of thermodynamic formalism and the multifractal spectrum. It is shown that at least in certain cases the quantization dimension function D(r)=Dr is a transform of the temperature function b(q), which is already known to be the Legendre transform of the multifractal spectrum f(a). Hence, these ideas are all closely related and it would be expected that progress in one area could lead to new results in another. It would also be expected that the results in this dissertation would extend to all probabilities for which a quantization dimension function exists. The cases considered here include probabilities generated by conformal iterated function systems (and include self-similar probabilities) and also probabilities generated by graph directed systems, which further generalize the idea of an iterated function system.
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Date: December 2001
Creator: Lindsay, Larry J.
Partner: UNT Libraries

Effect of Aggregation on Thermal Conduction in Colloidal Nanofluids

Description: Using effective medium theory we demonstrate that the thermal conductivity of nanofluids can be significantly enhanced by the aggregation of nanoparticles into clusters. The enhancement is based purely on conduction and does not require a novel mechanism. Predictions of the effective medium theory are in excellent agreement with detailed numerical calculations on model nanofluids involving fractal clusters and show the importance of cluster morphology on thermal conductivity enhancements.
Date: August 10, 2006
Creator: Prasher, R; Evans, W; Fish, J; Meakin, P; Phelan, P & Keblinski, Pawel
Partner: UNT Libraries Government Documents Department

A macroscopic relationship for preferential flow in the vadose zone: Theory and Validation

Description: Preferential flow commonly observed in unsaturated soils allows rapid movement of solute from the ground surface or vadose zone to the groundwater, bypassing a significant volume of unsaturated soil and increasing the risk of groundwater contamination. A variety of evidence indicates that complex preferential flow patterns observed from fields are fractals. This paper discusses a macroscopic rela-tionship for modeling preferential flow in the vadose zone. Conceptually, the flow domain can be di-vided into active and inactive regions. Flow occurs preferentially in the active region (characterized by fractals), and inactive region is simply bypassed. The portion of the active region was found to be a power function of saturation. The validity of this macroscopic relationship is demonstrated by its consistency with field observations and the related numerical experiments.
Date: February 15, 2010
Creator: Liu, H.H. & Zhang, R.D.
Partner: UNT Libraries Government Documents Department

The effect of resist on the transfer of line-edge roughness spatial metrics from mask to wafer

Description: Mask contributors to line-edge roughness (LER) have recently been shown to be an issue of concern for both the accuracy of current resist evaluation tests as well the ultimate LER requirements for the 22-nm production node. More recently, it has been shown that the power spectral density of the mask-induced roughness, is markedly different than that of intrinsic resist roughness and thus potentially serves as a mechanism for distinguishing mask effects from resist effects in experimental results. Further considering stochastic resist effects, however, demonstrates that such a test would only be viable in cases where the resist effects are completely negligible in terms of their contribution to the total LER compared to the mask effects. The results presented here lead us to the surprising conclusion that it is indeed possible for mask contributors to be the dominant source of LER while the spatial characteristics of the LER remain indistinguishable from the fractal characteristics of resist-induced LER.
Date: May 1, 2009
Creator: Naulleau, Patrick & Gallatin, Gregg
Partner: UNT Libraries Government Documents Department

Numerical Values of the Hausdorff and Packing Measures for Limit Sets of Iterated Function Systems

Description: In the context of fractal geometry, the natural extension of volume in Euclidean space is given by Hausdorff and packing measures. These measures arise naturally in the context of iterated function systems (IFS). For example, if the IFS is finite and conformal, then the Hausdorff and packing dimensions of the limit sets agree and the corresponding Hausdorff and packing measures are positive and finite. Moreover, the map which takes the IFS to its dimension is continuous. Developing on previous work, we show that the map which takes a finite conformal IFS to the numerical value of its packing measure is continuous. In the context of self-similar sets, we introduce the super separation condition. We then combine this condition with known density theorems to get a better handle on finding balls of maximum density. This allows us to extend the work of others and give exact formulas for the numerical value of packing measure for classes of Cantor sets, Sierpinski N-gons, and Sierpinski simplexes.
Date: August 2017
Creator: Reid, James Edward
Partner: UNT Libraries

Nonlinear extensions of a fractal-multifractal approach for environmental modeling

Description: We present the extension of a deterministic fractal geometric procedure aimed at representing the complexity of the spatio-temporal patterns encountered in environmental applications. The original procedure, which is based on transformations of multifractal distributions via fractal functions, is extended through the introduction of nonlinear perturbations to the underlying iterated linear maps. We demonstrate how the nonlinear perturbations generate yet a richer collection of patterns by means of various simulations that include evolutions of patterns based on changes in their parameters and in their statistical and multifractal properties. It is shown that the nonlinear extensions yield structures that closely resemble complex hydrologic temporal data sets, such as rainfall and runoff time series, and width-functions of river networks as a function of distance from the basin outlet. The implications of this nonlinear approach for environmental modeling and prediction are discussed.
Date: October 15, 2008
Creator: Cortis, A.; Puente, C.E. & Sivakumar, B.
Partner: UNT Libraries Government Documents Department

Bells Galore: Oscillations and circle-map dynamics from space-filling fractal functions

Description: The construction of a host of interesting patterns over one and two dimensions, as transformations of multifractal measures via fractal interpolating functions related to simple affine mappings, is reviewed. It is illustrated that, while space-filling fractal functions most commonly yield limiting Gaussian distribution measures (bells), there are also situations (depending on the affine mappings parameters) in which there is no limit. Specifically, the one-dimensional case may result in oscillations between two bells, whereas the two-dimensional case may give rise to unexpected circle map dynamics of an arbitrary number of two-dimensional circular bells. It is also shown that, despite the multitude of bells over two dimensions, whose means dance making regular polygons or stars inscribed on a circle, the iteration of affine maps yields exotic kaleidoscopes that decompose such an oscillatory pattern in a way that is similar to the many cases that converge to a single bell.
Date: October 15, 2008
Creator: Puente, C.E.; Cortis, A. & Sivakumar, B.
Partner: UNT Libraries Government Documents Department

Scale dependency of the effective matrix diffusion coefficient

Description: It has been recognized that matrix diffusion is an important process for retarding solute transport in fractured rock. Based on analyses of tracer transport data from a number of field tests, we demonstrate for the first time that the effective matrix-diffusion coefficient may be scale dependent and generally increases with test scale. A preliminary theoretical explanation of this scale dependency is also presented, based on the hypothesis that solute travel paths within a fracture network are fractals.
Date: May 30, 2003
Creator: Liu, H. H.; Bodvarsson, G. S. & Zhang, G.
Partner: UNT Libraries Government Documents Department

The use of fractally-designed waveforms in electroforming

Description: Pulsed electrodeposition offers the potential for superior control of deposit properties because of the additional control variables available. However, optimization of pulsed deposition processes is a challenge because of the complexity. E.g., the tendency of electroforms to acquire irregularities such as dendritic growths or other morphological instabilities, creates the need for methods to control these undesirable phenomena. One such method is periodic reverse pulses. Optimization of periodic reverse processes is not simple and can lead to local solutions that do not optimize all properties simultaneously. One method for global optimization that might, for example, control surface irregularities on several size scales, uses a periodic reverse design based on fractal time series. This incorporates deplating pulses of several lengths within one self- similar waveform. The properties of fractals permit control of highly complex designs with a small number of input variables. The creation of such waveforms, their properties, and their use in a lead- plating process are described. Speculation on the potential for further application of this method is offered. 26 figs, 11 refs.
Date: March 1, 1996
Creator: Bullock, J.S.; Lawson, R.L. & Kirkpatrick, J.R.
Partner: UNT Libraries Government Documents Department

Particle aggregation with simultaneous surface growth

Description: Particle aggregation with simultaneous surface growth was modeled using a dynamic Monte Carlo method. The Monte Carlo algorithm begins in the particle inception zone and constructs aggregates via ensemble-averaged collisions between spheres and deposition of gaseous species on the sphere surfaces. Simulations were conducted using four scenarios. The first, referred to as scenario 0, is used as a benchmark and simulates aggregation in the absence of surface growth. Scenario 1 forces all balls to grow at a uniform rate while scenario 2 only permits them to grow once they have collided and stuck to each other. The last one is a test scenario constructed to confirm conclusions drawn from scenarios 0-2. The transition between the coalescent and the fully-developed fractal aggregation regimes is investigated using shape descriptors to quantify particle geometry. They are used to define the transition between the coalescent and fractal growth regimes. The simulations demonstrate that the morphology of aggregating particles is intimately related to both the surface deposition and particle nucleation rates.
Date: April 29, 2003
Creator: pablo.mitchell@cal.Berkeley.EDU
Partner: UNT Libraries Government Documents Department

The fractal nature of vacuum arc cathode spots

Description: Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Several points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f {sup 2}, where f is frequency, supporting a fractal spot model associated with Brownian motion.
Date: May 27, 2005
Creator: Anders, Andre
Partner: UNT Libraries Government Documents Department


Description: Validation of numerical simulations, Le., the quantitative comparison of calculated results with experimental data, is an essential practice in computational fluid dynamics. These comparisons are particularly difficult in the field of shock-accelerated fluid mixing, which can be dominated by irregular structures induced by flow instabilities. Such flows exhibit non-deterministic behavior, which eliminates my direct way to establish correspondence between experimental data and numerical simulation. We examine the detailed structures of mixing experiments and their simulation for Richtmyer-Meshkov (RM) experiments of Prestridge et al., Tomkins et al., and Jacobs. Numerical simulations of these experiments will be performed with several different high-resolution shock capturing schemes, including a variety of finite volume Godunov methods. We compare the experimental data for cOnfigurations of one and two diffuse cylinders of SF6 in air with numerical results using several multiscale metrics: fractal analysis, continuous wavelet transforms, and generalized correlations; these measures complement traditional metrics such as PDFs, mix fractions, and integral mixing widths.
Date: January 1, 2001
Creator: Rider, William; Kamm, J. R. (James R.); Tomkins, C. D. (Chris D.); Prestridge, K. P. (Katherine P.); Rightley, P. M. (Paul M.); Benjamin, R. F. (Robert F.) et al.
Partner: UNT Libraries Government Documents Department

Physical Modelling of Sedimentary Basin

Description: The main goals of the first three years have been achieved, i.e., the development of particle-based and continuum-based algorithms for cross-scaleup-scale analysis of complex fluid flows. The U. Minnesota team has focused on particle-based methods, wavelets (Rustad et al., 2001) and visualization and has had great success with the dissipative and fluid particle dynamics algorithms, as applied to colloidal, polymeric and biological systems, wavelet filtering and visualization endeavors. We have organized two sessions in nonlinear geophysics at the A.G.U. Fall Meeting (2000,2002), which have indeed synergetically stimulated the community and promoted cross-disciplinary efforts in the geosciences. The LANL team has succeeded with continuum-based algorithms, in particular, fractal interpolating functions (fif). These have been applied to 1-D flow and transport equations (Travis, 2000; 2002) as a proof of principle, providing solutions that capture dynamics at all scales. In addition, the fif representations can be integrated to provide sub-grid-scale homogenization, which can be used in more traditional finite difference or finite element solutions of porous flow and transport. Another useful tool for fluid flow problems is the ability to solve inverse problems, that is, given present-time observations of a fluid flow, what was the initial state of that fluid system? We have demonstrated this capability for a large-scale problem of 3-D flow in the Earth's crust (Bunge, Hagelberg & Travis, 2002). Use of the adjoint method for sensitivity analysis (Marchuk, 1995) to compute derivatives of models makes the large-scale inversion feasible in 4-D, , space and time. Further, a framework for simulating complex fluid flow in the Earth's crust has been implemented (Dutrow et al, 2001). The remaining task of the first three-year campaign is to extend the implementation of the fif formalism to our 2-D and 3-D computer codes, which is straightforward, but involved.
Date: April 24, 2003
Creator: Yuen, David A.
Partner: UNT Libraries Government Documents Department

Modeling preferential water flow and solute transport in unsaturated soil using the active region model

Description: Preferential flow and solute transport are common processes in the unsaturated soil, in which distributions of soil water content and solute concentrations are often characterized as fractal patterns. An active region model (ARM) was recently proposed to describe the preferential flow and transport patterns. In this study, ARM governing equations were derived to model the preferential soil water flow and solute transport processes. To evaluate the ARM equations, dye infiltration experiments were conducted, in which distributions of soil water content and Cl{sup -} concentration were measured. Predicted results using the ARM and the mobile-immobile region model (MIM) were compared with the measured distributions of soil water content and Cl{sup -} concentration. Although both the ARM and the MIM are two-region models, they are fundamental different in terms of treatments of the flow region. The models were evaluated based on the modeling efficiency (ME). The MIM provided relatively poor prediction results of the preferential flow and transport with negative ME values or positive ME values less than 0.4. On the contrary, predicted distributions of soil water content and Cl- concentration using the ARM agreed reasonably well with the experimental data with ME values higher than 0.8. The results indicated that the ARM successfully captured the macroscopic behavior of preferential flow and solute transport in the unsaturated soil.
Date: March 15, 2009
Creator: Sheng, F.; Wang, K.; Zhang, R. & Liu, H.H.
Partner: UNT Libraries Government Documents Department

Elements of fractal generalization of dual-porosity model for solute transport in unsaturated fractured rocks

Description: In this study, new elements were developed to generalize the dual-porosity model for moisture infiltration on and solute transport in unsaturated rocks, taking into account fractal aspects of the percolation process. Random advection was considered as a basic mechanism of solute transport in self-similar fracture systems. In addition to spatial variations in the infiltration velocity field, temporal fluctuations were also taken into account. The rock matrix, a low-permeability component of the heterogeneous geologic medium, acts as a trap for solute particles and moisture. Scaling relations were derived for the moisture infiltration flux, the velocity correlation length, the average velocity of infiltration, and the velocity correlation function. The effect of temporal variations in precipitation intensity on the infiltration processes was analyzed. It showed that the mode of solute transport is determined by the power exponent in the advection velocity correlation function and the dimensionality of the trapping system, both of which may change with time. Therefore, depending on time, various transport regimes may be realized: superdiffusion, subdiffusion, or classical diffusion. The complex structure of breakthrough curves from changes in the transport regimes was also examined. A renormalization of the solute source strength due to characteristic fluctuations of highly disordered media was established.
Date: September 1, 2008
Creator: Bolshov, L.; Kondratenko, P.; Matveev, L. & Pruess, K.
Partner: UNT Libraries Government Documents Department

A corrected and generalized successive random additions algorithm for simulating fractional levy motions

Description: Simulation of subsurface heterogeneity is important for modeling subsurface flow and transport processes. Previous studies have indicated that subsurface property variations can often be characterized by fractional Brownian motion (fBm) or (truncated) fractional Levy motion (fLm). Because Levy-stable distributions have many novel and often unfamiliar properties, studies on generating fLm distributions are rare in the literature. In this study, we generalize a relatively simple and computationally efficient successive random additions (SRA) algorithm, originally developed for generating Gaussian fractals, to simulate fLm distributions. We also propose an additional important step in response to continued observations that the traditional SRA algorithm often generates fractal distributions having poor scaling and correlation properties. Finally, the generalized and modified SRA algorithm is validated through numerical tests.
Date: May 29, 2002
Creator: Liu, Hui-Hai; Bodvarsson, Gudmundur S.; Lu, Silong & Molz, Fred J.
Partner: UNT Libraries Government Documents Department

Understanding the impact of upscaling THM processes on performance assessment

Description: The major objective of Benchmark Test 2 (BMT2) is to quantitatively examine the reliability of estimates of repository host rock performance, using large-scale performance assessment (PA) models that are developed by upscaling small-scale parameters and processes. These small-scale properties and processes can be investigated based on either discrete-fracture-network (DFN) models or heterogeneous-porous-medium (HPM) models. While most research teams use DFN, we employ fractal-based HPM for upscaling purposes. Comparison of results based on fundamentally different approaches is useful for evaluating and bounding the uncertainties in estimating repository host rock performance. HPM has both advantages and limitations when compared with DFN. DFM is conceptually more appealing because it explicitly describes fractures and the flow and transport processes that occur within them. However, HPM is more consistent with approaches used to derive field measurements of hydraulic properties (such as permeability). These properties are generally determined based on assumptions related to the continuum approach. HPM is also more straightforward in describing spatial-correlation structures of measured hydraulic properties. For example, potential flow features in the Borrowdale Volcanic Group (BVG) were found to show marked spatial clustering (Nirex, 1997), which is expected to result in a long range correlation in measured permeability distributions. This important behavior may not be captured with conventional DFNs, in which random distribution (or similar distributions) of individual fractures is assumed. The usefulness of HPM will be partially demonstrated in this report by a satisfactory description of the short interval testing data using Levy-stable fractals. (Recently, Jackson et al. (2000) also showed that equivalent HPMs could approximately describe flow processes within subgrid fracture networks.) We use Monte Carlo simulations to determine flow and transport parameters at different scales. Since we have used a fractal-based approach supported by field measurements, effective properties will be scale-dependent. Effects of mechanical processes on flow and transport ...
Date: June 10, 2002
Creator: Liu, H. H.; Zhou, Q.; Rutqvist, J. & Bodvarsson, G. S.
Partner: UNT Libraries Government Documents Department

An Active Region Model for Capturing Fractal Flow Patterns inUnsaturated Soils: Model Development

Description: Preferential flow commonly observed in unsaturated soils allows rapid movement of solute from the soil surface or vadose zone to the groundwater, bypassing a significant volume of unsaturated soil and increasing the risk of groundwater contamination. A variety of evidence indicates that complex preferential patterns observed from fields are fractals. In this study, we developed a relatively simple active region model to incorporate the fractal flow pattern into the continuum approach. In the model, the flow domain is divided into active and inactive regions. Flow occurs preferentially in the active region (characterized by fractals), and inactive region is simply bypassed. A new constitutive relationship (the portion of the active region as a function of saturation) was derived. The validity of the proposed model is demonstrated by the consistency between field observations and the new constitutive relationship.
Date: June 11, 2005
Creator: Liu, Hui-Hai; Zhang, R. & Bodvarsson, Gudmundur S.
Partner: UNT Libraries Government Documents Department