bluuebunny/crossref_metadata_2025 huggingface dataset:
FLUCTUATION OF SURFACE IN POLISHING PROCESS
Authors: HASEGAWA Y. , MIYAZIMA S. , NAMBA Y.
Published: May 2003

A change of surface pattern of materials during polishing is simulated and analyzed from the fractal point of view. We have proposed a simple two-dimensional model for microscopic processes of polishing. We have obtained a result that the time dependent fluctuation of surface scales with the momentum of the polishing particle.
AC IMPEDANCE STUDY OF PATTERN FORMATION OF SILVER ELECTRODEPOSITS
Authors: MOGI IWAO , KAMIKO MASAO
Published: May 2003

Electrochemical impedance was examined in the two-dimensional growth of Ag electrodeposits to investigate the rate-determining step in the pattern formation of the aggregates. The frequency dispersions of the in-situ ac impedance during the electrodeposition demonstrated that the open-ramified growth is diffusion-limited, the dendritic growth is reaction-limited, the homogeneous growth is electric-migration-limited and the DBM (dense branching morphology) growth is both diffusion and electric-migration controlled.
FRACTAL FORM ANALYSIS
Authors: SUZUKI MASUO
Published: May 2003

The concept of fractal form analysis is introduced, in which fractal metrication is defined for partial objects of fractals as a cmD or b mD with the fractal dimensionality D.
NUMERICAL SIMULATION OF MIXING BY RAYLEIGH-TAYLOR INSTABILITY AND ITS FRACTAL STRUCTURES
Authors: HASEGAWA SUSUMU , NISHIHARA KATSUNOBU , SAKAGAMI HITOSHI
Published: May 2003

Turbulent interface caused by the 2-dimensional Rayleigh-Taylor instability is investigated by direct numerical simulation. It is shown that the interface becomes fractal spontaneously in the case where there are initially multimode perturbations on the interface. The generalized dimensions and the singularity spectrum are obtained by applying the multifractal theory to the turbulent interface. The fractal dimension of the line interface is found to be 1.7–1.8, which is greater than that of turbulent/nonturbulent interface in a turbulent flow. Time evolution of the fractal dimensions of the interface is also investigated.
FRACTAL LIMIT DISTRIBUTIONS IN RANDOM TRANSPORTS
Authors: TAKAYASU HIDEKI , KAWAKAMI TAKUO , TAGUCHI Y. -H. , KATSUYAMA TOMOO
Published: May 2003

We analyze a random transport model of a scalar quantity on a discrete space-time. By changing a parameter which is a portion of the quantity transported at a time, we observe a continuous change of steady-state distribution of fluctuations from Gaussian to a power-law when the mean value of the scalar quantity is not zero. In the symmetric case with zero mean, the steady-state converges either to a trivial no fluctuation state or to a Lorentzian fluctuation state with diverging variance independent of the parameter. We discuss a possible origin of the intermittent behaviors of fully-developed fluid turbulence as an application.
CALCULATION OF THE POWER LAW INDEX FOR A TIME SERIES BY MEANS OF ITS FRACTAL DIMENSION
Authors: YASUE SHINICHI , MUNAKATA KAZUOKI , KATO MASASHIGE , MORI SATORU
Published: May 2003

The relationship between the power-law index for a time series and the fractal dimensions for both the original and the integrated time series, is investigated by using a numerical experiment. This relationship is extended and applied to the cosmic ray time series recorded at the deep underground site at Matsushiro.

It is shown that we can use the present method in order to obtain the stable and reliable value of the power-law index of a time series, even if the time series has relatively large statistical fluctuations.
EFFECT OF BOUNDARY TETHERING ON VIBRATIONAL MODES OF FRACTALS
Authors: MUKHERJEE SONALI , NAKANISHI HISAO
Published: May 2003

We introduce a mapping between a tethered scalar elastic network and a diffusion problem with permanent traps. Various vibrational properties of progressively tethered fractals are discussed using this analogy both in terms of scaling ansatz and numerically by approximately diagonalizing the corresponding large random matrices, with the critical percolation cluster as an example of a fractal.
SELF-ORGANIZED CRITICALITY IN 1D TRAFFIC FLOW
Authors: NAGATANI TAKASHI
Published: May 2003

Annihilation process of traffic jams is investigated in a one-dimensional traffic flow on a highway. The one-dimensional fully asymmetric exclusion model with open boundaries for parallel update is extended to take into account stochastic transition of cars, where a car moves ahead with transition probability pt. Near pt=1, the system is driven asymptotically into a steady state exhibiting a self-organized criticality. Traffic jams with various lifetimes (or sizes) appear and disappear by colliding with an empty wave. The typical lifetime  of traffic jams scales as [Formula: see text], where ∆pt=1−pt. It is shown that the cumulative lifetime distribution Nm(∆pt) satisfies the scaling form [Formula: see text].
TIME-REVERSAL DUALITY AND PLANAR LATTICE DUALITY IN NON-EQUILIBRIUM LATTICE MODELS
Authors: KATORI MAKOTO
Published: May 2003

The contact process (CP) is a simple mathematical model for the spread of infection of a contagious disease. Though it has only nearest-neighbor interactions, phase transitions occur even in the one-dimensional system and non-equilibrium stationary states appear in supercritical phase. This implies violation of detailed balance. The appearance of such non-equilibrium states is related to directed percolation problems on the spatiotemporal plane. In the present paper, we study discretetime versions of the CP, the two-neighbor stochastic cellular automata (SCA), and clarify this viewpoint. We use two kinds of duality relations, the time-reversal duality and the planar lattice duality on the spatio-temporal plane, and give a good lower bound for the critical line of non-equilibrium phase transitions in the two-neighbor SCA.
AVALANCHES IN THE DIRECTED PERCOLATION DEPINNING AND SELF-ORGANIZED DEPINNING MODELS OF INTERFACE ROUGHENING
Authors: BULDYREV S. V. , AMARAL L. A. N. , BARABÁSI A. -L. , HARRINGTON S. T. , HAVLIN S. , KERTÉSZ J. , SADR-LAHIJANY R. , STANLEY H. E.
Published: May 2003

We review the recently introduced Directed Percolation Depinning (DPD) and Self-Organized Depinning (SOD) models for interface roughening with quenched disorder. The differences in the dynamics of the invasion process in these two models are discussed and different avalanche definitions are presented. The scaling properties of the avalanche size distribution and the properties of active cells are discussed.
A FRACTAL MODEL FOR THE FIRST STAGES OF THIN FILM GROWTH
Authors: JENSEN PABLO , BARABÁSI ALBERT-LÁSZLÓ , LARRALDE HERNÁN , HAVLIN SHLOMO , EUGENE STANLEY H.
Published: May 2003

In this paper, we briefly review a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. This model allows us to understand many experiments of thin film deposition. In the Sec. 1, we describe the model, which incorporates deposition, particle and cluster diffusion, and aggregation. In Sec. 2, we study the dynamical evolution of the model. Finally, we analyze the effects of small cluster mobility and show that the introduction of cluster diffusion dramatically affects the dynamics of film growth. Some of these effects can be tested experimentally.
SELF-ORGANIZED CRITICAL BEHAVIOR OF TWO-DIMENSIONAL FOAMS
Authors: KAWASAKI KYOZI , OKUZONO TOHRU
Published: May 2003

A simple dynamical model for two-dimensional dry foam rheology is constructed for which surface tension effects and viscous dissipation at Plateau borders (intersections of three cell boundaries) are taken into account and is studied by computer simulation. Under externally applied shear strain increasing at small rates, the system exhibits avalanche-like release of stress that has been accumulating under increasing strain. There is a close similarity with earthquake models that show self-organized criticality (SOC). We discuss related simulation of two-dimensional wet foams under statically applied strain by Hutzler et al. [Phil. Mag. B71, 277 (1995)] showing critical behavior.
LOCALIZATION OF FRACTONS, RANDOM WALKS AND LINEAR POLYMERS IN PERCOLATION
Authors: BUNDE A. , DRÄGER J. , HAVLIN S. , ROMAN H. E. , RUSS St.
Published: May 2003

We review analytical and numerical results for the vibrational amplitudes of localized excitations, the probability distribution of random walks and the distribution of linear polymers (modeled by self-avoiding walks of N steps) on percolation structures at criticality. Our numerical results show that the fluctuations of these quantities, at fixed shortest-path distance (“chemical length”) l from the center of localization, are considerably smaller than at fixed Euclidean distance r from the center. Using this fact, we derive via convolutional integrals explicit expressions for the averaged functions in r-space, and show analytically and numerically that three different localization regimes occur. In the short-distance regime, remarkably, the averages show a universal spatial decay behavior, with the same exponent for both fractons and random walks, while in the asymptotic regime, the averages depend explicitly on the number of configurations considered.
ANOMALOUS DIFFUSION IN THE KICKED HARPER SYSTEM
Authors: SAITÔ SATOSHI , NOMURA YASUYUKI , ICHIKAWA YOSHI H.
Published: May 2003

Stochastic property of the Hamiltonian dynamical systems exhibits anomalous behavior owing to intermittent processes between regular orbits and chaotic motion. In particular, the accelerator modes give rise to the anomalous enhancement of the diffusion process, which could be attributed to temporal fractal property. In order to explore the effect of the accelerator modes on the stochastic diffusion, the kicked Harper system is investigated in detail. It is found that the numerical observation of the diffusion coefficient shows good agreement with the analytical expression obtained by the characteristic function method, except in the domains where the accelerator modes exist. It is interesting to note that, unlike the case of the standard map, the multi-period, multi-step accelerator modes are responsible for much of the profound effect of the enhancement of diffusion even in the domain of larger stochastic parameters.
PERCOLATED CRACKS IN A SOLID CONTAINING MANY INITIAL DEFECTS
Authors: NISHIUMA SABUROU , HASEGAWA YUTAKA , MIYAZIMA SASUKE
Published: May 2003

Hydrogen-induced fracture of steel is characterized by the formation of internal voids caused by hydrogen precipitation at an inclusion-matrix interface, followed by the formation of microcrack array under the superposed action of internal hydrogen pressure and external forces. The propagation of the hydrogen-induced fracture is considerably random and the fracture develops by stepwise linking of the microcracks.

Crack growth in a solid containing many initial defects is studied by Monte Carlo simulation on a square lattice. Each initial defect is assumed to have two crack tips like the Griffith crack and percolated crack patterns in homogeneous medium are investigated. The effect of the density of the initial defects and the lattice size on percolation characteristics is also studied.
WATER EROSION ON FRACTAL SURFACE
Authors: LI R. , TAKAYASU H. , INAOKA H.
Published: May 2003

We study numerically the water erosion process under a variety of conditions. The water erosion model that we use leads to a universal exponent describing the fractal basin area distribution in the steady state.
FRACTAL ANALYSES FOR A MODEL OF IMPACT FRAGMENTATION
Authors: INAOKA HAJIME , TAKAYASU HIDEKI
Published: May 2003

We perform fractal analyses for a model of three-dimensional impact fragmentation. The fractal dimension of the whole crack configuration in the system is numerically estimated as D=2.3.
DOMAIN WALLS IN THE TRANSVERSE FIELD ISING SPIN GLASSES
Authors: LI MAI SUAN , CIEPLAK MAREK
Published: May 2003

Interfaces in Ising spin glasses in the transverse field are studied by the local mean field method. The quantum fluctuations are found to make the length of domain walls shorter and smoother and to reduce the fractal dimensionality of the wall. The domain wall are almost as narrow as in the classical Ising case.
CAN STATISTICAL PHYSICS CONTRIBUTE TO THE SCIENCE OF ECONOMICS?
Authors: STANLEY MICHAEL H. R. , AMARAL LUÍS A. N. , BULDYREV SERGEY V. , HAVLIN SHLOMO , LESCHHORN HEIKO , MAASS PHILLIPP , SALINGER MICHAEL A. , EUGENE STANLEY H.
Published: May 2003

In recent years, a breakthrough in statistical physics has occurred. Simply put, statistical physicists have determined that physical systems which consist of a large number of interacting particles obey universal laws that are independent of the microscopic details. This progress was mainly due to the development of scaling theory. Since economic systems also consist of a large number of interacting units, it is plausible that scaling theory can be applied to economics. To test this possibility we study the dynamics of firm size. This may help to build a more complete characterization of the nature and processes behind firm growth.

To date, the study of firm dynamics has primarily focused on whether small firms on average have higher growth rates than large firms. To a lesser extent, attention has been placed on the relationship between firm size and variation in growth rate. Our research goes beyond these questions by looking at the relationship between numerous firm characteristics and the entire distribution of growth rates. Thus, it may provide a better understanding of the mechanisms behind firm dynamics. In contrast to previous studies, this research analyzes data over many time scales, instead of just a single time interval.

From a scientific standpoint, this work could be useful because it will affect the formulation of firm modeling—one of the basic building blocks of all economic analysis. In addition, this work will have practical applications. For example, there are Federal policies that are designed to encourage small businesses. While such policies might be justified on grounds other than their contribution to growth, any systematic difference in the growth rates of small and large firms might be relevant for evaluating such policies. Also, there has traditionally been a concern that an excessive amount of economic activity might become concentrated in a small number of firms. A more detailed understanding of the firm growth process will provide evidence for whether such concerns have any scientific foundation.
Dynamical Degrees of Freedom of DNA Sequences by Local and Global Short-Range Prediction
Authors: Ragosta M. , Serio C. , Lanfredi M. T. , Macchiato M.
Published: May 2003

The dynamical properties of DNA sequence samples have been analyzed on the basis of a procedure able to distinguish chaos from randomness. The procedure relies on the concept of short-term (range) predictability of low-dimensional chaotic motions and can distinguish merely linear stochastic processes, e.g. fractional Brownian motion, from truly nonlinear deterministic systems. The method consists in obtaining forecasts on the basis of past events in the sequence. Two forecasting strategies are used. The local strategy views the sequence as the outcome of a nonlinear process, whereas the global approach considers the series as the outcome of a linear stochastic process. For both approaches, the predictive skill is computed and their inter-comparison allows us to get insight into and an understanding of the structure of DNA sequences. Nucleotidic sequences belonging to different taxonomic and functional groups have been analyzed. Different behaviors have been detected according to the existence of finite correlation dimension for specific groups of sequences.
Wavelets Transform of a Multifractal Measure in a Cool Flame Experiment
Authors: Nicollet M. , Lemarchand A. , Dumas G. M. L.
Published: May 2003

In order to characterize the chaotic variations of the cool flame temperature observed during the oxidation of a hydrocarbon at low temperature and under non-homogeneous conditions, we perform multifractal analyses of different measures. In the cool flame localization domain, the singularity spectrum obtained for the visited temperature histogram is comparable to the spectrum deduced from a wavelet transform. In the cool flame propagation domain where the temperature histogram is too narrow to be analyzed, the wavelet transform allows us to prove the multifractal character of the chaos observed. The choice of the parameter value retained to perform the wavelet transform is discussed in detail.
The Remarkable Kaleidoscopic Decompositions of the Bivariate Gaussian Distribution
Authors: Puente Carlos E.
Published: May 2003

The construction of bivariate Gaussian distributions by Puente and Klebanoff,1 as transformations of diffuse probability distributions via space-filling fractal interpolating functions is reviewed. It is shown that the ergodic theorem,2 which allows a simple computer implementation of the construction for some diffuse measures, leads in a great many instances, to unexpected kaleidoscopic patterns of exotic nature, which, when added, yield the bivariate Gaussian distribution. Examples of such patterns, some resembling natural shapes, are presented.
Is Network Traffic Self-Similar or Multifractal?
Authors: Taqqu Murad S. , Teverovsky Vadim , Willinger Walter
Published: May 2003

This paper addresses the question of whether self-similar processes are sufficient to model packet network traffic, or whether a broader class of multifractal processes is needed. By using the absolute moments of aggregate traffic measurements, we conclude that measured local-area network (LAN) and wide-area network (WAN) traffic traces, with the sample means subtracted, are well modeled by random processes that are either exactly or asymptotically self-similar.
Dynamical Characterization of Electroless Deposition in the Diffusion-Limited Regime
Authors: Argoul F. , Arneodo A. , Elezgaray J. , Kuhn A.
Published: May 2003

Electroless deposition of metallic aggregates in thin gap geometry has recently been recognized as a good candidate for producing DLA-like morphology. In the continuation of these studies, which were mainly focused on the fractal geometry of the growing aggregate, we address the issue of characterizing the interfacial dynamics via some local measurement of the growth velocity during an electroless deposition process. Direct computations of the harmonic measures of DLA and electroless clusters are compared with experimental estimations of the local growth velocity of these same clusters. This test is shown to be more relevant than the computation of statistical quantities like the generalized fractal dimensions Dq and the f(α) singularity spectrum, as advocated by the multifractal formalism. On the one hand, it does not require working with clusters of very large size. On the other, it provides a direct comparison of the theoretical and experimental local distributions of the growth velocity along the interface of the growing cluster. This experimental approach is therefore adapted to a real time determination of the regime during which the growth process can be reasonably approximated by a purely diffusion-limited process.
Numerical Analysis of Word Frequencies in Artificial and Natural Language Texts
Authors: Cohen A. , Mantegna R. N. , Havlin S.
Published: May 2003

We perform a numerical study of the statistical properties of natural texts written in English and of two types of artificial texts. As statistical tools we use the conventional Zipf analysis of the distribution of words and the inverse Zipf analysis of the distribution of frequencies of words, the analysis of vocabulary growth, the Shannon entropy and a quantity which is a nonlinear function of frequencies of words, the frequency "entropy". Our numerical results, obtained by investigation of eight complete books and sixteen related artificial texts, suggest that, among these analyses, the analysis of vocabulary growth shows the most striking difference between natural and artificial texts. Our results also suggest that, among these analyses, those who give a greater weight to low frequency words succeed better in distinguishing between natural and artificial texts. The inverse Zipf analysis seems to succeed better than the conventional Zipf analysis and the frequency "entropy" better than the usual word entropy. By studying the scaling behavior of both entropies as a function of the total number of words T of the investigated text, we find that the word relative entropy scales with the same functional form for both natural and artificial texts but with a different parameter, while the frequency relative "entropy" decreases monotonically with T for the artificial texts while having a minimum at T≈104 for the natural texts.
Fourier Series Expansion of Irregular Curves
Authors: Montiel M. Eugenia , Aguado Alberto S. , Zaluska Ed
Published: May 2003

Fourier theory provides an important approach to shape analyses; many methods for the analysis and synthesis of shapes use a description based on the expansion of a curve in Fourier series. Most of these methods have centered on modeling regular shapes, although irregular shapes defined by fractal functions have also been considered by using spectral synthesis. In this paper we propose a novel representation of irregular shapes based on Fourier analysis. We formulate a parametric description of irregular curves by using a geometric composition defined via Fourier expansion. This description allows us to model a wide variety of fractals which include not only fractal functions, but also fractals belonging to other families. The coefficients of the Fourier expansion can be parametrized in time in order to produce sequences of fractals useful for modeling chaotic dynamics. The aim of the novel characterization is to extend the potential of shape analyses based on Fourier theory by including a definition of irregular curves. The major advantage of this new approach is that it provides a way of studying geometric aspects useful for shape identification and extraction, such as symmetry and similarity as well as invariant features.
Individual Differeneces in the Perception of Fractal Curves
Authors: Geake John , Landini Gabriel
Published: May 2003

This study was prompted by the application of fractal geometry to histopathology, where diagnostic reliability can be limited by intra- and inter-observer variance of fractal image classification. The study was conducted in two stages. First, some of the characteristics of individual differences in human discriminability of complex fractal contours were measured. Second, the extent to which such individual perceptual differences are related to individual differences in basic cognitive abilities to encode information was investigated. Subjects with high abilities on simultaneous synthesis were best at a task of discriminating the fractal dimension of complex contours.
Ice Cubes and Hot Water Bottles
Authors: Vrobel Susie
Published: May 2003

Can the arrow of time we seem to perceive be explained by an overall increase in entropy? Several models suggest that the one macroscopic arrow of time which is associated with an overall increase in entropy may be identical to the arrows of time which are subject to our empirical knowledge. These models turn out to be difficult to maintain if one considers a freeze-frame picture (or one containing a minimal period of time) of nested systems of decreasing and increasing entropy. An observer who determines an arrow of time by measuring an increase or decrease in entropy must obviously be located somewhere. This observer position is in no case arbitrary — the individual situation of the observer determines, in each case, the outcome of the measurement.

A fractal model suggests that the direction-generating agent is not to be found in a system's increase in entropy, but rather in the choice of the observer's position. A thought experiment involving infinitely nested ice cubes and hot water bottles leads to the conclusion that for such freeze-frames involving a minimal time span, the concepts of isolated and open systems (which otherwise are indispensable concepts for the discussion of entropy) are unsuitable. If one considers observers placed within different nested levels of the ice cube and hot water bottle universe, it will be impossible for these observers to determine whether the embedding systems add up to a total increase or decrease of entropy: we will never know whether the "outermost embedding nest" is an ice cube or a hot water bottle.

An identification of the arrows of time which are subject to our empirical knowledge with an overall increase in entropy would not be plausible since there is no conceivable observer capable of monitoring the system as a whole. A fractal nested model suggests that there are nested arrows of time with differing directions. What direction we experience depends, in each case, entirely on the observer position chosen, i.e., the system we participate in. The only way to find out which arrow of time we are experiencing at the moment, say, in an ice cube, is to make contact with an observer in a hot water bottle — either with an observer in the hot water bottle embedding my ice cube or with one in the hot water bottle nested in my ice cube. The question: "Is there a way out?" must be discussed elsewhere. The arrow of time defined by an overall increase in entropy is not congruent with the arrows of time of our empirical knowledge.
Randomness in Geomagnetic Storms
Authors: Foti M. A. , Arizmendi C. M.
Published: May 2003

Although geomagnetic forecasting is extremely important, geomagnetic predictions usually rely on forecasters' experience in distinguishing events expected to be geoeffective. Initial investigations with powerful forecasting techniques such as neural networks have recently been applied to geomagnetic prediction, but these are based on the assumption that the phenomenon to be forecasted has only several degrees of freedom. Thus a basic question related to geomagnetic forecasting is whether the randomness associated with geomagnetic evolution is produced by linear Gaussian noise or by nonlinear chaotic dynamics with only a few degrees of freedom. In order to try to answer this important question, we took a geomagnetic index time series and applied a recently developed technique which distinguishes nonlinear deterministic systems from linear ones.
Strange Attractors in an Antiferromagnetic Ising Model
Authors: Ananikian N. S. , Dallakian S. K. , Izmailian N. Sh. , Oganessyan K. A.
Published: May 2003

The three-site antiferromagnetic Ising model on Husimi tree is investigated in an external magnetic field. The full bifurcation diagram, including chaos, of the magnetization is exhibited. With the "thermodynamic formalism", we investigate the antiferromagnetic Ising model in the case of fully developed chaos and describe the chaotic properties of this statistical mechanical system via the invariants characterizing a strange attractor. It is shown that this system displays in the chaotic region a phase transition at a positive "temperature" whereas in a class of maps close to x→ 4x(1-x), the phase transitions occur at negative "temperatures".

The Frobenius-Perron recursion equation is numerically solved and the density of the invariant measure is obtained.
Surface Selective Deconstruction
Authors: Reverberi A. P. , Scalas E.
Published: May 2003

Two toy models for surface and interface disaggregation are introduced and some considerations on their relevance for real physico-chemical processes are presented. The models are studied by means of Monte Carlo simulations in 1+1 dimensions and the scaling laws of the interface width w(L, t) are determined. In both cases, the scaling is in agreement with that obtained from the fourth order linear Langevin equations. The result is discussed in relation to another microscopic disaggregation model and to the microscopic growth model of Wolf and Villain.
Chemical Engineering, Fractal and Disordered System Theory
Authors: Giona Massimiliano
Published: May 2003

This article critically discusses the applications of fractal and disordered system theory to chemical engineering problems in order to highlight some promising research directions and the difficulties that may be encountered.

Starting from the analysis of transport and reaction kinetics, the question is addressed, with the aid of some examples, of whether and how engineering research could help in the study of complex phenomenologies on fractals and disordered systems. The effects of thermodynamical nonidealities in transport and adsorption, and the influence of nonlinearities in reaction kinetics are discussed in some detail. Examples of typical engineering problems in which fractal analysis may help towards a better understanding of the physical phenomenologies in the presence of complex porous substrata and fluid mixtures are discussed. The role played by the boundary conditions on transport phenomena involving fractal structures is also analyzed. A critical discussion on the perspectives in the characterization of disordered and fractal porous structures, and in the study of turbulent transport and mixing is also developed.
Mixing in Globally Chaotic Flows
Authors: Hobbs D. M. , Alvarez M. M. , Muzzio F. J.
Published: May 2003

The first half of this paper reviews mixing in chaotic flows. The sine-flow is employed as a two dimensional example to demonstrate techniques used for characterizing mixing behavior. Several manifestations of self-similarity are readily apparent. The results of tracer mixing simulations demonstrate a self-similar, iterative development of partially mixed structures in the flow. The spatial distribution of mixing intensities present in the flow is examined via computation of stretching. The probability density function (PDF) of the logarithm of stretching values reveals a Gaussian distribution over the central spectrum of stretching intensities for the globally chaotic case, but contains two peaks for a case with coexisting chaotic and regular regions: a broad Gaussian peak for higher stretching values, corresponding to the chaotic region, and a sharp peak of low stretching values corresponding to the regular regions. The self-similar stretching distributions can be collapsed to a single invariant distribution using an appropriate scaling based on the central limit theorem. The folding processes in the flow are examined through curvature calculations; PDFs for curvature collapse to time invariant self-similar distributions without the need for scaling. Direct computation of the striation thickness distribution (STD) provides the most fundamental (and computationally most expensive) measure of mixing; STDs develop a self-similar form that can be collapsed to an invariant distribution using a simple scaling. The second half of the paper focuses on a real, three-dimensional mixing system: the Kenics static mixer. Two alternate configurations of the Kenics mixer were analyzed: one in which elements have alternating right-handed and left-handed twist (R-L) and a second in which all elements have right-handed twist (R-R). Poincaré sections as well as experiments indicate that the R-L configuration is globally chaotic, while the R-R configuration contains significant segregated, regular regions. Stretching histories of material elements in the two flows were computed, once again revealing self-similar distributions that can be collapsed to an invariant limit using a scaling based on the central limit theorem.
Solution of Transport Schemes on Fractals by Means of Green Function Renormalization — Application to Integral Quantities
Authors: Giona M. , Adrover A. , Schwalm W. A. , Schwalm M. K.
Published: May 2003

Green function renormalization is applied to obtain exact recursions for integral quantities and integral transforms of concentration fields, involving a summation over a manifold of lattice sites or over the entire lattice. Definition of the Fourier transform of the Green functions, to some extent equivalent to the dynamic structure factor, is extremely useful to obtain quantitative information on the spatial behavior of concentration profiles and eigenfunctions. Some preliminary results on sorption properties of product lattices are presented. The application of anisotropic lattice models to study the volume-to-surface effects in adsorption and reaction is discussed. The properties of the Green function generating function are also analyzed.
The Effectiveness of Mass Fractal Catalysts
Authors: Coppens Marc-Olivier , Froment Gilbert F.
Published: May 2003

Many porous catalysts have a fractal surface, but only rarely do they have a fractal volume, the main exceptions being extremely porous aerogels. It has been suggested that a fractal shape of their volume would be ideal, because it has an infinite area per unit mass that is easily accessible by the reactants. This paper investigates the efficiency of mass fractals by comparing them with nonfractal catalysts. It is found that the specific surface areas of comparable nonfractal catalysts are of the same order of magnitude, if not higher than those of mass fractals. Despite the high effectiveness factor of mass fractals due to the exceptionally easy accessibility of their active sites, production in a nonfractal catalyst is often higher than in a mass fractal, because of the high porosity of the latter. For some strongly diffusion limited reactions, especially in mesoporous catalysts, an added mass fractal macroporosity, with a finite scaling regime, would increase the yields beyond what is possible with a nonfractal catalyst. Nonetheless, when transport through viscous flow in macropores is very rapid the effective reaction rates in classical bimodal catalysts are higher than in fractal catalysts with their high macroporosity.
Hydrodynamic Drag and Electrophoresis of Suspensions of Fractal Aggregates
Authors: Coelho D. , Thovert J.-F. , Thouy R. , Adler P. M.
Published: May 2003

The hydrodynamic properties of fractal aggregates are investigated numerically by solving the three-dimensional Stokes equations. Aggregates are built with a variety of sizes and fractal dimensions. Their hydraulic radii conductivities and mobilities are evaluated as functions of their volume fraction in the suspension. An influence of the fractal dimension is visible on the hydrodynamic and electrokinetic characteristics of the aggregates. In the dilute limit, our results compare well with the predictions of various mean-field arguments.
An Example of How Nonlinear Dynamics Tools Can be Successfully Applied to A Chemical System
Authors: Pellegrini L. , Possio C. Tablino , Biardi G.
Published: May 2003

The nonlinear dynamic behavior of a Proportional-Integral controlled Continuously Stirred Tank Reactor (CSTR) is analyzed in depth progressing from chaos characterization, through the high codimension bifurcation theory, up to the application of Controlling Chaos techniques.

All these tools can be successfully applied to recognize, to avoid and to use chaos in practical applications, so that the nonlinear dynamic theory turns out to be an indispensable science to constrain dynamic systems to work in the most suitable operative conditions.
On the Practical Relevance of Bifurcation and Chaos in Chemical and Biochemical Reaction Engineering
Authors: Elnashaie S. S. E. H. , Abasaeed A. E. , Ibrahim G.
Published: May 2003

This paper presents a condensed exposition of some of the research work on the bifurcation and chaotic behavior of industrially and fundamentally important chemical and biochemical reaction engineering systems. Two cases are presented: a forced industrial fluid catalytic cracking unit and an enzymatic system. The Poincare bifurcation diagrams obtained for both cases reveal their richness in dynamic behavior. Various routes to chaotic behavior have been identified including period doubling, intermittency, crisis.
PROBABILITY MODELS FOR SEQUENTIAL-STAGE SYSTEM RELIABILITY GROWTH VIA FAILURE MODE REMOVAL
Authors: GAVER DONALD P. , JACOBS PATRICIA A. , GLAZEBROOK KEVIN D. , SEGLIE ERNEST A.
Published: May 2003

This paper provides guidance for the planners of a test of any system that operates in sequential stages: only if the first stage functions properly (e.g., a vehicle's starter motor rotates adequately) can the second stage be activated (ignition system performs) and hence tested, followed by a third stage (engine starts and propels vehicle), with further stages such as wheels, and steering, and finally brakes eventually brought to test. Each sequential stage may fail to operate because its design, manufacture, or usage has faults or defects that may give rise to failure. Testing of all stages in the entire system in appropriate environments allows failures at the various stages to reveal defects, which are targets for removal. Early stages' fault activations thus postpone exposure of later stages to test. It is clear that only by allowing the entire system to be tested end-to-end, through all stages, and to observe several total system successes can one be assured that the integrated system is relatively free of defects and is likely to perform well if fielded.

The methodology of the paper permits a test planner to hypothesize the numbers of (design) faults present in each stage, and the stagewise probability of a fault activation, leading to a system failure at that stage, given survival to that stage. If the test item fails at some stage, then rectification ("fix") of the design occurs, and the fault is (likely) removed. Failure at that stage is hence less likely on future tests, allowing later stages to be activated, tested, and fixed. So reliability grows.

To allow many Test and Fix (TAF) cycles is obviously impractical. A stopping criterion proposed by E. A. Seglie that suggests test stopping as soon as an uninterrupted run/sequence of r (e.g., 5) consecutive system successes has been achieved is studied quantitatively here. It is shown how to calculate the probability of eventual field success if the design is frozen and the system fielded after such a sequential stopping criterion is achieved. The mean test length is also calculated. Many other calculations are possible, based on formulas presented.
GRAPHICAL APPROACH TO REPLACEMENT POLICY OF A K-OUT-OF-N SYSTEM SUBJECT TO SHOCKS
Authors: JUANG MUH-GUEY , SHEU SHEY-HUEI
Published: May 2003

This paper deals with the problem of determining an optimal age replacement by incorporating minimal repair, planned replacement, and unplanned replacement into a k-out-of-n system subject to shocks. In particular, two kinds of solution procedures are discussed to obtain the optimal replacement age, one is a straightforward procedure, and the other is a graphical approach based on the Total Time on Test (TTT) concept. A statistical solution procedure for estimating the optimal replacement time is proposed, and the optimal policies are obtained directly from real data.
THE LONG GRAFT IN FLEXOR TENDON REPAIR — A 30-YEAR EXPERIENCE
Authors: Matev Ivan
Published: May 2003

The author’s 30 years experience with long grafting procedure is presented and the essentials of the technique are outlined. When both flexor tendons are cut in Zone 2, secondary repair using long graft gives the possibility of better results than the conventional tendon grafting, when scarring exists in the palm.
MEASURED TENSION METHOD FOR SURGERY OF THE CLAW HAND
Authors: Thatte M.R. , Verma C.V. , Shah Pankil P. , Thatte R.L.
Published: May 2003

Ulnar Median Claw following trauma or Hansen’s disease is a fairly common problem in developing countries. The methods for correction of this deformity use a relatively arbitrary method for estimation and application of tension to the transferred tendon. The present paper outlines an objective and simple method of judging the tension required in these transferred tendon slips.
HERBERT SCREW FIXATION OF SCAPHOID FRACTURES
Authors: Low C. K. , Ang B. T.
Published: May 2003

Forty-four scaphoid fractures treated with open reduction and internal fixation using the Herbert screw were available for evaluation at an average follow-up period of 2.1 years and a range of 1 to 6 years. They were classified according to Herbert into 25 unstable (type B); 8 delayed unions (type C); and 11 nonunions (type D). Bone grafting was required in 22 cases. Sound radiological union was achieved in 42 cases at an average of 3.2 months. The two nonunions healed after revision grafting.

Using the Mayo wrist score, excellent results were achieved in 14 cases; good in 22; fair in 4; and poor in 4. Poor results were associated with nonunion in two; untreated scapholunate dissociation in 1; and screw protrusion in 1.
FUNCTIONAL ANATOMY OF THE INTEROSSEOUS MEMBRANE OF THE FOREARM — DYNAMIC CHANGES DURING ROTATION
Authors: Nakamura Toshiyasu , Yabe Yutaka , Horiuchi Yukio
Published: May 2003

The functional anatomy of the interosseous membrane (IOM) of the forearm was studied in 15 fresh frozen cadavers. The IOM consisted of three components: the tendinous part; the membranous part; and the dorsal oblique accessory cord. The tendinous part was a thick and strong complex of three to ten bundles which run from the proximal one third of the radius to the distal quarter of the ulna. The membranous part was recognised as a soft and thin structure, adjacent proximal and distal to the tendinous part. The dorsal oblique cord was found as a single cord on the dorsal side of the IOM from the proximal quarter of the ulna to the middle region of the radius. This cord was distinct from the oblique cord, which existed on the palmar side of the forearm separated from the IOM. The IOM was flat in the neutral position, while it flexed along the rotation axis in pronation and supination. Since the prominence of the curvature in the IOM was almost in the same direction as the fibres of the tendinous part, the tendinous part demonstrated only bending, similar to partial bending of an elastic board. The bending position was changed with the forearm position and the tightened bundles in the tendinous part were altered during rotation.
PIGMENTED VILLONODULAR SYNOVITIS OF THE HAND IN THE ASIAN POPULATION
Authors: Looi K. P. , Low C. K. , Yap Y. M.
Published: May 2003

Fifty-five localised pigmented villonodular synovitis (giant cell tumour of the tendon sheath) in the hands and wrists in 53 patients, treated in a local hospital over a 5-year period, were reviewed. The mean age at presentation was 39.9 years, with 84.9% of the cases being Chinese. There was a predilection for the ring finger and females. There was no significant association with antecedent trauma. 56.4% of patients had associated X-rays changes. All patients had complete excision of the tumour and 4 recurrences noted, giving a rate of 7.3%. Follow-up period range from 1 to 5 years. Postoperative morbidity consisted of two cases with mild stiffness. There was good local control with minimal morbidity and low recurrence rate.
THE POSTERIOR INTEROSSEOUS NERVE ANATOMICAL VARIATION AND SURGICAL CONSIDERATION — A CASE REPORT OF CADAVER STUDY
Authors: Seradge Houshang , Tian Wen , Baer Carrie , Seradge Ali
Published: May 2003

We found an anatomical variation of the posterior interosseous nerve (PIN) in a cadaver. The PIN entered the supinator muscle 3 cm distal to the radiohumeral joint, but exited from two sites. 50% of the nerve exited under the distal edge of the supinator muscle. The other half of the nerve pierced through the supinator muscle, 4.2 cm distal to the articular surface of the radial head and then joined the remaining PIN as it emerged from the supinator muscle distally. We did not find variations concerning the order and the manner of branches to the muscles. This variation in the PIN could be an additional compression site for this nerve; and therefore responsible for some of the atypical presentations of symptoms and for partial recovery after surgical decompression. A careful surgical dissection should be recommended to avoid injury to this branch.
METASTATIC HEPATOCELLULAR CARCINOMA OF THE DISTAL PHALANX OF THE THUMB: A CASE REPORT
Authors: Lee Kwang-Suk , Lee Soon-Hyuk , Kang Ki-Hoon , Oh Kwang-Joon
Published: May 2003

A case of metastatic hepatocellular carcinoma of the distal phalanx of the thumb is presented. This case illustrated a rare example of acrometastasis of hepatocellular carcinoma.
OBSTRUCTION OF THE RADIAL ARTERY PASSING BENEATH THE BICEPS BRACHII TENDON — A CASE REPORT
Authors: Ikeda Kazuo , Yokoyama Mitsuteru , Okada Kazuko , Tomita Katsuro
Published: May 2003

A case is reported of obstruction of the radial artery passing beneath the biceps brachii tendon. It may cause symptoms such as cold intolerance and ulcer formation. An elongation of the biceps with Z-plasty improved the circulation of the distal forearm.
MALIGNANT FIBROUS HISTIOCYTOMA OF THE DIGIT
Authors: Taniguchi Yasunori , Tamaki Tetsuya
Published: May 2003

We report a case of malignant fibrous histiocytoma of the middle finger in a 57-year-old male. The tumour arose from the perionychium of a digit, an extremely unusual occurrence
PERCUTANEOUS A1 PULLEY RELEASE A CLINICAL STUDY
Authors: Bain G. I. , Wallwork N. A.
Published: May 2003

Percutaneous A1 pulley release is being increasingly used as an alternative to open surgical release and injection of local steroids for the treatment of the trigger digit.

In 31 cases (26 patients), a percutaneous release was performed with a 14-gauge intravenous catheter needle under local anaesthesia in the outpatient setting.

We report a 97% successful release and only one case of incomplete release. There were no digital nerve injuries, flexor tendon injuries, bowstringing or infections. By two months, all the patients had no pain at the operative site, and their preoperative range of motion had returned or improved.

The percutaneous release is a safe and effective technique which provides significant cost savings. We recommend the percutaneous technique for typical cases of trigger finger with a palpable nodule and reproducible mechanical triggering. We recommend a steroid injection for patients with tenosynovitis and those who do not have reproducible triggering at the time of presentation. The open technique is reserved for complicated cases such as florid tenosynovitis, locked digit, failed percutaneous release or those involving the thumb.
DISTAL INTERPHALANGEAL JOINT ARTHRODESIS USING INTRAMEDULLARY AND INTEROSSEOUS FIXATION
Authors: Zavitsanos G. , Watkins F. , Britton E. , Somia N. , Gupta A. , Kleinert H.
Published: May 2003

Multiple fixation techniques have been developed for distal interphalangeal (DIP) joint arthrodesis. Delayed and nonunion rates varying from 0% to 20% have been reported. The senior author has refined a technique for DIP joint arthrodesis by using an intramedullary Kirschner wire and an interosseous wire for fusion of the DIP joint and interphalangeal (IP) joint of the thumb. In 24 joint arthrodeses in 19 patients, the nonunion rate was 4%, and the minor complication rate was 12%. The advantages of this technique include the absence of protruding hardware that would necessitate removal; consistency in achieving osteosynthesis, with a low nonunion rate; and technical simplicity.
LUNATE MORPHOLOGY OF KIENBÖCK'S DISEASE ON X-RAY STUDY
Authors: Kato H. , Nakamura R.
Published: May 2003

To investigate whether the lunate morphology proposed by Watson predisposes to Kienböck's disease, we investigated 23 patients with Kienböck's disease and 24 normal controls. Lateral X-ray films showed 17 of type D (dorsally lower height) lunate; 2 of type P (palmary lower height); and 1 of type N (equal palmar height to dorsal). In the control group, there were 21 of type D; 2 of type P; and 1 of type N, among 24 patients. The mean wedge ratio was 1.17 (1.08–1.35) in type D of the Kienböck group, and 1.11 (1.03–1.41) in type D of the control group. There were no statistically significant differences between the two groups, and palmar and dorsal lunate morphology is not believed to predispose to Kienböck's disease.