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An attempt is made to find the fractal cutoff of crack profiles on the tension face of concrete beams subjected to uni-axial bending. Previous work by the authors has shown that such cracking can be interpreted as a non-Fickian diffusive phenomenon resulting from a self-affine random fractal process: specifically fractional Brownian motion (fBm). In addition, a spatial description of the cracking geometry can be found from experimental data using both a (Hurst) scaling exponent and a diffusion-type coefficient. Herein the authors find that the fractal description of the crack profiles extends down to less than 0.75 microns. The use of a scanning electron microscope to probe the crack profile (and surface) at smaller scales is discussed and the synthesis of crack surfaces using fBm is described briefly., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

The bispectrum is the natural third-order generalization of the power spectrum. It provides information about correlations between different Fourier components of a signal or image, and about the statistics of Fourier phase. A number of numerical and experimental studies of the bispectra of chaotic systems have been published. In this paper we present the first analytical calculations of the bispectra of chaotic dynamical systems. First, for a generalization of the classical sawtooth or Renyi map, we calculate the bispectrum using symbolic dynamics. Also, for intermittent systems, we calculate the bispectrum using the relationship between these systems and renewal processes. We review the results of these calculations, drawing some conclusions about the characteristic features of the bispectra of chaotic systems, and compare them with the features of some financial time series., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

This document contains all accepted papers to Fractal 2000, the 6th International Multidisciplinary Conference, held 16-19 April 2000 in Singapore. One of the aims of the conference was to review the current status in the field of fractals within realm of complexity and to explore future directions. There is a plenitude of examples in nature displaying complex patterns. The couplings responsible for these intricate patterns give rise to processes and phenomena that are absent when couplings are not present. The universality of such systems can be observed over a wide range of scales, from sub-atomic domain to that of cosmology. Furthermore, in addition to physics, mathematics, and chemistry, where these phenomena were observed first, the existence of complex systems has been confirmed in many disciplines such as medicine, biology, economics and sociology. The underlying geometry is frequently non-Euclidean and can be best analyzed using the tools of fractal analysis., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. For individual articles, see

It is a common knowledge that both the solar plasma and the solar magnetic field have a cellular, discrete structure, which is indicative of their possible fractal origin. The questions of fine structuring of the solar magnetoplasma were considered, plausible mechanisms of its genesis were suggested, and possibilities of describing its fractal properties were put forward. The existence of a whole hierarchy of sizes of active features in the solar atmosphere has long been established. For example, it is well known that in addition to the granulation (1"-1.5"), such structures as the mesogranulation (8"-15"), the supergranulation (30"-40"), giant cells (20-40 degrees), and supergiant cells (80-110 degrees) exist on the Sun. The last two features refer to the so called large-scale organization of solar magnetic fields. The objective of this paper is to investigate the fractal properties of large-scale magnetic fields on different spatial scales., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

The purpose of the paper is to introduce a new application of the multifractals in the reliability engineering, risk analysis, historical chronology and others fields where we deal with series of events of various natures. The spectrum of such series is quite broad In particular, we do not know whether some temporal pattern is hidden in an apparently disordered set of events. The multifractal theory is a good basis for revealing such an order and describing the event sequence in time. It can provide a deeper understanding the nature of the event flow., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Weather and climate systems have low dimensional attractors. A consistent feature of weather and climate data is that they are aperiodic and their deviations from periodicity cannot be explained by conventional linear models of time series analysis. It is therefore essential that the nature of the sea level change is analyzed and modelled in order to assess the changes from one coastline to other or from the changes taking place in one ocean from the other neighboring oceans. In this study the approach to analyze and visualize such a comparison is done through calculating the fractal dimension of the time series on annual averages of mean sea level variations for different stations in four countries representing two different oceans regionally., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

The main topic presented in this paper concerns the reduction of the diffusion volume to convex isotropic Euclidean structures as polygons and convex polyhedrons in order to estimate the diffusive acoustic behavior of a fractal structure., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Intracavity doubled solid state lasers based on Nd-doped crystals are efficient and compact sources of coherent visible optical radiation. When such lasers operate in three or more longitudinal cavity modes, irregular fluctuations of the output intensity may occur. This behavior, referred to as the green problem, has been reported for the first time by Baer. He found that these instabilities arise from a coupling of the longitudinal modes of the laser by sum-frequency generation, which occur in the intracavity-doubling crystal. When the laser does not contain the nonlinear crystal or when it operates in a single longitudinal mode, its output is stable. In the case of two oscillating longitudinal modes, output intensity of the laser is stable only for small values of nonlinearity, otherwise both modes tend to pulse on and off out of phase with each other. When the number of lasing modes is larger than two, the laser can exhibit, depending on the parameters describing it, various behaviors like: aniphase dynamics, clustering, grouping and chaotic dynamics. The main goal of this communication is to study the possibilities of a stabilization of large amplitude fluctuations in such a laser, i.e., an intracavity-doubled Nd:YAG laser. The analysis is based on the Baer-type rate equations., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Chinese acupuncture-moxibustion is a therapeutic method for injecting or burning moxa (a kind of herb) on the acupuncture points (acupoints) of the body surface, used to treat diseases. There are over one thousand acupoints on the body surface. In the clinic, the acupoint system on the human body can be divided into two large parts: the channel system (macro-acupuncture) and the micro-acupuncture system. But the whole acupoint system can be divided into many different hierarchical holographic units. Such system possesses fractal structure., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Iterated Function Systems (IFS) have been widely used for image compression and for generating fractal objects. Using barycentric coordinates and an extension of the concept, a range of rendering methods, such as Lambert, Gouraud and Phong shading, can he generated using IFS. By rendering a scattered collection of individual points using z-buffer and shadow buffer, the problems of clipping, hidden surface elimination and shadow generation are reduced to very simple forms The method is relatively simple to program, but will not achieve the high speeds of current sophisticated rendering methods., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Global IFS seem to be suited best for compressed encoding of natural objects which are in most cases self affine even if not always exactly. Since affine transformations, the IFS-Codes, resp. the union of all their orbits generate an object (an IFS-Attractor), the detection of a non minimal set of these orbits solves the inverse IFS-Problem by calculating a superset of IFS-Codes, which has to be minimized. Here a method is presusted how these orbits (in particular those on the object boundary) can be calculated. Therefore a generalized convex hull; the sigma-Hull; is defined. This fractal hull is bounded by log spirals, that curves formed by the orbits. It is shown that log spirals can be represented by a continous function of powers of affine maps and that by using this "spiral equivalent" the generating transformations of the orbits by which an IFS-object is bound, can be calculated in the x/y-plane. Further more this representation can be used for the classification of the detected orbits, necessary to calculate the IFS-Codes of a minimal IFS from their generating transformations, subsequently., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

During the last decades great attention has been turned to chaotic vibrations of elastic beams, but not much has been done in the case of elastic-plastic deformations. Evidently the first paper in this field belongs to Symonds and Yu (1985), who considered the following problem. A fixed ended beam is subjected to short intensive pulse of transverse loading that produces plastic deformation. Since the ends of the beam are fixed membrane forces must be taken into account. Solving the equations of motion Symonds and Yu found that permanent deflection may be in direction opposite to the load. This phenomenon was investigated in several papers by Symonds and his collaborators. It turned out that the permanent deflection is very sensitive to small changes of load. Fractality and self-similarity which are characteristic to chaotic processes, were demonstrated. For the similarity dimension the value 0,78 and for the correlation fractal dimension ^1,44 were obtained., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

We study analytically the kinetics of growth of parallel needles using a conformal transformation to set up the iterative nonlinear equations. This allows to build the discrete Fokker-Planck equation for the probability of finding at time t a given distribution of needle lengths. We consider here two specific cases: we find the exact Fokker-Planck equation for pairs of needles and its solutions and the linear behavior of a set of n needles with equal initial lengths. The corresponding Fokker-Planck equations show the short-wavelength Mullins-Sekerka instability of these parallel needles and the possible structure of the screening leading to the scale invariance of the model., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Riemann's example of a continuous, non-differentiable function is given by the summation sin(n2x)/n2. This function is sufficiently irregular and its graph is fractal. Hardy proved that Riemann's non-differentiable function is not differentiable at any irrational point because of a square root singularity at these points. Careful investigation of the differentiability of Riemann's non-differentiable function was carried out by Gerver, who showed that this function has derivative equal to -1/2 at every rational point of a special type (forming the orbit of the point 1 under the theta-modular group). Different proofs of this surprising fact was given by other authors, providing also a close relation between Riemann's non-differentiable function and classical theta-function and Gauss sums. Duistermaat obtained an exact functional equations for this function under transformations of the theta-modular group. In this article we use functional equations for Riemann's non-differentiable function under theta-modular transformations to derive functional equations on Gauss sums generalizing Genocci-Schaar identity., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Multiple scattering of classical particles on a system of point scatterers distributed in space in a fractal fashion is considered in the small-angle approximation. The asymptotic regime of this process is described by a fractional differential equation generalizing the ordinary diffusion in the angle space equation. The solution of the problem is presented both in terms of stable distributions and in terms of Fox-functions. Main features of the obtained solutions are discussed., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Multifractal spectra are derived for 1- and 2-dimensional cross-sections of passively convected scalar fields; 2- and 3-dimensional single-scale velocity fields in the absence of KAM surfaces are considered. Both the Kraichnan model and real flows with non-zero correlation time are studied. The calculation of f(alpha)-curves is based on the probability density function of the stretching factors of fluid elements. It is shown that strict multifractality holds only for small values of alpha. New multifractal scalar field-"harmfulness"-is suggested to describe the propagation of environmentally dangerous substances., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

In the presence of oscillating singularities the standard Wavelet Transfrom Modulus Maxima (WTMM) method gives irrelevant information on the Hoelder regularity of the function. In general, two exponents h,beta are necessary to describe the singular behavior of a function f(x), namely the Hoelder exponent h and the oscillation exponent beta describing the local power law divergence of the instantaneous frequency. If f(x) contains oscillating singularities the regularity of the primitive of f(x) depends on beta. In this case the Hoelder exponent does not increase by 1 as in the case of a cusp singularity but by beta + 1. Thus, the singularity spectrum of general functions depends on both exponents, D(h,beta). In order to extract Hoelder exponents and to quantify at the same time the oscillating behavior we propose to use a family of complex progressive wavelets ?psi sub n! with an increasing number of vanishing moments., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Nature abounds with complex patterns and structures emerging from homogenous media operating far from thermodynamic equilibrium. Such phenomena, which are widely observed in both inanimate (non-biological) and biological media, can be modeled and studied via the CNN (Cellular Neural/Nonlinear Network) paradigm in an in-depth and unified way. Whether a homogeneous medium is capable of exhibiting complexity depends on whether the CNN cells, or its couplings, is locally active in a precise mathematical sense. This local activity principle is of universal generality and is responsible for all symmetry breaking phenomena observed in a great variety of non-equilibrium media ranging from the emergence of negative differential conductance in bulk semiconductor materials (e.g., Gallium Arsenide in Gunn Diodes) to the emergence of artificial life itself. The main result of this paper consists of a set of explicit analytical conditions for calculating the parameter ranges necessary for the emergence of a non-homogeneous static or dynamic pattern in a homogeneous medium operating under an influx of energy and/or matter. The resulting "complexity related" inequalities are applicable to all media, continuous or discrete, which have been mapped into a CNN paradigm., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Introducing the fractal theory into the study of wood and its porous properties will provide new insights. The fractal dimension of wood surface was first studied by using water-sorption. It was found that the fractal dimension was in the range of 2.5-2.8. An experiment with pressurized water absorption has confirmed the fractal nature of wood. The findings have shown that the pore space within wood could be characterized by fractal dimension or a set of fractal dimensions. But there was no explanation leading to the characterization of wood properties., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

We introduce a method to generate statistical textural transforms that improves the treatment of non-stationarity and leads to a sharper detection of the boundaries between distinct textures (texture segmentation). This method is based on a sliding window processing with fixed size. The basic idea proposed by the authors is to readjust the measuring window around each pixel so as to maximize homogeneity. We use this method with the dimensions D sub n(q) that are derived from the Generalized Multifractal Analysis formalism, to show that the D sub n(q)s can detect and quantify departures from multifractality, while providing the analog of the classical generalized dimension if the measure is multifractal., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

We demonstrate how to construct fractals which are generated by a combination of a cellular automaton and a substitution. Moreover, if the substitution and the cellular automaton exhibit certain symmetry features, the fractal will inherit these symmetries., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analyzing tick data of yen-dollar exchange rates we confirm two fractal properties: 1. the distribution of rate change in a fixed ticks is approximated by a symmetric stretched exponential function for a wide range of time intervals; 2. the interval time distribution of trades nearly follows a power law. Empirical fractal properties in companies' financial data, such as distributions and fluctuations in assets and incomes are discussed with a simple model. The importance of methods and theories for phase transitions is discussed., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

There is verified the hypothesis about multifractal nature of radioactive contamination due to nuclear explosions on Semipalatinsk test site (STS) in Kazakhstan. The fields of terrestrial contamination have extreme high variability caused by a number of nature processes. There are used the methods of multifractal formalism and computation topology. The results of analysis support the existence of multifractal scaling which is different for natural and man-made isotopes. It means that there are "hot spots" of man-made Cs isotope contamination dangerous for human health, which can't be detected by the traditional in Kazakhstan techniques of measurements from air. Moreover, the finding of self-similarity could be the base of new methods of diagnostics of large territories., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

By a slight modification of Saffman-Taylor's viscous finger, we remove its singularity and present a finite-length nonsingular Saffman-Taylor finger. Its dynamic evolution solutions, both one-step theory prediction and numerical simulation in the long-time limit with zero surface tension, give an alternative proof for the analytical selection demonstration of the Saffman-Taylor finger width in the absence of surface tension. As a simple example of pattern selection, which has real experimental background, this work not only contradicts the generally accepted belief that surface tension is indispensable for the selection of the 1/2 width finger but also provides more models to compute the evolution, competition and ramification of multiple fingers numerically in straight channel as well as circular disc geometry., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

A general model linking dynamics of informational entropy and the self-organization process in an open steady-state nonequilibrium system is proposed. Formulas for dynamics of the informational entropy flow and its rate are developed with respect to random process of influences exerted upon a system. It was revealed that the open system responds to a strong change of conditions by steep growth of the informational entropy flow up to a maximum value at the critical point associated with the self-organization process. An example of self-organization during elasto-plastic deformation of metal is considered., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Scale invariance (scaling) in a time series of an observable quantity is a symmetry law which when it exists can provide unique insights about the process in question. It describes variability and transitions at all scales and is often a result of nonlinear dynamics. It is well known that the spectra of atmospheric and climatic variables possess considerable power at low frequencies. Since "red" spectra often associate with scaling processes, it is reasonable to suppose that a search for scaling laws in climatic data might be fruitful. Consequently, the search for scaling in such data over the past decade has produced some exciting ways to describe climate variability. In the past and lately, there has been a growing interest in the existence of uniform in space temporal scaling laws for observable properties of the climate system, since such a property would provide a common rule describing temporal variability everywhere on the globe. Here we show that in spatially extended systems, uniform in space scaling demands that global averages be time invariant. A corollary to this is that where global averages do exhibit temporal variability, as in our climate system, spatial variation in scaling properties is required., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

In the framework of the Comprehensive Test Ban Treaty, development of reliable methods to discriminate between underground nuclear explosions and earthquakes at regional distances (less than 2500km) continues to be very important especially in connection with the last (in May, 1998) nuclear explosions conducted at Indian and Pakistan test sites. Since the lithosphere is a fractal, we suppose the signals, which propagate through the media, inherit its self similar' (scaling) features. We assumed that these features of explosions and earthquakes or their topological reconstructions (embeddings) have to be different. Scaling reflects correlations of more high order then it is possible to estimate by linear discriminating methods and can be used as base of non-linear discrimination. We propose to build a universal geometrical model of a seismic signal using the canon algorithm of F. Takens and to estimate scaling of the model. The scaling features were used as patterns of seismic signals for entering them into an artificial neural network. Records of nuclear explosions and earthquakes from different regions were included into the training set. The net was trained to classify types of seismic events. Results have shown 80% correct classification of the unknown signals. As additional tools for distinguishing between nuclear explosions and earthquakes we propose to use Hurst's method and the cross correlation method. Results of using these methods are demonstrated on examples of some explosions and earthquakes., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

We present numerical results for backscattering of electromagnetic waves by fractal aggregates of fractal dimension < 2. Single-scattering analytical result shows that Fourier transform of the density-density mass correlation function of the scatterer is the main contribution of the backscattering cross-section wavelength variation when wavelength is in the fractal range of the scattering object. This allows to conjecture that multispectral backscattering analysis could be used to measure the geometrical fractal dimension of the scatterer. Illustrative results are given by using several recently proposed numerical scattering codes accounting for multiple scattering. Applications to lidar experiments in the visible range are briefly discussed., Pres. at Fractal 2000, "Complexity and Fractals in the Sciences", 6th International Multidisciplinary Conference, 16-19 Apr 2000, Singapore. --Original contains color plates: All DTIC reproductions will be in black and white. This article is from ADA392358 Paradigms of Complexity. Fractals and Structures in the Sciences

Regenerative liquid propellant guns (RLPGs) have been studied for many years. RLPG firings almost always show large, high-frequency pressure oscillations. To study this phenomenon, a fluid dynamics model of the combustion chamher/gun tube of an RLPG has been developed. High-frequency oscillations are generated naturally by the physics modeled in the code. Dimensional analysis has been applied to the governing equations to furnish insight into the dynamic relationships among pressure, density, temperature, droplet size, etc. The dimensional analysis predicts a scaling law between different-sized fixtures. The computational results exactly match these predictions. This agreement establishes the basis of self-similarity in the physical processes (e.g., tradeoff between droplet size and burning rate) and, in addition, helps verify the computational model.

Understanding how host load changes over time is instrumental in predicting the execution time of tasks or jobs, such as in dynamic load balancing and distributed soft real-time systems. To improve this understanding, we collected week-long, 1 Hz resolution Unix load average traces on 38 different machines including production and research cluster machines, compute servers, and desktop workstations Separate sets of traces were collected at two different times of the year. The traces capture all of the dynamic load information available to user-level programs on these machines. We present a detailed statistical analysis of these traces here, including summary statistics, distributions, and time series analysis results. Two significant new results are that load is self-similar and that it displays epochal behavior. All of the traces exhibit a high degree of self similarity with Hurst parameters ranging from .63 to .97, strongly biased toward the top of that range. The traces also display epochal behavior in that the local frequency content of the load signal remains quite stable for long periods of time (150-450 seconds mean) and changes abruptly at epoch boundaries. CMS-9318163