bluuebunny/crossref_metadata_2025 huggingface dataset:
DIFFUSION LIMITED AGGREGATION FROM SHEAR STRESS AS A SIMPLE MODEL OF VASCULOGENESIS
Authors: FLEURY VINCENT , SCHWARTZ LAURENT
Published: April 2003

A model is proposed by which the formation of the vascular network in animals proceeds via progressive penetration of the vessel ramification into a capillary mesh, by means of a laplacian growth mechanism of hydrodynamical origin. In this model, the growth of both arteries and veins follows the directions of high shear stress provoked by the blood flow on the endothelial wall of a pre-existing capillary mesh. This process is shown to be identical to the phenomenon of dendritic growth, which is responsible for the formation of such well-known patterns as dendritic crystals, lightning sparks or branching aggregates of bacteria. A number of straightforward consequences of potentially important medical and physiological interests are deduced. These include the natural and spontaneous organization of the arterial and venal trees, the spontaneous and unavoidable tropism of arteries towards veins and vice-versa, the hierarchical character of the vessels and the possibility of computerized prediction of the vascular pattern from the shape of the capillary bed.
APPROXIMATION OF FRACTAL SETS BY JULIA SET ATTRACTORS OF POLYNOMIAL ITERATED FUNCTION SYSTEMS
Authors: MELNIKOV ALEXANDER V.
Published: April 2003

A novel computational solution of the fractal inverse problem is suggested. The method presented is based on the idea of approximating fractal sets by Julia set attractors of polynomial Iterated Function Systems (IFS). An implementation of this method has shown good results and stable convergence both for polynomial Julia sets and other sets with similar features.
INTERNAL AVALANCHES IN MODELS OF GRANULAR MEDIA
Authors: KRISHNAMURTHY SUPRIYA , HERRMANN HANS , LORETO VITTORIO , NICODEMI MARIO , ROUX STEPHANE
Published: April 2003

We study the phenomenon of internal avalanching within the context of recently introduced lattice models of granular media. The avalanche is produced by pulling out a grain at the base of the packing and then studying the number of grains to be rearranged before the packing is stable again. We find that the avalanches are long-ranged, decaying as a power law. We study the distribution of avalanches as a function of the density of the packing and find that the avalanche distribution is a very sensitive structural probe of the system.
BASIC PROPERTIES AND CHARACTERIZATION OF STOCHASTICALLY SELF-SIMILAR PROCESSES IN Rd
Authors: VENEZIANO DANIELE
Published: April 2003

The classical notion of self-similarity (ss) for random X(t) as invariance under the group of positive affine transformations {X→ arX, t→rt; ar>0} is extended by allowing ar to be a random variable. The resulting property of "stochastic self-similarity" (sss) is applied to both ordinary and generalized random processes in Rd, d≥1. The class of sss processes seems to correspond to that of multifractal processes (the latter are variously defined in the literature). The spectral measures of ordinary and generalized sss processes are themselves stochastically self-similar. Two characterizations of ss processes by Lamperti are extended to the sss case and several basic properties of ordinary and generalized sss processes are derived.
SELF-SIMILARITY AND THE GEOMETRIC REQUIREMENTS FOR FREQUENCY INDEPENDENCE IN ANTENNAE
Authors: HOHLFELD ROBERT G. , COHEN NATHAN
Published: April 2003

Self-similarity and origin symmetry are shown to be the key geometric constraints in the determination of frequency independent properties of antennae. Fractal antennae with origin symmetry meet these criteria of the extended version of Rumsey's principle. Frequency independence is not achieved by self-similarity alone. Self-complementarity plays no role in frequency independence, but does aid in smoothing out impedance variations for coarsely iterated frequency independent antennae. New families of practical designs arise from these geometric insights, which need not follow the usual constraints of angle-defined structure of the original Rumsey's principle.
DISCRIMINATION BETWEEN HEALTHY AND SICK CARDIAC AUTONOMIC NERVOUS SYSTEM BY DETRENDED HEART RATE VARIABILITY ANALYSIS
Authors: ASHKENAZY Y. , LEWKOWICZ M. , LEVITAN J. , HAVLIN S. , SAERMARK K. , MOELGAARD H. , THOMSEN P. E. BLOCH
Published: April 2003

Multiresolution Wavelet Transform and Detrended Fluctuation Analysis have recently been proven to be excellent methods in the analysis of Heart Rate Variability and in distinguishing between healthy subjects and patients with various dysfunctions of the cardiac nervous system. We argue that it is possible to obtain a distinction between healthy subjects/patients of at least similar quality by, first, detrending the time-series of RR-intervals by subtracting a running average based on a local window with a length of around 32 data points, then calculating the standard deviation of the detrended time-series. The results presented here indicate that the analysis can be based on very short time-series of RR-data (7–8 minutes), which is a considerable improvement relative to 24-hour Holter recordings.
ON IRREGULAR BEHAVIOR OF NEURON SPIKE TRAINS
Authors: SHAHVERDIAN A. YU. , APKARIAN A. V.
Published: April 2003

The computational analysis of neuron spike trains shows that the changes in monotony of interspike interval values can be described by a special type of real numbers. As a result of such an arithmetical approach, we establish the presence of chaos in neuron spike trains and arrive at the conclusion that in stationary conditions, brain activity is found asymptotically close to a multidimensional Cantor space with zero Lebesgue measure, which can be understood as the brain activity attractor. The self-affinity, power law dependence, and computational complexity of neuron spike trains are also briefly examined and discussed.
MULTISCALING TRANSPORT EQUATION ON FRACTALS
Authors: ZENG QIUHUA , LI HOUQIANG
Published: April 2003

The general transport equation of multiscaling disordered fractal media in three-dimensional case is derived from conservation of mass. Multiscaling fractional transport equation is obtained on the basis of discussing Brownian motion, fractional Brownian motion and standard diffusion equation of fractals, which is consistent with the result of literature.
FRACTAL SCALING OF THE TEEN BIRTH PHENOMENON
Authors: WEST BRUCE J. , HAMILTON PATTI , WEST DAMIEN J.
Published: April 2003

The collective behavior of complex physical models has often been used to model complex social phenomena. Herein, we describe one such process using a fractal stochastic point process. A coarse-graining of the relative dispersion, the ratio of the standard deviation to the mean in a time-series, is shown to decrease as a modulated inverse power law in time. This is an empirically motivated (renormalization group) model of teen birth statistics and only indirectly addresses the social mechanisms that promote sexual activity, subsequent pregnancy and finally child birth. This prediction agrees with the statistics observed across 27 years of data in Texas, and among twelve different Texan regions with differing demographics for 16 years.
TIME-DELAY EMBEDDINGS OF IFS ATTRACTORS
Authors: BAHAR SONYA
Published: April 2003

A modified type of iterated function system (IFS) has recently been shown to generate images qualitatively similar to "classical" chaotic attractors. Here, we use time-delay embedding reconstructions of time-series from this system to generate three-dimentional projections of IFS attractors. These reconstructions may be used to access the topological structure of the periodic orbits embedded within the attractor. This topological characterization suggests an approach by which a rigorous comparison of IFS attractors and classical chaotic systems may be attained.
SELF-SIMILARITY, COLLECTIVITY, AND EVOLUTION OF FRACTAL DYNAMICS DURING RETINOID-INDUCED DIFFERENTIATION OF CANCER CELL POPULATION
Authors: WALISZEWSKI PRZEMYSLAW , MOLSKI MARCIN , KONARSKI JERZY
Published: April 2003

From the reductionist perspective of molecular biology, proliferation or differentiation of eucaryotic cells is a well-defined temporal, spatial, and cell type-specific sequence of molecular cellular events. Some of those events, such as passing of the restriction point in the cell cycle, are of a stochastic nature. Results of this study indicate that, in spite of the intracellular stochasticity, cancer cells can form collective structures with fractal dimension and self-similarity. A transition from the monolayer culture to the aggregated colony facilitated interconnectedness between P19 cells, altered constitutive expression of randomly chosen retinoid-responsive genes, and increased fractal dimension of the entire population. Retinoid-induced emergence of neuron-like phenotype decreased fractal dimension significantly, slowing down dynamics of gene expression. Since the differentiated P19 cells retained both their cancer phenotype and a number of gene defects, we conclude that the appropriate dynamics of intracellular events is neccessary for the proper course of differentiation. Owing to self-similarity, dynamics of cellular expansion can be measured by a fractal dimension in a single cell or in the entire population.
ENGINEERING APPLICATIONS OF FRACTIONAL BROWNIAN MOTION: SELF-AFFINE AND SELF-SIMILAR RANDOM PROCESSES
Authors: ADDISON P. S. , NDUMU A. S.
Published: April 2003

The purpose of this paper is to explain the connection between fractional Brownian motion (fBm) and non-Fickian diffusive processes, and at the same time, highlight three engineering applications: two requiring self-affine fBm trace functions and the other requiring self-similar fBm spatial trajectories.
THE STUDY OF PHOTON TRANSMISSION IN THE FABRY-PEROT INTERFEROMETER
Authors: GASCON F. , GALVAN A.
Published: April 2003

This paper aims to study the phenomenon of light transmission through an interferometer by considering the passage of photons through the plates as a phenomenon of fractal percolation.

In addition to the percolation of contacts, porous percolation, the percolation of points and the percolation of rebounds are also studied here (in the form described below).
A MODIFIED DOUBLE TRACE MOMENT METHOD OF MULTIFRACTAL ANALYSIS
Authors: VENEZIANO DANIELE , FURCOLO PIERLUIGI
Published: April 2003

The Double Trace Moment method for the estimation of parameters of universal multifractal measures is revisited. It is found that the method applies strictly to bare measures but is approximate for dressed measures, which are the only observable ones. The approximation stems from the fact that the double dressed moments used by the method do not scale as required to produce unbiased estimates of the parameters. Modified moments are proposed, which correctly scale for both bare and dressed measures. The original and modified methods are compared theoretically and numerically. Conditions under which the original method gives accurate and heavily biased estimates are identified.
ANALYSIS OF FUNCTIONS DEFINED ON FRACTAL SETS
Authors: ESCRIBANO C. , REYES M.
Published: April 2003

In this paper, we consider the problem of the derivation of real functions defined on sets X⊂ℝ with respect to a measure μ on X such that 0<μ(X)<∞. In order to do so, we define the concept of derivation with respect to a measure μ: the μ-derivative. This concept is consistent and useful to distinguish among different increase kinds displayed by the functions defined on X. We study some properties and, when the functions are defined on a self-similar fractal with Hausdorff dimension s, a new derivation concept is considered, the Θs-derivative, which is easier to calculate than the previous one. Finally, we study the relation between the two derivation concepts and an algorithm for the calculation of the Θs-derivative.
DYNAMICAL SYSTEMS EXCITED BY TEMPORAL INPUTS: FRACTAL TRANSITION BETWEEN EXCITED ATTRACTORS
Authors: GOHARA KAZUTOSHI , OKUYAMA ARATA
Published: April 2003

This paper presents a framework for dissipative dynamical systems excited by external temporal inputs. We introduce a set {Il} of temporal inputs with finite intervals. The set {Il} defines two other sets of dynamical systems. The first is the set of continuous dynamical systems that are defined by a set {fl} of vector fields on the hyper-cylindrical phase space ℳ. The second is the set of discrete dynamical systems that are defined by a set {gl} of iterated functions on the global Poincaré section Σ. When the inputs are switched stochastically, a trajectory in the space ℳ converges to an attractive invariant set with fractal-like structure. We can analytically prove this result when all of the iterated functions satisfy a contraction property. Even without this property, we can numerically show that an attractive invariant set with fractal-like structure exists.
CONTINUOUS AND DISCRETE MODELS OF COOPERATION IN COMPLEX BACTERIAL COLONIES
Authors: COHEN I. , GOLDING I. , KOZLOVSKY Y. , BEN-JACOB E. , RON I. G.
Published: April 2003

In this paper, we study the effect of discreteness on various models for patterning in bacterial colonies (finite-size effect) and present two types of models to describe the growth of the bacterial colonies. The first model presented is the Communicating Walkers model (CWm), a hybrid model composed of both continuous fields and discrete entities — walkers, which are coarse-graining of the bacteria; coarse-graining may amplify the discreteness inherent to the biological system. Models of the second type are systems of reaction diffusion equations, where the branching of the pattern is due to non-constant diffusion coefficient of the bacterial field. The diffusion coefficient represents the effect of self-generated lubrication fluid on the bacterial movement. The representation of bacteria by a density field neglects their discreteness altogether. We implement the discreteness of the bacteria by introducing a cutoff in the growth term at low bacterial densities. We demonstrate that the cutoff does not improve the models in any way. The cutoff affects the dynamics by decreasing the effective surface tension of the front, making it more sensitive to anisotropy and decreasing the fractal dimension of the evolving patterns. We compare the continuous and semi-discrete models by introducing food chemotaxis and repulsive chemotactic signaling into the models. We find that the growth dynamics of the CWm and the growth dynamics of the Non-Linear Diffusion model (one of the continuous models) are affected in the same manner. From such similarities and from the insensitivity of the CWm to implicit anisotropy, we conclude that even the increased discreteness, introduced by the coarse-graining of the walkers, is small enough to be neglected. There are advantages and disadvantages to the two types of models. Employing both of them in parallel enables us to conclude that the discreteness of the bacteria does not significantly affect the growth dynamics (no finite-size effect).
WHEN IS A RECURRENT IFS ATTRACTOR A STANDARD IFS ATTRACTOR?
Authors: FRAME MICHAEL , LANSKI JENNIFER
Published: April 2003

Imposing restrictions on the allowed sequences of transformations of a standard IFS can give rise to attractors that are attractors of standard IFS consisting of a (larger) finite set of transformations, or a countably infinite set of transformations, or are not the attractor of any standard IFS. Whichever the case it can be read off from the transition graph of the restrictions.
ON SOLVING NONLINEAR FUNCTIONAL, FINITE DIFFERENCE, COMPOSITION, AND ITERATED EQUATIONS
Authors: BROWN RAY
Published: April 2003

In this letter, we present a general method for solving a wide range of nonlinear functional and finite difference equations, as well as iterated equations such as the Hénon and Mandelbrot equations. The method extends to differential equations using an Euler approximation to obtain a finite difference equation.
FRACTAL DIMENSION, PROBABILITY AND ENTROPY IN MATRIX AND SUMMATION SUBSTITUTION SYSTEMS
Authors: VOORHEES BURTON
Published: April 2003

The box-count method is used to obtain fractal dimensions, limiting probabilities and relative entropies for fractal and fractal-like objects generated by matrix and summation substitution systems. Results are based on the fact that a transition matrix formalism can be developed for these systems, yielding box counts at each iteration. The transition matrix is non-negative, and many results on non-negative matrices can be applied. The formalism developed is, up to a multiplicative constant, equivalent to a Markov process.
SPATIO-TEMPORAL SEISMICITY IN AN ELASTIC BLOCK LATTICE MODEL
Authors: LU CHUNSHENG , VERE-JONES DAVID , TAKAYASU HIDEKI , TRETYAKOV ALEX YU , TAKAYASU MISAKO
Published: April 2003

An elastic block lattice model is proposed to simulate the spatio-temporal seismicity and stress patterns in the Earth's brittle crust. The famous Gutenberg-Richter magnitude-frequency law in seismology is reproduced. The synthetic catalogs generated by this model are analyzed by using a linked stress release model, which incorporates the stress transfer and spatial interactions. The results highlight the triggering mechanism of earthquake occurrence and the evidence that the crust may lie in a near-critical or self-organized critical state due to the long-range spatial interaction of elastic stress. The spatio-temporal complexity of seismicity is closely related to both nonlinear dynamics of faults and heterogeneities in a seismic region.
FRACTAL TRANSITION: HIERARCHICAL STRUCTURE AND NOISE EFFECT
Authors: GOHARA KAZUTOSHI , OKUYAMA ARATA
Published: April 2003

A Sierpinski gasket with continuous trajectories is presented as an example of the fractal transition that characterizes the behavior of dissipative dynamical systems excited by external temporal inputs. Using this example, we investigate the fractal transition from two points of views, i.e. a hierarchical structure and a noise effect. Depending on internal and external parameters, the structure can be geometrically classified as one of three types, i.e. totally disconnected, just-touching, and overlapping. For the totally disconnected structure, continuous trajectories and their starting points can be characterized by a definite hierarchical tree structure. Even for the just-touching and overlapping structure, a similar hierarchy exists. White noise contaminating the external inputs breaks the hierarchy. In particular, small clustered structures are sensitive to the noise. In such a case, the difference between trajectories and starting points is remarkable in the hierarchy.
ESTIMATION OF THE FRACTAL DIMENSION OF FRACTURE SURFACE PATTERNS BY BOX-COUNTING METHOD
Authors: TANAKA MANABU , KAYAMA ATSUSHI , KATO RYUICHI , ITO YOSHIAKI
Published: April 2003

In the box-counting method, positioning of images do not significantly affect the estimation of the fractal dimension of river pattern on the brittle fracture surface, and that of dimple pattern on the ductile fracture surface of materials. A reasonable estimation of the fractal dimension can be made using the box-counting method by a single measurement on the fracture surface pattern. The fractal dimension of dimple pattern in pure Zn polycrystals (about 1.50) is larger than that of river pattern in soda-lime glass (about 1.30). Personal difference in image processing does not have a large influence on the estimation of the fractal dimension of grain-boundary fracture surface profile, compared with the effects of local variation in fracture pattern concerning image size.
SCALING LAWS OF SEISMIC EVENTS — A MODEL WITH FRACTAL GEOMETRY
Authors: GODANO C. , ALONZO M. L.
Published: April 2003

Most models of earthquakes attempt to reproduce the observed scaling laws of seismic events: the Gutenberg-Richter frequency magnitude distribution, but not the Omori law for aftershocks and the multifractal distribution of hypocenters location. Many of these models are based on the idea of Self-Organized Criticality (SOC). These are dynamic systems which organize themselves into a transitional state and can reproduce the Gutenberg-Richter distribution, but generally do not reproduce the space-time distribution. Here, we suggest a model based on a fractal geometry: the two sides of a fault are modeled by means of a fractal surface. As a first step, one of them is slipped of a random amount with periodic boundary conditions, then new contact points between the surfaces are found. The area surrounded by these points is assumed to be proportional to the area of the earthquake. The size distribution of events is in good agreement with the observed Gutenberg-Richter law and the local fluctuations of the b value are explained in terms of variations of the fractal dimension of the surface. Also the multifractal distribution of earthquakes in space is well-reproduced with global properties not depending on the fractal dimension of the surface. However, we are not able to obtain something similar to the Omori law simply because we do not control the time evolution of the model.
GEOMETRICAL EFFECT OF ISLAND SHAPE ON THE SPECIES RICHNESS
Authors: YAMASAKI KAZUHITO , CHIBA SATOSHI , NAGAHAMA HIROYUKI
Published: April 2003

We introduce a new immigration model which merges two aspects of island length. One aspect is determination of colonizer's chance of reaching recipient island, and the other is constraint on the statistical self-affinity (anisotropy) of island shapes. This immigration model derives the famous power law on species-area (SA) relation, which shows that the number of species on the anisotropic island is constrained by not only the size of the island area but also the shape of the island. From this viewpoint, we analyze an SA curve of the land snail fauna in Ryukyu arc, Japan. Moreover, we show that species of the most previous studies have immigrated along the island chain due to the stepping-stone dispersal.
FRACTAL CHARACTER OF GRAIN-SIZE DISTRIBUTION OF EXPANSIVE SOILS
Authors: XU YONGFU , LIU SONGYU
Published: April 2003

Fractal mass distribution of expansive soil grains is studied in this paper. It is found that there is different fractal mass distribution exponent of the grain-size distribution for different genesis of expansive soils. The expansiveness, physical properties and mechanical properties of expansive soils can be quantitatively described by the fractal mass distribution exponent of grain-size distribution of expansive soils. In consolidated tests, the fractal mass distribution exponent increases with increases in consolidated pressure, as well as increases in confining pressure in triaxial tests.
SCATTERED INTENSITY FROM HIGHER CONNECTED POLYMERS IN SOLUTION
Authors: ZEGHAIDER MUSTAPHA , BENHAMOU MABROUK
Published: April 2003

The aim of this work is to compute the structure factor of any arbitrary D-dimensionally-connected polymers (1≤D<2) in dilute solution. We use the standard cut-off function method, which is successfully applied to liquid systems and to fractal aggregates. For monodisperse systems, we find that the corresponding structure factor is simply given by the Gauss hypergeometric function 2F1, the three parameters of which depend explicitly on the fractal and the Euclidean dimensions. This function reproduces the two limiting behaviors, in the Guinier and intermediate regimes. This result is applied to several systems, namely, compact and convex polymeric objects, rod-like, linear and branched polymers. We then extend this result to polydisperse branched polymers. We show that polydispersity induces a change in the structure factor, from the simple hypergeometric function 2F1 to the generalized one 2F1, with four parameters that also depend on both fractal and Euclidean dimensions.
PROJECTIONS OFF FRACTAL FUNCTIONS: A NEW VISION OF NATURE'S COMPLEXITY
Authors: PUENTE CARLOS E. , OBREGON NELSON , ROBAYO OSCAR , PUENTE MARTA G. , SIMSEK DEMIRAY
Published: April 2003

The construction of a vast class of deterministic derived measures, defined as transformations of simple multinomial multifractals via fractal interpolating functions, is reviewed.1,2 It is illustrated that these objects, which are projections of unique measures defined over the graphs of fractal interpolating functions, provide a new vision to address the complexity of some of nature's tangled patterns over one and two dimensions, as they may be used to model: (a) Rainfall time series, (b) energy dissipation in fully developed turbulence, (c) two-dimensional contaminant plumes within a porous medium, and (d)"chaotic" and "stochastic" signals, as encountered in applications.

A recently discovered universal connection between arbitrary measures with continuous cumulative distributions and the univariate and bivariate Gaussian distributions, via plane- and space-filling fractal interpolating functions respectively, is also reviewed.3,4 It is explained how this relationship yields (via projections) an infinite class of two-dimensional symmetric crystalline sets making up exotic kaleidoscopes of arbitrary symmetries, which decompose the bivariate Gaussian distribution.5 It is shown that these ideas enhance the vision that projections may be useful in approaching natural complexity, as some of these sets closely resemble key biochemical structures which even include life's own DNA rosette.
A GEOMETRIC PLATONIC APPROACH TO MULTIFRACTALITY AND TURBULENCE
Authors: PUENTE CARLOS E. , OBREGON NELSON
Published: April 2003

A large family of deterministic measures built as projections off fractal functions has been introduced recently.1,2 These constructed measures, which transform either simple multifractals as defined by deterministic cascades3 or uniform measures via fractal interpolating functions,4,5 range from nontrivial multifractals to absolutely continuous measures, and include as a limiting case the Gaussian distribution.6 In this work, examples of deterministic measures which possess multiscaling properties when analyzed following the multifractal formalism are given. It is shown that suitable measures which not only preserve the singularity spectrum of turbulence but also capture the inherent details present in turbulent data sets may be obtained. These results suggest a plausible deterministic framework for the study of intermittent phenomena via a new geometric approach — one which closely evokes Plato's ideas that all we observe may be "shadows" of simple objects.7
IDENTIFICATION OF SELF-ORGANIZED CRITICALITY IN ATMOSPHERIC LOW FREQUENCY VARIABILITY
Authors: JOSHI R. R. , SELVAM A. M.
Published: April 2003

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as self-similar fractal geometry to the global cloud cover pattern concomitant with inverse power law form fB. Such non-local connections are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. Standard models in meteorological theory cannot explain satisfactorily the observed self-organized criticality in atmospheric flows. A recently developed cell dynamical model for atmospheric flows predicts the observed self-organized criticality as a direct consequence of quantumlike mechanics governing flow dynamics. The model predictions are in agreement with continuous periodogram power spectral analyses of two-day mean TOGA temperature time-series. The application of model concepts for prediction of atmospheric low frequency variability is discussed.
SELF-AFFINITY OF RECORDS OF FINANCIAL INDEXES
Authors: VALDEZ-CEPEDA RICARDO DAVID , SOLANO-HERRERA ENRIQUE
Published: April 2003

One-dimensional profiles of financial indexes can be characterized by the statistical fractal dimension D, estimated through the slopes of the log-log geostatistical semivariograms, assuming that the relationships between the average variances and the time increments are described by a power law. This assumption corresponds to the concept of self-affinity.

The industrial Dow Jones index is described by a D=1.332±0.11 indicating the persistence of trends along analyzed business 500 days period, while for almost the same period the German DAX Composite index (D = 1.688±0.026) is dominated by short-range variations, and the British Footsie (D=1.495±0.009) and the Australian Share Price (all ordinaries) (D=1.506±0.008) indexes have a behavior like the fractal Brownian motion (D=1.5). The Nikkei Cash index is characterized by a D=1.474±0.008 which implies that the short-range variation is almost as important as the long-term variation. Ds were evaluated by using scaling arguments, and multifractality was not evidenced.
A STUDY OF MANDELBROT AND JULIA SETS GENERATED FROM A GENERAL COMPLEX CUBIC ITERATION
Authors: YAN DEJUN , LIU XIANGDONG , ZHU WEIYONG
Published: April 2003

The structures of Mandelbrot and Julia sets generated from a general complex cubic iteration are studied, and the relation of the critical points and Julia sets is analyzed. In this paper, we put forward the theorems on the range of the Mandelbrot and Julia sets generated from a general complex cubic iteration. These theorems are important for plotting of the sets.
NUMERICAL STUDIES OF CONJUGATED INFINITE ELEMENTS FOR ACOUSTICAL RADIATION
Authors: ASTLEY R. J. , HAMILTON J. A.
Published: April 2003

Aspects of conjugated infinite element schemes for unbounded wave problems are reviewed and a general formulation is presented for elements of variable order based on separable shape functions expressed in terms of prolate and oblate spheroidal coordinates. The formulation encompasses both "conjugated Burnett" and "Astley–Leis" elements. The performance of the two approaches is compared for steady multipole wave fields and the effect of the radial basis on the condition number of the resulting equations is discussed. Transient formulations based on these elements are derived and methods for solving the resulting transient equations are discussed. The use of an implicit time stepping scheme coupled with an indirect iterative solver is shown to give fast transient solutions which do not require matrix inversion.
A REFLECTION FREE BOUNDARY CONDITION FOR PROPAGATION IN UNIFORM FLOW USING MAPPED INFINITE WAVE ENVELOPE ELEMENTS
Authors: EVERSMAN WALTER
Published: April 2003

Variable order mapped infinite wave envelope elements are developed for finite element modeling of acoustic radiation in a uniformly moving medium. These elements are used as a nonreflecting boundary condition for computations on an infinite domain in which a radiating body is immersed in a moving medium which is essentially undisturbed outside of the near field. The mapped elements provide a boundary condition equivalent to element stiffness, mass, and damping matrices appended to an inner standard FEM mesh. A demonstration of the performance of mapped elements as influenced by element order is given in the context of acoustic radiation from a turbofan inlet and exhaust.
ON FUNDAMENTAL ASPECTS OF EXTERIOR APPROXIMATIONS WITH INFINITE ELEMENTS
Authors: IHLENBURG FRANK
Published: April 2003

Over the last years, infinite elements have become a popular method of exterior approximation in scattering problems. Addressing the scalar case (Helmholtz equation), this paper gives a state-of-the-art review on the convergence theory for the approximation used in radial infinite elements. The focus is on the stability of different variational formulations that were proposed in the context of this approximation. Exterior approximation on partitions with finite and infinite elements is also considered. The review is preceded by an outline of the relevant general theory. Open questions are listed in the conclusion of the presentation.
FINITE ELEMENT SOLUTION OF TWO-DIMENSIONAL ACOUSTIC SCATTERING PROBLEMS USING ARBITRARILY SHAPED CONVEX ARTIFICIAL BOUNDARIES
Authors: DJELLOULI RABIA , FARHAT CHARBEL , MACEDO ANTONINI , TEZAUR RADEK
Published: April 2003

For elongated scatterers such as submarines, we show that the generalization of the Bayliss–Turkel nonreflecting boundary conditions to arbitrarily shaped convex artificial boundaries improves significantly the computational efficiency of finite element methods for the solution of acoustic scattering problems.
THIRD-ORDER DOUBLY ASYMPTOTIC APPROXIMATIONS FOR COMPUTATIONAL ACOUSTICS
Authors: GEERS THOMAS L. , TOOTHAKER BRADY J.
Published: April 2003

A fully and symmetrically matched, third-order doubly asymptotic computational boundary (DAA3) is presented in both operator and matrix forms. Its performance is then compared with that of other DAA boundaries for the spherical geometry, which admits an exact series solution. Based on stability, accuracy and passivity as performance criteria, DAA3 is found to be superior to all other DAAs formulated to date. However, there are other third-order forms that are nearly as good, and are easier to implement in boundary-element form. The existence of both DAA2 and DAA3 boundaries enables the analyst to assess solution accuracy for a given problem through the comparison of results produced with these higher approximations of different order.
ANALYTICAL AND NUMERICAL STUDIES OF A FINITE ELEMENT PML FOR THE HELMHOLTZ EQUATION
Authors: HARARI ISAAC , SLAVUTIN MICHAEL , TURKEL ELI
Published: April 2003

A symmetric PML formulation that is suitable for finite element computation of time-harmonic acoustic waves in exterior domains is analyzed. Dispersion analysis displays the dependence of the discrete representation of the PML parameters on mesh refinement. Stabilization by modification of the coefficients is employed to improve PML performance, in conjunction with standard stabilized finite elements in the Helmholtz region. Numerical results validate the good performance of this finite element PML approach.
CONTINUED-FRACTION ABSORBING BOUNDARY CONDITIONS FOR THE WAVE EQUATION
Authors: GUDDATI MURTHY N. , TASSOULAS JOHN L.
Published: April 2003

Absorbing boundary conditions are generally required for numerical modeling of wave phenomena in unbounded domains. Local absorbing boundary conditions are generally preferred for transient analysis because of their computational efficiency. However, their accuracy is severely limited because the more accurate high-order boundary conditions cannot be implemented easily. In this paper, a new arbitrarily high-order absorbing boundary condition based on continued fraction approximation is presented. Unlike the existing boundary conditions, this one does not contain high-order derivatives, thus making it amenable to implementation in conventional C0 finite element and finite difference methods. The superior numerical properties and implementation aspects of this boundary condition are discussed. Numerical examples are presented to illustrate the performance of these new high-order boundary condition.
OPTIMAL LOCAL NONREFLECTING BOUNDARY CONDITIONS FOR TIME-DEPENDENT WAVES
Authors: PATLASHENKO IGOR , GIVOLI DAN
Published: April 2003

Nonreflecting Boundary Conditions (NRBCs) are often used on artificial boundaries as a method for the numerical solution of wave problems in unbounded domains. Recently, a two-parameter hierarchy of optimal local NRBCs of increasing order has been developed for elliptic problems, including the problem of time-harmonic acoustic waves. The optimality is in the sense that the local NRBC best approximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary condition in the L2 norm for functions which can be Fourier-decomposed. The optimal NRBCs are combined with finite element discretization in the computational domain. Here this approach is extended to time-dependent acoustic waves. In doing this, the Semi-Discrete DtN approach is used as the starting point. Numerical examples involving propagating disturbances in two dimensions are given.
MIXED FINITE ELEMENTS WITH MASS-LUMPING FOR THE TRANSIENT WAVE EQUATION
Authors: COHEN GARY , FAUQUEUX SANDRINE
Published: April 2003

Solving the acoustics equation by finite elements with mass-lumping requires the use of spectral elements. Although avoiding the inversion of a mass-matrix at each time-step, these elements remain expensive from the point of view of the stiffness-matrix. In this paper, we give a mixed finite element method which provides a factorization of the stiffness-matrix which leads to a gain of storage and computation time which grows with the order of the method and the dimension in space. After proving the equivalence between classical spectral elements and this method, we give a dispersion analysis on nonregular periodic meshes. Then, we analyze the accuracy and the stability of Q3 and Q5 approximations on numerical tests in 2D.
SHORT WAVE MODELLING USING SPECIAL FINITE ELEMENTS
Authors: LAGHROUCHE OMAR , BETTESS PETER
Published: April 2003

The solutions to the Helmholtz equation in the plane are approximated by systems of plane waves. The aim is to develop finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength. At each node of the meshed domain, the wave potential is written as a combination of plane waves propagating in many possible directions. The resulting element matrices contain oscillatory functions and are evaluated using high order Gauss-Legendre integration. These finite elements are used to solve wave problems such as a diffracted potential from a cylinder. Many wavelengths are contained in a single finite element and the number of parameters in the problem is greatly reduced.
A NUMERICAL COMPARISON OF FINITE ELEMENT METHODS FOR THE HELMHOLTZ EQUATION
Authors: OBERAI ASSAD A. , PINSKY PETER M.
Published: April 2003

Three finite element formulations for the solution of the Helmholtz equation are considered. The performance of these methods is compared by performing a discrete dispersion analysis and by solving two canonical problems on nonuniform meshes. It is found that: (1) The scaled L2 error for the Galerkin method, using linear interpolation functions, grows as k(kh)2, indicating the pollution inherent in this method; (2) The Galerkin least squares method is more accurate, but does display significant pollution error; (3) The residual-based method of Oberai & Pinsky,8 which was designed to be almost pollution-free for uniform meshes retains its accuracy on nonuniform meshes; (4) The computational cost of implementing all these formulations is approximately the same.
EFFICIENT COMPUTATION OF MULTI-FREQUENCY FAR-FIELD SOLUTIONS OF THE HELMHOLTZ EQUATION USING PADÉ APPROXIMATION
Authors: MALHOTRA MANISH , PINSKY PETER M.
Published: April 2003

For many problems in exterior structural acoustics, the solution is required to be computed over multiple frequencies. For some classes of these problems, however, it may be sufficient to evaluate the multiple frequency solutions over restricted regions of the spatial domain. Examples include optimization and inverse problems based on the minimization of a functional defined over a specified surface or sub-region. For such problems, which include both near-field and far-field computations, we recently proposed an efficient algorithm to compute the partial-field solutions at multiple frequencies simultaneously. In this paper, we consider the particular case of far-field computations and simplify the recently proposed algorithm by exploiting the symmetry of linear operators. The approach involves a reformulation of the Dirichlet-to-Neumann (DtN) map based finite-element matrix problem into a transfer-function form that can efficiently describe the far-field solution. A multi-frequency approximation of the transfer function is developed by constructing matrix-valued Padé approximation of the transfer function via a symmetric, banded Lanczos process. Numerical tests illustrate the accuracy of the approach for a wide range of frequencies and cost reductions of an order of magnitude when compared to commonly used factorization based methods.
AN ITERATIVE TIME-STEPPING METHOD FOR SOLVING FIRST-ORDER TIME DEPENDENT PROBLEMS AND ITS APPLICATION TO THE WAVE EQUATION
Authors: SERIANI GÉZA
Published: April 2003

Equations describing dynamic problems, after spatial discretization by using the finite element or spectral element method, lead to solve large systems of ODE in time. A family of new time integration algorithms based on an iterative time-stepping (ITS) approach is proposed for solving these systems. The method is developed for first-and second-order differential equations, and applied, in particular, to wave equation. It is an implicit time marching method in which, at each time-step, the solution is computed by a fixed-point scheme. The analysis show that the method is accurate, unconditionally stable and that it allows for efficient and parallel implementations because no matrix inversion is required and only matrix-vector multiplications and vector scaling operations are involved.
A NUMERICAL STUDY OF ROUGH-SURFACE SCATTER
Authors: McDANIEL SUZANNE T.
Published: April 2003

A computationally efficient formulation of the method of moments is developed and applied to the problem of scattering from one-dimensional random pressure-release surfaces. Comparisons are made between the predictions of small-slope and operator expansions and a reference solution obtained by matrix inversion for surfaces characterized by a power-law wavenumber spectrum. For Fresnel parameters greater than unity, a significant increase in backscatter over a wide range of grazing angles is found that is inconsistent with composite-roughness theory, and which is only partially predicted by the various approximations. The small-slope approximation is then applied to the three-dimensional scattering problem, and it is shown that the failure of such approximations carries over from the two-dimensional case to three dimensions.
SEAFLOOR PROPERTIES DETERMINATION FROM ACOUSTIC BACKSCATTERING AT NORMAL INCIDENCE WITH A PARAMETRIC SOURCE
Authors: CAITI ANDREA
Published: April 2003

An inversion technique is proposed for the determination of the geoacoustic and morphological properties of the uppermost sediment layer. The methodology is based on the use of the backscattering acoustic return when the source is a parametric instrument steered at normal incidence with respect to the seafloor. The peculiarity of the parametric sonar (i.e., its narrow beam and the absence of sidelobes) allows for discriminating between the scattering effects due to surface roughness and those due to volume perturbations. The inversion procedure is based on the minimization of a discrepancy measure between data and model predictions. Model predictions are obtained as time series realization of a stochastic process, modeling the backscattering process with the Kirchoff approximation for surface scattering and the small perturbation theory for volume scattering. The BoRIS code is used to generate the time series predictions. It is important to note that the model is stochastic, i.e., the model predicted time series with the same nominal parameters may differ from one realization to another. However, by use of wavelet transform of the signals involved, and measuring the data-model discrepancy in a generalized time-frequency domain, the stochasticity of the problem is greatly reduced. In particular, the wavelet transform is insensitive to different model realizations obtained with the same set of parameters, and sensitive to changes in the parameters. By appropriately weighing the discrepancy in the wavelet domain, and exploiting the properties of the parametric source, it is possible to separately recover the parameters influencing the surface backscattering (acoustic impedance and surface roughness) and those influencing the volume backscattering (P-wave attenuation and volume inhomogeneity), avoiding ambiguities and nonuniqueness problems. The approach proposed requires, however, a precise calibration of the parametric sonar, in terms of source level and beam pattern. Comparison of inversion results with independently measured ground truth at three different sites in the Mediterranean Sea are reported.
MATCHED FIELD TOMOGRAPHIC INVERSION TO DETERMINE RANGE DEPENDENT GEOACOUSTIC PROPERTIES
Authors: CORRE V. , CHAPMAN N. R. , WILMUT M. J.
Published: April 2003

The paper describes a new broadband tomographic matched field method for estimating the geoacoustic properties of a range-dependent shallow water environment. This method is designed for a multiple acoustic element configuration (several sources and vertical arrays deployed in an ocean region) in order to estimate the range and cross-range properties of the sediment over the region. The synthetic pressure fields (replicas) for the tomographic inversion are computed using a ray model. A linear processor operating in the frequency domain is used to quantify the match between replica and measured fields. This processor is based on coherent summations over frequencies and receiver pairs. The method is demonstrated for a geoacoustic ocean model simulating the environment of the Haro Strait experiment. The area is divided into cells in which the geoacoustic properties are range independent but can vary from one cell to another. The layer thickness can vary within a cell. Results are presented for the estimation of the compressional velocity and sediment layer thickness in the ideal case of a noise free synthetic data set.
IDENTIFYING MODAL ARRIVALS IN SHALLOW WATER FOR BOTTOM GEOACOUSTIC INVERSIONS
Authors: TAROUDAKIS MICHAEL I.
Published: April 2003

A mode identification process that can be applied to broadband acoustic transmissions in the ocean is presented. The process is associated with a modal travel time inversion scheme for geoacoustic or tomographic inversions. The process is based on the assumption that a reference (background) environment is known and the identification process is based on information on the group (modal) velocities of the reference environment only. Using two characteristic examples corresponding to shallow water environments it is shown that the identification process works well at least for the lower order modes.
OBJECTIVE FUNCTIONS FOR OCEAN ACOUSTIC INVERSION DERIVED BY LIKELIHOOD METHODS
Authors: MECKLENBRÄUKER CHRISTOPH F. , GERSTOFT PETER
Published: April 2003

Selection of a suitable objective function is an integral part of the inverse problem, and poor selection can have a strong influence on the inverse result. Objective functions are here derived for many practical occasions such as for single frequency and broadband, with and without knowledge of source strength, and with and without the received signal phase. These objective functions are all derived from a unified approach based on maximum likelihood and additive Gaussian noise models. The assumptions for the objective function are thus clear and the resulting estimator has good properties. From a Bayesian point of view, the solution to the inverse problem is the a posteriori probability distribution of the unknown parameters, which can be found from the likelihood function. Thus using objective functions based on likelihood functions facilitates computing the a posteriori distributions.