Fractal electrodynamics via non-integer dimensional space approach
Tarasov, Vasily E.
2015-09-01
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.
Elasticity of fractal materials using the continuum model with non-integer dimensional space
Tarasov, Vasily E.
2015-01-01
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.
Vector calculus in non-integer dimensional space and its applications to fractal media
Tarasov, Vasily E.
2015-02-01
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.
Anisotropic fractal media by vector calculus in non-integer dimensional space
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2014-01-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media
Anisotropic fractal media by vector calculus in non-integer dimensional space
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)
2014-08-15
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
Anisotropic fractal media by vector calculus in non-integer dimensional space
Tarasov, Vasily E.
2014-08-01
A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.
International Nuclear Information System (INIS)
Elezović-Hadžić, S; Živić, I
2013-01-01
We have studied the problem of force pulling self-interacting linear polymers situated in fractal containers that belong to the Sierpinski gasket (SG) family of fractals embedded in three-dimensional (3D) space. Each member of this family is labeled with an integer b (2 ≤ b ≤ ∞). The polymer chain is modeled by a self-avoiding walk (SAW) with one end anchored to one of the four boundary walls of the lattice, while the other (floating in the bulk of the fractal) is the position at which the force is acting. By applying an exact renormalization group (RG) method we have established the phase diagrams, including the critical force–temperature dependence, for fractals with b = 2,3 and 4. Also, for the same fractals, in all polymer phases, we examined the generating function G 1 for the numbers of all possible SAWs with one end anchored to the boundary wall. We found that besides the usual power-law singularity of G 1 , governed by the critical exponent γ 1 , whose specific values are worked out for all cases studied, in some regimes the function G 1 displays an essential singularity in its behavior. (paper)
A short history of fractal-Cantorian space-time
International Nuclear Information System (INIS)
Marek-Crnjac, L.
2009-01-01
The article attempts to give a short historical overview of the discovery of fractal-Cantorian space-time starting from the 17th century up to the present. In the last 25 years a great number of scientists worked on fractal space-time notably Garnet Ord in Canada, Laurent Nottale in France and Mohamed El Naschie in England who gave an exact mathematical procedure for the derivation of the dimensionality and curvature of fractal space-time fuzzy manifold.
Dimensional analysis, scaling and fractals
International Nuclear Information System (INIS)
Timm, L.C.; Reichardt, K.; Oliveira Santos Bacchi, O.
2004-01-01
Dimensional analysis refers to the study of the dimensions that characterize physical entities, like mass, force and energy. Classical mechanics is based on three fundamental entities, with dimensions MLT, the mass M, the length L and the time T. The combination of these entities gives rise to derived entities, like volume, speed and force, of dimensions L 3 , LT -1 , MLT -2 , respectively. In other areas of physics, four other fundamental entities are defined, among them the temperature θ and the electrical current I. The parameters that characterize physical phenomena are related among themselves by laws, in general of quantitative nature, in which they appear as measures of the considered physical entities. The measure of an entity is the result of its comparison with another one, of the same type, called unit. Maps are also drawn in scale, for example, in a scale of 1:10,000, 1 cm 2 of paper can represent 10,000 m 2 in the field. Entities that differ in scale cannot be compared in a simple way. Fractal geometry, in contrast to the Euclidean geometry, admits fractional dimensions. The term fractal is defined in Mandelbrot (1982) as coming from the Latin fractus, derived from frangere which signifies to break, to form irregular fragments. The term fractal is opposite to the term algebra (from the Arabic: jabara) which means to join, to put together the parts. For Mandelbrot, fractals are non topologic objects, that is, objects which have as their dimension a real, non integer number, which exceeds the topologic dimension. For the topologic objects, or Euclidean forms, the dimension is an integer (0 for the point, 1 for a line, 2 for a surface, and 3 for a volume). The fractal dimension of Mandelbrot is a measure of the degree of irregularity of the object under consideration. It is related to the speed by which the estimate of the measure of an object increases as the measurement scale decreases. An object normally taken as uni-dimensional, like a piece of a
The Validity of Dimensional Regularization Method on Fractal Spacetime
Directory of Open Access Journals (Sweden)
Yong Tao
2013-01-01
Full Text Available Svozil developed a regularization method for quantum field theory on fractal spacetime (1987. Such a method can be applied to the low-order perturbative renormalization of quantum electrodynamics but will depend on a conjectural integral formula on non-integer-dimensional topological spaces. The main purpose of this paper is to construct a fractal measure so as to guarantee the validity of the conjectural integral formula.
Fractal geometry in an expanding, one-dimensional, Newtonian universe.
Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel
2007-09-01
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.
Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions
Lapidus, Michel L; Žubrinić, Darko
2017-01-01
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the f...
FRACTAL DIMENSIONALITY ANALYSIS OF MAMMARY GLAND THERMOGRAMS
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Yu. E. Lyah
2016-06-01
Full Text Available Thermography may enable early detection of a cancer tumour within a mammary gland at an early, treatable stage of the illness, but thermogram analysis methods must be developed to achieve this goal. This study analyses the feasibility of applying the Hurst exponent readings algorithm for evaluation of the high dimensionality fractals to reveal any possible difference between normal thermograms (NT and malignant thermograms (MT.
Pulmonary vasculature in dogs assessed by three-dimensional fractal analysis and chemometrics
DEFF Research Database (Denmark)
Müller, Anna V; Marschner, Clara B; Kristensen, Annemarie T
2017-01-01
Fractal analysis of canine pulmonary vessels could allow quantification of their space-filling properties. Aims of this prospective, analytical, cross-sectional study were to describe methods for reconstructing three dimensional pulmonary arterial vascular trees from computed tomographic pulmonary...... angiogram, applying fractal analyses of these vascular trees in dogs with and without diseases that are known to predispose to thromboembolism, and testing the hypothesis that diseased dogs would have a different fractal dimension than healthy dogs. A total of 34 dogs were sampled. Based on computed...... for each dog using a semiautomated segmentation technique. Vascular three-dimensional reconstructions were then evaluated using fractal analysis. Fractal dimensions were analyzed, by group, using analysis of variance and principal component analysis. Fractal dimensions were significantly different among...
Incomplete information and fractal phase space
International Nuclear Information System (INIS)
Wang, Qiuping A.
2004-01-01
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter ω which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of ω on the basis of fractal phase space. ω is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process
Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael
2016-02-01
One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.
Three-dimensional fractal geometry for gas permeation in microchannels
Malankowska, Magdalena; Schlautmann, Stefan; Berenschot, Erwin J.W.; Tiggelaar, Roald M.; Pina, Maria Pilar; Mallada, Reyes; Tas, Niels R.; Gardeniers, Han
2018-01-01
The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The
Fractals and spectra related to fourier analysis and function spaces
Triebel, Hans
1997-01-01
Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy
2017-01-01
This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Fractal dimensions from a 3-dimensional intermittency analysis in e+e- annihilation
International Nuclear Information System (INIS)
Behrend, H.J.; Criegee, L.; Field, J.H.; Franke, G.; Jung, H.; Meyer, J.; Podobrin, O.; Schroeder, V.; Winter, G.G.; Bussey, P.J.; Campbell, A.J.; Hendry, D.; Lumsdon, S.J.; Skillicorn, I.O.; Ahme, J.; Blobel, V.; Feindt, M.; Fenner, H.; Harjes, J.; Koehne, J.H.; Peters, J.H.; Spitzer, H.; Weihrich, T.; Boer, W. de; Buschhorn, G.; Grindhammer, G.; Gunderson, B.; Kiesling, C.; Kotthaus, R.; Kroha, H.; Lueers, D.; Oberlack, H.; Schacht, P.; Scholz, S.; Wiedenmann, W.; Davier, M.; Grivaz, J.F.; Haissinski, J.; Journe, V.; Le Diberder, F.; Veillet, J.J.; Cozzika, G.; Ducros, Y.; Alexander, G.; Beck, A.; Bella, G.; Grunhaus, J.; Klatchko, A.; Levy, A.; Milstene, C.
1990-10-01
The intermittency structure of multihadronic e + e - annihilation is analyzed by evaluating the factorial moments F 2 -F 5 in 3-dimensional Lorentz invariant phase space as a function of the resolution scale. We interpret our data in the language of fractal objects. It turns out that the fractal dimension depends on the resolution scale in a way that can be attributed to geometrical resolution effects and dynamical effects, such as the π 0 Dalitz decay. The LUND 7.2 hadronization model provides an excellent description of the data. There is no indication of unexplained multiplicity fluctuations in small phase space regions. (orig.)
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Davis, Ethan, E-mail: ethan.davis4@huskers.unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States); Liu, Ying; Jiang, Lijia; Lu, Yongfeng [Laser Assisted Nano Engineering Lab, Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, 209N Scott Engineering Center, Lincoln, NE 68588-0511 (United States); Ndao, Sidy, E-mail: sndao2@unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States)
2017-01-15
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
International Nuclear Information System (INIS)
Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy
2017-01-01
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Electromagnetic fields in fractal continua
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Mena, Baltasar [Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F. (Mexico); Patiño, Julián [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Morales, Daniel [Instituto Mexicano del Petróleo, México D.F., 07730 Mexico (Mexico)
2013-04-01
Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum Φ{sub D}{sup 3}⊂E{sup 3} with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space F{sup α} accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.
The fractional finite Hankel transform and its applications in fractal space
International Nuclear Information System (INIS)
Jiang Xiaoyun; Xu Mingyu
2009-01-01
In the present work, a generalized finite Hankel transform is derived which is useful in solving equations in fractal dimension d f and involving a fractal diffusion coefficient D 0 r -θ . The corresponding inversion formula is established and some properties are given. Then, the transform is successfully used to solve a class of time-fractional diffusion equations in fractional spatial dimension with an absorbent term and Schroedinger equation in fractional-dimensional space. Green's functions and exact wave function of the above problems are found.
Directory of Open Access Journals (Sweden)
Le Wang
2015-11-01
Full Text Available Based on phase space reconstruction and fractal dynamics in nonlinear dynamics, a method is proposed to extract and analyze the dynamics of the rotating stall in the impeller of centrifugal compressor, and some numerical examples are given to verify the results as well. First, the rotating stall of an existing low speed centrifugal compressor (LSCC is numerically simulated, and the time series of pressure in the rotating stall is obtained at various locations near the impeller outlet. Then, the phase space reconstruction is applied to these pressure time series, and a low-dimensional dynamical system, which the dynamics properties are included in, is reconstructed. In phase space reconstruction, C–C method is used to obtain the key parameters, such as time delay and the embedding dimension of the reconstructed phase space. Further, the fractal characteristics of the rotating stall are analyzed in detail, and the fractal dimensions are given for some examples to measure the complexity of the flow in the post-rotating stall. The results show that the fractal structures could reveal the intrinsic dynamics of the rotating stall flow and could be considered as a characteristic to identify the rotating stall.
Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale
Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian
2018-06-01
Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.
Random walk through fractal environments
Isliker, H.; Vlahos, L.
2002-01-01
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...
On fractal space-time and fractional calculus
Directory of Open Access Journals (Sweden)
Hu Yue
2016-01-01
Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.
Feature extraction algorithm for space targets based on fractal theory
Tian, Balin; Yuan, Jianping; Yue, Xiaokui; Ning, Xin
2007-11-01
In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.
Fractal spectra in generalized Fibonacci one-dimensional magnonic quasicrystals
Energy Technology Data Exchange (ETDEWEB)
Costa, C.H.O. [Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Vasconcelos, M.S., E-mail: manoelvasconcelos@yahoo.com.br [Escola de Ciencias e Tecnologia, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Barbosa, P.H.R.; Barbosa Filho, F.F. [Departamento de Fisica, Universidade Federal do Piaui, 64049-550 Teresina-Pi (Brazil)
2012-07-15
In this work we carry out a theoretical analysis of the spectra of magnons in quasiperiodic magnonic crystals arranged in accordance with generalized Fibonacci sequences in the exchange regime, by using a model based on a transfer-matrix method together random-phase approximation (RPA). The generalized Fibonacci sequences are characterized by an irrational parameter {sigma}(p,q), which rules the physical properties of the system. We discussed the magnonic fractal spectra for first three generalizations, i.e., silver, bronze and nickel mean. By varying the generation number, we have found that the fragmentation process of allowed bands makes possible the emergence of new allowed magnonic bulk bands in spectra regions that were magnonic band gaps before, such as which occurs in doped semiconductor devices. This interesting property arises in one-dimensional magnonic quasicrystals fabricated in accordance to quasiperiodic sequences, without the need to introduce some deferent atomic layer or defect in the system. We also make a qualitative and quantitative investigations on these magnonic spectra by analyzing the distribution and magnitude of allowed bulk bands in function of the generalized Fibonacci number F{sub n} and as well as how they scale as a function of the number of generations of the sequences, respectively. - Highlights: Black-Right-Pointing-Pointer Quasiperiodic magnonic crystals are arranged in accordance with the generalized Fibonacci sequence. Black-Right-Pointing-Pointer Heisenberg model in exchange regime is applied. Black-Right-Pointing-Pointer We use a theoretical model based on a transfer-matrix method together random-phase approximation. Black-Right-Pointing-Pointer Fractal spectra are characterized. Black-Right-Pointing-Pointer We analyze the distribution of allowed bulk bands in function of the generalized Fibonacci number.
Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors
Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.
2017-11-01
Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.
Effective degrees of freedom of a random walk on a fractal
Balankin, Alexander S.
2015-12-01
We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.
International Nuclear Information System (INIS)
Nagao, Michinobu; Murase, Kenya
2002-01-01
This review article describes a method for quantifying heterogeneous distribution on Technegas ( 99m Tc-carbon particle radioaerosol) SPECT images by three-dimensional fractal analysis (3D-FA). Technegas SPECT was performed to quantify the severity of pulmonary emphysema. We delineated the SPECT images by using five cut-offs (15, 20, 25, 30 and 35% of the maximal voxel radioactivity), and measured the total number of voxels in the areas surrounded by the contours obtained with each cut-off level. We calculated fractal dimensions from the relationship between the total number of voxels and the cut-off levels transformed into natural logarithms. The fractal dimension derived from 3D-FA is the relative and objective measurement, which can assess the heterogeneous distribution on Technegas SPECT images. The fractal dimension strongly correlate pulmonary function in patients with emphysema and well documented the overall and regional severity of emphysema. (author)
Živić, I.; Elezović-Hadžić, S.; Milošević, S.
2018-01-01
We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b ≥ 2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1 ,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b = 2 , 3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.
The distribution function of a probability measure on a space with a fractal structure
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Granero, M.A.; Galvez-Rodriguez, J.F.
2017-07-01
In this work we show how to define a probability measure with the help of a fractal structure. One of the keys of this approach is to use the completion of the fractal structure. Then we use the theory of a cumulative distribution function on a Polish ultrametric space and describe it in this context. Finally, with the help of fractal structures, we prove that a function satisfying the properties of a cumulative distribution function on a Polish ultrametric space is a cumulative distribution function with respect to some probability measure on the space. (Author)
Fractal systems of central places based on intermittency of space-filling
International Nuclear Information System (INIS)
Chen Yanguang
2011-01-01
Highlights: → The idea of intermittency is introduced into central place model. → The revised central place model suggests incomplete space filling. → New central place fractals are presented for urban analysis. → The average nearest distance is proposed to estimate the fractal dimension. → The concept of distance-based space is replaced by that of dimension-based space. - Abstract: The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d = 2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D < d = 2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to explain the real patterns of urban places very well. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.
Two-dimensional fractal geometry, critical phenomena and conformal invariance
International Nuclear Information System (INIS)
Duplantier, B.
1988-01-01
The universal properties of critical geometrical systems in two-dimensions (2D) like the O (n) and Potts models, are described in the framework of Coulomb gas methods and conformal invariance. The conformal spectrum of geometrical critical systems obtained is made of a discrete infinite series of scaling dimensions. Specific applications involve the fractal properties of self-avoiding walks, percolation clusters, and also some non trivial critical exponents or fractal dimensions associated with subsets of the planar Brownian motion. The statistical mechanics of the same critical models on a random 2D lattice (namely in presence of a critically-fluctuating metric, in the so-called 2D quantum gravity) is also addressed, and the above critical geometrical systems are shown to be exactly solvable in this case. The new ''gravitational'' conformal spectrum so derived is found to satisfy the recent Knizhnik, Polyakov and Zamolodchikov quadratic relation which links it to the standard conformal spectrum in the plane
International Nuclear Information System (INIS)
Barton, C.C.; Larsen, E.
1985-01-01
Fracture traces exposed on three 214- to 260-m 2 pavements in the same Miocene ash-flow tuff at Yucca Mountain, southwestern Nevada, have been mapped at a scale of 1:50. The maps are two-dimensional sections through the three-dimensional network of strata-bound fractures. All fractures with trace lengths greater than 0.20 m were mapped. The distribution of fracture-trace lengths is log-normal. The fractures do not exhibit well-defined sets based on orientation. Since fractal characterization of such complex fracture-trace networks may prove useful for modeling fracture flow and mechanical responses of fractured rock, an analysis of each of the three maps was done to test whether such networks are fractal. These networks proved to be fractal and the fractal dimensions (D) are tightly clustered (1.12, 1.14, 1.16) for three laterally separated pavements, even though visually the fracture networks appear quite different. The fractal analysis also indicates that the network patterns are scale independent over two orders of magnitude for trace lengths ranging from 0.20 to 25 m. 7 refs., 7 figs
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
. Instead, I outline a fractal approach to the study of space, society, and infrastructure. A fractal orientation requires a number of related conceptual reorientations. It has implications for thinking about scale and perspective, and (sociotechnical) relations, and for considering the role of the social...... and a fractal social theory....
Encounters with chaos and fractals
Gulick, Denny
2012-01-01
Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.
Weakly infinite-dimensional spaces
International Nuclear Information System (INIS)
Fedorchuk, Vitalii V
2007-01-01
In this survey article two new classes of spaces are considered: m-C-spaces and w-m-C-spaces, m=2,3,...,∞. They are intermediate between the class of weakly infinite-dimensional spaces in the Alexandroff sense and the class of C-spaces. The classes of 2-C-spaces and w-2-C-spaces coincide with the class of weakly infinite-dimensional spaces, while the compact ∞-C-spaces are exactly the C-compact spaces of Haver. The main results of the theory of weakly infinite-dimensional spaces, including classification via transfinite Lebesgue dimensions and Luzin-Sierpinsky indices, extend to these new classes of spaces. Weak m-C-spaces are characterised by means of essential maps to Henderson's m-compacta. The existence of hereditarily m-strongly infinite-dimensional spaces is proved.
International Nuclear Information System (INIS)
Huang, F.; Peng, R. D.; Liu, Y. H.; Chen, Z. Y.; Ye, M. F.; Wang, L.
2012-01-01
Fractal dust grains of different shapes are observed in a radially confined magnetized radio frequency plasma. The fractal dimensions of the dust structures in two-dimensional (2D) horizontal dust layers are calculated, and their evolution in the dust growth process is investigated. It is found that as the dust grains grow the fractal dimension of the dust structure decreases. In addition, the fractal dimension of the center region is larger than that of the entire region in the 2D dust layer. In the initial growth stage, the small dust particulates at a high number density in a 2D layer tend to fill space as a normal surface with fractal dimension D = 2. The mechanism of the formation of fractal dust grains is discussed.
Poiseuille equation for steady flow of fractal fluid
Tarasov, Vasily E.
2016-07-01
Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.
Steady laminar flow of fractal fluids
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)
2017-02-12
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.
Projective limits of state spaces IV. Fractal label sets
Lanéry, Suzanne; Thiemann, Thomas
2018-01-01
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski (1977) to represent quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces (see Lanéry (2016) [1] for a concise introduction to this formalism). One can thus bypass the need to select a vacuum state for the theory, and still be provided with an explicit and constructive description of the quantum state space, at least as long as the label set indexing the projective structure is countable. Because uncountable label sets are much less practical in this context, we develop in the present article a general procedure to trim an originally uncountable label set down to countable cardinality. In particular, we investigate how to perform this tightening of the label set in a way that preserves both the physical content of the algebra of observables and its symmetries. This work is notably motivated by applications to the holonomy-flux algebra underlying Loop Quantum Gravity. Building on earlier work by Okołów (2013), a projective state space was introduced for this algebra in Lanéry and Thiemann (2016). However, the non-trivial structure of the holonomy-flux algebra prevents the construction of satisfactory semi-classical states (Lanéry and Thiemann, 2017). Implementing the general procedure just mentioned in the case of a one-dimensional version of this algebra, we show how a discrete subalgebra can be extracted without destroying universality nor diffeomorphism invariance. On this subalgebra, quantum states can then be constructed which are more regular than was possible on the original algebra. In particular, this allows the design of semi-classical states whose semi-classicality is enforced step by step, starting from collective, macroscopic degrees of freedom and going down progressively toward smaller and smaller scales.
International Nuclear Information System (INIS)
Grizzi, Fabio; Russo, Carlo; Colombo, Piergiuseppe; Franceschini, Barbara; Frezza, Eldo E; Cobos, Everardo; Chiriva-Internati, Maurizio
2005-01-01
Modeling the complex development and growth of tumor angiogenesis using mathematics and biological data is a burgeoning area of cancer research. Architectural complexity is the main feature of every anatomical system, including organs, tissues, cells and sub-cellular entities. The vascular system is a complex network whose geometrical characteristics cannot be properly defined using the principles of Euclidean geometry, which is only capable of interpreting regular and smooth objects that are almost impossible to find in Nature. However, fractal geometry is a more powerful means of quantifying the spatial complexity of real objects. This paper introduces the surface fractal dimension (D s ) as a numerical index of the two-dimensional (2-D) geometrical complexity of tumor vascular networks, and their behavior during computer-simulated changes in vessel density and distribution. We show that D s significantly depends on the number of vessels and their pattern of distribution. This demonstrates that the quantitative evaluation of the 2-D geometrical complexity of tumor vascular systems can be useful not only to measure its complex architecture, but also to model its development and growth. Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex form of branched anatomical structures, in an attempt to define more appropriate methods of describing them quantitatively. This knowledge can be used to predict the aggressiveness of malignant tumors and design compounds that can halt the process of angiogenesis and influence tumor growth
International Nuclear Information System (INIS)
Xie Tao; Zhao Shang-Zhuo; Fang He; Yu Wen-Jin; He Yi-Jun; Perrie, William
2016-01-01
Sea surface current has a significant influence on electromagnetic (EM) backscattering signals and may constitute a dominant synthetic aperture radar (SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section (NRCS) discrepancies between the model for a coupled wave-current fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle, as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface. (paper)
Neutron scattering from fractals
DEFF Research Database (Denmark)
Kjems, Jørgen; Freltoft, T.; Richter, D.
1986-01-01
The scattering formalism for fractal structures is presented. Volume fractals are exemplified by silica particle clusters formed either from colloidal suspensions or by flame hydrolysis. The determination of the fractional dimensionality through scattering experiments is reviewed, and recent small...
Dimensional regularization in configuration space
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.
1995-09-01
Dimensional regularization is introduced in configuration space by Fourier transforming in D-dimensions the perturbative momentum space Green functions. For this transformation, Bochner theorem is used, no extra parameters, such as those of Feynman or Bogoliubov-Shirkov are needed for convolutions. The regularized causal functions in x-space have ν-dependent moderated singularities at the origin. They can be multiplied together and Fourier transformed (Bochner) without divergence problems. The usual ultraviolet divergences appear as poles of the resultant functions of ν. Several example are discussed. (author). 9 refs
Flat tori in three-dimensional space and convex integration.
Borrelli, Vincent; Jabrane, Saïd; Lazarus, Francis; Thibert, Boris
2012-05-08
It is well-known that the curvature tensor is an isometric invariant of C(2) Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C(1). This unexpected flexibility has many paradoxical consequences, one of them is the existence of C(1) isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and 1980s, M. Gromov, revisiting Nash's results introduced convex integration theory offering a general framework to solve this type of geometric problems. In this research, we convert convex integration theory into an algorithm that produces isometric maps of flat tori. We provide an implementation of a convex integration process leading to images of an embedding of a flat torus. The resulting surface reveals a C(1) fractal structure: Although the tangent plane is defined everywhere, the normal vector exhibits a fractal behavior. Isometric embeddings of flat tori may thus appear as a geometric occurrence of a structure that is simultaneously C(1) and fractal. Beyond these results, our implementation demonstrates that convex integration, a theory still confined to specialists, can produce computationally tractable solutions of partial differential relations.
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
Charaterisation of function spaces via mollification; fractal quantities for distributions
Directory of Open Access Journals (Sweden)
Hans Triebel
2003-01-01
Full Text Available The aim of this paper is twofold. First we characterise elements f belonging to the Besov spaces Bpqs(ℝn with s∈ℝ, 0
Fractal space frames and metamaterials for high mechanical efficiency
Farr, R. S.; Mao, Y.
2010-01-01
A solid slender beam of length $L$, made from a material of Young's modulus $Y$ and subject to a gentle compressive force $F$, requires a volume of material proportional to $L^{3}f^{1/2}$ [where $f\\equiv F/(YL^{2})\\ll 1$] in order to be stable against Euler buckling. By constructing a hierarchical space frame, we are able to systematically change the scaling of required material with $f$ so that it is proportional to $L^{3}f^{(G+1)/(G+2)}$, through changing the number of hierarchical levels $...
Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem.
Yue, Yi-xiang; Zhang, Tong; Yue, Qun-xing
2015-01-01
Vehicle Routing Problem (VRP) is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA) based on Fractal Space Filling Curves (SFC) method and Genetic Algorithm (GA) is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon's benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA.
International Nuclear Information System (INIS)
Ree, Suhan
2003-01-01
Fractal analysis is performed to measure the chaoticity of a classical hard-wall billiard with openings. We use the circular billiard with a straight cut with two openings, and a two-dimensional (2D) set of initial conditions that produce all possible trajectories of a particle injected from one opening. We numerically compute the fractal dimension of singular points of the function that maps an initial condition to the number of collisions with the wall before the exit, using the box-counting algorithm that uses uniformly distributed points inside the 2D set of initial conditions. Finally, the classical chaotic properties are observed while the parameters of the billiard are varied, and the results are compared with those with the one-dimensional set of initial conditions
Random walk through fractal environments
International Nuclear Information System (INIS)
Isliker, H.; Vlahos, L.
2003-01-01
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D F of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D F ≤2 can thus be considered as defective Levy walks. The distribution of jump increments for D F >2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D F F >2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations
On the space dimensionality based on metrics
International Nuclear Information System (INIS)
Gorelik, G.E.
1978-01-01
A new approach to space time dimensionality is suggested, which permits to take into account the possibility of altering dimensionality depending on the phenomenon scale. An attempt is made to give the definition of dimensionality, equivalent to a conventional definition for the Euclidean space and variety. The conventional definition of variety dimensionality is connected with the possibility of homeomorphic reflection of the Euclidean space on some region of each variety point
Space-Filling Supercapacitor Carpets: Highly scalable fractal architecture for energy storage
Tiliakos, Athanasios; Trefilov, Alexandra M. I.; Tanasǎ, Eugenia; Balan, Adriana; Stamatin, Ioan
2018-04-01
Revamping ground-breaking ideas from fractal geometry, we propose an alternative micro-supercapacitor configuration realized by laser-induced graphene (LIG) foams produced via laser pyrolysis of inexpensive commercial polymers. The Space-Filling Supercapacitor Carpet (SFSC) architecture introduces the concept of nested electrodes based on the pre-fractal Peano space-filling curve, arranged in a symmetrical equilateral setup that incorporates multiple parallel capacitor cells sharing common electrodes for maximum efficiency and optimal length-to-area distribution. We elucidate on the theoretical foundations of the SFSC architecture, and we introduce innovations (high-resolution vector-mode printing) in the LIG method that allow for the realization of flexible and scalable devices based on low iterations of the Peano algorithm. SFSCs exhibit distributed capacitance properties, leading to capacitance, energy, and power ratings proportional to the number of nested electrodes (up to 4.3 mF, 0.4 μWh, and 0.2 mW for the largest tested model of low iteration using aqueous electrolytes), with competitively high energy and power densities. This can pave the road for full scalability in energy storage, reaching beyond the scale of micro-supercapacitors for incorporating into larger and more demanding applications.
Speculations on self-avoiding surfaces in fractals. A mean field treatment
International Nuclear Information System (INIS)
Pandey, R.B.; Kumar, N.; Stauffer, D.
1984-08-01
We estimate the exponents characterizing the self-avoiding surfaces using an approximation in the framework of a Flory-type theory. We find for planar self-avoiding surfaces embedded randomly in a fractal of dimensionality D':theta=3/(4+D'); for random surfaces of fractal dimension D embedded in a Euclidian space of dimensionality d:theta=3/(2D+d-2); and for fractal surfaces embedded in a structure of fractal dimensionality D':theta=3/(2D+D'-2). (author)
Four Dimensional Trace Space Measurement
Energy Technology Data Exchange (ETDEWEB)
Hernandez, M.
2005-02-10
Future high energy colliders and FELs (Free Electron Lasers) such as the proposed LCLS (Linac Coherent Light Source) at SLAC require high brightness electron beams. In general a high brightness electron beam will contain a large number of electrons that occupy a short longitudinal duration, can be focused to a small transverse area while having small transverse divergences. Therefore the beam must have a high peak current and occupy small areas in transverse phase space and so have small transverse emittances. Additionally the beam should propagate at high energy and have a low energy spread to reduce chromatic effects. The requirements of the LCLS for example are pulses which contain 10{sup 10} electrons in a temporal duration of 10 ps FWHM with projected normalized transverse emittances of 1{pi} mm mrad[1]. Currently the most promising method of producing such a beam is the RF photoinjector. The GTF (Gun Test Facility) at SLAC was constructed to produce and characterize laser and electron beams which fulfill the LCLS requirements. Emittance measurements of the electron beam at the GTF contain evidence of strong coupling between the transverse dimensions of the beam. This thesis explores the effects of this coupling on the determination of the projected emittances of the electron beam. In the presence of such a coupling the projected normalized emittance is no longer a conserved quantity. The conserved quantity is the normalized full four dimensional phase space occupied by the beam. A method to determine the presence and evaluate the strength of the coupling in emittance measurements made in the laboratory is developed. A method to calculate the four dimensional volume the beam occupies in phase space using quantities available in the laboratory environment is also developed. Results of measurements made of the electron beam at the GTF that demonstrate these concepts are presented and discussed.
Teleportation schemes in infinite dimensional Hilbert spaces
International Nuclear Information System (INIS)
Fichtner, Karl-Heinz; Freudenberg, Wolfgang; Ohya, Masanori
2005-01-01
The success of quantum mechanics is due to the discovery that nature is described in infinite dimension Hilbert spaces, so that it is desirable to demonstrate the quantum teleportation process in a certain infinite dimensional Hilbert space. We describe the teleportation process in an infinite dimensional Hilbert space by giving simple examples
Directory of Open Access Journals (Sweden)
Hai-Feng Zhang
2017-07-01
Full Text Available In this paper, the properties of photonic band gaps (PBGs and defect modes of two-dimensional (2D fractal plasma photonic crystals (PPCs under a transverse-magnetic (TM wave are theoretically investigated by a modified plane wave expansion (PWE method. The configuration of 2D PPCs is the square lattices with the iteration rule of the Fibonacci sequence whose constituents are homogeneous and isotropic. The proposed 2D PPCs is filled with the dielectric cylinders in the plasma background. The accuracy and convergence of the present modified PWE method also are validated by a numerical example. The calculated results illustrate that the enough accuracy and good convergence can be achieved compared to the conventional PWE method, if the number of meshed grids is large enough. The dispersion curves of the proposed PPCs and 2D PPCs with a conventional square lattice are theoretically computed to study the properties of PBGs and defect modes. The simulated results demonstrate that the advantaged properties can be obtained in the proposed PPCs compared to the 2D conventional PPCs with similar lattices. If the Fibonacci sequence is introduced into the 2D PPCs, the larger PBGs and higher cutoff frequency can be achieved. The lower edges of PBGs are flat, which are originated from the Mie resonances. The defect modes can be considered as the quasi-localized states since the Fibonacci sequence has the self-similarity and non-periodicity at the same time. The effects of configurational parameters on the characters of the present PPCs are investigated. The results show that the PBGs and defect modes can be easily manipulated by tuning those parameters.
Physical model of dimensional regularization
Energy Technology Data Exchange (ETDEWEB)
Schonfeld, Jonathan F.
2016-12-15
We explicitly construct fractals of dimension 4-ε on which dimensional regularization approximates scalar-field-only quantum-field theory amplitudes. The construction does not require fractals to be Lorentz-invariant in any sense, and we argue that there probably is no Lorentz-invariant fractal of dimension greater than 2. We derive dimensional regularization's power-law screening first for fractals obtained by removing voids from 3-dimensional Euclidean space. The derivation applies techniques from elementary dielectric theory. Surprisingly, fractal geometry by itself does not guarantee the appropriate power-law behavior; boundary conditions at fractal voids also play an important role. We then extend the derivation to 4-dimensional Minkowski space. We comment on generalization to non-scalar fields, and speculate about implications for quantum gravity. (orig.)
Non extensive statistics and entropic gravity in a non-integer dimensional space
International Nuclear Information System (INIS)
Abreu, Everton M.C.; Ananias Neto, Jorge; Godinho, Cresus F.L.
2013-01-01
Full text: The idea that gravity can be originated from thermodynamics features has begun with the discovering that black hole physics is connected to the thermodynamics laws. These concepts were strongly boosted after Jacobson's work, where the Einstein equations were obtained from general thermodynamics approaches. In a recent work, Padmanabhan obtained an interpretation of gravity as an equipartition law. In Verlinde's thermo gravitational formalism, the temperature and the acceleration are connected via Unruh effect. At the same time, he combined the holographic principle with an equipartition law, where the number of bits is proportional to the area of the holographic surface. Bits were used to define the microscopic degrees of freedom. With these ingredients, the entropic force combined with the holographic principle and the equipartition law originated the Newton's law of gravitation. The possible interpretation of Verlinde's result is that gravity is not an underlying concept, but an emergent one. It originates from the statistical behavior of the holographic screen microscopic degrees of freedom. Following these ideas, the current literature has grown in an accelerated production from Coulomb force and symmetry considerations of entropic force to cosmology and loop quantum. In this work we introduced the Newton's constant in a fractal space as a function of the non extensive one. With this result we established a relation between the Tsallis non extensive parameter and the dimension of this fractal space. Using Verlinde's formalism we used these fractal ideas combined with the concept of entropic gravity to calculate the number of bits of an holographic surface in this non-integer dimensional space, a fractal holographic screen. We introduced a fundamental length, a Planck-like length, into this space as a function of this fractal holographic screen radius. Finally, we consider superior dimensions in this analysis. (author)
Weibel, Peter; Ord, Garnet; Rössler, Otto
2005-01-01
Space and Time are the prison bars of reality. Space Time Physics and Fractality is an attempt to tunnel through the rigidity of it all -- by turning everything into dust or smoke. These two ancient traditions are brought together here for the first time -- in the spirit of Democritus and Anaxagoras. Mohamed El Naschie, the sexagenarian, is the "dust dragon". The book contains papers by people who are infected by the same virus of desperately wanting to understand, and represents an incomparable breakthrough.
Coset space dimensional reduction of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Kapetanakis, D. (Physik Dept., Technische Univ. Muenchen, Garching (Germany)); Zoupanos, G. (CERN, Geneva (Switzerland))
1992-10-01
We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.).
Discrete symmetries and coset space dimensional reduction
International Nuclear Information System (INIS)
Kapetanakis, D.; Zoupanos, G.
1989-01-01
We consider the discrete symmetries of all the six-dimensional coset spaces and we apply them in gauge theories defined in ten dimensions which are dimensionally reduced over these homogeneous spaces. Particular emphasis is given in the consequences of the discrete symmetries on the particle content as well as on the symmetry breaking a la Hosotani of the resulting four-dimensional theory. (orig.)
Coset space dimensional reduction of gauge theories
International Nuclear Information System (INIS)
Kapetanakis, D.; Zoupanos, G.
1992-01-01
We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.)
Statistics of semiflexible self-avoiding trails on a family of two-dimensional compact fractals
International Nuclear Information System (INIS)
Živić, I; Elezović-Hadžić, S; Milošević, S
2011-01-01
We have applied the exact and Monte Carlo renormalization group (MCRG) method to study the statistics of semiflexible self-avoiding trails (SATs) on the family of plane-filling (PF) fractals. Each fractal of the family is compact, that is, the fractal dimension d f is equal to 2 for all members of the PF family, which are enumerated by an odd integer b, 3≤b<∞. Varying values of the stiffness parameter s of trails from 1 to 0 (so that when s decreases the trail stiffness increases) we calculate exactly (for 3 ≤ b ≤ 7) and through the MCRG approach (for b ≤ 201) the sets of the critical exponents ν (associated with the mean squared end-to-end distances of SATs) and γ (associated with the total number of different SATs). Our results show that critical exponents are stiffness dependent functions, so that ν(s) is a monotonically decreasing function of s, for each studied b, whereas γ(s) displays a non-monotonic behavior for some values of b. On the other hand, by fixing the stiffness parameter s, our results show clearly that for highly flexible trails (with s = 1 and 0.9) ν is a non-monotonic function of b, while for stiffer SATs (with s ≤ 0.7) ν monotonically decreases with b. We also show that γ(b) increases with increasing b, independently of s. Finally, we compare the obtained SAT data with those obtained for the semiflexible self-avoiding walk (SAW) model on the same fractal family, and for both models we discuss behavior of the studied exponents in the fractal-to-Euclidean crossover region b→∞
Esbenshade, Donald H., Jr.
1991-01-01
Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)
On dimensional reduction over coset spaces
International Nuclear Information System (INIS)
Kapetanakis, D.; Zoupanos, G.
1990-01-01
Gauge theories defined in higher dimensions can be dimensionally reduced over coset spaces giving definite predictions for the resulting four-dimensional theory. We present the most interesting features of these theories as well as an attempt to construct a model with realistic low energy behaviour within this framework. (author)
Random-fractal Ansatz for the configurations of two-dimensional critical systems.
Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki
2016-12-01
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.
International Nuclear Information System (INIS)
Dickau, Jonathan J.
2009-01-01
The use of fractals and fractal-like forms to describe or model the universe has had a long and varied history, which begins long before the word fractal was actually coined. Since the introduction of mathematical rigor to the subject of fractals, by Mandelbrot and others, there have been numerous cosmological theories and analyses of astronomical observations which suggest that the universe exhibits fractality or is by nature fractal. In recent years, the term fractal cosmology has come into usage, as a description for those theories and methods of analysis whereby a fractal nature of the cosmos is shown.
Baryshev, Yuri
2002-01-01
This is the first book to present the fascinating new results on the largest fractal structures in the universe. It guides the reader, in a simple way, to the frontiers of astronomy, explaining how fractals appear in cosmic physics, from our solar system to the megafractals in deep space. It also offers a personal view of the history of the idea of self-similarity and of cosmological principles, from Plato's ideal architecture of the heavens to Mandelbrot's fractals in the modern physical cosmos. In addition, this invaluable book presents the great fractal debate in astronomy (after Luciano Pi
Evolution of fractality in space plasmas of interest to geomagnetic activity
Muñoz, Víctor; Domínguez, Macarena; Alejandro Valdivia, Juan; Good, Simon; Nigro, Giuseppina; Carbone, Vincenzo
2018-03-01
We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from the Dst data and from a magnetohydrodynamic shell model for turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds, which suggest that it is possible, by means of the fractal dimension, to characterize the complexity of the magnetic cloud structure.
Relativistic phase space: dimensional recurrences
International Nuclear Information System (INIS)
Delbourgo, R; Roberts, M L
2003-01-01
We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius R and taking the limit as R→∞. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension
International Nuclear Information System (INIS)
Conte, Elio; Khrennikov, Andrei; Federici, Antonio; Zbilut, Joseph P.
2009-01-01
We develop a new method for analysis of fundamental brain waves as recorded by the EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given. We also discuss the link of such formulation with H. Weiss and V. Weiss golden ratio found in the brain, and with El Naschie fractal Cantorian space-time theory.
Fractality and the law of the wall
Xu, Haosen H. A.; Yang, X. I. A.
2018-05-01
Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.
Fractal dimension evolution and spatial replacement dynamics of urban growth
International Nuclear Information System (INIS)
Chen Yanguang
2012-01-01
Highlights: ► The fractal dimension growth can be modeled by Boltzmann’s equation. ► Boltzmann’s model suggests urban spatial replacement dynamics. ► If the rate of urban growth is too high, periodic oscillations or chaos will arise. ► Chaos is associated with fractals by the fractal dimension evolution model. ► The fractal dimension of urban form implies the space-filling ratio of a city. - Abstract: This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to interpret the fractal dimension of urban form. The fractal dimension evolution of urban growth can be empirically modeled with Boltzmann’s equation. For the normalized data, Boltzmann’s equation is just equivalent to the logistic function. The logistic equation can be transformed into the well-known 1-dimensional logistic map, which is based on a 2-dimensional map suggesting spatial replacement dynamics of city development. The 2-dimensional recurrence relations can be employed to generate the nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is thus made in this article that, for the fractal dimension growth following the logistic curve, the normalized dimension value is the ratio of space filling. If the rate of spatial replacement (urban growth) is too high, the periodic oscillations and chaos will arise. The spatial replacement dynamics can be extended to general replacement dynamics, and bifurcation and chaos mirror a process of complex replacement.
On infinite-dimensional state spaces
International Nuclear Information System (INIS)
Fritz, Tobias
2013-01-01
It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V −1 U 2 V=U 3 , then finite-dimensionality entails the relation UV −1 UV=V −1 UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V −1 U 2 V=U 3 holds only up to ε and then yields a lower bound on the dimension.
On infinite-dimensional state spaces
Fritz, Tobias
2013-05-01
It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.
Dimensional reduction from entanglement in Minkowski space
International Nuclear Information System (INIS)
Brustein, Ram; Yarom, Amos
2005-01-01
Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its vacuum state. This is reminiscent of area scaling of entanglement entropy but applies to quantum expectation values in a pure state, rather than to statistical averages over a mixed state. We then show, in a specific case, that fluctuations in the bulk have a lower-dimensional representation in terms of a boundary theory at high temperature. (author)
Riccion from higher-dimensional space-time with D-dimensional ...
Indian Academy of Sciences (India)
suggest that space-time above 3 05¢1016 GeV should be fractal. .... Here VD is the volume of SD, g´4·Dµ is the determinant of the metric tensor gMN (M ...... means that above 3.05x1016 GeV, SD is not a smooth surface whereas M4 is smooth.
Extended supersymmetry in four-dimensional Euclidean space
International Nuclear Information System (INIS)
McKeon, D.G.C.; Sherry, T.N.
2000-01-01
Since the generators of the two SU(2) groups which comprise SO(4) are not Hermitian conjugates of each other, the simplest supersymmetry algebra in four-dimensional Euclidean space more closely resembles the N=2 than the N=1 supersymmetry algebra in four-dimensional Minkowski space. An extended supersymmetry algebra in four-dimensional Euclidean space is considered in this paper; its structure resembles that of N=4 supersymmetry in four-dimensional Minkowski space. The relationship of this algebra to the algebra found by dimensionally reducing the N=1 supersymmetry algebra in ten-dimensional Euclidean space to four-dimensional Euclidean space is examined. The dimensional reduction of N=1 super Yang-Mills theory in ten-dimensional Minkowski space to four-dimensional Euclidean space is also considered
International Nuclear Information System (INIS)
Mookerjee, A.
1984-09-01
The problem of spin-glass to ferromagnetic transition with increasing concentration is then one of the familiar nearest neighbour percolation but on the background of IIC. In the regime p<=psub(c) at T=Tsub(g)(p), the IIC forms a fractal background on which ferromagnetic percolation takes place. The equivalent statement is that the mobility edge Jsub(c)(p) moves outwards as p increases and at a critical psub(c) coincides with the band edge Jsub(B). At and above these concentrations the mode with highest energy is extended and we have the familiar paramagnetic to ferromagnetic transition as temperature is lowered across Jsub(B)/ksub(B). The physical justification of this picture is not at all transparent as in the case of the cluster percolation ideas. To this date no reliable estimates of the behaviour of Jsub(c)(p) as a function of p, for a purely off diagonal random matrix J(R) have been made
Directory of Open Access Journals (Sweden)
Cahill R. T.
2012-07-01
Full Text Available Experiments have revealed that the Fresnel drag effect is not present in RF coaxial cables, contrary to a previous report. This enables a very sensitive, robust and compact detector, that is 1st order in v / c and using one clock, to detect the dynamical space passing the earth, revealing the sidereal rotation of the earth, together with significant wave / turbulence e ff ects. These are “gravitational waves”, and previously detected by Cahill 2006, using an Optical-Fibre – RF Coaxial Cable Detector, and Cahill 2009, using a preliminary version of the Dual RF Coaxial Cable Detector. The gravitational waves have a 1 / f spectrum, implying a fractal structure to the textured dynamical 3- space.
Changes in Dimensionality and Fractal Scaling Suggest Soft-Assembled Dynamics in Human EEG
DEFF Research Database (Denmark)
Wiltshire, Travis; Euler, Matthew J.; McKinney, Ty
2017-01-01
Humans are high-dimensional, complex systems consisting of many components that must coordinate in order to perform even the simplest of activities. Many behavioral studies, especially in the movement sciences, have advanced the notion of soft-assembly to describe how systems with many components...
Saw, Vee-Liem; Chew, Lock Yue
2013-01-01
We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line ...
International Nuclear Information System (INIS)
Zivic, I.; Elezovic-Hadzic, S.; Milosevic, S.
2009-01-01
We study the polymer system consisting of two-polymer chains situated in a fractal container that belongs to the three-dimensional Sierpinski Gasket (3D SG) family of fractals. The two-polymer system is modeled by two interacting self-avoiding walks (SAW) immersed in a good solvent. To conceive the inter-chain interactions we apply the model of two crossing self-avoiding walks (CSAW) in which the chains can cross each other. By applying renormalization group (RG) method, we establish the relevant phase diagrams for b=2 and b=3 members of the 3D SG fractal family. Also, at the appropriate transition fixed points we calculate the contact critical exponents φ, associated with the number of contacts between monomers of different chains. For larger b(2≤b≤30) we apply Monte Carlo renormalization group (MCRG) method, and compare the obtained results for φ with phenomenological proposals for the contact critical exponent, as well as with results obtained for other similar models of two-polymer system.
International Nuclear Information System (INIS)
Gottlieb, I.; Agop, M.; Jarcau, M.
2004-01-01
One builds the vacuum metrics of the stationary electromagnetic field through the complex potential model. There are thus emphasized both a variational principle, independent on the Ricci tensor, and some internal symmetries of the vacuum solutions. One shows that similar results may be obtained using the Barbiliant's group. By analytical continuation of a Barbilian transformation the link between the fixed points of the modular groups of the vacuum and the golden mean PHI=(1/(1+PHI))=(√5-1)/2 of ε (∞) space-time is established. Finally, a Cantorian fractal axiomatic model of the space-time is presented. The model is explained using a set of coupled equations which may describe the self organizing processes at the solid-liquid, plasma-plasma, and superconductor-superconductor interfaces
3-dimensional interactive space (3DIS)
International Nuclear Information System (INIS)
Veitch, S.; Veitch, J.; West, S.J.
1991-01-01
This paper reports on the 3DIS security system which uses standard CCTV cameras to create 3-Dimensional detection zones around valuable assets within protected areas. An intrusion into a zone changes light values and triggers an alarm that is annunciated, while images from multiple cameras are recorded. 3DIS lowers nuisance alarm rates and provides superior automated surveillance capability. Performance is improved over 2-D systems because activity around, above or below the zone does to cause an alarm. Invisible 3-D zones protect assets as small as a pin or as large as a 747 jetliner. Detection zones are created by excising subspaces from the overlapping fields of view of two or more video cameras. Hundred of zones may co-exist, operating simultaneously. Intrusion into any 3-D zone will cause a coincidental change in light values, triggering an alarm specific to that space
Mappings with closed range and finite dimensional linear spaces
International Nuclear Information System (INIS)
Iyahen, S.O.
1984-09-01
This paper looks at two settings, each of continuous linear mappings of linear topological spaces. In one setting, the domain space is fixed while the range space varies over a class of linear topological spaces. In the second setting, the range space is fixed while the domain space similarly varies. The interest is in when the requirement that the mappings have a closed range implies that the domain or range space is finite dimensional. Positive results are obtained for metrizable spaces. (author)
Model space dimensionalities for multiparticle fermion systems
International Nuclear Information System (INIS)
Draayer, J.P.; Valdes, H.T.
1985-01-01
A menu driven program for determining the dimensionalities of fixed-(J) [or (J,T)] model spaces built by distributing identical fermions (electrons, neutrons, protons) or two distinguihable fermion types (neutron-proton and isospin formalisms) among any mixture of positive and negative parity spherical orbitals is presented. The algorithm, built around the elementary difference formula d(J)=d(M=J)-d(M=J+1), takes full advantage of M->-M and particle-hole symmetries. A 96 K version of the program suffices for as compilated a case as d[(+1/2, +3/2, + 5/2, + 7/2-11/2)sup(n-26)J=2 + ,T=7]=210,442,716,722 found in the 0hω valence space of 56 126 Ba 70 . The program calculates the total fixed-(Jsup(π)) or fixed-(Jsup(π),T) dimensionality of a model space generated by distributing a specified number of fermions among a set of input positive and negative parity (π) spherical (j) orbitals. The user is queried at each step to select among various options: 1. formalism - identical particle, neutron-proton, isospin; 2. orbits -bumber, +/-2*J of all orbits; 3. limits -minimum/maximum number of particles of each parity; 4. specifics - number of particles, +/-2*J (total), 2*T; 5. continue - same orbit structure, new case quit. Though designed for nuclear applications (jj-coupling), the program can be used in the atomic case (LS-coupling) so long as half integer spin values (j=l+-1/2) are input for the valnce orbitals. Mutiple occurrences of a given j value are properly taken into account. A minor extension provides labelling information for a generalized seniority classification scheme. The program logic is an adaption of methods used in statistical spectroscopy to evaluate configuration averages. Indeed, the need for fixed symmetry leve densities in spectral distribution theory motivated this work. The methods extend to other group structures where there are M-like additive quantum labels. (orig.)
Barnsley, Michael F
2012-01-01
""Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs."" - Alan E. Wessel, Santa Clara University""The style of writing is technically excellent, informative, and entertaining."" - Robert McCartyThis new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of
Electromagnetism on anisotropic fractal media
Ostoja-Starzewski, Martin
2013-04-01
Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.
Charged fluid distribution in higher dimensional spheroidal space-time
Indian Academy of Sciences (India)
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
Two-dimensional black holes and non-commutative spaces
International Nuclear Information System (INIS)
Sadeghi, J.
2008-01-01
We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon
The Impact of The Fractal Paradigm on Geography
De Cola, L.
2001-12-01
Being itself somewhat fractal, Benoit Mandelbrot's magnum opus THE FRACTAL GEOMETRY OF NATURE may be deconstructed in many ways, including geometrically, systematically, and epistemologically. Viewed as a work of geography it may be used to organize the major topics of interest to scientists preoccupied with the understanding of real-world space in astronomy, geology, meteorology, hydrology, and biology. We shall use it to highlight such recent geographic accomplishments as automated feature detection, understanding urban growth, and modeling the spread of disease in space and time. However, several key challenges remain unsolved, among them: 1. It is still not possible to move continuously from one map scale to another so that objects change their dimension smoothly. I.e. as a viewer zooms in on a map the zero-dimensional location of a city should gradually become a 2-dimensional polygon, then a network of 1-dimensional streets, then 3-dimensional buildings, etc. 2. Spatial autocorrelation continues to be regarded more as an econometric challenge than as a problem of scaling. Similarities of values among closely-spaced observation is not so much a problem to be overcome as a source of information about spatial structure. 3. Although the fractal paradigm is a powerful model for data analysis, its ideas and techniques need to be brought to bear on the problems of understanding such hierarchies as ecosystems (the flow networks of energy and matter), taxonomies (biological classification), and knowledge (hierarchies of bureaucratic information, networks of linked data, etc).
Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga
2016-04-01
for the reservoir' hydraulic units distribution in space and time, as well as for the corresponding well testing data. References: 1. Mandelbrot, B., 1995. Foreword to Fractals in Petroleum Geology and Earth Processes, Edited by: Christopher C. Barton and Paul R. La Pointe, Plenum Press, New York: vii-xii. 2. Jin-Zhou Zhao, Cui-Cui Sheng, Yong_Ming Li, and Shun-Chu Li, 2015. A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir. J. of Chemistry, ID 596597, 8p. 3. Siler, T. , 2007. Fractal Reactor. International Conference Series on Emerging Nuclear Energy Systems 4. Corbett, P. W. M., 2012. The Role of Geoengineering in field development. INTECH, Chapter 8: 181- 198. 5. Nelson, P.H. and J. Kibler, 2003. A Catalog of Porosity and Permeability from core plugs in siliciclastic rocks. U.S. Geological Survey. 6. Per Bak and Kan Chen, 1989. The Physics of Fractals. Physica D 38: 5-12.
Baker, Robert G. V.
2017-02-01
Self-similar matrices of the fine structure constant of solar electromagnetic force and its inverse, multiplied by the Carrington synodic rotation, have been previously shown to account for at least 98% of the top one hundred significant frequencies and periodicities observed in the ACRIM composite irradiance satellite measurement and the terrestrial 10.7cm Penticton Adjusted Daily Flux data sets. This self-similarity allows for the development of a time-space differential equation (DE) where the solutions define a solar model for transmissions through the core, radiative, tachocline, convective and coronal zones with some encouraging empirical and theoretical results. The DE assumes a fundamental complex oscillation in the solar core and that time at the tachocline is smeared with real and imaginary constructs. The resulting solutions simulate for tachocline transmission, the solar cycle where time-line trajectories either 'loop' as Hermite polynomials for an active Sun or 'tail' as complementary error functions for a passive Sun. Further, a mechanism that allows for the stable energy transmission through the tachocline is explored and the model predicts the initial exponential coronal heating from nanoflare supercharging. The twisting of the field at the tachocline is then described as a quaternion within which neutrinos can oscillate. The resulting fractal bubbles are simulated as a Julia Set which can then aggregate from nanoflares into solar flares and prominences. Empirical examples demonstrate that time and space fractals are important constructs in understanding the behaviour of the Sun, from the impact on climate and biological histories on Earth, to the fractal influence on the spatial distributions of the solar system. The research suggests that there is a fractal clock underpinning solar frequencies in packages defined by the fine structure constant, where magnetic flipping and irradiance fluctuations at phase changes, have periodically impacted on the
Development and application of 3-D fractal reservoir model based on collage theorem
Energy Technology Data Exchange (ETDEWEB)
Kim, I.K.; Kim, K.S.; Sung, W.M. [Hanyang Univ., Seoul (Korea, Republic of)
1995-04-30
Reservoir characterization is the essential process to accurately evaluate the reservoir and has been conducted by geostatistical method, SRA algorithm, and etc. The characterized distribution of heterogeneous property by these methods shows randomly distributed phenomena, and does not present anomalous shape of property variation at discontinued space as compared with the observed shape in nature. This study proposed a new algorithm of fractal concept based on collage theorem, which can virtually present not only geometric shape of irregular and anomalous pore structures or coastlines, but also property variation for discontinuously observed data. With a basis of fractal concept, three dimensional fractal reservoir model was developed to more accurately characterize the heterogeneous reservoir. We performed analysis of pre-predictable hypothetically observed permeability data by using the fractal reservoir model. From the results, we can recognize that permeability distributions in the areal view or the cross-sectional view were consistent with the observed data. (author). 8 refs., 1 tab., 6 figs.
Fractals in Power Reactor Noise
International Nuclear Information System (INIS)
Aguilar Martinez, O.
1994-01-01
In this work the non- lineal dynamic problem of power reactor is analyzed using classic concepts of fractal analysis as: attractors, Hausdorff-Besikovics dimension, phase space, etc. A new non-linear problem is also analyzed: the discrimination of chaotic signals from random neutron noise signals and processing for diagnosis purposes. The advantages of a fractal analysis approach in the power reactor noise are commented in details
How the flip target behaves in four-dimensional space
International Nuclear Information System (INIS)
Antillon, A.; Kats, J.
1985-01-01
We use available coupling theory for understanding how a flip target in a 4-dimensional phase space reduces a gaussian beam of particles. Experimental evidence at the AGS can be qualitatively explained by this theory
Dimensional Analysis with space discrimination applied to Fickian difussion phenomena
International Nuclear Information System (INIS)
Diaz Sanchidrian, C.; Castans, M.
1989-01-01
Dimensional Analysis with space discrimination is applied to Fickian difussion phenomena in order to transform its partial differen-tial equations into ordinary ones, and also to obtain in a dimensionl-ess fom the Ficks second law. (Author)
Execution spaces for simple higher dimensional automata
DEFF Research Database (Denmark)
Raussen, Martin
2012-01-01
Higher dimensional automata (HDA) are highly expressive models for concurrency in Computer Science, cf van Glabbeek (Theor Comput Sci 368(1–2): 168–194, 2006). For a topologist, they are attractive since they can be modeled as cubical complexes—with an inbuilt restriction for directions of allowa......Higher dimensional automata (HDA) are highly expressive models for concurrency in Computer Science, cf van Glabbeek (Theor Comput Sci 368(1–2): 168–194, 2006). For a topologist, they are attractive since they can be modeled as cubical complexes—with an inbuilt restriction for directions...
Fractal tomography and its application in 3D vision
Trubochkina, N.
2018-01-01
A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.
Mishra, Jibitesh
2007-01-01
The book covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Key Features: - Fractals generated from L-System including hybrid fractals - Dimension calculation for L-system fractals - Images & codes for L-system fractals - Research directions in the area of L-system fractals - Usage of various freely downloadable tools in this area - Fractals generated from L-System including hybrid fractals- Dimension calculation for L-system fractals- Images & codes for L-system fractals- Research directions in the area of L-system fractals- Usage of various freely downloadable tools in this area
Green function and scattering amplitudes in many dimensional space
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.
1991-06-01
Methods for solving scattering are studied in many dimensional space. Green function and scattering amplitudes are given in terms of the requested asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many dimensional space. Phase-shift analysis are developed for hypercentral potentials and for non-hypercentral potentials with the hyperspherical adiabatic approximation. (author) 16 refs., 3 figs
Green functions and scattering amplitudes in many-dimensional space
International Nuclear Information System (INIS)
Fabre de la Ripelle, M.
1993-01-01
Methods for solving scattering are studied in many-dimensional space. Green function and scattering amplitudes are given in terms of the required asymptotic behaviour of the wave function. The Born approximation and the optical theorem are derived in many-dimensional space. Phase-shift analyses are performed for hypercentral potentials and for non-hypercentral potentials by use of the hyperspherical adiabatic approximation. (author)
Execution spaces for simple higher dimensional automata
DEFF Research Database (Denmark)
Raussen, Martin
Higher Dimensional Automata (HDA) are highly expressive models for concurrency in Computer Science, cf van Glabbeek [26]. For a topologist, they are attractive since they can be modeled as cubical complexes - with an inbuilt restriction for directions´of allowable (d-)paths. In Raussen [25], we...
Dimensionally Stable Structural Space Cable, Phase I
National Aeronautics and Space Administration — In response to the need for an affordable exoplanet-analysis science mission, NASA has recently embarked on the ROSES Technology Development for Exoplanet Missions...
Embedding of attitude determination in n-dimensional spaces
Bar-Itzhack, Itzhack Y.; Markley, F. Landis
1988-01-01
The problem of attitude determination in n-dimensional spaces is addressed. The proper parameters are found, and it is shown that not all three-dimensional methods have useful extensions to higher dimensions. It is demonstrated that Rodriguez parameters are conveniently extendable to other dimensions. An algorithm for using these parameters in the general n-dimensional case is developed and tested with a four-dimensional example. The correct mathematical description of angular velocities is addressed, showing that angular velocity in n dimensions cannot be represented by a vector but rather by a tensor of the second rank. Only in three dimensions can the angular velocity be described by a vector.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Hai-Feng, E-mail: hanlor@163.com [College of Optoelectronic Engineering, Nanjing University of Posts and Telecommunications, Nanjing, 210023 ,China (China); Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing Univ. Aeronaut. Astronaut.), Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016 (China); Liu, Shao-Bin [Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing Univ. Aeronaut. Astronaut.), Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016 (China)
2016-08-15
In this paper, the properties of photonic band gaps (PBGs) in two types of two-dimensional plasma-dielectric photonic crystals (2D PPCs) under a transverse-magnetic (TM) wave are theoretically investigated by a modified plane wave expansion (PWE) method where Monte Carlo method is introduced. The proposed PWE method can be used to calculate the band structures of 2D PPCs which possess arbitrary-shaped filler and any lattice. The efficiency and convergence of the present method are discussed by a numerical example. The configuration of 2D PPCs is the square lattices with fractal Sierpinski gasket structure whose constituents are homogeneous and isotropic. The type-1 PPCs is filled with the dielectric cylinders in the plasma background, while its complementary structure is called type-2 PPCs, in which plasma cylinders behave as the fillers in the dielectric background. The calculated results reveal that the enough accuracy and good convergence can be obtained, if the number of random sampling points of Monte Carlo method is large enough. The band structures of two types of PPCs with different fractal orders of Sierpinski gasket structure also are theoretically computed for a comparison. It is demonstrate that the PBGs in higher frequency region are more easily produced in the type-1 PPCs rather than in the type-2 PPCs. Sierpinski gasket structure introduced in the 2D PPCs leads to a larger cutoff frequency, enhances and induces more PBGs in high frequency region. The effects of configurational parameters of two types of PPCs on the PBGs are also investigated in detail. The results show that the PBGs of the PPCs can be easily manipulated by tuning those parameters. The present type-1 PPCs are more suitable to design the tunable compacted devices.
Directory of Open Access Journals (Sweden)
Amato P
2008-01-01
Full Text Available Abstract Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.
Identification of Architectural Functions in A Four-Dimensional Space
Directory of Open Access Journals (Sweden)
Firza Utama
2012-06-01
Full Text Available This research has explored the possibilities and concept of architectural space in a virtual environment. The virtual environment exists as a different concept, and challenges the constraints of the physical world. One of the possibilities in a virtual environment is that it is able to extend the spatial dimension higher than the physical three-dimension. To take the advantage of this possibility, this research has applied some geometrical four-dimensional (4D methods to define virtual architectural space. The spatial characteristics of 4D space is established by analyzing the four-dimensional structure that can be comprehended by human participant for its spatial quality, and by developing a system to control the fourth axis of movement. Multiple three-dimensional spaces that fluidly change their volume have been defined as one of the possibilities of virtual architecturalspace concept in order to enrich our understanding of virtual spatial experience.
On the Lipschitz condition in the fractal calculus
International Nuclear Information System (INIS)
Golmankhaneh, Alireza K.; Tunc, Cemil
2017-01-01
In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.
Three-dimensional space charge calculation method
International Nuclear Information System (INIS)
Lysenko, W.P.; Wadlinger, E.A.
1981-01-01
A method is presented for calculating space-charge forces suitable for use in a particle tracing code. Poisson's equation is solved in three dimensions with boundary conditions specified on an arbitrary surface by using a weighted residual method. Using a discrete particle distribution as our source input, examples are shown of off-axis, bunched beams of noncircular crosssection in radio-frequency quadrupole (RFQ) and drift-tube linac geometries
a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution
Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin
Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.
Comparison of two fractal interpolation methods
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
Visualising very large phylogenetic trees in three dimensional hyperbolic space
Directory of Open Access Journals (Sweden)
Liberles David A
2004-04-01
Full Text Available Abstract Background Common existing phylogenetic tree visualisation tools are not able to display readable trees with more than a few thousand nodes. These existing methodologies are based in two dimensional space. Results We introduce the idea of visualising phylogenetic trees in three dimensional hyperbolic space with the Walrus graph visualisation tool and have developed a conversion tool that enables the conversion of standard phylogenetic tree formats to Walrus' format. With Walrus, it becomes possible to visualise and navigate phylogenetic trees with more than 100,000 nodes. Conclusion Walrus enables desktop visualisation of very large phylogenetic trees in 3 dimensional hyperbolic space. This application is potentially useful for visualisation of the tree of life and for functional genomics derivatives, like The Adaptive Evolution Database (TAED.
Spinors and supersymmetry in four-dimensional Euclidean space
International Nuclear Information System (INIS)
McKeon, D.G.C.; Sherry, T.N.
2001-01-01
Spinors in four-dimensional Euclidean space are treated using the decomposition of the Euclidean space SO(4) symmetry group into SU(2)xSU(2). Both 2- and 4-spinor representations of this SO(4) symmetry group are shown to differ significantly from the corresponding spinor representations of the SO(3, 1) symmetry group in Minkowski space. The simplest self conjugate supersymmetry algebra allowed in four-dimensional Euclidean space is demonstrated to be an N=2 supersymmetry algebra which resembles the N=2 supersymmetry algebra in four-dimensional Minkowski space. The differences between the two supersymmetry algebras gives rise to different representations; in particular an analysis of the Clifford algebra structure shows that the momentum invariant is bounded above by the central charges in 4dE, while in 4dM the central charges bound the momentum invariant from below. Dimensional reduction of the N=1 SUSY algebra in six-dimensional Minkowski space (6dM) to 4dE reproduces our SUSY algebra in 4dE. This dimensional reduction can be used to introduce additional generators into the SUSY algebra in 4dE. Well known interpolating maps are used to relate the N=2 SUSY algebra in 4dE derived in this paper to the N=2 SUSY algebra in 4dM. The nature of the spinors in 4dE allows us to write an axially gauge invariant model which is shown to be both Hermitian and anomaly-free. No equivalent model exists in 4dM. Useful formulae in 4dE are collected together in two appendixes
Topology as fluid geometry two-dimensional spaces, volume 2
Cannon, James W
2017-01-01
This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two...
Mannheim Curves in Nonflat 3-Dimensional Space Forms
Directory of Open Access Journals (Sweden)
Wenjing Zhao
2015-01-01
Full Text Available We consider the Mannheim curves in nonflat 3-dimensional space forms (Riemannian or Lorentzian and we give the concept of Mannheim curves. In addition, we investigate the properties of nonnull Mannheim curves and their partner curves. We come to the conclusion that a necessary and sufficient condition is that a linear relationship with constant coefficients will exist between the curvature and the torsion of the given original curves. In the case of null curve, we reveal that there are no null Mannheim curves in the 3-dimensional de Sitter space.
The use of virtual reality to reimagine two-dimensional representations of three-dimensional spaces
Fath, Elaine
2015-03-01
A familiar realm in the world of two-dimensional art is the craft of taking a flat canvas and creating, through color, size, and perspective, the illusion of a three-dimensional space. Using well-explored tricks of logic and sight, impossible landscapes such as those by surrealists de Chirico or Salvador Dalí seem to be windows into new and incredible spaces which appear to be simultaneously feasible and utterly nonsensical. As real-time 3D imaging becomes increasingly prevalent as an artistic medium, this process takes on an additional layer of depth: no longer is two-dimensional space restricted to strategies of light, color, line and geometry to create the impression of a three-dimensional space. A digital interactive environment is a space laid out in three dimensions, allowing the user to explore impossible environments in a way that feels very real. In this project, surrealist two-dimensional art was researched and reimagined: what would stepping into a de Chirico or a Magritte look and feel like, if the depth and distance created by light and geometry were not simply single-perspective illusions, but fully formed and explorable spaces? 3D environment-building software is allowing us to step into these impossible spaces in ways that 2D representations leave us yearning for. This art project explores what we gain--and what gets left behind--when these impossible spaces become doors, rather than windows. Using sketching, Maya 3D rendering software, and the Unity Engine, surrealist art was reimagined as a fully navigable real-time digital environment. The surrealist movement and its key artists were researched for their use of color, geometry, texture, and space and how these elements contributed to their work as a whole, which often conveys feelings of unexpectedness or uneasiness. The end goal was to preserve these feelings while allowing the viewer to actively engage with the space.
Fractal universe and quantum gravity.
Calcagni, Gianluca
2010-06-25
We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
International Nuclear Information System (INIS)
Popescu, E.; Ardeleanu, L.; Bazacliu, O.; Popa, M.; Radulian, M.; Rizescu, M.
2002-01-01
now (first two stages) refer to the determination of the fractal properties of the time and space distributions for the Vrancea subcrustal earthquakes. The application of the variation coefficient method in time domain outlines the existence of different types of generation models in the two segments delimited on depth in the Vrancea subcrustal region: crack-like events (M D ≤ 3.6) which are more clustered in the upper segment of the subducted lithosphere; asperity-like events (M D > 3.6) which on the contrary are more clustered in the lower segment of the subducted lithosphere. Application of fractal statistics leads us to the following conclusions: Time fractal dimension, D t , of the Vrancea subcrustal earthquakes varies in a relative small interval, D t with in the range [0.81 - 0.92]; these values indicate a clustering tendency in all analyzed cases; Data set is well approximated by a fractal model for a time domain τ with in the range [2 to 2 7 days]; in the same time interval, deviations from the linearity are also noticed, indicating a superposition of the scale invariance behavior (fractal properties) with a Poisson distribution (random). As concerns the space clustering properties of the Vrancea subcrustal events, our purpose is to test the hypothesis of segmentation on depth of the subducted lithosphere. Our work emphasized consequently the existence of two maxima in the depth-earthquake distribution: a) 60 ≤ h ≤110 km; b)110 < h ≤ 220 km. The space clustering analysis showed also that: 1. In the case of the upper segment, the fractal dimension of the epicenter distribution decreases in time from 1.83 to 1.71; 2. In the case of the lower segment, the fractal dimension of the epicenter distribution has a tendency of increase in time from 1.65 to 1.91; 3. In the case of the whole subducted slab, there is a trend of increase in time from 1.65 to 1.91. In conclusion, the analysis of the clustering properties in time and space in the case of Vrancea
Directory of Open Access Journals (Sweden)
J. Antonio Paramo
2015-01-01
Full Text Available Hydrozincite (Zn5(OH6(CO32 is, among others, a popular precursor used to synthesize nanoscale ZnO with complex morphologies. For many existing and potential applications utilizing nanostructures, performance is determined by the surface and subsurface properties. Current understanding of the relationship between the morphology and the defect properties of nanocrystalline ZnO and hydrozincite systems is still incomplete. Specifically, for the latter nanomaterial the structure-property correlations are largely unreported in the literature despite the extensive use of hydrozincite in the synthesis applications. In our work, we addressed this issue by studying precipitated nanostructures of Zn5(OH6(CO32 with varying quasi-fractal dimensionalities containing relatively small amounts of a ZnO phase. Crystal morphology of the samples was accurately controlled by the growth time. We observed a strong correlation between the morphology of the samples and their optoelectronic properties. Our results indicate that a substantial increase of the free surface in the nanocrystal samples generates higher relative concentration of defects, consistent with the model of defect-rich surface and subsurface layers.
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
International Nuclear Information System (INIS)
Yang, Zhanfeng; Liu, Guozhi; Shao, Hao; Chen, Changhua; Sun, Jun
2013-01-01
This paper reports the space-charge limited current (SLC) and virtual cathode behaviors in one-dimensional grounded drift space. A simple general analytical solution and an approximate solution for the planar diode are given. Through a semi-analytical method, a general solution for SLC in one-dimensional drift space is obtained. The behaviors of virtual cathode in the drift space, including dominant frequency, electron transit time, position, and transmitted current, are yielded analytically. The relationship between the frequency of the virtual cathode oscillation and the injected current presented may explain previously reported numerical works. Results are significant in facilitating estimations and further analytical studies
Fractals via iterated functions and multifunctions
International Nuclear Information System (INIS)
Singh, S.L.; Prasad, Bhagwati; Kumar, Ashish
2009-01-01
Fractals have wide applications in biology, computer graphics, quantum physics and several other areas of applied sciences (see, for instance [Daya Sagar BS, Rangarajan Govindan, Veneziano Daniele. Preface - fractals in geophysics. Chaos, Solitons and Fractals 2004;19:237-39; El Naschie MS. Young double-split experiment Heisenberg uncertainty principles and cantorian space-time. Chaos, Solitons and Fractals 1994;4(3):403-09; El Naschie MS. Quantum measurement, information, diffusion and cantorian geodesics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 191-205; El Naschie MS. Iterated function systems, information and the two-slit experiment of quantum mechanics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 185-9; El Naschie MS, Rossler OE, Prigogine I. Forward. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995; El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 2004;19:209-36; El Naschie MS. Fractal black holes and information. Chaos, Solitons and Fractals 2006;29:23-35; El Naschie MS. Superstring theory: what it cannot do but E-infinity could. Chaos, Solitons and Fractals 2006;29:65-8). Especially, the study of iterated functions has been found very useful in the theory of black holes, two-slit experiment in quantum mechanics (cf. El Naschie, as mentioned above). The intent of this paper is to give a brief account of recent developments of fractals arising from IFS. We also discuss iterated multifunctions.
Fractal profit landscape of the stock market.
Grönlund, Andreas; Yi, Il Gu; Kim, Beom Jun
2012-01-01
We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.
Few helium atoms in quasi two-dimensional space
International Nuclear Information System (INIS)
Kilic, Srecko; Vranjes, Leandra
2003-01-01
Two, three and four 3 He and 4 He atoms in quasi two-dimensional space above graphite and cesium surfaces and in 'harmonic' potential perpendicular to the surface have been studied. Using some previously examined variational wave functions and the Diffusion Monte Carlo procedure, it has been shown that all molecules: dimers, trimers and tetramers, are bound more strongly than in pure two- and three-dimensional space. The enhancement of binding with respect to unrestricted space is more pronounced on cesium than on graphite. Furthermore, for 3 He 3 ( 3 He 4 ) on all studied surfaces, there is an indication that the configuration of a dimer and a 'free' particle (two dimers) may be equivalently established
2-D Fractal Carpet Antenna Design and Performance
Barton, C. C.; Tebbens, S. F.; Ewing, J. J.; Peterman, D. J.; Rizki, M. M.
2017-12-01
A 2-D fractal carpet antenna uses a fractal (self-similar) pattern to increase its perimeter by iteration and can receive or transmit electromagnetic radiation within its perimeter-bounded surface area. 2-D fractals are shapes that, at their mathematical limit (infinite iterations) have an infinite perimeter bounding a finite surface area. The fractal dimension describes the degree of space filling and lacunarity which quantifies the size and spatial distribution of open space bounded by a fractal shape. A key aspect of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that are very compact, wideband and multiband. As the number of iterations increases, the antenna operates at higher and higher frequencies. Manifestly different from traditional antenna designs, a fractal antenna can operate at multiple frequencies simultaneously. We have created a MATLAB code to generate deterministic and stochastic modes of Sierpinski carpet fractal antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, number of iterations, and lacunarities have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance
Lévy processes on a generalized fractal comb
Sandev, Trifce; Iomin, Alexander; Méndez, Vicenç
2016-09-01
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial kernels. In particular, the fractal structure of the fingers, which is controlled by the spatial kernel in both the real and the Fourier spaces, leads to the Lévy processes (Lévy flights) and superdiffusion. This generalization of the fractional diffusion is described by the Riesz space fractional derivative. In the framework of this generalized fractal comb model, Lévy processes are considered, and exact solutions for the probability distribution functions are obtained in terms of the Fox H-function for a variety of the memory kernels, and the rate of the superdiffusive spreading is studied by calculating the fractional moments. For a special form of the memory kernels, we also observed a competition between long rests and long jumps. Finally, we considered the fractal structure of the fingers controlled by a Weierstrass function, which leads to the power-law kernel in the Fourier space. This is a special case, when the second moment exists for superdiffusion in this competition between long rests and long jumps.
Lévy processes on a generalized fractal comb
International Nuclear Information System (INIS)
Sandev, Trifce; Iomin, Alexander; Méndez, Vicenç
2016-01-01
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial kernels. In particular, the fractal structure of the fingers, which is controlled by the spatial kernel in both the real and the Fourier spaces, leads to the Lévy processes (Lévy flights) and superdiffusion. This generalization of the fractional diffusion is described by the Riesz space fractional derivative. In the framework of this generalized fractal comb model, Lévy processes are considered, and exact solutions for the probability distribution functions are obtained in terms of the Fox H -function for a variety of the memory kernels, and the rate of the superdiffusive spreading is studied by calculating the fractional moments. For a special form of the memory kernels, we also observed a competition between long rests and long jumps. Finally, we considered the fractal structure of the fingers controlled by a Weierstrass function, which leads to the power-law kernel in the Fourier space. This is a special case, when the second moment exists for superdiffusion in this competition between long rests and long jumps. (paper)
Excitation gap of fractal quantum hall states in graphene
International Nuclear Information System (INIS)
Luo, Wenchen; Chakraborty, Tapash
2016-01-01
In the presence of a magnetic field and an external periodic potential the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter’s butterfly. In this work, we develop a Hartree–Fock theory to deal with the electron-electron interaction in the Hofstadter’s butterfly state in a finite-size graphene with periodic boundary conditions, where we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. A phase transition between the liquid phase and the fractal crystal phase can be observed. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation. (paper)
Supersymmetric quantum mechanics in three-dimensional space, 1
International Nuclear Information System (INIS)
Ui, Haruo
1984-01-01
As a direct generalization of the model of supersymmetric quantum mechanics by Witten, which describes the motion of a spin one-half particle in the one-dimensional space, we construct a model of the supersymmetric quantum mechanics in the three-dimensional space, which describes the motion of a spin one-half particle in central and spin-orbit potentials in the context of the nonrelativistic quantum mechanics. With the simplest choice of the (super) potential, this model is shown to reduce to the model of the harmonic oscillator plus constant spin-orbit potential of unit strength of both positive and negative signs, which was studied in detail in our recent paper in connection with ''accidental degeneracy'' as well as the ''graded groups''. This simplest model is discussed in some detail as an example of the three-dimensional supersymmetric quantum mechanical system, where the supersymmetry is an exact symmetry of the system. More general choice of a polynomial superpotential is also discussed. It is shown that the supersymmetry cannot be spontaneously broken for any polynomial superpotential in our three-dimensional model; this result is contrasted to the corresponding one in the one-dimensional model. (author)
Quantum phase space points for Wigner functions in finite-dimensional spaces
Luis Aina, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas.
Quantum phase space points for Wigner functions in finite-dimensional spaces
International Nuclear Information System (INIS)
Luis, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas
Taylor dispersion on a fractal
International Nuclear Information System (INIS)
Mazo, R.M.
1998-01-01
Taylor dispersion is the greatly enhanced diffusion in the direction of a fluid flow caused by ordinary diffusion in directions orthogonal to the flow. It is essential that the system be bounded in space in the directions orthogonal to the flow. We investigate the situation where the medium through which the flow occurs has fractal properties so that diffusion in the orthogonal directions is anomalous and non-Fickian. The effective diffusion in the flow direction remains normal; its width grows proportionally with the time. However, the proportionality constant depends on the fractal dimension of the medium as well as its walk dimension. (author)
Geometry of quantum dynamics in infinite-dimensional Hilbert space
Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana
2018-04-01
We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.
Quantum interest in (3+1)-dimensional Minkowski space
International Nuclear Information System (INIS)
Abreu, Gabriel; Visser, Matt
2009-01-01
The so-called 'quantum inequalities', and the 'quantum interest conjecture', use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a timelike observer, potentially preventing the existence of exotic phenomena such as 'Alcubierre warp drives' or 'traversable wormholes'. Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or nonexistence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple variational proof of one version of the quantum interest conjecture in (3+1)-dimensional Minkowski space.
Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions
Lapidus, Michael L
1999-01-01
A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...
Quantum vacuum energy in two dimensional space-times
International Nuclear Information System (INIS)
Davies, P.C.W.; Fulling, S.A.
1977-01-01
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed. (author)
Quantum vacuum energy in two dimensional space-times
Energy Technology Data Exchange (ETDEWEB)
Davies, P C.W.; Fulling, S A [King' s Coll., London (UK). Dept. of Mathematics
1977-04-21
The paper presents in detail the renormalization theory of the energy-momentum tensor of a two dimensional massless scalar field which has been used elsewhere to study the local physics in a model of black hole evaporation. The treatment is generalized to include the Casimir effect occurring in spatially finite models. The essence of the method is evaluation of the field products in the tensor as functions of two points, followed by covariant subtraction of the discontinuous terms arising as the points coalesce. In two dimensional massless theories, conformal transformations permit exact calculations to be performed. The results are applied here to some special cases, primarily space-times of constant curvature, with emphasis on the existence of distinct 'vacuum' states associated naturally with different conformal coordinate systems. The relevance of the work to the general problems of defining observables and of classifying and interpreting states in curved-space quantum field theory is discussed.
Naked singularities in higher dimensional Vaidya space-times
International Nuclear Information System (INIS)
Ghosh, S. G.; Dadhich, Naresh
2001-01-01
We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension
Manifold learning to interpret JET high-dimensional operational space
International Nuclear Information System (INIS)
Cannas, B; Fanni, A; Pau, A; Sias, G; Murari, A
2013-01-01
In this paper, the problem of visualization and exploration of JET high-dimensional operational space is considered. The data come from plasma discharges selected from JET campaigns from C15 (year 2005) up to C27 (year 2009). The aim is to learn the possible manifold structure embedded in the data and to create some representations of the plasma parameters on low-dimensional maps, which are understandable and which preserve the essential properties owned by the original data. A crucial issue for the design of such mappings is the quality of the dataset. This paper reports the details of the criteria used to properly select suitable signals downloaded from JET databases in order to obtain a dataset of reliable observations. Moreover, a statistical analysis is performed to recognize the presence of outliers. Finally data reduction, based on clustering methods, is performed to select a limited and representative number of samples for the operational space mapping. The high-dimensional operational space of JET is mapped using a widely used manifold learning method, the self-organizing maps. The results are compared with other data visualization methods. The obtained maps can be used to identify characteristic regions of the plasma scenario, allowing to discriminate between regions with high risk of disruption and those with low risk of disruption. (paper)
Introducing the Dimensional Continuous Space-Time Theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2013-01-01
This article is an introduction to a new theory. The name of the theory is justified by the dimensional description of the continuous space-time of the matter, energy and empty space, that gathers all the real things that exists in the universe. The theory presents itself as the consolidation of the classical, quantum and relativity theories. A basic equation that describes the formation of the Universe, relating time, space, matter, energy and movement, is deduced. The four fundamentals physics constants, light speed in empty space, gravitational constant, Boltzmann's constant and Planck's constant and also the fundamentals particles mass, the electrical charges, the energies, the empty space and time are also obtained from this basic equation. This theory provides a new vision of the Big-Bang and how the galaxies, stars, black holes and planets were formed. Based on it, is possible to have a perfect comprehension of the duality between wave-particle, which is an intrinsic characteristic of the matter and energy. It will be possible to comprehend the formation of orbitals and get the equationing of atomics orbits. It presents a singular comprehension of the mass relativity, length and time. It is demonstrated that the continuous space-time is tridimensional, inelastic and temporally instantaneous, eliminating the possibility of spatial fold, slot space, worm hole, time travels and parallel universes. It is shown that many concepts, like dark matter and strong forces, that hypothetically keep the cohesion of the atomics nucleons, are without sense.
The space-time model according to dimensional continuous space-time theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2014-01-01
This article results from the Dimensional Continuous Space-Time Theory for which the introductory theoretician was presented in [1]. A theoretical model of the Continuous Space-Time is presented. The wave equation of time into absolutely stationary empty space referential will be described in detail. The complex time, that is the time fixed on the infinite phase time speed referential, is deduced from the New View of Relativity Theory that is being submitted simultaneously with this article in this congress. Finally considering the inseparable Space-Time is presented the duality equation wave-particle.
FELICIA RAMONA BIRAU
2012-01-01
In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and...
Fractal description of fractures
International Nuclear Information System (INIS)
Lung, C.W.
1991-06-01
Recent studies on the fractal description of fractures are reviewed. Some problems on this subject are discussed. It seems hopeful to use the fractal dimension as a parameter for quantitative fractography and to apply fractal structures to the development of high toughness materials. (author). 28 refs, 7 figs
Fractal dimension of turbulent black holes
Westernacher-Schneider, John Ryan
2017-11-01
We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.
Directory of Open Access Journals (Sweden)
FELICIA RAMONA BIRAU
2012-05-01
Full Text Available In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and of course, the manner in which they interpret that information may be different. Also, Fractal Market Hypothesis refers to the way that liquidity and investment horizons influence the behaviour of financial investors.
Three-dimensional studies on resorption spaces and developing osteons.
Tappen, N C
1977-07-01
Resorption spaces and their continuations as developing osteons were traced in serial cross sections from decalcified long bones of dogs, baboons and a man, and from a human rib. Processes of formation of osteons and transverse (Volkmann's) canals can be inferred from three-dimensional studies. Deposits of new osseous tissue begin to line the walls of the spaces soon after termination of resorption. The first deposits are osteoid, usually stained very darkly by the silver nitrate procedure utilized, but a lighter osteoid zone adjacent to the canals occurs frequently. Osteoid linings continue to be produced as lamellar bone forms around them; the large canals of immature osteons usually narrow very gradually. Frequently they terminate both proximally and distally as resorption spaces, indicating that osteons often advance in opposite directions as they develop. Osteoclasts of resorption spaces tunnel preferentially into highly mineralized bone, and usually do not use previously existing canals as templates for their advance. Osteons evidently originate by localized resorption of one side of the wall of an existing vascular channel in bone, with subsequent orientation of the resorption front along the axis of the shaft. Advancing resorption spaces also apparently stimulate the formation of numerous additional transverse canal connections to neighboring longitudinal canals. Serial tracing and silver nitrate differential staining combine to reveal many of the processes of bone remodeling at work, and facilitate quantitative treatment of the data. Further uses in studies of bone tissue and associated cells are recommended.
2-D Fractal Wire Antenna Design and Performance
Tebbens, S. F.; Barton, C. C.; Peterman, D. J.; Ewing, J. J.; Abbott, C. S.; Rizki, M. M.
2017-12-01
A 2-D fractal wire antenna uses a fractal (self-similar) pattern to increase its length by iteration and can receive or transmit electromagnetic radiation. 2-D fractals are shapes that, at their mathematical limit (of infinite iterations) have an infinite length. The fractal dimension describes the degree of space filling. A fundamental property of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that can be very compact, wideband and multiband. As the number of iterations increases, the antenna tends to have additional frequencies that minimize far field return loss. This differs from traditional antenna designs in that a single fractal antenna can operate well at multiple frequencies. We have created a MATLAB code to generate deterministic and stochastic modes of fractal wire antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, and number of iterations have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance.
Coherent states on horospheric three-dimensional Lobachevsky space
Energy Technology Data Exchange (ETDEWEB)
Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by; Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by [Institute of Physics, National Academy of Sciences of Belarus, 68 Nezalezhnasci Ave., Minsk 220072 (Belarus); Rybak, I., E-mail: Ivan.Rybak@astro.up.pt [Institute of Physics, National Academy of Sciences of Belarus, 68 Nezalezhnasci Ave., Minsk 220072 (Belarus); Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das Estrelas, 4150-762 Porto (Portugal); Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)
2016-08-15
In the paper it is shown that due to separation of variables in the Laplace-Beltrami operator (Hamiltonian of a free quantum particle) in horospheric and quasi-Cartesian coordinates of three dimensional Lobachevsky space, it is possible to introduce standard (“conventional” according to Perelomov [Generalized Coherent States and Their Applications (Springer-Verlag, 1986), p. 320]) coherent states. Some problems (oscillator on horosphere, charged particle in analogy of constant uniform magnetic field) where coherent states are suitable for treating were considered.
Irreducible quantum group modules with finite dimensional weight spaces
DEFF Research Database (Denmark)
Pedersen, Dennis Hasselstrøm
a finitely generated U q -module which has finite dimensional weight spaces and is a sum of those. Our approach follows the procedures used by S. Fernando and O. Mathieu to solve the corresponding problem for semisimple complex Lie algebra modules. To achieve this we have to overcome a number of obstacles...... not present in the classical case. In the process we also construct twisting functors rigerously for quantum group modules, study twisted Verma modules and show that these admit a Jantzen filtration with corresponding Jantzen sum formula....
Coset Space Dimensional Reduction approach to the Standard Model
International Nuclear Information System (INIS)
Farakos, K.; Kapetanakis, D.; Koutsoumbas, G.; Zoupanos, G.
1988-01-01
We present a unified theory in ten dimensions based on the gauge group E 8 , which is dimensionally reduced to the Standard Mode SU 3c xSU 2 -LxU 1 , which breaks further spontaneously to SU 3L xU 1em . The model gives similar predictions for sin 2 θ w and proton decay as the minimal SU 5 G.U.T., while a natural choice of the coset space radii predicts light Higgs masses a la Coleman-Weinberg
Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces
International Nuclear Information System (INIS)
Robinson, James C
2009-01-01
This paper treats the embedding of finite-dimensional subsets of a Banach space B into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X − X is finite, d H (X − X) k are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hölder continuous inverse when the box-counting dimension of X is finite and k > 2d B (X). A related argument shows that if the Assouad dimension of X − X is finite and k > d A (X − X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L ∞ (X)
Intertwined Hamiltonians in two-dimensional curved spaces
International Nuclear Information System (INIS)
Aghababaei Samani, Keivan; Zarei, Mina
2005-01-01
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle
Thermal properties of bodies in fractal and cantorian physics
International Nuclear Information System (INIS)
Zmeskal, Oldrich; Buchnicek, Miroslav; Vala, Martin
2005-01-01
Fundamental laws describing the heat diffusion in fractal environment are discussed. It is shown that for the three-dimensional space the heat radiation process occur in structures with fractal dimension D element of heat conduction and convection have the upper hand (generally in the real gases). To describe the heat diffusion a new law has been formulated. Its validity is more general than the Plank's radiation law based on the quantum heat diffusion theory. The energy density w = f (K, D), where K is the fractal measure and D is the fractal dimension exhibit typical dependency peaking with agreement with Planck's radiation law and with the experimental data for the absolutely black body in the energy interval kT m m kT m ∼ 1.5275. The agreement of the fractal model with the experimental outcomes is documented for the spectral characteristics of the Sun. The properties of stellar objects (black holes, relict radiation, etc.) and the elementary particles fields and interactions between them (quarks, leptons, mesons, baryons, bosons and their coupling constants) will be discussed with the help of the described mathematic apparatus in our further contributions. The general gas law for real gases in its more applicable form than the widely used laws (e.g. van der Waals, Berthelot, Kammerlingh-Onnes) has been also formulated. The energy density, which is in this case represented by the gas pressure p = f (K, D), can gain generally complex value and represents the behaviour of real (cohesive) gas in interval D element of (1,3>. The gas behaves as the ideal one only for particular values of the fractal dimensions (the energy density is real-valued). Again, it is shown that above the critical temperature (kT > K h c) and for fractal dimension D m > 2.0269 the results are comparable to the kinetics theory of real (ideal) gas (van der Waals equation of state, compressibility factor, Boyle's temperature). For the critical temperature (K h c = kT r ) the compressibility
Electron spin-lattice relaxation in fractals
International Nuclear Information System (INIS)
Shrivastava, K.N.
1986-08-01
We have developed the theory of the spin-fracton interaction for paramagnetic ions in fractal structures. The interaction is exponentially damped by the self-similarity length of the fractal and by the range dimensionality d Φ . The relaxation time of the spin due to the absorption and emission of the fracton has been calculated for a general dimensionality called the Raman dimensionality d R , which for the fractons differs from the Hausdorff (fractal) dimensionality, D, as well as from the Euclidean dimensionality, d. The exponent of the energy level separation in the relaxation rate varies with d R d Φ /D. We have calculated the spin relaxation rate due to a new type of Raman process in which one fracton is absorbed to affect a spin transition from one electronic level to another and later another fracton is emitted along with a spin transition such that the difference in the energies of the two fractons is equal to the electronic energy level separation. The temperature and the dimensionality dependence of such a process has been found in several approximations. In one of the approximations where the van Vleck relaxation rate for a spin in a crystal is known to vary with temperature as T 9 , our calculated variation for fractals turns out to be T 6.6 , whereas the experimental value for Fe 3+ in frozen solutions of myoglobin azide is T 6.3 . Since we used d R =4/3 and the fracton range dimensionality d Φ =D/1.8, we expect to measure the dimensionalities of the problem by measuring the temperature dependence of the relaxation times. We have also calculated the shift of the paramagnetic resonance transition for a spin in a fractal for general dimensionalities. (author)
Electromagnetic-field equations in the six-dimensional space-time R6
International Nuclear Information System (INIS)
Teli, M.T.; Palaskar, D.
1984-01-01
Maxwell's equations (without monopoles) for electromagnetic fields are obtained in six-dimensional space-time. The equations possess structural symmetry in space and time, field and source densities. Space-time-symmetric conservation laws and field solutions are obtained. The results are successfully correlated with their four-dimensional space-time counterparts
Some fractal properties of the percolating backbone in two dimensions
International Nuclear Information System (INIS)
Laidlaw, D.; MacKay, G.; Jan, N.
1987-01-01
A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that fractal dimensionality of the backbone is d/sub f//sup BB/ = 1.61 +/- 0.01, the chemical dimensionality is d/sub t/ = 1.40 +/- 0.01, and the fractal dimension of the minimum path d/sub min/ = 1.15 +/- 0.02 for the two-dimensional triangular lattice
Horizontal biases in rats’ use of three-dimensional space
Jovalekic, Aleksandar; Hayman, Robin; Becares, Natalia; Reid, Harry; Thomas, George; Wilson, Jonathan; Jeffery, Kate
2011-01-01
Rodent spatial cognition studies allow links to be made between neural and behavioural phenomena, and much is now known about the encoding and use of horizontal space. However, the real world is three dimensional, providing cognitive challenges that have yet to be explored. Motivated by neural findings suggesting weaker encoding of vertical than horizontal space, we examined whether rats show a similar behavioural anisotropy when distributing their time freely between vertical and horizontal movements. We found that in two- or three-dimensional environments with a vertical dimension, rats showed a prioritization of horizontal over vertical movements in both foraging and detour tasks. In the foraging tasks, the animals executed more horizontal than vertical movements and adopted a “layer strategy” in which food was collected from one horizontal level before moving to the next. In the detour tasks, rats preferred the routes that allowed them to execute the horizontal leg first. We suggest three possible reasons for this behavioural bias. First, as suggested by Grobety and Schenk [5], it allows minimisation of energy expenditure, inasmuch as costly vertical movements are minimised. Second, it may be a manifestation of the temporal discounting of effort, in which animals value delayed effort as less costly than immediate effort. Finally, it may be that at the neural level rats encode the vertical dimension less precisely, and thus prefer to bias their movements in the more accurately encoded horizontal dimension. We suggest that all three factors are related, and all play a part. PMID:21419172
Fractals, malware, and data models
Jaenisch, Holger M.; Potter, Andrew N.; Williams, Deborah; Handley, James W.
2012-06-01
We examine the hypothesis that the decision boundary between malware and non-malware is fractal. We introduce a novel encoding method derived from text mining for converting disassembled programs first into opstrings and then filter these into a reduced opcode alphabet. These opcodes are enumerated and encoded into real floating point number format and used for characterizing frequency of occurrence and distribution properties of malware functions to compare with non-malware functions. We use the concept of invariant moments to characterize the highly non-Gaussian structure of the opcode distributions. We then derive Data Model based classifiers from identified features and interpolate and extrapolate the parameter sample space for the derived Data Models. This is done to examine the nature of the parameter space classification boundary between families of malware and the general non-malware category. Preliminary results strongly support the fractal boundary hypothesis, and a summary of our methods and results are presented here.
Fractal dimension analysis of complexity in Ligeti piano pieces
Bader, Rolf
2005-04-01
Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.
Fractal nature of hydrocarbon deposits. 2. Spatial distribution
International Nuclear Information System (INIS)
Barton, C.C.; Schutter, T.A; Herring, P.R.; Thomas, W.J.; Scholz, C.H.
1991-01-01
Hydrocarbons are unevenly distributed within reservoirs and are found in patches whose size distribution is a fractal over a wide range of scales. The spatial distribution of the patches is also fractal and this can be used to constrain the design of drilling strategies also defined by a fractal dimension. Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. The authors have performed fractal analyses on the spatial distribution of producing and showing wells combined and of dry wells in 1,600-mi 2 portions of the Denver and Powder River basins that were nearly completely drilled on quarter-mile square-grid spacings. They have limited their analyses to wells drilled to single stratigraphic intervals so that the map pattern revealed by drilling is representative of the spatial patchiness of hydrocarbons at depth. The fractal dimensions for the spatial patchiness of hydrocarbons in the two basins are 1.5 and 1.4, respectively. The fractal dimension for the pattern of all wells drilled is 1.8 for both basins, which suggests a drilling strategy with a fractal dimension significantly higher than the dimensions 1.5 and 1.4 sufficient to efficiently and economically explore these reservoirs. In fact, the fractal analysis reveals that the drilling strategy used in these basins approaches a fractal dimension of 2.0, which is equivalent to random drilling with no geologic input. Knowledge of the fractal dimension of a reservoir prior to drilling would provide a basis for selecting and a criterion for halting a drilling strategy for exploration whose fractal dimension closely matches that of the spatial fractal dimension of the reservoir, such a strategy should prove more efficient and economical than current practice
Fuzzy fractals, chaos, and noise
Energy Technology Data Exchange (ETDEWEB)
Zardecki, A.
1997-05-01
To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.
International Nuclear Information System (INIS)
Naumis, Gerardo G.; Bazan, A.; Torres, M.; Aragon, J.L.; Quintero-Torres, R.
2008-01-01
One of the few examples in which the physical properties of an incommensurable system reflect an underlying higher dimensionality is presented. Specifically, we show that the reflectivity distribution of an incommensurable one-dimensional cavity is given by the density of states of a tight-binding Hamiltonian in a two-dimensional triangular lattice. Such effect is due to an independent phase decoupling of the scattered waves, produced by the incommensurable nature of the system, which mimics a random noise generator. This principle can be applied to design a cavity that avoids resonant reflections for almost any incident wave. An optical analogy, by using three mirrors with incommensurable distances between them, is also presented. Such array produces a countable infinite fractal set of reflections, a phenomena which is opposite to the effect of optical invisibility
Random walks of oriented particles on fractals
International Nuclear Information System (INIS)
Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko
2014-01-01
Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features. (paper)
On Nonextensive Statistics, Chaos and Fractal Strings
Castro, C
2004-01-01
Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics ( with a non-additive $ q$-entropy ) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...
Asymptotic analysis of fundamental solutions of Dirac operators on even dimensional Euclidean spaces
International Nuclear Information System (INIS)
Arai, A.
1985-01-01
We analyze the short distance asymptotic behavior of some quantities formed out of fundamental solutions of Dirac operators on even dimensional Euclidean spaces with finite dimensional matrix-valued potentials. (orig.)
Cahill, Reginald T.
2012-01-01
Experiments have revealed that the Fresnel drag effect is not present in RF coaxial cables, contrary to a previous report. This enables a very sensitive, robust and compact detector, that is 1st order in v / c and using one clock, to detect the dynamical space passing the earth, revealing the sidereal rotation of the earth, together with significant wave / turbulence e ff ects. These are “gravitational waves”, and previously detected by Cahill ...
On Materiality and Dimensionality of the Space. Is There Some Unit of the Field?
Directory of Open Access Journals (Sweden)
Belyakov A. V.
2014-10-01
Full Text Available The article presents arguments with a view to recognize that space is material and has possibly a fractal dimension in the range of from three to two. It is proposed that along to the unit of substance (atom Some Unit of the field (vortex tubes should be set. It is shown that the formation of the field structures being a kind “ doubles” of atomic ones is possible. The existence of the three-zone electron structure is confirmed. It is indicated that this concept have already resulted in to the successful explanation of phenomena and to finding of their important parameters at different levels of the organization of matter.
Fractal analysis of rainfall occurrence observed in the synoptic ...
African Journals Online (AJOL)
Fractal analysis is important for characterizing and modeling rainfall's space-time variations in hydrology. The purpose of this study consists on determining, in a mono-fractal framework, the scale invariance of rainfall series in Benin synopticstations located in two main geographical area: Cotonou, Bohicon , Savè in a sub ...
Categorization of fractal plants
International Nuclear Information System (INIS)
Chandra, Munesh; Rani, Mamta
2009-01-01
Fractals in nature are always a result of some growth process. The language of fractals which has been created specifically for the description of natural growth process is called L-systems. Recently, superior iterations (essentially, investigated by Mann [Mann WR. Mean value methods in iteration. Proc Am Math Soc 1953;4:506-10 [MR0054846 (14,988f)
Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L.
1997-01-01
We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.
Thermodynamics for Fractal Statistics
da Cruz, Wellington
1998-01-01
We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Iterons, fractals and computations of automata
Siwak, Paweł
1999-03-01
Processing of strings by some automata, when viewed on space-time (ST) diagrams, reveals characteristic soliton-like coherent periodic objects. They are inherently associated with iterations of automata mappings thus we call them the iterons. In the paper we present two classes of one-dimensional iterons: particles and filtrons. The particles are typical for parallel (cellular) processing, while filtrons, introduced in (32) are specific for serial processing of strings. In general, the images of iterated automata mappings exhibit not only coherent entities but also the fractals, and quasi-periodic and chaotic dynamics. We show typical images of such computations: fractals, multiplication by a number, and addition of binary numbers defined by a Turing machine. Then, the particles are presented as iterons generated by cellular automata in three computations: B/U code conversion (13, 29), majority classification (9), and in discrete version of the FPU (Fermi-Pasta-Ulam) dynamics (7, 23). We disclose particles by a technique of combinational recoding of ST diagrams (as opposed to sequential recoding). Subsequently, we recall the recursive filters based on FCA (filter cellular automata) window operators, and considered by Park (26), Ablowitz (1), Fokas (11), Fuchssteiner (12), Bruschi (5) and Jiang (20). We present the automata equivalents to these filters (33). Some of them belong to the class of filter automata introduced in (30). We also define and illustrate some properties of filtrons. Contrary to particles, the filtrons interact nonlocally in the sense that distant symbols may influence one another. Thus their interactions are very unusual. Some examples have been given in (32). Here we show new examples of filtron phenomena: multifiltron solitonic collisions, attracting and repelling filtrons, trapped bouncing filtrons (which behave like a resonance cavity) and quasi filtrons.
Topological properties of function spaces $C_k(X,2)$ over zero-dimensional metric spaces $X$
Gabriyelyan, S.
2015-01-01
Let $X$ be a zero-dimensional metric space and $X'$ its derived set. We prove the following assertions: (1) the space $C_k(X,2)$ is an Ascoli space iff $C_k(X,2)$ is $k_\\mathbb{R}$-space iff either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (2) $C_k(X,2)$ is a $k$-space iff either $X$ is a topological sum of a Polish locally compact space and a discrete space or $X$ is not locally compact but $X'$ is compact, (3) $C_k(X,2)$ is a sequential space iff $X$ is a Pol...
Quantum waveguide theory of a fractal structure
International Nuclear Information System (INIS)
Lin Zhiping; Hou Zhilin; Liu Youyan
2007-01-01
The electronic transport properties of fractal quantum waveguide networks in the presence of a magnetic field are studied. A Generalized Eigen-function Method (GEM) is used to calculate the transmission and reflection coefficients of the studied systems unto the fourth generation Sierpinski fractal network with node number N=123. The relationship among the transmission coefficient T, magnetic flux Φ and wave vector k is investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux Φ are observed and discussed, and compared with the results of the tight-binding model
Factorial-moment and fractal analyses of γ families from atmospheric cascades
International Nuclear Information System (INIS)
Kalmakhelidze, M. E.; Roinishvili, N. N.; Svanidze, M. S.; Khizanishvili, L. A.; Chadranyan, L. Kh.
1997-01-01
Methods of factorial moments and fractal dimensions are used to analyze γ families from nuclear-electromagnetic cascades in the atmosphere. The analysis aims at estimating the sensitivity of these methods to multiparticle density fluctuations in γ families as considered in spaces of various variables. The mean characteristics of factorial and fractal moments in the azimuthal plane are studied and compared with those of the statistical ensemble of random families. It is shown that fluctuations of the photon distribution in the azimuthal angle Φ are of a dynamic origin. The mean model parameters are analyzed as functions of the radius vector R, an analog of pseudorapidity, and the product ER (E is the energy of an individual photon), an analog of the transverse momentum. Particle densities for two-dimensional partitions into both rings (in the radius R) and sectors (in the azimuthal angle Φ), d 2 N/dΦdR, are also considered. The distributions of various factorial and fractal features of individual γ families are compared with those for the statistical ensemble of random families. Correlations of these features for a γ family treated in terms of different variables (sectors and rings) are studied. Correlations between different factorial-fractal parameters of γ families are analyzed
Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals
Steinhurst, Benjamin; Teplyaev, Alexander
2012-01-01
We show that if a Barlow-Evans Markov process on a vermiculated space is symmetric, then one can study the spectral properties of the corresponding Laplacian using projective limits. For some examples, such as the Laakso spaces and a Spierpinski P\\^ate \\`a Choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. Also, one can construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhu...
The literary uses of high-dimensional space
Directory of Open Access Journals (Sweden)
Ted Underwood
2015-12-01
Full Text Available Debates over “Big Data” shed more heat than light in the humanities, because the term ascribes new importance to statistical methods without explaining how those methods have changed. What we badly need instead is a conversation about the substantive innovations that have made statistical modeling useful for disciplines where, in the past, it truly wasn’t. These innovations are partly technical, but more fundamentally expressed in what Leo Breiman calls a new “culture” of statistical modeling. Where 20th-century methods often required humanists to squeeze our unstructured texts, sounds, or images into some special-purpose data model, new methods can handle unstructured evidence more directly by modeling it in a high-dimensional space. This opens a range of research opportunities that humanists have barely begun to discuss. To date, topic modeling has received most attention, but in the long run, supervised predictive models may be even more important. I sketch their potential by describing how Jordan Sellers and I have begun to model poetic distinction in the long 19th century—revealing an arc of gradual change much longer than received literary histories would lead us to expect.
Three-dimensional reciprocal space x-ray coherent scattering tomography of two-dimensional object.
Zhu, Zheyuan; Pang, Shuo
2018-04-01
X-ray coherent scattering tomography is a powerful tool in discriminating biological tissues and bio-compatible materials. Conventional x-ray scattering tomography framework can only resolve isotropic scattering profile under the assumption that the material is amorphous or in powder form, which is not true especially for biological samples with orientation-dependent structure. Previous tomography schemes based on x-ray coherent scattering failed to preserve the scattering pattern from samples with preferred orientations, or required elaborated data acquisition scheme, which could limit its application in practical settings. Here, we demonstrate a simple imaging modality to preserve the anisotropic scattering signal in three-dimensional reciprocal (momentum transfer) space of a two-dimensional sample layer. By incorporating detector movement along the direction of x-ray beam, combined with a tomographic data acquisition scheme, we match the five dimensions of the measurements with the five dimensions (three in momentum transfer domain, and two in spatial domain) of the object. We employed a collimated pencil beam of a table-top copper-anode x-ray tube, along with a panel detector to investigate the feasibility of our method. We have demonstrated x-ray coherent scattering tomographic imaging at a spatial resolution ~2 mm and momentum transfer resolution 0.01 Å -1 for the rotation-invariant scattering direction. For any arbitrary, non-rotation-invariant direction, the same spatial and momentum transfer resolution can be achieved based on the spatial information from the rotation-invariant direction. The reconstructed scattering profile of each pixel from the experiment is consistent with the x-ray diffraction profile of each material. The three-dimensional scattering pattern recovered from the measurement reveals the partially ordered molecular structure of Teflon wrap in our sample. We extend the applicability of conventional x-ray coherent scattering tomography to
Directory of Open Access Journals (Sweden)
Ali Asghar Sepahi-Gerow
2017-03-01
Full Text Available In aplites of Khaku area, located in the east of the Alvand body, tourmaline noduleswith spherical and dendritic shapes are dispersed. Some of these nodules have light halothat is actually a transition zone between the core of nodules and the host aplites.Geometrically, these nodules are fractal shapes. In these nodules fractal dimension vary from 1.46 in dendritic nodules to 1.92 in spherical nodules. In three-dimensionalreconstructions of the studied nodule, the average volume for the core is 34% and 66%for its margin. Based on evidences such as lack of veins between nodules, tourmalineswith anhedral forms, presence of a leucocratic halo in the aureole of some nodules, theirspherical shape, their linear and flow dispersion in the host rock these nodules have been crystallized in magmatic condition. In the final stages of magma crystallizationand the B content increment followed by beginning of unmixing in the melt, distinctspherical bubbles have been developed which gave rise to nodules formation. Magmaticsystem acts as chaotic systems and the presence of rotational and limited closed areas inthe vicinity of areas with disturbed paths has led to the formation of rounded anddendritic nodules beside each other.
Fractal analysis for heat extraction in geothermal system
Directory of Open Access Journals (Sweden)
Shang Xiaoji
2017-01-01
Full Text Available Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy’s velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.
Lectures on fractal geometry and dynamical systems
Pesin, Yakov
2009-01-01
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular "chaotic" motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples o...
Vibration modes of 3n-gaskets and other fractals
Energy Technology Data Exchange (ETDEWEB)
Bajorin, N; Chen, T; Dagan, A; Emmons, C; Hussein, M; Khalil, M; Mody, P; Steinhurst, B; Teplyaev, A [Department of Mathematics, University of Connecticut, Storrs CT 06269 (United States)
2008-01-11
We rigorously study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals, which include the Sierpinski gasket and other 3n-gaskets. We consider the classical Laplacian on fractals which generalizes the usual one-dimensional second derivative, is the generator of the self-similar diffusion process, and has possible applications as the quantum Hamiltonian. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations. Our analysis, in particular, allows the computation of the spectral zeta function on fractals and the limiting distribution of eigenvalues (i.e., integrated density of states). We consider such examples as the level-3 Sierpinski gasket, a fractal 3-tree, and the diamond fractal.
Superconductivity and the existence of Nambu's three-dimensional phase space mechanics
International Nuclear Information System (INIS)
Angulo, R.; Gonzalez-Bernardo, C.A.; Rodriguez-Gomez, J.; Kalnay, A.J.; Perez-M, F.; Tello-Llanos, R.A.
1984-01-01
Nambu proposed a generalization of hamiltonian mechanics such that three-dimensional phase space is allowed. Thanks to a recent paper by Holm and Kupershmidt we are able to show the existence of such three-dimensional phase space systems in superconductivity. (orig.)
A covariant form of the Maxwell's equations in four-dimensional spaces with an arbitrary signature
International Nuclear Information System (INIS)
Lukac, I.
1991-01-01
The concept of duality in the four-dimensional spaces with the arbitrary constant metric is strictly mathematically formulated. A covariant model for covariant and contravariant bivectors in this space based on three four-dimensional vectors is proposed. 14 refs
We live in the quantum 4-dimensional Minkowski space-time
Hwang, W-Y. Pauchy
2015-01-01
We try to define "our world" by stating that "we live in the quantum 4-dimensional Minkowski space-time with the force-fields gauge group $SU_c(3) \\times SU_L(2) \\times U(1) \\times SU_f(3)$ built-in from the outset". We begin by explaining what "space" and "time" are meaning for us - the 4-dimensional Minkowski space-time, then proceeding to the quantum 4-dimensional Minkowski space-time. In our world, there are fields, or, point-like particles. Particle physics is described by the so-called ...
Low dimensionality semiconductors: modelling of excitons via a fractional-dimensional space
Christol, P.; Lefebvre, P.; Mathieu, H.
1993-09-01
An interaction space with a fractionnal dimension is used to calculate in a simple way the binding energies of excitons confined in quantum wells, superlattices and quantum well wires. A very simple formulation provides this energy versus the non-integer dimensionality of the physical environment of the electron-hole pair. The problem then comes to determining the dimensionality α. We show that the latter can be expressed from the characteristics of the microstructure. α continuously varies from 3 (bulk material) to 2 for quantum wells and superlattices, and from 3 to 1 for quantum well wires. Quite a fair agreement is obtained with other theoretical calculations and experimental data, and this model coherently describes both three-dimensional limiting cases for quantum wells (L_wrightarrow 0 and L_wrightarrow infty) and the whole range of periods of the superlattice. Such a simple model presents a great interest for spectroscopists though it does not aim to compete with accurate but often tedious variational calculations. Nous utilisons un espace des interactions doté d'une dimension fractionnaire pour calculer simplement l'énergie de liaison des excitons confinés dans les puits quantiques, superréseaux et fils quantiques. Une formulation très simple donne cette énergie en fonction de la dimensionalité non-entière de l'environnement physique de la paire électron-trou. Le problème revient alors à déterminer cette dimensionalité α, dont nous montrons qu'une expression peut être déduite des caractéristiques de la microstructure. α varie continûment de 3 (matériau massif) à 2 pour un puits quantique ou un superréseau, et de 3 à 1 pour un fil quantique, selon le confinement du mouvement des porteurs. Les comparaisons avec d'autres calculs théoriques et données expérimentales sont toujours très convenables, et cette théorie décrit d'une façon cohérente les limites tridimensionnelles du puits quantique (L_wrightarrow 0 et L
Directory of Open Access Journals (Sweden)
Adewale Amosu
2018-02-01
Full Text Available Reservoir modeling of carbonate rocks requires a proper understanding of the pore space distribution and its relationship to permeability. Using a pigeonhole fractal model we characterize the fractal geometry of moldic pore spaces and extract the fractal dimension. We apply the Kozeny-Carman equation and equations relating the tortuosity and the porosity to the fractal dimension to derive an empirical relationship between permeability and porosity.
Willson, Stephen J.
1991-01-01
Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)
Peleg, M
1993-01-01
Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.
Fractal growth in impurity-controlled solidification in lipid monolayers
DEFF Research Database (Denmark)
Fogedby, Hans C.; Sørensen, Erik Schwartz; Mouritsen, Ole G.
1987-01-01
A simple two-dimensional microscopic model is proposed to describe solidifcation processes in systems with impurities which are miscible only in the fluid phase. Computer simulation of the model shows that the resulting solids are fractal over a wide range of impurity concentrations and impurity...... diffusional constants. A fractal-forming mechanism is suggested for impurity-controlled solidification which is consistent with recent experimental observations of fractal growth of solid phospholipid domains in monolayers. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....
Fractal design concepts for stretchable electronics.
Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A
2014-01-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal design concepts for stretchable electronics
Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.
2014-02-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Three-dimensional oscillator and Coulomb systems reduced from Kaehler spaces
International Nuclear Information System (INIS)
Nersessian, Armen; Yeranyan, Armen
2004-01-01
We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kaehler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kaehler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid originate. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to a monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is a non-Kaehler one. Finally, we extend these results to the family of Kaehler spaces with conic singularities
Transmission and reflection properties of terahertz fractal metamaterials
DEFF Research Database (Denmark)
Malureanu, Radu; Lavrinenko, Andrei; Cooke, David
2010-01-01
We use THz time-domain spectroscopy to investigate transmission and reflection properties of metallic fractal metamaterial structures. We observe loss of free-space energy at certain resonance frequencies, indicating excitation of surface modes of the metamaterial.......We use THz time-domain spectroscopy to investigate transmission and reflection properties of metallic fractal metamaterial structures. We observe loss of free-space energy at certain resonance frequencies, indicating excitation of surface modes of the metamaterial....
Fractal and mechanical micro- and nanorange properties of sylvite and halite crystals
Directory of Open Access Journals (Sweden)
Valery N. Aptukov
2017-09-01
Full Text Available This article involves the treatment of micro- and nanorange scanning and indentation data for salt rock crystals obtained with help of the scanning microscope Dimension Icon using the mathematical models. It also describes the basic methods of fractal analysis. It shows the effectiveness of the method of minimal covering which is chosen to research the fractal properties of salt rock crystal surfaces. The article includes the algorithm of this method and the description of its generalization for the two-dimensional case. The values of fractal index and multifractal parameters have been calculated on the basis of the minimal covering method. The article also involves the anisotropy effects for fractal properties, comparison of fractal behavior on different scale levels. It gives the values of hardness for different parts of the crystals and studies the correlation between hardness and fractal index and describes the character of the influence of fractal dimension on roughness.
Charged fluid distribution in higher dimensional spheroidal space-time
Indian Academy of Sciences (India)
associated 3-spaces obtained as hypersurfaces t = constant, 3-spheroids, are suit- ... pressure. Considering the Vaidya–Tikekar [12] spheroidal geometry, ... a relativistic star in hydrostatic equilibrium having the spheroidal geometry of the .... K = 1, the spheroidal 3-space degenerates into a flat 3-space and when K = 0 it.
International Nuclear Information System (INIS)
Ren Xincheng; Guo Lixin
2008-01-01
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)
Dirac equation in 5- and 6-dimensional curved space-time manifolds
International Nuclear Information System (INIS)
Vladimirov, Yu.S.; Popov, A.D.
1984-01-01
The program of plotting unified multidimensional theory of gravitation, electromagnetism and electrically charged matter with transition from 5-dimensional variants to 6-dimensional theory possessing signature (+----+) is developed. For recording the Dirac equation in 5- and 6-dimensional curved space-time manifolds the tetrad formalism and γ-matrix formulation of the General Relativity Theory are used. It is shown that the 6-dimensional theory case unifies the two private cases of 5-dimensional theory and corresponds to two possibilities of the theory developed by Kadyshevski
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti
2017-08-17
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti; Jiang, Qiu; Mashraei, Yousof; Salama, Khaled N.; Alshareef, Husam N.
2017-01-01
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
Continuous imaging space in three-dimensional integral imaging
International Nuclear Information System (INIS)
Zhang Lei; Yang Yong; Wang Jin-Gang; Zhao Xing; Fang Zhi-Liang; Yuan Xiao-Cong
2013-01-01
We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Efficient and accurate nearest neighbor and closest pair search in high-dimensional space
Tao, Yufei; Yi, Ke; Sheng, Cheng; Kalnis, Panos
2010-01-01
Nearest Neighbor (NN) search in high-dimensional space is an important problem in many applications. From the database perspective, a good solution needs to have two properties: (i) it can be easily incorporated in a relational database, and (ii
The curvature and the algebra of Killing vectors in five-dimensional space
International Nuclear Information System (INIS)
Rcheulishvili, G.
1990-12-01
This paper presents the Killing vectors for a five-dimensional space with the line element. The algebras which are formed by these vectors are written down. The curvature two-forms are described. (author). 10 refs
Positron annihilation near fractal surfaces
International Nuclear Information System (INIS)
Lung, C.W.; Deng, K.M.; Xiong, L.Y.
1991-07-01
A model for positron annihilation in the sub-surface region near a fractal surface is proposed. It is found that the power law relationship between the mean positron implantation depth and incident positron energy can be used to measure the fractal dimension of the fractal surface in materials. (author). 10 refs, 2 figs
Spinorial characterizations of surfaces into 3-dimensional psuedo-Riemannian space forms
Lawn , Marie-Amélie; Roth , Julien
2011-01-01
9 pages; We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well ...
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
of fractals. Measuring the Length of a Curve. Consider the problem of measuring the length of a ..... a two dimensional smooth surface embedded in 3 dimen- ... interesting measure of a I-dimensional object is its length and not the volume.
On High Dimensional Searching Spaces and Learning Methods
DEFF Research Database (Denmark)
Yazdani, Hossein; Ortiz-Arroyo, Daniel; Choros, Kazimierz
2017-01-01
, and similarity functions and discuss the pros and cons of using each of them. Conventional similarity functions evaluate objects in the vector space. Contrarily, Weighted Feature Distance (WFD) functions compare data objects in both feature and vector spaces, preventing the system from being affected by some...
Influence of cusps and intersections on the Wilson loop in ν-dimensional space
International Nuclear Information System (INIS)
Bezerra, V.B.
1984-01-01
A discussion is given about the influence of cusps and intersections on the calculation of the Wilson loop in ν-dimensional space. In particular, for the two-dimensional case, it is shown that there are no divergences. (Author) [pt
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
DEFF Research Database (Denmark)
Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.
2010-01-01
applications. THz radiation can be employed for various purposes, among them the study of vibrations in biological molecules, motion of electrons in semiconductors and propagation of acoustic shock waves in crystals. We propose here a new THz fractal MTM design that shows very high transmission in the desired...... frequency range as well as a clear differentiation between one polarisation and another. Based on theoretical predictions we fabricated and measured a fractal based THz metamaterial that shows more than 60% field transmission at around 1THz for TE polarized light while the TM waves have almost 80% field...... transmission peak at 0.6THz. One of the main characteristics of this design is its tunability by design: by simply changing the length of the fractal elements one can choose the operating frequency window. The modelling, fabrication and characterisation results will be presented in this paper. Due to the long...
Davarpanah, A.; Babaie, H. A.
2012-12-01
The interaction of the thermally induced stress field of the Yellowstone hotspot (YHS) with existing Basin and Range (BR) fault blocks, over the past 17 m.y., has produced a new, spatially and temporally variable system of normal faults around the Snake River Plain (SRP) in Idaho and Wyoming-Montana area. Data about the trace of these new cross faults (CF) and older BR normal faults were acquired from a combination of satellite imageries, DEM, and USGS geological maps and databases at scales of 1:24,000, 1:100,000, 1:250,000, 1:1000, 000, and 1:2,500, 000, and classified based on their azimuth in ArcGIS 10. The box-counting fractal dimension (Db) of the BR fault traces, determined applying the Benoit software, and the anisotropy intensity (ellipticity) of the fractal dimensions, measured with the modified Cantor dust method applying the AMOCADO software, were measured in two large spatial domains (I and II). The Db and anisotropy of the cross faults were studied in five temporal domains (T1-T5) classified based on the geologic age of successive eruptive centers (12 Ma to recent) of the YHS along the eastern SRP. The fractal anisotropy of the CF system in each temporal domain was also spatially determined in the southern part (domain S1), central part (domain S2), and northern part (domain S3) of the SRP. Line (fault trace) density maps for the BR and CF polylines reveal a higher linear density (trace length per unit area) for the BR traces in the spatial domain I, and a higher linear density of the CF traces around the present Yellowstone National Park (S1T5) where most of the seismically active faults are located. Our spatio-temporal analysis reveals that the fractal dimension of the BR system in domain I (Db=1.423) is greater than that in domain II (Db=1.307). It also shows that the anisotropy of the fractal dimension in domain I is less eccentric (axial ratio: 1.242) than that in domain II (1.355), probably reflecting the greater variation in the trend of the BR
International Nuclear Information System (INIS)
Saveliev, M.V.
1983-01-01
In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)
FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY
Directory of Open Access Journals (Sweden)
Hynek Lauschmann
2011-05-01
Full Text Available The morphology of fatigue fracture surface (caused by constant cycle loading is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness. Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.
International Nuclear Information System (INIS)
Li, W.; Bak, P.
1986-01-01
At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D = 1 to the cantorus is governed by an exponent ν = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent
Fractal actors and infrastructures
DEFF Research Database (Denmark)
Bøge, Ask Risom
2011-01-01
-network-theory (ANT) into surveillance studies (Ball 2002, Adey 2004, Gad & Lauritsen 2009). In this paper, I further explore the potential of this connection by experimenting with Marilyn Strathern’s concept of the fractal (1991), which has been discussed in newer ANT literature (Law 2002; Law 2004; Jensen 2007). I...... under surveillance. Based on fieldwork conducted in 2008 and 2011 in relation to my Master’s thesis and PhD respectively, I illustrate fractal concepts by describing the acts, actors and infrastructure that make up the ‘DNA surveillance’ conducted by the Danish police....
Unitarity in three-dimensional flat space higher spin theories
International Nuclear Information System (INIS)
Grumiller, D.; Riegler, M.; Rosseel, J.
2014-01-01
We investigate generic flat-space higher spin theories in three dimensions and find a no-go result, given certain assumptions that we spell out. Namely, it is only possible to have at most two out of the following three properties: unitarity, flat space, non-trivial higher spin states. Interestingly, unitarity provides an (algebra-dependent) upper bound on the central charge, like c=42 for the Galilean W_4"("2"−"1"−"1") algebra. We extend this no-go result to rule out unitary “multi-graviton” theories in flat space. We also provide an example circumventing the no-go result: Vasiliev-type flat space higher spin theory based on hs(1) can be unitary and simultaneously allow for non-trivial higher-spin states in the dual field theory.
Attractive and repulsive quantum forces from dimensionality of space
DEFF Research Database (Denmark)
Bialynicki-Birula, I.; Cirone, M.A.; Dahl, Jens Peder
2002-01-01
Two particles of identical mass attract and repel each other even when there exist no classical external forces and their average relative momentum vanishes. This quantum force depends crucially on the number of dimensions of space.......Two particles of identical mass attract and repel each other even when there exist no classical external forces and their average relative momentum vanishes. This quantum force depends crucially on the number of dimensions of space....
Lorentz covariant tempered distributions in two-dimensional space-time
International Nuclear Information System (INIS)
Zinov'ev, Yu.M.
1989-01-01
The problem of describing Lorentz covariant distributions without any spectral condition has hitherto remained unsolved even for two-dimensional space-time. Attempts to solve this problem have already been made. Zharinov obtained an integral representation for the Laplace transform of Lorentz invariant distributions with support in the product of two-dimensional future light cones. However, this integral representation does not make it possible to obtain a complete description of the corresponding Lorentz invariant distributions. In this paper the author gives a complete description of Lorentz covariant distributions for two-dimensional space-time. No spectral conditions is assumed
Biometric feature extraction using local fractal auto-correlation
International Nuclear Information System (INIS)
Chen Xi; Zhang Jia-Shu
2014-01-01
Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme: (i) using two-dimensional Gabor filter to extract the texture features of biometric images; (ii) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and (iii) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach. (condensed matter: structural, mechanical, and thermal properties)
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Three-dimensional space-charge calculation method
International Nuclear Information System (INIS)
Lysenko, W.P.; Wadlinger, E.A.
1980-09-01
A method is presented for calculating space-charge forces on individual particles in a particle tracing simulation code. Poisson's equation is solved in three dimensions with boundary conditions specified on an arbitrary surface. When the boundary condition is defined by an impressed radio-frequency field, the external electric fields as well as the space-charge fields are determined. A least squares fitting procedure is used to calculate the coefficients of expansion functions, which need not be orthogonal nor individually satisfy the boundary condition
Geodesics on a hot plate: an example of a two-dimensional curved space
International Nuclear Information System (INIS)
Erkal, Cahit
2006-01-01
The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion
Geodesics on a hot plate: an example of a two-dimensional curved space
Energy Technology Data Exchange (ETDEWEB)
Erkal, Cahit [Department of Geology, Geography, and Physics, University of Tennessee, Martin, TN 38238 (United States)
2006-07-01
The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion.
T.A. Knoch (Tobias); J. Langowski (Jörg)
2000-01-01
textabstractDespite the successful linear sequencing of the human genome its three-dimensional structure is widely unknown, although it is important for gene regulation and replication. For a long time the interphase nucleus has been viewed as a 'spaghetti soup' of DNA without much internal
Data analysis in high-dimensional sparse spaces
DEFF Research Database (Denmark)
Clemmensen, Line Katrine Harder
classification techniques for high-dimensional problems are presented: Sparse discriminant analysis, sparse mixture discriminant analysis and orthogonality constrained support vector machines. The first two introduces sparseness to the well known linear and mixture discriminant analysis and thereby provide low...... are applied to classifications of fish species, ear canal impressions used in the hearing aid industry, microbiological fungi species, and various cancerous tissues and healthy tissues. In addition, novel applications of sparse regressions (also called the elastic net) to the medical, concrete, and food...
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Semiflexible crossing-avoiding trails on plane-filling fractals
International Nuclear Information System (INIS)
Živić, I.; Elezović-Hadžić, S.; Milošević, S.
2015-01-01
We have studied the statistics of semiflexible polymer chains modeled by crossing-avoiding trails (CAT) situated on the family of plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension d_f is equal to 2 for all members of the fractal family. By applying the exact and Monte Carlo real-space renormalization group method we have calculated the critical exponent ν, which governs the scaling behavior of the end-to-end distance of the polymer, as well as the entropic critical exponent γ, for a large set of fractals, and various values of polymer flexibility. Our results, obtained for CAT model on PF fractals, show that both critical exponents depend on the polymer flexibility, in such a way that less flexible polymer chains display enlarged values of ν, and diminished values of γ. We have compared the obtained results for CAT model with the known results for the self-avoiding walk and self-avoiding trail models and discussed the influence of excluded volume effect on the values of semiflexible polymer critical exponents, for a large set of studied compact fractals.
The algebra of Killing vectors in five-dimensional space
International Nuclear Information System (INIS)
Rcheulishvili, G.L.
1990-01-01
This paper presents algebras which are formed by the found earlier Killing vectors in the space with linear element ds. Under some conditions, an explicit dependence of r is given for the functions entering in linear element ds. The curvature two-forms are described. 7 refs
Aspects of high-dimensional theories in embedding spaces
International Nuclear Information System (INIS)
Maia, M.D.; Mecklenburg, W.
1983-01-01
The question of whether physical meaning may be attributed to the extra dimensions provided by embedding procedures as applied to physical space-times is discussed. The similarities and differences of the present picture to that of conventional Kaluza-Klein pictures are commented. (Author) [pt
To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space
International Nuclear Information System (INIS)
Khrennikov, Andrei
2007-01-01
We study asymptotic expansions of Gaussian integrals of analytic functionals on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an asymptotic equality coupling the Gaussian integral and the trace of the composition of scaling of the covariation operator of a Gaussian measure and the second (Frechet) derivative of a functional. In this way we couple classical average (given by an infinite-dimensional Gaussian integral) and quantum average (given by the von Neumann trace formula). We can interpret this mathematical construction as a procedure of 'dequantization' of quantum mechanics. We represent quantum mechanics as an asymptotic projection of classical statistical mechanics with infinite-dimensional phase space. This space can be represented as the space of classical fields, so quantum mechanics is represented as a projection of 'prequantum classical statistical field theory'
Rare event simulation in finite-infinite dimensional space
International Nuclear Information System (INIS)
Au, Siu-Kui; Patelli, Edoardo
2016-01-01
Modern engineering systems are becoming increasingly complex. Assessing their risk by simulation is intimately related to the efficient generation of rare failure events. Subset Simulation is an advanced Monte Carlo method for risk assessment and it has been applied in different disciplines. Pivotal to its success is the efficient generation of conditional failure samples, which is generally non-trivial. Conventionally an independent-component Markov Chain Monte Carlo (MCMC) algorithm is used, which is applicable to high dimensional problems (i.e., a large number of random variables) without suffering from ‘curse of dimension’. Experience suggests that the algorithm may perform even better for high dimensional problems. Motivated by this, for any given problem we construct an equivalent problem where each random variable is represented by an arbitrary (hence possibly infinite) number of ‘hidden’ variables. We study analytically the limiting behavior of the algorithm as the number of hidden variables increases indefinitely. This leads to a new algorithm that is more generic and offers greater flexibility and control. It coincides with an algorithm recently suggested by independent researchers, where a joint Gaussian distribution is imposed between the current sample and the candidate. The present work provides theoretical reasoning and insights into the algorithm.
Fractal-based exponential distribution of urban density and self-affine fractal forms of cities
International Nuclear Information System (INIS)
Chen Yanguang; Feng Jian
2012-01-01
Highlights: ► The model of urban population density differs from the common exponential function. ► Fractal landscape influences the exponential distribution of urban density. ► The exponential distribution of urban population suggests a self-affine fractal. ► Urban space can be divided into three layers with scaling and non-scaling regions. ► The dimension of urban form with characteristic scale can be treated as 2. - Abstract: Urban population density always follows the exponential distribution and can be described with Clark’s model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark’s model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark’s model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.
Temporal fractals in seabird foraging behaviour: diving through the scales of time
Macintosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan
2013-05-01
Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (216 data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.
Navigation performance in virtual environments varies with fractal dimension of landscape
Juliani, Arthur W.; Bies, Alexander J.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.
2016-01-01
Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans’ ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D...
A variable-order fractal derivative model for anomalous diffusion
Directory of Open Access Journals (Sweden)
Liu Xiaoting
2017-01-01
Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.
Fractals in several electrode materials
Energy Technology Data Exchange (ETDEWEB)
Zhang, Chunyong, E-mail: zhangchy@njau.edu.cn [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); Wu, Jingyu [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Fu, Degang [Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); State Key Laboratory of Bioelectronics, Southeast University, Nanjing 210096 (China)
2014-09-15
Highlights: • Fractal geometry was employed to characterize three important electrode materials. • The surfaces of all studied electrodes were proved to be very rough. • The fractal dimensions of BDD and ACF were scale dependent. • MMO film was more uniform than BDD and ACF in terms of fractal structures. - Abstract: In the present paper, the fractal properties of boron-doped diamond (BDD), mixed metal oxide (MMO) and activated carbon fiber (ACF) electrode have been studied by SEM imaging at different scales. Three materials are self-similar with mean fractal dimension in the range of 2.6–2.8, confirming that they all exhibit very rough surfaces. Specifically, it is found that MMO film is more uniform in terms of fractal structure than BDD and ACF. As a result, the intriguing characteristics make these electrodes as ideal candidates for high-performance decontamination processes.
Six-dimensional real and reciprocal space small-angle X-ray scattering tomography.
Schaff, Florian; Bech, Martin; Zaslansky, Paul; Jud, Christoph; Liebi, Marianne; Guizar-Sicairos, Manuel; Pfeiffer, Franz
2015-11-19
When used in combination with raster scanning, small-angle X-ray scattering (SAXS) has proven to be a valuable imaging technique of the nanoscale, for example of bone, teeth and brain matter. Although two-dimensional projection imaging has been used to characterize various materials successfully, its three-dimensional extension, SAXS computed tomography, poses substantial challenges, which have yet to be overcome. Previous work using SAXS computed tomography was unable to preserve oriented SAXS signals during reconstruction. Here we present a solution to this problem and obtain a complete SAXS computed tomography, which preserves oriented scattering information. By introducing virtual tomography axes, we take advantage of the two-dimensional SAXS information recorded on an area detector and use it to reconstruct the full three-dimensional scattering distribution in reciprocal space for each voxel of the three-dimensional object in real space. The presented method could be of interest for a combined six-dimensional real and reciprocal space characterization of mesoscopic materials with hierarchically structured features with length scales ranging from a few nanometres to a few millimetres--for example, biomaterials such as bone or teeth, or functional materials such as fuel-cell or battery components.
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
Categorization of new fractal carpets
International Nuclear Information System (INIS)
Rani, Mamta; Goel, Saurabh
2009-01-01
Sierpinski carpet is one of the very beautiful fractals from the historic gallery of classical fractals. Carpet designing is not only a fascinating activity in computer graphics, but it has real applications in carpet industry as well. One may find illusionary delighted carpets designed here, which are useful in real designing of carpets. In this paper, we attempt to systematize their generation and put them into categories. Each next category leads to a more generalized form of the fractal carpet.
Bilipschitz embedding of homogeneous fractals
Lü, Fan; Lou, Man-Li; Wen, Zhi-Ying; Xi, Li-Feng
2014-01-01
In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.
Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms
International Nuclear Information System (INIS)
Lawn, Marie-Amélie; Roth, Julien
2011-01-01
We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. This generalizes a recent work of the first author for spacelike immersed Lorentzian surfaces in ℝ 2,1 to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0, 2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.
Quantum theory of spinor field in four-dimensional Riemannian space-time
International Nuclear Information System (INIS)
Shavokhina, N.S.
1996-01-01
The review deals with the spinor field in the four-dimensional Riemannian space-time. The field beys the Dirac-Fock-Ivanenko equation. Principles of quantization of the spinor field in the Riemannian space-time are formulated which in a particular case of the plane space-time are equivalent to the canonical rules of quantization. The formulated principles are exemplified by the De Sitter space-time. The study of quantum field theory in the De Sitter space-time is interesting because it itself leads to a method of an invariant well for plane space-time. However, the study of the quantum spinor field theory in an arbitrary Riemannian space-time allows one to take into account the influence of the external gravitational field on the quantized spinor field. 60 refs
FONT DISCRIMINATIO USING FRACTAL DIMENSIONS
Directory of Open Access Journals (Sweden)
S. Mozaffari
2014-09-01
Full Text Available One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dimension was introduced in this paper for the first time. Our feature extraction methods which consider font recognition as texture identification are independent of document content. Experimental results on different pages written by several font types show that fractal geometry can overcome the complexities of font recognition problem.
International Nuclear Information System (INIS)
Chen, G.S.; Christenson, J.M.
1985-01-01
In this paper, the authors present some initial results from an investigation of the application of a locally one-dimensional (LOD) finite difference method to the solution of the two-dimensional, two-group reactor kinetics equations. Although the LOD method is relatively well known, it apparently has not been previously applied to the space-time kinetics equations. In this investigation, the LOD results were benchmarked against similar computational results (using the same computing environment, the same programming structure, and the same sample problems) obtained by the TWIGL program. For all of the problems considered, the LOD method provided accurate results in one-half to one-eight of the time required by the TWIGL program
Partially ordered sets, transfinite topology and the dimension of Cantorian-fractal spacetime
Energy Technology Data Exchange (ETDEWEB)
Marek-Crnjac, L. [Institute of Mathematics and Physics, University of Maribor (Slovenia)], E-mail: leila.marek@guest.arnes.si
2009-11-15
We introduce partially ordered sets and relate them to random Cantor sets of E-infinity theory. Subsequently we derive the dimensionality of Cantorian-fractal spacetime using posets and E-infinity transfinite Cantor sets.
Axes of resistance for tooth movement: does the center of resistance exist in 3-dimensional space?
Viecilli, Rodrigo F; Budiman, Amanda; Burstone, Charles J
2013-02-01
The center of resistance is considered the most important reference point for tooth movement. It is often stated that forces through this point will result in tooth translation. The purpose of this article is to report the results of numeric experiments testing the hypothesis that centers of resistance do not exist in space as 3-dimensional points, primarily because of the geometric asymmetry of the periodontal ligament. As an alternative theory, we propose that, for an arbitrary tooth, translation references can be determined by 2-dimensional projection intersections of 3-dimensional axes of resistance. Finite element analyses were conducted on a maxillary first molar model to determine the position of the axes of rotation generated by 3-dimensional couples. Translation tests were performed to compare tooth movement by using different combinations of axes of resistance as references. The couple-generated axes of rotation did not intersect in 3 dimensions; therefore, they do not determine a 3-dimensional center of resistance. Translation was obtained by using projection intersections of the 2 axes of resistance perpendicular to the force direction. Three-dimensional axes of resistance, or their 2-dimensional projection intersections, should be used to plan movement of an arbitrary tooth. Clinical approximations to a small 3-dimensional "center of resistance volume" might be adequate in nearly symmetric periodontal ligament cases. Copyright © 2013 American Association of Orthodontists. Published by Mosby, Inc. All rights reserved.
Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time
Energy Technology Data Exchange (ETDEWEB)
Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)
2014-11-15
This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)
Absolute continuity of autophage measures on finite-dimensional vector spaces
Energy Technology Data Exchange (ETDEWEB)
Raja, C R.E. [Stat-Math Unit, Indian Statistical Institute, Bangalore (India); [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)]. E-mail: creraja@isibang.ac.in
2002-06-01
We consider a class of measures called autophage which was introduced and studied by Szekely for measures on the real line. We show that the autophage measures on finite-dimensional vector spaces over real or Q{sub p} are infinitely divisible without idempotent factors and are absolutely continuous with bounded continuous density. We also show that certain semistable measures on such vector spaces are absolutely continuous. (author)
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation ... involving scaling and memory effects. But most of ..... begin by recalling the definition of the Riemann integral in ordinary calculus [33]. Let g: [a ...
An event driven algorithm for fractal cluster formation
González, S.; Thornton, Anthony Richard; Luding, Stefan
2010-01-01
A new cluster based event-driven algorithm is developed to simulate the formation of clusters in a two dimensional gas: particles move freely until they collide and "stick" together irreversibly. These clusters aggregate into bigger structures in an isotompic way, forming fractal structures whose
An event driven algorithm for fractal cluster formation
González, S.; Gonzalez Briones, Sebastián; Thornton, Anthony Richard; Luding, Stefan
2011-01-01
A new cluster based event-driven algorithm is developed to simulate the formation of clusters in a two dimensional gas: particles move freely until they collide and "stick" together irreversibly. These clusters aggregate into bigger structures in an isotompic way, forming fractal structures whose
Three dimensional monocular human motion analysis in end-effector space
DEFF Research Database (Denmark)
Hauberg, Søren; Lapuyade, Jerome; Engell-Nørregård, Morten Pol
2009-01-01
In this paper, we present a novel approach to three dimensional human motion estimation from monocular video data. We employ a particle filter to perform the motion estimation. The novelty of the method lies in the choice of state space for the particle filter. Using a non-linear inverse kinemati...
Large parallel volumes of finite and compact sets in d-dimensional Euclidean space
DEFF Research Database (Denmark)
Kampf, Jürgen; Kiderlen, Markus
The r-parallel volume V (Cr) of a compact subset C in d-dimensional Euclidean space is the volume of the set Cr of all points of Euclidean distance at most r > 0 from C. According to Steiner’s formula, V (Cr) is a polynomial in r when C is convex. For finite sets C satisfying a certain geometric...
The N=4 supersymmetric E8 gauge theory and coset space dimensional reduction
International Nuclear Information System (INIS)
Olive, D.; West, P.
1983-01-01
Reasons are given to suggest that the N=4 supersymmetric E 8 gauge theory be considered as a serious candidate for a physical theory. The symmetries of this theory are broken by a scheme based on coset space dimensional reduction. The resulting theory possesses four conventional generations of low-mass fermions together with their mirror particles. (orig.)
Quantum theory of string in the four-dimensional space-time
International Nuclear Information System (INIS)
Pron'ko, G.P.
1986-01-01
The Lorentz invariant quantum theory of string is constructed in four-dimensional space-time. Unlike the traditional approach whose result was breaking of Lorentz invariance, our method is based on the usage of other variables for description of string configurations. The method of an auxiliary spectral problem for periodic potentials is the main tool in construction of these new variables
Faster exact algorithms for computing Steiner trees in higher dimensional Euclidean spaces
DEFF Research Database (Denmark)
Fonseca, Rasmus; Brazil, Marcus; Winter, Pawel
The Euclidean Steiner tree problem asks for a network of minimum total length interconnecting a finite set of points in d-dimensional space. For d ≥ 3, only one practical algorithmic approach exists for this problem --- proposed by Smith in 1992. A number of refinements of Smith's algorithm have...
Modeling Dispersion of Chemical-Biological Agents in Three Dimensional Living Space
International Nuclear Information System (INIS)
William S. Winters
2002-01-01
This report documents a series of calculations designed to demonstrate Sandia's capability in modeling the dispersal of chemical and biological agents in complex three-dimensional spaces. The transport of particles representing biological agents is modeled in a single room and in several connected rooms. The influence of particle size, particle weight and injection method are studied
Collapsing perfect fluid in self-similar five dimensional space-time and cosmic censorship
International Nuclear Information System (INIS)
Ghosh, S.G.; Sarwe, S.B.; Saraykar, R.V.
2002-01-01
We investigate the occurrence and nature of naked singularities in the gravitational collapse of a self-similar adiabatic perfect fluid in a five dimensional space-time. The naked singularities are found to be gravitationally strong in the sense of Tipler and thus violate the cosmic censorship conjecture
Three-dimensional space: locomotory style explains memory differences in rats and hummingbirds.
Flores-Abreu, I Nuri; Hurly, T Andrew; Ainge, James A; Healy, Susan D
2014-06-07
While most animals live in a three-dimensional world, they move through it to different extents depending on their mode of locomotion: terrestrial animals move vertically less than do swimming and flying animals. As nearly everything we know about how animals learn and remember locations in space comes from two-dimensional experiments in the horizontal plane, here we determined whether the use of three-dimensional space by a terrestrial and a flying animal was correlated with memory for a rewarded location. In the cubic mazes in which we trained and tested rats and hummingbirds, rats moved more vertically than horizontally, whereas hummingbirds moved equally in the three dimensions. Consistent with their movement preferences, rats were more accurate in relocating the horizontal component of a rewarded location than they were in the vertical component. Hummingbirds, however, were more accurate in the vertical dimension than they were in the horizontal, a result that cannot be explained by their use of space. Either as a result of evolution or ontogeny, it appears that birds and rats prioritize horizontal versus vertical components differently when they remember three-dimensional space.
Nonrenormalizable quantum field models in four-dimensional space-time
International Nuclear Information System (INIS)
Raczka, R.
1978-01-01
The construction of no-cutoff Euclidean Green's functions for nonrenormalizable interactions L/sub I/(phi) = lambda∫ddelta (epsilon): expepsilonphi: in four-dimensional space-time is carried out. It is shown that all axioms for the generating functional of the Euclidean Green's function are satisfied except perhaps SO(4) invariance
Hyper dimensional phase-space solver and its application to laser-matter
Energy Technology Data Exchange (ETDEWEB)
Kondoh, Yoshiaki; Nakamura, Takashi; Yabe, Takashi [Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, Kanagawa (Japan)
2000-03-01
A new numerical scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space is described. At each time step, the distribution function and its first derivatives are advected in phase space by the Cubic Interpolated Propagation (CIP) scheme. Although a cell within grid points is interpolated by a cubic-polynomial, any matrix solutions are not required. The scheme guarantees the exact conservation of the mass. The numerical results show good agreement with the theory. Even if we reduce the number of grid points in the v-direction, the scheme still gives stable, accurate and reasonable results with memory storage comparable to particle simulations. Owing to this fact, the scheme has succeeded to be generalized in a straightforward way to deal with the six-dimensional, or full-dimensional problems. (author)
On renormalisation of the quantum stress tensor in curved space-time by dimensional regularisation
International Nuclear Information System (INIS)
Bunch, T.S.
1979-01-01
Using dimensional regularisation, a prescription is given for obtaining a finite renormalised stress tensor in curved space-time. Renormalisation is carried out by renormalising coupling constants in the n-dimensional Einstein equation generalised to include tensors which are fourth order in derivatives of the metric. Except for the special case of a massless conformal field in a conformally flat space-time, this procedure is not unique. There exists an infinite one-parameter family of renormalisation ansatze differing from each other in the finite renormalisation that takes place. Nevertheless, the renormalised stress tensor for a conformally invariant field theory acquires a nonzero trace which is independent of the renormalisation ansatz used and which has a value in agreement with that obtained by other methods. A comparison is made with some earlier work using dimensional regularisation which is shown to be in error. (author)
Hyper dimensional phase-space solver and its application to laser-matter
International Nuclear Information System (INIS)
Kondoh, Yoshiaki; Nakamura, Takashi; Yabe, Takashi
2000-01-01
A new numerical scheme for solving the hyper-dimensional Vlasov-Poisson equation in phase space is described. At each time step, the distribution function and its first derivatives are advected in phase space by the Cubic Interpolated Propagation (CIP) scheme. Although a cell within grid points is interpolated by a cubic-polynomial, any matrix solutions are not required. The scheme guarantees the exact conservation of the mass. The numerical results show good agreement with the theory. Even if we reduce the number of grid points in the v-direction, the scheme still gives stable, accurate and reasonable results with memory storage comparable to particle simulations. Owing to this fact, the scheme has succeeded to be generalized in a straightforward way to deal with the six-dimensional, or full-dimensional problems. (author)
Fractals and multifractals in physics
International Nuclear Information System (INIS)
Arcangelis, L. de.
1987-01-01
We present a general introduction to the world of fractals. The attention is mainly devoted to stress how fractals do indeed appear in the real world and to find quantitative methods for characterizing their properties. The idea of multifractality is also introduced and it is presented in more details within the framework of the percolation problem
Simoson, Andrew J.
2009-01-01
This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)
Turbulent wakes of fractal objects
Staicu, A.D.; Mazzi, B.; Vassilicos, J.C.; Water, van de W.
2003-01-01
Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density.
Distribution of high-dimensional entanglement via an intra-city free-space link.
Steinlechner, Fabian; Ecker, Sebastian; Fink, Matthias; Liu, Bo; Bavaresco, Jessica; Huber, Marcus; Scheidl, Thomas; Ursin, Rupert
2017-07-24
Quantum entanglement is a fundamental resource in quantum information processing and its distribution between distant parties is a key challenge in quantum communications. Increasing the dimensionality of entanglement has been shown to improve robustness and channel capacities in secure quantum communications. Here we report on the distribution of genuine high-dimensional entanglement via a 1.2-km-long free-space link across Vienna. We exploit hyperentanglement, that is, simultaneous entanglement in polarization and energy-time bases, to encode quantum information, and observe high-visibility interference for successive correlation measurements in each degree of freedom. These visibilities impose lower bounds on entanglement in each subspace individually and certify four-dimensional entanglement for the hyperentangled system. The high-fidelity transmission of high-dimensional entanglement under real-world atmospheric link conditions represents an important step towards long-distance quantum communications with more complex quantum systems and the implementation of advanced quantum experiments with satellite links.
Nomura, A; Yamazaki, Y; Tsuji, T; Kawasaki, Y; Tanaka, S
1996-09-15
For all biological particles such as cells or cellular organelles, there are three-dimensional coordinates representing the centroid or center of gravity. These coordinates and other numerical parameters such as volume, fluorescence intensity, surface area, and shape are referred to in this paper as geometric properties, which may provide critical information for the clarification of in situ mechanisms of molecular and cellular functions in living organisms. We have established a method for the elucidation of these properties, designated the three-dimensional labeling program (3DLP). Algorithms of 3DLP are so simple that this method can be carried out through the use of software combinations in image analysis on a personal computer. To evaluate 3DLP, it was applied to a 32-cell-stage sea urchin embryo, double stained with FITC for cellular protein of blastomeres and propidium iodide for nuclear DNA. A stack of optical serial section images was obtained by confocal laser scanning microscopy. The method was found effective for determining geometric properties and should prove applicable to the study of many different kinds of biological particles in three-dimensional space.
International Nuclear Information System (INIS)
Sumadi A H A; H, Zainuddin
2014-01-01
Using Isham's group-theoretic quantization scheme, we construct the canonical groups of the systems on the two-dimensional sphere and one-dimensional complex projective space, which are homeomorphic. In the first case, we take SO(3) as the natural canonical Lie group of rotations of the two-sphere and find all the possible Hamiltonian vector fields, and followed by verifying the commutator and Poisson bracket algebra correspondences with the Lie algebra of the group. In the second case, the same technique is resumed to define the Lie group, in this case SU (2), of CP'.We show that one can simply use a coordinate transformation from S 2 to CP 1 to obtain all the Hamiltonian vector fields of CP 1 . We explicitly show that the Lie algebra structures of both canonical groups are locally homomorphic. On the other hand, globally their corresponding canonical groups are acting on different geometries, the latter of which is almost complex. Thus the canonical group for CP 1 is the double-covering group of SO(3), namely SU(2). The relevance of the proposed formalism is to understand the idea of CP 1 as a space of where the qubit lives which is known as a Bloch sphere
Contour fractal analysis of grains
Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB
2017-06-01
Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.
Self-dual phase space for (3 +1 )-dimensional lattice Yang-Mills theory
Riello, Aldo
2018-01-01
I propose a self-dual deformation of the classical phase space of lattice Yang-Mills theory, in which both the electric and magnetic fluxes take value in the compact gauge Lie group. A local construction of the deformed phase space requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which is reviewed here. The results is a full-fledged finite-dimensional and gauge-invariant phase space, the self-duality properties of which are largely enhanced in (3 +1 ) spacetime dimensions. This enhancement is due to a correspondence with the moduli space of an auxiliary noncommutative flat connection living on a Riemann surface defined from the lattice itself, which in turn equips the duality between electric and magnetic fluxes with a neat geometrical interpretation in terms of a Heegaard splitting of the space manifold. Finally, I discuss the consequences of the proposed deformation on the quantization of the phase space, its quantum gravitational interpretation, as well as its relevance for the construction of (3 +1 )-dimensional topological field theories with defects.
Fractal diffusion coefficient from dynamical zeta functions
Energy Technology Data Exchange (ETDEWEB)
Cristadoro, Giampaolo [Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, D 01187 Dresden (Germany)
2006-03-10
Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero. (letter to the editor)
Fractal diffusion coefficient from dynamical zeta functions
International Nuclear Information System (INIS)
Cristadoro, Giampaolo
2006-01-01
Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero. (letter to the editor)
Fractals: Giant impurity nonlinearities in optics of fractal clusters
International Nuclear Information System (INIS)
Butenko, A.V.; Shalaev, V.M.; Stockman, M.I.
1988-01-01
A theory of nonlinear optical properties of fractals is developed. Giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal. This enhancement occurs if the exciting radiation frequency lies within the absorption band of the fractal. The giant optical nonlinearities are due to existence of high local electric fields in the sites of impurity locations. Such fields are due to the inhomogeneously broadened character of a fractal spectrum, i.e. partial conservation of individuality of fractal-forming particles (monomers). The field enhancement is proportional to the Q-factor of the resonance of a monomer. The effects of coherent anti-Stokes Raman scattering (CARS) and phase conjugation (PC) of light waves are enhanced to a much greater degree than generation of higher harmonics. In a general case the susceptibility of a higher-order is enhanced in the maximum way if the process includes ''subtraction'' of photons (at least one of the strong field frequencies enters the susceptibility with the minus sign). Alternatively, enhancement for the highest-order harmonic generation (when all the photons are ''accumulated'') is minimal. The predicted phenomena bear information on spectral properties of both impurity molecules and a fractal. In particular, in the CARS spectra a narrow (with the natural width) resonant structure, which is proper to an isolated monomer of a fractal, is predicted to be observed. (orig.)
International Nuclear Information System (INIS)
Terauchi, Masami; Takahashi, Mariko; Tanaka, Michiyoshi
1994-01-01
The convergent-beam electron diffraction (CBED) method for determining three-dimensional space groups is extended to the determination of the (3 + 1)-dimensional space groups for one-dimensional incommensurately modulated crystals. It is clarified than an approximate dynamical extinction line appears in the CBED discs of the reflections caused by an incommensurate modulation. The extinction enables the space-group determination of the (3 + 1)-dimensional crystals or the one-dimensional incommensurately modulated crystals. An example of the dynamical extinction line is shown using an incommensurately modulated crystal of Sr 2 Nb 2 O 7 . Tables of the dynamical extinction lines appearing in CBED patterns are given for all the (3 + 1)-dimensional space groups of the incommensurately modulated crystal. (orig.)
Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests
International Nuclear Information System (INIS)
Zilhao, Miguel; Herdeiro, Carlos; Witek, Helvi; Nerozzi, Andrea; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo
2010-01-01
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.
Fractal Analysis of Mobile Social Networks
International Nuclear Information System (INIS)
Zheng Wei; Pan Qian; Sun Chen; Deng Yu-Fan; Zhao Xiao-Kang; Kang Zhao
2016-01-01
Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks (MSNs) are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs. (paper)
Time-dependent gravitating solitons in five dimensional warped space-times
Giovannini, Massimo
2007-01-01
Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for fixed value of the conformal time coordinate. Time dependent solutions containing both topological and non-topological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multi-soliton solutions may describe time-dependent kink-antikink systems.
International Nuclear Information System (INIS)
Jack, B.; Leach, J.; Franke-Arnold, S.; Ireland, D. G.; Padgett, M. J.; Yao, A. M.; Barnett, S. M.; Romero, J.
2010-01-01
We use spatial light modulators (SLMs) to measure correlations between arbitrary superpositions of orbital angular momentum (OAM) states generated by spontaneous parametric down-conversion. Our technique allows us to fully access a two-dimensional OAM subspace described by a Bloch sphere, within the higher-dimensional OAM Hilbert space. We quantify the entanglement through violations of a Bell-type inequality for pairs of modal superpositions that lie on equatorial, polar, and arbitrary great circles of the Bloch sphere. Our work shows that SLMs can be used to measure arbitrary spatial states with a fidelity sufficient for appropriate quantum information processing systems.
Navigation performance in virtual environments varies with fractal dimension of landscape.
Juliani, Arthur W; Bies, Alexander J; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E
2016-09-01
Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.
Fractal apertures in waveguides, conducting screens and cavities analysis and design
Ghosh, Basudeb; Kartikeyan, M V
2014-01-01
This book deals with the design and analysis of fractal apertures in waveguides, conducting screens and cavities using numerical electromagnetics and field-solvers. The aim is to obtain design solutions with improved accuracy for a wide range of applications. To achieve this goal, a few diverse problems are considered. The book is organized with adequate space dedicated for the design and analysis of fractal apertures in waveguides, conducting screens, and cavities, microwave/millimeter wave applications followed by detailed case-study problems to infuse better insight and understanding of the subject. Finally, summaries and suggestions are given for future work. Fractal geometries were widely used in electromagnetics, specifically for antennas and frequency selective surfaces (FSS). The self-similarity of fractal geometry gives rise to a multiband response, whereas the space-filling nature of the fractal geometries makes it an efficient element in antenna and FSS unit cell miniaturization. Until now, no e...
Directory of Open Access Journals (Sweden)
Cahill R. T.
2014-10-01
Full Text Available Space speed fluctuations, which have a 1 / f spectrum, are shown to be the cause of solar flares. The direction and magnitude of the space flow has been detected from numer- ous different experimental techniques, and is close to the normal to the plane of the ecliptic. Zener diode data shows that the fluctuations in the space speed closely match the Sun Solar Cycle 23 flare count, and reveal that major solar flares follow major space speed fluctuations by some 6 days. This implies that a warning period of some 5 days in predicting major solar flares is possible using such detectors. This has significant conse- quences in being able to protect various spacecraft and Earth located electrical systems from the subsequent arrival of ejected plasma from a solar flare. These space speed fluctuations are the actual gravitational waves, and have a significant magnitude. This discovery is a significant application of the dynamical space phenomenon and theory. We also show that space flow turbulence impacts on the Earth’s climate, as such tur- bulence can input energy into systems, which is the basis of the Zener Diode Quantum Detector. Large scale space fluctuations impact on both the sun and the Earth, and as well explain temperature correlations with solar activity, but that the Earth temperatures are not caused by such solar activity. This implies that the Earth climate debate has been missing a key physical process. Observed diminishing gravitational waves imply a cooling epoch for the Earth for the next 30 years.
Dimensionality analysis of multiparticle production at high energies
International Nuclear Information System (INIS)
Chilingaryan, A.A.
1989-01-01
An algorithm of analysis of multiparticle final states is offered. By the Renyi dimensionalities, which were calculated according to experimental data, though it were hadron distribution over the rapidity intervals or particle distribution in an N-dimensional momentum space, we can judge about the degree of correlation of particles, separate the momentum space projections and areas where the probability measure singularities are observed. The method is tested in a series of calculations with samples of fractal object points and with samples obtained by means of different generators of pseudo- and quasi-random numbers. 27 refs.; 11 figs
Fractal analysis of sulphidic mineral
Directory of Open Access Journals (Sweden)
Miklúová Viera
2002-03-01
Full Text Available In this paper, the application of fractal theory in the characterization of fragmented surfaces, as well as the mass-size distributions are discussed. The investigated mineral-chalcopyrite of Slovak provenience is characterised after particle size reduction processes-crushing and grinding. The problem how the different size reduction methods influence the surface irregularities of obtained particles is solved. Mandelbrot (1983, introducing the fractal geometry, offered a new way of characterization of surface irregularities by the fractal dimension. The determination of the surface fractal dimension DS consists in measuring the specific surface by the BET method in several fractions into which the comminuted chalcopyrite is sieved. This investigation shows that the specific surface of individual fractions were higher for the crushed sample than for the short-term (3 min ground sample. The surface fractal dimension can give an information about the adsorption sites accessible to molecules of nitrogen and according to this, the value of the fractal dimension is higher for crushed sample.The effect of comminution processes on the mass distribution of particles crushed and ground in air as well as in polar liquids is also discussed. The estimation of fractal dimensions of particles mass distribution is done on the assumption that the particle size distribution is described by the power-law (1. The value of fractal dimension for the mass distribution in the crushed sample is lower than in the sample ground in air, because it is influenced by the energy required for comminution.The sample of chalcopyrite was ground (10min in ethanol and i-butanol [which according to Ikazaki (1991] are characterized by the parameter µ /V, where µ is its dipole moment and V is the molecular volume. The values of µ /V for the used polar liquids are of the same order. That is why the expressive differences in particle size distributions as well as in the values of
Moghilevsky, Débora Estela
2011-01-01
A lo largo de los últimos años del siglo veinte se ha desarrollado la teoría de la complejidad. Este modelo relaciona las ciencias duras tales como la matemática, la teoría del caos, la física cuántica y la geometría fractal con las llamadas seudo ciencias. Dentro de este contexto podemos definir la Psicología Fractal como la ciencia que estudia los aspectos psíquicos como dinámicamente fractales.
Energy Technology Data Exchange (ETDEWEB)
Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)
2014-12-01
In this paper we ask whether the wormhole solutions exist in different dimensional noncommutativity-inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point-like object by a smeared object. Here we have chosen the Lorentzian distribution as the density function in the noncommutativity-inspired spacetime. We have observed that the wormhole solutions exist only in four and five dimensions; however, in higher than five dimensions no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In the usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Breban, Romulus [Institut Pasteur, Paris Cedex 15 (France)
2016-09-15
Five-dimensional (5D) space-time symmetry greatly facilitates how a 4D observer perceives the propagation of a single spinless particle in a 5D space-time. In particular, if the 5D geometry is independent of the fifth coordinate then the 5D physics may be interpreted as 4D quantum mechanics. In this work we address the case where the symmetry is approximate, focusing on the case where the 5D geometry depends weakly on the fifth coordinate. We show that concepts developed for the case of exact symmetry approximately hold when other concepts such as decaying quantum states, resonant quantum scattering, and Stokes drag are adopted, as well. We briefly comment on the optical model of the nuclear interactions and Millikan's oil drop experiment. (orig.)
Quantization of coset space σ-models coupled to two-dimensional gravity
International Nuclear Information System (INIS)
Korotkin, D.; Samtleben, H.
1996-07-01
The mathematical framework for an exact quantization of the two-dimensional coset space σ-models coupled to dilaton gravity, that arise from dimensional reduction of gravity and supergravity theories, is presented. The two-time Hamiltonian formulation is obtained, which describes the complete phase space of the model in the whole isomonodromic sector. The Dirac brackets arising from the coset constraints are calculated. Their quantization allows to relate exact solutions of the corresponding Wheeler-DeWitt equations to solutions of a modified (Coset) Knizhnik-Zamolodchikov system. On the classical level, a set of observables is identified, that is complete for essential sectors of the theory. Quantum counterparts of these observables and their algebraic structure are investigated. Their status in alternative quantization procedures is discussed, employing the link with Hamiltonian Chern-Simons theory. (orig.)
Room Scanner representation and measurement of three-dimensional spaces using a smartphone
International Nuclear Information System (INIS)
Bejarano Rodriguez, Mauricio
2013-01-01
An algorithm was designed to measure and represent three-dimensional spaces using the resources available on a smartphone. The implementation of the fusion sensor has enabled to use basic trigonometry to calculate the lengths of the walls and the corners of the room. The OpenGL library was used to create and visualize the three-dimensional model of the measured internal space. A library was created to export the represented model to other commercial formats. A certain level of degradation is obtained once an attempt is made to measure long distances because the algorithm depends on the degree of inclination of the smarthphone to perform the measurements. For this reason, at higher elevations are obtained more accurate measurements. The capture process was changed in order to correct the margin of error to measure soccer field. The algorithm has recorded measurements less than 3% margin of error through the process of subdividing the measurement area. (author) [es
Eigenmodes of three-dimensional spherical spaces and their application to cosmology
International Nuclear Information System (INIS)
Lehoucq, Roland; Weeks, Jeffrey; Uzan, Jean-Philippe; Gausmann, Evelise; Luminet, Jean-Pierre
2002-01-01
This paper investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented. Three complementary numerical methods are developed and compared with our analytic results and previous investigations. The cosmological applications of these results are discussed, focusing on the cosmic microwave background (CMB) anisotropies. In particular, whereas in the Euclidean case too-small universes are excluded by present CMB data, in the spherical case, candidate topologies will always exist even if the total energy density parameter of the universe is very close to unity
Eigenmodes of three-dimensional spherical spaces and their application to cosmology
Energy Technology Data Exchange (ETDEWEB)
Lehoucq, Roland [CE-Saclay, DSM/DAPNIA/Service d' Astrophysique, F-91191 Gif sur Yvette (France); Weeks, Jeffrey [15 Farmer St, Canton, NY 13617-1120 (United States); Uzan, Jean-Philippe [Institut d' Astrophysique de Paris, GReCO, CNRS-FRE 2435, 98 bis, Bd Arago, 75014 Paris (France); Gausmann, Evelise [Instituto de Fisica Teorica, Rua Pamplona, 145 Bela Vista - Sao Paulo - SP, CEP 01405-900 (Brazil); Luminet, Jean-Pierre [Laboratoire Univers et Theories, CNRS-FRE 2462, Observatoire de Paris, F-92195 Meudon (France)
2002-09-21
This paper investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented. Three complementary numerical methods are developed and compared with our analytic results and previous investigations. The cosmological applications of these results are discussed, focusing on the cosmic microwave background (CMB) anisotropies. In particular, whereas in the Euclidean case too-small universes are excluded by present CMB data, in the spherical case, candidate topologies will always exist even if the total energy density parameter of the universe is very close to unity.
Dynamics of a neuron model in different two-dimensional parameter-spaces
Rech, Paulo C.
2011-03-01
We report some two-dimensional parameter-space diagrams numerically obtained for the multi-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and we show that regardless of the combination of parameters, a typical scenario is preserved: for all choice of two parameters, the parameter-space presents a comb-shaped chaotic region immersed in a large periodic region. We also show that exist regions close these chaotic region, separated by the comb teeth, organized themselves in period-adding bifurcation cascades.
Optical asymmetric cryptography using a three-dimensional space-based model
International Nuclear Information System (INIS)
Chen, Wen; Chen, Xudong
2011-01-01
In this paper, we present optical asymmetric cryptography combined with a three-dimensional (3D) space-based model. An optical multiple-random-phase-mask encoding system is developed in the Fresnel domain, and one random phase-only mask and the plaintext are combined as a series of particles. Subsequently, the series of particles is translated along an axial direction, and is distributed in a 3D space. During image decryption, the robustness and security of the proposed method are further analyzed. Numerical simulation results are presented to show the feasibility and effectiveness of the proposed optical image encryption method
The new Big Bang Theory according to dimensional continuous space-time theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2014-01-01
This New View of the Big Bang Theory results from the Dimensional Continuous Space-Time Theory, for which the introduction was presented in [1]. This theory is based on the concept that the primitive Universe before the Big Bang was constituted only from elementary cells of potential energy disposed side by side. In the primitive Universe there were no particles, charges, movement and the Universe temperature was absolute zero Kelvin. The time was always present, even in the primitive Universe, time is the integral part of the empty space, it is the dynamic energy of space and it is responsible for the movement of matter and energy inside the Universe. The empty space is totally stationary; the primitive Universe was infinite and totally occupied by elementary cells of potential energy. In its event, the Big Bang started a production of matter, charges, energy liberation, dynamic movement, temperature increase and the conformation of galaxies respecting a specific formation law. This article presents the theoretical formation of the Galaxies starting from a basic equation of the Dimensional Continuous Space-time Theory.
Price-Jones, Natalie; Bovy, Jo
2018-03-01
Chemical tagging of stars based on their similar compositions can offer new insights about the star formation and dynamical history of the Milky Way. We investigate the feasibility of identifying groups of stars in chemical space by forgoing the use of model derived abundances in favour of direct analysis of spectra. This facilitates the propagation of measurement uncertainties and does not pre-suppose knowledge of which elements are important for distinguishing stars in chemical space. We use ˜16 000 red giant and red clump H-band spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and perform polynomial fits to remove trends not due to abundance-ratio variations. Using expectation maximized principal component analysis, we find principal components with high signal in the wavelength regions most important for distinguishing between stars. Different subsamples of red giant and red clump stars are all consistent with needing about 10 principal components to accurately model the spectra above the level of the measurement uncertainties. The dimensionality of stellar chemical space that can be investigated in the H band is therefore ≲10. For APOGEE observations with typical signal-to-noise ratios of 100, the number of chemical space cells within which stars cannot be distinguished is approximately 1010±2 × (5 ± 2)n - 10 with n the number of principal components. This high dimensionality and the fine-grained sampling of chemical space are a promising first step towards chemical tagging based on spectra alone.
The New Big Bang Theory according to Dimensional Continuous Space-Time Theory
Martini, Luiz Cesar
2014-04-01
This New View of the Big Bang Theory results from the Dimensional Continuous Space-Time Theory, for which the introduction was presented in [1]. This theory is based on the concept that the primitive Universe before the Big Bang was constituted only from elementary cells of potential energy disposed side by side. In the primitive Universe there were no particles, charges, movement and the Universe temperature was absolute zero Kelvin. The time was always present, even in the primitive Universe, time is the integral part of the empty space, it is the dynamic energy of space and it is responsible for the movement of matter and energy inside the Universe. The empty space is totally stationary; the primitive Universe was infinite and totally occupied by elementary cells of potential energy. In its event, the Big Bang started a production of matter, charges, energy liberation, dynamic movement, temperature increase and the conformation of galaxies respecting a specific formation law. This article presents the theoretical formation of the Galaxies starting from a basic equation of the Dimensional Continuous Space-time Theory.
Directory of Open Access Journals (Sweden)
WANG Ling
2007-08-01
Full Text Available The solidification microstructure and fractal characteristics of the solid-liquid interfaces of Inconel 718, under different cooling rates during directional solidification, were investigated by using SEM. Results showed that 5 μm/s was the cellular-dendrite transient rate. The prime dendrite arm spacing (PDAS was measured by Image Tool and it decreased with the cooling rate increased. The fractal dimension of the interfaces was calculated and it changes from 1.204310 to 1.517265 with the withdrawal rate ranging from 10 to 100 μm/s. The physical significance of the fractal dimension was analyzed by using fractal theory. It was found that the fractal dimension of the dendrites can be used to describe the solidification microstructure and parameters at low cooling rate, but both the fractal dimension and the dendrite arm spacing are needed in order to integrally describe the evaluation of the solidification microstructure completely.
Three-dimensional theory for interaction between atomic ensembles and free-space light
International Nuclear Information System (INIS)
Duan, L.-M.; Cirac, J.I.; Zoller, P.
2002-01-01
Atomic ensembles have shown to be a promising candidate for implementations of quantum information processing by many recently discovered schemes. All these schemes are based on the interaction between optical beams and atomic ensembles. For description of these interactions, one assumed either a cavity-QED model or a one-dimensional light propagation model, which is still inadequate for a full prediction and understanding of most of the current experimental efforts that are actually taken in the three-dimensional free space. Here, we propose a perturbative theory to describe the three-dimensional effects in interaction between atomic ensembles and free-space light with a level configuration important for several applications. The calculations reveal some significant effects that were not known before from the other approaches, such as the inherent mode-mismatching noise and the optimal mode-matching conditions. The three-dimensional theory confirms the collective enhancement of the signal-to-noise ratio which is believed to be one of the main advantages of the ensemble-based quantum information processing schemes, however, it also shows that this enhancement needs to be understood in a more subtle way with an appropriate mode-matching method
Method of solving conformal models in D-dimensional space I
International Nuclear Information System (INIS)
Fradkin, E.S.; Palchik, M.Y.
1996-01-01
We study the Hilbert space of conformal field theory in D-dimensional space. The latter is shown to have model-independent structure. The states of matter fields and gauge fields form orthogonal subspaces. The dynamical principle fixing the choice of model may be formulated either in each of these subspaces or in their direct sum. In the latter case, gauge interactions are necessarily present in the model. We formulate the conditions specifying the class of models where gauge interactions are being neglected. The anomalous Ward identities are derived. Different values of anomalous parameters (D-dimensional analogs of a central charge, including operator ones) correspond to different models. The structure of these models is analogous to that of 2-dimensional conformal theories. Each model is specified by D-dimensional analog of null vector. The exact solutions of the simplest models of this type are examined. It is shown that these models are equivalent to Lagrangian models of scalar fields with a triple interaction. The values of dimensions of such fields are calculated, and the closed sets of differential equations for higher Green functions are derived. Copyright copyright 1996 Academic Press, Inc
Development of the three dimensional flow model in the SPACE code
International Nuclear Information System (INIS)
Oh, Myung Taek; Park, Chan Eok; Kim, Shin Whan
2014-01-01
SPACE (Safety and Performance Analysis CodE) is a nuclear plant safety analysis code, which has been developed in the Republic of Korea through a joint research between the Korean nuclear industry and research institutes. The SPACE code has been developed with multi-dimensional capabilities as a requirement of the next generation safety code. It allows users to more accurately model the multi-dimensional flow behavior that can be exhibited in components such as the core, lower plenum, upper plenum and downcomer region. Based on generalized models, the code can model any configuration or type of fluid system. All the geometric quantities of mesh are described in terms of cell volume, centroid, face area, and face center, so that it can naturally represent not only the one dimensional (1D) or three dimensional (3D) Cartesian system, but also the cylindrical mesh system. It is possible to simulate large and complex domains by modelling the complex parts with a 3D approach and the rest of the system with a 1D approach. By 1D/3D co-simulation, more realistic conditions and component models can be obtained, providing a deeper understanding of complex systems, and it is expected to overcome the shortcomings of 1D system codes. (author)
Free massless fermionic fields of arbitrary spin in d-dimensional anti-de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Vasiliev, M A
1988-04-25
Free massless fermionic fields of arbitrary spins, corresponding to fully symmetric tensor-spinor irreducible representations of the flat little group SO(d-2), are described in d-dimensional anti-de Sitter space in terms of differential forms. Appropriate linearized higher-spin curvature 2-forms are found. Explicitly gauge invariant higher-spin actions are constructed in terms of these linearized curvatures.
Quantum limits to information about states for finite dimensional Hilbert space
International Nuclear Information System (INIS)
Jones, K.R.W.
1990-01-01
A refined bound for the correlation information of an N-trial apparatus is developed via an heuristic argument for Hilbert spaces of arbitrary finite dimensionality. Conditional upon the proof of an easily motivated inequality it was possible to find the optimal apparatus for large ensemble quantum Inference, thereby solving the asymptotic optimal state determination problem. In this way an alternative inferential uncertainty principle, is defined which is then contrasted with the usual Heisenberg uncertainty principle. 6 refs
International Nuclear Information System (INIS)
Raczka, R.
1979-01-01
Construction of non-cutoff Euclidean Green's functions for nonrenormalizable interactions Lsub(I)(phi)=lambda∫dσ(epsilon):expepsilonphi: in four-dimensional space-time is presented. It is shown that all axioms for the generating functional of E.G.F. are satisfied except perhaps the SO(4) invariance. It is shown that the singularities of E.G.F. for coinciding points are not worse than those of the free theory. (author)
Efficient and accurate nearest neighbor and closest pair search in high-dimensional space
Tao, Yufei
2010-07-01
Nearest Neighbor (NN) search in high-dimensional space is an important problem in many applications. From the database perspective, a good solution needs to have two properties: (i) it can be easily incorporated in a relational database, and (ii) its query cost should increase sublinearly with the dataset size, regardless of the data and query distributions. Locality-Sensitive Hashing (LSH) is a well-known methodology fulfilling both requirements, but its current implementations either incur expensive space and query cost, or abandon its theoretical guarantee on the quality of query results. Motivated by this, we improve LSH by proposing an access method called the Locality-Sensitive B-tree (LSB-tree) to enable fast, accurate, high-dimensional NN search in relational databases. The combination of several LSB-trees forms a LSB-forest that has strong quality guarantees, but improves dramatically the efficiency of the previous LSH implementation having the same guarantees. In practice, the LSB-tree itself is also an effective index which consumes linear space, supports efficient updates, and provides accurate query results. In our experiments, the LSB-tree was faster than: (i) iDistance (a famous technique for exact NN search) by two orders ofmagnitude, and (ii) MedRank (a recent approximate method with nontrivial quality guarantees) by one order of magnitude, and meanwhile returned much better results. As a second step, we extend our LSB technique to solve another classic problem, called Closest Pair (CP) search, in high-dimensional space. The long-term challenge for this problem has been to achieve subquadratic running time at very high dimensionalities, which fails most of the existing solutions. We show that, using a LSB-forest, CP search can be accomplished in (worst-case) time significantly lower than the quadratic complexity, yet still ensuring very good quality. In practice, accurate answers can be found using just two LSB-trees, thus giving a substantial
Gauge fields in nonlinear group realizations involving two-dimensional space-time symmetry
International Nuclear Information System (INIS)
Machacek, M.E.; McCliment, E.R.
1975-01-01
It is shown that gauge fields may be consistently introduced into a model Lagrangian previously considered by the authors. The model is suggested by the spontaneous breaking of a Lorentz-type group into a quasiphysical two-dimensional space-time and one internal degree of freedom, loosely associated with charge. The introduction of zero-mass gauge fields makes possible the absorption via the Higgs mechanism of the Goldstone fields that appear in the model despite the fact that the Goldstone fields do not transform as scalars. Specifically, gauge invariance of the Yang-Mills type requires the introduction of two sets of massless gauge fields. The transformation properties in two-dimensional space-time suggest that one set is analogous to a charge doublet that behaves like a second-rank tensor in real four-dimensional space time. The other set suggests a spin-one-like charge triplet. Via the Higgs mechanism, the first set absorbs the Goldstone fields and acquires mass. The second set remains massless. If massive gauge fields are introduced, the associated currents are not conserved and the Higgs mechanism is no longer fully operative. The Goldstone fields are not eliminated, but coupling between the Goldstone fields and the gauge fields does shift the mass of the antisymmetric second-rank-tensor gauge field components
State-space dimensionality in short-memory hidden-variable theories
International Nuclear Information System (INIS)
Montina, Alberto
2011-01-01
Recently we have presented a hidden-variable model of measurements for a qubit where the hidden-variable state-space dimension is one-half the quantum-state manifold dimension. The absence of a short memory (Markov) dynamics is the price paid for this dimensional reduction. The conflict between having the Markov property and achieving the dimensional reduction was proved by Montina [A. Montina, Phys. Rev. A 77, 022104 (2008)] using an additional hypothesis of trajectory relaxation. Here we analyze in more detail this hypothesis introducing the concept of invertible process and report a proof that makes clearer the role played by the topology of the hidden-variable space. This is accomplished by requiring suitable properties of regularity of the conditional probability governing the dynamics. In the case of minimal dimension the set of continuous hidden variables is identified with an object living an N-dimensional Hilbert space whose dynamics is described by the Schroedinger equation. A method for generating the economical non-Markovian model for the qubit is also presented.
The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction.
Najafi, Elham; Darooneh, Amir H
2015-01-01
A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.
The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction
Najafi, Elham; Darooneh, Amir H.
2015-01-01
A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction. PMID:26091207
Map of fluid flow in fractal porous medium into fractal continuum flow.
Balankin, Alexander S; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Thermal transport in fractal systems
DEFF Research Database (Denmark)
Kjems, Jørgen
1992-01-01
Recent experiments on the thermal transport in systems with partial fractal geometry, silica aerogels, are reviewed. The individual contributions from phonons, fractons and particle modes, respectively, have been identified and can be described by quantitative models consistent with heat capacity...
Fractal analysis in oral leukoplakia
Directory of Open Access Journals (Sweden)
Prashant Bhai Pandey
2015-01-01
Full Text Available Introduction: Fractal analysis (FA quantifies complex geometric structures by generating a fractal dimension (FD, which can measure the complexity of mucosa. FA is a quantitative tool used to measure the complexity of self-similar or semi-self-similar structures. Aim and Objective: The study was done to perform the FA of oral mucosa with keratotic changes, as it is also made up of self-similar tissues, and thus, its FD can be calculated. Results: In oral leukoplakia, keratinization increases the complexity of mucosa, which denotes fractal geometry. We evaluated and compared pretreated and post-treated oral leukoplakia in 50 patients with clinically proven oral leukoplakia and analyzed the normal oral mucosa and lesional or keratinized mucosa in oral leukoplakia patients through FA using box counting method. Conclusion: FA using the fractal geometry is an efficient, noninvasive prediction tool for early detection of oral leukoplakia and other premalignant conditions in patients.
Launching the chaotic realm of iso-fractals: A short remark
Energy Technology Data Exchange (ETDEWEB)
O' Schmidt, Nathan [Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725 (United States); Katebi, Reza [Department of Physics, California State University in Fullerton, 800 North State College Boulevard, Fullerton, CA 92831 (United States); Corda, Christian [Institute for Theoretical Physics and Advanced Mathematics Einstein-Galilei (IFM), Via Santa Gonda 14, 59100 Prato (Italy)
2015-03-10
In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete case examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.
Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects
Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.
2013-04-01
This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to
Modeling extreme (Carrington-type) space weather events using three-dimensional MHD code simulations
Ngwira, C. M.; Pulkkinen, A. A.; Kuznetsova, M. M.; Glocer, A.
2013-12-01
There is growing concern over possible severe societal consequences related to adverse space weather impacts on man-made technological infrastructure and systems. In the last two decades, significant progress has been made towards the modeling of space weather events. Three-dimensional (3-D) global magnetohydrodynamics (MHD) models have been at the forefront of this transition, and have played a critical role in advancing our understanding of space weather. However, the modeling of extreme space weather events is still a major challenge even for existing global MHD models. In this study, we introduce a specially adapted University of Michigan 3-D global MHD model for simulating extreme space weather events that have a ground footprint comparable (or larger) to the Carrington superstorm. Results are presented for an initial simulation run with ``very extreme'' constructed/idealized solar wind boundary conditions driving the magnetosphere. In particular, we describe the reaction of the magnetosphere-ionosphere system and the associated ground induced geoelectric field to such extreme driving conditions. We also discuss the results and what they might mean for the accuracy of the simulations. The model is further tested using input data for an observed space weather event to verify the MHD model consistence and to draw guidance for future work. This extreme space weather MHD model is designed specifically for practical application to the modeling of extreme geomagnetically induced electric fields, which can drive large currents in earth conductors such as power transmission grids.
Three-dimensional space changes after premature loss of a maxillary primary first molar.
Park, Kitae; Jung, Da-Woon; Kim, Ji-Yeon
2009-11-01
A space maintainer is generally preferred when a primary first molar is lost before or during active eruption of the first permanent molars in order to prevent space loss. However, controversy prevails regarding the space loss after eruption of the permanent first molars. The purpose of this study was to examine spatial changes subsequent to premature loss of a maxillary primary first molar after the eruption of the permanent first molars. Thirteen children, five girls and eight boys, expecting premature extraction of a maxillary primary first molar because of caries and/or failed pulp therapy, were selected. Spatial changes were investigated using a three-dimensional laser scanner by comparing the primary molar space, arch width, arch length, and arch perimeter before and after the extraction of a maxillary primary first molar. Also, the inclination and angulation changes in the maxillary primary canines, primary second molars, and permanent first molars adjacent to the extraction site were investigated before and after the extraction of the maxillary primary first molar in order to examine the source of space loss. There was no statistically significant space loss on the extraction side compared to the control side (P = 0.33). No consistent findings were seen on the inclination and angulation changes on the extraction side. The premature loss of a maxillary primary first molar, in cases with class I molar relationship, has limited influence on the space in permanent dentition.
Three-dimensional space charge distribution measurement in electron beam irradiated PMMA
International Nuclear Information System (INIS)
Imaizumi, Yoichi; Suzuki, Ken; Tanaka, Yasuhiro; Takada, Tatsuo
1996-01-01
The localized space charge distribution in electron beam irradiated PMMA was investigated using pulsed electroacoustic method. Using a conventional space charge measurement system, the distribution only in the depth direction (Z) can be measured assuming the charges distributed uniformly in the horizontal (X-Y) plane. However, it is difficult to measure the distribution of space charge accumulated in small area. Therefore, we have developed the new system to measure the three-dimensional space charge distribution using pulsed electroacoustic method. The system has a small electrode with a diameter of 1mm and a motor-drive X-Y stage to move the sample. Using the data measured at many points, the three-dimensional distribution were obtained. To estimate the system performance, the electron beam irradiated PMMA was used. The electron beam was irradiated from transmission electron microscope (TEM). The depth of injected electron was controlled using the various metal masks. The measurement results were compared with theoretically calculated values of electron range. (author)
Towards Video Quality Metrics Based on Colour Fractal Geometry
Directory of Open Access Journals (Sweden)
Richard Noël
2010-01-01
Full Text Available Vision is a complex process that integrates multiple aspects of an image: spatial frequencies, topology and colour. Unfortunately, so far, all these elements were independently took into consideration for the development of image and video quality metrics, therefore we propose an approach that blends together all of them. Our approach allows for the analysis of the complexity of colour images in the RGB colour space, based on the probabilistic algorithm for calculating the fractal dimension and lacunarity. Given that all the existing fractal approaches are defined only for gray-scale images, we extend them to the colour domain. We show how these two colour fractal features capture the multiple aspects that characterize the degradation of the video signal, based on the hypothesis that the quality degradation perceived by the user is directly proportional to the modification of the fractal complexity. We claim that the two colour fractal measures can objectively assess the quality of the video signal and they can be used as metrics for the user-perceived video quality degradation and we validated them through experimental results obtained for an MPEG-4 video streaming application; finally, the results are compared against the ones given by unanimously-accepted metrics and subjective tests.
Dynamics of a neuron model in different two-dimensional parameter-spaces
International Nuclear Information System (INIS)
Rech, Paulo C.
2011-01-01
We report some two-dimensional parameter-space diagrams numerically obtained for the multi-parameter Hindmarsh-Rose neuron model. Several different parameter planes are considered, and we show that regardless of the combination of parameters, a typical scenario is preserved: for all choice of two parameters, the parameter-space presents a comb-shaped chaotic region immersed in a large periodic region. We also show that exist regions close these chaotic region, separated by the comb teeth, organized themselves in period-adding bifurcation cascades. - Research highlights: → We report parameter-spaces obtained for the Hindmarsh-Rose neuron model. → Regardless of the combination of parameters, a typical scenario is preserved. → The scenario presents a comb-shaped chaotic region immersed in a periodic region. → Periodic regions near the chaotic region are in period-adding bifurcation cascades.
Euclidean scalar Green function in a higher dimensional global monopole space-time
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
2002-01-01
We construct the explicit Euclidean scalar Green function associated with a massless field in a higher dimensional global monopole space-time, i.e., a (1+d)-space-time with d≥3 which presents a solid angle deficit. Our result is expressed in terms of an infinite sum of products of Legendre functions with Gegenbauer polynomials. Although this Green function cannot be expressed in a closed form, for the specific case where the solid angle deficit is very small, it is possible to develop the sum and obtain the Green function in a more workable expression. Having this expression it is possible to calculate the vacuum expectation value of some relevant operators. As an application of this formalism, we calculate the renormalized vacuum expectation value of the square of the scalar field, 2 (x)> Ren , and the energy-momentum tensor, μν (x)> Ren , for the global monopole space-time with spatial dimensions d=4 and d=5
Possibilities of identifying cyber attack in noisy space of n-dimensional abstract system
Energy Technology Data Exchange (ETDEWEB)
Jašek, Roman; Dvořák, Jiří; Janková, Martina; Sedláček, Michal [Tomas Bata University in Zlin Nad Stranemi 4511, 760 05 Zlin, Czech republic jasek@fai.utb.cz, dvorakj@aconte.cz, martina.jankova@email.cz, michal.sedlacek@email.cz (Czech Republic)
2016-06-08
This article briefly mentions some selected options of current concept for identifying cyber attacks from the perspective of the new cyberspace of real system. In the cyberspace, there is defined n-dimensional abstract system containing elements of the spatial arrangement of partial system elements such as micro-environment of cyber systems surrounded by other suitably arranged corresponding noise space. This space is also gradually supplemented by a new image of dynamic processes in a discreet environment, and corresponding again to n-dimensional expression of time space defining existence and also the prediction for expected cyber attacksin the noise space. Noises are seen here as useful and necessary for modern information and communication technologies (e.g. in processes of applied cryptography in ICT) and then the so-called useless noises designed for initial (necessary) filtering of this highly aggressive environment and in future expectedly offensive background in cyber war (e.g. the destruction of unmanned means of an electromagnetic pulse, or for destruction of new safety barriers created on principles of electrostatic field or on other principles of modern physics, etc.). The key to these new options is the expression of abstract systems based on the models of microelements of cyber systems and their hierarchical concept in structure of n-dimensional system in given cyberspace. The aim of this article is to highlight the possible systemic expression of cyberspace of abstract system and possible identification in time-spatial expression of real environment (on microelements of cyber systems and their surroundings with noise characteristics and time dimension in dynamic of microelements’ own time and externaltime defined by real environment). The article was based on a partial task of faculty specific research.
Possibilities of identifying cyber attack in noisy space of n-dimensional abstract system
International Nuclear Information System (INIS)
Jašek, Roman; Dvořák, Jiří; Janková, Martina; Sedláček, Michal
2016-01-01
This article briefly mentions some selected options of current concept for identifying cyber attacks from the perspective of the new cyberspace of real system. In the cyberspace, there is defined n-dimensional abstract system containing elements of the spatial arrangement of partial system elements such as micro-environment of cyber systems surrounded by other suitably arranged corresponding noise space. This space is also gradually supplemented by a new image of dynamic processes in a discreet environment, and corresponding again to n-dimensional expression of time space defining existence and also the prediction for expected cyber attacksin the noise space. Noises are seen here as useful and necessary for modern information and communication technologies (e.g. in processes of applied cryptography in ICT) and then the so-called useless noises designed for initial (necessary) filtering of this highly aggressive environment and in future expectedly offensive background in cyber war (e.g. the destruction of unmanned means of an electromagnetic pulse, or for destruction of new safety barriers created on principles of electrostatic field or on other principles of modern physics, etc.). The key to these new options is the expression of abstract systems based on the models of microelements of cyber systems and their hierarchical concept in structure of n-dimensional system in given cyberspace. The aim of this article is to highlight the possible systemic expression of cyberspace of abstract system and possible identification in time-spatial expression of real environment (on microelements of cyber systems and their surroundings with noise characteristics and time dimension in dynamic of microelements’ own time and externaltime defined by real environment). The article was based on a partial task of faculty specific research.
Possibilities of identifying cyber attack in noisy space of n-dimensional abstract system
Jašek, Roman; Dvořák, Jiří; Janková, Martina; Sedláček, Michal
2016-06-01
This article briefly mentions some selected options of current concept for identifying cyber attacks from the perspective of the new cyberspace of real system. In the cyberspace, there is defined n-dimensional abstract system containing elements of the spatial arrangement of partial system elements such as micro-environment of cyber systems surrounded by other suitably arranged corresponding noise space. This space is also gradually supplemented by a new image of dynamic processes in a discreet environment, and corresponding again to n-dimensional expression of time space defining existence and also the prediction for expected cyber attacksin the noise space. Noises are seen here as useful and necessary for modern information and communication technologies (e.g. in processes of applied cryptography in ICT) and then the so-called useless noises designed for initial (necessary) filtering of this highly aggressive environment and in future expectedly offensive background in cyber war (e.g. the destruction of unmanned means of an electromagnetic pulse, or for destruction of new safety barriers created on principles of electrostatic field or on other principles of modern physics, etc.). The key to these new options is the expression of abstract systems based on the models of microelements of cyber systems and their hierarchical concept in structure of n-dimensional system in given cyberspace. The aim of this article is to highlight the possible systemic expression of cyberspace of abstract system and possible identification in time-spatial expression of real environment (on microelements of cyber systems and their surroundings with noise characteristics and time dimension in dynamic of microelements' own time and externaltime defined by real environment). The article was based on a partial task of faculty specific research.
A fractal nature for polymerized laminin.
Directory of Open Access Journals (Sweden)
Camila Hochman-Mendez
Full Text Available Polylaminin (polyLM is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM, scanning electron microscopy (SEM and atomic force microscopy (AFM to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.
A fractal nature for polymerized laminin.
Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana
2014-01-01
Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.
International Nuclear Information System (INIS)
Silva O, G.; Garcia G, P.
2004-01-01
In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three dimensional Minkowski metric. (Author)
Superintegrability in two-dimensional Euclidean space and associated polynomial solutions
International Nuclear Information System (INIS)
Kalnins, E.G.; Miller, W. Jr; Pogosyan, G.S.
1996-01-01
In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the spectral functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial base for each of the nonsubgroup base, not just the subgroup cartesian and polar coordinate case, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the N-dimensional isotropic quantum oscillator. 28 refs., 1 tab
The Application of a Three-Dimensional Printed Product to Fill the Space After Organ Removal.
Weng, Jui-Yu; Wang, Che-Chuna; Chen, Pei-Jar; Lim, Sher-Wei; Kuo, Jinn-Rung
2017-11-01
Maintaining body integrity, especially in Asian societies, is an independent predictor of organ donation. Herein, we report the case of an 18-year-old man who suffered a traumatic brain injury with ensuing brain death caused by a car accident. According to the family's wishes, we used a 3-dimensional printer to create simulated heart, kidneys, and liver to fill the spaces after the patient's organs were removed. This is the first case report to introduce this new clinical application of 3-dimensional printed products during transplantation surgery. This new clinical application may have supportive psychological effects on the family and caregivers; however, given the varied responses to our procedure, this ethical issue is worth discussing. Copyright © 2017 Elsevier Inc. All rights reserved.
Multiple-canister flow and transport code in 2-dimensional space. MCFT2D: user's manual
International Nuclear Information System (INIS)
Lim, Doo-Hyun
2006-03-01
A two-dimensional numerical code, MCFT2D (Multiple-Canister Flow and Transport code in 2-Dimensional space), has been developed for groundwater flow and radionuclide transport analyses in a water-saturated high-level radioactive waste (HLW) repository with multiple canisters. A multiple-canister configuration and a non-uniform flow field of the host rock are incorporated in the MCFT2D code. Effects of heterogeneous flow field of the host rock on migration of nuclides can be investigated using MCFT2D. The MCFT2D enables to take into account the various degrees of the dependency of canister configuration for nuclide migration in a water-saturated HLW repository, while the dependency was assumed to be either independent or perfectly dependent in previous studies. This report presents features of the MCFT2D code, numerical simulation using MCFT2D code, and graphical representation of the numerical results. (author)
The Group Evacuation Behavior Based on Fire Effect in the Complicated Three-Dimensional Space
Directory of Open Access Journals (Sweden)
Jun Hu
2014-01-01
Full Text Available In order to effectively depict the group evacuation behavior in the complicated three-dimensional space, a novel pedestrian flow model is proposed with three-dimensional cellular automata. In this model the calculation methods of floor field and fire gain are elaborated at first, and the transition gain of target position at the next moment is defined. Then, in consideration of pedestrian intimacy and velocity change, the group evacuation strategy and evolution rules are given. Finally, the experiments were conducted with the simulation platform to study the relationships of evacuation time, pedestrian density, average system velocity, and smoke spreading velocity. The results had shown that large-scale group evacuation should be avoided, and in case of large pedestrian density, the shortest route of evacuation strategy would extend system evacuation time.
High-dimensional free-space optical communications based on orbital angular momentum coding
Zou, Li; Gu, Xiaofan; Wang, Le
2018-03-01
In this paper, we propose a high-dimensional free-space optical communication scheme using orbital angular momentum (OAM) coding. In the scheme, the transmitter encodes N-bits information by using a spatial light modulator to convert a Gaussian beam to a superposition mode of N OAM modes and a Gaussian mode; The receiver decodes the information through an OAM mode analyser which consists of a MZ interferometer with a rotating Dove prism, a photoelectric detector and a computer carrying out the fast Fourier transform. The scheme could realize a high-dimensional free-space optical communication, and decodes the information much fast and accurately. We have verified the feasibility of the scheme by exploiting 8 (4) OAM modes and a Gaussian mode to implement a 256-ary (16-ary) coding free-space optical communication to transmit a 256-gray-scale (16-gray-scale) picture. The results show that a zero bit error rate performance has been achieved.
Non-Euclidean geometry and curvature two-dimensional spaces, volume 3
Cannon, James W
2017-01-01
This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, wh...
International Nuclear Information System (INIS)
Marchiolli, M.A.; Ruzzi, M.
2012-01-01
We propose a self-consistent theoretical framework for a wide class of physical systems characterized by a finite space of states which allows us, within several mathematical virtues, to construct a discrete version of the Weyl–Wigner–Moyal (WWM) formalism for finite-dimensional discrete phase spaces with toroidal topology. As a first and important application from this ab initio approach, we initially investigate the Robertson–Schrödinger (RS) uncertainty principle related to the discrete coordinate and momentum operators, as well as its implications for physical systems with periodic boundary conditions. The second interesting application is associated with a particular uncertainty principle inherent to the unitary operators, which is based on the Wiener–Khinchin theorem for signal processing. Furthermore, we also establish a modified discrete version for the well-known Heisenberg–Kennard–Robertson (HKR) uncertainty principle, which exhibits additional terms (or corrections) that resemble the generalized uncertainty principle (GUP) into the context of quantum gravity. The results obtained from this new algebraic approach touch on some fundamental questions inherent to quantum mechanics and certainly represent an object of future investigations in physics. - Highlights: ► We construct a discrete version of the Weyl–Wigner–Moyal formalism. ► Coherent states for finite-dimensional discrete phase spaces are established. ► Discrete coordinate and momentum operators are properly defined. ► Uncertainty principles depend on the topology of finite physical systems. ► Corrections for the discrete Heisenberg uncertainty relation are also obtained.
Engineering flat electronic bands in quasiperiodic and fractal loop geometries
Energy Technology Data Exchange (ETDEWEB)
Nandy, Atanu, E-mail: atanunandy1989@gmail.com; Chakrabarti, Arunava, E-mail: arunava_chakrabarti@yahoo.co.in
2015-11-06
Exact construction of one electron eigenstates with flat, non-dispersive bands, and localized over clusters of various sizes is reported for a class of quasi-one-dimensional looped networks. Quasiperiodic Fibonacci and Berker fractal geometries are embedded in the arms of the loop threaded by a uniform magnetic flux. We work out an analytical scheme to unravel the localized single particle states pinned at various atomic sites or over clusters of them. The magnetic field is varied to control, in a subtle way, the extent of localization and the location of the flat band states in energy space. In addition to this we show that an appropriate tuning of the field can lead to a re-entrant behavior of the effective mass of the electron in a band, with a periodic flip in its sign. - Highlights: • Exact construction of eigenstates with flat and dispersive bands is reported. • Competition between translational order and growth of aperiodicity is discussed. • The effect of magnetic field on the location of flat band states is shown. • Flux tunable re-entrant behavior of the effective mass of electron is studied.
Influence of cusps and intersections on the calculation of the Wilson loop in ν-dimensional space
International Nuclear Information System (INIS)
Bezerra, V.B.
1984-01-01
A discussion is given about the influence of cusps and intersections on the calculation of the Wilson Loop in ν-dimensional space. In particular, for the two-dimensional case, it is shown that there are no divergences. (Author) [pt
Application of data mining in three-dimensional space time reactor model
International Nuclear Information System (INIS)
Jiang Botao; Zhao Fuyu
2011-01-01
A high-fidelity three-dimensional space time nodal method has been developed to simulate the dynamics of the reactor core for real time simulation. This three-dimensional reactor core mathematical model can be composed of six sub-models, neutron kinetics model, cay heat model, fuel conduction model, thermal hydraulics model, lower plenum model, and core flow distribution model. During simulation of each sub-model some operation data will be produced and lots of valuable, important information reflecting the reactor core operation status could be hidden in, so how to discovery these information becomes the primary mission people concern. Under this background, data mining (DM) is just created and developed to solve this problem, no matter what engineering aspects or business fields. Generally speaking, data mining is a process of finding some useful and interested information from huge data pool. Support Vector Machine (SVM) is a new technique of data mining appeared in recent years, and SVR is a transformed method of SVM which is applied in regression cases. This paper presents only two significant sub-models of three-dimensional reactor core mathematical model, the nodal space time neutron kinetics model and the thermal hydraulics model, based on which the neutron flux and enthalpy distributions of the core are obtained by solving the three-dimensional nodal space time kinetics equations and energy equations for both single and two-phase flows respectively. Moreover, it describes that the three-dimensional reactor core model can also be used to calculate and determine the reactivity effects of the moderator temperature, boron concentration, fuel temperature, coolant void, xenon worth, samarium worth, control element positions (CEAs) and core burnup status. Besides these, the main mathematic theory of SVR is introduced briefly next, on the basis of which SVR is applied to dealing with the data generated by two sample calculation, rod ejection transient and axial
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-01-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape
A fractal-based image encryption system
Abd-El-Hafiz, S. K.; Radwan, Ahmed Gomaa; Abdel Haleem, Sherif H.; Barakat, Mohamed L.
2014-01-01
single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved
Energy Technology Data Exchange (ETDEWEB)
Castellani, Marco; Giuli, Massimiliano, E-mail: massimiliano.giuli@univaq.it [University of L’Aquila, Department of Information Engineering, Computer Science and Mathematics (Italy)
2016-02-15
We study pseudomonotone and quasimonotone quasivariational inequalities in a finite dimensional space. In particular we focus our attention on the closedness of some solution maps associated to a parametric quasivariational inequality. From this study we derive two results on the existence of solutions of the quasivariational inequality. On the one hand, assuming the pseudomonotonicity of the operator, we get the nonemptiness of the set of the classical solutions. On the other hand, we show that the quasimonoticity of the operator implies the nonemptiness of the set of nonzero solutions. An application to traffic network is also considered.
International Nuclear Information System (INIS)
Castellani, Marco; Giuli, Massimiliano
2016-01-01
We study pseudomonotone and quasimonotone quasivariational inequalities in a finite dimensional space. In particular we focus our attention on the closedness of some solution maps associated to a parametric quasivariational inequality. From this study we derive two results on the existence of solutions of the quasivariational inequality. On the one hand, assuming the pseudomonotonicity of the operator, we get the nonemptiness of the set of the classical solutions. On the other hand, we show that the quasimonoticity of the operator implies the nonemptiness of the set of nonzero solutions. An application to traffic network is also considered
A three-dimensional radiation image display on a real space image created via photogrammetry
Sato, Y.; Ozawa, S.; Tanifuji, Y.; Torii, T.
2018-03-01
The Fukushima Daiichi Nuclear Power Station (FDNPS), operated by Tokyo Electric Power Company Holdings, Inc., went into meltdown after the occurrence of a large tsunami caused by the Great East Japan Earthquake of March 11, 2011. The radiation distribution measurements inside the FDNPS buildings are indispensable to execute decommissioning tasks in the reactor buildings. We have developed a three-dimensional (3D) image reconstruction method for radioactive substances using a compact Compton camera. Moreover, we succeeded in visually recognizing the position of radioactive substances in real space by the integration of 3D radiation images and the 3D photo-model created using photogrammetry.
Neutrino stress tensor regularization in two-dimensional space-time
International Nuclear Information System (INIS)
Davies, P.C.W.; Unruh, W.G.
1977-01-01
The method of covariant point-splitting is used to regularize the stress tensor for a massless spin 1/2 (neutrino) quantum field in an arbitrary two-dimensional space-time. A thermodynamic argument is used as a consistency check. The result shows that the physical part of the stress tensor is identical with that of the massless scalar field (in the absence of Casimir-type terms) even though the formally divergent expression is equal to the negative of the scalar case. (author)
Two-Dimensional Space-Time Dependent Multi-group Diffusion Equation with SLOR Method
International Nuclear Information System (INIS)
Yulianti, Y.; Su'ud, Z.; Waris, A.; Khotimah, S. N.
2010-01-01
The research of two-dimensional space-time diffusion equations with SLOR (Successive-Line Over Relaxation) has been done. SLOR method is chosen because this method is one of iterative methods that does not required to defined whole element matrix. The research is divided in two cases, homogeneous case and heterogeneous case. Homogeneous case has been inserted by step reactivity. Heterogeneous case has been inserted by step reactivity and ramp reactivity. In general, the results of simulations are agreement, even in some points there are differences.
A three-dimensional phase space dynamical model of the Earth's radiation belt
International Nuclear Information System (INIS)
Boscher, D. M.; Beutier, T.; Bourdarie, S.
1996-01-01
A three dimensional phase space model of the Earth's radiation belt is presented. We have taken into account the magnetic and electric radial diffusions, the pitch angle diffusions due to Coulomb interactions and interactions with the plasmaspheric hiss, and the Coulomb drag. First, a steady state of the belt is presented. Two main maxima are obtained, corresponding to the inner and outer parts of the belt. Then, we have modelled a simple injection at the external boundary. The particle transport seems like what was measured aboard satellites. A high energy particle loss is found, by comparing the model results and the measurements. It remains to be explained
International Nuclear Information System (INIS)
Keller, Kai Johannes
2010-04-01
The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmermann. A relation to the alternative approach to renormalization theory using Hopf algebras is established. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Keller, Kai Johannes
2010-04-15
The present work contains a consistent formulation of the methods of dimensional regularization (DimReg) and minimal subtraction (MS) in Minkowski position space. The methods are implemented into the framework of perturbative Algebraic Quantum Field Theory (pAQFT). The developed methods are used to solve the Epstein-Glaser recursion for the construction of time-ordered products in all orders of causal perturbation theory. A solution is given in terms of a forest formula in the sense of Zimmermann. A relation to the alternative approach to renormalization theory using Hopf algebras is established. (orig.)
State-space representation of instationary two-dimensional airfoil aerodynamics
Energy Technology Data Exchange (ETDEWEB)
Meyer, Marcus; Matthies, Hermann G. [Institute of Scientific Computing, Technical University Braunschweig, Hans-Sommer-Str. 65, Braunschweig 38106 (Germany)
2004-03-01
In the aero-elastic analysis of wind turbines the need to include a model of the local, two-dimensional instationary aerodynamic loads, commonly referred to as dynamic stall model, has become obvious in the last years. In this contribution an alternative choice for such a model is described, based on the DLR model. Its derivation is governed by the flow physics, thus enabling interpolation between different profile geometries. An advantage of the proposed model is its state-space form, i.e. a system of differential equations, which facilitates the important tasks of aeroelastic stability and sensitivity investigations. The model is validated with numerical calculations.
Conformal symmetry in two-dimensional space: recursion representation of conformal block
International Nuclear Information System (INIS)
Zamolodchikov, A.B.
1988-01-01
The four-point conformal block plays an important part in the analysis of the conformally invariant operator algebra in two-dimensional space. The behavior of the conformal block is calculated in the present paper in the limit in which the dimension Δ of the intermediate operator tends to infinity. This makes it possible to construct a recursion relation for this function that connects the conformal block at arbitrary Δ to the blocks corresponding to the dimensions of the zero vectors in the degenerate representations of the Virasoro algebra. The relation is convenient for calculating the expansion of the conformal block in powers of the uniformizing parameters q = i π tau
Efficient fractal-based mutation in evolutionary algorithms from iterated function systems
Salcedo-Sanz, S.; Aybar-Ruíz, A.; Camacho-Gómez, C.; Pereira, E.
2018-03-01
In this paper we present a new mutation procedure for Evolutionary Programming (EP) approaches, based on Iterated Function Systems (IFSs). The new mutation procedure proposed consists of considering a set of IFS which are able to generate fractal structures in a two-dimensional phase space, and use them to modify a current individual of the EP algorithm, instead of using random numbers from different probability density functions. We test this new proposal in a set of benchmark functions for continuous optimization problems. In this case, we compare the proposed mutation against classical Evolutionary Programming approaches, with mutations based on Gaussian, Cauchy and chaotic maps. We also include a discussion on the IFS-based mutation in a real application of Tuned Mass Dumper (TMD) location and optimization for vibration cancellation in buildings. In both practical cases, the proposed EP with the IFS-based mutation obtained extremely competitive results compared to alternative classical mutation operators.
Effects of fractal pore on coal devolatilization
Energy Technology Data Exchange (ETDEWEB)
Chen, Yongli; He, Rong [Tsinghua Univ., Beijing (China). Dept. of Thermal Engineering; Wang, Xiaoliang; Cao, Liyong [Dongfang Electric Corporation, Chengdu (China). Centre New Energy Inst.
2013-07-01
Coal devolatilization is numerically investigated by drop tube furnace and a coal pyrolysis model (Fragmentation and Diffusion Model). The fractal characteristics of coal and char pores are investigated. Gas diffusion and secondary reactions in fractal pores are considered in the numerical simulations of coal devolatilization, and the results show that the fractal dimension is increased firstly and then decreased later with increased coal conversions during devolatilization. The mechanisms of effects of fractal pores on coal devolatilization are analyzed.
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.
2014-08-28
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fan, Jieran; Wang, Di; DeVault, Clayton
2016-01-01
We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure.......We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure....
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
Ngwira, Chigomezyo M.; Pulkkinen, Antti; Kuznetsova, Maria M.; Glocer, Alex
2014-06-01
There is a growing concern over possible severe societal consequences related to adverse space weather impacts on man-made technological infrastructure. In the last two decades, significant progress has been made toward the first-principles modeling of space weather events, and three-dimensional (3-D) global magnetohydrodynamics (MHD) models have been at the forefront of this transition, thereby playing a critical role in advancing our understanding of space weather. However, the modeling of extreme space weather events is still a major challenge even for the modern global MHD models. In this study, we introduce a specially adapted University of Michigan 3-D global MHD model for simulating extreme space weather events with a Dst footprint comparable to the Carrington superstorm of September 1859 based on the estimate by Tsurutani et. al. (2003). Results are presented for a simulation run with "very extreme" constructed/idealized solar wind boundary conditions driving the magnetosphere. In particular, we describe the reaction of the magnetosphere-ionosphere system and the associated induced geoelectric field on the ground to such extreme driving conditions. The model setup is further tested using input data for an observed space weather event of Halloween storm October 2003 to verify the MHD model consistence and to draw additional guidance for future work. This extreme space weather MHD model setup is designed specifically for practical application to the modeling of extreme geomagnetically induced electric fields, which can drive large currents in ground-based conductor systems such as power transmission grids. Therefore, our ultimate goal is to explore the level of geoelectric fields that can be induced from an assumed storm of the reported magnitude, i.e., Dst˜=-1600 nT.
Three-dimensionality of space and the quantum bit: an information-theoretic approach
International Nuclear Information System (INIS)
Müller, Markus P; Masanes, Lluís
2013-01-01
It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry ‘minimal amounts of direction information’, interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d = 3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements. (paper)
Numerical Study of Three Dimensional Effects in Longitudinal Space-Charge Impedance
Energy Technology Data Exchange (ETDEWEB)
Halavanau, A. [NICADD, DeKalb; Piot, P. [NICADD, DeKalb
2015-06-01
Longitudinal space-charge (LSC) effects are generally considered as detrimental in free-electron lasers as they can seed instabilities. Such “microbunching instabilities” were recently shown to be potentially useful to support the generation of broadband coherent radiation pulses [1, 2]. Therefore there has been an increasing interest in devising accelerator beamlines capable of sustaining this LSC instability as a mechanism to produce a coherent light source. To date most of these studies have been carried out with a one-dimensional impedance model for the LSC. In this paper we use a N-body “Barnes-Hut” algorithm [3] to simulate the 3D space charge force in the beam combined with elegant [4] and explore the limitation of the 1D model often used
Crossover from Nonequilibrium Fractal Growth to Equilibrium Compact Growth
DEFF Research Database (Denmark)
Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.
1988-01-01
Solidification controlled by vacancy diffusion is studied by Monte Carlo simulations of a two-dimensional Ising model defined by a Hamiltonian which models a thermally driven fluid-solid phase transition. The nonequilibrium morphology of the growing solid is studied as a function of time as the s...... as the system relaxes into equilibrium described by a temperature. At low temperatures the model exhibits fractal growth at early times and crossover to compact solidification as equilibrium is approached....
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.
2014-08-28
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape separated by a vertical distance from a lower first metal plate with a complementary fractal shape; and a substrate above which the capacitor body is suspended.
An enhanced fractal image denoising algorithm
International Nuclear Information System (INIS)
Lu Jian; Ye Zhongxing; Zou Yuru; Ye Ruisong
2008-01-01
In recent years, there has been a significant development in image denoising using fractal-based method. This paper presents an enhanced fractal predictive denoising algorithm for denoising the images corrupted by an additive white Gaussian noise (AWGN) by using quadratic gray-level function. Meanwhile, a quantization method for the fractal gray-level coefficients of the quadratic function is proposed to strictly guarantee the contractivity requirement of the enhanced fractal coding, and in terms of the quality of the fractal representation measured by PSNR, the enhanced fractal image coding using quadratic gray-level function generally performs better than the standard fractal coding using linear gray-level function. Based on this enhanced fractal coding, the enhanced fractal image denoising is implemented by estimating the fractal gray-level coefficients of the quadratic function of the noiseless image from its noisy observation. Experimental results show that, compared with other standard fractal-based image denoising schemes using linear gray-level function, the enhanced fractal denoising algorithm can improve the quality of the restored image efficiently
Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...
African Journals Online (AJOL)
In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...
Fractal Theory for Permeability Prediction, Venezuelan and USA Wells
Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana
2014-05-01
Inferring petrophysical parameters such as permeability, porosity, water saturation, capillary pressure, etc, from the analysis of well logs or other available core data has always been of critical importance in the oil industry. Permeability in particular, which is considered to be a complex parameter, has been inferred using both empirical and theoretical techniques. The main goal of this work is to predict permeability values on different wells using Fractal Theory, based on a method proposed by Pape et al. (1999). This approach uses the relationship between permeability and the geometric form of the pore space of the rock. This method is based on the modified equation of Kozeny-Carman and a fractal pattern, which allows determining permeability as a function of the cementation exponent, porosity and the fractal dimension. Data from wells located in Venezuela and the United States of America are analyzed. Employing data of porosity and permeability obtained from core samples, and applying the Fractal Theory method, we calculated the prediction equations for each well. At the beginning, this was achieved by training with 50% of the data available for each well. Afterwards, these equations were tested inferring over 100% of the data to analyze possible trends in their distribution. This procedure gave excellent results in all the wells in spite of their geographic distance, generating permeability models with the potential to accurately predict permeability logs in the remaining parts of the well for which there are no core samples, using even porority logs. Additionally, empirical models were used to determine permeability and the results were compared with those obtained by applying the fractal method. The results indicated that, although there are empirical equations that give a proper adjustment, the prediction results obtained using fractal theory give a better fit to the core reference data.
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0.......0002) in monozygotic twins than in dizygotic twins (0.108, P = 0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, dominant genetic effects explained 54% of the variation and 46% was individually environmentally determined. Conclusions: In young adult twins...
Towards thermomechanics of fractal media
Ostoja-Starzewski, Martin
2007-11-01
Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.
Lam, Nina Siu-Ngan; Qiu, Hong-Lie; Quattrochi, Dale A.; Emerson, Charles W.; Arnold, James E. (Technical Monitor)
2001-01-01
The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.
A non-Abelian SO(8) monopole as generalization of Dirac-Yang monopoles for a 9-dimensional space
International Nuclear Information System (INIS)
Le, Van-Hoang; Nguyen, Thanh-Son
2011-01-01
We establish an explicit form of a non-Abelian SO(8) monopole in a 9-dimensional space and show that it is indeed a direct generalization of Dirac and Yang monopoles. Using the generalized Hurwitz transformation, we have found a connection between a 16-dimensional harmonic oscillator and a 9-dimensional hydrogenlike atom in the field of the SO(8) monopole (MICZ-Kepler problem). Using the built connection the group of dynamical symmetry of the 9-dimensional MICZ-Kepler problem is found as SO(10, 2).
Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model
Energy Technology Data Exchange (ETDEWEB)
Ito, Yuta [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Graduate University for Advanced Studies (SOKENDAI),1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan); Tsuchiya, Asato [Department of Physics, Shizuoka University,836 Ohya, Suruga-ku, Shizuoka 422-8529 (Japan)
2017-03-27
The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous breaking of the 9-dimensional rotational symmetry to the 3-dimensional one. This result, however, was obtained after regularizing the original matrix integration by introducing “infrared” cutoffs on the quadratic moments of the Hermitian matrices. In this paper, we generalize the form of the cutoffs in such a way that it involves an arbitrary power (2p) of the matrices. By performing Monte Carlo simulation of a simplified model, we find that the results become independent of p and hence universal for p≳1.3. For p as large as 2.0, however, we find that large-N scaling behaviors do not show up, and we cannot take a sensible large-N limit. Thus we find that there is a certain range of p in which a universal large-N limit can be taken. Within this range of p, the dynamical space-time dimensionality turns out to be (3+1), while for p=2.0, where we cannot take a sensible large-N limit, we observe a (5+1)d structure.
Li, Dong; Wei, Zhen; Song, Dawei; Sun, Wenfeng; Fan, Xiaoyan
2016-11-01
With the development of space technology, the number of spacecrafts and debris are increasing year by year. The demand for detecting and identification of spacecraft is growing strongly, which provides support to the cataloguing, crash warning and protection of aerospace vehicles. The majority of existing approaches for three-dimensional reconstruction is scattering centres correlation, which is based on the radar high resolution range profile (HRRP). This paper proposes a novel method to reconstruct the threedimensional scattering centre structure of target from a sequence of radar ISAR images, which mainly consists of three steps. First is the azimuth scaling of consecutive ISAR images based on fractional Fourier transform (FrFT). The later is the extraction of scattering centres and matching between adjacent ISAR images using grid method. Finally, according to the coordinate matrix of scattering centres, the three-dimensional scattering centre structure is reconstructed using improved factorization method. The three-dimensional structure is featured with stable and intuitive characteristic, which provides a new way to improve the identification probability and reduce the complexity of the model matching library. A satellite model is reconstructed using the proposed method from four consecutive ISAR images. The simulation results prove that the method has gotten a satisfied consistency and accuracy.
Classical testing particles and (4 + N)-dimensional theories of space-time
International Nuclear Information System (INIS)
Nieto-Garcia, J.A.
1986-01-01
The Lagrangian theory of a classical relativistic spinning test particle (top) developed by Hanson and Regge and by Hojman is briefly reviewed. Special attention is devoted to the constraints imposed on the dynamical variables associated with the system of this theory. The equations for a relativistic top are formulated in a way suitable for use in the study of geometrical properties of the 4 + N-dimensional Kaluza-Klein background. It is shown that the equations of motion of a top in five dimensions reduce to the Hanson-Regge generalization of the Bargmann-Michel-Telegdi equations of motion in four dimensions when suitable conditions on the spin tensor are imposed. The classical bosonic relativistic string theory is discussed and the connection of this theory with the top theory is examined. It is found that the relation between the string and the top leads naturally to the consideration of a 3-dimensional extended system (called terron) which sweeps out a 4-dimensional surface as it evolves in a space-time. By using a square root procedure based on ideas by Teitelboim a theory of a supersymmetric top is developed. The quantization of the new supersymmetric system is discussed. Conclusions and suggestions for further research are given
Chen, Hao; Lv, Wen; Zhang, Tongtong
2018-05-01
We study preconditioned iterative methods for the linear system arising in the numerical discretization of a two-dimensional space-fractional diffusion equation. Our approach is based on a formulation of the discrete problem that is shown to be the sum of two Kronecker products. By making use of an alternating Kronecker product splitting iteration technique we establish a class of fixed-point iteration methods. Theoretical analysis shows that the new method converges to the unique solution of the linear system. Moreover, the optimal choice of the involved iteration parameters and the corresponding asymptotic convergence rate are computed exactly when the eigenvalues of the system matrix are all real. The basic iteration is accelerated by a Krylov subspace method like GMRES. The corresponding preconditioner is in a form of a Kronecker product structure and requires at each iteration the solution of a set of discrete one-dimensional fractional diffusion equations. We use structure preserving approximations to the discrete one-dimensional fractional diffusion operators in the action of the preconditioning matrix. Numerical examples are presented to illustrate the effectiveness of this approach.
A New Ensemble Method with Feature Space Partitioning for High-Dimensional Data Classification
Directory of Open Access Journals (Sweden)
Yongjun Piao
2015-01-01
Full Text Available Ensemble data mining methods, also known as classifier combination, are often used to improve the performance of classification. Various classifier combination methods such as bagging, boosting, and random forest have been devised and have received considerable attention in the past. However, data dimensionality increases rapidly day by day. Such a trend poses various challenges as these methods are not suitable to directly apply to high-dimensional datasets. In this paper, we propose an ensemble method for classification of high-dimensional data, with each classifier constructed from a different set of features determined by partitioning of redundant features. In our method, the redundancy of features is considered to divide the original feature space. Then, each generated feature subset is trained by a support vector machine, and the results of each classifier are combined by majority voting. The efficiency and effectiveness of our method are demonstrated through comparisons with other ensemble techniques, and the results show that our method outperforms other methods.
Compound Structure-Independent Activity Prediction in High-Dimensional Target Space.
Balfer, Jenny; Hu, Ye; Bajorath, Jürgen
2014-08-01
Profiling of compound libraries against arrays of targets has become an important approach in pharmaceutical research. The prediction of multi-target compound activities also represents an attractive task for machine learning with potential for drug discovery applications. Herein, we have explored activity prediction in high-dimensional target space. Different types of models were derived to predict multi-target activities. The models included naïve Bayesian (NB) and support vector machine (SVM) classifiers based upon compound structure information and NB models derived on the basis of activity profiles, without considering compound structure. Because the latter approach can be applied to incomplete training data and principally depends on the feature independence assumption, SVM modeling was not applicable in this case. Furthermore, iterative hybrid NB models making use of both activity profiles and compound structure information were built. In high-dimensional target space, NB models utilizing activity profile data were found to yield more accurate activity predictions than structure-based NB and SVM models or hybrid models. An in-depth analysis of activity profile-based models revealed the presence of correlation effects across different targets and rationalized prediction accuracy. Taken together, the results indicate that activity profile information can be effectively used to predict the activity of test compounds against novel targets. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Fractals control in particle's velocity
International Nuclear Information System (INIS)
Zhang Yongping; Liu Shutang; Shen Shulan
2009-01-01
Julia set, a fractal set of the literature of nonlinear physics, has significance for the engineering applications. For example, the fractal structure characteristics of the generalized M-J set could visually reflect the change rule of particle's velocity. According to the real world requirement, the system need show various particle's velocity in some cases. Thus, the control of the nonlinear behavior, i.e., Julia set, has attracted broad attention. In this work, an auxiliary feedback control is introduced to effectively control the Julia set that visually reflects the change rule of particle's velocity. It satisfies the performance requirement of the real world problems.
Applications of fractals in ecology.
Sugihara, G; M May, R
1990-03-01
Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
, the retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficients. Falconer's formula and quantitative genetic models were used to determine the genetic component of variation. Results: The mean...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0...
Synergetics and fractals in tribology
Janahmadov, Ahad Kh
2016-01-01
This book examines the theoretical and practical aspects of tribological process using synergy, fractal and multifractal methods, and the fractal and multifractal models of self-similar tribosystems developed on their basis. It provides a comprehensive analysis of their effectiveness, and also considers the method of flicker noise spectroscopy with detailed parameterization of surface roughness friction. All models, problems and solutions are taken and tested on the set of real-life examples of oil-gas industry. The book is intended for researchers, graduate students and engineers specialising in the field of tribology, and also for senior students of technical colleges.
International Nuclear Information System (INIS)
Nguyen Buong.
1992-11-01
The purpose of this paper is to investigate convergence rates for an operator version of Tikhonov regularization constructed by dual mapping for nonlinear ill-posed problems involving monotone operators in real reflective Banach spaces. The obtained results are considered in combination with finite-dimensional approximations for the space. An example is considered for illustration. (author). 15 refs
International Nuclear Information System (INIS)
Arsen'ev, A.A.
1979-01-01
Example of a classical dynamical system with the infinite-dimensional phase space, satisfying the analogue of the Kubo-Martin-Schwinger conditions for classical dynamics, is constructed explicitly. Connection between the system constructed and the Fock space dynamics is pointed out
Directory of Open Access Journals (Sweden)
Haiwen Li
2018-01-01
Full Text Available The estimation speed of positioning parameters determines the effectiveness of the positioning system. The time of arrival (TOA and direction of arrival (DOA parameters can be estimated by the space-time two-dimensional multiple signal classification (2D-MUSIC algorithm for array antenna. However, this algorithm needs much time to complete the two-dimensional pseudo spectral peak search, which makes it difficult to apply in practice. Aiming at solving this problem, a fast estimation method of space-time two-dimensional positioning parameters based on Hadamard product is proposed in orthogonal frequency division multiplexing (OFDM system, and the Cramer-Rao bound (CRB is also presented. Firstly, according to the channel frequency domain response vector of each array, the channel frequency domain estimation vector is constructed using the Hadamard product form containing location information. Then, the autocorrelation matrix of the channel response vector for the extended array element in frequency domain and the noise subspace are calculated successively. Finally, by combining the closed-form solution and parameter pairing, the fast joint estimation for time delay and arrival direction is accomplished. The theoretical analysis and simulation results show that the proposed algorithm can significantly reduce the computational complexity and guarantee that the estimation accuracy is not only better than estimating signal parameters via rotational invariance techniques (ESPRIT algorithm and 2D matrix pencil (MP algorithm but also close to 2D-MUSIC algorithm. Moreover, the proposed algorithm also has certain adaptability to multipath environment and effectively improves the ability of fast acquisition of location parameters.
An Integrated Approach to Parameter Learning in Infinite-Dimensional Space
Energy Technology Data Exchange (ETDEWEB)
Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Wendelberger, Joanne Roth [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-09-14
The availability of sophisticated modern physics codes has greatly extended the ability of domain scientists to understand the processes underlying their observations of complicated processes, but it has also introduced the curse of dimensionality via the many user-set parameters available to tune. Many of these parameters are naturally expressed as functional data, such as initial temperature distributions, equations of state, and controls. Thus, when attempting to find parameters that match observed data, being able to navigate parameter-space becomes highly non-trivial, especially considering that accurate simulations can be expensive both in terms of time and money. Existing solutions include batch-parallel simulations, high-dimensional, derivative-free optimization, and expert guessing, all of which make some contribution to solving the problem but do not completely resolve the issue. In this work, we explore the possibility of coupling together all three of the techniques just described by designing user-guided, batch-parallel optimization schemes. Our motivating example is a neutron diffusion partial differential equation where the time-varying multiplication factor serves as the unknown control parameter to be learned. We find that a simple, batch-parallelizable, random-walk scheme is able to make some progress on the problem but does not by itself produce satisfactory results. After reducing the dimensionality of the problem using functional principal component analysis (fPCA), we are able to track the progress of the solver in a visually simple way as well as viewing the associated principle components. This allows a human to make reasonable guesses about which points in the state space the random walker should try next. Thus, by combining the random walker's ability to find descent directions with the human's understanding of the underlying physics, it is possible to use expensive simulations more efficiently and more quickly arrive at the
Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability
Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.
2018-02-01
As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi
International Nuclear Information System (INIS)
Jo, Junghyo; Periwal, Vipul; Hörnblad, Andreas; Ahlgren, Ulf; Kilimnik, German; Hara, Manami
2013-01-01
The islets of Langerhans, responsible for controlling blood glucose levels, are dispersed within the pancreas. A universal power law governing the fractal spatial distribution of islets in two-dimensional pancreatic sections has been reported. However, the fractal geometry in the actual three-dimensional pancreas volume, and the developmental process that gives rise to such a self-similar structure, has not been investigated. Here, we examined the three-dimensional spatial distribution of islets in intact mouse pancreata using optical projection tomography and found a power law with a fractal dimension of 2.1. Furthermore, based on two-dimensional pancreatic sections of human autopsies, we found that the distribution of human islets also follows a universal power law with a fractal dimension of 1.5 in adult pancreata, which agrees with the value previously reported in smaller mammalian pancreas sections. Finally, we developed a self-avoiding growth model for the development of the islet distribution and found that the fractal nature of the spatial islet distribution may be associated with the self-avoidance in the branching process of vascularization in the pancreas. (paper)
Fractal model for estimating fracture toughness of carbon nanotube reinforced aluminum oxide
International Nuclear Information System (INIS)
Rishabh, Abhishek; Joshi, Milind R.; Balani, Kantesh
2010-01-01
The current work focuses on predicting the fracture toughness of Al 2 O 3 ceramic matrix composites using a modified Mandelbrot's fractal approach. The first step confirms that the experimental fracture toughness values fluctuate within the fracture toughness range predicted as per the modified fractal approach. Additionally, the secondary reinforcements [such as carbon nanotubes (CNTs)] have shown to enhance the fracture toughness of Al 2 O 3 . Conventional fractural toughness evaluation via fractal approach underestimates the fracture toughness by considering the shortest crack path. Hence, the modified Mandelbrot's fractal approach considers the crack propagation along the CNT semicircumferential surface (three-dimensional crack path propagation) for achieving an improved fracture toughness estimation of Al 2 O 3 -CNT composite. The estimations obtained in the current approach range within 4% error regime of the experimentally measured fracture toughness values of the Al 2 O 3 -CNT composite.
Directory of Open Access Journals (Sweden)
Chia-Hung Lin
2010-01-01
Full Text Available This paper proposes combining the biometric fractal pattern and particle swarm optimization (PSO-based classifier for fingerprint recognition. Fingerprints have arch, loop, whorl, and accidental morphologies, and embed singular points, resulting in the establishment of fingerprint individuality. An automatic fingerprint identification system consists of two stages: digital image processing (DIP and pattern recognition. DIP is used to convert to binary images, refine out noise, and locate the reference point. For binary images, Katz's algorithm is employed to estimate the fractal dimension (FD from a two-dimensional (2D image. Biometric features are extracted as fractal patterns using different FDs. Probabilistic neural network (PNN as a classifier performs to compare the fractal patterns among the small-scale database. A PSO algorithm is used to tune the optimal parameters and heighten the accuracy. For 30 subjects in the laboratory, the proposed classifier demonstrates greater efficiency and higher accuracy in fingerprint recognition.
Shirazinodeh, Alireza; Noubari, Hossein Ahmadi; Rabbani, Hossein; Dehnavi, Alireza Mehri
2015-01-01
Recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. It is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. In this paper, for fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section using a computationally efficient two-dimensional box-counting algorithm. Furthermore, using appropriate wavelet sub-bands and image Reconstruction based on modified wavelet coefficients, it is shown that it is possible to arrive at enhanced features for detection of cancerous zones. In this paper, we have attempted to benefit from the advantages of both fractals and wavelets by introducing a new algorithm. By using a new algorithm named F1W2, the original image is first segmented into appropriate fractal boxes, and the fractal dimension of each windowed section is extracted. Following from that, by applying a maximum level threshold on fractal dimensions matrix, the best-segmented boxes are selected. In the next step, the segmented Cancerous zones which are candidates are then decomposed by utilizing standard orthogonal wavelet transform and db2 wavelet in three different resolution levels, and after nullifying wavelet coefficients of the image at the first scale and low frequency band of the third scale, the modified reconstructed image is successfully utilized for detection of breast cancer regions by applying an appropriate threshold. For detection of cancerous zones, our simulations indicate the accuracy of 90.9% for masses and 88.99% for microcalcifications detection results using the F1W2 method. For classification of detected mictocalcification into benign and malignant cases, eight features are identified and
Atypical extended electronic states in an infinite Vicsek fractal: An exact result
International Nuclear Information System (INIS)
Chakrabarti, A.; Bhattacharyya, B.
1996-01-01
We present a class of extended electronic wave functions on a Vicsek fractal. The transmittivity of arbitrarily large fractal lattices corresponding to these particular extended-state eigenvalues exhibits a power-law decay with increasing system size. The eigenvalues corresponding to the above extended states as well as the scaling law for the transmittivity have been exactly calculated using a real-space renormalization-group method. copyright 1996 The American Physical Society
Atkinson, D; Peijnenburg, A.J.M.
2012-01-01
This paper is the third and final one in a sequence of three. All three papers emphasize that a proposition can be justified by an infinite regress, on condition that epistemic justification is interpreted probabilistically. The first two papers showed this for one-dimensional chains and for
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost ... Here a(t) is the cosmic scale factor and it measures the expansion of the Universe. ..... effectively appear as self-conserved dark energy, with a non-trivial ...
Fractals in DNA sequence analysis
Institute of Scientific and Technical Information of China (English)
Yu Zu-Guo(喻祖国); Vo Anh; Gong Zhi-Min(龚志民); Long Shun-Chao(龙顺潮)
2002-01-01
Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance,and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view)to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.
Classical and quantum investigations of four-dimensional maps with a mixed phase space
International Nuclear Information System (INIS)
Richter, Martin
2012-01-01
Systems with more than two degrees of freedom are of fundamental importance for the understanding of problems ranging from celestial mechanics to molecules. Due to the dimensionality the classical phase-space structure of such systems is more difficult to understand than for systems with two or fewer degrees of freedom. This thesis aims for a better insight into the classical as well as the quantum mechanics of 4D mappings representing driven systems with two degrees of freedom. In order to analyze such systems, we introduce 3D sections through the 4D phase space which reveal the regular and chaotic structures. We introduce these concepts by means of three example mappings of increasing complexity. After a classical analysis the systems are investigated quantum mechanically. We focus especially on two important aspects: First, we address quantum mechanical consequences of the classical Arnold web and demonstrate how quantum mechanics can resolve this web in the semiclassical limit. Second, we investigate the quantum mechanical tunneling couplings between regular and chaotic regions in phase space. We determine regular-to-chaotic tunneling rates numerically and extend the fictitious integrable system approach to higher dimensions for their prediction. Finally, we study resonance-assisted tunneling in 4D maps.
Positioning with stationary emitters in a two-dimensional space-time
International Nuclear Information System (INIS)
Coll, Bartolome; Ferrando, Joan Josep; Morales, Juan Antonio
2006-01-01
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D 73, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make relativistic gravimetry. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coordinate system constituted by the electromagnetic signals broadcasting the proper time of the emitters are the so called emission coordinates, and we show that, in such emission coordinates, the trajectories of the emitters in both situations, the absence and presence of a gravitational field, are identical. The interesting point is that, in spite of this fact, particular additional information on the system or on the user allows us not only to distinguish both space-times, but also to complete the dynamical description of emitters and user and even to measure the mass of the gravitational field. The precise information under which these dynamical and gravimetric results may be obtained is carefully pointed out
Large self-affine fractality in $\\pi^{+}p$ and $K^{+}p$ collisions at 250 GeV/c
Agababian, N M
1996-01-01
Taking into account the anisotropy of phase space in multiparticle production, a self-affine analysis of factorial moments was carried out on the NA22 data for $\\pi^{+}p$ and $K^{+}p$ collisions at 250 GeV/$c$. Within the transverse plane, the Hurst exponents measuring the anisotropy are consistent with unit value (i.e. no anisotropy). They are, however, only half that value when the longitudinal direction is compared to the transverse ones. Fractality, indeed, turns out to be self-affine rather than self-similar in multiparticle production. In three-dimensional phase space, power-law scaling is observed to be better realized in self-affine than in self-similar analysis.
An efficient fractal image coding algorithm using unified feature and DCT
International Nuclear Information System (INIS)
Zhou Yiming; Zhang Chao; Zhang Zengke
2009-01-01
Fractal image compression is a promising technique to improve the efficiency of image storage and image transmission with high compression ratio, however, the huge time consumption for the fractal image coding is a great obstacle to the practical applications. In order to improve the fractal image coding, efficient fractal image coding algorithms using a special unified feature and a DCT coder are proposed in this paper. Firstly, based on a necessary condition to the best matching search rule during fractal image coding, the fast algorithm using a special unified feature (UFC) is addressed, and it can reduce the search space obviously and exclude most inappropriate matching subblocks before the best matching search. Secondly, on the basis of UFC algorithm, in order to improve the quality of the reconstructed image, a DCT coder is combined to construct a hybrid fractal image algorithm (DUFC). Experimental results show that the proposed algorithms can obtain good quality of the reconstructed images and need much less time than the baseline fractal coding algorithm.
Fractal nature of humic materials
International Nuclear Information System (INIS)
Rice, J.A.
1992-01-01
Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this ''disorder within disorder.'' Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fraction has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis
Turbulent premixed flames on fractal-grid-generated turbulence
Energy Technology Data Exchange (ETDEWEB)
Soulopoulos, N; Kerl, J; Sponfeldner, T; Beyrau, F; Hardalupas, Y; Taylor, A M K P [Mechanical Engineering Department, Imperial College London, London SW7 2AZ (United Kingdom); Vassilicos, J C, E-mail: ns6@ic.ac.uk [Department of Aeronautics, Imperial College London, London SW7 2AZ (United Kingdom)
2013-12-15
A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area. (paper)
Three-Dimensional, Transgenic Cell Models to Quantify Space Genotoxic Effects
Gonda, S. R.; Sognier, M. A.; Wu, H.; Pingerelli, P. L.; Glickman, B. W.; Dawson, David L. (Technical Monitor)
1999-01-01
The space environment contains radiation and chemical agents known to be mutagenic and carcinogenic to humans. Additionally, microgravity is a complicating factor that may modify or synergize induced genotoxic effects. Most in vitro models fail to use human cells (making risk extrapolation to humans more difficult), overlook the dynamic effect of tissue intercellular interactions on genotoxic damage, and lack the sensitivity required to measure low-dose effects. Currently a need exists for a model test system that simulates cellular interactions present in tissue, and can be used to quantify genotoxic damage induced by low levels of radiation and chemicals, and extrapolate assessed risk to humans. A state-of-the-art, three-dimensional, multicellular tissue equivalent cell culture model will be presented. It consists of mammalian cells genetically engineered to contain multiple copies of defined target genes for genotoxic assessment,. NASA-designed bioreactors were used to coculture mammalian cells into spheroids, The cells used were human mammary epithelial cells (H184135) and Stratagene's (Austin, Texas) Big Blue(TM) Rat 2 lambda fibroblasts. The fibroblasts were genetically engineered to contain -a high-density target gene for mutagenesis (60 copies of lacl/LacZ per cell). Tissue equivalent spheroids were routinely produced by inoculation of 2 to 7 X 10(exp 5) fibroblasts with Cytodex 3 beads (150 micrometers in diameter). at a 20:1 cell:bead ratio, into 50-ml HARV bioreactors (Synthecon, Inc.). Fibroblasts were cultured for 5 days, an equivalent number of epithelial cells added, and the fibroblast/epithelial cell coculture continued for 21 days. Three-dimensional spheroids with diameters ranging from 400 to 600 micrometers were obtained. Histological and immunohistochemical Characterization revealed i) both cell types present in the spheroids, with fibroblasts located primarily in the center, surrounded by epithelial cells; ii) synthesis of extracellular matrix
On the intersection of irreducible components of the space of finite-dimensional Lie algebras
International Nuclear Information System (INIS)
Gorbatsevich, Vladimir V
2012-01-01
The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra is considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.
Digital chaos-masked optical encryption scheme enhanced by two-dimensional key space
Liu, Ling; Xiao, Shilin; Zhang, Lu; Bi, Meihua; Zhang, Yunhao; Fang, Jiafei; Hu, Weisheng
2017-09-01
A digital chaos-masked optical encryption scheme is proposed and demonstrated. The transmitted signal is completely masked by interference chaotic noise in both bandwidth and amplitude with analog method via dual-drive Mach-Zehnder modulator (DDMZM), making the encrypted signal analog, noise-like and unrecoverable by post-processing techniques. The decryption process requires precise matches of both the amplitude and phase between the cancellation and interference chaotic noises, which provide a large two-dimensional key space with the help of optical interference cancellation technology. For 10-Gb/s 16-quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) signal over the maximum transmission distance of 80 km without dispersion compensation or inline amplifier, the tolerable mismatch ranges of amplitude and phase/delay at the forward error correction (FEC) threshold of 3.8×10-3 are 0.44 dB and 0.08 ns respectively.
On higher-dimensional loop algebras, pseudodifferential operators and Fock space realizations
International Nuclear Information System (INIS)
Westerberg, A.
1997-01-01
We discuss a previously discovered extension of the infinite-dimensional Lie algebra map(M,g) which generalizes the Kac-Moody algebras in 1+1 dimensions and the Mickelsson-Faddeev algebras in 3+1 dimensions to manifolds M of general dimensions. Furthermore, we review the method of regularizing current algebras in higher dimensions using pseudodifferential operator (PSDO) symbol calculus. In particular, we discuss the issue of Lie algebra cohomology of PSDOs and its relation to the Schwinger terms arising in the quantization process. Finally, we apply this regularization method to the algebra with partial success, and discuss the remaining obstacles to the construction of a Fock space representation. (orig.)
International Nuclear Information System (INIS)
Staff, Jan E.; Niebergal, Brian P.; Ouyed, Rachid; Pudritz, Ralph E.; Cai, Kai
2010-01-01
We perform state-of-the-art, three-dimensional, time-dependent simulations of magnetized disk winds, carried out to simulation scales of 60 AU, in order to confront optical Hubble Space Telescope observations of protostellar jets. We 'observe' the optical forbidden line emission produced by shocks within our simulated jets and compare these with actual observations. Our simulations reproduce the rich structure of time-varying jets, including jet rotation far from the source, an inner (up to 400 km s -1 ) and outer (less than 100 km s -1 ) component of the jet, and jet widths of up to 20 AU in agreement with observed jets. These simulations when compared with the data are able to constrain disk wind models. In particular, models featuring a disk magnetic field with a modest radial spatial variation across the disk are favored.
Three-Dimensional Navier-Stokes Calculations Using the Modified Space-Time CESE Method
Chang, Chau-lyan
2007-01-01
The space-time conservation element solution element (CESE) method is modified to address the robustness issues of high-aspect-ratio, viscous, near-wall meshes. In this new approach, the dependent variable gradients are evaluated using element edges and the corresponding neighboring solution elements while keeping the original flux integration procedure intact. As such, the excellent flux conservation property is retained and the new edge-based gradients evaluation significantly improves the robustness for high-aspect ratio meshes frequently encountered in three-dimensional, Navier-Stokes calculations. The order of accuracy of the proposed method is demonstrated for oblique acoustic wave propagation, shock-wave interaction, and hypersonic flows over a blunt body. The confirmed second-order convergence along with the enhanced robustness in handling hypersonic blunt body flow calculations makes the proposed approach a very competitive CFD framework for 3D Navier-Stokes simulations.
Geometry of lengths, areas, and volumes two-dimensional spaces, volume 1
Cannon, James W
2017-01-01
This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving c...
Black objects and hoop conjecture in five-dimensional space-time
Energy Technology Data Exchange (ETDEWEB)
Yamada, Yuta; Shinkai, Hisa-aki, E-mail: m1m08a26@info.oit.ac.j, E-mail: shinkai@is.oit.ac.j [Faculty of Information Science and Technology, Osaka Institute of Technology, 1-79-1 Kitayama, Hirakata, Osaka 573-0196 (Japan)
2010-02-21
We numerically investigated the sequences of initial data of a thin spindle and a thin ring in five-dimensional space-time in the context of the cosmic censorship conjecture. We modeled the matter in non-rotating homogeneous spheroidal or toroidal configurations under the momentarily static assumption, solved the Hamiltonian constraint equation and searched the apparent horizons. We discussed when S{sup 3} (black-hole) or S{sup 1} x S{sup 2} (black-ring) horizons ('black objects') are formed. By monitoring the location of the maximum Kretchmann invariant, an appearance of 'naked singularity' or 'naked ring' under special situations is suggested. We also discuss the validity of the hyper-hoop conjecture using a minimum area around the object, and show that the appearance of the ring horizon does not match with this hoop.
Global Tracking Control of Quadrotor VTOL Aircraft in Three-Dimensional Space
Directory of Open Access Journals (Sweden)
Duc Khac Do
2014-07-01
Full Text Available This paper presents a method to design controllers that force a quadrotor vertical take-off and landing (VTOL aircraft to globally asymptotically track a reference trajectory in three-dimensional space. Motivated by the vehicle's steering practice, the roll and pitch angles are considered as immediate controls plus the total thrust force provided by the aircraft's four rotors to control the position and yaw angle of the aircraft. The control design is based on the newly introduced one-step ahead backstepping, the standard backstepping and Lyapunov's direct methods. A combination of Euler angles and unit-quaternion for the attitude representation of the aircraft is used to obtain global tracking control results. The paper also includes a design of observers that exponentially estimate the aircraft's linear velocity vector and disturbances. Simulations illustrate the results.
International Nuclear Information System (INIS)
Oono, Y.; Ohta, T.; Freed, K.F.
1981-01-01
A dimensional regularization approach to the renormalization group treatment of polymer excluded volume is formulated in chain conformation space where monomers are specified by their spatial positions and their positions along the chain and the polymers may be taken to be monodisperse. The method utilizes basic scale invariance considerations. First, it is recognized that long wavelength macroscopic descriptions must be well defined in the limit that the minimum atomic or molecular scale L is set to zero. Secondly, the microscopic theory is independent of the conveniently chosen macroscopic scale of length k. The freedom of choice of k is exploited along with the assumed renormalizability of the theory to provide the renormalization group equations which directly imply the universal scaling laws for macroscopic properties. The renormalizability of the model implies the existence of the general relations between the basic macroparameters, such as chain length, excluded volume, etc., and their microscopic counterparts in the microscopic model for the system. These macro--micro relations are defined through the condition that macroscopic quantities be well defined for polymer chains for any spatial dimensionality. The method is illustrated by calculating the end vector distribution function for all values of end vectors R. The evaluation of this distribution function currently requires the use of expansions in e = 4-d. In this case our distribution reduces to known limits for R→0 or infinity. Subsequent papers will present calculations of the polymer coherent scattering function, the monomer spatial distribution function, and concentration dependent properties
Quantum trajectories in complex space: One-dimensional stationary scattering problems
International Nuclear Information System (INIS)
Chou, C.-C.; Wyatt, Robert E.
2008-01-01
One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems
Massive quantum field theory in two-dimensional Robertson-Walker space-time
International Nuclear Information System (INIS)
Bunch, T.S.; Christensen, S.M.; Fulling, S.A.
1978-01-01
The stress tensor of a massive scalar field, as an integral over normal modes (which are not mere plane waves), is regularized by covariant point separation. When the expectation value in a Parker-Fulling adiabatic vacuum state is expanded in the limit of small curvature-to-mass ratios, the series coincides in each order with the Schwinger-DeWitt-Christensen proper-time expansion. The renormalization ansatz suggested by these expansions (which applies to arbitrary curvature-to-mass ratios and arbitrary quantum state) can be implemented at the integrand level for practical computations. The renormalized tensor (1) passes in the massless limit, for appropriate choice of state, to the known vacuum stress of a massless field, (2) agrees with the explicit results of Bernard and Duncan for a special model, and (3) has a nonzero vacuum expectation value in the two-dimensional ''Milne universe'' (flat space in hyperbolic coordinates). Following Wald, we prove that the renormalized tensor is conserved and point out that there is no arbitrariness in the renormalization procedure. The general approach of this paper is applicable to four-dimensional models
Order-fractal transitions in abstract paintings
Energy Technology Data Exchange (ETDEWEB)
Calleja, E.M. de la, E-mail: elsama79@gmail.com [Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS (Brazil); Cervantes, F. [Department of Applied Physics, CINVESTAV-IPN, Carr. Antigua a Progreso km.6, Cordemex, C.P.97310, Mérida, Yucatán (Mexico); Calleja, J. de la [Department of Informatics, Universidad Politécnica de Puebla, 72640 (Mexico)
2016-08-15
In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.
Scale-dependent Patterns in One-dimensional Fracture Spacing and Aperture Data
Roy, A.; Perfect, E.
2013-12-01
One-dimensional scanline data about fracture spacing and size attributes such as aperture or length are mostly considered in separate studies that compute the cumulative frequency of these attributes without regard to their actual spatial sequence. In a previous study, we showed that spacing data can be analyzed using lacunarity to identify whether fractures occur in clusters. However, to determine if such clusters also contain the largest fractures in terms of a size attribute such as aperture, it is imperative that data about the size attribute be integrated with information about fracture spacing. While for example, some researchers have considered aperture in conjunction with spacing, their analyses were either applicable only to a specific type of data (e.g. multifractal) or failed to characterize the data at different scales. Lacunarity is a technique for analyzing multi-scale non-binary data and is ideally-suited for characterizing scanline data with spacing and aperture values. We present a technique that can statistically delineate the relationship between size attributes and spatial clustering. We begin by building a model scanline that has complete partitioning of fractures with small and large apertures between the intercluster regions and clusters. We demonstrate that the ratio of lacunarity for this model to that of its counterpart for a completely randomized sequence of apertures can be used to determine whether large-aperture fractures preferentially occur next to each other. The technique is then applied to two natural fracture scanline datasets, one with most of the large apertures occurring in fracture clusters, and the other with more randomly-spaced fractures, without any specific ordering of aperture values. The lacunarity ratio clearly discriminates between these two datasets and, in the case of the first example, it is also able to identify the range of scales over which the widest fractures are clustered. The technique thus developed for
Fractal approach to computer-analytical modelling of tree crown
International Nuclear Information System (INIS)
Berezovskaya, F.S.; Karev, G.P.; Kisliuk, O.F.; Khlebopros, R.G.; Tcelniker, Yu.L.
1993-09-01
In this paper we discuss three approaches to the modeling of a tree crown development. These approaches are experimental (i.e. regressive), theoretical (i.e. analytical) and simulation (i.e. computer) modeling. The common assumption of these is that a tree can be regarded as one of the fractal objects which is the collection of semi-similar objects and combines the properties of two- and three-dimensional bodies. We show that a fractal measure of crown can be used as the link between the mathematical models of crown growth and light propagation through canopy. The computer approach gives the possibility to visualize a crown development and to calibrate the model on experimental data. In the paper different stages of the above-mentioned approaches are described. The experimental data for spruce, the description of computer system for modeling and the variant of computer model are presented. (author). 9 refs, 4 figs
Maximal superintegrability of the generalized Kepler-Coulomb system on N-dimensional curved spaces
International Nuclear Information System (INIS)
Ballesteros, Angel; Herranz, Francisco J
2009-01-01
The superposition of the Kepler-Coulomb potential on the 3D Euclidean space with three centrifugal terms has recently been shown to be maximally superintegrable (Verrier and Evans 2008 J. Math. Phys. 49 022902) by finding an additional (hidden) integral of motion which is quartic in the momenta. In this paper, we present the generalization of this result to the N-dimensional spherical, hyperbolic and Euclidean spaces by making use of a unified symmetry approach that makes use of the curvature parameter. The resulting Hamiltonian, formed by the (curved) Kepler-Coulomb potential together with N centrifugal terms, is shown to be endowed with 2N - 1 functionally independent integrals of the motion: one of them is quartic and the remaining ones are quadratic. The transition from the proper Kepler-Coulomb potential, with its associated quadratic Laplace-Runge-Lenz N-vector, to the generalized system is fully described. The role of spherical, nonlinear (cubic) and coalgebra symmetries in all these systems is highlighted
Individual-based models for adaptive diversification in high-dimensional phenotype spaces.
Ispolatov, Iaroslav; Madhok, Vaibhav; Doebeli, Michael
2016-02-07
Most theories of evolutionary diversification are based on equilibrium assumptions: they are either based on optimality arguments involving static fitness landscapes, or they assume that populations first evolve to an equilibrium state before diversification occurs, as exemplified by the concept of evolutionary branching points in adaptive dynamics theory. Recent results indicate that adaptive dynamics may often not converge to equilibrium points and instead generate complicated trajectories if evolution takes place in high-dimensional phenotype spaces. Even though some analytical results on diversification in complex phenotype spaces are available, to study this problem in general we need to reconstruct individual-based models from the adaptive dynamics generating the non-equilibrium dynamics. Here we first provide a method to construct individual-based models such that they faithfully reproduce the given adaptive dynamics attractor without diversification. We then show that a propensity to diversify can be introduced by adding Gaussian competition terms that generate frequency dependence while still preserving the same adaptive dynamics. For sufficiently strong competition, the disruptive selection generated by frequency-dependence overcomes the directional evolution along the selection gradient and leads to diversification in phenotypic directions that are orthogonal to the selection gradient. Copyright © 2015 Elsevier Ltd. All rights reserved.
Training astronauts using three-dimensional visualisations of the International Space Station.
Rycroft, M; Houston, A; Barker, A; Dahlstron, E; Lewis, N; Maris, N; Nelles, D; Bagaoutdinov, R; Bodrikov, G; Borodin, Y; Cheburkov, M; Ivanov, D; Karpunin, P; Katargin, R; Kiselyev, A; Kotlayarevsky, Y; Schetinnikov, A; Tylerov, F
1999-03-01
Recent advances in personal computer technology have led to the development of relatively low-cost software to generate high-resolution three-dimensional images. The capability both to rotate and zoom in on these images superposed on appropriate background images enables high-quality movies to be created. These developments have been used to produce realistic simulations of the International Space Station on CD-ROM. This product is described and its potentialities demonstrated. With successive launches, the ISS is gradually built up, and visualised over a rotating Earth against the star background. It is anticipated that this product's capability will be useful when training astronauts to carry out EVAs around the ISS. Simulations inside the ISS are also very realistic. These should prove invaluable when familiarising the ISS crew with their future workplace and home. Operating procedures can be taught and perfected. "What if" scenario models can be explored and this facility should be useful when training the crew to deal with emergency situations which might arise. This CD-ROM product will also be used to make the general public more aware of, and hence enthusiastic about, the International Space Station programme.
Visuospatial biases in preschool children: Evidence from line bisection in three-dimensional space.
Patro, Katarzyna; Nuerk, Hans-Christoph; Brugger, Peter
2018-04-09
Spatial attention in adults is characterized by systematic asymmetries across all three spatial dimensions. These asymmetries are evident when participants bisect horizontal, vertical, or radial lines and misplace their midpoints to the left, the top, or far from the body, respectively. However, bisection errors are rarely examined during early childhood. In this study, we examined the development of spatial-attentional asymmetries in three-dimensional (3D) space by asking preschool children (aged 3-6 years) to bisect horizontal, vertical, and radial lines. Children erred to the left with horizontal lines and to the top with vertical lines, consistent with the pattern reported in adults. These biases got stronger with age and were absent in the youngest preschoolers. However, by controlling for a possible failure in hitting the line, we observed an additional unpredicted pattern: Children's pointing systematically deviated away from the line to an empty space on its left side (for vertical and radial lines) or above it (for horizontal lines). Notably, this task-irrelevant deviation was pronounced in children as young as 3 or 4 years. We conclude that asymmetries in spatial-attentional functions should be measured not only in task-relevant dimensions but also in task-irrelevant dimensions because the latter may reveal biases in very young children not typically observed in task-relevant measures. Copyright © 2018 Elsevier Inc. All rights reserved.
Fractal structures and fractal functions as disease indicators
Escos, J.M; Alados, C.L.; Emlen, J.M.
1995-01-01
Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.
Resonance and Fractal Geometry
Broer, Henk W.
The phenomenon of resonance will be dealt with from the viewpoint of dynamical systems depending on parameters and their bifurcations. Resonance phenomena are associated to open subsets in the parameter space, while their complement corresponds to quasi-periodicity and chaos. The latter phenomena
Bifurcation and Fractal of the Coupled Logistic Map
Wang, Xingyuan; Luo, Chao
The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.
Experimental Investigation of a Direct Methanol Fuel Cell with Hilbert Fractal Current Collectors
Directory of Open Access Journals (Sweden)
Jing-Yi Chang
2014-01-01
Full Text Available The Hilbert curve is a continuous type of fractal space-filling curve. This fractal curve visits every point in a square grid with a size of 2×2, 4×4, or any other power of two. This paper presents Hilbert fractal curve application to direct methanol fuel cell (DMFC current collectors. The current collectors are carved following first, second, and third order Hilbert fractal curves. These curves give the current collectors different free open ratios and opening perimeters. We conducted an experimental investigation into DMFC performance as a function of the free open ratio and opening perimeter on the bipolar plates. Nyquist plots of the bipolar plates are made and compared using electrochemical impedance spectroscopy (EIS experiments to understand the phenomena in depth. The results obtained in this paper could be a good reference for future current collector design.
Evaluation of Reduced Power Spectra from Three-Dimensional k-Space
Saur, J.; von Papen, M.
2014-12-01
We present a new tool to evaluate one dimensional reduced power spectral densities (PSD) from arbitrary energy distributions in kk-space. This enables us to calculate the power spectra as they are measured in spacecraft frame for any given measurement geometry assuming Taylor's frozen-in approximation. It is possible to seperately calculate the diagonal elements of the spectral tensor and also to insert additional, non-turbulent energy in kk-space (e.g. mirror mode waves). Given a critically balanced turbulent cascade with k∥˜kα⊥k_\\|sim k_perp^alpha, we explore the implications on the spectral form of the PSD and the functional dependence of the spectral index κkappa on the field-to-flow angle θtheta between plasma flow and background magnetic field. We show that critically balanced turbulence develops a θtheta-independent cascade with the spectral slope of the perpendicular cascade κ(θ=90∘)kappa(theta{=}90^circ). This happens at frequencies f>fmaxf>f_mathrm{max}, where fmax(L,α,θ)f_mathrm{max}(L,alpha,theta) is a function of outer scale LL, critical balance exponent αalpha and field-to-flow angle θtheta. We also discuss potential damping terms acting on the kk-space distribution of energy and their effect on the PSD. Further, we show that the functional dependence κ(θ)kappa(theta) as found by textit{Horbury et al.} (2008) and textit{Chen et al.} (2010) can be explained with a damped critically balanced turbulence model.
Conference on Fractals and Related Fields III
Seuret, Stéphane
2017-01-01
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
Chaos, Fractals and Their Applications
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
The fractal dimension of architecture
Ostwald, Michael J
2016-01-01
Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along...
Correlation of optical properties with the fractal microstructure of black molybdenum coatings
Energy Technology Data Exchange (ETDEWEB)
Barrera, Enrique; Gonzalez, Federico [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Rodriguez, Eduardo [Area de Computacion y Sistemas, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Alvarez-Ramirez, Jose, E-mail: jjar@xanum.uam.mx [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico)
2010-01-01
Coating is commonly used for improving the optical properties of surfaces for solar collector applications. The coating morphology depends on the deposition conditions, and this determines the final optical characteristics. Coating morphologies are irregular and of fractal nature, so a suitable approach for its characterization should use methods borrowed from fractal analysis. The aim of this work is to study the fractal characteristics of black molybdenum coatings on copper and to relate the fractal parameters to the optical properties. To this end, coating surfaces were prepared via immersion in a solution of ammonium paramolybdate for different deposition periods. The fractal analysis was carried out for SEM and AFM images of the coating surface and the fractal properties were obtained with a recently developed high-dimensional extension of the well-known detrended fluctuation analysis (DFA). The most salient parameter drawn from the application of the DFA is the Hurst index, a parameter related to the roughness of the coating surface, and the multifractality index, which is related to the non-linearity features of the coating morphology. The results showed that optical properties, including absorptance and emittance, are decreasing functions of the Hurst and multifractality indices. This suggests that coating surfaces with high absorptance and emittance values are related to complex coating morphologies conformed within a non-linear structure.
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-01-01
reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics
Kuppermann, Aron
2011-05-14
The row-orthonormal hyperspherical coordinate (ROHC) approach to calculating state-to-state reaction cross sections and bound state levels of N-atom systems requires the use of angular momentum tensors and Wigner rotation functions in a space of dimension N - 1. The properties of those tensors and functions are discussed for arbitrary N and determined for N = 5 in terms of the 6 Euler angles involved in 4-dimensional space.
Node insertion in Coalescence Fractal Interpolation Function
International Nuclear Information System (INIS)
Prasad, Srijanani Anurag
2013-01-01
The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed
Fractional hydrodynamic equations for fractal media
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2005-01-01
We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered
Power Load Prediction Based on Fractal Theory
Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song
2015-01-01
The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...
Fractal Metrology for biogeosystems analysis
Directory of Open Access Journals (Sweden)
V. Torres-Argüelles
2010-11-01
Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Fractal geometry mathematical foundations and applications
Falconer, Kenneth
2013-01-01
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applica
A fractal model of the Universe
Gottlieb, Ioan
The book represents a revisioned, extended, completed and translated version of the book "Superposed Universes. A scientific novel and a SF story" (1995). The book contains a hypothesis by the author concerning the complexity of the Nature. An introduction to the theories of numbers, manyfolds and topology is given. The possible connection with the theory of evolution of the Universe is discussed. The book contains also in the last chapter a SF story based on the hypothesis presented. A connection with fractals theory is given. A part of his earlier studies (1955-1956) were subsequently published without citation by Ali Kyrala (Phys. Rev. vol.117, No.5, march 1, 1960). The book contains as an important appendix the early papers (some of which are published in the coauthoprship with his scientific advisors): 1) T.T. Vescan, A. Weiszmann and I.Gottlieb, Contributii la studiul problemelor geometrice ale teoriei relativitatii restranse. Academia R.P.R. Baza Timisoara. Lucrarile consfatuirii de geometrie diferentiala din 9-12 iunie 1955. In this paper the authors show a new method of the calculation of the metrics. 2) Jean Gottlieb, L'hyphotese d'un modele de la structure de la matiere, Revista Matematica y Fisica Teorica, Serie A, Volumen XY, No.1, y.2, 1964 3) I. Gottlieb, Some hypotheses on space, time and gravitation, Studies in Gravitation Theory, CIP Press, Bucharest, 1988, pp.227-234 as well as some recent papers (published in the coauthorship with his disciples): 4)M. Agop, Gottlieb speace-time. A fractal axiomatic model of the Universe. in Particles and Fields, Editors: M.Agop and P.D. Ioannou, Athens University Press, 2005, pp. 59-141 5) I. Gottlieb, M.Agop and V.Enache, Games with Cantor's dust. Chaos, Solitons and Fractals, vol.40 (2009) pp. 940-945 6) I. Gottlieb, My picture over the World, Bull. of the Polytechnic Institute of Iasi. Tom LVI)LX, Fasc. 1, 2010, pp. 1-18. The book contains also a dedication to father Vasile Gottlieb and wife Cleopatra
Subjective figure reversal in two- and three-dimensional perceptual space.
Radilová, J; Radil-Weiss, T
1984-08-01
A permanently illuminated pattern of Mach's truncated pyramid can be perceived according to the experimental instruction given, either as a three-dimensional reversible figure with spontaneously changing convex and concave interpretation (in one experiment), or as a two-dimensional reversible figure-ground pattern (in another experiment). The reversal rate was about twice as slow, without the subjects being aware of it, if it was perceived as a three-dimensional figure compared to the situation when it was perceived as two-dimensional. It may be hypothetized that in the three-dimensional case, the process of perception requires more sequential steps than in the two-dimensional one.
Linearized fermion-gravitation system in a (2+1)-dimensional space-time with Chern-Simons data
International Nuclear Information System (INIS)
Mello, E.R.B. de.
1990-01-01
The fermion-graviton system at linearized level in a (2+1)-dimensional space-time with the gravitational Chern-Simons term is studied. In this approximation it is shown that this system presents anomalous rotational properties and spin, in analogy with the gauge field-matter system. (A.C.A.S.) [pt
A five dimensional experimental design, i.e. a five component ion mixture design for nitrate, phosphate, potassium, sodium and chloride projected across a total ion concentration gradient of 1-30 mM was utilized to map the ion-based, scenopoetic, or ‘Grinnellian’, niche space for two freshwater alga...
International Nuclear Information System (INIS)
Witek, Helvi; Nerozzi, Andrea; Zilhao, Miguel; Herdeiro, Carlos; Gualtieri, Leonardo; Cardoso, Vitor; Sperhake, Ulrich
2010-01-01
Higher dimensional black holes play an exciting role in fundamental physics, such as high energy physics. In this paper, we use the formalism and numerical code reported in [1] to study the head-on collision of two black holes. For this purpose we provide a detailed treatment of gravitational wave extraction in generic D dimensional space-times, which uses the Kodama-Ishibashi formalism. For the first time, we present the results of numerical simulations of the head-on collision in five space-time dimensions, together with the relevant physical quantities. We show that the total radiated energy, when two black holes collide from rest at infinity, is approximately (0.089±0.006)% of the center of mass energy, slightly larger than the 0.055% obtained in the four-dimensional case, and that the ringdown signal at late time is in very good agreement with perturbative calculations.
A variational principle for the Hausdorff dimension of fractal sets
DEFF Research Database (Denmark)
Olsen, Lars; Cutler, Colleen D.
1994-01-01
Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)......Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)...
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-05-01
In this work, Paper-based inkjet-printed Ultra-wide band (UWB) fractal antennas are presented. Three new designs, a combined UWB fractal monopole based on the fourth order Koch Snowflake fractal which utilizes a Sierpinski Gasket fractal for ink reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics. It is shown that fractals prove to be a successful method of reducing fabrication cost in inkjet printed antennas while retaining or enhancing printed antenna performance.
International Nuclear Information System (INIS)
Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut
2014-01-01
To compare the accuracy of diagnosing aqueductal patency and image quality between high spatial resolution three-dimensional (3D) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE) at 3-T in patients with hydrocephalus. This retrospective study included 99 patients diagnosed with hydrocephalus. T2W 3D-SPACE was added to the routine sequences which consisted of T2W 2D-TSE, 3D-constructive interference steady state (CISS), and cine phase-contrast MRI (PC-MRI). Two radiologists evaluated independently the patency of cerebral aqueduct and image quality on the T2W 2D-TSE and T2W 3D-SPACE. PC-MRI and 3D-CISS were used as the reference for aqueductal patency and image quality, respectively. Inter-observer agreement was calculated using kappa statistics. The evaluation of the aqueductal patency by T2W 3D-SPACE and T2W 2D-TSE were in agreement with PC-MRI in 100% (99/99; sensitivity, 100% [83/83]; specificity, 100% [16/16]) and 83.8% (83/99; sensitivity, 100% [67/83]; specificity, 100% [16/16]), respectively (p < 0.001). No significant difference in image quality between T2W 2D-TSE and T2W 3D-SPACE (p = 0.056) occurred. The kappa values for inter-observer agreement were 0.714 for T2W 2D-TSE and 0.899 for T2W 3D-SPACE. Three-dimensional-SPACE is superior to 2D-TSE for the evaluation of aqueductal patency in hydrocephalus. T2W 3D-SPACE may hold promise as a highly accurate alternative treatment to PC-MRI for the physiological and morphological evaluation of aqueductal patency.
Energy Technology Data Exchange (ETDEWEB)
Ucar, Murat; Guryildirim, Melike; Tokgoz, Nil; Kilic, Koray; Borcek, Alp; Oner, Yusuf; Akkan, Koray; Tali, Turgut [School of Medicine, Gazi University, Ankara (Turkey)
2014-12-15
To compare the accuracy of diagnosing aqueductal patency and image quality between high spatial resolution three-dimensional (3D) high-sampling-efficiency technique (sampling perfection with application optimized contrast using different flip angle evolutions [SPACE]) and T2-weighted (T2W) two-dimensional (2D) turbo spin echo (TSE) at 3-T in patients with hydrocephalus. This retrospective study included 99 patients diagnosed with hydrocephalus. T2W 3D-SPACE was added to the routine sequences which consisted of T2W 2D-TSE, 3D-constructive interference steady state (CISS), and cine phase-contrast MRI (PC-MRI). Two radiologists evaluated independently the patency of cerebral aqueduct and image quality on the T2W 2D-TSE and T2W 3D-SPACE. PC-MRI and 3D-CISS were used as the reference for aqueductal patency and image quality, respectively. Inter-observer agreement was calculated using kappa statistics. The evaluation of the aqueductal patency by T2W 3D-SPACE and T2W 2D-TSE were in agreement with PC-MRI in 100% (99/99; sensitivity, 100% [83/83]; specificity, 100% [16/16]) and 83.8% (83/99; sensitivity, 100% [67/83]; specificity, 100% [16/16]), respectively (p < 0.001). No significant difference in image quality between T2W 2D-TSE and T2W 3D-SPACE (p = 0.056) occurred. The kappa values for inter-observer agreement were 0.714 for T2W 2D-TSE and 0.899 for T2W 3D-SPACE. Three-dimensional-SPACE is superior to 2D-TSE for the evaluation of aqueductal patency in hydrocephalus. T2W 3D-SPACE may hold promise as a highly accurate alternative treatment to PC-MRI for the physiological and morphological evaluation of aqueductal patency.
The extensions of space-time. Physics in the 8-dimensional homogeneous space D = SU(2,2)/K
International Nuclear Information System (INIS)
Barut, A.O.
1993-07-01
The Minkowski space-time is only a boundary of a bigger homogeneous space of the conformal group. The conformal group is the symmetry group of our most fundamental massless wave equations. These extended groups and spaces have many remarkable properties and physical implications. (author). 36 refs
Directory of Open Access Journals (Sweden)
L.V. Arun Shalin
2016-01-01
Full Text Available Clustering is a process of grouping elements together, designed in such a way that the elements assigned to similar data points in a cluster are more comparable to each other than the remaining data points in a cluster. During clustering certain difficulties related when dealing with high dimensional data are ubiquitous and abundant. Works concentrated using anonymization method for high dimensional data spaces failed to address the problem related to dimensionality reduction during the inclusion of non-binary databases. In this work we study methods for dimensionality reduction for non-binary database. By analyzing the behavior of dimensionality reduction for non-binary database, results in performance improvement with the help of tag based feature. An effective multi-clustering anonymization approach called Discrete Component Task Specific Multi-Clustering (DCTSM is presented for dimensionality reduction on non-binary database. To start with we present the analysis of attribute in the non-binary database and cluster projection identifies the sparseness degree of dimensions. Additionally with the quantum distribution on multi-cluster dimension, the solution for relevancy of attribute and redundancy on non-binary data spaces is provided resulting in performance improvement on the basis of tag based feature. Multi-clustering tag based feature reduction extracts individual features and are correspondingly replaced by the equivalent feature clusters (i.e. tag clusters. During training, the DCTSM approach uses multi-clusters instead of individual tag features and then during decoding individual features is replaced by corresponding multi-clusters. To measure the effectiveness of the method, experiments are conducted on existing anonymization method for high dimensional data spaces and compared with the DCTSM approach using Statlog German Credit Data Set. Improved tag feature extraction and minimum error rate compared to conventional anonymization
Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study
Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana
2016-04-01
The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with
Forward Modeling of Reduced Power Spectra from Three-dimensional k-space
von Papen, Michael; Saur, Joachim
2015-06-01
We present results from a numerical forward model to evaluate one-dimensional reduced power spectral densities (PSDs) from arbitrary energy distributions in {\\boldsymbol{k}} -space. In this model, we can separately calculate the diagonal elements of the spectral tensor for incompressible axisymmetric turbulence with vanishing helicity. Given a critically balanced turbulent cascade with {{k}\\parallel }∼ k\\bot α and α \\lt 1, we explore the implications on the reduced PSD as a function of frequency. The spectra are obtained under the assumption of Taylor’s hypothesis. We further investigate the functional dependence of the spectral index κ on the field-to-flow angle θ between plasma flow and background magnetic field from MHD to electron kinetic scales. We show that critically balanced turbulence asymptotically develops toward θ-independent spectra with a slope corresponding to the perpendicular cascade. This occurs at a transition frequency {{f}2D}(L,α ,θ ), which is analytically estimated and depends on outer scale L, critical balance exponent α, and field-to-flow angle θ. We discuss anisotropic damping terms acting on the {\\boldsymbol{k}} -space distribution of energy and their effects on the PSD. Further, we show that the spectral anisotropies κ (θ ) as found by Horbury et al. and Chen et al. in the solar wind are in accordance with a damped critically balanced cascade of kinetic Alfvén waves. We also model power spectra obtained by Papen et al. in Saturn’s plasma sheet and find that the change of spectral indices inside 9 {{R}s} can be explained by damping on electron scales.
Ahn, Junyeong; Yang, Bohm-Jung
2017-04-01
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.
All ASD complex and real 4-dimensional Einstein spaces with Λ≠0 admitting a nonnull Killing vector
Chudecki, Adam
2016-12-01
Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant Λ equipped with a nonnull Killing vector are considered. It is shown that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer-Finley-Plebański equation (Toda field equation). Some alternative forms of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex Einstein spaces with Λ≠0 admitting a nonnull Killing vector are found.
Directory of Open Access Journals (Sweden)
Renkuan Liao
2014-01-01
Full Text Available The water absorption capacity of superabsorbent polymers (SAPs is important for agricultural drought resistance. However, herbicides may leach into the soil and affect water absorption by damaging the SAP three-dimensional membrane structures. We used 100-mesh sieves, electron microscopy, and fractal theory to study swelling and water absorption in SAPs in the presence of three common herbicides (atrazine, alachlor, and tribenuron-methyl at concentrations of 0.5, 1.0, and 2.0 mg/L. In the sieve experiments it was found that 2.0 mg/L atrazine reduces the capacity by 9.64–23.3% at different swelling points; no significant diminution was observed for the other herbicides or for lower atrazine concentrations. We found that the hydrogel membrane pore distributions have fractal characteristics in both deionized water and atrazine solution. The 2.0 mg/L atrazine destroyed the water-retaining polymer membrane pores and reduced the water-absorbing mass by modifying its three-dimensional membrane structure. A linear correlation was observed between the fractal analysis and the water-absorbing mass. Multifractal analysis characterized the membrane pore distribution by using the range of singularity indexes Δα (relative distinguishing range of 16.54–23.44%, which is superior to single-fractal analysis that uses the fractal dimension D (relative distinguishing range of 2.5–4.0%.
Interacting noise sources shape patterns of arm movement variability in three-dimensional space.
Apker, Gregory A; Darling, Timothy K; Buneo, Christopher A
2010-11-01
Reaching movements are subject to noise in both the planning and execution phases of movement production. The interaction of these noise sources during natural movements is not well understood, despite its importance for understanding movement variability in neurologically intact and impaired individuals. Here we examined the interaction of planning and execution related noise during the production of unconstrained reaching movements. Subjects performed sequences of two movements to targets arranged in three vertical planes separated in depth. The starting position for each sequence was also varied in depth with the target plane; thus required movement sequences were largely contained within the vertical plane of the targets. Each final target in a sequence was approached from two different directions, and these movements were made with or without visual feedback of the moving hand. These combined aspects of the design allowed us to probe the interaction of execution and planning related noise with respect to reach endpoint variability. In agreement with previous studies, we found that reach endpoint distributions were highly anisotropic. The principal axes of movement variability were largely aligned with the depth axis, i.e., the axis along which visual planning related noise would be expected to dominate, and were not generally well aligned with the direction of the movement vector. Our results suggest that visual planning-related noise plays a dominant role in determining anisotropic patterns of endpoint variability in three-dimensional space, with execution noise adding to this variability in a movement direction-dependent manner.
Contribution of execution noise to arm movement variability in three-dimensional space.
Apker, Gregory A; Buneo, Christopher A
2012-01-01
Reaching movements are subject to noise associated with planning and execution, but precisely how these noise sources interact to determine patterns of endpoint variability in three-dimensional space is not well understood. For frontal plane movements, variability is largest along the depth axis (the axis along which visual planning noise is greatest), with execution noise contributing to this variability along the movement direction. Here we tested whether these noise sources interact in a similar way for movements directed in depth. Subjects performed sequences of two movements from a single starting position to targets that were either both contained within a frontal plane ("frontal sequences") or where the first was within the frontal plane and the second was directed in depth ("depth sequences"). For both sequence types, movements were performed with or without visual feedback of the hand. When visual feedback was available, endpoint distributions for frontal and depth sequences were generally anisotropic, with the principal axes of variability being strongly aligned with the depth axis. Without visual feedback, endpoint distributions for frontal sequences were relatively isotropic and movement direction dependent, while those for depth sequences were similar to those with visual feedback. Overall, the results suggest that in the presence of visual feedback, endpoint variability is dominated by uncertainty associated with planning and updating visually guided movements. In addition, the results suggest that without visual feedback, increased uncertainty in hand position estimation effectively unmasks the effect of execution-related noise, resulting in patterns of endpoint variability that are highly movement direction dependent.
Relativistic three-dimensional Lippmann-Schwinger cross sections for space radiation applications
Werneth, C. M.; Xu, X.; Norman, R. B.; Maung, K. M.
2017-12-01
Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world's best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic three-dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scattering Theory (MST) that uses 5 parameterizations-3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations-predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame (TLab) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which TLab > 220MeV /n .
Noise-induced phase space transport in two-dimensional Hamiltonian systems.
Pogorelov, I V; Kandrup, H E
1999-08-01
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of periodic driving. The objective was to quantify and understand the manner in which "sticky" chaotic orbits that, in the absence of perturbations, are confined near regular islands for very long times, can become "unstuck" much more quickly when subjected to even very weak perturbations. For both noise and periodic driving, the typical escape time scales logarithmically with the amplitude of the perturbation. For white noise, the details seem unimportant: Additive and multiplicative noise typically have very similar effects, and the presence or absence of a friction related to the noise by a fluctuation-dissipation theorem is also largely irrelevant. Allowing for colored noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that there is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. Similarly, periodic driving is relatively inefficient when the driving frequency is not comparable to these natural frequencies. This suggests that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. The logarithmic dependence of the escape time on amplitude reflects the fact that the time required for perturbed and unperturbed orbits to diverge a given distance scales logarithmically in the amplitude of the perturbation.
Positioning in a flat two-dimensional space-time: The delay master equation
International Nuclear Information System (INIS)
Coll, Bartolome; Ferrando, Joan Josep; Morales-Lladosa, Juan Antonio
2010-01-01
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [B. Coll, J. J. Ferrando, and J. A. Morales, Phys. Rev. D 73, 084017 (2006); ibid.74, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here, generic relativistic positioning systems in the Minkowski plane are studied. The information that can be obtained from the data received by a user of the positioning system is analyzed in detail. In particular, it is shown that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so-called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. These results are illustrated with the obtention of the dynamics of the emitters and of the user from specific sets of data received by the user.
International Nuclear Information System (INIS)
Das, S.R.; Mukherji, S.
1994-01-01
We study black hole formation in a model of two dimensional dilaton gravity and 24 massless scalar fields with a boundary. We find the most general boundary condition consistent with perfect reflection of matter and the constraints. We show that in the semiclassical approximation and for the generic value of a parameter which characterizes the boundary conditions, the boundary starts receding to infinity at the speed of light whenever the total energy of the incoming matter flux exceeds a certain critical value. This is also the critical energy which marks the onset of black hole formation. We then compute the quantum fluctuations of the boundary and of the rescaled scalar curvature and show that as soon as the incoming energy exceeds this critical value, and asymptotic observer using normal time resolutions will always measure large quantum fluctuations of space-time near the horizon, even though the freely falling observer does not. This is an aspect of black hole complementarity relating directly to quantum gravity effects. (author). 30 refs, 4 figs
Energy Technology Data Exchange (ETDEWEB)
Hechler, S.; Nawrodt, R.; Nietzsche, S.; Vodel, W.; Seidel, P. [Friedrich-Schiller-Univ. Jena (Germany). Inst. fuer Festkoerperphysik; Dittus, H. [ZARM, Univ. Bremen (Germany); Loeffler, F. [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany)
2007-07-01
Superconducting quantum interference devices (SQUIDs) are used for high precise gravitational experiments. One of the most impressive experiments is the satellite test of the equivalence principle (STEP) of NASA/ESA. The STEP mission aims to prove a possible violation of Einstein's equivalence principle at an extreme level of accuracy of 1 part in 10{sup 18} in space. In this contribution we present an automatically working measurement equipment to characterize 3-dimensional superconducting thin film components like i.e. pick-up coils and test masses for STEP. The characterization is done by measurements of the transition temperature between the normal and the superconducting state using a special built anti-cryostat. Above all the setup was designed for use in normal LHe transport Dewars. The sample chamber has a volume of 150 cm{sup 3} and can be fully temperature controlled over a range from 4.2 K to 300 K with a resolution of better then 100 mK. (orig.)
Three dimensional range geometry and texture data compression with space-filling curves.
Chen, Xia; Zhang, Song
2017-10-16
This paper presents a novel method to effectively store three-dimensional (3D) data and 2D texture data into a regular 24-bit image. The proposed method uses the Hilbert space-filling curve to map the normalized unwrapped phase map to two 8-bit color channels, and saves the third color channel for 2D texture storage. By further leveraging existing 2D image and video compression techniques, the proposed method can achieve high compression ratios while effectively preserving data quality. Since the encoding and decoding processes can be applied to most of the current 2D media platforms, this proposed compression method can make 3D data storage and transmission available for many electrical devices without requiring special hardware changes. Experiments demonstrate that if a lossless 2D image/video format is used, both original 3D geometry and 2D color texture can be accurately recovered; if lossy image/video compression is used, only black-and-white or grayscale texture can be properly recovered, but much higher compression ratios (e.g., 1543:1 against the ASCII OBJ format) are achieved with slight loss of 3D geometry quality.
Moghaderi, Hamid; Dehghan, Mehdi; Donatelli, Marco; Mazza, Mariarosa
2017-12-01
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Grünwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.
Extending the Generalised Pareto Distribution for Novelty Detection in High-Dimensional Spaces.
Clifton, David A; Clifton, Lei; Hugueny, Samuel; Tarassenko, Lionel
2014-01-01
Novelty detection involves the construction of a "model of normality", and then classifies test data as being either "normal" or "abnormal" with respect to that model. For this reason, it is often termed one-class classification. The approach is suitable for cases in which examples of "normal" behaviour are commonly available, but in which cases of "abnormal" data are comparatively rare. When performing novelty detection, we are typically most interested in the tails of the normal model, because it is in these tails that a decision boundary between "normal" and "abnormal" areas of data space usually lies. Extreme value statistics provides an appropriate theoretical framework for modelling the tails of univariate (or low-dimensional) distributions, using the generalised Pareto distribution (GPD), which can be demonstrated to be the limiting distribution for data occurring within the tails of most practically-encountered probability distributions. This paper provides an extension of the GPD, allowing the modelling of probability distributions of arbitrarily high dimension, such as occurs when using complex, multimodel, multivariate distributions for performing novelty detection in most real-life cases. We demonstrate our extension to the GPD using examples from patient physiological monitoring, in which we have acquired data from hospital patients in large clinical studies of high-acuity wards, and in which we wish to determine "abnormal" patient data, such that early warning of patient physiological deterioration may be provided.
Learning the inverse kinetics of an octopus-like manipulator in three-dimensional space.
Giorelli, M; Renda, F; Calisti, M; Arienti, A; Ferri, G; Laschi, C
2015-05-13
This work addresses the inverse kinematics problem of a bioinspired octopus-like manipulator moving in three-dimensional space. The bioinspired manipulator has a conical soft structure that confers the ability of twirling around objects as a real octopus arm does. Despite the simple design, the soft conical shape manipulator driven by cables is described by nonlinear differential equations, which are difficult to solve analytically. Since exact solutions of the equations are not available, the Jacobian matrix cannot be calculated analytically and the classical iterative methods cannot be used. To overcome the intrinsic problems of methods based on the Jacobian matrix, this paper proposes a neural network learning the inverse kinematics of a soft octopus-like manipulator driven by cables. After the learning phase, a feed-forward neural network is able to represent the relation between manipulator tip positions and forces applied to the cables. Experimental results show that a desired tip position can be achieved in a short time, since heavy computations are avoided, with a degree of accuracy of 8% relative average error with respect to the total arm length.
METHOD FOR OPTIMAL RESOLUTION OF MULTI-AIRCRAFT CONFLICTS IN THREE-DIMENSIONAL SPACE
Directory of Open Access Journals (Sweden)
Denys Vasyliev
2017-03-01
Full Text Available Purpose: The risk of critical proximities of several aircraft and appearance of multi-aircraft conflicts increases under current conditions of high dynamics and density of air traffic. The actual problem is a development of methods for optimal multi-aircraft conflicts resolution that should provide the synthesis of conflict-free trajectories in three-dimensional space. Methods: The method for optimal resolution of multi-aircraft conflicts using heading, speed and altitude change maneuvers has been developed. Optimality criteria are flight regularity, flight economy and the complexity of maneuvering. Method provides the sequential synthesis of the Pareto-optimal set of combinations of conflict-free flight trajectories using multi-objective dynamic programming and selection of optimal combination using the convolution of optimality criteria. Within described method the following are defined: the procedure for determination of combinations of aircraft conflict-free states that define the combinations of Pareto-optimal trajectories; the limitations on discretization of conflict resolution process for ensuring the absence of unobservable separation violations. Results: The analysis of the proposed method is performed using computer simulation which results show that synthesized combination of conflict-free trajectories ensures the multi-aircraft conflict avoidance and complies with defined optimality criteria. Discussion: Proposed method can be used for development of new automated air traffic control systems, airborne collision avoidance systems, intelligent air traffic control simulators and for research activities.
Gajda, Steven; Chen, Jie
2012-03-01
To experimentally quantify the effects of the loop design on three-dimensional orthodontic load systems of two types of commercial closing loop archwires: Teardrop and Keyhole. An orthodontic force tester and custom-made dentoform were used to measure the load systems produced on two teeth during simulated space closure. The system included three force components along and three moment components about three clinically defined axes on two target teeth: the left maxillary canine and the lateral incisor. The archwires were attached to the dentoform and were activated following a standard clinical procedure. The resulting six load components produced by the two archwires were reported and compared. The results were also compared with those of the T-loop archwire published previously. The three designs deliver similar loading patterns; however, the component magnitudes are dependent on the design. All of the designs result in lingual tipping of the teeth, canine lingual-mesial displacement, canine crown-mesial-in rotation, and incisor crown-distal-in rotation.
A Novel High Efficiency Fractal Multiview Video Codec
Directory of Open Access Journals (Sweden)
Shiping Zhu
2015-01-01
Full Text Available Multiview video which is one of the main types of three-dimensional (3D video signals, captured by a set of video cameras from various viewpoints, has attracted much interest recently. Data compression for multiview video has become a major issue. In this paper, a novel high efficiency fractal multiview video codec is proposed. Firstly, intraframe algorithm based on the H.264/AVC intraprediction modes and combining fractal and motion compensation (CFMC algorithm in which range blocks are predicted by domain blocks in the previously decoded frame using translational motion with gray value transformation is proposed for compressing the anchor viewpoint video. Then temporal-spatial prediction structure and fast disparity estimation algorithm exploiting parallax distribution constraints are designed to compress the multiview video data. The proposed fractal multiview video codec can exploit temporal and spatial correlations adequately. Experimental results show that it can obtain about 0.36 dB increase in the decoding quality and 36.21% decrease in encoding bitrate compared with JMVC8.5, and the encoding time is saved by 95.71%. The rate-distortion comparisons with other multiview video coding methods also demonstrate the superiority of the proposed scheme.
International Nuclear Information System (INIS)
Edelen, Dominic G B
2003-01-01
Local action of the fundamental group SO(a, 4 + k - a) is used to show that any solution of an algebraically closed differential system, that is generated from matrix Lie algebra valued 1-forms on a four-dimensional parameter space, will generate families of immersions of four-dimensional spacetimes R 4 in flat (4 + k)-dimensional spaces M 4+k with compatible signature. The algorithm is shown to work with local action of SO(a, 4 + k - a) replaced by local action of GL(4 + k). Immersions generated by local action of the Poincare group on the target spacetime are also obtained. Evaluations of the line elements, immersion loci and connection and curvature forms of these immersions are algebraic. Families of immersions that depend on one or more arbitrary functions are calculated for 1 ≤ k ≤ 4. Appropriate sections of graphs of the conformal factor for two and three interacting line singularities immersed in M 6 are given in appendix A. The local immersion theorem given in appendix B shows that all local solutions of the immersion problem are obtained by use of this method and an algebraic extension in exceptional cases
Ogle, K.; Fell, M.; Barber, J. J.
2016-12-01
Empirical, field studies of plant functional traits have revealed important trade-offs among pairs or triplets of traits, such as the leaf (LES) and wood (WES) economics spectra. Trade-offs include correlations between leaf longevity (LL) vs specific leaf area (SLA), LL vs mass-specific leaf respiration rate (RmL), SLA vs RmL, and resistance to breakage vs wood density. Ordination analyses (e.g., PCA) show groupings of traits that tend to align with different life-history strategies or taxonomic groups. It is unclear, however, what underlies such trade-offs and emergent spectra. Do they arise from inherent physiological constraints on growth, or are they more reflective of environmental filtering? The relative importance of these mechanisms has implications for predicting biogeochemical cycling, which is influenced by trait distributions of the plant community. We address this question using an individual-based model of tree growth (ACGCA) to quantify the theoretical trait space of trees that emerges from physiological constraints. ACGCA's inputs include 32 physiological, anatomical, and allometric traits, many of which are related to the LES and WES. We fit ACGCA to 1.6 million USFS FIA observations of tree diameters and heights to obtain vectors of trait values that produce realistic growth, and we explored the structure of this trait space. No notable correlations emerged among the 496 trait pairs, but stepwise regressions revealed complicated multi-variate structure: e.g., relationships between pairs of traits (e.g., RmL and SLA) are governed by other traits (e.g., LL, radiation-use efficiency [RUE]). We also simulated growth under various canopy gap scenarios that impose varying degrees of environmental filtering to explore the multi-dimensional trait space (hypervolume) of trees that died vs survived. The centroid and volume of the hypervolumes differed among dead and live trees, especially under gap conditions leading to low mortality. Traits most predictive
International Nuclear Information System (INIS)
Liu, Yilin; Yin, Fang-Fang; Cai, Jing; Chen, Nan-kuei; Chu, Mei-Lan
2015-01-01
Purpose: Current four dimensional magnetic resonance imaging (4D-MRI) techniques lack sufficient temporal/spatial resolution and consistent tumor contrast. To overcome these limitations, this study presents the development and initial evaluation of a new strategy for 4D-MRI which is based on retrospective k-space reordering. Methods: We simulated a k-space reordered 4D-MRI on a 4D digital extended cardiac-torso (XCAT) human phantom. A 2D echo planar imaging MRI sequence [frame rate (F) = 0.448 Hz; image resolution (R) = 256 × 256; number of k-space segments (N KS ) = 4] with sequential image acquisition mode was assumed for the simulation. Image quality of the simulated “4D-MRI” acquired from the XCAT phantom was qualitatively evaluated, and tumor motion trajectories were compared to input signals. In particular, mean absolute amplitude differences (D) and cross correlation coefficients (CC) were calculated. Furthermore, to evaluate the data sufficient condition for the new 4D-MRI technique, a comprehensive simulation study was performed using 30 cancer patients’ respiratory profiles to study the relationships between data completeness (C p ) and a number of impacting factors: the number of repeated scans (N R ), number of slices (N S ), number of respiratory phase bins (N P ), N KS , F, R, and initial respiratory phase at image acquisition (P 0 ). As a proof-of-concept, we implemented the proposed k-space reordering 4D-MRI technique on a T2-weighted fast spin echo MR sequence and tested it on a healthy volunteer. Results: The simulated 4D-MRI acquired from the XCAT phantom matched closely to the original XCAT images. Tumor motion trajectories measured from the simulated 4D-MRI matched well with input signals (D = 0.83 and 0.83 mm, and CC = 0.998 and 0.992 in superior–inferior and anterior–posterior directions, respectively). The relationship between C p and N R was found best represented by an exponential function (C P =100(1−e −0.18N R ), when N S
Fractal analysis of polar bear hairs
Directory of Open Access Journals (Sweden)
Wang Qing-Li
2015-01-01
Full Text Available Hairs of a polar bear (Ursus maritimus are of superior properties such as the excellent thermal protection. Why do polar bears can resist such cold environment? The paper concludes that its fractal porosity plays an important role, and its fractal dimensions are very close to the golden mean, 1.618, revealing the possible optimal structure of polar bear hair.
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-09-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP; SCHWARZ, UJ
1991-01-01
To study the structure of interstellar clouds we used the so-called perimeter-area relation to estimate fractal dimensions. We studied the reliability of the method by applying it to artificial fractals and discuss some of the problems and pitfalls. Results for two different cloud types
Fractal Image Coding with Digital Watermarks
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Z. Klenovicova
2000-12-01
Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
1994-01-01
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
Undergraduate Experiment with Fractal Diffraction Gratings
Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.
2011-01-01
We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
Clausse, A.; Delmastro, D.F.
1990-01-01
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es
International Nuclear Information System (INIS)
Fradkin, E.S.; Palchik, M.Ya.
1996-02-01
We study a family of exactly solvable models of conformally-invariant quantum field theory in D-dimensional space. We demonstrate the existence of D-dimensional analogs of primary and secondary fields. Under the action of energy-momentum tensor and conserved currents, the primary fields creates an infinite set of (tensor) secondary fields of different generations. The commutators of secondary fields with zero components of current and energy-momentum tensor include anomalous operator terms. We show that the Hilbert space of conformal theory has a special sector which structure is solely defined by the Ward identities independently on the choice of dynamical model. The states of this sector are constructed from secondary fields. Definite self-consistent conditions on the states of the latter sector fix the choice of the field model uniquely. In particular, Lagrangian models do belong to this class of models. The above self-consistent conditions are formulated as follows. Special superpositions Q s , s = 1,2,... of secondary fields are constructed. Each superposition is determined by the requirement that the form of its commutators with energy-momentum tensor and current (i.e. transformation properties) should be identical to that of a primary field. Each equation Q s (x) = 0 is consistent, and defines an exactly solvable model for D ≥ 3. The structure of these models are analogous to that of well-known two dimensional conformal models. The states Q s (x) modul 0> are analogous to the null-vectors of two dimensional theory. In each of these models one can obtain a closed set of differential equations for all the higher Green functions, as well as algebraic equations relating the scale dimension of fundamental field to the D-dimensional analog of a central charge. As an example, we present a detailed discussion of a pair of exactly solvable models in even-dimensional space D ≥ 4. (author). 28 refs
LaFleur, Karl; Cassady, Kaitlin; Doud, Alexander; Shades, Kaleb; Rogin, Eitan; He, Bin
2013-01-01
Objective At the balanced intersection of human and machine adaptation is found the optimally functioning brain-computer interface (BCI). In this study, we report a novel experiment of BCI controlling a robotic quadcopter in three-dimensional physical space using noninvasive scalp EEG in human subjects. We then quantify the performance of this system using metrics suitable for asynchronous BCI. Lastly, we examine the impact that operation of a real world device has on subjects’ control with comparison to a two-dimensional virtual cursor task. Approach Five human subjects were trained to modulate their sensorimotor rhythms to control an AR Drone navigating a three-dimensional physical space. Visual feedback was provided via a forward facing camera on the hull of the drone. Individual subjects were able to accurately acquire up to 90.5% of all valid targets presented while travelling at an average straight-line speed of 0.69 m/s. Significance Freely exploring and interacting with the world around us is a crucial element of autonomy that is lost in the context of neurodegenerative disease. Brain-computer interfaces are systems that aim to restore or enhance a user’s ability to interact with the environment via a computer and through the use of only thought. We demonstrate for the first time the ability to control a flying robot in the three-dimensional physical space using noninvasive scalp recorded EEG in humans. Our work indicates the potential of noninvasive EEG based BCI systems to accomplish complex control in three-dimensional physical space. The present study may serve as a framework for the investigation of multidimensional non-invasive brain-computer interface control in a physical environment using telepresence robotics. PMID:23735712
Fractal Analysis of Rock Joint Profiles
Audy, Ondřej; Ficker, Tomáš
2017-10-01
Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.
A random walk through fractal dimensions
Kaye, Brian H
2008-01-01
Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science.From reviews of the first edition:''...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.'' MRS Bulletin
Fractal properties of percolation clusters in Euclidian neural networks
International Nuclear Information System (INIS)
Franovic, Igor; Miljkovic, Vladimir
2009-01-01
The process of spike packet propagation is observed in two-dimensional recurrent networks, consisting of locally coupled neuron pools. Local population dynamics is characterized by three key parameters - probability for pool connectedness, synaptic strength and neuron refractoriness. The formation of dynamic attractors in our model, synfire chains, exhibits critical behavior, corresponding to percolation phase transition, with probability for non-zero synaptic strength values representing the critical parameter. Applying the finite-size scaling method, we infer a family of critical lines for various synaptic strengths and refractoriness values, and determine the Hausdorff-Besicovitch fractal dimension of the percolation clusters.
Nam, Julia EunJu; Mueller, Klaus
2013-02-01
Gaining a true appreciation of high-dimensional space remains difficult since all of the existing high-dimensional space exploration techniques serialize the space travel in some way. This is not so foreign to us since we, when traveling, also experience the world in a serial fashion. But we typically have access to a map to help with positioning, orientation, navigation, and trip planning. Here, we propose a multivariate data exploration tool that compares high-dimensional space navigation with a sightseeing trip. It decomposes this activity into five major tasks: 1) Identify the sights: use a map to identify the sights of interest and their location; 2) Plan the trip: connect the sights of interest along a specifyable path; 3) Go on the trip: travel along the route; 4) Hop off the bus: experience the location, look around, zoom into detail; and 5) Orient and localize: regain bearings in the map. We describe intuitive and interactive tools for all of these tasks, both global navigation within the map and local exploration of the data distributions. For the latter, we describe a polygonal touchpad interface which enables users to smoothly tilt the projection plane in high-dimensional space to produce multivariate scatterplots that best convey the data relationships under investigation. Motion parallax and illustrative motion trails aid in the perception of these transient patterns. We describe the use of our system within two applications: 1) the exploratory discovery of data configurations that best fit a personal preference in the presence of tradeoffs and 2) interactive cluster analysis via cluster sculpting in N-D.
3D-Ising model as a string theory in three-dimensional euclidean space
International Nuclear Information System (INIS)
Sedrakyan, A.
1992-11-01
A three-dimensional string model is analyzed in the strong coupling regime. The contribution of surfaces with different topology to the partition function is essential. A set of corresponding models is discovered. Their critical indices, which depend on two integers (m,n) are calculated analytically. The critical indices of the three-dimensional Ising model should belong to this set. A possible connection with the chain of three dimensional lattice Pott's models is pointed out. (author) 22 refs.; 2 figs
Noise-induced phase space transport in two-dimensional Hamiltonian systems
International Nuclear Information System (INIS)
Pogorelov, I.V.; Kandrup, H.E.
1999-01-01
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of periodic driving. The objective was to quantify and understand the manner in which open-quotes stickyclose quotes chaotic orbits that, in the absence of perturbations, are confined near regular islands for very long times, can become open-quotes unstuckclose quotes much more quickly when subjected to even very weak perturbations. For both noise and periodic driving, the typical escape time scales logarithmically with the amplitude of the perturbation. For white noise, the details seem unimportant: Additive and multiplicative noise typically have very similar effects, and the presence or absence of a friction related to the noise by a fluctuation-dissipation theorem is also largely irrelevant. Allowing for colored noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that there is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. Similarly, periodic driving is relatively inefficient when the driving frequency is not comparable to these natural frequencies. This suggests that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. The logarithmic dependence of the escape time on amplitude reflects the fact that the time required for perturbed and unperturbed orbits to diverge a given distance scales logarithmically in the amplitude of the perturbation. copyright 1999 The American Physical Society
Pre-Service Teachers' Concept Images on Fractal Dimension
Karakus, Fatih
2016-01-01
The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…
Directory of Open Access Journals (Sweden)
Painter Page R
2005-08-01
Full Text Available Abstract Background A prominent theoretical explanation for 3/4-power allometric scaling of metabolism proposes that the nutrient exchange surface of capillaries has properties of a space-filling fractal. The theory assumes that nutrient exchange surface area has a fractal dimension equal to or greater than 2 and less than or equal to 3 and that the volume filled by the exchange surface area has a fractal dimension equal to or greater than 3 and less than or equal to 4. Results It is shown that contradicting predictions can be derived from the assumptions of the model. When errors in the model are corrected, it is shown to predict that metabolic rate is proportional to body mass (proportional scaling. Conclusion The presence of space-filling fractal nutrient exchange surfaces does not provide a satisfactory explanation for 3/4-power metabolic rate scaling.
Fractal analysis of urban environment: land use and sewer system
Gires, A.; Ochoa Rodriguez, S.; Van Assel, J.; Bruni, G.; Murla Tulys, D.; Wang, L.; Pina, R.; Richard, J.; Ichiba, A.; Willems, P.; Tchiguirinskaia, I.; ten Veldhuis, M. C.; Schertzer, D. J. M.
2014-12-01
Land use distribution are usually obtained by automatic processing of satellite and airborne pictures. The complexity of the obtained patterns which are furthermore scale dependent is enhanced in urban environment. This scale dependency is even more visible in a rasterized representation where only a unique class is affected to each pixel. A parameter commonly analysed in urban hydrology is the coefficient of imperviousness, which reflects the proportion of rainfall that will be immediately active in the catchment response. This coefficient is strongly scale dependent with a rasterized representation. This complex behaviour is well grasped with the help of the scale invariant notion of fractal dimension which enables to quantify the space occupied by a geometrical set (here the impervious areas) not only at a single scale but across all scales. This fractal dimension is also compared to the ones computed on the representation of the catchments with the help of operational semi-distributed models. Fractal dimensions of the corresponding sewer systems are also computed and compared with values found in the literature for natural river networks. This methodology is tested on 7 pilot sites of the European NWE Interreg IV RainGain project located in France, Belgium, Netherlands, United-Kingdom and Portugal. Results are compared between all the case study which exhibit different physical features (slope, level of urbanisation, population density...).
Self-stabilized Fractality of Sea-coasts Through Damped Erosion
Sapoval, B.; Baldassari, A.; Gabrielli, A.
2004-05-01
Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).
Morphometric relations of fractal-skeletal based channel network model
Directory of Open Access Journals (Sweden)
B. S. Daya Sagar
1998-01-01
Full Text Available A fractal-skeletal based channel network (F-SCN model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F-SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
2006-01-01
In this paper we present, in a integral form, the Euclidean Green function associated with a massless scalar field in the five-dimensional Kaluza-Klein magnetic monopole superposed to a global monopole, admitting a nontrivial coupling between the field with the geometry. This Green function is expressed as the sum of two contributions: the first one related with uncharged component of the field, is similar to the Green function associated with a scalar field in a four-dimensional global monopole space-time. The second contains the information of all the other components. Using this Green function it is possible to study the vacuum polarization effects on this space-time. Explicitly we calculate the renormalized vacuum expectation value * (x)Φ(x)> Ren , which by its turn is also expressed as the sum of two contributions
Directory of Open Access Journals (Sweden)
Ailawalia Praveen
2015-01-01
Full Text Available The purpose of this paper is to study the two dimensional deformation of fibre reinforced micropolar thermoelastic medium in the context of Green-Lindsay theory of thermoelasticity. A mechanical force is applied along the interface of fluid half space and fibre reinforced micropolar thermoelastic half space. The normal mode analysis has been applied to obtain the exact expressions for displacement component, force stress, temperature distribution and tangential couple stress. The effect of anisotropy and micropolarity on the displacement component, force stress, temperature distribution and tangential couple stress has been depicted graphically.
International Nuclear Information System (INIS)
Nariai, Hidekazu; Ishihara, Hideki.
1983-01-01
Various geometrical properties of Nariai's less-familiar solution of the vacuum Einstein equations R sub( mu nu ) = lambda g sub( mu nu ) is f irst summarized in comparison with de Sitter's well-known solution. Next an extension of both solutions is performed in a six-dimensional space on the supposition that such an extension will in future become useful to elucidate more closely the creation of particles in an inflationary stage of the big-bang universe. For preparation, the behavior of a massive scalar field in the extended space-time is studied in a classical level. (author)
A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer.
Canning, Sara; Walker, Alan J; Roach, Paul A
2016-12-17
Piezoelectric ultrasonic transducers have the potential to operate as both a sensor and as an actuator of ultrasonic waves. Currently, manufactured transducers operate effectively over narrow bandwidths as a result of their regular structures which incorporate a single length scale. To increase the operational bandwidth of these devices, consideration has been given in the literature to the implementation of designs which contain a range of length scales. In this paper, a mathematical model of a novel Sierpinski tetrix fractal-inspired transducer for sensor applications is presented. To accompany the growing body of research based on fractal-inspired transducers, this paper offers the first sensor design based on a three-dimensional fractal. The three-dimensional model reduces to an effective one-dimensional model by allowing for a number of assumptions of the propagating wave in the fractal lattice. The reception sensitivity of the sensor is investigated. Comparisons of reception force response (RFR) are performed between this novel design along with a previously investigated Sierpinski gasket-inspired device and standard Euclidean design. The results indicate that the proposed device surpasses traditional design sensors.