The Weyl law for contractive maps
International Nuclear Information System (INIS)
Spina, Maria E; Rivas, Alejandro M F; Carlo, Gabriel
2013-01-01
We find an empirical Weyl law followed by the eigenvalues of contractive maps. An important property is that it is mainly insensitive to the dimension of the corresponding invariant classical set, the strange attractor. The usual explanation for the fractal Weyl law emergence in scattering systems (i.e., having a projective opening) is based on the classical phase space distributions evolved up to the quantum to classical correspondence (Ehrenfest) time. In the contractive case this reasoning fails to describe it. Instead, we conjecture that the support for this behavior is essentially given by the strong non-orthogonality of the eigenvectors of the contractive superoperator. We test the validity of the Weyl law and this conjecture on two paradigmatic systems, the dissipative baker and kicked top maps. (paper)
Fractal harmonic law and waterproof/dustproof
Directory of Open Access Journals (Sweden)
Kong Hai-Yan
2014-01-01
Full Text Available The fractal harmonic law admits that the friction between the pure water and the moving surface is the minimum when fractal dimensions of water in Angstrom scale are equal to fractal dimensions of the moving surface in micro scale. In the paper, the fractal harmonic law is applied to demonstrate the mechanism of waterproof/ dustproof. The waterproof phenomenon of goose feathers and lotus leaves is illustrated to verify our results and experimental results agree well with our theoretical analysis.
Violation of Ohm's law in a Weyl metal
Shin, Dongwoo; Lee, Yongwoo; Sasaki, M.; Jeong, Yoon Hee; Weickert, Franziska; Betts, Jon B.; Kim, Heon-Jung; Kim, Ki-Seok; Kim, Jeehoon
2017-11-01
Ohm's law is a fundamental paradigm in the electrical transport of metals. Any transport signatures violating Ohm's law would give an indisputable fingerprint for a novel metallic state. Here, we uncover the breakdown of Ohm's law owing to a topological structure of the chiral anomaly in the Weyl metal phase. We observe nonlinear I-V characteristics in Bi0.96Sb0.04 single crystals in the diffusive limit, which occurs only for a magnetic-field-aligned electric field (E∥B). The Boltzmann transport theory with the charge pumping effect reveals the topological-in-origin nonlinear conductivity, and it leads to a universal scaling function of the longitudinal magnetoconductivity, which completely describes our experimental results. As a hallmark of Weyl metals, the nonlinear conductivity provides a venue for nonlinear electronics, optical applications, and the development of a topological Fermi-liquid theory beyond the Landau Fermi-liquid theory.
The fractal harmonic law and its application to swimming suit
Directory of Open Access Journals (Sweden)
Kong Hai-Yan
2012-01-01
Full Text Available Decreasing friction force between a swimming suit and water is the key factor to design swimming suits. Water continuum mechanics forbids discontinuous fluids, but in angstrom scale water is indeed discontinuous. Swimming suit is smooth on large scale, but it is discontinuous when the scale becomes smaller. If fractal dimensions of swimming suit and water are the same, a minimum of friction force is predicted, which means fractal harmonization. In the paper, fractal harmonic law is introduced to design a swimsuit whose surface fractal dimensions on a macroscopic scale should be equal to or closed to the water's fractal dimensions on an Angstrom scale. Various possible microstructures of fabric are analyzed and a method to obtain perfect fractal structure of fabric is proposed by spraying nanofibers to its surface. The fractal harmonic law can be used to design a moving surface with a minimal friction.
Power-law hereditariness of hierarchical fractal bones.
Deseri, Luca; Di Paola, Mario; Zingales, Massimiliano; Pollaci, Pietro
2013-12-01
In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann-Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law. Copyright © 2013 John Wiley & Sons, Ltd.
The generalized 20/80 law using probabilistic fractals applied to petroleum field size
Crovelli, R.A.
1995-01-01
Fractal properties of the Pareto probability distribution are used to generalize "the 20/80 law." The 20/80 law is a heuristic law that has evolved over the years into the following rule of thumb for many populations: 20 percent of the population accounts for 80 percent of the total value. The general p100/q100 law in probabilistic form is defined with q as a function of p, where p is the population proportion and q is the proportion of total value. Using the Pareto distribution, the p100/q100 law in fractal form is derived with the parameter q being a fractal, where q unexpectedly possesses the scale invariance property. The 20/80 law is a special case of the p100/q100 law in fractal form. The p100/q100 law in fractal form is applied to petroleum fieldsize data to obtain p and q such that p100% of the oil fields greater than any specified scale or size in a geologic play account for q100% of the total oil of the fields. The theoretical percentages of total resources of oil using the fractal q are extremely close to the empirical percentages from the data using the statistic q. Also, the empirical scale invariance property of the statistic q for the petroleum fieldsize data is in excellent agreement with the theoretical scale invariance property of the fractal q. ?? 1995 Oxford University Press.
Seepage Characteristics Study on Power-Law Fluid in Fractal Porous Media
Directory of Open Access Journals (Sweden)
Meijuan Yun
2014-01-01
Full Text Available We present fractal models for the flow rate, velocity, effective viscosity, apparent viscosity, and effective permeability for power-law fluid based on the fractal properties of porous media. The proposed expressions realize the quantitative description to the relation between the properties of the power-law fluid and the parameters of the microstructure of the porous media. The model predictions are compared with related data and good agreement between them is found. The analytical expressions will contribute to the revealing of physical principles for the power-law fluid flow in porous media.
Directory of Open Access Journals (Sweden)
Xiao-Hua Tan
2014-01-01
Full Text Available This work studies the pressure transient of power-law fluids in porous media embedded with a tree-shaped fractal network. A pressure transient model was created based on the fractal properties of tree-shaped capillaries, generalized Darcy’s law and constitutive equation for power-law fluids. The dimensionless pressure model was developed using the Laplace transform and Stehfest numerical inversion method. According to the model’s solution, the bi-logarithmic type curves of power-law fluids in porous media embedded with a tree-shaped fractal network are illustrated. The influences of different fractal factors and Power-law fluids parameters on pressure transient responses are discussed.
A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions
Czech Academy of Sciences Publication Activity Database
Zborovský, Imrich
2018-01-01
Roč. 33, č. 10 (2018), č. článku 1850057. ISSN 0217-751X R&D Projects: GA MŠk(CZ) LG15052 Institutional support: RVO:61389005 Keywords : Hadron interactions * self-similarity * fractality * conservation laws * quanta Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.597, year: 2016
Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency
International Nuclear Information System (INIS)
Paradisi, Paolo; Allegrini, Paolo
2015-01-01
In many complex systems the non-linear cooperative dynamics determine the emergence of self-organized, metastable, structures that are associated with a birth–death process of cooperation. This is found to be described by a renewal point process, i.e., a sequence of crucial birth–death events corresponding to transitions among states that are faster than the typical long-life time of the metastable states. Metastable states are highly correlated, but the occurrence of crucial events is typically associated with a fast memory drop, which is the reason for the renewal condition. Consequently, these complex systems display a power-law decay and, thus, a long-range or scale-free behavior, in both time correlations and distribution of inter-event times, i.e., fractal intermittency. The emergence of fractal intermittency is then a signature of complexity. However, the scaling features of complex systems are, in general, affected by the presence of added white or short-term noise. This has been found also for fractal intermittency. In this work, after a brief review on metastability and noise in complex systems, we discuss the emerging paradigm of Temporal Complexity. Then, we propose a model of noisy fractal intermittency, where noise is interpreted as a renewal Poisson process with event rate r p . We show that the presence of Poisson noise causes the emergence of a normal diffusion scaling in the long-time range of diffusion generated by a telegraph signal driven by noisy fractal intermittency. We analytically derive the scaling law of the long-time normal diffusivity coefficient. We find the surprising result that this long-time normal diffusivity depends not only on the Poisson event rate, but also on the parameters of the complex component of the signal: the power exponent μ of the inter-event time distribution, denoted as complexity index, and the time scale T needed to reach the asymptotic power-law behavior marking the emergence of complexity. In particular
Afsar, Ozgur; Tirnakli, Ugur
2014-04-01
We numerically introduce the relationships among correlation, fractality, Lyapunov divergence and q-Gaussian distributions. The scaling arguments between the range of the q-Gaussian and correlation, fractality, Lyapunov divergence are obtained for periodic windows (i.e., periods 2, 3 and 5) of the logistic map as chaos threshold is approached. Firstly, we show that the range of the q-Gaussian (g) tends to infinity as the measure of the deviation from the correlation dimension (D=0.5) at the chaos threshold, (this deviation will be denoted by l), approaches to zero. Moreover, we verify that a scaling law of type 1/g∝lτ is evident with the critical exponent τ=0.23±0.01. Similarly, as chaos threshold is approached, the quantity l scales as l∝(, where the exponent is γ=0.84±0.01. Secondly, we also show that the range of the q-Gaussian exhibits a scaling law with the correlation length (1/g∝ξ), Lyapunov divergence (1/g∝λμ) and the distance to the critical box counting fractal dimension (1/g∝() with the same exponent μ≅0.43. Finally, we numerically verify that these three quantities (ξ, λ, D-Dc) scale with the distance to the critical control parameter of the map (i.e., a-ac) in accordance with the universal Huberman-Rudnick scaling law with the same exponent ν=0.448±0.003. All these findings can be considered as a new evidence supporting that the central limit behaviour at the chaos threshold is given by a q-Gaussian.
THE “SPORT” OF ROUGH CONTACTS AND THE FRACTAL PARADOX IN WEAR LAWS
Directory of Open Access Journals (Sweden)
Michele Ciavarella
2018-02-01
Full Text Available In a recent paper in Science, namely, “The Contact Sport of Rough Surfaces”, Carpick summarizes recent efforts in a “contact challenge” to predict in detail an elastic contact between the mathematically defined fractal rough surfaces under (very little adhesion. He also suggests the next steps that are needed to “fulfill da Vinci’s dream of understanding what causes friction”. However, this is disappointing as friction has been studied since the times of Leonardo and in 500 years, no predictive model has emerged, nor any significant improvement from rough contact models. Similarly, a very large effort we have spent on the “sport” of studying rough surfaces has not made us any closer to being able to predict the coefficient of proportionality between wear loss and friction dissipation which was already observed by Reye in 1860. Recent nice simulations by Aghababaei, Warner and Molinari have confirmed the criterion for the formation of debris of a single particle, proposed in 1958 by Rabinowicz, as well as Reye’s assumption for the proportionality with frictional loss, which is very close to Archard anyway. More recent investigations under variable loads suggest that Reye’s assumption is probably much more general than Archard’s law. The attempts to obtain exact coefficients with rough surfaces models are very far from predictive, essentially because for fractals most authors fail to recognize that resolution-dependence of the contact area makes the models very ill-defined. We also suggest that in the models of wear, rough contacts should be considered “plastic” and “adhesive” and introduce a new length scale in the problem.
The role of Weyl symmetry in hydrodynamics
Diles, Saulo
2018-04-01
This article is dedicated to the analysis of Weyl symmetry in the context of relativistic hydrodynamics. Here is discussed how this symmetry is properly implemented using the prescription of minimal coupling: ∂ → ∂ + ωA. It is shown that this prescription has no problem to deal with curvature since it gives the correct expressions for the commutator of covariant derivatives. In hydrodynamics, Weyl gauge connection emerges from the degrees of freedom of the fluid: it is a combination of the expansion and entropy gradient. The remaining degrees of freedom, shear, vorticity and the metric tensor, are see in this context as charged fields under the Weyl gauge connection. The gauge nature of the connection provides natural dynamics to it via equations of motion analogous to the Maxwell equations for electromagnetism. As a consequence, a charge for the Weyl connection is defined and the notion of local charge is analyzed generating the conservation law for the Weyl charge.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325
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
Fractal approach towards power-law coherency to measure cross-correlations between time series
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2017-01-01
Roč. 50, č. 1 (2017), s. 193-200 ISSN 1007-5704 R&D Projects: GA ČR(CZ) GP14-11402P Institutional support: RVO:67985556 Keywords : power-law coherency * power-law cross-correlations * correlations Subject RIV: AH - Economics OBOR OECD: Applied Economics, Econometrics Impact factor: 2.784, year: 2016 http://library.utia.cas.cz/separaty/2017/E/kristoufek-0473066.pdf
Modelling groundwater fractal flow with fractional differentiation via Mittag-Leffler law
Ahokposi, D. P.; Atangana, Abdon; Vermeulen, D. P.
2017-04-01
Modelling the flow of groundwater within a network of fractures is perhaps one of the most difficult exercises within the field of geohydrology. This physical problem has attracted the attention of several scientists across the globe. Already two different types of differentiations have been used to attempt modelling this problem including the classical and the fractional differentiation. In this paper, we employed the most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, to reshape the model of groundwater fractal flow. We presented the existence of positive solution of the new model. Using the fixed-point approach, we established the uniqueness of the positive solution. We solve the new model with three different numerical schemes including implicit, explicit and Crank-Nicholson numerical methods. Experimental data collected from four constant discharge tests conducted in a typical fractured crystalline rock aquifer of the Northern Limb (Bushveld Complex) in the Limpopo Province (South Africa) are compared with the numerical solutions. It is worth noting that the four boreholes (BPAC1, BPAC2, BPAC3, and BPAC4) are located on Faults.
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)
Weyl's Equidistribution Theorem
Indian Academy of Sciences (India)
groups and matrix representations. It was during his re- search into representation theory that Weyl discovered his theorem on equidistribution. Subsequently a vast amount of literature was devoted to the review of his proof. However, there remain to this day, several unan- swered questions which arose in the aftermath of ...
Classical Weyl transverse gravity
Energy Technology Data Exchange (ETDEWEB)
Oda, Ichiro [University of the Ryukyus, Department of Physics, Faculty of Science, Nishihara, Okinawa (Japan)
2017-05-15
We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge-fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct a covariantly conserved energy-momentum tensor, which is achieved on the basis of this equivalence relation. Thirdly, we demonstrate that the Noether current for the Weyl transformation is identically vanishing, thereby implying that the Weyl symmetry existing in both the conformally invariant scalar tensor gravity and the WTDiff gravity is a ''fake'' symmetry. We find it possible to extend this proof to all matter fields, i.e. the Weyl-invariant scalar, vector and spinor fields. Fourthly, it is explicitly shown that in the WTDiff gravity the Schwarzschild black hole metric and a charged black hole one are classical solutions to the equations of motion only when they are expressed in the Cartesian coordinate system. Finally, we consider the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology and provide some exact solutions. (orig.)
Selvam, A. M.
2017-01-01
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and, therefore, the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (1) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (2) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (3) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the sub-atomic dynamics of quantum systems such as the photon or electron. (4) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900-2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. On a global scale, man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales. Model concepts and results of analyses are discussed with reference
Türker, Oǧuz; Moroz, Sergej
2018-02-01
We consider three-dimensional fermionic band theories that exhibit Weyl nodal surfaces defined as two-band degeneracies that form closed surfaces in the Brillouin zone. We demonstrate that topology ensures robustness of these objects under small perturbations of a Hamiltonian. This topological robustness is illustrated in several four-band models that exhibit nodal surfaces protected by unitary or antiunitary symmetries. Surface states and Nielsen-Ninomiya doubling of nodal surfaces are also investigated.
Hermann Weyl and Representation Theory
Indian Academy of Sciences (India)
Abstract. Weyl was a universal mathematician whose fundamental contributionsto mathematics encompassed all areas, and provideda unification seldom seen. His work on the theory ofLie groups was motivated by his life-long interest in quantummechanics and relativity. When Weyl entered Lie theory,it mostly focussed on ...
Hermann Weyl and Representation Theory
Indian Academy of Sciences (India)
His work on the theory ofLie groups was motivated by his life-long interest in quantummechanics and relativity. When Weyl entered Lie theory,it mostly focussed on the infinitesimal, and he strove to bringin a global perspective. Time and again, Weyl's ideas arisingin one context have been adapted and applied to wholly ...
Hermann Weyl and Representation Theory
Indian Academy of Sciences (India)
by his grace, readily jumped through hoops; such was the magic of Hermann Weyl! Weyl was a universal mathematician whose fundamental con- tributions to mathematics encompassed all areas, and pro- vided a unification seldom seen. His work on the theory of. Lie groups was motivated by his life-long interest in quan-.
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....
Fractals in biology and medicine
Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Ossadnik, S. M.; Peng, C. K.; Simons, M.; Stanley, H. E.
1995-01-01
Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.
Energy Technology Data Exchange (ETDEWEB)
Perez-Nadal, Guillem [Universidad de Buenos Aires, Buenos Aires (Argentina)
2017-07-15
We consider a non-relativistic free scalar field theory with a type of anisotropic scale invariance in which the number of coordinates ''scaling like time'' is generically greater than one. We propose the Cartesian product of two curved spaces, the metric of each space being parameterized by the other space, as a notion of curved background to which the theory can be extended. We study this type of geometries, and find a family of extensions of the theory to curved backgrounds in which the anisotropic scale invariance is promoted to a local, Weyl-type symmetry. (orig.)
Weyl relativity: a novel approach to Weyl's ideas
Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J.
2017-06-01
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the conformal invariance of the gravitational field. We highlight that changing the local symmetry group of spacetime permits to construct a theory in which these two symmetries are combined into a putative gauge symmetry but with second-order field equations and non-trivial mass scales, unlike the original higher-order construction by Weyl. We prove that the gravitational field equations are equivalent to the (trace-free) Einstein field equations, ensuring their compatibility with known tests of general relativity. As a corollary, the effective cosmological constant is rendered radiatively stable due to Weyl invariance. A novel phenomenological consequence characteristic of this construction, potentially relevant for cosmological observations, is the existence of an energy scale below which effects associated with the non-integrability of spacetime distances, and an effective mass for the electromagnetic field, appear simultaneously (as dual manifestations of the use of Weyl connections). We explain how former criticisms against Weyl's ideas lose most of their power in its present reincarnation, which we refer to as Weyl relativity, as it represents a Weyl-invariant, unified description of both the Einstein and Maxwell field equations.
Henningson, M; Henningson, Mans; Skenderis, Kostas
1998-01-01
We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general covariance. Up to a constant, the anomaly only depends on the dimension d of the manifold on which the conformal field theory is defined. We present concrete expressions for the anomaly in the physically relevant cases d = 2, 4 and 6. In d = 2 we find for the central charge c = 3 l/ 2 G_N in agreement with considerations based on the asymptotic symmetry algebra of adS_3. In d = 4 the anomaly agrees precisely with that of the corresponding N = 4 superconformal SU(N) gauge theory. The result in d = 6 provides new information for the (0, 2) theory, since its Weyl anomaly has not been computed previously. The anomaly in this case grows as N^3, where N is the number of coincident M5 branes, and it vanishes for a Ricci-flat background.
Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga
2016-04-01
The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established
Fractals analysis of cardiac arrhythmias.
Saeed, Mohammed
2005-09-06
Heart rhythms are generated by complex self-regulating systems governed by the laws of chaos. Consequently, heart rhythms have fractal organization, characterized by self-similar dynamics with long-range order operating over multiple time scales. This allows for the self-organization and adaptability of heart rhythms under stress. Breakdown of this fractal organization into excessive order or uncorrelated randomness leads to a less-adaptable system, characteristic of aging and disease. With the tools of nonlinear dynamics, this fractal breakdown can be quantified with potential applications to diagnostic and prognostic clinical assessment. In this paper, I review the methodologies for fractal analysis of cardiac rhythms and the current literature on their applications in the clinical context. A brief overview of the basic mathematics of fractals is also included. Furthermore, I illustrate the usefulness of these powerful tools to clinical medicine by describing a novel noninvasive technique to monitor drug therapy in atrial fibrillation.
Evertsz, Carl Joseph Gabriel
1989-01-01
Laplacian Fractals are physical models for the fractal properties encountered in a selected group of natural phenomena. The basis models in this class are the Dialectric Breakdown Model and the closely related Diffusion- Limited Aggregration model and Laplacian Random Walks. A full mathematical
Gibbons, Gary W.; Volkov, Mikhail S.
2017-05-01
We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.
Weyl's Lagrangian in teleparallel form
International Nuclear Information System (INIS)
Burnett, James; Vassiliev, Dmitri
2009-01-01
The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable - the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.
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
Quantum Weyl invariance and cosmology
Energy Technology Data Exchange (ETDEWEB)
Dabholkar, Atish, E-mail: atish@ictp.it [International Centre for Theoretical Physics, ICTP-UNESCO, Strada Costiera 11, Trieste 34151 (Italy); Sorbonne Universités, UPMC Univ Paris 06, CNRS UMR 7589, LPTHE, F-75005, Paris (France)
2016-09-10
Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.
Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points.
Belopolski, Ilya; Yu, Peng; Sanchez, Daniel S; Ishida, Yukiaki; Chang, Tay-Rong; Zhang, Songtian S; Xu, Su-Yang; Zheng, Hao; Chang, Guoqing; Bian, Guang; Jeng, Horng-Tay; Kondo, Takeshi; Lin, Hsin; Liu, Zheng; Shin, Shik; Hasan, M Zahid
2017-10-16
Through intense research on Weyl semimetals during the past few years, we have come to appreciate that typical Weyl semimetals host many Weyl points. Nonetheless, the minimum nonzero number of Weyl points allowed in a time-reversal invariant Weyl semimetal is four. Realizing such a system is of fundamental interest and may simplify transport experiments. Recently, it was predicted that TaIrTe 4 realizes a minimal Weyl semimetal. However, the Weyl points and Fermi arcs live entirely above the Fermi level, making them inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES). Here, we use pump-probe ARPES to directly access the band structure above the Fermi level in TaIrTe 4 . We observe signatures of Weyl points and topological Fermi arcs. Combined with ab initio calculation, our results show that TaIrTe 4 is a Weyl semimetal with the minimum number of four Weyl points. Our work provides a simpler platform for accessing exotic transport phenomena arising in Weyl semimetals.Weyl semimetals are interesting because they are characterized by topological invariants, but specific examples discovered to date tend to have complicated band structures with many Weyl points. Here, the authors show that TaIrTe 4 has only four Weyl points, the minimal number required by time-reversal symmetry.
Jurgens, Hartmut; And Others
1990-01-01
The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)
Darwinian Evolution and Fractals
Carr, Paul H.
2009-05-01
Did nature's beauty emerge by chance or was it intelligently designed? Richard Dawkins asserts that evolution is blind aimless chance. Michael Behe believes, on the contrary, that the first cell was intelligently designed. The scientific evidence is that nature's creativity arises from the interplay between chance AND design (laws). Darwin's ``Origin of the Species,'' published 150 years ago in 1859, characterized evolution as the interplay between variations (symbolized by dice) and the natural selection law (design). This is evident in recent discoveries in DNA, Madelbrot's Fractal Geometry of Nature, and the success of the genetic design algorithm. Algorithms for generating fractals have the same interplay between randomness and law as evolution. Fractal statistics, which are not completely random, characterize such phenomena such as fluctuations in the stock market, the Nile River, rainfall, and tree rings. As chaos theorist Joseph Ford put it: God plays dice, but the dice are loaded. Thus Darwin, in discovering the evolutionary interplay between variations and natural selection, was throwing God's dice!
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.
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
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.
Titchmarsh-Weyl theory for canonical systems
Directory of Open Access Journals (Sweden)
Keshav Raj Acharya
2014-11-01
Full Text Available The main purpose of this paper is to develop Titchmarsh- Weyl theory of canonical systems. To this end, we first observe the fact that Schrodinger and Jacobi equations can be written into canonical systems. We then discuss the theory of Weyl m-function for canonical systems and establish the relation between the Weyl m-functions of Schrodinger equations and that of canonical systems which involve Schrodinger equations.
Bottorff, Mark; Ferland, Gary
2001-03-01
This paper examines whether a fractal cloud geometry can reproduce the emission-line spectra of active galactic nuclei (AGNs). The nature of the emitting clouds is unknown, but many current models invoke various types of magnetohydrodynamic confinement. Recent studies have argued that a fractal distribution of clouds, in which subsets of clouds occur in self-similar hierarchies, is a consequence of such confinement. Whatever the confinement mechanism, fractal cloud geometries are found in nature and may be present in AGNs too. We first outline how a fractal geometry can apply at the center of a luminous quasar. Scaling laws are derived that establish the number of hierarchies, typical sizes, column densities, and densities. Photoionization simulations are used to predict the integrated spectrum from the ensemble. Direct comparison with observations establishes all model parameters so that the final predictions are fully constrained. Theory suggests that denser clouds might form in regions of higher turbulence and that larger turbulence results in a wider dispersion of physical gas densities. An increase in turbulence is expected deeper within the gravitational potential of the black hole, resulting in a density gradient. We mimic this density gradient by employing two sets of clouds with identical fractal structuring but different densities. The low-density clouds have a lower column density and large covering factor similar to the warm absorber. The high-density clouds have high column density and smaller covering factor similar to the broad-line region (BLR). A fractal geometry can simultaneously reproduce the covering factor, density, column density, BLR emission-line strengths, and BLR line ratios as inferred from observation. Absorption properties of the model are consistent with the integrated line-of-sight column density as determined from observations of X-ray absorption, and when scaled to a Seyfert galaxy, the model is consistent with the number of
Amato P; Cerofolini GF; Narducci D; Romano E
2008-01-01
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.
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
Cael, B. B.; Bisson, Kelsey; Lambert, Bennett Spencer
2015-01-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of p...
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
Fractal electrodynamics via non-integer dimensional space approach
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2015-09-25
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. - Highlights: • Electrodynamics of fractal media is described by non-integer dimensional spaces. • Applications of the fractal Gauss's and Ampere's laws are suggested. • Fractal Poisson equation, equation for fractal stream of charges are considered.
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
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.
Weyl multiplets of N=2 conformal supergravity in five dimensions
Bergshoeff, E; de Wit, T; Halbersma, R; Cucu, S; Van Proeyen, A; Derix, M.
We construct the Weyl multiplets of N = 2 conformal supergravity in five dimensions. We show that there exist two different versions of the Weyl multiplet, which contain the same gauge fields but differ in the matter field content: the Standard Weyl multiplet and the Dilaton Weyl multiplet. At the
Inflation with light Weyl ghost
Directory of Open Access Journals (Sweden)
Tokareva Anna
2016-01-01
Full Text Available Inflationary perturbations are considered in a renormalizable but non-unitary theory of gravity with the additional Weyl term. We obtained that ghost degrees of freedom do not spoil the inflation and the scalar perturbation amplitude at the linear level even in a case of the ghost with mass smaller than Hubble parameter at inflation. The ghost impact to the observables is also estimated to be negligible for the range of masses allowed by the experiment. The non-linear level of the theory and its possible application are also discussed.
Fractals and cosmological large-scale structure
Luo, Xiaochun; Schramm, David N.
1992-01-01
Observations of galaxy-galaxy and cluster-cluster correlations as well as other large-scale structure can be fit with a 'limited' fractal with dimension D of about 1.2. This is not a 'pure' fractal out to the horizon: the distribution shifts from power law to random behavior at some large scale. If the observed patterns and structures are formed through an aggregation growth process, the fractal dimension D can serve as an interesting constraint on the properties of the stochastic motion responsible for limiting the fractal structure. In particular, it is found that the observed fractal should have grown from two-dimensional sheetlike objects such as pancakes, domain walls, or string wakes. This result is generic and does not depend on the details of the growth process.
Weyl magnons in noncoplanar stacked kagome antiferromagnets
Owerre, S. A.
2018-03-01
Weyl nodes have been experimentally realized in photonic, electronic, and phononic crystals. However, magnonic Weyl nodes are yet to be seen experimentally. In this paper, we propose Weyl magnon nodes in noncoplanar stacked frustrated kagome antiferromagnets, naturally available in various real materials. Most crucially, the Weyl nodes in the current system occur at the lowest excitation and possess a topological thermal Hall effect, therefore they are experimentally accessible at low temperatures due to the population effect of bosonic quasiparticles. In stark contrast to other magnetic systems, the current Weyl nodes do not rely on time-reversal symmetry breaking by the magnetic order. Rather, they result from explicit macroscopically broken time reversal symmetry by the scalar spin chirality of noncoplanar spin textures and can be generalized to chiral spin liquid states. Moreover, the scalar spin chirality gives a real space Berry curvature which is not available in previously studied magnetic Weyl systems. We show the existence of magnon arc surface states connecting projected Weyl magnon nodes on the surface Brillouin zone. We also uncover the first realization of triply-degenerate nodal magnon point in the noncollinear regime with zero scalar spin chirality.
Harper, David William (Inventor)
2017-01-01
A structural support having fractal-stiffening and method of fabricating the support is presented where an optimized location of at least three nodes is predetermined prior to fabricating the structural support where a first set of webs is formed on one side of the support and joined to the nodes to form a first pocket region. A second set of webs is formed within the first pocket region forming a second pocket region where the height of the first set of webs extending orthogonally from the side of the support is greater than the second set of webs extending orthogonally from the support.
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
theorist in analyzing such relations. I find empirical illustration in the case of the development of electronic patient records in Danish health care. The role of the social theorist is explored through a comparison of the political and normative stance enabled, respectively, by a critical social theory......The relationship between the supposedly small-the micro-and the supposedly large-the macro-has been a long-standing concern in social theory. However, although many attempts have been made to link these two seemingly disjoint dimensions, in the present paper I argue against such an endeavour...... and a fractal social theory....
Anomalous hydrodynamics of Weyl materials
Monteiro, Gustavo; Abanov, Alexander
Kinetic theory is a useful tool to study transport in Weyl materials when the band-touching points are hidden inside a Fermi surface. It accounts, for example, for the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations (SdH effect) in the magnetoresistance together within the same framework. As an alternative approach to kinetic theory we also consider the regime of strong interactions where hydrodynamics can be applicable. A variational principle of these hydrodynamic equations can be found in and provide a natural framework to study hydrodynamic surface modes which correspond to the strongly-interacting physics signature of Fermi arcs. G.M. acknowledges the financial support from FAPESP.
Kleshchev, Alexander
2017-01-01
The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules-one for each real positive root for the corresponding affine root system {\\tt X}_l^{(1)}, as well as irreducible imaginary modules-one for each l-multiplication. The authors study imaginary modules by means of "imaginary Schur-Weyl duality" and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.
Fractal properties of nanostructured semiconductors
Energy Technology Data Exchange (ETDEWEB)
Zhanabaev, Z.Zh. [Al-Farabi Khazakh National University, Tole bi Street, 96, Almaty 050012 (Kazakhstan); Grevtseva, T.Yu. [Al-Farabi Khazakh National University, Tole bi Street, 96, Almaty 050012 (Kazakhstan)]. E-mail: kenwp@mail.ru
2007-03-15
A theory for the temperature and time dependence of current carrier concentration in semiconductors with different non-equilibrium nanocluster structure has been developed. It was shown that the scale-invariant fractal self-similar and self-affine laws can exist near by the transition point to the equilibrium state. Results of the theory have been compared to the experimental data from electrical properties of semiconductor films with nanoclusters.
Apparent negative magnetoresistance without independent Weyl pockets in the Weyl semimetal TaP
Energy Technology Data Exchange (ETDEWEB)
Hassinger, Elena; Arnold, Frank; Naumann, Marcel; Wu, Shu-Chun; Sun, Yan; Donizeth dos Reis, Ricardo; Ajeesh, Mukkattu O.; Shekhar, Chandra; Kumar, Nitesh; Schmidt, Marcus; Baenitz, Michael; Borrmann, Horst; Nicklas, Michael; Felser, Claudia [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Grushin, Adolfo; Bardarson, Jens [Max Planck Institute for Physics of Complex Systems, Dresden (Germany); Yan, Binghai [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Max Planck Institute for Physics of Complex Systems, Dresden (Germany)
2016-07-01
In the recently discovered Weyl semimetals, an unconventional negative longitudinal magnetoresistance is expected due to a phenomenon called chiral anomaly. An open question is, how close the Fermi energy needs to be to the Weyl nodes, in order to detect this phenomenon. This question can only be addressed by knowing the electronic bandstructure, i.e. the position of the Fermi energy, and the intrinsic longitudinal magnetoresistance precisely. Here, we report the detailed Fermi surface topology of the Weyl semimetal TaP determined via angle-resolved quantum oscillation spectra combined with band-structure calculations. The Fermi surface consists of an electron and a hole banana without independent pockets around the Weyl points. Although the absence of independent Fermi surface pockets around the Weyl points means that no chiral anomaly is expected, we detect a negative longitudinal magnetoresistance. We discuss possible origins.
Holographic Floquet states I: a strongly coupled Weyl semimetal
Hashimoto, Koji; Kinoshita, Shunichiro; Murata, Keiju; Oka, Takashi
2017-05-01
Floquet states can be realized in quantum systems driven by continuous time-periodic perturbations. It is known that a state known as the Floquet Weyl semimetal can be realized when free Dirac fermions are placed in a rotating electric field. What will happen if strong interaction is introduced to this system? Will the interaction wash out the characteristic features of Weyl semimetals such as the Hall response? Is there a steady state and what is its thermodynamic behavior? We answer these questions using AdS/CFT correspondence in the N = 2 supersymmetric massless QCD in a rotating electric field in the large N c limit realizing the first example of a "holographic Floquet state". In this limit, gluons not only mediate interaction, but also act as an energy reservoir and stabilize the nonequilibrium steady state (NESS). We obtain the electric current induced by a rotating electric field: in the high frequency region, the Ohm's law is satisfied, while we recover the DC nonlinear conductivity at low frequency, which was obtained holographically in a previous work. The thermodynamic properties of the NESS, e.g., fluctuation-dissipation relation, is characterized by the effective Hawking temperature that is defined from the effective horizon giving a holographic meaning to the "periodic thermodynamic" concept. In addition to the strong (pump) rotating electric field, we apply an additional weak (probe) electric field in the spirit of the pump-probe experiments done in condensed matter experiments. Weak DC and AC probe analysis in the background rotating electric field shows Hall currents as a linear response, therefore the Hall response of Floquet Weyl semimetals survives at the strong coupling limit. We also find frequency mixed response currents, i.e., a heterodyning effect, characteristic to periodically driven Floquet systems.
Barton, Ray
1990-01-01
Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)
Chaos, Fractals, and Polynomials.
Tylee, J. Louis; Tylee, Thomas B.
1996-01-01
Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)
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...
Thamrin, Cindy; Stern, Georgette; Frey, Urs
2010-06-01
There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment. Copyright 2010 Elsevier Ltd. All rights reserved.
Weyl gravity and Cartan geometry
Attard, J.; François, J.; Lazzarini, S.
2016-04-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].
Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions
International Nuclear Information System (INIS)
Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander
2010-01-01
A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/r D ∝r -D where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A 'box-counting' procedure could also be applied giving the 'capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term 'fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis.The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are
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
Weyl relativity: a novel approach to Weyl's ideas
Energy Technology Data Exchange (ETDEWEB)
Barceló, Carlos [Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Carballo-Rubio, Raúl [The Cosmology and Gravity Group and the Laboratory for Quantum Gravity and Strings, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7701 (South Africa); Garay, Luis J., E-mail: carlos@iaa.es, E-mail: raul.carballo-rubio@uct.ac.za, E-mail: luisj.garay@ucm.es [Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid (Spain)
2017-06-01
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the conformal invariance of the gravitational field. We highlight that changing the local symmetry group of spacetime permits to construct a theory in which these two symmetries are combined into a putative gauge symmetry but with second-order field equations and non-trivial mass scales, unlike the original higher-order construction by Weyl. We prove that the gravitational field equations are equivalent to the (trace-free) Einstein field equations, ensuring their compatibility with known tests of general relativity. As a corollary, the effective cosmological constant is rendered radiatively stable due to Weyl invariance. A novel phenomenological consequence characteristic of this construction, potentially relevant for cosmological observations, is the existence of an energy scale below which effects associated with the non-integrability of spacetime distances, and an effective mass for the electromagnetic field, appear simultaneously (as dual manifestations of the use of Weyl connections). We explain how former criticisms against Weyl's ideas lose most of their power in its present reincarnation, which we refer to as Weyl relativity, as it represents a Weyl-invariant, unified description of both the Einstein and Maxwell field equations.
Weyl relativity: a novel approach to Weyl's ideas
International Nuclear Information System (INIS)
Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J.
2017-01-01
In this paper we revisit the motivation and construction of a unified theory of gravity and electromagnetism, following Weyl's insights regarding the appealing potential connection between the gauge invariance of electromagnetism and the conformal invariance of the gravitational field. We highlight that changing the local symmetry group of spacetime permits to construct a theory in which these two symmetries are combined into a putative gauge symmetry but with second-order field equations and non-trivial mass scales, unlike the original higher-order construction by Weyl. We prove that the gravitational field equations are equivalent to the (trace-free) Einstein field equations, ensuring their compatibility with known tests of general relativity. As a corollary, the effective cosmological constant is rendered radiatively stable due to Weyl invariance. A novel phenomenological consequence characteristic of this construction, potentially relevant for cosmological observations, is the existence of an energy scale below which effects associated with the non-integrability of spacetime distances, and an effective mass for the electromagnetic field, appear simultaneously (as dual manifestations of the use of Weyl connections). We explain how former criticisms against Weyl's ideas lose most of their power in its present reincarnation, which we refer to as Weyl relativity, as it represents a Weyl-invariant, unified description of both the Einstein and Maxwell field equations.
Fraboni, Michael; Moller, Trisha
2008-01-01
Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…
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
Holographic superconductor with momentum relaxation and Weyl correction
Directory of Open Access Journals (Sweden)
Yi Ling
2017-04-01
Full Text Available We construct a holographic model with Weyl corrections in five dimensional spacetime. In particular, we introduce a coupling term between the axion fields and the Maxwell field such that the momentum is relaxed even in the probe limit in this model. We investigate the Drude behavior of the optical conductivity in low frequency region. It is interesting to find that the incoherent part of the conductivity is suppressed with the increase of the axion parameter k/T, which is in contrast to other holographic axionic models at finite density. Furthermore, we study the superconductivity associated with the condensation of a complex scalar field and evaluate the critical temperature for condensation in both analytical and numerical manner. It turns out that the critical temperature decreases with k˜, indicating that the condensation becomes harder in the presence of the axions, while it increases with Weyl parameter γ. We also discuss the change of the gap in optical conductivity with coupling parameters. Finally, we evaluate the charge density of the superfluid in zero temperature limit, and find that it exhibits a linear relation with σ˜DC(Tc˜Tc˜, such that a modified version of Homes' law is testified.
FRACTAL ANALYSIS OF FRACTURE SYSTEMS IN UPPER TRIASSIC DOLOMITES IN ŽUMBERAK MOUNTAIN, CROATIA
Ivica Pavičić; Ivan Dragičević; Tatjana Vlahović; Tonći Grgasović
2017-01-01
This paper presents results of fractal analysis of fracture systems in upper Triassic dolomites in Žumberak Mountain, Croatia. Mechanical rock characteristics together with structural and diagenetic processes results with fracture systems that can be considered as fractals. They are scale-invariant in specific range of scales. Distribution of fractures can be than described with power law distribution and fractal dimension. Fractal dimension is a measure of how fractures fill the space. Fract...
Semiclassical dynamics and magnetic Weyl calculus
International Nuclear Information System (INIS)
Lein, Maximilian Stefan
2011-01-01
Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators. (orig.)
Gauge invariance and Weyl-polymer quantization
Strocchi, Franco
2016-01-01
The book gives an introduction to Weyl non-regular quantization suitable for the description of physically interesting quantum systems, where the traditional Dirac-Heisenberg quantization is not applicable. The latter implicitly assumes that the canonical variables describe observables, entailing necessarily the regularity of their exponentials (Weyl operators). However, in physically interesting cases -- typically in the presence of a gauge symmetry -- non-observable canonical variables are introduced for the description of the states, namely of the relevant representations of the observable algebra. In general, a gauge invariant ground state defines a non-regular representation of the gauge dependent Weyl operators, providing a mathematically consistent treatment of familiar quantum systems -- such as the electron in a periodic potential (Bloch electron), the Quantum Hall electron, or the quantum particle on a circle -- where the gauge transformations are, respectively, the lattice translations, the magne...
Semiclassical dynamics and magnetic Weyl calculus
Energy Technology Data Exchange (ETDEWEB)
Lein, Maximilian Stefan
2011-01-19
Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered by existing theory as proofs involving usual Weyl calculus break down. This is the regime of the so-called quantum Hall effect where quantization of transverse conductance is observed. To rigorously derive semiclassical equations of motion, one needs to systematically develop a magnetic Weyl calculus which contains a semiclassical parameter. Mathematically, the operators involved in the analysis are magnetic pseudodifferential operators, a topic which by itself is of interest for the mathematics and mathematical physics community alike. Hence, we will devote two additional chapters to further understanding of properties of those operators. (orig.)
AC conductivity for a holographic Weyl semimetal
Energy Technology Data Exchange (ETDEWEB)
Grignani, Gianluca; Marini, Andrea; Peña-Benitez, Francisco; Speziali, Stefano [Dipartimento di Fisica e Geologia, Università di Perugia,I.N.F.N. Sezione di Perugia,Via Pascoli, I-06123 Perugia (Italy)
2017-03-23
We study the AC electrical conductivity at zero temperature in a holographic model for a Weyl semimetal. At small frequencies we observe a linear dependence in the frequency. The model shows a quantum phase transition between a topological semimetal (Weyl semimetal phase) with a non vanishing anomalous Hall conductivity and a trivial semimetal. The AC conductivity has an intermediate scaling due to the presence of a quantum critical region in the phase diagram of the system. The phase diagram is reconstructed using the scaling properties of the conductivity. We compare with the experimental data of https://www.doi.org/10.1103/PhysRevB.93.121110 obtaining qualitative agreement.
Simple recipe for holographic Weyl anomaly
Energy Technology Data Exchange (ETDEWEB)
Bugini, F. [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción,Casilla 160-C, Concepción (Chile); Diaz, D.E. [Departamento de Ciencias Físicas, Facultad de Ciencias Exactas, Universidad Andres Bello,Autopista Concepción-Talcahuano 7100, Talcahuano (Chile)
2017-04-20
We propose a recipe — arguably the simplest — to compute the holographic type-B Weyl anomaly for general higher-derivative gravity in asymptotically AdS spacetimes. In 5 and 7 dimensions we identify a suitable basis of curvature invariants that allows to read off easily, without any further computation, the Weyl anomaly coefficients of the dual CFT. We tabulate the contributions from quadratic, cubic and quartic purely algebraic curvature invariants and also from terms involving derivatives of the curvature. We provide few examples, where the anomaly coefficients have been obtained by other means, to illustrate the effectiveness of our prescription.
Note on Weyl versus conformal invariance in field theory
Energy Technology Data Exchange (ETDEWEB)
Wu, Feng [Nanchang University, Department of Physics, Nanchang (China)
2017-12-15
It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that generically unitarity alone is not sufficient for a conformal field theory to be Weyl invariant. Furthermore, we show explicitly that when a unitary conformal field theory couples to gravity in a Weyl-invariant way, each primary scalar operator that is either relevant or marginal in the unitary conformal field theory corresponds to a Weyl-covariant operator in the curved background. (orig.)
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.
Fractal Image Informatics: from SEM to DEM
Oleschko, K.; Parrot, J.-F.; Korvin, G.; Esteves, M.; Vauclin, M.; Torres-Argüelles, V.; Salado, C. Gaona; Cherkasov, S.
2008-05-01
In this paper, we introduce a new branch of Fractal Geometry: Fractal Image Informatics, devoted to the systematic and standardized fractal analysis of images of natural systems. The methods of this discipline are based on the properties of multiscale images of selfaffine fractal surfaces. As proved in the paper, the image inherits the scaling and lacunarity of the surface and of its reflectance distribution [Korvin, 2005]. We claim that the fractal analysis of these images must be done without any smoothing, thresholding or binarization. Two new tools of Fractal Image Informatics, firmagram analysis (FA) and generalized lacunarity (GL), are presented and discussed in details. These techniques are applicable to any kind of image or to any observed positive-valued physical field, and can be used to correlate between images. It will be shown, by a modified Grassberger-Hentschel-Procaccia approach [Phys. Lett. 97A, 227 (1983); Physica 8D, 435 (1983)] that GL obeys the same scaling law as the Allain-Cloitre lacunarity [Phys. Rev. A 44, 3552 (1991)] but is free of the problems associated with gliding boxes. Several applications are shown from Soil Physics, Surface Science, and other fields.
Weyl and Marchaud Derivatives: A Forgotten History
Directory of Open Access Journals (Sweden)
Fausto Ferrari
2018-01-01
Full Text Available In this paper, we recall the contribution given by Hermann Weyl and André Marchaud to the notion of fractional derivative. In addition, we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics.
Weyl and Marchaud derivatives: a forgotten history
Ferrari, Fausto
2017-01-01
In this paper, we recall the contribution given by Hermann Weyl and André Marchaud to the notion of fractional derivative. In addition, we discuss some relationships between the fractional Laplace operator and Marchaud derivative in the perspective to generalize these objects to different fields of the mathematics.
Fractal dimension for fractal structures: A Hausdorff approach
Fernández-Martínez, M.; Sánchez-Granero, M.A.
2012-01-01
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a suitable discretization of the Hausdorff theory of fractal dimension. We also find some connections between our definition and the classical ones and also with fractal dimensions I & II (see http://arxiv.org/submit/0080421/pdf). Therefore, we generalize them and ...
Construction of fractal surfaces by recurrent fractal interpolation curves
International Nuclear Information System (INIS)
Yun, Chol-hui; O, Hyong-chol; Choi, Hui-chol
2014-01-01
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system (RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible constructions of fractal surfaces
Exploring Fractals in the Classroom.
Naylor, Michael
1999-01-01
Describes an activity involving six investigations. Introduces students to fractals, allows them to study the properties of some famous fractals, and encourages them to create their own fractal artwork. Contains 14 references. (ASK)
Fractals: To Know, to Do, to Simulate.
Talanquer, Vicente; Irazoque, Glinda
1993-01-01
Discusses the development of fractal theory and suggests fractal aggregates as an attractive alternative for introducing fractal concepts. Describes methods for producing metallic fractals and a computer simulation for drawing fractals. (MVL)
The fractal nature of vacuum arc cathode spots
International Nuclear Information System (INIS)
Anders, Andre
2005-01-01
Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Several points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f 2 , where f is frequency, supporting a fractal spot model associated with Brownian motion
Representing fractals by superoscillations
International Nuclear Information System (INIS)
Berry, M V; Morley-Short, S
2017-01-01
Fractals provide an extreme test of representing fine detail in terms of band-limited functions, i.e. by superoscillations. We show that this is possible, using the example of the Weierstrass nondifferentiable fractal. If this is truncated at an arbitrarily fine scale, it can be expressed to any desired accuracy with a simple superoscillatory function. In illustrative simulations, fractals truncated with fastest frequency 2 16 are easily represented by superoscillations with fastest Fourier frequency 1. (letter)
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
Fractal Geometry of Architecture
Lorenz, Wolfgang E.
In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.
Canceling the Weyl anomaly from a position-dependent coupling
Nakayama, Yu
2018-02-01
Once we put a quantum field theory on a curved manifold, it is natural to further assume that coupling constants are position-dependent. The position-dependent coupling constants then provide an extra contribution to the Weyl anomaly so that we may attempt to cancel the entire Weyl anomaly on the curved manifold. We show that such a cancellation is possible for constant Weyl transformation or infinitesimal but generic Weyl transformation in two- and four-dimensional conformal field theories with exactly marginal deformations. When the Weyl scaling factor is annihilated by conformal powers of Laplacian (e.g., by the Fradkin-Tseytlin-Riegert-Paneitz operator in four dimensions), the cancellation persists even at the finite order thanks to a nice mathematical property of the Q curvature under the Weyl transformation.
Studies of Dirac and Weyl fermions by angle resolved photoemission spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Huang, Lunan [Iowa State Univ., Ames, IA (United States)
2016-01-01
This dissertation consists of three parts. First, we study magnetic domains in Nd_{2}Fe_{14}B single crystals using high resolution magnetic force microscopy (MFM). In addition to the elongated, wavy nano-domains reported by a previous MFM study, we found that the micrometer size, star-shaped fractal pattern is constructed of an elongated network of nano-domains about 20 nm in width, with resolution-limited domain walls thinner than 2 nm. Second, we studied extra Dirac cones of multilayer graphene on SiC surface by ARPES and SPA-LEED. We discovered extra Dirac cones on Fermi surface due to SiC 6 x 6 and graphene 6√ 3 6√ 3 coincidence lattice on both single-layer and three-layer graphene sheets. We interpreted the position and intensity of the Dirac cone replicas, based on the scattering vectors from LEED patterns. We found the positions of replica Dirac cones are determined mostly by the 6 6 SiC superlattice even graphene layers grown thicker. Finally, we studied the electronic structure of MoTe_{2} by ARPES and experimentally con rmed the prediction of type II Weyl state in this material. By combining the result of Density Functional Theory calculations and Berry curvature calculations with out experimental data, we identi ed Fermi arcs, track states and Weyl points, all features predicted to exist in a type II Weyl semimetal. This material is an excellent playground for studies of exotic Fermions.
Hochschild cohomology of the Weyl algebra and Vasiliev's equations
Sharapov, Alexey A.; Skvortsov, Evgeny D.
2017-12-01
We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as well as for the smash products of the Weyl algebra and a finite group of linear symplectic transformations. A relationship with the higher-spin field theory is briefly discussed.
Weyl gravity as a gauge theory
Trujillo, Juan Teancum
In 1920, Rudolf Bach proposed an action based on the square of the Weyl tensor or CabcdCabcd where the Weyl tensor is an invariant under a scaling of the metric. A variation of the metric leads to the field equation known as the Bach equation. In this dissertation, the same action is analyzed, but as a conformal gauge theory. It is shown that this action is a result of a particular gauging of this group. By treating it as a gauge theory, it is natural to vary all of the gauge fields independently, rather than performing the usual fourth-order metric variation only. We show that solutions of the resulting vacuum field equations are all solutions to the vacuum Einstein equation, up to a conformal factor---a result consistent with local scale freedom. We also show how solutions for the gauge fields imply there is no gravitational self energy.
Weyl versus conformal invariance in quantum field theory
Farnsworth, Kara; Luty, Markus A.; Prilepina, Valentina
2017-10-01
We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions d ≤ 10. We also study possible curvature corrections to the Weyl transformations of operators, and show that these are absent for operators of sufficiently low dimensionality and spin. We find possible `anomalous' Weyl transformations proportional to the Weyl (Cotton) tensor for d > 3 ( d = 3). The arguments are based on algebraic consistency conditions similar to the Wess-Zumino consistency conditions that classify possible local anomalies. The arguments can be straightforwardly extended to larger operator dimensions and higher d with additional algebraic complexity.
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
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)
Space-time singularities in Weyl manifolds
Energy Technology Data Exchange (ETDEWEB)
Lobo, I.P. [CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Sapienza Universita di Roma, Dipartimento di Fisica, Rome (Italy); Barreto, A.B.; Romero, C. [Universidade Federal da Paraiba, Departamento de Fisica, C. Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame. (orig.)
Weyl-Heisenberg frames for subspaces
DEFF Research Database (Denmark)
Christensen, Ole
2001-01-01
A Weyl-Heisenberg frame {E(mb)T(na)g}(m, n Z) = {e(2 pi imb(.)) g(.-na)}(m, n is an element of Z) for L-2 (R) allows every function f is an element of L-2(R) to be written as an infinite linear combination of translated and modulated versions of the fixed function g is an element of L-2(R...
Projective normality of Weyl group quotients
Indian Academy of Sciences (India)
Abstract. In this note, we prove that for the standard representation Vof the Weyl group W of a semi-simple algebraic group of type An, Bn,Cn, Dn, F4 and G2 over C, the projective variety P(Vm)/W is projectively normal with respect to the descent of. O(1)⊗|W|, where Vm denote the direct sum of m copies of V. Keywords.
Automata and cells in affine Weyl groups
Gunnells, Paul E.
2008-01-01
Let W~ be an affine Weyl group, and let C be a left, right, or two-sided Kazhdan--Lusztig cell in W~. Let Reduced (C) be the set of all reduced expressions of elements of C, regarded as a formal language in the sense of the theory of computation. We show that Reduced (C) is a regular language. Hence the reduced expressions of the elements in any Kazhdan--Lusztig cell can be enumerated by a finite state automaton.
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
Weyl-gauge symmetry of graphene
International Nuclear Information System (INIS)
Iorio, Alfredo
2011-01-01
Research highlights: → Graphene action's Weyl symmetry identifies shapes for which the DOS is invariant. → Electrons on graphene might experience a general-relativistic-like spacetime. → Rich mathematical structures, such as the Liouville's equation, naturally arise. - Abstract: The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed.
Fractal and multifractal analyses of bipartite networks
Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua
2017-03-01
Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed. Copyright © 2014 Elsevier B.V. All rights reserved.
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.
Small-Angle Scattering from Nanoscale Fat Fractals.
Anitas, E M; Slyamov, A; Todoran, R; Szakacs, Z
2017-12-01
Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and scaling factors at each structural level. This is in agreement with general results deduced in the context of small-angle scattering analysis of a system of randomly oriented, non-interacting, nano-/micro-fractals. We apply our results to a two-dimensional fat Cantor-like fractal, calculating analytic expressions for the scattering intensities and structure factors. We explain how the structural properties can be computed from experimental data and show their correlation to the variation of the scaling factor with the iteration number. The model can be used to interpret recorded experimental SAS data in the framework of fat fractals and can reveal structural properties of materials characterized by a regular law of changing of the fractal dimensions. It can describe successions of power-law decays, with arbitrary decreasing values of the scattering exponents, and interleaved by regions of constant intensity.
Pond fractals in a tidal flat.
Cael, B B; Lambert, Bennett; Bisson, Kelsey
2015-11-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.
Cael, B. B.; Lambert, Bennett; Bisson, Kelsey
2015-11-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.
Directory of Open Access Journals (Sweden)
Kyril Tintarev
2007-05-01
Full Text Available The paper studies energy functionals on quasimetric spaces, defined by quadratic measure-valued Lagrangeans. This general model of medium, known as metric fractals, includes nested fractals and sub-Riemannian manifolds. In particular, the quadratic form of the Lagrangean satisfies Sobolev inequalities with the critical exponent determined by the (quasimetric homogeneous dimension, which is also involved in the asymptotic distribution of the form's eigenvalues. This paper verifies that the axioms of the metric fractal are preserved by space products, leading thus to examples of non-differentiable media of arbitrary intrinsic dimension.
Recipe for generating Weyl semimetals with extended topologically protected features
Wang, R.; Zhao, J. Z.; Jin, Y. J.; Xu, W. P.; Gan, L.-Y.; Wu, X. Z.; Xu, H.; Tong, S. Y.
2017-09-01
We present a recipe that leads to Weyl semimetals with extended topologically protected features. We show that compounds in a family that possess time-reversal symmetry and share a noncentrosymmetric cubic structure with the space group F -43 m (no. 216) host robust Weyl fermions with extended and easily measurable protected features. The candidates in this family are compounds with different chemical formulas, A B2 , ABC, AB C2 , and ABCD, and their Fermi levels are predominantly populated by nontrivial Weyl fermions. Symmetry of the system requires that the Weyl nodes with opposite chirality are well separated in momentum space. Adjacent Weyl points have the same chirality; thus these Weyl nodes would not annihilate each other with respect to lattice perturbations. As Fermi arcs and surface states connect Weyl nodes with opposite chirality, the large separation of the latter in momentum space guarantees the appearance of very long arcs and surface states. This work demonstrates that the use of system symmetry by first-principles calculations is a powerful approach for discovering new Weyl semimetals with attractive features whose protected fermions may be candidates of many applications.
A note on a generalisation of Weyl's theory of gravitation
International Nuclear Information System (INIS)
Dereli, T.; Tucker, R.W.
1982-01-01
A scale-invariant gravitational theory due to Bach and Weyl is generalised by the inclusion of space-time torsion. The difference between the arbitrary and zero torsion constrained variations of the Weyl action is elucidated. Conformal rescaling properties of the gravitational fields are discussed. A new class of classical solutions with torsion is presented. (author)
Weyl points and Fermi arcs in a chiral phononic crystal
Li, Feng; Huang, Xueqin; Lu, Jiuyang; Ma, Jiahong; Liu, Zhengyou
2018-01-01
Topological semimetals are materials whose band structure contains touching points that are topologically nontrivial and can host quasiparticle excitations that behave as Dirac or Weyl fermions. These so-called Weyl points not only exist in electronic systems, but can also be found in artificial periodic structures with classical waves, such as electromagnetic waves in photonic crystals and acoustic waves in phononic crystals. Due to the lack of spin and a difficulty in breaking time-reversal symmetry for sound, however, topological acoustic materials cannot be achieved in the same way as electronic or optical systems. And despite many theoretical predictions, experimentally realizing Weyl points in phononic crystals remains challenging. Here, we experimentally realize Weyl points in a chiral phononic crystal system, and demonstrate surface states associated with the Weyl points that are topological in nature, and can host modes that propagate only in one direction. As with their photonic counterparts, chiral phononic crystals bring topological physics to the macroscopic scale.
Holographic p-wave superconductor models with Weyl corrections
Directory of Open Access Journals (Sweden)
Lu Zhang
2015-04-01
Full Text Available We study the effect of the Weyl corrections on the holographic p-wave dual models in the backgrounds of AdS soliton and AdS black hole via a Maxwell complex vector field model by using the numerical and analytical methods. We find that, in the soliton background, the Weyl corrections do not influence the properties of the holographic p-wave insulator/superconductor phase transition, which is different from that of the Yang–Mills theory. However, in the black hole background, we observe that similarly to the Weyl correction effects in the Yang–Mills theory, the higher Weyl corrections make it easier for the p-wave metal/superconductor phase transition to be triggered, which shows that these two p-wave models with Weyl corrections share some similar features for the condensation of the vector operator.
Fractal physiology and the fractional calculus: a perspective.
West, Bruce J
2010-01-01
fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks.
Fractal generalized Pascal matrices
Burlachenko, E.
2016-01-01
Set of generalized Pascal matrices whose elements are generalized binomial coefficients is considered as an integral object. The special system of generalized Pascal matrices, based on which we are building fractal generalized Pascal matrices, is introduced. Pascal matrix (Pascal triangle) is the Hadamard product of the fractal generalized Pascal matrices. The concept of zero generalized Pascal matrices, an example of which is the Pascal triangle modulo 2, arise in connection with the system ...
Fractal Electromagnetic Showers
Anchordoqui, L. A.; Kirasirova, M.; McCauley, T. P.; Paul, T.; Reucroft, S.; Swain, J. D.
2000-01-01
We study the self-similar structure of electromagnetic showers and introduce the notion of the fractal dimension of a shower. Studies underway of showers in various materials and at various energies are presented, and the range over which the fractal scaling behaviour is observed is discussed. Applications to fast shower simulations and identification, particularly in the context of extensive air showers, are also discussed.
The Weyl group of the Cuntz algebra
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
and sufficient algorithmic combinatorial condition is found for deciding when a polynomial endomorphism lambda_u restricts to an automorphism of the canonical diagonal MASA. Some steps towards a general criterion for invertibility of lambda_u on the whole of O_n are also taken. A condition for verifying......The Weyl group of the Cuntz algebra O_n is investigated. This is (isomorphic to) the group of polynomial automorphisms lambda_u of O_n, namely those induced by unitaries u that can be written as finite sums of words in the canonical generating isometries S_i and their adjoints. A necessary...
Sánchez, Iván; Uzcátegui, Gladys
2011-04-01
To systematically review applications of fractal geometry in different aspects of dental practice. In this review, we present a short introduction to fractals and specifically address the following topics: treatment and healing monitoring, dental materials, dental tissue, caries, osteoporosis, periodontitis, cancer, Sjögren's syndrome, diagnosis of several other conditions and a discussion on the reliability of FD determinations from dental radiographs. Google Scholar, Ovid MEDLINE, ScienceDirect, etc. (up to August 2010). The review considered original studies, reviews and conference proceedings, published in English or Spanish. Abstracts and posters were not taken into account. Fractal geometry has found plenty of applications in several branches of dental practice. It provides a way to quantify the complexity of structures. Whereas one desires to study a radiograph, an histological section or the signal from a transducer, there are several methods available to determine the degree of complexity using fractal analysis. Several pathological conditions can alter the complexity of anatomical structures, and this change can be detectable with the help of fractal parameters. Although during the last two decades there have been plenty of works on the field, reported cases having enough reproducibility, with different groups showing similar results are not very common. Further replications are needed before we can establish statistically significant correlations amongst fractal parameters and pathological conditions. Copyright © 2011 Elsevier Ltd. All rights reserved.
Recovery of the Dirac system from the rectangular Weyl matrix function
International Nuclear Information System (INIS)
Fritzsche, B; Kirstein, B; Roitberg, I Ya; Sakhnovich, A L
2012-01-01
Weyl theory for Dirac systems with rectangular matrix potentials is non-classical. The corresponding Weyl functions are rectangular matrix functions. Furthermore, they are non-expansive in the upper semi-plane. Inverse problems are studied for such Weyl functions, and some results are new even for the square Weyl functions. High-energy asymptotics of Weyl functions and Borg–Marchenko-type uniqueness results are derived too. (paper)
Weyl Semimetals as Hydrogen Evolution Catalysts.
Rajamathi, Catherine R; Gupta, Uttam; Kumar, Nitesh; Yang, Hao; Sun, Yan; Süß, Vicky; Shekhar, Chandra; Schmidt, Marcus; Blumtritt, Horst; Werner, Peter; Yan, Binghai; Parkin, Stuart; Felser, Claudia; Rao, C N R
2017-05-01
The search for highly efficient and low-cost catalysts is one of the main driving forces in catalytic chemistry. Current strategies for the catalyst design focus on increasing the number and activity of local catalytic sites, such as the edge sites of molybdenum disulfides in the hydrogen evolution reaction (HER). Here, the study proposes and demonstrates a different principle that goes beyond local site optimization by utilizing topological electronic states to spur catalytic activity. For HER, excellent catalysts have been found among the transition-metal monopnictides-NbP, TaP, NbAs, and TaAs-which are recently discovered to be topological Weyl semimetals. Here the study shows that the combination of robust topological surface states and large room temperature carrier mobility, both of which originate from bulk Dirac bands of the Weyl semimetal, is a recipe for high activity HER catalysts. This approach has the potential to go beyond graphene based composite photocatalysts where graphene simply provides a high mobility medium without any active catalytic sites that have been found in these topological materials. Thus, the work provides a guiding principle for the discovery of novel catalysts from the emerging field of topological materials. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Two-parameter asymptotics in magnetic Weyl calculus
International Nuclear Information System (INIS)
Lein, Max
2010-01-01
This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ε, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) ε<< 1 and λ<< 1, (ii) ε<< 1 and λ= 1, as well as (iii) ε= 1 and λ<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.
Passage through X-ray protection having the structure of homogeneous fractals
Churikov Viktor Anatolyevich
2014-01-01
In this paper we generalize the law of Bouguer-Lambert in the case of a homogeneous fractal. With detailed analysis in terms of d-output operator generalized law of BouguerLambert-Beer law, which in particular includes the classical law of optics Bouguer-LambertBeer.
Fractals, Their importance in geology. Simulation of fractal natural patterns
Gumiel Martínez, Pablo
1996-01-01
An introduction to the Symposium 16 on Fractals and Geology is presented in this contribution. A summary on fractal concepts and natural geometrical fractal patterns are showed. Finally, computational simulations of natural geological structures are performed, using techniques of Iterated Function Systems (IFS of Barnsley, 1988)
The fractal forest: fractal geometry and applications in forest science.
Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary
1994-01-01
Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.
Fractal Patterns and Chaos Games
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
Transversal magnetotransport in Weyl semimetals: Exact numerical approach
Behrends, Jan; Kunst, Flore K.; Sbierski, Björn
2018-02-01
Magnetotransport experiments on Weyl semimetals are essential for investigating the intriguing topological and low-energy properties of Weyl nodes. If the transport direction is perpendicular to the applied magnetic field, experiments have shown a large positive magnetoresistance. In this work we present a theoretical scattering matrix approach to transversal magnetotransport in a Weyl node. Our numerical method confirms and goes beyond the existing perturbative analytical approach by treating disorder exactly. It is formulated in real space and is applicable to mesoscopic samples as well as in the bulk limit. In particular, we study the case of clean and strongly disordered samples.
Higher dimensional bivectors and classification of the Weyl operator
International Nuclear Information System (INIS)
Coley, Alan; Hervik, Sigbjoern
2010-01-01
We develop the bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise to a refinement in dimensions higher than four of the usual alignment (boost-weight) classification, in terms of the irreducible representations of the spins. We are consequently able to define a number of new algebraically special cases. In particular, the classification in five dimensions is discussed in some detail. In addition, utilizing the (refined) algebraic classification, we are able to prove some interesting results when the Weyl tensor has (additional) symmetries.
A local potential for the Weyl tensor in all dimensions
International Nuclear Information System (INIS)
Edgar, S Brian; Senovilla, Jose M M
2004-01-01
In all dimensions n ≥ 4 and arbitrary signature, we demonstrate the existence of a new local potential-a double (2, 3)-form, P ab cde -for the Weyl curvature tensor C abcd , and more generally for all tensors W abcd with the symmetry properties of the Weyl tensor. The classical four-dimensional Lanczos potential for a Weyl tensor-a double (2, 1)-form, H ab c -is proven to be a particular case of the new potential: its double dual. (letter to the editor)
Nonequilibrium transport in the pseudospin-1 Dirac-Weyl system
Wang, Cheng-Zhen; Xu, Hong-Ya; Huang, Liang; Lai, Ying-Cheng
2017-09-01
Recently, solid state materials hosting pseudospin-1 quasiparticles have attracted a great deal of attention. In these materials, the energy band contains a pair of Dirac cones and a flatband through the connecting point of the cones. As the "caging" of carriers with a zero group velocity, the flatband itself has zero conductivity. However, in a nonequilibrium situation where a constant electric field is suddenly switched on, the flatband can enhance the resulting current in both the linear and nonlinear response regimes through distinct physical mechanisms. Using the (2 +1 )-dimensional pseudospin-1 Dirac-Weyl system as a concrete setting, we demonstrate that, in the weak field regime, the interband current is about twice larger than that for pseudospin-1/2 system due to the interplay between the flatband and the negative band, with the scaling behavior determined by the Kubo formula. In the strong field regime, the intraband current is √{2 } times larger than that in the pseudospin-1/2 system, due to the additional contribution from particles residing in the flatband. In this case, the current and field follow the scaling law associated with Landau-Zener tunneling. These results provide a better understanding of the role of the flatband in nonequilibrium transport and are experimentally testable using electronic or photonic systems.
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Results are presented of a preliminary investigation of the fractal nature of the plan-view shapes of lava flows in Hawaii (based on field measurements and aerial photographs), as well as in Idaho and the Galapagos Islands (using aerial photographs only). The shapes of the lava flow margins are found to be fractals: lava flow shape is scale-invariant. This observation suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. A'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14-1.23). The analysis is extended to other planetary bodies by measuring flows from orbital images of Venus, Mars, and the moon. All are fractal and have D consistent with the range of terrestrial a'a and have D consistent with the range of terrestrial a'a and pahoehoe values.
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 radar scattering from soil
Oleschko, Klaudia; Korvin, Gabor; Figueroa, Benjamin; Vuelvas, Marco Antonio; Balankin, Alexander S.; Flores, Lourdes; Carreón, Dora
2003-04-01
A general technique is developed to retrieve the fractal dimension of self-similar soils through microwave (radar) scattering. The technique is based on a mathematical model relating the fractal dimensions of the georadargram to that of the scattering structure. Clear and different fractal signatures have been observed over four geosystems (soils and sediments) compared in this work.
Electronic transport property in Weyl semimetal with local Weyl cone tilt
Jiang, Liwei; Feng, Lanting; Yao, Haibo; Zheng, Yisong
2018-03-01
In realistic materials of Weyl semimetal (WSM), the Weyl cone tilt (WCT) is allowed due to the absence of Lorentz invariance in condensed matter physics. In this context, we theoretically study the electronic transport property in WSM with the local WCT as the scattering mechanism. In so doing, we establish an electronic transport structure of WSM with the WCT occurring only in the central region sandwiched between two pieces of semi-infinite WSM without the WCT. By means of two complementary theoretical approaches, i.e. the continuum-model method and the lattice-model method, the electronic transmission probability, the conductivity and the Fano factor as functions of the incident electron energy are calculated respectively. We find that the WCT can give rise to nontrivial intervalley scattering, as a result, the Klein tunneling is notably suppressed. More importantly, the minimal conductivity of a WSM shifts in energy from the Weyl nodal point. The Fano factor of the shot noise deviates obviously from the sub-Poissonian value in a two dimensional WSM with the WCT.
Fractal physiology and the fractional calculus: a perspective
Directory of Open Access Journals (Sweden)
Bruce J West
2010-10-01
Full Text Available This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. We review the allometric aggregation approach to the processing of physiologic time series as a way of determining the fractal character of the underlying phenomena. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. Fractional operators acting on fractal functions yield fractal functions, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine. Allometric control incorporates long-time memory, inverse power-law (IPL correlations, and long-range interactions in complex phenomena as manifest by IPL distributions. We hypothesize that allometric control, rather than homeostatic control, maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can be described using the fractional calculus to capture the dynamics of complex physiologic networks. This hypothesis is supported by a number of physiologic time series data.
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...
Detecting monopole charge in Weyl semimetals via quantum interference transport
Dai, Xin; Lu, Hai-Zhou; Shen, Shun-Qing; Yao, Hong
2016-04-01
Topological Weyl semimetals can host Weyl nodes with monopole charges in momentum space. How to detect the signature of the monopole charges in quantum transport remains a challenging topic. Here, we reveal the connection between the parity of monopole charge in topological semimetals and the quantum interference corrections to the conductivity. We show that the parity of monopole charge determines the sign of the quantum interference correction, with odd and even parity yielding the weak antilocalization and weak localization effects, respectively. This is attributed to the Berry phase difference between time-reversed trajectories circulating the Fermi sphere that encloses the monopole charges. From standard Feynman diagram calculations, we further show that the weak-field magnetoconductivity at low temperatures is proportional to +√{B } in double-Weyl semimetals and -√{B } in single-Weyl semimetals, respectively, which could be verified experimentally.
Which symmetry? Noether, Weyl, and conservation of electric charge
Brading, Katherine A.
In 1918, Emmy Noether published a (now famous) theorem establishing a general connection between continuous 'global' symmetries and conserved quantities. In fact, Noether's paper contains two theorems, and the second of these deals with 'local' symmetries; prima facie, this second theorem has nothing to do with conserved quantities. In the same year, Hermann Weyl independently made the first attempt to derive conservation of electric charge from a postulated gauge symmetry. In the light of Noether's work, it is puzzling that Weyl's argument uses local gauge symmetry. This paper explores the relationships between Weyl's work, Noether's two theorems, and the modern connection between gauge symmetry and conservation of electric charge. This includes showing that Weyl's connection is essentially an application of Noether's second theorem, with a novel twist.
Chirality blockade of Andreev reflection in a magnetic Weyl semimetal
Bovenzi, N.; Breitkreiz, M.; Baireuther, P.; O'Brien, T. E.; Tworzydło, J.; Adagideli, I.; Beenakker, C. W. J.
2017-07-01
A Weyl semimetal with broken time-reversal symmetry has a minimum of two species of Weyl fermions, distinguished by their opposite chirality, in a pair of Weyl cones at opposite momenta ±K that are displaced in the direction of the magnetization. Andreev reflection at the interface between a Weyl semimetal in the normal state (N) and a superconductor (S) that pairs ±K must involve a switch of chirality, otherwise it is blocked. We show that this "chirality blockade" suppresses the superconducting proximity effect when the magnetization lies in the plane of the NS interface. A Zeeman field at the interface can provide the necessary chirality switch and activate Andreev reflection.
Coulomb interaction effect in tilted Weyl fermion in two dimensions
Isobe, Hiroki; Nagaosa, Naoto
Weyl fermions with tilted linear dispersions characterized by several different velocities appear in some systems including the quasi-two-dimensional organic semiconductor α-(BEDT-TTF)2I3 and three-dimensional WTe2. The Coulomb interaction between electrons modifies the velocities in an essential way in the low energy limit, where the logarithmic corrections dominate. Taking into account the coupling to both the transverse and longitudinal electromagnetic fields, we derive the renormalization group equations for the velocities of the tilted Weyl fermions in two dimensions, and found that they increase as the energy decreases and eventually hit the velocity of light c to result in the Cherenkov radiation. Especially, the system restores the isotropic Weyl cone even when the bare Weyl cone is strongly tilted and the velocity of electrons becomes negative in certain directions.
Weyl states and Fermi arcs in parabolic bands
Doria, Mauro M.; Perali, Andrea
2017-07-01
Weyl fermions are shown to exist inside a parabolic band in a single electronic layer, where the kinetic energy of carriers is given by the non-relativistic Schroedinger equation. There are Fermi arcs as a direct consequence of the folding of a ring-shaped Fermi surface inside the first Brillouin zone. Our results stem from the decomposition of the kinetic energy into the sum of the square of the Weyl state, the coupling to the local magnetic field and the Rashba interaction. The Weyl fermions break the space and time reflection symmetries present in the kinetic energy, thus allowing for the onset of a weak three-dimensional magnetic field around the layer. This field brings topological stability to the current-carrying states through a Chern number. In the special limit for which the Weyl state becomes gapless, this magnetic interaction is shown to be purely attractive, thus suggesting the onset of a superconducting condensate of zero helicity states.
Global topology of Weyl semimetals and Fermi arcs
Mathai, Varghese; Thiang, Guo Chuan
2017-03-01
We provide a manifestly topological classification scheme for generalised Weyl semimetals, in any spatial dimension and with arbitrary Weyl surfaces which may be non-trivially linked. The classification naturally incorporates that of Chern insulators. Our analysis refines, in a mathematically precise sense, some well-known 3D constructions to account for subtle but important global aspects of the topology of semimetals. Using a fundamental locality principle, we derive a generalized charge cancellation condition for the Weyl surface components. We analyse the bulk-boundary correspondence under a duality transformation, which reveals explicitly the topological nature of the resulting surface Fermi arcs. We also analyse the effect of moving Weyl points on the bulk and boundary topological semimetal invariants.
Directory of Open Access Journals (Sweden)
T.-W. Wang
1996-09-01
Full Text Available Fractal theory is applied in a quantitative analysis of geomagnetic storms. Fractal dimensions (D of the attractor for storm data from the Beijing observatory (40.0°N, 116.2°E using several time intervals are calculated. A maximum value of 1.4 has been obtained for a geomagnetic storm; on quite days the dimension is only slightly larger than 0.5. Data from two storms are analyzed here. Results show that a combination of both D and the magnetic index, k, can perhaps describe the degree of solar disturbance better than the single parameter k.
FRACTAL ANALYSIS OF FRACTURE SYSTEMS IN UPPER TRIASSIC DOLOMITES IN ŽUMBERAK MOUNTAIN, CROATIA
Directory of Open Access Journals (Sweden)
Ivica Pavičić
2017-01-01
Full Text Available This paper presents results of fractal analysis of fracture systems in upper Triassic dolomites in Žumberak Mountain, Croatia. Mechanical rock characteristics together with structural and diagenetic processes results with fracture systems that can be considered as fractals. They are scale-invariant in specific range of scales. Distribution of fractures can be than described with power law distribution and fractal dimension. Fractal dimension is a measure of how fractures fill the space. Fractal dimension can be estimated form photographs of outcrops by converting photographs to binary photographs. In binary photo there is only black (rock or fractures and white (fractures or rock. Fractal dimension is then estimated based on box-counting method. In this paper we present results of fractal analysis from three outcrops. Results are very similar to previous published results from outcrops of dolomites in Slovenia. Obtained fractal dimensions are in range 2,69-2,78 and it depends on how fracture systems are distributed in the outcrop. Lower values indicate smaller number of fractures and higher significance of larger fractures. Higher values indicate distribution of more similar sized fractures throughout whole outcrop. Fractal dimension is very significant parameter in rock fracture system characterisation sense it describes how fractures are distributed in the outcrop. It can be used in discrete fracture network modelling if spatial distribution of fractures is represented with power law distribution.
z -Weyl gravity in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Moon, Taeyoon; Oh, Phillial, E-mail: dpproject@skku.edu, E-mail: ploh@skku.edu [Department of Physics and Institute of Basic Science, Sungkyunkwan University, Suwon 440-746 (Korea, Republic of)
2017-09-01
We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the foliation preserving diffeomorphism invariance adapted to the extra dimensions, thus keeping the general covariance only for the four dimensional spacetime. The conformally invariant gravity can be constructed with an extra (Weyl) scalar field and a real parameter z which describes the degree of anisotropy of conformal transformation between the spacetime and extra dimensional metrics. In the zero mode effective 4D action, it reduces to four-dimensional scalar-tensor theory coupled with nonlinear sigma model described by extra dimensional metrics. There are no restrictions on the value of z at the classical level and possible applications to the cosmological constant problem with a specific choice of z are discussed.
Torus as phase space: Weyl quantization, dequantization, and Wigner formalism
Energy Technology Data Exchange (ETDEWEB)
Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it [Dipartimento di Matematica, Università di Bari, I-70125 Bari (Italy)
2016-08-15
The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.
Dimensional Reduction of Conformal Tensors and Einstein-Weyl Spaces
Jackiw, Roman
2007-09-01
Conformal Weyl and Cotton tensors are dimensionally reduced by a Kaluza-Klein procedure. Explicit formulas are given for reducing from four and three dimensions to three and two dimensions, respectively. When the higher dimensional conformal tensor vanishes because the space is conformallly flat, the lower-dimensional Kaluza-Klein functions satisfy equations that coincide with the Einstein-Weyl equations in three dimensions and kink equations in two dimensions.
Fractal elements and their applications
Gil’mutdinov, Anis Kharisovich; El-Khazali, Reyad
2017-01-01
This book describes a new type of passive electronic components, called fractal elements, from a theoretical and practical point of view. The authors discuss in detail the physical implementation and design of fractal devices for application in fractional-order signal processing and systems. The concepts of fractals and fractal signals are explained, as well as the fundamentals of fractional calculus. Several implementations of fractional impedances are discussed, along with comparison of their performance characteristics. Details of design, schematics, fundamental techniques and implementation of RC-based fractal elements are provided. .
Optical Interface States Protected by Synthetic Weyl Points
Directory of Open Access Journals (Sweden)
Qiang Wang
2017-08-01
Full Text Available Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here, we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments, which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points, and the trajectories of these states in the parameter space resembles those of Weyl semimetal “Fermi arc surface states” in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.
Optical Interface States Protected by Synthetic Weyl Points
Wang, Qiang; Xiao, Meng; Liu, Hui; Zhu, Shining; Chan, C. T.
2017-07-01
Weyl fermions have not been found in nature as elementary particles, but they emerge as nodal points in the band structure of electronic and classical wave crystals. Novel phenomena such as Fermi arcs and chiral anomaly have fueled the interest in these topological points which are frequently perceived as monopoles in momentum space. Here, we report the experimental observation of generalized optical Weyl points inside the parameter space of a photonic crystal with a specially designed four-layer unit cell. The reflection at the surface of a truncated photonic crystal exhibits phase vortexes due to the synthetic Weyl points, which in turn guarantees the existence of interface states between photonic crystals and any reflecting substrates. The reflection phase vortexes have been confirmed for the first time in our experiments, which serve as an experimental signature of the generalized Weyl points. The existence of these interface states is protected by the topological properties of the Weyl points, and the trajectories of these states in the parameter space resembles those of Weyl semimetal "Fermi arc surface states" in momentum space. Tracing the origin of interface states to the topological character of the parameter space paves the way for a rational design of strongly localized states with enhanced local field.
Evidence for topological type-II Weyl semimetal WTe2
Li, Peng
2017-12-11
Recently, a type-II Weyl fermion was theoretically predicted to appear at the contact of electron and hole Fermi surface pockets. A distinguishing feature of the surfaces of type-II Weyl semimetals is the existence of topological surface states, so-called Fermi arcs. Although WTe2 was the first material suggested as a type-II Weyl semimetal, the direct observation of its tilting Weyl cone and Fermi arc has not yet been successful. Here, we show strong evidence that WTe2 is a type-II Weyl semimetal by observing two unique transport properties simultaneously in one WTe2 nanoribbon. The negative magnetoresistance induced by a chiral anomaly is quite anisotropic in WTe2 nanoribbons, which is present in b-axis ribbon, but is absent in a-axis ribbon. An extra-quantum oscillation, arising from a Weyl orbit formed by the Fermi arc and bulk Landau levels, displays a two dimensional feature and decays as the thickness increases in WTe2 nanoribbon.
Weight-lattice discretization of Weyl-orbit functions
Energy Technology Data Exchange (ETDEWEB)
Hrivnák, Jiří, E-mail: jiri.hrivnak@fjfi.cvut.cz, E-mail: walton@uleth.ca [Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, CZ-115 19 Prague (Czech Republic); Walton, Mark A., E-mail: jiri.hrivnak@fjfi.cvut.cz, E-mail: walton@uleth.ca [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada)
2016-08-15
Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have also been discretized, using a refinement of the coweight lattice, so that digitized data on the fundamental region can be Fourier-analyzed. The discretized orbit function has arguments that are redundant if related by the affine Weyl group, while its labels, the Weyl-orbit representatives, invoke the dual affine Weyl group. Here we discretize the orbit functions in a novel way, by using the weight lattice. A cleaner theory results with symmetry between the arguments and labels of the discretized orbit functions. Orthogonality of the new discretized orbit functions is proved, and leads to the construction of unitary, symmetric matrices with Weyl-orbit-valued elements. For one type of orbit function, the matrix coincides with the Kac-Peterson modular S matrix, important for Wess-Zumino-Novikov-Witten conformal field theory.
Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity
Energy Technology Data Exchange (ETDEWEB)
Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary Prospect 7a, 117312 Moscow (Russian Federation)
2017-01-01
We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the 'usual' hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by 'the particle creation law', proportional to the square of the Weyl tensor (following the famous result by Ya.B. Zel'dovich and A.A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A.D. Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the 'empty vacuum', there may exist the 'dynamical vacuum', which is nothing more but the Dirac sea. The latter is described by the unexpectedly elegant equation which includes both the Bach and Einstein tensors and the cosmological terms.
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
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...
The number of elementary particles in a fractal M-theory of 11.2360667977 dimensions
International Nuclear Information System (INIS)
He, J.-H.
2007-01-01
It is generally accepted that there are 60 experimentally found particles. The standard model strongly predicts two more hypothetical particles, the Higgs and the graviton. This paper reveals other possible scenario for predicting 69 particles at different energy scales in 11+φ 3 fractal dimensions of a fractal M theory, where φ=(5-1)/2. A modified Newton's law is suggested to experimentally verify our predictions at extremely small quantum scales. The modified Newton's law is in harmony with Heisenberg's uncertainty principle
Fractal analysis of the fractal ultra-wideband signals
International Nuclear Information System (INIS)
Chernogor, L.F.; Lazorenko, O.V.; Onishchenko, A.A.
2015-01-01
The results of fractal analysis of the fractal ultra-wideband (FUWB) signals were proposed. With usage of the continuous wavelet transform the time-frequency structure of that signals was investigated. Calculating the box and the regularization dimensions for each model signal with various its parameters values, three different estimators were applied. The optimal estimations of the fractal dimension value for each FUWB signal model were defined
Wei Shen
2011-01-01
The self-similar is a common phenomena arising in the field of geology. It has been shown that geochemical element data, mineral deposits, and spacial distribution conform to a fractal structure. A fractal distribution requires that the number of objects larger than a specified size have a power-law dependence on size. This paper shows that a number of distributions, including power-function, Pareto, lognormal, and Zipf, display fractal properties under certain conditions and that this may be...
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.
Fractals in geology and geophysics
Turcotte, Donald L.
1989-01-01
The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.
Phase Transitions on Fractals and Networks
Stauffer, D.
2007-01-01
For Encyclopedia of Complexist and System Science No abstract given I. Definition and Introduction II. Ising Model III. Fractals IV. Diffusion on Fractals V. Ising Model on Fractals VI. Other Subjects ? VII. Networks VIII. Future Directions
A multiple fractal model for estimating permeability of dual-porosity media
Li, Bo; Liu, Richeng; Jiang, Yujing
2016-09-01
A multiple fractal model that considers the fractal properties of both porous matrices and fracture networks is proposed for the permeability of dual-porosity media embedded with randomly distributed fractures. In this model, the aperture distribution is verified to follow the fractal scaling law, and the porous matrix is assumed to comprise a bundle of tortuous capillaries that also follow the fractal scaling law. Analytical expressions for fractal aperture distribution, total flow rate, total equivalent permeability, and dimensionless permeability are established, where the dimensionless permeability is defined as the ratio of permeability of the porous matrices to that of the fracture networks. The dimensionless permeability is closely correlated to the structural parameters (i.e., α, θ, Dtf, Dtp, De, Dp, emax, λmax) of the dual-porosity media, and it is more sensitive to the fractal dimension for the size distribution of fracture aperture than to that for the size distribution of pore/capillary diameter. The maximum pore/capillary diameter has a greater impact on the dimensionless permeability than that of the maximum fracture aperture. The dimensionless permeability of fracture networks constructed by the fractal aperture distribution has close values with those of models with lognormal aperture distribution. The proposed multiple fractal model does not involve any empirical constants that do not have clear physical meanings, which could serve as a quick estimation method for assessing permeability of dual-porosity media.
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.
Nodal-line semimetals from Weyl superlattices
Behrends, Jan; Rhim, Jun-Won; Liu, Shang; Grushin, Adolfo G.; Bardarson, Jens H.
2017-12-01
The existence and topological classification of lower-dimensional Fermi surfaces is often tied to the crystal symmetries of the underlying lattice systems. Artificially engineered lattices, such as heterostructures and other superlattices, provide promising avenues to realize desired crystal symmetries that protect lower-dimensional Fermi surfaces, such as nodal lines. In this work, we investigate a Weyl semimetal subjected to spatially periodic onsite potential, giving rise to several phases, including a nodal-line semimetal phase. In contrast to proposals that purely focus on lattice symmetries, the emergence of the nodal line in this setup does not require small spin-orbit coupling, but rather relies on its presence. We show that the stability of the nodal line is understood from reflection symmetry and a combination of a fractional lattice translation and charge-conjugation symmetry. Depending on the choice of parameters, this model exhibits drumhead surface states that are exponentially localized at the surface, or weakly localized surface states that decay into the bulk at all energies.
Rethinking antiparticles. Hermann Weyl's contribution to neutrino physics
De Bianchi, Silvia
2018-02-01
This paper focuses on Hermann Weyl's two-component theory and frames it within the early development of different theories of spinors and the history of the discovery of parity violation in weak interactions. In order to show the implications of Weyl's theory, the paper discusses the case study of Ettore Majorana's symmetric theory of electron and positron (1937), as well as its role in inspiring Case's formulation of parity violation for massive neutrinos in 1957. In doing so, this paper clarifies the relevance of Weyl's and Majorana's theories for the foundations of neutrino physics and emphasizes which conceptual aspects of Weyl's approach led to Lee's and Yang's works on neutrino physics and to the solution of the theta-tau puzzle in 1957. This contribution thus sheds a light on the alleged "re-discovery" of Weyl's and Majorana's theories in 1957, by showing that this did not happen all of a sudden. On the contrary, the scientific community was well versed in applying these theories in the 1950s on the ground of previous studies that involved important actors in both Europe and United States.
Evidence for magnetic Weyl fermions in a correlated metal
Kuroda, K.; Tomita, T.; Suzuki, M.-T.; Bareille, C.; Nugroho, A. A.; Goswami, P.; Ochi, M.; Ikhlas, M.; Nakayama, M.; Akebi, S.; Noguchi, R.; Ishii, R.; Inami, N.; Ono, K.; Kumigashira, H.; Varykhalov, A.; Muro, T.; Koretsune, T.; Arita, R.; Shin, S.; Kondo, Takeshi; Nakatsuji, S.
2017-11-01
Weyl fermions have been observed as three-dimensional, gapless topological excitations in weakly correlated, inversion-symmetry-breaking semimetals. However, their realization in spontaneously time-reversal-symmetry-breaking phases of strongly correlated materials has so far remained hypothetical. Here, we report experimental evidence for magnetic Weyl fermions in Mn3Sn, a non-collinear antiferromagnet that exhibits a large anomalous Hall effect, even at room temperature. Detailed comparison between angle-resolved photoemission spectroscopy (ARPES) measurements and density functional theory (DFT) calculations reveals significant bandwidth renormalization and damping effects due to the strong correlation among Mn 3d electrons. Magnetotransport measurements provide strong evidence for the chiral anomaly of Weyl fermions--namely, the emergence of positive magnetoconductance only in the presence of parallel electric and magnetic fields. Since weak magnetic fields (approximately 10 mT) are adequate to control the distribution of Weyl points and the large fictitious fields (equivalent to approximately a few hundred T) produced by them in momentum space, our discovery lays the foundation for a new field of science and technology involving the magnetic Weyl excitations of strongly correlated electron systems such as Mn3Sn.
Electronic properties of disordered Weyl semimetals at charge neutrality
Holder, Tobias; Huang, Chia-Wei; Ostrovsky, Pavel M.
2017-11-01
Weyl semimetals have been intensely studied as a three-dimensional realization of a Dirac-like excitation spectrum where the conduction bands and valence bands touch at isolated Weyl points in momentum space. Like in graphene, this property entails various peculiar electronic properties. However, recent theoretical studies have suggested that resonant scattering from rare regions can give rise to a nonzero density of states even at charge neutrality. Here, we give a detailed account of this effect and demonstrate how the semimetallic nature is suppressed at the lowest scales. To this end, we develop a self-consistent T -matrix approach to investigate the density of states beyond the limit of weak disorder. Our results show a nonvanishing density of states at the Weyl point, which exhibits a nonanalytic dependence on the impurity density. This unusually strong effect of rare regions leads to a revised estimate for the conductivity close to the Weyl point and emphasizes possible deviations from semimetallic behavior in dirty Weyl semimetals at charge neutrality even with very low impurity concentration.
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...
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems. ... for the treatment of diffusion, heat conduction, waves, etc., on self-similar fractals [25–28]. Harmonic ... differential equations offer possibilities of modeling dynamical behaviours naturally for which ordinary differential ...
Local couplings, double insertions and the Weyl consistency condition
International Nuclear Information System (INIS)
Kraus, E.; Sibold, K.
1992-05-01
Within massless φ 4 4 -theory we set up the formalism which is needed, when the coupling λ is permitted to become an external field, i.e. a function of space-time. In particular we have worked out the action of the corresponding Callan-Symanzik operator and conformal transformations on the vertex functions, and furthermore how the Weyl transformations act on the theory with the energy-momentum tensor invariantly coupled. With the help of the Weyl consistency condition we have shown that in the limit of constant coupling the Weyl braking can entirely be written in terms of differential operators, but that otherwise, for truely local coupling, new breaking terms survive. (orig.)
Consistent hydrodynamic theory of chiral electrons in Weyl semimetals
Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.
2018-03-01
The complete set of Maxwell's and hydrodynamic equations for the chiral electrons in Weyl semimetals is presented. The formulation of the Euler equation takes into account the explicit breaking of the Galilean invariance by the ion lattice. It is shown that the Chern-Simons (or Bardeen-Zumino) contributions should be added to the electric current and charge densities in Maxwell's equations that provide the information on the separation of Weyl nodes in energy and momentum. On the other hand, these topological contributions do not directly affect the Euler equation and the energy conservation relation for the electron fluid. By making use of the proposed consistent hydrodynamic framework, we show that the Chern-Simons contributions strongly modify the dispersion relations of collective modes in Weyl semimetals. This is reflected, in particular, in the existence of distinctive anomalous Hall waves, which are sustained by the local anomalous Hall currents.
Dissolution of topological Fermi arcs in a dirty Weyl semimetal
Slager, Robert-Jan; Juričić, Vladimir; Roy, Bitan
2017-11-01
Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide a condensed matter realization of chiral anomaly, feature topologically protected Fermi arc surface states, and sustain sharp chiral Weyl quasiparticles up to a critical disorder at which a continuous quantum phase transition (QPT) drives the system into a metallic phase. We here numerically demonstrate that with increasing strength of disorder, the Fermi arc gradually loses its sharpness, and close to the WSM-metal QPT it completely dissolves into the metallic bath of the bulk. The predicted topological nature of the WSM-metal QPT and the resulting bulk-boundary correspondence across this transition can be directly observed in angle-resolved photoemission spectroscopy (ARPES) and Fourier transformed scanning tunneling microscopy (STM) measurements by following the continuous deformation of the Fermi arcs with increasing disorder in recently discovered Weyl materials.
Paar, Vladimir; Pavin, Nenad; Rubčić, Antun; Rubčić, Jasna
2002-01-01
We show that stable isotopes display a fractal pattern in the N,Z-chart and abundance-weighted chart of isotopes with the fractal dimension df ≈ 1.2. On this basis a scale invariant power law for atomic and molecular weights can be introduced and applied to systematics of Chemical elements and compounds.
The Schwarzschild/CFT Correspondence: Weyl Rescaled Case
Sadeghi, Jafar; Shajiee, Vahid Reza
2015-01-01
In this work, the CFT dual of the Schwarzschild black hole is investigated. A Weyl rescaling factor is presented, so that the Weyl rescaled Schwarzschild metric, after a coordinate transformation, has an $AdS_{2} \\times S_{2}$ geometry at vicinity of its origin. Since the near origin spacetime admits an $AdS_{2}$ factor, it is dealt with a 2D effective gravity which is dimensionally reduced from the near origin solution. It is exhibited that the dual CFT has a central charge $c=96 M^3$ which ...
Weyl type theorems for algebraically Quasi-$\\mathcal{HNP}$ operators
Rashid, M. H. M.; Prasad, T.
2015-01-01
In this paper, by introducing the class of quasi hereditarily normaloid polaroid operators, we obtain a theoretical and general framework from which Weyl type theorems may be promptly established for many of these classes of operators. This framework also entails Weyl type theorems for perturbations $f(T + A)$, where $A$ is algebraic and commutes with $T,$ and $f$ is an analytic function, defined on an open neighborhood of the spectrum of $T +A$, such that $f$ is non constant on each of the c...
Standard Model Vacuum Stability and Weyl Consistency Conditions
DEFF Research Database (Denmark)
Antipin, Oleg; Gillioz, Marc; Krog, Jens
2013-01-01
At high energy the standard model possesses conformal symmetry at the classical level. This is reflected at the quantum level by relations between the different beta functions of the model. These relations are known as the Weyl consistency conditions. We show that it is possible to satisfy them...... order by order in perturbation theory, provided that a suitable coupling constant counting scheme is used. As a direct phenomenological application, we study the stability of the standard model vacuum at high energies and compare with previous computations violating the Weyl consistency conditions....
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.
Fractals and the Kepler equation
Kasten, Volker
1992-09-01
The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.
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.)
Terahertz spectroscopy of plasmonic fractals.
Agrawal, A; Matsui, T; Zhu, W; Nahata, A; Vardeny, Z V
2009-03-20
We use terahertz time-domain spectroscopy to study the transmission properties of metallic films perforated with aperture arrays having deterministic or stochastic fractal morphologies ("plasmonic fractals"), and compare them with random aperture arrays. All of the measured plasmonic fractals show transmission resonances and antiresonances at frequencies that correspond to prominent features in their structure factors in k space. However, in sharp contrast to periodic aperture arrays, the resonant transmission enhancement decreases with increasing array size. This property is explained using a density-density correlation function, and is utilized for determining the underlying fractal dimensionality, D(fractals relative to the transmission of the corresponding random aperture arrays is obtained, and is shown to be universal.
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.
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)
Kondo effect in three-dimensional Dirac and Weyl systems
Mitchell, Andrew K.; Fritz, Lars
2015-01-01
Magnetic impurities in three-dimensional Dirac and Weyl systems are shown to exhibit a fascinatingly diverse range of Kondo physics, with distinctive experimental spectroscopic signatures. When the Fermi level is precisely at the Dirac point, Dirac semimetals are in fact unlikely candidates for a
Strong magnetic field induces superconductivity in a Weyl semimetal
Rosenstein, Baruch; Shapiro, B. Ya.; Li, Dingping; Shapiro, I.
2017-12-01
Microscopic theory of the normal-to-superconductor coexistence line of a multiband Weyl superconductor subjected to magnetic field is constructed. It is shown that the Weyl semimetal that is nonsuperconducting or having a small critical temperature Tc at zero field might become a superconductor at higher temperatures when the magnetic field is tuned to a series of quantized values Hn. The pairing occurs on Landau levels. It is argued that the phenomenon is detectable much easier in Weyl semimetals than in parabolic band metals since the quantum limit already has been approached in several Weyl materials. The effect of Zeeman coupling leading to splitting of the reentrant superconducting regions on the magnetic phase diagram is considered. An experimental signature of the superconductivity on Landau levels is the reduction of magnetoresistivity. This has been observed already in Cd3As2 and several other compounds. The novel kind of quantum oscillations of magnetoresistance detected in ZrTe5 is discussed along these lines.
Anomalous Nernst effect in type-II Weyl semimetals
Saha, Subhodip; Tewari, Sumanta
2018-01-01
Topological Weyl semimetals (WSM), a new state of quantum matter with gapless nodal bulk spectrum and open Fermi arc surface states, have recently sparked enormous interest in condensed matter physics. Based on the symmetry and fermiology, it has been proposed that WSMs can be broadly classified into two types, type-I and type-II Weyl semimetals. While the undoped, conventional, type-I WSMs have point like Fermi surface and vanishing density of states (DOS) at the Fermi energy, the type-II Weyl semimetals break Lorentz symmetry explicitly and have tilted conical spectra with electron and hole pockets producing finite DOS at the Fermi level. The tilted conical spectrum and finite DOS at Fermi level in type-II WSMs have recently been shown to produce interesting effects such as a chiral anomaly induced longitudinal magnetoresistance that is strongly anisotropic in direction and a novel anomalous Hall effect. In this work, we consider the anomalous Nernst effect in type-II WSMs in the absence of an external magnetic field using the framework of semi-classical Boltzmann theory. Based on both a linearized model of time-reversal breaking WSM with a higher energy cut-off and a more realistic lattice model, we show that the anomalous Nernst response in these systems is strongly anisotropic in space, and can serve as a reliable signature of type-II Weyl semimetals in a host of magnetic systems with spontaneously broken time reversal symmetry.
Weyl Phases in a Three Dimensional Network Model
Wang, Hailong; Chong, Yidong; theoretical photonics Team
We study the topological properties of 3D ``Floquet'' band structures, defined using unitary evolution matrices rather than Hamiltonians. Such band structures can be realized in coherent-wave networks or lattices subjected to time-periodic drives. Previously, 2D Floquet band structures have been shown to exhibit unusual topological behaviors such as topologically-nontrivial zero-Chern-number phases. Here, we analyze the Floquet band structure of a 3D network model, which exhibits an Floquet analogue of a Weyl phase. The surface states exhibit topologically-protected ``Fermi'' arcs, similar to the recently-discovered Weyl semi-metals; however, the Weyl points in different quasi-energy gaps are related by a particle-hole symmetry which is unique to the Floquet system. By tuning the coupling parameters of the network, we can drive a transition between conventional insulator, weak topological insulator, and Weyl phases. Finally, we discuss the possibility of realizing this model using custom-designed electromagnetic networks. GRANT: Supported by Singapore National Research Foundation under Grant No. NRFF2012-02.
Central extensions for the Weyl CCR in Curved space
International Nuclear Information System (INIS)
Emch, G.G.
1993-01-01
For non-necessarily flat homogeneous configuration spaces, we illustrate how the cohomological choices made in the definition a Weyl group of the CCR are reflected in the momentum map for the action of this group on its co-adjoint orbit of maximal dimension. (Author) 8 refs
Anomalous DC Hall response in noncentrosymmetric tilted Weyl semimetals
Mukherjee, S. P.; Carbotte, J. P.
2018-03-01
Weyl nodes come in pairs of opposite chirality. For broken time reversal symmetry (TR) they are displaced in momentum space by {Q} and the anomalous DC Hall conductivity σxy is proportional to {Q} at charge neutrality. For finite doping there are additive corrections to σxy which depend on the chemical potential as well as on the tilt (C ) of the Dirac cones and on their relative orientation. If inversion symmetry (I) is also broken the Weyl nodes are shifted in energy by an amount Q0 . This introduces further changes in σxy and we provide simple analytic formulas for these modifications for both type I (Ctype II (C>1 , overtilted) Weyl. For type I when the Weyl nodes have equal magnitude but oppositely directed tilts, the correction to σxy is proportional to the chemical potential μ and completely independent of the energy shift Q0 . When instead the tilts are parallel, the correction is linear in Q0 and μ drops out. For type II the corrections involve both μ and Q0 , are nonlinear and also involve a momentum cut off. We discuss the implied changes to the Nernst coefficient and to the thermal Hall effect of a finite Q0 .
Weyl and Riemann-Liouville multifractional Ornstein-Uhlenbeck processes
International Nuclear Information System (INIS)
Lim, S C; Teo, L P
2007-01-01
This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established
From Herman Weyl to Yang and Mills to quantum chromodynamics
Czech Academy of Sciences Publication Activity Database
Chýla, Jiří
2005-01-01
Roč. 749, - (2005), 23c-32c ISSN 0375-9474 Institutional research plan: CEZ:AV0Z1010920 Keywords : quantum field theory * gauge invariance * Weyl, Yang , Mills * quarks * gluons Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 1.950, year: 2005
Weyl transforms associated with the Riemann-Liouville operator
Directory of Open Access Journals (Sweden)
N. B. Hamadi
2006-01-01
Full Text Available For the Riemann-Liouville transform ℛα, α∈ℝ+, associated with singular partial differential operators, we define and study the Weyl transforms Wσ connected with ℛα, where σ is a symbol in Sm, m∈ℝ. We give criteria in terms of σ for boundedness and compactness of the transform Wσ.
Probing the Chiral Anomaly via Nonlocal Transport in Weyl Semimetals
Parameswaran, Siddharth; Grover, Tarun; Vishwanath, Ashvin
2013-03-01
Weyl semimetals are three-dimensional analogs of graphene in which a pair of bands touch at points in momentum space, known as Weyl nodes. Electrons originating from a single Weyl node possess a definite topological charge, the chirality. Consequently, they exhibit the Adler-Jackiw-Bell anomaly, which in this condensed matter realization implies that application of parallel electric (E) and magnetic fields (B) pumps electrons between nodes of opposite chirality at a rate proportional to E . B . We argue that this pumping is measurable via transport experiments, in the limit of weak internode scattering. Specifically, we show that injecting a current in a Weyl semimetal subject to an E . B term leads to nonlocal features in transport. We acknowledge support of the Simons Foundation, NSF Grant PHY-1066293 and the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231
Weyl and Riemann Liouville multifractional Ornstein Uhlenbeck processes
Lim, S. C.; Teo, L. P.
2007-06-01
This paper considers two new multifractional stochastic processes, namely the Weyl multifractional Ornstein-Uhlenbeck process and the Riemann-Liouville multifractional Ornstein-Uhlenbeck process. Basic properties of these processes such as locally self-similar property and Hausdorff dimension are studied. The relationship between the multifractional Ornstein-Uhlenbeck processes and the corresponding multifractional Brownian motions is established.
Criteria for Directly Detecting Topological Fermi Arcs in Weyl Semimetals.
Belopolski, Ilya; Xu, Su-Yang; Sanchez, Daniel S; Chang, Guoqing; Guo, Cheng; Neupane, Madhab; Zheng, Hao; Lee, Chi-Cheng; Huang, Shin-Ming; Bian, Guang; Alidoust, Nasser; Chang, Tay-Rong; Wang, BaoKai; Zhang, Xiao; Bansil, Arun; Jeng, Horng-Tay; Lin, Hsin; Jia, Shuang; Hasan, M Zahid
2016-02-12
The recent discovery of the first Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature and demonstrates a novel type of anomalous surface state, the Fermi arc. Like topological insulators, the bulk topological invariants of a Weyl semimetal are uniquely fixed by the surface states of a bulk sample. Here we present a set of distinct conditions, accessible by angle-resolved photoemission spectroscopy (ARPES), each of which demonstrates topological Fermi arcs in a surface state band structure, with minimal reliance on calculation. We apply these results to TaAs and NbP. For the first time, we rigorously demonstrate a nonzero Chern number in TaAs by counting chiral edge modes on a closed loop. We further show that it is unreasonable to directly observe Fermi arcs in NbP by ARPES within available experimental resolution and spectral linewidth. Our results are general and apply to any new material to demonstrate a Weyl semimetal.
Majorana and Majorana-Weyl fermions in lattice gauge theory
International Nuclear Information System (INIS)
Inagaki, Teruaki; Suzuki, Hiroshi
2004-01-01
In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1 + 8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factorized form of the Dirac determinant. Similarly, in 2 + 8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factorized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find. (author)
An elementary aspect of the Weyl-Wigner representation
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W.P.
2003-01-01
It is an elementary aspect of the Weyl-Wigner representation of quantum mechanics that the dynamical phase-space function corresponding to the square of a quantum-mechanical operator is, in general, different from the square of the function representing the operator itself. We call attention...
Wicks, Keith R
1991-01-01
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fracta...
Multi-fractal measures of city-size distributions based on the three-parameter Zipf model
International Nuclear Information System (INIS)
Chen Yanguang; Zhou Yixing
2004-01-01
A multi-fractal framework of urban hierarchies is presented to address the rank-size distribution of cities. The three-parameter Zipf model based on a pair of exponential-type scaling laws is generalized to multi-scale fractal measures. Then according to the equivalent relationship between Zipf's law and Pareto distribution, a set of multi-fractal equations are derived using dual conversion and the Legendre transform. The US city population data coming from the 2000 census are employed to verify the multi-fractal models and the results are satisfying. The multi-fractal measures reveal some strange symmetry regularity of urban systems. While explaining partially the remains of the hierarchical step-like frequency distribution of city sizes suggested by central place theory, the mathematical framework can be interpreted with the entropy-maximizing principle and some related ideas from self-organization
Losa, Gabriele A
2009-01-01
The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".
The transience of virtual fractals.
Taylor, R P
2012-01-01
Artists have a long and fruitful tradition of exploiting electronic media to convert static images into dynamic images that evolve with time. Fractal patterns serve as an example: computers allow the observer to zoom in on virtual images and so experience the endless repetition of patterns in a matter that cannot be matched using static images. This year's featured cover artist, Susan Lowedermilk, instead plans to employ persistence of human vision to bring virtual fractals to life. This will be done by incorporating her prints of fractal patterns into zoetropes and phenakistoscopes.
Semiclassical theory of anomalous transport in type-II topological Weyl semimetals
McCormick, Timothy M.; McKay, Robert C.; Trivedi, Nandini
2017-12-01
Weyl semimetals possess low-energy excitations which act as monopoles of Berry curvature in momentum space. These emergent monopoles are at the heart of the many novel transport properties that Weyl semimetals exhibit. The singular nature of the Berry curvature around the nodal points in Weyl semimetals allows for the possibility of large anomalous transport coefficients in zero applied magnetic field. Recently, a new class, termed type-II Weyl semimetals, has been demonstrated in a variety of materials, where the Weyl nodes are tilted. We present here a theoretical study of anomalous transport in this new class of Weyl semimetals. We find that the parameter governing the tilt of these type-II Weyl points is intimately related to the zero-field transverse transport properties. We also find that the temperature dependence of the chemical potential plays an important role in determining how the transport coefficients can effectively probe the Berry curvature of the type-II Weyl points. In particular, we find that the transverse thermoelectric transport coefficient Lxy E T is strongly enhanced with the tilt of the type-II Weyl nodes and with increasing temperature. We also discuss the experimental implications of our work for time-reversal breaking type-II Weyl semimetals.
Chang, Guoqing; Singh, Bahadur; Xu, Su-Yang; Bian, Guang; Huang, Shin-Ming; Hsu, Chuang-Han; Belopolski, Ilya; Alidoust, Nasser; Sanchez, Daniel S.; Zheng, Hao; Lu, Hong; Zhang, Xiao; Bian, Yi; Chang, Tay-Rong; Jeng, Horng-Tay; Bansil, Arun; Hsu, Han; Jia, Shuang; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid
2018-01-01
Weyl semimetals are novel topological conductors that host Weyl fermions as emergent quasiparticles. In this Rapid Communication, we propose a new type of Weyl semimetal state that breaks both time-reversal symmetry and inversion symmetry in the R AlGe (R =rare -earth ) family. Compared to previous predictions of magnetic Weyl semimetal candidates, the prediction of Weyl nodes in R AlGe is more robust and less dependent on the details of the magnetism because the Weyl nodes are generated already by the inversion breaking and the ferromagnetism acts as a simple Zeeman coupling that shifts the Weyl nodes in k space. Moreover, R AlGe offers remarkable tunability, which covers all varieties of Weyl semimetals including type I, type II, inversion breaking, and time-reversal breaking, depending on a suitable choice of the rare-earth elements. Furthermore, the unique noncentrosymmetric and ferromagnetic Weyl semimetal state in R AlGe enables the generation of spin currents.
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 model of anomalous diffusion
Gmachowski, Lech
2015-01-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An...
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
Fractal pattern of canine trichoblastoma.
De Vico, Gionata; Cataldi, Marielda; Maiolino, Paola; Carella, Francesca; Beltraminelli, Stefano; Losa, Gabriele A
2011-06-01
To assess by fractal analysis the specific architecture, growth pattern, and tissue distribution that characterize subtypes of canine trichoblastoma, a benign tumor derived from or reduplicating the primitive hair germ of embryonic follicular development. Tumor masks and outlines obtained from immunohistologic images by gray threshold segmentation of epithelial components were analyzed by fractal and conventional morphometry. The fractal dimension [FD] of each investigated case was determined from the slope of the regression line describing the fractal region within a bi-asymptotic curve experimentally established. All tumor masks and outlines obtained by gray threshold segmentation of epithelial components showed fractal self-similar properties that were evaluated by peculiar FDs. However, only masks revealed significantly different FD values, ranging from 1.75 to 1.85, enabling the discrimination of canine trichoblastoma subtypes. The FD data suggest that an iterative morphogenetic process, involving both the air germ and associated dermal papilla, may be responsible of the peculiar tissue architecture of trichoblastoma. The present study emphasized the reliability of fractal analysis in achieving the objective characterization of canine trichoblastoma.
Generating hierarchial scale-free graphs from fractals
Energy Technology Data Exchange (ETDEWEB)
Komjathy, Julia, E-mail: komyju@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary); Simon, Karoly, E-mail: simonk@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary)
2011-08-15
Highlights: > We generate deterministic scale-free networks using graph-directed self similar IFS. > Our model exhibits similar clustering, power law decay properties to real networks. > The average length of shortest path and the diameter of the graph are determined. > Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal {Lambda}. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal {Lambda} we generate random graph sequence sharing similar properties.
Generating hierarchial scale-free graphs from fractals
International Nuclear Information System (INIS)
Komjathy, Julia; Simon, Karoly
2011-01-01
Highlights: → We generate deterministic scale-free networks using graph-directed self similar IFS. → Our model exhibits similar clustering, power law decay properties to real networks. → The average length of shortest path and the diameter of the graph are determined. → Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal Λ. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.
Weyl calculus in QED I. The unitary group
Amour, L.; Lascar, R.; Nourrigat, J.
2017-01-01
In this work, we consider fixed 1/2 spin particles interacting with the quantized radiation field in the context of quantum electrodynamics. We investigate the time evolution operator in studying the reduced propagator (interaction picture). We first prove that this propagator belongs to the class of infinite dimensional Weyl pseudodifferential operators recently introduced in Amour et al. [J. Funct. Anal. 269(9), 2747-2812 (2015)] on Wiener spaces. We give a semiclassical expansion of the symbol of the reduced propagator up to any order with estimates on the remainder terms. Next, taking into account analyticity properties for the Weyl symbol of the reduced propagator, we derive estimates concerning transition probabilities between coherent states.
Weyl-Euler-Lagrange Equations of Motion on Flat Manifold
Directory of Open Access Journals (Sweden)
Zeki Kasap
2015-01-01
Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.
The semiclassical coherent state propagator in the Weyl representation
International Nuclear Information System (INIS)
Braun, Carol; Li, Feifei; Garg, Anupam; Stone, Michael
2015-01-01
It is shown that the semiclassical coherent state propagator takes its simplest form when the quantum mechanical Hamiltonian is replaced by its Weyl symbol in defining the classical action, in that there is then no need for a Solari-Kochetov correction. It is also shown that such a correction exists if a symbol other than the Weyl symbol is chosen and that its form is different depending on the symbol chosen. The various forms of the propagator based on different symbols are shown to be equivalent provided the correspondingly correct Solari-Kochetov correction is included. All these results are shown for both particle and spin coherent state propagators. The global anomaly in the fluctuation determinant is further elucidated by a study of the connection between the discrete fluctuation determinant and the discrete Jacobi equation
p-wave holographic superconductors with Weyl corrections
Momeni, D.; Majd, N.; Myrzakulov, R.
2012-03-01
We study the (3+1)-dimensional p-wave holographic superconductors with Weyl corrections both numerically and analytically. We describe numerically the behavior of the critical temperature Tc with respect to charge density ρ in a limited range of Weyl coupling parameter γ and we find in general that the condensation becomes harder with the increase of the parameter γ. In the strong-coupling limit of Yang-Mills theory, we show that the minimum value of Tc obtained from the analytical approach is in good agreement with the numerical results, and finally show how we got remarkably a similar result for the critical exponent \\frac{1}{2} of the chemical potential μ and the order parameterlangJ1xrang with the numerical curves of the superconductors.
The Weyl-Cartan Space Problem in Purely Affine Theory
von Borzeszkowski, Horst-Heino; Treder, Hans-Jürgen
1997-04-01
According to Poincaré, only the ``epistemological sum of geometry and physics is measurable". Of course, there are requirements of measurement to be imposed on geometry because otherwise the theory resting on this geometry cannot be physically interpreted. In particular, the Weyl--Cartan space problem must be solved, i.e., it must be guaranteed that the comparison of distances is compatible with the Levi-Civita transport. In the present paper, we discuss these requirements of measurement and show that in the (purely affine) Einstein-Schrödinger unified field theory the solution of the Weyl-Cartan space problem simultaneously determines the matter via Einstein's equations. Here the affine field $\\Gamma^ikl$ represents Poincaré's sum, and the solution of the space problem means its splitting in a metrical space and in matter fields, where the latter are given by the torsion tensor $\\Gamma^i_{[kl]}$.
Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
Yang, Hao; Sun, Yan; Zhang, Yang; Shi, Wu-Jun; Parkin, Stuart S. P.; Yan, Binghai
2017-01-01
Recent experiments revealed that Mn3Sn and Mn3Ge exhibit a strong anomalous Hall effect at room temperature, provoking us to explore their electronic structures for topological properties. By ab initio band structure calculations, we have observed the existence of multiple Weyl points in the bulk and corresponding Fermi arcs on the surface, predicting antiferromagnetic Weyl semimetals in Mn3Ge and Mn3Sn. Here the chiral antiferromagnetism in the Kagome-type lattice structure is essential to determine the positions and numbers of Weyl points. Our work further reveals a new guiding principle to search for magnetic Weyl semimetals among materials that exhibit a strong anomalous Hall effect.
Spacetimes of Weyl and Ricci type N in higher dimensions
Czech Academy of Sciences Publication Activity Database
Kuchynka, M.; Pravdová, Alena
2016-01-01
Roč. 33, č. 11 (2016), s. 115006 ISSN 0264-9381 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : Weyl type N * Ricci type N * higher dimensions Subject RIV: BA - General Mathematics Impact factor: 3.119, year: 2016 http://iopscience.iop.org/article/10.1088/0264-9381/33/11/115006
Magnetotransport phenomena related to the chiral anomaly in Weyl semimetals
Spivak, B. Z.; Andreev, A. V.
2016-02-01
We present a theory of magnetotransport phenomena related to the chiral anomaly in Weyl semimetals. We show that conductivity, thermal conductivity, thermoelectric, and the sound absorption coefficients exhibit strong and anisotropic magnetic field dependencies. We also discuss properties of magnetoplasmons and magnetopolaritons, whose existences are entirely determined by the chiral anomaly. Finally, we discuss the conditions of applicability of the quasiclassical description of electron transport phenomena related to the chiral anomaly.
Toeplitz quantization and asymptotic expansions : Peter Weyl decomposition
Czech Academy of Sciences Publication Activity Database
Engliš, Miroslav; Upmeier, H.
2010-01-01
Roč. 68, č. 3 (2010), s. 427-449 ISSN 0378-620X R&D Projects: GA ČR GA201/09/0473 Institutional research plan: CEZ:AV0Z10190503 Keywords : bounded symmetric domain * real symmetric domain * star product * Toeplitz operator * Peter-Weyl decomposition Subject RIV: BA - General Mathematics Impact factor: 0.521, year: 2010 http://link.springer.com/article/10.1007%2Fs00020-010-1808-5
The influence of the fractal particle size distribution on the mobility of dry granular materials
Directory of Open Access Journals (Sweden)
Vallejo Luis E.
2017-01-01
Full Text Available This study presents an experimental analysis on the influence of the particle size distribution (psd on the mobility of dry granular materials. The psd obeys a power law of the form: N(L>d=kd-Df, where N is the number of particles with diameter L greater than a given diameter d, k is a proportionality constant, and Df is the fractal dimension of the psd. No laboratory or numerical study has been conducted to date analysing how a fractal psd influences the mobility of granular flows as in the case of rock avalanches. In this study, the flow characteristics of poly-dispersed granular materials that have a fractal psd were investigated in the laboratory. Granular mixtures having different fractal psd values were placed in a hollow cylinder. The cylinder was lifted and the distance of flow of the mixture was measured with respect to the original position of the cylinder. It was determined that the distance of flow of the mixtures was directly related to their fractal psd values. That is, the larger the distance of flow of the mixture, the larger is the fractal psd of the granular mixture tested. Thus, the fractal psd in dry granular mixtures seems to have a large influence on the easiness by which dry granular mixtures move in the field.
Separating Fractal and Oscillatory Components in the Power Spectrum of Neurophysiological Signal.
Wen, Haiguang; Liu, Zhongming
2016-01-01
Neurophysiological field-potential signals consist of both arrhythmic and rhythmic patterns indicative of the fractal and oscillatory dynamics arising from likely distinct mechanisms. Here, we present a new method, namely the irregular-resampling auto-spectral analysis (IRASA), to separate fractal and oscillatory components in the power spectrum of neurophysiological signal according to their distinct temporal and spectral characteristics. In this method, we irregularly resampled the neural signal by a set of non-integer factors, and statistically summarized the auto-power spectra of the resampled signals to separate the fractal component from the oscillatory component in the frequency domain. We tested this method on simulated data and demonstrated that IRASA could robustly separate the fractal component from the oscillatory component. In addition, applications of IRASA to macaque electrocorticography and human magnetoencephalography data revealed a greater power-law exponent of fractal dynamics during sleep compared to wakefulness. The temporal fluctuation in the broadband power of the fractal component revealed characteristic dynamics within and across the eyes-closed, eyes-open and sleep states. These results demonstrate the efficacy and potential applications of this method in analyzing electrophysiological signatures of large-scale neural circuit activity. We expect that the proposed method or its future variations would potentially allow for more specific characterization of the differential contributions of oscillatory and fractal dynamics to distributed neural processes underlying various brain functions.
Scaling of light scattered from fractal aggregates at resonance
Ortiz, Guillermo P.; Mochán, W. Luis
2003-05-01
Due to the scale invariance of fractal aggregates, light scattered from them often decays as a power of the scattering wave vector. The exponent in this power law has been usually interpreted as the geometrical fractal dimension. However, the validity of this interpretation is questionable for frequencies close to the resonances of the system, for which multiple scattering becomes important. In this work we calculate the dipole moments optically induced in fractal aggregates and the corresponding self-consistent field, as well as the electromagnetic normal modes. To this end, we develop a multiresolution hierarchical representation of the aggregate that allows the study of large systems taking fully into account the long range of the interactions. We analyze the scaling properties of the dynamically induced dipolar distribution. We find that under resonant conditions, scaling with the geometric fractal dimension is only observed for systems much larger than a length scale that is related to the linewidth of each individual resonance. The relevance to this result for the interpretation of light scattering experiments is discussed.
Fractal scale-free networks resistant to disease spread
International Nuclear Information System (INIS)
Zhang, Zhongzhi; Zhou, Shuigeng; Zou, Tao; Chen, Guisheng
2008-01-01
The conventional wisdom is that scale-free networks are prone to epidemic propagation; in the paper we demonstrate that, on the contrary, disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show that it simultaneously has the following rich topological properties: scale-free degree distribution, tunable clustering coefficient, 'large-world' behavior, and fractal scaling. Existing network models do not display these characteristics. Then, we investigate the susceptible–infected–removed (SIR) model of the propagation of diseases in our fractal scale-free networks by mapping it to the bond percolation process. We establish the existence of non-zero tunable epidemic thresholds by making use of the renormalization group technique, which implies that power law degree distribution does not suffice to characterize the epidemic dynamics on top of scale-free networks. We argue that the epidemic dynamics are determined by the topological properties, especially the fractality and its accompanying 'large-world' behavior
Weyl's theorem for algebraically totally hereditarily normaloid operators
Duggal, B. P.
2005-08-01
A Banach space operator is said to be totally hereditarily normaloid, T[set membership, variant]THN, if every part of T is normaloid and every invertible part of T has a normaloid inverse. The operator T is said to be an H(q) operator for some integer q[greater-or-equal, slanted]1, T[set membership, variant]H(q), if the quasi-nilpotent part H0(T-[lambda])=(T-[lambda])-q(0) for every complex number [lambda]. It is proved that if T is algebraically H(q), or T is algebraically THN and is separable, then f(T) satisfies Weyl's theorem for every function f analytic in an open neighborhood of [sigma](T), and T* satisfies a-Weyl's theorem. If also T* has the single valued extension property, then f(T) satisfies a-Weyl's theorem for every analytic function f which is non-constant on the connected components of the open neighborhood of [sigma](T) on which it is defined.
Matched Weyl-Heisenberg expansions of nonstationary environments
International Nuclear Information System (INIS)
Kozek, W.
1996-09-01
This thesis is about various aspects of linear time-varying systems and nonstationary processes (together nonstationary environments). Such nonstationary environments play an important role in modern communication engineering, particularly as models for natural signals or time-varying communication channels. Emphasis is on time-frequency-parametrized representations of nonstationary environments, i.e., time-varying power spectra and time varying transfer functions. Introduction of the generalized Weyl correspondence enables a unified formulation of classical, so far seemingly disparate definitions like Priestley's evolutionary spectrum, the Wigner-Ville spectrum, Zadeh's time-varying transfer function (Kohn-Nirenberg symbol) and the Weyl symbol. Nonstationary Wiener filtering provides an illustrative example for the limited applicability of these time-frequency concepts to a straight forward generalization of frequency domain solutions. We introduce a fundamental classification into underspread/overspread environments based on characterizing the underlying linear operator by the essential support of its spreading function. For underspread environments it is shown that the time-frequency-parametrized representations get essentially definition-independent and can be used in the same manner as the frequency-parametrized representations of stationary environments. Combining the practical efficiency of time-frequency-parametrized representations with the theoretical optimality of a diagonalizing transform leads to window matching criteria for the short-time Fourier transform/ Gabor expansion (discrete/continuous Weyl-Heisenberg expansion) of signals and linear systems. (author)
Surface spectra of Weyl semimetals through self-adjoint extensions
Seradjeh, Babak; Vennettilli, Michael
2018-02-01
We apply the method of self-adjoint extensions of Hermitian operators to the low-energy, continuum Hamiltonians of Weyl semimetals in bounded geometries and derive the spectrum of the surface states on the boundary. This allows for the full characterization of boundary conditions and the surface spectra on surfaces both normal to the Weyl node separation as well as parallel to it. We show that the boundary conditions for quadratic bulk dispersions are, in general, specified by a U (2 ) matrix relating the wave function and its derivatives normal to the surface. We give a general procedure to obtain the surface spectra from these boundary conditions and derive them in specific cases of bulk dispersion. We consider the role of global symmetries in the boundary conditions and their effect on the surface spectrum. We point out several interesting features of the surface spectra for different choices of boundary conditions, such as a Mexican-hat shaped dispersion on the surface normal to Weyl node separation. We find that the existence of bound states, Fermi arcs, and the shape of their dispersion, depend on the choice of boundary conditions. This illustrates the importance of the physics at and near the boundaries in the general statement of bulk-boundary correspondence.
Fractal fluctuations in cardiac time series
West, B. J.; Zhang, R.; Sanders, A. W.; Miniyar, S.; Zuckerman, J. H.; Levine, B. D.; Blomqvist, C. G. (Principal Investigator)
1999-01-01
Human heart rate, controlled by complex feedback mechanisms, is a vital index of systematic circulation. However, it has been shown that beat-to-beat values of heart rate fluctuate continually over a wide range of time scales. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show, by systematically aggregating the data, that the correlation in the beat-to-beat cardiac time series is a modulated inverse power law. This scaling property indicates the existence of long-time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal. We argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling.
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.
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.
Sound absorption by Menger sponge fractal.
Kawabe, Tetsuji; Miyazaki, Takatsuna; Oka, Daisuke; Koyanagi, Sin'ichiro; Hinokidani, Atsushi
2009-05-01
For the purpose of investigation on acoustic properties of fractals, the sound absorption coefficients are experimentally measured by using the Menger sponge which is one of typical three-dimensional fractals. From the two-microphone measurement, the frequency range of effectively absorbing sound waves is shown to broaden with degree of fractality, which comes from the fractal property of the homothetic character. It is shown that experimental features are qualitatively explained by an electrical equivalent circuit model for the Menger sponge.
Exploring topological double-Weyl semimetals with cold atoms in optical lattices
Mai, Xue-Ying; Zhang, Dan-Wei; Li, Zhi; Zhu, Shi-Liang
2017-06-01
We explore the topological properties of double-Weyl semimetals with cold atoms in optical lattices. We first propose a tight-binding model of simulating the double-Weyl semimetal with a pair of double-Weyl points by engineering the atomic hopping in a three-dimensional optical lattice. We show that the double-Weyl points with topological charges of ±2 behave as the sink and source of Berry flux in momentum space connecting by two Fermi arcs and they are stabilized by the C4 h point-group symmetry. By applying a realizable C4 breaking term, we find that each double-Weyl point splits into two single-Weyl points and obtain rich phase diagrams in the parameter space spanned by the strengths of an effective Zeeman term and the C4 breaking term, which contains a topological and a normal insulating phase and two topological Weyl semimetal phases with eight and four single-Weyl points, apart from the double-Weyl semimetal phase. Furthermore, we demonstrate with numerical simulations that (i) the mimicked double- and single-Weyl points can be detected by measuring the atomic transfer fractions after a Bloch oscillation; (ii) the Chern number of different quantum phases in the phase diagram can be extracted from the center shift of the hybrid Wannier functions, which can be directly measured with time-of-flight imaging; (iii) the band topology of the C4-symmetric Bloch Hamiltonian can be detected simply from measuring the spin polarization at the high-symmetry momentum points with a condensate in the optical lattice. The proposed system would provide a promising platform for elaborating the intrinsic exotic physics of double-Weyl semimetals and the related topological phase transitions.
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 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.
Fractal Dimension and the Cantor Set
Indian Academy of Sciences (India)
IAS Admin
1000. RESONANCE ⎜ November 2014. GENERAL ⎜ ARTICLE. Fractal Dimension and the Cantor Set. Shailesh A Shirali. Keywords. Dimension, topological dimen- sion, Hausdorff–Besicovitch di- mension, fractal dimension, fractal, Cantor set, Sierpinski triangle, Koch curve. Shailesh Shirali is. Director of Sahyadri School.
Multiple wave scattering from fractal aggregates
Energy Technology Data Exchange (ETDEWEB)
Korvin, Gabor E-mail: gabor@kfupm.edu.sa; Oleschko, Klavdia
2004-01-01
Multiple scattered waves from fractal aggregates create spurious resonances in the high-frequency part of the wave-field's Fourier spectrum. It is shown by a probabilistic convolutional model that for extended fractal media with strong scattering cross-section, multiple scattering can affect the value of the fractal dimension estimated from the wave-field's Fourier power spectrum.
Fractal characterization of the coal surface
Directory of Open Access Journals (Sweden)
Miklúová Viera
1998-09-01
Full Text Available The aim of this paper is to point up to the characterization of the brown coal using the fractal theory. On the base of BET measurements on the adsorption surface, the surface fractal dimension of crushed and milled coal samples have been determined. These values of the fractal dimension are used in the estimation of the processes by the energy input.
Fractal analysis of time varying data
Vo-Dinh, Tuan; Sadana, Ajit
2002-01-01
Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.
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.
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
Fractal density modeling of crustal heterogeneity from the KTB deep hole
Chen, Guoxiong; Cheng, Qiuming
2017-03-01
Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α-dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low-porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high-pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.
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 spatial distribution of pancreatic islets in three dimensions: a self-avoiding growth model
Jo, Junghyo; Hörnblad, Andreas; Kilimnik, German; Hara, Manami; Ahlgren, Ulf; Periwal, Vipul
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, have 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, 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 fractal dimension 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. PMID:23629025
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.
Pressure Transient Analysis of Dual Fractal Reservoir
Directory of Open Access Journals (Sweden)
Xiao-Hua Tan
2013-01-01
Full Text Available A dual fractal reservoir transient flow model was created by embedding a fracture system simulated by a tree-shaped fractal network into a matrix system simulated by fractal porous media. The dimensionless bottom hole pressure model was created using the Laplace transform and Stehfest numerical inversion methods. According to the model's solution, the bilogarithmic type curves of the dual fractal reservoirs are illustrated, and the influence of different fractal factors on pressure transient responses is discussed. This semianalytical model provides a practical and reliable method for empirical applications.
Siegel, Edward Carl-Ludwig
2015-04-01
Siegel(2012) 10-DIGITS[0 --> 9] AVERAGE PROBABILITY LOG-Law SCALE-INVARIANCE UTTER-SIMPLICITY: Kabbala SEPHIROT SCENARIO AUTOMATICALLY CREATES a UNIVERSE: (1) a big-bang[bosons(BEQS) created from Newcomb[Am.J.Math.4(1),39(1881;THE discovery of the QUANTUM!!!)-Poincare[Calcul des Probabilites,313(12)]-Weyl[Goett.Nach.(14);Math.Ann.77,313(16)] DIGITS AVERAGE STATISTICS LOG-Law[ = log(1 +1/d) = log([d +1]/d)] algebraic-inversion, (2)[initial (at first space-time point created) c = ∞ elongating to timelike-pencil spreading into finite-c light-cone] hidden-dark-energy (HDE)[forming at every-spacetime-point], (3) inflation[logarithm algebraic-inversion-to exponential], (4) hidden[in Siegel(87) ``COMPLEX quantum-statistics in (Nottale-Linde)FRACTAL-dimensions'' expansion around unit-circle/roots-of-unity]-dark-matter(HDM), (4)null massless bosons(E) --> Mellin-(light-speed squared)-transform/Englert-Higgs ``mechanism'' -->(timelike) massive fermions(m), (5) cosmic-microwave-background (CMB)[power-spectrum] Zipf-law HYPERBOLICITY, (6) supersymmetry(SUSY) [projective-geometry conic-sections/conics merging in R/ C projective-plane point at ∞]. UTTER-SIMPLICITY!!!
Chen, Wen-Jie; Xiao, Meng; Chan, C. T.
2016-01-01
Weyl points, as monopoles of Berry curvature in momentum space, have captured much attention recently in various branches of physics. Realizing topological materials that exhibit such nodal points is challenging and indeed, Weyl points have been found experimentally in transition metal arsenide and phosphide and gyroid photonic crystal whose structure is complex. If realizing even the simplest type of single Weyl nodes with a topological charge of 1 is difficult, then making a real crystal carrying higher topological charges may seem more challenging. Here we design, and fabricate using planar fabrication technology, a photonic crystal possessing single Weyl points (including type-II nodes) and multiple Weyl points with topological charges of 2 and 3. We characterize this photonic crystal and find nontrivial 2D bulk band gaps for a fixed kz and the associated surface modes. The robustness of these surface states against kz-preserving scattering is experimentally observed for the first time. PMID:27703140
Fermi-surface topology of the Weyl semimetal NbP
Energy Technology Data Exchange (ETDEWEB)
Klotz, J.; Wosnitza, J. [Hochfeld-Magnetlabor (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf (Germany); Institut fuer Festkoerperphysik, TU Dresden (Germany); Wu, Shu-Chun; Shekhar, Chandra; Sun, Yan; Schmidt, Marcus; Nicklas, Michael; Baenitz, Michael; Felser, Claudia [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Uhlarz, M. [Hochfeld-Magnetlabor (HLD-EMFL), Helmholtz-Zentrum Dresden-Rossendorf (Germany); Yan, Binghai [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Max Planck Institute for the Physics of Complex Systems, Dresden (Germany)
2016-07-01
The recent discovery of Weyl semimetals in transition-metal monopnictides revealed an exotic topological matter. Weyl semimetals feature band crossings with massless dispersions in their bulk band structure, termed Weyl points. Here, we present a Fermi-surface study on the Weyl semimetal NbP that combines both experimental data and band-structure calculations. We employed torque magnetometry in order to measure the angular dependence of the de Haas-van Alphen effect in a 12 T / 350 mK system. The excellent agreement between measured and calculated quantum-oscillation frequencies evidences the existence of two electron and two hole pockets and allows to locate the position of the Weyl points with respect to the Fermi energy.
Fractals in the nervous system: conceptual implications for theoretical neuroscience.
Werner, Gerhard
2010-01-01
This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review.
Marks-Tarlow, Terry
2010-01-01
In this article, the author draws on contemporary science to illuminate the relationship between early play experiences, processes of self-development, and the later emergence of the fractal self. She argues that orientation within social space is a primary function of early play and developmentally a two-step process. With other people and with…
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......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 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...
Fractal transforms and Feature invariance
Paul M. de Zeeuw; B.A.M. Ben Schouten
2000-01-01
In this paper, fractal transforms are employed with the aim of image recognition. It is known that such transforms are highly sensitive to distortions like a small shift of an image. However, by using features based on statistics kept during the actual decomposition we can derive features from
Weyl-Wigner correspondence in two space dimensions
DEFF Research Database (Denmark)
Dahl, Jens Peder; Varro, S.; Wolf, A.
2007-01-01
We consider Wigner functions in two space dimensions. In particular, we focus on Wigner functions corresponding to energy eigenstates of a non-relativistic particle moving in two dimensions in the absence of a potential. With the help of the Weyl-Wigner correspondence we first transform the eigen...... the eigenvalue equations for energy and angular momentum into phase space. As a result we arrive at partial differential equations in phase space which determine the corresponding Wigner function. We then solve the resulting equations using appropriate coordinates....
From LHC physics to Dirac-Weyl materials
International Nuclear Information System (INIS)
Raya, Alfredo
2016-01-01
The quantum field theoretical description of particle physics under extreme conditions, namely, at finite temperature, density and in the presence of external magnetic fields, can naturally be extended to describe phenomenology in other branches of physics. In this contribution, I review some aspects of particle physics in the realm of condensed matter physics, particularly graphene and other Dirac-Weyl materials carried out in Mexico. I explore several features of the dynamics of fermions in (2+1)-dimensions which are relevant to heavy ion experiments, but that can be tested in table top experiments. (paper)
Subspace gaps and Weyl's theorem for an elementary operator
Directory of Open Access Journals (Sweden)
B. P. Duggal
2005-01-01
Full Text Available A range-kernal orthogonality property is established for the elementary operators ℰ(X=∑i=1nAiXBi and ℰ*(X=∑i=1nAi*XBi*, where A=(A1,A2,…,An and B=(B1,B2,…,Bn are n-tuples of mutually commuting scalar operators (in the sense of Dunford in the algebra B(H of operators on a Hilbert space H. It is proved that the operator ℰ satisfies Weyl's theorem in the case in which A and B are n-tuples of mutually commuting generalized scalar operators.
Weyl and Dirac semimetals in three-dimensional solids
Armitage, N. P.; Mele, E. J.; Vishwanath, Ashvin
2018-01-01
Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.
Weyl's search for a difference between 'physical' and 'mathematical' automorphisms
Scholz, Erhard
2018-02-01
During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories.
Fractal nature of humic materials
Rice, J. A.; Lin, J. S.
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 fractions 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.
Fractals and Forecasting in Earthquakes and Finance
Rundle, J. B.; Holliday, J. R.; Turcotte, D. L.
2011-12-01
It is now recognized that Benoit Mandelbrot's fractals play a critical role in describing a vast range of physical and social phenomena. Here we focus on two systems, earthquakes and finance. Since 1942, earthquakes have been characterized by the Gutenberg-Richter magnitude-frequency relation, which in more recent times is often written as a moment-frequency power law. A similar relation can be shown to hold for financial markets. Moreover, a recent New York Times article, titled "A Richter Scale for the Markets" [1] summarized the emerging viewpoint that stock market crashes can be described with similar ideas as large and great earthquakes. The idea that stock market crashes can be related in any way to earthquake phenomena has its roots in Mandelbrot's 1963 work on speculative prices in commodities markets such as cotton [2]. He pointed out that Gaussian statistics did not account for the excessive number of booms and busts that characterize such markets. Here we show that both earthquakes and financial crashes can both be described by a common Landau-Ginzburg-type free energy model, involving the presence of a classical limit of stability, or spinodal. These metastable systems are characterized by fractal statistics near the spinodal. For earthquakes, the independent ("order") parameter is the slip deficit along a fault, whereas for the financial markets, it is financial leverage in place. For financial markets, asset values play the role of a free energy. In both systems, a common set of techniques can be used to compute the probabilities of future earthquakes or crashes. In the case of financial models, the probabilities are closely related to implied volatility, an important component of Black-Scholes models for stock valuations. [2] B. Mandelbrot, The variation of certain speculative prices, J. Business, 36, 294 (1963)
Robustness of the fractal regime for the multiple-scattering structure factor
Katyal, Nisha; Botet, Robert; Puri, Sanjay
2016-08-01
In the single-scattering theory of electromagnetic radiation, the fractal regime is a definite range in the photon momentum-transfer q, which is characterized by the scaling-law behavior of the structure factor: S(q) ∝ 1 /q df. This allows a straightforward estimation of the fractal dimension df of aggregates in Small-Angle X-ray Scattering (SAXS) experiments. However, this behavior is not commonly studied in optical scattering experiments because of the lack of information on its domain of validity. In the present work, we propose a definition of the multiple-scattering structure factor, which naturally generalizes the single-scattering function S(q). We show that the mean-field theory of electromagnetic scattering provides an explicit condition to interpret the significance of multiple scattering. In this paper, we investigate and discuss electromagnetic scattering by three classes of fractal aggregates. The results obtained from the TMatrix method show that the fractal scaling range is divided into two domains: (1) a genuine fractal regime, which is robust; (2) a possible anomalous scaling regime, S(q) ∝ 1 /qδ, with exponent δ independent of df, and related to the way the scattering mechanism uses the local morphology of the scatterer. The recognition, and an analysis, of the latter domain is of importance because it may result in significant reduction of the fractal regime, and brings into question the proper mechanism in the build-up of multiple-scattering.
Lung cancer—a fractal viewpoint
Lennon, Frances E.; Cianci, Gianguido C.; Cipriani, Nicole A.; Hensing, Thomas A.; Zhang, Hannah J.; Chen, Chin-Tu; Murgu, Septimiu D.; Vokes, Everett E.; W. Vannier, Michael; Salgia, Ravi
2016-01-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed. PMID:26169924
Lung cancer-a fractal viewpoint.
Lennon, Frances E; Cianci, Gianguido C; Cipriani, Nicole A; Hensing, Thomas A; Zhang, Hannah J; Chen, Chin-Tu; Murgu, Septimiu D; Vokes, Everett E; Vannier, Michael W; Salgia, Ravi
2015-11-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.
Siegel, Edward Carl-Ludwig; Young, Frederic; Wignall, Janis
2013-04-01
SEPHIROT: Siegel[http://fqxi.org/community/forum/topic/1553]: Ten-[0->9]-Digits; Average Log-Law SCALE-Invariance; Utter-Simplicity: ``Complexity'' (vs. ``Complicatedness''); Zipf-law/Hyperbolicity/ Inevitability SCENARIO AUTOMATICALLY CREATES & EVOLVES a UNIVERSE: inflation, a big-bang, bosons(E)->Mellin-(c2)-tranform->fermions(m), hidden-dark-energy(HDE), hidden-dark-matter (HDM), cosmic-microwave-background(CMB), supersymmetry(SUSY), PURPOSELY NO: theories,models,mechanisms,processes, parameters,assumptions,WHATSOEVER: It's a ``Jack-in-the-Box'' Universe!!!: ONLY VIA: Newcomb [Am.J.Math.4(1),39(1881)]QUANTUM-discovery!!!-Benford-Siegel-Antonoff[AMS.Joint-Mtg.(02)-Abs.#973-60-124!!!] inversion to ONLY BEQS with d=0 BEC: ``Digit-Physics''!; Log fixed-point invariance(s): [base=units=SCALE] of digits classic (not classical!) average [CAUSING] log statistical-correlations =log(1+1/d), with physics-crucial d=0 BEC singularity/pole, permits SEPHIROT!!!: ``digits are quanta are bosons because bosons are and always were digits!!!'': Digits = Bosons with d=0 BEC(!!!) & expansion to Zipf-law Hyperbolicity INEVITABILITY CMB!
Fractal patterns of fractures in granites
Velde, B.; Dubois, J.; Moore, D.; Touchard, G.
1991-01-01
Fractal measurements using the Cantor's dust method in a linear one-dimensional analysis mode were made on the fracture patterns revealed on two-dimensional, planar surfaces in four granites. This method allows one to conclude that: 1. (1)|The fracture systems seen on two-dimensional surfaces in granites are consistent with the part of fractal theory that predicts a repetition of patterns on different scales of observation, self similarity. Fractal analysis gives essentially the same values of D on the scale of kilometres, metres and centimetres (five orders of magnitude) using mapped, surface fracture patterns in a Sierra Nevada granite batholith (Mt. Abbot quadrangle, Calif.). 2. (2)|Fractures show the same fractal values at different depths in a given batholith. Mapped fractures (main stage ore veins) at three mining levels (over a 700 m depth interval) of the Boulder batholith, Butte, Mont. show the same fractal values although the fracture disposition appears to be different at different levels. 3. (3)|Different sets of fracture planes in a granite batholith, Central France, and in experimental deformation can have different fractal values. In these examples shear and tension modes have the same fractal values while compressional fractures follow a different fractal mode of failure. The composite fracture patterns are also fractal but with a different, median, fractal value compared to the individual values for the fracture plane sets. These observations indicate that the fractal method can possibly be used to distinguish fractures of different origins in a complex system. It is concluded that granites fracture in a fractal manner which can be followed at many scales. It appears that fracture planes of different origins can be characterized using linear fractal analysis. ?? 1991.
International Nuclear Information System (INIS)
Jha, Shailendra K.; Kant, Rama
2010-01-01
We developed a mathematical model for the first order homogeneous catalytic chemical reaction coupled with an electron transfer (EC') on a rough working electrode. Results are obtained for the various roughness models of electrode corrugations, viz., (i) roughness as an exact periodic function, (ii) roughness as a random function with known statistical properties, and (iii) roughness as a random function with statistical self-affine fractality over a finite range of length scales. Method of Green's function is used in the formulation to obtain second-order perturbation (in roughness profile) expressions for the concentration, the local current density and the current transients. A general operator structure between these quantities and arbitrary roughness profile is emphasized. The statistically averaged (randomly rough) electrode response is obtained by an ensemble averaging over all possible surface configurations. An elegant mathematical formula between the average electrochemical current transient and surface structure factor or power-spectrum of roughness is obtained. This formula is used to obtain an explicit equation for the current on an approximately self-affine (or realistic) fractal electrode with a limited range of length scales of irregularities. This description of realistic fractal is obtained by cutoff power law power-spectrum of roughness. The realistic fractal power-spectrum consists of four physical characteristics, viz., the fractal dimension (D H ), lower (l) and upper (L) cutoff length scales of fractality and a proportionality factor (μ), which is related to the topothesy or strength of fractality. Numerical calculations are performed on final results to understand the effect of catalytic reaction and fractal morphological characteristics on potentiostatic current transients.
Health, 'small-worlds', fractals and complex networks: an emerging field.
Mutch, W Alan; Lefevre, Gerald R
2003-05-01
The importance of 'small-worlds', fractals and complex networks to medicine are discussed. The interrelationship between the concepts is highlighted. 'Small-worlds'--where large populations are linked at the level of the individual have considerable importance for understanding disease transmission. Complex networks where linkages are based on the concept 'the rich get richer' are fundamental in the medical sciences--from enzymatic interactions at the subcellular level to social interactions such as sexual liaisons. Mathematically 'the rich get richer' can be modeled as a power law. Fractal architecture and time sequences can also be modeled by power laws and are ubiquitous in nature with many important examples in medicine. The potential of fractal life support--the return of physiological time sequences to devices such as mechanical ventilators and cardiopulmonary bypass pumps--is presented in the context of a failing complex network. Experimental work suggests that using fractal time sequences improves support of failing organs. Medicine, as a science has much to gain by embracing the interrelated concepts of 'small-worlds', fractals and complex networks. By so doing, medicine will move from the historical reductionist approach toward a more holistic one.
The black hole interior and the type II Weyl fermions
Zubkov, M. A.
2018-03-01
It was proposed recently that the black hole may undergo a transition to the state, where inside the horizon the Fermi surface is formed that reveals an analogy with the recently discovered type II Weyl semimetals. In this scenario, the low energy effective theory outside of the horizon is the Standard Model, which describes excitations that reside near a certain point P(0) in momentum space of the hypothetical unified theory. Inside the horizon the low energy physics is due to the excitations that reside at the points in momentum space close to the Fermi surface. We argue that those points may be essentially distant from P(0) and, therefore, inside the black hole the quantum states are involved in the low energy dynamics that are not described by the Standard Model. We analyze the consequences of this observation for the physics of the black holes and present the model based on the direct analogy with the type II Weyl semimetals, which illustrates this pattern.
Topological Nodal Cooper Pairing in Doped Weyl Metals
Li, Yi; Haldane, F. D. M.
2018-02-01
We generalize the concept of Berry connection of the single-electron band structure to that of a two-particle Cooper pairing state between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing Berry phase acquires nontrivial monopole structure. Consequently, pairing gap functions have topologically protected nodal structure as vortices in the momentum space with the total vorticity solely determined by the pair monopole charge qp. The nodes of gap function behave as the Weyl-Majorana points of the Bogoliubov-de Gennes pairing Hamiltonian. Their relation with the connection patterns of the surface modes from the Weyl band structure and the Majorana surface modes inside the pairing gap is also discussed. Under the approximation of spherical Fermi surfaces, the pairing symmetry are represented by monopole harmonic functions. The lowest possible pairing channel carries angular momentum number j =|qp|, and the corresponding gap functions are holomorphic or antiholomorphic functions on Fermi surfaces. After projected on the Fermi surfaces with nontrivial topology, all the partial-wave channels of pairing interactions acquire the monopole charge qp independent of concrete pairing mechanism.
Single-particle excitations in disordered Weyl fluids
Pixley, J. H.; Chou, Yang-Zhi; Goswami, Pallab; Huse, David A.; Nandkishore, Rahul; Radzihovsky, Leo; Das Sarma, S.
2017-06-01
We theoretically study the single-particle Green function of a three-dimensional disordered Weyl semimetal using a combination of techniques. These include analytic T -matrix and renormalization group methods with complementary regimes of validity and an exact numerical approach based on the kernel polynomial technique. We show that at any nonzero disorder, Weyl excitations are not ballistic: They instead have a nonzero linewidth that for weak short-range disorder arises from nonperturbative resonant impurity scattering. Perturbative approaches find a quantum critical point between a semimetal and a metal at a finite disorder strength, but this transition is avoided due to nonperturbative effects. At moderate disorder strength and intermediate energies the avoided quantum critical point renormalizes the scaling of single-particle properties. In this regime we compute numerically the anomalous dimension of the fermion field and find η =0.13 ±0.04 , which agrees well with a renormalization group analysis (η =0.125 ). Our predictions can be directly tested by ARPES and STM measurements in samples dominated by neutral impurities.
Weyl geometry and the nonlinear mechanics of distributed point defects
Yavari, A.
2012-09-05
The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.
Weyl-Kondo semimetal in heavy-fermion systems
Lai, Hsin-Hua; Grefe, Sarah E.; Paschen, Silke; Si, Qimiao
2018-01-01
Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently. In systems with strong correlations, they have yet to be identified. Heavy-fermion semimetals are a prototype of strongly correlated systems and, given their strong spin-orbit coupling, present a natural setting to make progress. Here, we advance a Weyl-Kondo semimetal phase in a periodic Anderson model on a noncentrosymmetric lattice. The quasiparticles near the Weyl nodes develop out of the Kondo effect, as do the surface states that feature Fermi arcs. We determine the key signatures of this phase, which are realized in the heavy-fermion semimetal Ce3Bi4Pd3. Our findings provide the much-needed theoretical foundation for the experimental search of topological metals with strong correlations and open up an avenue for systematic studies of such quantum phases that naturally entangle multiple degrees of freedom.
Similar ultrafast dynamics of several dissimilar Dirac and Weyl semimetals
Weber, Chris P.; Berggren, Bryan S.; Masten, Madison G.; Ogloza, Thomas C.; Deckoff-Jones, Skylar; Madéo, Julien; Man, Michael K. L.; Dani, Keshav M.; Zhao, Lingxiao; Chen, Genfu; Liu, Jinyu; Mao, Zhiqiang; Schoop, Leslie M.; Lotsch, Bettina V.; Parkin, Stuart S. P.; Ali, Mazhar
2017-12-01
Recent years have seen the rapid discovery of solids whose low-energy electrons have a massless, linear dispersion, such as Weyl, line-node, and Dirac semimetals. The remarkable optical properties predicted in these materials show their versatile potential for optoelectronic uses. However, little is known of their response in the picoseconds after absorbing a photon. Here, we measure the ultrafast dynamics of four materials that share non-trivial band structure topology but that differ chemically, structurally, and in their low-energy band structures: ZrSiS, which hosts a Dirac line node and Dirac points; TaAs and NbP, which are Weyl semimetals; and Sr1-yMn1-zSb2, in which Dirac fermions coexist with broken time-reversal symmetry. After photoexcitation by a short pulse, all four relax in two stages, first sub-picosecond and then few-picosecond. Their rapid relaxation suggests that these and related materials may be suited for optical switches and fast infrared detectors. The complex change of refractive index shows that photoexcited carrier populations persist for a few picoseconds.
Sieroka, Norman
2018-02-01
This paper aims at closing a gap in recent Weyl research by investigating the role played by Leibniz for the development and consolidation of Weyl's notion of theoretical (symbolic) construction. For Weyl, just as for Leibniz, mathematics was not simply an accompanying tool when doing physics-for him it meant the ability to engage in well-guided speculations about a general framework of reality and experience. The paper first introduces some of the background of Weyl's notion of theoretical construction and then discusses particular Leibnizian inheritances in Weyl's 'Philosophie der Mathematik und Naturwissenschaft', such as the general appreciation of the principles of sufficient reason and of continuity. Afterwards the paper focuses on three themes: first, Leibniz's primary quality phenomenalism, which according to Weyl marked the decisive step in realizing that physical qualities are never apprehended directly; second, the conceptual relation between continuity and freedom; and third, Leibniz's notion of 'expression', which allows for a certain type of (surrogative) reasoning by structural analogy and which gave rise to Weyl's optimism regarding the scope of theoretical construction.
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.
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.
Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
International Nuclear Information System (INIS)
Senovilla, Jose M M
2010-01-01
The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)
Weyl Group Multiple Dirichlet Series Type A Combinatorial Theory (AM-175)
Brubaker, Ben; Friedberg, Solomon
2011-01-01
Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series an
Weyl modules, demazure modules, KR-modules, crystals, fusion products and limit constructions
Fourier, G.; Littelmann, P.
2007-01-01
We study finite dimensional representations of current algebras, loop algebras and their quantized versions. For the current algebra of a simple Lie algebra of type {\\tt ADE}, we show that Kirillov-Reshetikhin modules and Weyl modules are in fact all Demazure modules. As a consequence one obtains an elementary proof of the dimension formula for Weyl modules for the current and the loop algebra. Further, we show that the crystals of the Weyl and the Demazure module are the same up to some addi...
FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES
Directory of Open Access Journals (Sweden)
Alim. Abed Al-Zobaede
2014-01-01
Full Text Available The paper considers a model of damage accumulation in parts of machines and structures which is based on a theory of fractals. Hidden process of destruction prior to the formation of macroscopic cracks is usually associated with the accumulation of micro-damages. Various models of damage accumulation and crack growth under the influence of power and thermal loads. However, models describing the accumulation process of micro-damages and their outgrowth into macro-crack are practically non-existent. Fractal structures with self-similarity are an adequate model of the fracture process. The MacDonald correlation function describing the medium structure allows to present the self-similarity of structures within a certain range of scales.The paper reviews models of damage accumulation near an opening in a composite medium and at layer boundaries. The Cantor model in a forward algorithm and a backward algorithm have been used in order to describe the model of damage accumulation. As it is known, the Cantor fractal (Cantor dust is obtained by using a recursive algorithm being applied to fracture mechanics can be regarded as a model of stepwise formation of dispersed micro-damages. The process of damage accumulation (latent destruction phase and its transition in the formation process of macro-cracks and their unification in a through-thickness crack can be described, for example, by the Paris' law.
Fractal dimension analysis of malignant and benign endobronchial ultrasound nodes
International Nuclear Information System (INIS)
Fiz, José Antonio; Monte-Moreno, Enrique; Andreo, Felipe; Auteri, Santiago José; Sanz-Santos, José; Serra, Pere; Bonet, Gloria; Castellà, Eva; Manzano, Juan Ruiz
2014-01-01
Endobronchial ultrasonography (EBUS) has been applied as a routine procedure for the diagnostic of hiliar and mediastinal nodes. The authors assessed the relationship between the echographic appearance of mediastinal nodes, based on endobronchial ultrasound images, and the likelihood of malignancy. The images of twelve malignant and eleven benign nodes were evaluated. A previous processing method was applied to improve the quality of the images and to enhance the details. Texture and morphology parameters analyzed were: the image texture of the echographies and a fractal dimension that expressed the relationship between area and perimeter of the structures that appear in the image, and characterizes the convoluted inner structure of the hiliar and mediastinal nodes. Processed images showed that relationship between log perimeter and log area of hilar nodes was lineal (i.e. perimeter vs. area follow a power law). Fractal dimension was lower in the malignant nodes compared with non-malignant nodes (1.47(0.09), 1.53(0.10) mean(SD), Mann–Whitney U test p < 0.05)). Fractal dimension of ultrasonographic images of mediastinal nodes obtained through endobronchial ultrasound differ in malignant nodes from non-malignant. This parameter could differentiate malignat and non-malignat mediastinic and hiliar nodes
Surface fractals in liposome aggregation.
Roldán-Vargas, Sándalo; Barnadas-Rodríguez, Ramon; Quesada-Pérez, Manuel; Estelrich, Joan; Callejas-Fernández, José
2009-01-01
In this work, the aggregation of charged liposomes induced by magnesium is investigated. Static and dynamic light scattering, Fourier-transform infrared spectroscopy, and cryotransmission electron microscopy are used as experimental techniques. In particular, multiple intracluster scattering is reduced to a negligible amount using a cross-correlation light scattering scheme. The analysis of the cluster structure, probed by means of static light scattering, reveals an evolution from surface fractals to mass fractals with increasing magnesium concentration. Cryotransmission electron microscopy micrographs of the aggregates are consistent with this interpretation. In addition, a comparative analysis of these results with those previously reported in the presence of calcium suggests that the different hydration energy between lipid vesicles when these divalent cations are present plays a fundamental role in the cluster morphology. This suggestion is also supported by infrared spectroscopy data. The kinetics of the aggregation processes is also analyzed through the time evolution of the mean diffusion coefficient of the aggregates.
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...
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
Fractal properties of financial markets
Budinski-Petković, Lj.; Lončarević, I.; Jakšić, Z. M.; Vrhovac, S. B.
2014-09-01
We present an analysis of the USA stock market using a simple fractal function. Financial bubbles preceding the 1987, 2000 and 2007 crashes are investigated using the Besicovitch-Ursell fractal function. Fits show a good agreement with the S&P 500 data when a complete financial growth is considered, starting at the threshold of the abrupt growth and ending at the peak. Moving the final time of the fitting interval towards earlier dates causes growing discrepancy between two curves. On the basis of a detailed analysis of the financial index behavior we propose a method for identifying the stage of the current financial growth and estimating the time in which the index value is going to reach the maximum.
Fractal Scattering of Microwaves from Soils
Oleschko, K.; Korvin, G.; Balankin, A. S.; Khachaturov, R. V.; Flores, L.; Figueroa, B.; Urrutia, J.; Brambila, F.
2002-10-01
Using a combination of laboratory experiments and computer simulation we show that microwaves reflected from and transmitted through soil have a fractal dimension correlated to that of the soil's hierarchic permittivity network. The mathematical model relating the ground-penetrating radar record to the mass fractal dimension of soil structure is also developed. The fractal signature of the scattered microwaves correlates well with some physical and mechanical properties of soils.
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...... vasculature may affect the retinal response to potential vascular disease in later life....
Fractal Metrology for biogeosystems analysis
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-11-01
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 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 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
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.
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)...
Robustness of the Fractal Regime for the Multiple-Scattering Structure Factor
Katyal, Nisha; Botet, Robert; Puri, Sanjay
2016-01-01
In the single-scattering theory of electromagnetic radiation, the {\\it fractal regime} is a definite range in the photon momentum-transfer $q$, which is characterized by the scaling-law behavior of the structure factor: $S(q) \\propto 1/q^{d_f}$. This allows a straightforward estimation of the fractal dimension $d_f$ of aggregates in {\\it Small-Angle X-ray Scattering} (SAXS) experiments. However, this behavior is not commonly studied in optical scattering experiments because of the lack of inf...
Fractal analysis of palmar electronographic images. Medical anthropological perspectives.
Guja, Cornelia; Voinea, V; Baciu, Adina; Ciuhuţa, M; Crişan, Daniela A
2008-01-01
The present paper brings to the medical specialists' attention a possibility of multivalent imagistic investigation--the palmar electrographic method submitted to a totally new analysis by the fractal method. Its support for information recording is the radiosensitive film. This makes it resemble the radiological investigation, which opened the way of correlating the shape of certain structures of the organism with their function. By the specific electromagnetic impressing of the ultra photosensitive film, palmar electrography has the advantage of catching the shape of certain radiative phenomena, generated by certain structures in their functional dynamics--at the level of the human palmar tegument. This makes it resemble the EEG, EKG and EMG investigations. The purpose of this presentation is to highlight a new modality of studying the states of the human organism in its permanent adaptation to the living environment, using a new anthropological, informational vision--by fractal processing and by the couple of concepts system / interface--much closer to reality than the present systemic thinking. The human palm, which has a special medial-anthropological relevance, is analysed as a complex adaptive biological and socio-cultural interface between the internal and external environment. The fractal phenomena recorded on the image are ubicuitary in nature and especially in the living world and their shapes may he described mathematically and used for decoding their informational laws. They may have very useful implications in the medical act. The paper presents a few introductory elements to the fractal theory, and, in the final part, the pursued objectives are concretely shown by grouping the EG images according to certain more important medical-anthropological themes.
Zhang, Zhongzhi; Wu, Bin; Zhang, Hongjuan; Zhou, Shuigeng; Guan, Jihong; Wang, Zhigang
2010-03-01
The family of Vicsek fractals is one of the most important and frequently studied regular fractal classes, and it is of considerable interest to understand the dynamical processes on this treelike fractal family. In this paper, we investigate discrete random walks on the Vicsek fractals, with the aim to obtain the exact solutions to the global mean-first-passage time (GMFPT), defined as the average of first-passage time (FPT) between two nodes over the whole family of fractals. Based on the known connections between FPTs, effective resistance, and the eigenvalues of graph Laplacian, we determine implicitly the GMFPT of the Vicsek fractals, which is corroborated by numerical results. The obtained closed-form solution shows that the GMFPT approximately grows as a power-law function with system size (number of all nodes), with the exponent lies between 1 and 2. We then provide both the upper bound and lower bound for GMFPT of general trees, and show that the leading behavior of the upper bound is the square of system size and the dominating scaling of the lower bound varies linearly with system size. We also show that the upper bound can be achieved in linear chains and the lower bound can be reached in star graphs. This study provides a comprehensive understanding of random walks on the Vicsek fractals and general treelike networks.
Coulomb Interaction Effect in Weyl Fermions with Tilted Energy Dispersion in Two Dimensions
Isobe, Hiroki; Nagaosa, Naoto
2016-03-01
Weyl fermions with tilted linear dispersions characterized by several different velocities appear in some systems including the quasi-two-dimensional organic semiconductor α -(BEDT -TTF )2I3 and three-dimensional WTe2 . The Coulomb interaction between electrons modifies the velocities in an essential way in the low-energy limit, where the logarithmic corrections dominate. Taking into account the coupling to both the transverse and longitudinal electromagnetic fields, we derive the renormalization group equations for the velocities of the tilted Weyl fermions in two dimensions, and found that they increase as the energy decreases and eventually hit the speed of light c to result in the Cherenkov radiation. Especially, the system restores the isotropic Weyl cone even when the bare Weyl cone is strongly tilted and the velocity of electrons becomes negative in certain directions.
Completeness in quantum mechanics and the Weyl-Titchmarsh-Kodaira theorem
Energy Technology Data Exchange (ETDEWEB)
Palma, G [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile); Prado, H; Reyes, E G, E-mail: guillermo.palma@usach.c, E-mail: humberto.prado@usach.c, E-mail: ereyes@fermat.usach.c [Departamento de Matematica y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago (Chile)
2010-06-25
We discuss the completeness of (generalized) eigenfunctions in quantum mechanics using the classical theory developed by Weyl, Titchmarsh, and Kodaira. As applications, we rigorously prove the completeness of generalized eigenfunctions for the step and well potentials.
Unveiling a crystalline topological insulator in a Weyl semimetal with time-reversal symmetry
Arrachea, Liliana; Aligia, Armando A.
2014-09-01
We consider a natural generalization of the lattice model for a periodic array of two layers, A and B, of spinless electrons proposed by Fu [Phys. Rev. Lett. 106, 106802 (2011), 10.1103/PhysRevLett.106.106802] as a prototype for a crystalline insulator. This model has time-reversal symmetry and broken inversion symmetry. We show that when the intralayer next-nearest-neighbor hoppings t2a,a=A,B vanish, this model supports a Weyl semimetal phase for a wide range of the remaining model parameters. When the effect of t2a is considered, topological crystalline insulating phases take place within the Weyl semimetal one. By mapping to an effective Weyl Hamiltonian we derive some analytical results for the phase diagram as well as for the structure of the nodes in the spectrum of the Weyl semimetal.
Intertwined Rashba, Dirac, and Weyl Fermions in Hexagonal Hyperferroelectrics.
Di Sante, Domenico; Barone, Paolo; Stroppa, Alessandro; Garrity, Kevin F; Vanderbilt, David; Picozzi, Silvia
2016-08-12
By means of density functional theory based calculations, we study the role of spin-orbit coupling in the new family of ABC hyperferroelectrics [Garrity, Rabe, and Vanderbilt Phys. Rev. Lett. 112, 127601 (2014)]. We unveil an extremely rich physics strongly linked to ferroelectric properties, ranging from the electric control of bulk Rashba effect to the existence of a three-dimensional topological insulator phase, with concomitant topological surface states even in the ultrathin film limit. Moreover, we predict that the topological transition, as induced by alloying, is followed by a Weyl semimetal phase of finite concentration extension, which is robust against disorder, putting forward hyperferroelectrics as promising candidates for spin-orbitronic applications.
Reconstruction of black hole metric perturbations from the Weyl curvature
International Nuclear Information System (INIS)
Lousto, Carlos O.; Whiting, Bernard F.
2002-01-01
Perturbation theory of rotating black holes is usually described in terms of Weyl scalars ψ 4 and ψ 0 , which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials Ψ in outgoing or ingoing radiation gauges. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e. ψ 4 and ψ 0 . We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole
Superconductivity in Weyl semimetal candidate MoTe{sub 2}
Energy Technology Data Exchange (ETDEWEB)
Qi, Yanpeng; Naumov, Pavel; Rajamathi, Catherine; Barkalov, Oleg; Wu, Shu-Chun; Shekhar, Chandra; Sun, Yan; Suess, Vicky; Schmidt, Marcus; Schwarz, Ulrich; Schnelle, Walter; Felser, Claudia; Medvedev, Sergey [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Ali, Mazhar; Cava, Robert [Department of Chemistry, Princeton University, Princeton (United States); Hanfland, Michael [European Synchrotron Radiation Facility, Grenoble (France); Pippel, Eckhard; Werner, Peter; Hillebrand, Reinald; Parkin, Stuart [Max Planck Institute of Microstructure Physics, Halle (Germany); Foerster, Tobias; Kampert, Erik [Dresden High Magnetic Field Laboratory, Dresden (Germany); Yan, Binghai [Max Planck Institute for Chemical Physics of Solids, Dresden (Germany); Max Planck Institute for the Physics of Complex Systems, Dresden (Germany)
2016-07-01
In this work, we investigate the sister compound of WTe{sub 2}, MoTe{sub 2}, which is also predicted to be a Weyl semimetal and a quantum spin Hall insulator in bulk and monolayer form, respectively. We find that MoTe{sub 2} exhibits superconductivity with a resistive transition temperature T{sub c} of 0.1 K. The application of a small pressure is shown to dramatically enhance the T{sub c}, with a maximum value of 8.2 K being obtained at 11.7 GPa (a more than 80-fold increase in Tc). This yields a dome-shaped superconducting phase diagram. Further explorations into the nature of the superconductivity in this system may provide insights into the interplay between superconductivity and topological physics.
Krawiecki, A; Matyjaskiewicz, S; Holyst, J A
2003-01-01
The origin of log-periodic oscillations around the power-law trend of the escape probability from a precritical attractor and of the noise-free stochastic multiresonance, found in numerical simulations in chaotic systems close to crises is discussed. It is shown that multiple maxima of the spectral power amplification vs. the control parameter result from a fractal structure of a precritical attractor colliding with a possibly fractal basin of attraction at the crisis point. Qualitative explanation of the multiresonance, based on a concept of fractal self-similarity, or discrete-scale invariance, is given and compared with numerical results and analytic theory using a simple geometric models of the colliding fractal sets.
Bianchi type I expanding universe in Weyl-invariant gravity with a quartic interaction term
Energy Technology Data Exchange (ETDEWEB)
Kao, W.F.; Lin, Ing-Chen [National Chiao Tung University, Institute of Physics, Hsinchu (China)
2017-11-15
We will focus on the effect of a Weyl-invariant model with a quadratic interaction term and a free scalar field ψ. A set of analytic solutions will be obtained for this model. This model provides a dynamical alternative to the standard ΛCDM model. In particular, we will show that the quartic Weyl-invariant model prediction is consistent with the Hubble diagram observations. (orig.)
Present accelerated expansion of the universe from new Weyl-integrable gravity approach
Energy Technology Data Exchange (ETDEWEB)
Aguila, Ricardo; Madriz Aguilar, Jose Edgar; Moreno, Claudia [Universidad de Guadalajara (UdG), Departamento de Matematicas, Centro Universitario de Ciencias Exactas e ingenierias (CUCEI), Guadalajara, Jalisco (Mexico); Bellini, Mauricio [Universidad Nacional de Mar del Plata (UNMdP), Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Mar del Plata (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), La Plata (Argentina)
2014-11-15
We investigate if a recently introduced formulation of general relativity on a Weyl-integrable geometry contains cosmological solutions exhibiting acceleration in the present cosmic expansion. We derive the general conditions to have acceleration in the expansion of the universe and obtain a particular solution for the Weyl scalar field describing a cosmological model for the present time in concordance with the data combination Planck + WP + BAO + SN. (orig.)
Directory of Open Access Journals (Sweden)
Leandro Redin Vestena
2010-08-01
Full Text Available Os objetivos deste trabalho foram estimar e avaliar a dimensão fractal da rede de drenagem da bacia hidrográfica do Caeté, em Alfredo Wagner, SC, a partir de diferentes métodos, com o propósito de caracterizar as formas geomorfológicas irregulares. A rede de drenagem apresenta propriedades multifractais. As dimensões fractais para os segmentos individuais (df e para a rede de drenagem inteira (Df foram determinadas por métodos que se fundamentaram nas razões de Horton e pelo método da contagem de caixas (Box-Counting. A rede de drenagem tem característica de autoafinidade. A dimensão fractal proveniente da relação de parâmetros obtidos pelas Leis de Horton apresentou resultados dentro dos limiares da teoria da geometria fractal.The objective of the present work was to evaluate the fractal dimensions of the drainage network of the Caeté river watershed, Alfredo Wagner/SC, with different methods in order to characterize the irregular geomorphologic forms. The drainage network possesses multi-fractal properties. That is why the fractal dimensions for the individual segments (df and for the entire network (Df were evaluated with Horton's Laws and the Box-Counting method. The drainage network has self-affinity characteristics. The fractal dimension obtained through the parameters relationship of Horton's Laws showed the results within the thresholds of the fractal geometry theory.
Introduction to the special issue Hermann Weyl and the philosophy of the 'New Physics'
De Bianchi, Silvia; Catren, Gabriel
2018-02-01
This Special Issue Hermann Weyl and the Philosophy of the 'New Physics' has two main objectives: first, to shed fresh light on the relevance of Weyl's work for modern physics and, second, to evaluate the importance of Weyl's work and ideas for contemporary philosophy of physics. Regarding the first objective, this Special Issue emphasizes aspects of Weyl's work (e.g. his work on spinors in n dimensions) whose importance has recently been emerging in research fields across both mathematical and experimental physics, as well as in the history and philosophy of physics. Regarding the second objective, this Special Issue addresses the relevance of Weyl's ideas regarding important open problems in the philosophy of physics, such as the problem of characterizing scientific objectivity and the problem of providing a satisfactory interpretation of fundamental symmetries in gauge theories and quantum mechanics. In this Introduction, we sketch the state of the art in Weyl studies and we summarize the content of the contributions to the present volume.
Concurrence of superconductivity and structure transition in Weyl semimetal TaP under pressure
Energy Technology Data Exchange (ETDEWEB)
Li, Yufeng; Zhou, Yonghui; Guo, Zhaopeng; Han, Fei; Chen, Xuliang; Lu, Pengchao; Wang, Xuefei; An, Chao; Zhou, Ying; Xing, Jie; Du, Guan; Zhu, Xiyu; Yang, Huan; Sun, Jian; Yang, Zhaorong; Yang, Wenge; Mao, Ho-Kwang; Zhang, Yuheng; Wen, Hai-Hu
2017-12-01
Weyl semimetal defines a material with three-dimensional Dirac cones, which appear in pair due to the breaking of spatial inversion or time reversal symmetry. Superconductivity is the state of quantum condensation of paired electrons. Turning a Weyl semimetal into superconducting state is very important in having some unprecedented discoveries. In this work, by doing resistive measurements on a recently recognized Weyl semimetal TaP under pressures up to about 100 GPa, we show the concurrence of superconductivity and a structure transition at about 70 GPa. It is found that the superconductivity becomes more pronounced when decreasing pressure and retains when the pressure is completely released. High-pressure x-ray diffraction measurements also confirm the structure phase transition from I41md to P-6m2 at about 70 GPa. More importantly, ab-initial calculations reveal that the P-6m2 phase is a new Weyl semimetal phase and has only one set of Weyl points at the same energy level. Our discovery of superconductivity in TaP by high pressure will stimulate investigations on superconductivity and Majorana fermions in Weyl semimetals.
Flat band in disorder-driven non-Hermitian Weyl semimetals
Zyuzin, A. A.; Zyuzin, A. Yu.
2018-01-01
We study the interplay of disorder and band-structure topology in a Weyl semimetal with a tilted conical spectrum around the Weyl points. The spectrum of particles is given by the eigenvalues of a non-Hermitian matrix, which contains contributions from a Weyl Hamiltonian and complex self-energy due to electron elastic scattering on disorder. We find that the tilt-induced matrix structure of the self-energy gives rise to either a flat band or a nodal line segment at the interface of the electron and hole pockets in the bulk band structure of type-II Weyl semimetals depending on the Weyl cone inclination. For the tilt in a single direction in momentum space, each Weyl point expands into a flat band lying on the plane, which is transverse to the direction of the tilt. The spectrum of the flat band is fully imaginary and is separated from the in-plane dispersive part of the spectrum by the "exceptional nodal ring" where the matrix of the Green's function in momentum-frequency space is defective. The tilt in two directions might shrink a flat band into a nodal line segment with "exceptional edge points." We discuss the connection to the non-Hermitian topological theory.
Riemann's and Helmholtz-Lie's problems of space from Weyl's relativistic perspective
Bernard, Julien
2018-02-01
I reconstruct Riemann's and Helmholtz-Lie's problems of space, from some perspectives that allow for a fruitful comparison with Weyl. In Part II. of his inaugural lecture, Riemann justifies that the infinitesimal metric is the square root of a quadratic form. Thanks to Finsler geometry, I clarify both the implicit and explicit hypotheses used for this justification. I explain that Riemann-Finsler's kind of method is also appropriate to deal with indefinite metrics. Nevertheless, Weyl shares with Helmholtz a strong commitment to the idea that the notion of group should be at the center of the foundations of geometry. Riemann missed this point, and that is why, according to Weyl, he dealt with the problem of space in a "too formal" way. As a consequence, to solve the problem of space, Weyl abandoned Riemann-Finsler's methods for group-theoretical ones. However, from a philosophical point of view, I show that Weyl and Helmholtz are in strong opposition. The meditation on Riemann's inaugural lecture, and its clear methodological separation between the infinitesimal and the finite parts of the problem of space, must have been crucial for Weyl, while searching for strong epistemological foundations for the group-theoretical methods, avoiding Helmholtz's unjustified transition from the finite to the infinitesimal.
Chen, X.; Yao, G.; Cai, J.
2017-12-01
Pore structure characteristics are important factors in influencing the fluid transport behavior of porous media, such as pore-throat ratio, pore connectivity and size distribution, moreover, wettability. To accurately characterize the diversity of pore structure among HFUs, five samples selected from different HFUs (porosities are approximately equal, however permeability varies widely) were chosen to conduct micro-computerized tomography test to acquire direct 3D images of pore geometries and to perform mercury injection experiments to obtain the pore volume-radii distribution. To characterize complex and high nonlinear pore structure of all samples, three classic fractal geometry models were applied. Results showed that each HFU has similar box-counting fractal dimension and generalized fractal dimension in the number-area model, but there are significant differences in multifractal spectrums. In the radius-volume model, there are three obvious linear segments, corresponding to three fractal dimension values, and the middle one is proved as the actual fractal dimension according to the maximum radius. In the number-radius model, the spherical-pore size distribution extracted by maximum ball algorithm exist a decrease in the number of small pores compared with the fractal power rate rather than the traditional linear law. Among the three models, only multifractal analysis can classify the HFUs accurately. Additionally, due to the tightness and low-permeability in reservoir rocks, connate water film existing in the inner surface of pore channels commonly forms bound water. The conventional model which is known as Yu-Cheng's model has been proved to be typically not applicable. Considering the effect of irreducible water saturation, an improved fractal permeability model was also deduced theoretically. The comparison results showed that the improved model can be applied to calculate permeability directly and accurately in such unconventional rocks.
Fractals in petroleum geology and earth processes
Barton, Christopher C.; La Pointe, Paul R.
1995-01-01
In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results.
Fractal basins in an ecological model
Directory of Open Access Journals (Sweden)
I. Djellit
2013-09-01
Full Text Available Complex dynamics is detected in an ecological model of host-parasitoid interaction. It illustrates fractalization of basins with self-similarity and chaotic attractors. This paper describes these dynamic behaviors, bifurcations, and chaos. Fractals basins are displayed by numerical simulations.
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…
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
Directory of Open Access Journals (Sweden)
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.
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
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
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.
Textural characterization of coals using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Mahamud, Manuel; Lopez, Oscar [Faculty of Chemistry, Department of Chemical and Environmental Engineering, University of Oviedo, Campus de El Cristo, 33071 Oviedo (Spain); Pis, Jose Juan; Pajares, Jesus Alberto [Instituto Nacional del Carbon (C.S.I.C.), Apartado 73, 33080 Oviedo (Spain)
2003-05-15
The aim of this study is to show how fractal analysis can be effectively used to characterize the texture of porous solids. The materials under study were series of coals oxidized in air at various temperatures for different time intervals. Data from mercury porosimetry determinations of samples was analyzed using fractal models. The methods employed were those proposed by Neimark, Friesen and Mikula and that developed by Zhang and Li. Some methods are able to supply a fractal profile or 'fractal fingerprint' of materials, i.e. ranges of pore sizes with different fractal dimensions are detected. These fractal profiles are very sensitive to the oxidation treatment. The average fractal dimension can also be used as a valid parameter to monitor the textural evolution of the coals as the treatment progresses, as this behaves in a similar way to other textural parameters. The use of fractal analysis in conjunction with the results of classical characterization methods leads to a better understanding of textural modifications in the processing of materials.
Fractal Music: The Mathematics Behind "Techno" Music
Padula, Janice
2005-01-01
This article describes sound waves, their basis in the sine curve, Fourier's theorem of infinite series, the fractal equation and its application to the composition of music, together with algorithms (such as those employed by meteorologist Edward Lorenz in his discovery of chaos theory) that are now being used to compose fractal music on…
[Molecular structure and fractal analysis of oligosaccharide].
Liu, Wen-long; Wang, Lu-man; He, Dong-qi; Zhang, Tian-lan; Gou, Bao-di; Li, Qing
2014-10-18
To propose a calculation method of oligosaccharides' fractal dimension, and to provide a new approach to studying the drug molecular design and activity. By using the principle of energy optimization and computer simulation technology, the steady structures of oligosaccharides were found, and an effective way of oligosaccharides fractal dimension's calculation was further established by applying the theory of box dimension to the chemical compounds. By using the proposed method, 22 oligosaccharides' fractal dimensions were calculated, with the mean 1.518 8 ± 0.107 2; in addition, the fractal dimensions of the two activity multivalent oligosaccharides which were confirmed by experiments, An-2 and Gu-4, were about 1.478 8 and 1.516 0 respectively, while C-type lectin-like receptor Dectin-1's fractal dimension was about 1.541 2. The experimental and computational results were expected to help to find a class of glycoside drugs whose target receptor was Dectin-1. Fractal dimension, differing from other known macro parameters, is a useful tool to characterize the compound molecules' microscopic structure and function, which may play an important role in the molecular design and biological activity study. In the process of oligosaccharides drug screening, the fractal dimension of receptor and designed oligosaccharides or glycoclusters can be calculated respectively. The oligosaccharides with fractal dimension close to that of target receptor should then take priority compared with others, to get the drug molecules with latent activity.
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.
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.
Fractal organization of feline oocyte cytoplasm
Directory of Open Access Journals (Sweden)
G De Vico
2009-06-01
Full Text Available The present study aimed at verifying whether immature cat oocytes with morphologic irregular cytoplasm display selfsimilar features which can be analytically described by fractal analysis. Original images of oocytes collected by ovariectomy were acquired at a final magnification of 400 X with a CCD video camera connected to an optic microscope. After greyscale thresholding segmentation of cytoplasm, image profiles were submitted to fractal analysis using FANAL++, a program which provided an analytical standard procedure for determining the fractal dimension (FD. The presentation of the oocyte influenced the magnitude of the fractal dimension with the highest FD of 1.91 measured on grey-dark cytoplasm characterized by a highly connected network of lipid droplets and intracellular membranes. Fractal analysis provides an effective quantitative descriptor of the real cytoplasm morphology, which can influence the acquirement of in vitro developmental competence, without introducing any bias or shape approximation and thus contributes to an objective and reliable classification of feline oocytes.
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
Designing fractal nanostructured biointerfaces for biomedical applications.
Zhang, Pengchao; Wang, Shutao
2014-06-06
Fractal structures in nature offer a unique "fractal contact mode" that guarantees the efficient working of an organism with an optimized style. Fractal nanostructured biointerfaces have shown great potential for the ultrasensitive detection of disease-relevant biomarkers from small biomolecules on the nanoscale to cancer cells on the microscale. This review will present the advantages of fractal nanostructures, the basic concept of designing fractal nanostructured biointerfaces, and their biomedical applications for the ultrasensitive detection of various disease-relevant biomarkers, such microRNA, cancer antigen 125, and breast cancer cells, from unpurified cell lysates and the blood of patients. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Stochastic self-similar and fractal universe
International Nuclear Information System (INIS)
Iovane, G.; Laserra, E.; Tortoriello, F.S.
2004-01-01
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical structures by using a comparison between quantum quantities and astrophysical ones. We present the observed segregated Universe as the result of a fundamental self-similar law, which generalizes the Compton wavelength relation. It appears that the Universe has a memory of its quantum origin as suggested by R. Penrose with respect to quasi-crystal. A more accurate analysis shows that the present theory can be extended from the astrophysical to the nuclear scale by using generalized (stochastically) self-similar random process. This transition is connected to the relevant presence of the electromagnetic and nuclear interactions inside the matter. In this sense, the presented rule is correct from a subatomic scale to an astrophysical one. We discuss the near full agreement at organic cell scale and human scale too. Consequently the Universe, with its structures at all scales (atomic nucleus, organic cell, human, planet, solar system, galaxy, clusters of galaxy, super clusters of galaxy), could have a fundamental quantum reason. In conclusion, we analyze the spatial dimensions of the objects in the Universe as well as space-time dimensions. The result is that it seems we live in an El Naschie's E-infinity Cantorian space-time; so we must seriously start considering fractal geometry as the geometry of nature, a type of arena where the laws of physics appear at each scale in a self-similar way as advocated long ago by the Swedish school of astrophysics
Barreto, A. B.; Pucheu, M. L.; Romero, C.
2018-02-01
We consider scalar–tensor theories of gravity defined in Weyl integrable space-time and show that for time-lapse extended Robertson–Walker metrics in the ADM formalism a class of Weyl transformations corresponding to change of frames induce canonical transformations between different representations of the phase space. In this context, we discuss the physical equivalence of two distinct Weyl frames at the classical level.
Fractal scaling in bottlenose dolphin (Tursiops truncatus) echolocation: A case study
Perisho, Shaun T.; Kelty-Stephen, Damian G.; Hajnal, Alen; Houser, Dorian; Kuczaj, Stan A., II
2016-02-01
Fractal scaling patterns, which entail a power-law relationship between magnitude of fluctuations in a variable and the scale at which the variable is measured, have been found in many aspects of human behavior. These findings have led to advances in behavioral models (e.g. providing empirical support for cascade-driven theories of cognition) and have had practical medical applications (e.g. providing new methods for early diagnosis of medical conditions). In the present paper, fractal analysis is used to investigate whether similar fractal scaling patterns exist in inter-click interval and peak-peak amplitude measurements of bottlenose dolphin click trains. Several echolocation recordings taken from two male bottlenose dolphins were analyzed using Detrended Fluctuation Analysis and Higuchi's (1988) method for determination of fractal dimension. Both animals were found to exhibit fractal scaling patterns near what is consistent with persistent long range correlations. These findings suggest that recent advances in human cognition and medicine may have important parallel applications to echolocation as well.
Numerical construction and flow simulation in networks of fractures using fractals
Energy Technology Data Exchange (ETDEWEB)
Yortsos, Y.C.; Acuna, J.A.
1991-11-01
Present models for the representation of naturally fractured systems rely on the double-porosity Warren-Root model or on random arrays of fractures. However, field observation in outcrops has demonstrated the existence of multiple length scales in many naturally fractured media. The existing models fail to capture this important fractal property. In this paper, we use concepts from the theory of fragmentation and from fractal geometry for the numerical construction of networks of fractures that have fractal characteristics. The method is based mainly on the work of Barnsley (1) and allows for great flexibility in the development of patterns. Numerical techniques are developed for the simulation of unsteady single phase flow in such networks. It is found that the pressure transient response of finite fractals behaves according to the analytical predictions of Chang and Yortsos (6), provided that there exists a power law in the mass-radius relationship around the test well location. Otherwise, the finite size effects become significant and interfere severely with the identification of the underlying fractal structure. 21 refs., 13 figs.
Random sequential adsorption on fractals.
Ciesla, Michal; Barbasz, Jakub
2012-07-28
Irreversible adsorption of spheres on flat collectors having dimension d fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.
Fractal dimension of bioconvection patterns
Noever, David A.
1990-01-01
Shallow cultures of the motile algal strain, Euglena gracilis, were concentrated to 2 x 10 to the 6th organisms per ml and placed in constant temperature water baths at 24 and 38 C. Bioconvective patterns formed an open two-dimensional structure with random branches, similar to clusters encountered in the diffusion-limited aggregation (DLA) model. When averaged over several example cultures, the pattern was found to have no natural length scale, self-similar branching, and a fractal dimension (d about 1.7). These agree well with the two-dimensional DLA.
Fractal dimension of wind speed time series
International Nuclear Information System (INIS)
Chang, Tian-Pau; Ko, Hong-Hsi; Liu, Feng-Jiao; Chen, Pai-Hsun; Chang, Ying-Pin; Liang, Ying-Hsin; Jang, Horng-Yuan; Lin, Tsung-Chi; Chen, Yi-Hwa
2012-01-01
Highlights: ► Fractal dimension of wind speeds in Taiwan is studied considering climate factors. ► Relevant algorithms for the calculation of fractal dimension are presented graphically. ► Fractal dimension reveals negative correlation with mean wind speed. ► Fractal dimension is not lower even wind distribution is well described by Weibull pdf. - Abstract: The fluctuation of wind speed within a specific time period affects a lot the energy conversion rate of wind turbine. In this paper, the concept of fractal dimension in chaos theory is applied to investigate wind speed characterizations; numerical algorithms for the calculation of the fractal dimension are presented graphically. Wind data selected is observed at three wind farms experiencing different climatic conditions from 2006 to 2008 in Taiwan, where wind speed distribution can be properly classified to high wind season from October to March and low wind season from April to September. The variations of fractal dimensions among different wind farms are analyzed from the viewpoint of climatic conditions. The results show that the wind speeds studied are characterized by medium to high values of fractal dimension; the annual dimension values lie between 1.61 and 1.66. Because of monsoon factor, the fluctuation of wind speed during high wind months is not as significant as that during low wind months; the value of fractal dimension reveals negative correlation with that of mean wind speed, irrespective of wind farm considered. For a location where the wind distribution is well described by Weibull function, its fractal dimension is not necessarily lower. These findings are useful to wind analysis.
Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs
Directory of Open Access Journals (Sweden)
Xiaochun Huang
2015-08-01
Full Text Available Weyl semimetal is the three-dimensional analog of graphene. According to quantum field theory, the appearance of Weyl points near the Fermi level will cause novel transport phenomena related to chiral anomaly. In the present paper, we report the experimental evidence for the long-anticipated negative magnetoresistance generated by the chiral anomaly in a newly predicted time-reversal-invariant Weyl semimetal material TaAs. Clear Shubnikov de Haas (SdH oscillations have been detected starting from a very weak magnetic field. Analysis of the SdH peaks gives the Berry phase accumulated along the cyclotron orbits as π, indicating the existence of Weyl points.
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…
Random fractal characters and length uncertainty of the continental ...
Indian Academy of Sciences (India)
2Collaborative Innovation Center on Yellow River Civilization of Henan Province, Kaifeng 475 001, China. ∗. Corresponding author. e-mail: mjh@henu.edu.cn. A coastline is a random fractal ... research showed that the fractal dimension (D) of. Keywords. Continental coastline of China; scaling region; random fractal; fractal ...
Fractal gait patterns are retained after entrainment to a fractal stimulus.
Rhea, Christopher K; Kiefer, Adam W; Wittstein, Matthew W; Leonard, Kelsey B; MacPherson, Ryan P; Wright, W Geoffrey; Haran, F Jay
2014-01-01
Previous work has shown that fractal patterns in gait can be altered by entraining to a fractal stimulus. However, little is understood about how long those patterns are retained or which factors may influence stronger entrainment or retention. In experiment one, participants walked on a treadmill for 45 continuous minutes, which was separated into three phases. The first 15 minutes (pre-synchronization phase) consisted of walking without a fractal stimulus, the second 15 minutes consisted of walking while entraining to a fractal visual stimulus (synchronization phase), and the last 15 minutes (post-synchronization phase) consisted of walking without the stimulus to determine if the patterns adopted from the stimulus were retained. Fractal gait patterns were strengthened during the synchronization phase and were retained in the post-synchronization phase. In experiment two, similar methods were used to compare a continuous fractal stimulus to a discrete fractal stimulus to determine which stimulus type led to more persistent fractal gait patterns in the synchronization and post-synchronization (i.e., retention) phases. Both stimulus types led to equally persistent patterns in the synchronization phase, but only the discrete fractal stimulus led to retention of the patterns. The results add to the growing body of literature showing that fractal gait patterns can be manipulated in a predictable manner. Further, our results add to the literature by showing that the newly adopted gait patterns are retained for up to 15 minutes after entrainment and showed that a discrete visual stimulus is a better method to influence retention.
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.
DEFF Research Database (Denmark)
Mäkikallio, T H; Høiber, S; Køber, L
1999-01-01
variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling...... (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction ... variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death...
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.
On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: a review.
Pippa, Natassa; Dokoumetzidis, Aristides; Demetzos, Costas; Macheras, Panos
2013-11-18
Fractals have been very successful in quantifying nature's geometrical complexity, and have captured the imagination of scientific community. The development of fractal dimension and its applications have produced significant results across a wide variety of biomedical applications. This review deals with the application of fractals in pharmaceutical sciences and attempts to account the most important developments in the fields of pharmaceutical technology, especially of advanced Drug Delivery nano Systems and of biopharmaceutics and pharmacokinetics. Additionally, fractal kinetics, which has been applied to enzyme kinetics, drug metabolism and absorption, pharmacokinetics and pharmacodynamics are presented. This review also considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain information and more realistic description on different parts of pharmaceutical sciences. As a conclusion, the purpose of the present work is to highlight the presence of fractal geometry in almost all fields of pharmaceutical research. Copyright © 2013 Elsevier B.V. All rights reserved.
Heat diffusion in fractal geometry cooling surface
Directory of Open Access Journals (Sweden)
Ramšak Matjaz
2012-01-01
Full Text Available In the paper the numerical simulation of heat diffusion in the fractal geometry of Koch snowflake is presented using multidomain mixed Boundary Element Method. The idea and motivation of work is to improve the cooling of small electronic devices using fractal geometry of surface similar to cooling ribs. The heat diffusion is assumed as the only principle of heat transfer. The results are compared to the heat flux of a flat surface. The limiting case of infinite small fractal element is computed using Richardson extrapolation.
Measurement Based Quantum Computation on Fractal Lattices
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Michal Hajdušek
2010-06-01
Full Text Available In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fang, Jieran; Wang, Di; DeVault, Clayton T
2017-01-01
optical absorption, which hinders its incorporation with modern photodetecting systems. In this work, we propose a gold snowflake-like fractal metasurface design to realize broadband and polarization-insensitive plasmonic enhancement in graphene photodetector. We experimentally obtain an enhanced...... photovoltage from the fractal metasurface that is an order of magnitude greater than that generated at a plain gold-graphene edge and such an enhancement in the photovoltage sustains over the entire visible spectrum. We also observed a relatively constant photoresponse with respect to polarization angles...... of incident light, as a result of the combination of two orthogonally oriented concentric hexagonal fractal geometries in one metasurface....
Fractal boundaries in chaotic hamiltonian systems
Viana, R. L.; Mathias, A. C.; Marcus, F. A.; Kroetz, T.; Caldas, I. L.
2017-10-01
Fractal structures are typically present in the dynamics of chaotic orbits in non-integrable open Hamiltonian systems and result from the extremely complicated nature of the invariant manifolds of unstable periodic orbits. Exit basins, the set of initial conditions leading to orbits escaping through a given exit, have very frequently fractal boundaries. In this work we analyze exit basin boundaries in a dynamical system of physical interest, namely the motion of charged particles in a magnetized plasma subjected to electrostatic drift waves, and characterize in a quantitative way the fractality of these structures and their observable consequences, as the final-state uncertainty.
From Hermann Weyl to Yang and Mills to Quantum Chromodynamics
Chýla, J.
2005-03-01
This is a personal view of the developments from the invention of the concept of gauge invariance to our present understanding that it provides the fundamental principle for the construction of theories of forces between the basic blocs of matter. This journey was full of twists and turns and marked by fascinating moments. It is these aspects of the development of gauge theories that I will concentrate on. Although Yang-Mills theories provide the basic framework for both strong and electroweak interactions, my contribution concerns almost exclusively the former only. There are many excellent articles discussing various aspects of the development of Yang-Mills theories [D. Gross: Twenty five years of asymptotic freedom, Nucl. Phys. (Proc. Suppl.) 74 (1999) 426, hep-ph/98, A. de Rujula: Fifty years of Yang-Mills theories: a phenomenological point of view, hep-ph/0404215, S. Weinberg: The Making of the Standard Model, Eur. Phys. J. C 34 (2004) 5]. The contribution of Weyl toward the concept of gauge invariance is discussed in [N. Straumann: Early Histrory of Gauge Theories and Weak Interactions, Invited talk at the PSI Summer School in Physics, Zuoz, Switzerland, August 1996].
Shear-free perfect fluids with zero magnetic Weyl tensor
International Nuclear Information System (INIS)
Collins, C.B.
1984-01-01
Rotating, shear-free general-relativistic perfect fluids are investigated. It is first shown that, if the fluid pressure, p, and energy density, μ, are related by a barotropic equation of state p = p( μ) satifying μ+pnot =0, and if the magnetic part of the Weyl tensor (with respect to the fluid flow) vanishes, then the fluid's volume expansion is zero. The class of all such fluids is subsequently characterized. Further analysis of the solutions shows that, in general, the space-times may be regarded as being locally stationary and axisymmetric (they admit a two-dimensional Abelian isometry group with timelike orbits, which is in fact orthogonally transistive), although various specializations can occur, with the ''most special'' case being the well-known Goedel model, which is space-time homogeneous (it admits a five-dimensional isometry group acting multiply transitively on the space-time). all solutions are of Petrov type D. The fact that there are any solutions in the class at all means that a theorem appearing in the literature is invalid, and the existence of some special solutions in which the fluid's vorticity vector is orthogonal to the acceleration reveals the incompleteness of a previous study of a class of space-times, in which there are Killing vectors parallel to the fluid four-velocity and to the vorticity vector
Euclidean supersymmetric solutions with the self-dual Weyl tensor
Directory of Open Access Journals (Sweden)
Masato Nozawa
2017-07-01
Full Text Available We explore the Euclidean supersymmetric solutions admitting the self-dual gauge field in the framework of N=2 minimal gauged supergravity in four dimensions. According to the classification scheme utilizing the spinorial geometry or the bilinears of Killing spinors, the general solution preserves one quarter of supersymmetry and is described by the Przanowski–Tod class with the self-dual Weyl tensor. We demonstrate that there exists an additional Killing spinor, provided the Przanowski–Tod metric admits a Killing vector that commutes with the principal one. The proof proceeds by recasting the metric into another Przanowski–Tod form. This formalism enables us to show that the self-dual Reissner–Nordström–Taub–NUT–AdS metric possesses a second Killing spinor, which has been missed over many years. We also address the supersymmetry when the Przanowski–Tod space is conformal to each of the self-dual ambi-toric Kähler metrics. It turns out that three classes of solutions are all reduced to the self-dual Carter family, by virtue of the nondegenerate Killing–Yano tensor.
Disorder effect on chiral edge modes and anomalous Hall conductance in Weyl semimetals
International Nuclear Information System (INIS)
Takane, Yositake
2016-01-01
Typical Weyl semimetals host chiral surface states and hence show an anomalous Hall response. Although a Weyl semimetal phase is known to be robust against weak disorder, the effect of disorder on chiral states has not been fully clarified so far. We study the behavior of such chiral states in the presence of disorder and its consequences on an anomalous Hall response, focusing on a thin slab of Weyl semimetal with chiral surface states along its edge. It is shown that weak disorder does not disrupt chiral edge states but crucially affects them owing to the renormalization of a mass parameter: the number of chiral edge states changes depending on the strength of disorder. It is also shown that the Hall conductance is quantized when the Fermi level is located near Weyl nodes within a finite-size gap. This quantization of the Hall conductance collapses once the strength of disorder exceeds a critical value, suggesting that it serves as a probe to distinguish a Weyl semimetal phase from a diffusive anomalous Hall metal phase. (author)
Klein-Weyl's program and the ontology of gauge and quantum systems
Catren, Gabriel
2018-02-01
We distinguish two orientations in Weyl's analysis of the fundamental role played by the notion of symmetry in physics, namely an orientation inspired by Klein's Erlangen program and a phenomenological-transcendental orientation. By privileging the former to the detriment of the latter, we sketch a group(oid)-theoretical program-that we call the Klein-Weyl program-for the interpretation of both gauge theories and quantum mechanics in a single conceptual framework. This program is based on Weyl's notion of a "structure-endowed entity" equipped with a "group of automorphisms". First, we analyze what Weyl calls the "problem of relativity" in the frameworks provided by special relativity, general relativity, and Yang-Mills theories. We argue that both general relativity and Yang-Mills theories can be understood in terms of a localization of Klein's Erlangen program: while the latter describes the group-theoretical automorphisms of a single structure (such as homogenous geometries), local gauge symmetries and the corresponding gauge fields (Ehresmann connections) can be naturally understood in terms of the groupoid-theoretical isomorphisms in a family of identical structures. Second, we argue that quantum mechanics can be understood in terms of a linearization of Klein's Erlangen program. This stance leads us to an interpretation of the fact that quantum numbers are "indices characterizing representations of groups" ((Weyl, 1931a), p.xxi) in terms of a correspondence between the ontological categories of identity and determinateness.
Chiral anomaly, dimensional reduction, and magnetoresistivity of Weyl and Dirac semimetals
Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.
2014-02-01
By making use of the Kubo formula, we calculate the conductivity of Dirac and Weyl semimetals in a magnetic field. We find that the longitudinal (along the direction of the magnetic field) magnetoresistivity is negative at sufficiently large magnetic fields for both Dirac and Weyl semimetals. The physical reason of this phenomenon is intimately connected with the dimensional spatial reduction 3→1 in the dynamics of the lowest Landau level. The off-diagonal component of the transverse (with respect to the direction of the magnetic field) conductivity in Weyl semimetals contains an anomalous contribution directly proportional to the momentum-space separation between the Weyl nodes. This contribution comes exclusively from the lowest Landau level and, as expected, is independent of the temperature, chemical potential, and magnetic field. The other part of the off-diagonal conductivity is the same as in Dirac semimetals and is connected with a nonzero density of charge carriers. The signatures for experimental distinguishing Weyl semimetals from Dirac ones through the measurements of conductivity are discussed.
Breakdown of the Chiral Anomaly in Weyl Semimetals in a Strong Magnetic Field
Kim, Pilkwang; Ryoo, Ji Hoon; Park, Cheol-Hwan
2017-12-01
The low-energy quasiparticles of Weyl semimetals are a condensed-matter realization of the Weyl fermions introduced in relativistic field theory. Chiral anomaly, the nonconservation of the chiral charge under parallel electric and magnetic fields, is arguably the most important phenomenon of Weyl semimetals and has been explained as an imbalance between the occupancies of the gapless, zeroth Landau levels with opposite chiralities. This widely accepted picture has served as the basis for subsequent studies. Here we report the breakdown of the chiral anomaly in Weyl semimetals in a strong magnetic field based on ab initio calculations. A sizable energy gap that depends sensitively on the direction of the magnetic field may open up due to the mixing of the zeroth Landau levels associated with the opposite-chirality Weyl points that are away from each other in the Brillouin zone. Our study provides a theoretical framework for understanding a wide range of phenomena closely related to the chiral anomaly in topological semimetals, such as magnetotransport, thermoelectric responses, and plasmons, to name a few.
Quantifying inhomogeneity in fractal sets
Fraser, Jonathan M.; Todd, Mike
2018-04-01
An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the ‘most difficult location and scale’ at which to cover the set and its difference from box dimension can be thought of as a first-level overall measure of how inhomogeneous the set is. For the next level of analysis, we develop a quantitative theory of inhomogeneity by considering the measure of the set of points around which the set exhibits a given level of inhomogeneity at a certain scale. For a set of examples, a family of -invariant subsets of the 2-torus, we show that this quantity satisfies a large deviations principle. We compare members of this family, demonstrating how the rate function gives us a deeper understanding of their inhomogeneity.
Fractal cartography of urban areas.
Encarnação, Sara; Gaudiano, Marcos; Santos, Francisco C; Tenedório, José A; Pacheco, Jorge M
2012-01-01
In a world in which the pace of cities is increasing, prompt access to relevant information is crucial to the understanding and regulation of land use and its evolution in time. In spite of this, characterization and regulation of urban areas remains a complex process, requiring expert human intervention, analysis and judgment. Here we carry out a spatio-temporal fractal analysis of a metropolitan area, based on which we develop a model which generates a cartographic representation and classification of built-up areas, identifying (and even predicting) those areas requiring the most proximate planning and regulation. Furthermore, we show how different types of urban areas identified by the model co-evolve with the city, requiring policy regulation to be flexible and adaptive, acting just in time. The algorithmic implementation of the model is applicable to any built-up area and simple enough to pave the way for the automatic classification of urban areas worldwide.
Model of fractal aggregates induced by shear
Directory of Open Access Journals (Sweden)
Wan Zhanhong
2013-01-01
Full Text Available It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.
A Parallel Approach to Fractal Image Compression
Lubomir Dedera
2004-01-01
The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
1000 Fractal Dimension and the Cantor Set
Indian Academy of Sciences (India)
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. GENERALARTICLES. 977 How did Cantor Discover Set Theory and Topology? S M Srivastava. 1000 Fractal Dimension and the Cantor Set. Shailesh A Shirali. 1005 Biofilms: Community Behavior by Bacteria. Vinita Shivakumar and ...
Nonlinear fractals: applications in physiology and ophthalmology
Directory of Open Access Journals (Sweden)
M. V. Zueva
2014-07-01
Full Text Available Fractal geometry and nonlinear dynamics have applications in the field of biology and medicine. Many complex structures of living systems reveal fractal-like geometry. Among them, nonlinearity of human anatomic structures and physiologic functions are of special interest. Here, we review several multidisciplinary studies that demonstrate multi-scale nonlinear complexity of physiological functions and fractal geometry of anatomical structures of a healthy human including retina. With ageing and diseases, these entities become simpler or more complex. Pathologic conditions contribute to highly periodic dynamics of processes that dominates on a time scale. Nonlinear dynamics application in ophthalmology and physiology of visual system can be promoted by the studies of fractal flickeringbackground and its impact on retina and visual cortex electrical activity. The next step will be the development of novel electrophysiological diagnostics and visual system impairment treatment
Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent Than Others?
Georgoulis, Manolis K.
2012-02-01
Multiple recent investigations of solar magnetic-field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17 733 magnetograms in total) observed by SOHO’s Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i) a widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii) a lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately, for major solar-flare prediction.
Heat kernels and zeta functions on fractals
International Nuclear Information System (INIS)
Dunne, Gerald V
2012-01-01
On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
Modelo fractal de substâncias húmicas Fractal model of humic substances
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Alessandro Costa da Silva
2001-10-01
Full Text Available A teoria fractal, por meio da determinação da dimensão fractal (D, tem sido considerada como uma alternativa para explicar a conforma��ão de agregados moleculares. Sua utilização no estudo de substâncias húmicas (SH reside na tentativa de descrever (representar a estrutura ramificada ou a superfície rugosa e distorcida destas substâncias. A presença de um modelo fractal por sistemas naturais implica que este pode ser decomposto em partes, em que cada uma, subseqüentemente, é cópia do todo. Do ponto de vista experimental, a dimensão fractal de sistemas húmicos pode ser determinada a partir de técnicas como turbidimetria, raios x, espalhamento de neutrons, dentre outras. Este trabalho pretende facilitar o entendimento sobre a aplicação de fractais ao estudo conformacional de SH, introduzindo conceitos e informações sobre o fundamento dos modelos fractais, bem como sobre o uso da técnica turbidimétrica na determinação do valor D.Fractal theoria application by determination of fractal dimension has been considered an alternative tool to explain the conformation of molecular aggregates. Its utilization in the study of humic substances (HS aims the attempt to describe the limbed structure or the rugous and distorced surface of these substances. The presence of fractal models indicates that the system may be decomposed in parts, each part being a copy of the whole. In the experimental point of view the fractals models of natural systems may be measured through techniques as turbidimetry, x- ray and neutrons scattering. This paper seeks to facilitate the understanding on the application of the fractals in the conformational study of HS, supply information about fractal models foundation and use of the turbidimetry in the determination of fractal dimension.
Pulse regime in formation of fractal fibers
Energy Technology Data Exchange (ETDEWEB)
Smirnov, B. M., E-mail: bmsmirnov@gmail.com [Joint Institute for High Temperatures (Russian Federation)
2016-11-15
The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gas flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.
Textural characterization of chars using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Mahamud, Manuel; Lopez, Oscar [Department of Chemical and Environmental Engineering, Faculty of Chemistry, University of Oviedo, Campus de El Cristo, 33071 Oviedo (Spain); Pis, Jose Juan; Pajares, Jesus Alberto [Instituto Nacional del Carbon C.S.I.C., Apartado 73, 33080 Oviedo (Spain)
2004-11-25
The aim of this study is to explore the potential of fractal analysis in helping to understand the textural changes of materials during the manufacture of active carbons. Textural characterization of the chars is carried out in order to obtain a better understanding of the phenomena underlying char formation. The materials selected for study were a series of chars obtained from coals oxidized in air at various temperatures for different periods of time. The data from mercury porosimetry were analyzed using fractal models. The average fractal dimensions for the chars were calculated by using the methods proposed by Friesen and Mikula and that of Zhang and Li. Fractal profiles of the chars obtained by the method of Neimark were compared with the corresponding fractal profiles of the precursor coals. Pore development during carbonization depends-among other factors that are kept constant in this study-on the textural properties of the precursor coal, the devolatilization process and the plastic properties of coals. The evolution of the fractal characteristics of the chars is also studied. At the same time pore volume development is analyzed. These analyses help to clarify the role that various phenomena occurring during carbonization have on the textural properties of the chars.
Evolution of an ensemble of fractal aggregates in a colloidal system
International Nuclear Information System (INIS)
Elfimova, E. A.; Zubarev, A. Yu.; Ivanov, A. O.
2006-01-01
A theoretical study is presented of primary-minimum aggregation of colloidal particles, which generally leads to the formation of ramified fractal clusters. The focus is placed on the cooperative effects due to competition between aggregates for particles moving freely in the colloidal suspension. An analysis shows that the competition leads to aggregate density distributions and aggregation kinetics governed by more complicated laws as compared to those established in previous numerical and analytical studies of single-cluster growth
Roy, Sthitadhi; Kolodrubetz, Michael; Goldman, Nathan; Grushin, Adolfo G.
2018-04-01
In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally dependent shifts of the corresponding Weyl momenta. First, we introduce two realistic models, inspired by recent cold-atom developments, which are particularly suitable for the exploration of these synthetic axial gauge fields. Second, we describe how to realize and measure the effects of such axial fields through center-of-mass observables, based on semiclassical equations of motion and exact numerical simulations. In particular, we suggest realistic protocols to reveal an axial Hall response due to the axial electric field \
On the Weyl anomaly of 4D conformal higher spins: a holographic approach
Acevedo, S.; Aros, R.; Bugini, F.; Diaz, D. E.
2017-11-01
We present a first attempt to derive the full (type-A and type-B) Weyl anomaly of four dimensional conformal higher spin (CHS) fields in a holographic way. We obtain the type-A and type-B Weyl anomaly coefficients for the whole family of 4D CHS fields from the one-loop effective action for massless higher spin (MHS) Fronsdal fields evaluated on a 5D bulk Poincaré-Einstein metric with an Einstein metric on its conformal boundary. To gain access to the type-B anomaly coefficient we assume, for practical reasons, a Lichnerowicz-type coupling of the bulk Fronsdal fields with the bulk background Weyl tensor. Remarkably enough, our holographic findings under this simplifying assumption are certainly not unknown: they match the results previously found on the boundary counterpart under the assumption of factorization of the CHS higher-derivative kinetic operator into Laplacians of "partially massless" higher spins on Einstein backgrounds.
Non-Weyl asymptotics for quantum graphs with general coupling conditions
International Nuclear Information System (INIS)
Davies, E Brian; Exner, Pavel; Lipovsky, JirI
2010-01-01
Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in the case of Kirchhoff or anti-Kirchhoff conditions. While for graphs without permutation symmetry numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight into what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with unequal edge weights.
Chiral anomaly, charge density waves, and axion strings from Weyl semimetals
Wang, Zhong; Zhang, Shou-Cheng
2013-04-01
We study dynamical instability and chiral symmetry breaking in three-dimensional Weyl semimetals, which turns Weyl semimetals into “axion insulators.” Charge density waves (CDWs) are found to be the natural consequence of chiral symmetry breaking. The phase mode of this charge density wave state is identified as the axion, which couples to an electromagnetic field in the topological θE·B term. One of our main results is that “axion strings” can be realized as the (screw or edge) dislocations in the charge density wave, which provides a simple physical picture for the elusive axion strings. These axion strings carry gapless chiral modes, therefore they have important implications for dissipationless transport properties of Weyl semimetals with broken symmetry.
Zheng, Hao; Xu, Su-Yang; Bian, Guang; Guo, Cheng; Chang, Guoqing; Sanchez, Daniel S; Belopolski, Ilya; Lee, Chi-Cheng; Huang, Shin-Ming; Zhang, Xiao; Sankar, Raman; Alidoust, Nasser; Chang, Tay-Rong; Wu, Fan; Neupert, Titus; Chou, Fangcheng; Jeng, Horng-Tay; Yao, Nan; Bansil, Arun; Jia, Shuang; Lin, Hsin; Hasan, M Zahid
2016-01-26
Weyl semimetals may open a new era in condensed matter physics, materials science, and nanotechnology after graphene and topological insulators. We report the first atomic scale view of the surface states of a Weyl semimetal (NbP) using scanning tunneling microscopy/spectroscopy. We observe coherent quantum interference patterns that arise from the scattering of quasiparticles near point defects on the surface. The measurements reveal the surface electronic structure both below and above the chemical potential in both real and reciprocal spaces. Moreover, the interference maps uncover the scattering processes of NbP's exotic surface states. Through comparison between experimental data and theoretical calculations, we further discover that the orbital and/or spin texture of the surface bands may suppress certain scattering channels on NbP. These results provide a comprehensive understanding of electronic properties on Weyl semimetal surfaces.
Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials.
Hübener, Hannes; Sentef, Michael A; De Giovannini, Umberto; Kemper, Alexander F; Rubio, Angel
2017-01-17
Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na 3 Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet-Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.
Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP.
Arnold, Frank; Shekhar, Chandra; Wu, Shu-Chun; Sun, Yan; Dos Reis, Ricardo Donizeth; Kumar, Nitesh; Naumann, Marcel; Ajeesh, Mukkattu O; Schmidt, Marcus; Grushin, Adolfo G; Bardarson, Jens H; Baenitz, Michael; Sokolov, Dmitry; Borrmann, Horst; Nicklas, Michael; Felser, Claudia; Hassinger, Elena; Yan, Binghai
2016-05-17
Weyl semimetals (WSMs) are topological quantum states wherein the electronic bands disperse linearly around pairs of nodes with fixed chirality, the Weyl points. In WSMs, nonorthogonal electric and magnetic fields induce an exotic phenomenon known as the chiral anomaly, resulting in an unconventional negative longitudinal magnetoresistance, the chiral-magnetic effect. However, it remains an open question to which extent this effect survives when chirality is not well-defined. Here, we establish the detailed Fermi-surface topology of the recently identified WSM TaP via combined angle-resolved quantum-oscillation spectra and band-structure calculations. The Fermi surface forms banana-shaped electron and hole pockets surrounding pairs of Weyl points. Although this means that chirality is ill-defined in TaP, we observe a large negative longitudinal magnetoresistance. We show that the magnetoresistance can be affected by a magnetic field-induced inhomogeneous current distribution inside the sample.
Nonsymmorphic Weyl superconductivity in UPt3 based on E2 u representation
Yanase, Youichi
2016-11-01
We show that a heavy fermion superconductor UPt3 is a topological Weyl superconductor with tunable Weyl nodes. Adopting a generic order parameter in the E2 u representation allowed by nonsymmorphic crystal symmetry, we clarify unusual gap structure and associated topological properties. The pair creation, pair annihilation, and coalescence of Weyl nodes are demonstrated in the time-reversal symmetry broken B-phase. At most 98 point nodes compatible with Blount's theorem give rise to line-node-like behaviors in low-energy excitations, consistent with experimental results. We also show an arc node protected by the nonsymmorphic crystal symmetry on the Brillouin zone face, which is a counterexample of Blount's theorem.
Band structures in fractal grading porous phononic crystals
Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin
2018-05-01
In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.
The utility of fractal analysis in clinical neuroscience.
John, Ann M; Elfanagely, Omar; Ayala, Carlos A; Cohen, Michael; Prestigiacomo, Charles J
2015-01-01
Physicians and scientists can use fractal analysis as a tool to objectively quantify complex patterns found in neuroscience and neurology. Fractal analysis has the potential to allow physicians to make predictions about clinical outcomes, categorize pathological states, and eventually generate diagnoses. In this review, we categorize and analyze the applications of fractal theory in neuroscience found in the literature. We discuss how fractals are applied and what evidence exists for fractal analysis in neurodegeneration, neoplasm, neurodevelopment, neurophysiology, epilepsy, neuropharmacology, and cell morphology. The goal of this review is to introduce the medical community to the utility of applying fractal theory in clinical neuroscience.
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.
Computer simulation of microwave propagation in heterogeneous and fractal media
Korvin, Gabor; Khachaturov, Ruben V.; Oleschko, Klaudia; Ronquillo, Gerardo; Correa López, María de jesús; García, Juan-josé
2017-03-01
Maxwell's equations (MEs) are the starting point for all calculations involving surface or borehole electromagnetic (EM) methods in Petroleum Industry. In well-log analysis numerical modeling of resistivity and induction tool responses has became an indispensable step of interpretation. We developed a new method to numerically simulate electromagnetic wave propagation through heterogeneous and fractal slabs taking into account multiple scattering in the direction of normal incidence. In simulation, the gray-scale image of the porous medium is explored by monochromatic waves. The gray-tone of each pixel can be related to the dielectric permittivity of the medium at that point by two different equations (linear dependence, and fractal or power law dependence). The wave equation is solved in second order difference approximation, using a modified sweep technique. Examples will be shown for simulated EM waves in carbonate rocks imaged at different scales by electron microscopy and optical photography. The method has wide ranging applications in remote sensing, borehole scanning and Ground Penetrating Radar (GPR) exploration.
TRANSIENT CHAOS AND FRACTAL STRUCTURES IN PLANETARY FEEDING ZONES
Energy Technology Data Exchange (ETDEWEB)
Kovács, T. [Also at University of Applied Sciences, Nagy Lajos kir. útja 1-9, H-1148 Budapest, Hungary. (Hungary); Regály, Zs. [Konkoly Observatory of the Hungarian Academy of Sciences, P.O. Box 67, H-1525 Budapest (Hungary)
2015-01-01
The circular restricted three-body problem is investigated in the context of accretion and scattering processes. In our model, a large number of identical non-interacting mass-less planetesimals are considered in the planar case orbiting a star-planet system. This description allows us to investigate the gravitational scattering and possible capture of the particles by the forming planetary embryo in a dynamical systems approach. Although the problem serves a large variety of complex motions, the results can be easily interpreted because of the low dimensionality of the phase space. We show that initial conditions define isolated regions of the disk, where planetesimals accrete or escape, which have, in fact, a fractal structure. The fractal geometry of these ''basins'' implies that the dynamics is very complex. Based on the calculated escape rates and escape times, it is also demonstrated that the planetary accretion rate is exponential for short times and follows a power law for longer integration. A new numerical calculation of the maximum mass that a planet can reach (described by the expression of the isolation mass) is also derived.
International Nuclear Information System (INIS)
Bender, B.; Sparwasser, R.
1988-01-01
Environmental law is discussed exhaustively in this book. Legal and scientific fundamentals are taken into account, a systematic orientation is given, and hints for further information are presented. The book covers general environmental law, plan approval procedures, protection against nuisances, atomic law and radiation protection law, water protection law, waste management law, laws on chemical substances, conservation law. (HSCH) [de
International Nuclear Information System (INIS)
Chen Yanguang
2009-01-01
A pair of nonlinear programming models is built to explain the fractal structure of systems of cities and those of rivers. The hierarchies of cities can be characterized by a set of exponential functions, which is identical in form to the Horton-Strahler's laws of the river networks. Four power laws can be derived from these exponential functions. The evolution of both systems of cities and rivers are then represented as nonlinear dual programming models: to maximize information entropy subject to a certain energy use or to minimize energy dissipation subject to certain information capacity. The optimal solutions of the programming problems are just the exponential equations associated with scaling relations. By doing so, fractals and the self-organized criticality marked by the power laws are interpreted using the idea from the entropy-maximization principle, which gives further weight to the suggestion that optimality of the system as a whole defines the dynamical origin of fractal forms in both nature and society.
Methods of Weyl representation of the phase space and canonical transformations. 1
International Nuclear Information System (INIS)
Budanov, V.G.
1984-01-01
The kernel structure of canonical transformation and differential equation for the intertwining operator is found. The Weyl symbol of operators producing linear canonical transformations is associated with the Cayley transformation of classical canonical transformation. Due to the invariance of the Weyl formalism a complete study of singularity and factorization of these symbols is manageable. In particular, one can study the symbols of Green functions and elements of Lie groups and find the spectra of arbitrary stationary quadratic Hamiltonians with the help of the known classification of the spectra of classical systems
Dynamic current-current susceptibility in three-dimensional Dirac and Weyl semimetals
Thakur, Anmol; Sadhukhan, Krishanu; Agarwal, Amit
2018-01-01
We study the linear response of doped three-dimensional Dirac and Weyl semimetals to vector potentials, by calculating the wave-vector- and frequency-dependent current-current response function analytically. The longitudinal part of the dynamic current-current response function is then used to study the plasmon dispersion and the optical conductivity. The transverse response in the static limit yields the orbital magnetic susceptibility. In a Weyl semimetal, along with the current-current response function, all these quantities are significantly impacted by the presence of parallel electric and magnetic fields (a finite E .B term) and can be used to experimentally explore the chiral anomaly.
Weyl fermions in a family of Gödel-type geometries with a topological defect
Garcia, G. Q.; Oliveira, J. R. De S.; Furtado, C.
In this paper, we study Weyl fermions in a family of Gödel-type geometries in Einstein general relativity. We also consider that these solutions are embedded in a topological defect background. We solve the Weyl equation and find the energy eigenvalues and eigenspinors for all three cases of Gödel-type geometries where a topological defect is passing through them. We show that the presence of a topological defect in these geometries contributes to the modification of the spectrum of energy. The energy zero modes for all three cases of the Gödel geometries are discussed.
Fractal Dimension in Epileptic EEG Signal Analysis
Uthayakumar, R.
Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include
International Nuclear Information System (INIS)
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-01-01
Highlights: • Fractal theory is introduced into the prediction of VOC diffusion coefficient. • MSFC model of the diffusion coefficient is developed for porous building materials. • The MSFC model contains detailed pore structure parameters. • The accuracy of the MSFC model is verified by independent experiments. - Abstract: Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.
Energy Technology Data Exchange (ETDEWEB)
Liu, Yanfeng, E-mail: lyfxjd@163.com; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-12-15
Highlights: • Fractal theory is introduced into the prediction of VOC diffusion coefficient. • MSFC model of the diffusion coefficient is developed for porous building materials. • The MSFC model contains detailed pore structure parameters. • The accuracy of the MSFC model is verified by independent experiments. - Abstract: Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.
Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis
Metze, Konradin
2013-01-01
Fractal characteristics of chromatin, revealed by light or electron microscopy, have been reported during the last 20 years. Fractal features can easily be estimated in digitalized microscopic images and are helpful for diagnosis and prognosis of neoplasias. During carcinogenesis and tumor progression, an increase of the fractal dimension (FD) of stained nuclei has been shown in intraepithelial lesions of the uterine cervix and the anus, oral squamous cell carcinomas or adenocarcinomas of the pancreas. Furthermore, an increased FD of chromatin is an unfavorable prognostic factor in squamous cell carcinomas of the oral cavity and the larynx, melanomas and multiple myelomas. High goodness-of-fit of the regression line of the FD is a favorable prognostic factor in acute leukemias and multiple myelomas. The nucleus has fractal and power-law organization in several different levels, which might in part be interrelated. Some possible relations between modifications of the chromatin organization during carcinogenesis and tumor progression and an increase of the FD of stained chromatin are suggested. Furthermore, increased complexity of the chromatin structure, loss of heterochromatin and a less-perfect self-organization of the nucleus in aggressive neoplasias are discussed. PMID:24063399
Favela, Luis H; Coey, Charles A; Griff, Edwin R; Richardson, Michael J
2016-07-28
The present work used fractal time series analysis (detrended fluctuation analysis; DFA) to examine the spontaneous activity of single neurons in an anesthetized animal model, specifically, the mitral cells in the rat main olfactory bulb. DFA bolstered previous research in suggesting two subclasses of mitral cells. Although there was no difference in the fractal scaling of the interspike interval series at the shorter timescales, there was a significant difference at longer timescales. Neurons in Group B exhibited fractal, power-law scaled interspike intervals, whereas neurons in Group A exhibited random variation. These results raise questions about the role of these different cells within the olfactory bulb and potential explanations of their dynamics. Specifically, self-organized criticality has been proposed as an explanation of fractal scaling in many natural systems, including neural systems. However, this theory is based on certain assumptions that do not clearly hold in the case of spontaneous neural activity, which likely reflects intrinsic cell dynamics rather than activity driven by external stimulation. Moreover, it is unclear how self-organized criticality might account for the random dynamics observed in Group A, and how these random dynamics might serve some functional role when embedded in the typical activity of the olfactory bulb. These theoretical considerations provide direction for additional experimental work. Published by Elsevier Ireland Ltd.
A Fractal Approach to Dynamic Inference and Distribution Analysis
Directory of Open Access Journals (Sweden)
Marieke M.J.W. van Rooij
2013-01-01
Full Text Available Event-distributions inform scientists about the variability and dispersion of repeated measurements. This dispersion can be understood from a complex systems perspective, and quantified in terms of fractal geometry. The key premise is that a distribution’s shape reveals information about the governing dynamics of the system that gave rise to the distribution. Two categories of characteristic dynamics are distinguished: additive systems governed by component-dominant dynamics and multiplicative or interdependent systems governed by interaction-dominant dynamics. A logic by which systems governed by interaction-dominant dynamics are expected to yield mixtures of lognormal and inverse power-law samples is discussed. These mixtures are described by a so-called cocktail model of response times derived from human cognitive performances. The overarching goals of this article are twofold: First, to offer readers an introduction to this theoretical perspective and second, to offer an overview of the related statistical methods.
From dendrimers to fractal polymers and beyond
Directory of Open Access Journals (Sweden)
Charles N. Moorefield
2013-01-01
Full Text Available The advent of dendritic chemistry has facilitated materials research by allowing precise control of functional component placement in macromolecular architecture. The iterative synthetic protocols used for dendrimer construction were developed based on the desire to craft highly branched, high molecular weight, molecules with exact mass and tailored functionality. Arborols, inspired by trees and precursors of the utilitarian macromolecules known as dendrimers today, were the first examples to employ predesigned, 1 → 3 C-branched, building blocks; physical characteristics of the arborols, including their globular shapes, excellent solubilities, and demonstrated aggregation, combined to reveal the inherent supramolecular potential (e.g., the unimolecular micelle of these unique species. The architecture that is a characteristic of dendritic materials also exhibits fractal qualities based on self-similar, repetitive, branched frameworks. Thus, the fractal design and supramolecular aspects of these constructs are suggestive of a larger field of fractal materials that incorporates repeating geometries and are derived by complementary building block recognition and assembly. Use of terpyridine-M2+-terpyridine (where, M = Ru, Zn, Fe, etc connectivity in concert with mathematical algorithms, such as forms the basis for the Seirpinski gasket, has allowed the beginning exploration of fractal materials construction. The propensity of the fractal molecules to self-assemble into higher order architectures adds another dimension to this new arena of materials and composite construction.
Multirate diversity strategy of fractal modulation
International Nuclear Information System (INIS)
Yuan Yong; Shi Si-Hong; Luo Mao-Kang
2011-01-01
Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters are unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment. (general)
Rheological and fractal hydrodynamics of aerobic granules.
Tijani, H I; Abdullah, N; Yuzir, A; Ujang, Zaini
2015-06-01
The structural and hydrodynamic features for granules were characterized using settling experiments, predefined mathematical simulations and ImageJ-particle analyses. This study describes the rheological characterization of these biologically immobilized aggregates under non-Newtonian flows. The second order dimensional analysis defined as D2=1.795 for native clusters and D2=1.099 for dewatered clusters and a characteristic three-dimensional fractal dimension of 2.46 depicts that these relatively porous and differentially permeable fractals had a structural configuration in close proximity with that described for a compact sphere formed via cluster-cluster aggregation. The three-dimensional fractal dimension calculated via settling-fractal correlation, U∝l(D) to characterize immobilized granules validates the quantitative measurements used for describing its structural integrity and aggregate complexity. These results suggest that scaling relationships based on fractal geometry are vital for quantifying the effects of different laminar conditions on the aggregates' morphology and characteristics such as density, porosity, and projected surface area. Copyright © 2015 Elsevier Ltd. All rights reserved.
Fractal dimensions of spatial digital noise by scintillation camera
International Nuclear Information System (INIS)
Iwata, Kazuro; Hamada, Nobuo; Sumita, Mitsugu; Ueda, Suguru
1987-01-01
The fractal dimensions of the spatial digital noise by scintillation camera were measured under the various conditions. It was found that fractal dimension decreases with increasing total counts, and that fractal dimension by the point source is larger than that by the collimated plane source. When a simple pattern is added to the spatial noise, the fractal dimension decreases and is separated into two components. (Auth.)
Lau, Alexander; Ortix, Carmine
2017-01-01
We propose a different route to time-reversal invariant Weyl semimetals employing multilayer heterostructures comprising ordinary "trivial" insulators and nontrivial insulators with \\textit{pairs} of protected Dirac cones on the surface. We consider both the case of weak topological insualtors,
Resistivity of Weyl semimetals NbP and TaP under pressure
Energy Technology Data Exchange (ETDEWEB)
Einaga, M.; Shimizu, K. [KYOKUGEN, Graduate School of Engineering Science, Osaka University, Toyonaka (Japan); Hu, J.; Mao, Z.Q. [Department of Physics and Engineering Physics, Tulane University, New Orleans, LA (United States); Politano, A. [Fondazione Istituto Italiano di Tecnologia, Graphene Labs, Genova (Italy)
2017-08-15
The resistivity of Weyl semimetals NbP and TaP has been investigated as a function of pressure and temperature. The behaviour of the resistivity as a function of pressure and temperature is closely correlated to the location of the Weyl points compared to the Fermi energy. The rapid increase of the resistivity in TaP and NbP under the application of 4.5 and 8.0 GPa is related with the shift of Weyl points, which affords a finite density of states near the Fermi energy. Specifically, we find that under pressure the Weyl points are situated above the Fermi energy. As regards the temperature behaviour, we detect a nonmonotonous behaviour of resistivity in TaP at 8.7 and 9.8 GPa as a function of temperature, whereas in the case of NbP the behaviour is more complicate. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Magneto-optic measurements of the Weyl semimetal NbAs
Armstrong, Nathan; Shao, Yinming; Yuan, Zhujun; Jia, Shuang; Basov, D. N.; Timusk, Thomas
NbAs is among the newly discovered Weyl semimetals that are of great interest because they have the potential to confirm the chiral anomaly predicted by particle physics. It has been theorized that two separated Weyl nodes of opposite chirality can have a chiral current flow between them with the application electric and magnetic fields parallel to the displacement of the nodes. Indeed, magnetoresistance measurements on TaAs and NbAs found a negative magnetoresistance with these fields. ARPES and band structure calculations show that NbAs has two different groups of Weyl nodes with all the node splittings in kx -ky planes. In addition to the Weyl nodes there are other trivial bands that create Fermi pockets elsewhere in the BZ that are also observed in reflectance measurements. We will present magneto-optics results from far infrared optical data of NbAs in Voigt geometry up to 8 Tesla. In the far infrared at large fields there are two strong features that show an 11% and 3% change of reflectance in field at 60 and 480 cm-1 , respectively. We evaluate these data with comparison to the above mentioned band structure of NbAs.
A noncompact Weyl-Einstein-Yang-Mills model: A semiclassical quantum gravity
Dengiz, Suat
2017-08-01
We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a 3 + 1-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus SU(N) phase invariant Higgs-like field,conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable vacua. The model is unitary in de Sitter and flat vacua around which a massless graviton, N2 - 1 massless scalar bosons, N massless Dirac fermions, N2 - 1 Proca-type massive Abelian and non-Abelian vector bosons are generically propagated.
Weyl-Heisenberg frames, translation invariant systems, and the Walnut representation
DEFF Research Database (Denmark)
Casazza, P.G.; Christensen, Ole; Janssen, A. J. E. M.
2001-01-01
We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation. We give a deep analysis of necessary conditions and sufficient conditions for converge...
Optical signature of Weyl electronic structures in tantalum pnictides Ta P n (P n = P, As)
Kimura, Shin-ichi; Yokoyama, Hiroko; Watanabe, Hiroshi; Sichelschmidt, Jörg; Süß, Vicky; Schmidt, Marcus; Felser, Claudia
2017-08-01
To investigate the electronic structure of Weyl semimetals Ta P n (P n = P, As), optical conductivity [σ (ω )] spectra are measured over a wide range of photon energies and temperatures, and these measured values are compared with band calculations. Two significant structures can be observed: a bending structure at ℏ ω ˜85 meV in TaAs, and peaks at ℏ ω ˜ 50 meV (TaP) and ˜30 meV (TaAs). The bending structure can be explained by the interband transition between saddle points connecting a set of W2 Weyl points. The temperature dependence of the peak intensity can be fitted by assuming the interband transition between saddle points connecting a set of W1 Weyl points. Owing to the different temperature dependence of the Drude weight in both materials, it is found that the Weyl points of TaAs are located near the Fermi level, whereas those of TaP are further away.
Large anomalous magnetic moment in three-dimensional Dirac and Weyl semimetals
Van Der Wurff, E. C I; Stoof, H. T C
2016-01-01
We investigate the effect of Coulomb interactions on the electromagnetic response of three-dimensional Dirac and Weyl semimetals. In a calculation reminiscent of Schwinger's seminal work on quantum electrodynamics, we find three physically distinct effects for the anomalous magnetic moment of the
Momani, Shaher; Ibrahim, Rabha W.
2008-03-01
In this paper, we study the existence of periodic solutions for a nonlinear integral equation of periodic functions involving Weyl-Riesz fractional integral operator under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions. The fixed point theorems due to Dhage are the main tool in carrying out our proofs.
Remarks on an equation common to Weyl's gauge field, Yang-Mills field and Toda lattice
International Nuclear Information System (INIS)
Nishioka, M.
1984-01-01
In this letter a remark is presented on an equation of a gauge-invariant Weyl's gauge field and it is shown that the equation is common to Yang's approach to the self-duality condition for SU 2 gauge field and the simplest Toda lattice
Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators
International Nuclear Information System (INIS)
Zielinski, Lech
2006-01-01
We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hoelder continuous derivatives of first order
Chiral Anomaly from Strain-Induced Gauge Fields in Dirac and Weyl Semimetals
Directory of Open Access Journals (Sweden)
D. I. Pikulin
2016-10-01
Full Text Available Dirac and Weyl semimetals form an ideal platform for testing ideas developed in high-energy physics to describe massless relativistic particles. One such quintessentially field-theoretic idea of the chiral anomaly already resulted in the prediction and subsequent observation of the pronounced negative magnetoresistance in these novel materials for parallel electric and magnetic fields. Here, we predict that the chiral anomaly occurs—and has experimentally observable consequences—when real electromagnetic fields E and B are replaced by strain-induced pseudo-electromagnetic fields e and b. For example, a uniform pseudomagnetic field b is generated when a Weyl semimetal nanowire is put under torsion. In accordance with the chiral anomaly equation, we predict a negative contribution to the wire resistance proportional to the square of the torsion strength. Remarkably, left- and right-moving chiral modes are then spatially segregated to the bulk and surface of the wire forming a “topological coaxial cable.” This produces hydrodynamic flow with potentially very long relaxation time. Another effect we predict is the ultrasonic attenuation and electromagnetic emission due to a time-periodic mechanical deformation causing pseudoelectric field e. These novel manifestations of the chiral anomaly are most striking in the semimetals with a single pair of Weyl nodes but also occur in Dirac semimetals such as Cd_{3}As_{2} and Na_{3}Bi and Weyl semimetals with unbroken time-reversal symmetry.
Chiral Anomaly from Strain-Induced Gauge Fields in Dirac and Weyl Semimetals
Pikulin, D. I.; Chen, Anffany; Franz, M.
2016-10-01
Dirac and Weyl semimetals form an ideal platform for testing ideas developed in high-energy physics to describe massless relativistic particles. One such quintessentially field-theoretic idea of the chiral anomaly already resulted in the prediction and subsequent observation of the pronounced negative magnetoresistance in these novel materials for parallel electric and magnetic fields. Here, we predict that the chiral anomaly occurs—and has experimentally observable consequences—when real electromagnetic fields E and B are replaced by strain-induced pseudo-electromagnetic fields e and b . For example, a uniform pseudomagnetic field b is generated when a Weyl semimetal nanowire is put under torsion. In accordance with the chiral anomaly equation, we predict a negative contribution to the wire resistance proportional to the square of the torsion strength. Remarkably, left- and right-moving chiral modes are then spatially segregated to the bulk and surface of the wire forming a "topological coaxial cable." This produces hydrodynamic flow with potentially very long relaxation time. Another effect we predict is the ultrasonic attenuation and electromagnetic emission due to a time-periodic mechanical deformation causing pseudoelectric field e . These novel manifestations of the chiral anomaly are most striking in the semimetals with a single pair of Weyl nodes but also occur in Dirac semimetals such as Cd3 As2 and Na3Bi and Weyl semimetals with unbroken time-reversal symmetry.
Semiclassical Weyl Formula for a Class of Weakly Regular Elliptic Operators
Energy Technology Data Exchange (ETDEWEB)
Zielinski, Lech [Universite du Littoral, LMPA, Centre Mi-Voix (France)], E-mail: Lech.Zielinski@lmpa.univ-littoral.fr
2006-02-15
We investigate the semiclassical Weyl formula describing the asymptotic behaviour of the counting function for the number of eigenvalues in the case of self-adjoint elliptic differential operators satisfying weak regularity hypotheses. We consider symbols with possible critical points and with coefficients which have Hoelder continuous derivatives of first order.
The bicovariant differential calculus on the κ-Poincare and κ-Weyl groups
International Nuclear Information System (INIS)
Przanowski, K.
1997-01-01
The bicovariant differential calculus on four-dimensional κ-Poincare group and corresponding Lie-algebra-like structure for any metric tensor are described. The bicovariant differential calculus on four-dimensional κ-Weyl group and corresponding Lie-algebra-like structure for any metric tensor in the reference frame in which g 00 = 0 are considered. (author). 6 refs
Weyl-van der Waerden spinor technic for spin-3/2 fermions
International Nuclear Information System (INIS)
Novaes, S.F.; Spehler, D.
1991-09-01
We use the Weyl-van der Waerden spinor technic to construct helicity wave functions for massless and massive spin-3/2 fermions. We apply our formalism to evaluate helicity amplitudes taking into account some phenomenological couplings involving these particles. (author)
Generalized Warburg impedance on realistic self-affine fractals ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals.
Fractals and the irreducibility of consciousness in plants and animals.
Gardiner, John
2013-08-01
In both plants and animals consciousness is fractal. Since fractals can only pass information in one direction it is impossible to extrapolate backward to find the rule that governs the fractal. Thus, similarly, it will be impossible to completely determine the rule or rules that govern consciousness.
Investigation into How 8th Grade Students Define Fractals
Karakus, Fatih
2015-01-01
The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…
Generalized Warburg impedance on realistic self-affine fractals
Indian Academy of Sciences (India)
We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals. The information about the ...
Monitoring of dry sliding wear using fractal analysis
Zhang, Jindang; Regtien, Paulus P.L.; Korsten, Maarten J.
2005-01-01
Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power
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
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.
International Nuclear Information System (INIS)
Smitha, K A; Gupta, A K; Jayasree, R S
2015-01-01
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades. (paper)
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-07
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades.
Lifshitz Transitions, Type-II Dirac and Weyl Fermions, Event Horizon and All That
Volovik, G. E.; Zhang, K.
2017-12-01
The type-II Weyl and type-II Dirac points emerge in semimetals and also in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. In this case the horizon with Painlevé-Gullstrand metric serves as the surface of the Lifshitz transition. This relativistic analogy allows us to simulate the black hole horizon and Hawking radiation using the fermionic superfluid with supercritical velocity, and the Dirac and Weyl semimetals with the interface separating the type-I and type-II states. The difference between such type of the artificial event horizon and that which arises in acoustic metric is discussed. At the Lifshitz transition between type-I and type-II fermions the Dirac lines may also emerge, which are supported by the combined action of topology and symmetry. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. Different configurations of the Fermi surfaces, involved in such Lifshitz transition, are discussed. In one case the type-II Weyl point connects the Fermi pockets and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition the Weyl point is released from both Fermi surfaces. They loose their Berry flux, which guarantees the global stability, and without the topological support the inner surface disappears after shrinking to a point at the second Lifshitz transition. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds. For the interacting electrons, the Lifshitz transitions may lead to the formation of the dispersionless (flat) band with zero energy and singular density of states, which opens the route to room
A fractal-based image encryption system
Abd-El-Hafiz, S. K.
2014-12-01
This study introduces a novel image encryption system based on diffusion and confusion processes in which the image information is hidden inside the complex details of fractal images. A simplified encryption technique is, first, presented using a 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 through several parameters: feedback delay, multiplexing and independent horizontal or vertical shifts. The effect of each parameter is studied separately and, then, they are combined to illustrate their influence on the encryption quality. The encryption quality is evaluated using different analysis techniques such as correlation coefficients, differential attack measures, histogram distributions, key sensitivity analysis and the National Institute of Standards and Technology (NIST) statistical test suite. The obtained results show great potential compared to other techniques.
Retinal fractals and acute lacunar stroke.
Cheung, Ning; Liew, Gerald; Lindley, Richard I; Liu, Erica Y; Wang, Jie Jin; Hand, Peter; Baker, Michelle; Mitchell, Paul; Wong, Tien Y
2010-07-01
This study aimed to determine whether retinal fractal dimension, a quantitative measure of microvascular branching complexity and density, is associated with lacunar stroke. A total of 392 patients presenting with acute ischemic stroke had retinal fractal dimension measured from digital photographs, and lacunar infarct ascertained from brain imaging. After adjusting for age, gender, and vascular risk factors, higher retinal fractal dimension (highest vs lowest quartile and per standard deviation increase) was independently and positively associated with lacunar stroke (odds ratio [OR], 4.27; 95% confidence interval [CI], 1.49-12.17 and OR, 1.85; 95% CI, 1.20-2.84, respectively). Increased retinal microvascular complexity and density is associated with lacunar stroke.
Dynamic structure factor of vibrating fractals.
Reuveni, Shlomi; Klafter, Joseph; Granek, Rony
2012-02-10
Motivated by novel experimental work and the lack of an adequate theory, we study the dynamic structure factor S(k,t) of large vibrating fractal networks at large wave numbers k. We show that the decay of S(k,t) is dominated by the spatially averaged mean square displacement of a network node, which evolves subdiffusively in time, ((u[over →](i)(t)-u[over →](i)(0))(2))∼t(ν), where ν depends on the spectral dimension d(s) and fractal dimension d(f). As a result, S(k,t) decays as a stretched exponential S(k,t)≈S(k)e(-(Γ(k)t)(ν)) with Γ(k)∼k(2/ν). Applications to a variety of fractal-like systems are elucidated.
Chaos, fractals, and our concept of disease.
Varela, Manuel; Ruiz-Esteban, Raul; Mestre de Juan, Maria Jose
2010-01-01
The classic anatomo-clinic paradigm based on clinical syndromes is fraught with problems. Nevertheless, for multiple reasons, clinicians are reluctant to embrace a more pathophysiological approach, even though this is the prevalent paradigm under "which basic sciences work. In recent decades, nonlinear dynamics ("chaos theory") and fractal geometry have provided powerful new tools to analyze physiological systems. However, these tools are embedded in the pathophysiological perspective and are not easily translated to our classic syndromes. This article comments on the problems raised by the conventional anatomo-clinic paradigm and reviews three areas in which the influence of nonlinear dynamics and fractal geometry can be especially prominent: disease as a loss of complexity, the idea of homeostasis, and fractals in pathology.
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.
Computer Security: The dilemma of fractal defence
Stefan Lueders, Computer Security Team
2015-01-01
Aren’t mathematical fractals just beautiful? The Mandelbrot set and the Julia set, the Sierpinski gasket, the Menger sponge, the Koch curve (see here)… Based on very simple mathematical rules, they quickly develop into a mosaic of facets slightly different from each other. More and more features appear the closer you zoom into a fractal and expose similar but not identical features of the overall picture. Computer security is like these fractals, only much less pretty: simple at first glance, but increasingly complex and complicated when you look more closely at the details. The deeper you dig, the more and more possibilities open up for malicious people as the attack surface grows, just like that of “Koch’s snowflakes”, where the border length grows exponentially. Consequently, the defensive perimeter also increases when we follow the bits and bytes layer by layer from their processing in the CPU, trickling up the software stack thro...
Casimir effect due to a single boundary as a manifestation of the Weyl problem
Kolomeisky, Eugene B.; Straley, Joseph P.; Langsjoen, Luke S.; Zaidi, Hussain
2010-09-01
The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases, the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary, we explore the relationship between such approaches, with the goal of better understanding of the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978 J. Phys. A: Math. Gen. 11 895) and Deutsch and Candelas (1979 Phys. Rev. D 20 3063) that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases, the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having a geometrical origin, and an 'intrinsic' term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff and a non-geometrical intrinsic term. As by-products, we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.
Directory of Open Access Journals (Sweden)
Potapov A. A.
2008-10-01
Full Text Available Main results of theoretical and experimental investigations since eighties of XX that led to formation and developing of new fundamental science discipline: “Fractal Radio Physics and Fractal Radio Electronics: Fractal Radio Systems Designing” are briefly classified in the paper.
The virtual education fractality: nature and organization
Directory of Open Access Journals (Sweden)
Osbaldo Turpo Gebera
2013-04-01
Full Text Available The potential generated by ICT in education raises reflect on the underlying frameworks. In this sense, the fractal is an opportunity to explain how it organizes and manages virtual education.This approach recognizes that educational dynamics are recursive and iterative processes instituted as progressive sequences, by way of fractals. This understanding enables becoming as mediated and articulated successive levels. In each dimension are embodied own activities and in turn, involves the recurrence of subsequent levels as possible solving of problem situations. Thus, the knowledge built in response to a collaborative action, participation in networks, ranging from autonomous to the cultural level or conversely.
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
Random walk statistics on fractal structures
Rammal, R.
1984-09-01
We consider some statistical properties of simple random walks on fractal structures viewed as networks of sites and bonds: range, renewal theory, mean first passage time, etc. Asymptotic behaviors are shown to be controlled by the fractal ( ¯d) and spectral ( ¯d) dimensionalities of the considered structure. A simple decimation procedure giving the value of ( ¯d) is outlined and illustrated in the case of the Sierpinski gaskets. Recent results for the trapping problem, the self-avoiding walk, and the true-self-avoiding walk are briefly reviewed. New numerical results for diffusion on percolation clusters are also presented.
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
Capillary pressure in a porous medium with distinct pore surface and pore volume fractal dimensions.
Deinert, M R; Dathe, A; Parlange, J-Y; Cady, K B
2008-02-01
The relationship between capillary pressure and saturation in a porous medium often exhibits a power-law dependence. The physical basis for this relation has been substantiated by assuming that capillary pressure is directly related to the pore radius. When the pore space of a medium exhibits fractal structure this approach results in a power-law relation with an exponent of 3-D(v), where D(v) is the pore volume fractal dimension. However, larger values of the exponent than are realistically allowed by this result have long been known to occur. Using a thermodynamic formulation for equilibrium capillary pressure we show that the standard result is a special case of the more general exponent (3-D(v))(3-D(s)) where D(s) is the surface fractal dimension of the pores. The analysis reduces to the standard result when D(s)=2, indicating a Euclidean relationship between a pore's surface area and the volume it encloses, and allows for a larger value for the exponent than the standard result when D(s)>2 .
Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.
2016-10-01
Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the
Exploring scaling laws in surface topography
International Nuclear Information System (INIS)
Abedini, M.J.; Shaghaghian, M.R.
2009-01-01
Surface topography affects many soil properties and processes, particularly surface water storage and runoff. Application of fractal analysis helps understand the scaling laws inherent in surface topography at a wide range of spatial scales and climatic regimes. In this research, a high resolution digital elevation model with a 3 mm resolution on one side of the spectrum and large scale DEMs, with a 500 m spatial resolution on the other side were used to explore scaling laws in surface topography. With appropriate exploratory spatial data analysis of both types of data sets, two conventional computational procedures - variogram and Box Counting Methods (BCM) - address scaling laws in surface topography. The results respect scaling laws in surface topography to some extent as neither the plot treatment nor the direction treatment has a significant impact on fractal dimension variability. While in the variogram method, the change in slope in Richardson's plots appears to be the norm rather than the exception; Richardson's plots resulting from box counting implementation lack such mathematical behavior. These breaks in slope might have useful implications for delineating homogeneous hydrologic units and detecting change in trend in hydrologic time series. Furthermore, it is shown that fractal dimension cannot be used to capture anisotropic variabilities both within and among micro-plots. In addition, its numerical value remains insignificant at the 5% level in moving from one direction to another and also from one spatial scale to another while the ordinate intercept could discriminate the surface roughness variability from one spatial scale to another.
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volume 1 of Eric Hammel's Fractal Dimensions, Volume 2 is filled wit
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1 and 2 of Eric Hammel's Fractal Dimensions, Volume 3 is fil
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1, 2, and 3 of Eric Hammel's Fractal Dimensions, Volume 4 is
DEFF Research Database (Denmark)
Föh, Kennet Fischer; Mandøe, Lene; Tinten, Bjarke
Business Law is a translation of the 2nd edition of Erhvervsjura - videregående uddannelser. It is an educational textbook for the subject of business law. The textbook covers all important topic?s within business law such as the Legal System, Private International Law, Insolvency Law, Contract law...
Black carbon fractal morphology and short-wave radiative impact: a modelling study
Directory of Open Access Journals (Sweden)
M. Kahnert
2011-11-01
Full Text Available We investigate the impact of the morphological properties of freshly emitted black carbon aerosols on optical properties and on radiative forcing. To this end, we model the optical properties of fractal black carbon aggregates by use of numerically exact solutions to Maxwell's equations within a spectral range from the UVC to the mid-IR. The results are coupled to radiative transfer computations, in which we consider six realistic case studies representing different atmospheric pollution conditions and surface albedos. The spectrally integrated radiative impacts of black carbon are compared for two different fractal morphologies, which brace the range of recently reported experimental observations of black carbon fractal structures. We also gauge our results by performing corresponding calculations based on the homogeneous sphere approximation, which is commonly employed in climate models. We find that at top of atmosphere the aggregate models yield radiative impacts that can be as much as 2 times higher than those based on the homogeneous sphere approximation. An aggregate model with a low fractal dimension can predict a radiative impact that is higher than that obtained with a high fractal dimension by a factor ranging between 1.1–1.6. Although the lower end of this scale seems like a rather small effect, a closer analysis reveals that the single scattering optical properties of more compact and more lacy aggregates differ considerably. In radiative flux computations there can be a partial cancellation due to the opposing effects of different error sources. However, this cancellation effect can strongly depend on atmospheric conditions and is therefore quite unpredictable. We conclude that the fractal morphology of black carbon aerosols and their fractal parameters can have a profound impact on their radiative forcing effect, and that the use of the homogeneous sphere model introduces unacceptably high biases in radiative impact studies. We
Fractal Structure and Entropy Production within the Central Nervous System
Directory of Open Access Journals (Sweden)
Andrew J. E. Seely
2014-08-01
Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.
FRACTAL DIMENSIONING OF SAND GRAINS USING IMAGE ANALYSIS SYSTEM
Directory of Open Access Journals (Sweden)
Suat AKBULUT
2002-03-01
Full Text Available Engineers and earth scientists have successfully used the concept of fractal theory to better analyze the roughness of soil and/or rock particles, and how it affects the permeability, structure and distribution of pores in sedimentary rocks and their influence on strength. Use of fractals as a way to describe irregular or rough objects has been highlighted in articles by researchers working in fields such as powder mechanics, rock and soil mechanics, sedimentary petrography and geoenvironmental applications. Fractal scaling has been found appropriate to express such scale independence for collection of soil particles and aggregates. In many aspects, soil is a fractal medium and fractal models are available for the fragmentation of aggregates with fractal pore space, and with fractal surface. Applications of fractal concepts encompass description of soil physical properties such as pore-size distribution, pore surface area, and grain-size distribution. The roughness of particulate soils is an important characteristic that affects the mass behavior of the soil. The area-perimeter technique was used to predict the fractal dimension using image analysis system. This paper presents the effects of the roughness and sorting of the sand patterns with different shapes on fractal dimension. Results confirmed the significance of the roughness effect on fractal dimension.
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.
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 (…) ...
[Chaos and fractals and their applications in electrocardial signal research].
Jiao, Qing; Guo, Yongxin; Zhang, Zhengguo
2009-06-01
Chaos and fractals are ubiquitous phenomena of nature. A system with fractal structure usually behaves chaos. As a complicated nonlinear dynamics system, heart has fractals structure and behaves as chaos. The deeper inherent mechanism of heart can be opened out when the chaos and fractals theory is utilized in the research of the electrical activity of heart. Generally a time series of a system was used for describing the status of the strange attractor of the system. The indices include Poincare plot, fractals dimension, Lyapunov exponent, entropy, scaling exponent, Hurst index and so on. In this article, the basic concepts and the methods of chaos and fractals were introduced firstly. Then the applications of chaos and fractals theories in the study of electrocardial signal were expounded with example of how they are used for ventricular fibrillation.
Plant microtubule cytoskeleton complexity: microtubule arrays as fractals.
Gardiner, John; Overall, Robyn; Marc, Jan
2012-01-01
Biological systems are by nature complex and this complexity has been shown to be important in maintaining homeostasis. The plant microtubule cytoskeleton is a highly complex system, with contributing factors through interactions with microtubule-associated proteins (MAPs), expression of multiple tubulin isoforms, and post-translational modification of tubulin and MAPs. Some of this complexity is specific to microtubules, such as a redundancy in factors that regulate microtubule depolymerization. Plant microtubules form partial helical fractals that play a key role in development. It is suggested that, under certain cellular conditions, other categories of microtubule fractals may form including isotropic fractals, triangular fractals, and branched fractals. Helical fractal proteins including coiled-coil and armadillo/beta-catenin repeat proteins and the actin cytoskeleton are important here too. Either alone, or in combination, these fractals may drive much of plant development.
Fractal structure of lunar topography: An interpretation of topographic characteristics
Cao, Wei; Cai, Zhanchuan; Tang, Zesheng
2015-06-01
Over the years, fractal geometry has been applied extensively in many fields of geoscience. Based on the global gridded data generated from the Lunar Reconnaissance Orbiter, we carry out our fractal measure to interpret lunar fractures by using qualitative (similar ratio) and quantitative (fractal dimension) approaches of fractal geometry. We find that most of the lunar surface exhibits fractal behavior over the given scales ranging from 1 to 256 m. Lunar maria have higher fractal dimensions than other geological units, while those of volcanic areas and highlands are lower than their surroundings. Simple and flat surfaces have low values of similar ratios and these areas indicate low surface roughness and young ages. Older-aged areas, such as the Hertzsprung basin, have low fractal dimensions and high similar ratios by their complicated topography.
Exploring fractal behaviour of blood oxygen saturation in preterm babies
Zahari, Marina; Hui, Tan Xin; Zainuri, Nuryazmin Ahmat; Darlow, Brian A.
2017-04-01
Recent evidence has been emerging that oxygenation instability in preterm babies could lead to an increased risk of retinal injury such as retinopathy of prematurity. There is a potential that disease severity could be better understood using nonlinear methods for time series data such as fractal theories [1]. Theories on fractal behaviours have been employed by researchers in various disciplines who were motivated to look into the behaviour or structure of irregular fluctuations in temporal data. In this study, an investigation was carried out to examine whether fractal behaviour could be detected in blood oxygen time series. Detection for the presence of fractals in oxygen data of preterm infants was performed using the methods of power spectrum, empirical probability distribution function and autocorrelation function. The results from these fractal identification methods indicate the possibility that these data exhibit fractal nature. Subsequently, a fractal framework for future research was suggested for oxygen time series.
Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales
Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei
2017-11-01
Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.
Directory of Open Access Journals (Sweden)
Gao Feng
2017-01-01
Full Text Available In this paper we address the general fractional calculus of Liouville-Weyl and Liouville-Caputo general fractional derivative types with non-singular power-law kernel for the first time. The Fourier transforms and the anomalous diffusions are discussed in detail. The formulations are adopted to describe complex phenomena of the heat transfer problems.
Solar Cycle Phase Dependence of Supergranular Fractal ...
Indian Academy of Sciences (India)
Solar Cycle Phase Dependence of Supergranular Fractal Dimension. U. Paniveni1,2,∗. , V. Krishan2, J. Singh2 & R. Srikanth3,4. 1NIE Institute of Technology, Mysore, India. 2Indian Institute of Astrophysics, Bangalore, India. 3Poornaprajna Institute of Research, 4 Sadashivnagar, Bangalore, India. 4Optics Group, Raman ...
Temporal fractals in movies and mind.
Cutting, James E; DeLong, Jordan E; Brunick, Kaitlin L
2018-01-01
Fractal patterns are seemingly everywhere. They can be analyzed through Fourier and power analyses, and other methods. Cutting, DeLong, and Nothelfer (2010) analyzed as time-series data the fluctuations of shot durations in 150 popular movies released over 70 years. They found that these patterns had become increasingly fractal-like and concluded that they might be linked to those found in the results of psychological tasks involving attention. To explore this possibility further, we began by analyzing the shot patterns of almost twice as many movies released over a century. The increasing fractal-like nature of shot patterns is affirmed, as determined by both a slope measure and a long-range dependence measure, neither of which is sensitive to the vector lengths of their inputs within the ranges explored here. But the main reason for increased long-range dependence is related to, but not caused by, the increasing vector length of the shot-series samples. It appears that, in generating increasingly fractal-like patterns, filmmakers have systematically explored dimensions that are important for holding our attention-shot durations, scene durations, motion, and sound amplitude-and have crafted fluctuations in them like those of our endogenous attention patterns. Other dimensions-luminance, clutter, and shot scale-are important to film style but their variations seem not to be important to holding viewers' moment-to-moment attention and have not changed in their fractional dimension over time.
Design of silicon-based fractal antennas
Ghaffar, Farhan A.
2012-11-20
This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
In this work the use of fractal scaling exponents for geological mapping was first investigated using theoretical models, and results from the analysis showed that the scaling exponents mapped isolated bodies but did not properly resolve bodies close to each other. However application on real data (the Mamfe basin, the ...
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
... in Nigeria) showed good correlation with the geological maps of the areas. The results also indicated that basement rocks can generally be represented by scaling exponents with values ranging between -3.0 and -2.0. Keywords: Fractal, dimension, susceptibility, spectra, scaling exponent. Nigerian Journal of Physics Vol.
Fractal structures and intermittency in QCD
International Nuclear Information System (INIS)
Gustafson, Goesta.
1990-04-01
New results are presented for fractal structures and intermittency in QCD parton showers. A geometrical interpretation of the anomalous dimension in QCD is given. It is shown that model predications for factorial moments in the PEP-PETRA energy range are increased. if the properties of directly produced pions are more carefully taken into account
Fractal tiles associated with shift radix systems.
Berthé, Valérie; Siegel, Anne; Steiner, Wolfgang; Surer, Paul; Thuswaldner, Jörg M
2011-01-15
Shift radix systems form a collection of dynamical systems depending on a parameter r which varies in the d -dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings. In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters r these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (non-monic) expanding polynomials. We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter r of the shift radix system, these tiles provide multiple tilings and even tilings of the d -dimensional real vector space. These tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above. Such a tiling may consist of tiles having infinitely many different shapes. Moreover, the tiles need not be self-affine (or graph directed self-affine).
FRACTAL DIMENSIONALITY ANALYSIS OF MAMMARY GLAND THERMOGRAMS
Yu. E. Lyah; V. G. Guryanov; E. A. Yakobson
2016-01-01
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).
DEFF Research Database (Denmark)
Teisbæk, Henrik Bjørn; Jakobsen, Kaj Bjarne
2009-01-01
A Yagi-Uda antenna constructed of three Koch fractal elements is presented. Simulated and measured characteristics of the antenna shows a half-power beam-width of 64◦ achieved with dimensions below a third of a wavelength. Furthermore, the Koch dipole and its size miniaturization capabilities are...
A Parallel Approach to Fractal Image Compression
Directory of Open Access Journals (Sweden)
Lubomir Dedera
2004-01-01
Full Text Available The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
Fractal analysis of the Navassa Island seascape
Zawada, David G.
2011-01-01
This release provides the numerical results of the fractal analyses discussed in Zawada and others (2010) for the Navassa Island reefscape. The project represents the continuation of a U.S. Geological Survey (USGS) research effort begun in 2006 (Zawada and others, 2006) to understand the patterns and scalability of roughness and topographic complexity from individual corals to complete reefscapes.
Fractal Rock Slope Dynamics Anticipating a Collapse
Czech Academy of Sciences Publication Activity Database
Paluš, Milan; Novotná, Dagmar; Zvelebil, Jiří
2004-01-01
Roč. 70 (2004), 036212 ISSN 1063-651X R&D Projects: GA ČR GA205/00/1055 Institutional research plan: CEZ:AV0Z1030915 Keywords : fractal * scaling * unstable rock slope * collapse prediction * engineering geology Subject RIV: BA - General Mathematics Impact factor: 2.352, year: 2004
Relations between a typical scale and averages in the breaking of fractal distribution
Ishikawa, Atushi; Suzuki, Tadao
2004-11-01
We study distributions which have both fractal and non-fractal scale regions by introducing a typical scale into a scale invariant system. As one of models in which distributions follow power law in the large-scale region and deviate further from the power law in the smaller-scale region, we employ 2-dim quantum gravity modified by the R2 term. As examples of distributions in the real world which have similar property to this model, we consider those of personal income in Japan over latest twenty fiscal years. We find relations between the typical scale and several kinds of averages in this model, and observe that these relations are also valid in recent personal income distributions in Japan with sufficient accuracy. We show the existence of the fiscal years so called bubble term in which the gap has arisen in power law, by observing that the data are away from one of these relations. We confirm, therefore, that the distribution of this model has close similarity to those of personal income. In addition, we can estimate the value of Pareto index and whether a big gap exists in power law by using only these relations. As a result, we point out that the typical scale is an useful concept different from average value and that the distribution function derived in this model is an effective tool to investigate these kinds of distributions.
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)
Shedding light on fractals: exploration of the Sierpinski carpet optical antenna
Chen, T.L.
2015-01-01
We describe experimental and theoretical investigations of the properties of a fractal optical antenna-the Sierpinski carpet optical antenna. Fractal optical antennas are inspired by fractal antennas designed in radio frequency (RF) region. Shrinking the size of fractal optical antennas from fractal
Aesthetic Responses to Exact Fractals Driven by Physical Complexity.
Bies, Alexander J; Blanc-Goldhammer, Daryn R; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E
2016-01-01
Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a
International Nuclear Information System (INIS)
Ketteler, G.; Kippels, K.
1988-01-01
In section I 'Basic principles' the following topics are considered: Constitutional-legal aspects of environmental protection, e.g. nuclear hazards and the remaining risk; European environmental law; international environmental law; administrative law, private law and criminal law relating to the environment; basic principles of environmental law, the instruments of public environmental law. Section II 'Special areas of law' is concerned with the law on water and waste, prevention of air pollution, nature conservation and care of the countryside. Legal decisions and literature up to June 1988 have been taken into consideration. (orig./RST) [de
Link between truncated fractals and coupled oscillators in biological systems.
Paar, V; Pavin, N; Rosandić, M
2001-09-07
This article aims at providing a new theoretical insight into the fundamental question of the origin of truncated fractals in biological systems. It is well known that fractal geometry is one of the characteristics of living organisms. However, contrary to mathematical fractals which are self-similar at all scales, the biological fractals are truncated, i.e. their self-similarity extends at most over a few orders of magnitude of separation. We show that nonlinear coupled oscillators, modeling one of the basic features of biological systems, may generate truncated fractals: a truncated fractal pattern for basin boundaries appears in a simple mathematical model of two coupled nonlinear oscillators with weak dissipation. This fractal pattern can be considered as a particular hidden fractal property. At the level of sufficiently fine precision technique the truncated fractality acts as a simple structure, leading to predictability, but at a lower level of precision it is effectively fractal, limiting the predictability of the long-term behavior of biological systems. We point out to the generic nature of our result. Copyright 2001 Academic Press.
FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY
Directory of Open Access Journals (Sweden)
Ian Parkinson
2011-05-01
Full Text Available A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge. The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals, with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.
Novel optical password security technique based on optical fractal synthesizer
Wu, Kenan; Hu, Jiasheng; Wu, Xu
2009-06-01
A novel optical security technique for safeguarding user passwords based on an optical fractal synthesizer is proposed. A validating experiment has been carried out. In the proposed technique, a user password is protected by being converted to a fractal image. When a user sets up a new password, the password is transformed into a fractal pattern, and the fractal pattern is stored in authority. If the user is online-validated, his or her password is converted to a fractal pattern again to compare with the previous stored fractal pattern. The converting process is called the fractal encoding procedure, which consists of two steps. First, the password is nonlinearly transformed to get the parameters for the optical fractal synthesizer. Then the optical fractal synthesizer is operated to generate the output fractal image. The experimental result proves the validity of our method. The proposed technique bridges the gap between digital security systems and optical security systems and has many advantages, such as high security level, convenience, flexibility, hyper extensibility, etc. This provides an interesting optical security technique for the protection of digital passwords.
Fractal analysis of fractures and microstructures in rocks
International Nuclear Information System (INIS)
Merceron, T.; Nakashima, S.; Velde, B.; Badri, A.
1991-01-01
Fractal geometry was used to characterize the distribution of fracture fields in rocks, which represent main pathways for material migration such as groundwater flow. Fractal investigations of fracture distribution were performed on granite along Auriat and Shikoku boreholes. Fractal dimensions range between 0.3 and 0.5 according to the different sets of fracture planes selected for the analyses. Shear, tension and compressional modes exhibit different fractal values while the composite fracture patterns are also fractal but with a different, median, fractal value. These observations indicate that the fractal method can be used to distinguish fracture types of different origins in a complex system. Fractal results for Shikoku borehole also correlate with geophysical parameters recorded along, drill-holes such as resistivity and possibly permeability. These results represent the first steps of the fractal investigation along drill-holes. Future studies will be conducted to verify relationships between fractal dimensions and permeability by using available geophysical data. Microstructures and microcracks were analysed in the Inada granite. Microcrack patterns are fractal but fractal dimensions values vary according to both mineral type and orientations of measurement within the mineral. Microcracks in quartz are characterized by more irregular distribution (average D = 0.40) than those in feldspars (D = 0.50) suggesting a different mode of rupture. Highest values of D are reported along main cleavage planes for feldspars or C axis for quartz. Further fractal investigations of microstructure in granite will be used to characterize the potential pathways for fluid migration and diffusion in the rock matrix. (author)
Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.
Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K
2014-08-01
Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.
Araki, Hiromu; Fukui, Takahiro; Hatsugai, Yasuhiro
2017-10-01
We propose characterization of the three-dimensional topological insulator by using the Chern number for the entanglement Hamiltonian (entanglement Chern number). Here we take the extensive spin partition of the system, that pulls out the quantum entanglement between up spin and down spin of the many-body ground state. In three dimensions, the topological insulator phase is described by the section entanglement Chern number, which is the entanglement Chern number for a periodic plane in the Brillouin zone. The section entanglement Chern number serves as an interpolation of the Z2 invariants defined on time-reversal invariant planes. We find that the change of the section entanglement Chern number protects the Weyl point of the entanglement Hamiltonian, and the parity of the number of Weyl points distinguishes the strong topological insulator phase from the weak topological insulator phase.
A cosmological model in Weyl-Cartan spacetime: II. Magnitude-redshift relation
Puetzfeld, D
2002-01-01
In this second part of our series of papers on alternative cosmological models, we investigate the observational consequences for the new Weyl-Cartan model proposed earlier. We review the derivation of the magnitude-redshift relation within the standard Friedmann-Lemaitre-Robertson-Walker model and characterize its dependence on the underlying cosmological model. With this knowledge at hand, we derive the magnitude-redshift relation within our new Weyl-Cartan model. We search for the best-fit parameters by using the combined data set of 92 SNe of type Ia as compiled by Wang, which is based on the recent supernova data of Perlmutter et al and Riess et al. Additionally, we compare our best-fit parameters with the results of several other groups which performed similar analysis within the standard cosmological model as well as in non-standard models.
Quantum Yang-Mills-Weyl Dynamics in the Schrödinger paradigm
Dynin, A.
2014-04-01
Inspired by F. Wilczek's QCD Lite, quantum Yang-Mills-Weyl Dynamics (YMWD) describes quantum interaction between gauge bosons (associated with a simple gauge group ) and larks (massless chiral fields charged by an irreducible unitary representation of ). Schrödinger representation of this quantum Yang-Mills-Weyl theory is based on a sesqui-holomorphic operator calculus of infinite-dimensional operators with variational derivatives. The spectrum of quantum YMWD in a compact bag is a sequence of eigenvalues convergent to +∞. The eigenvalues have finite multiplicities with respect to a von Neumann algebra with a regular trace. The spectrum is inversely proportional to the square of the running coupling constant. The rigorous mathematical theory is nonperturbative with a running coupling constant as the only ad hoc parameter. The application of the first mathematical principles is based on the properties of the compact simple Lie group.
Kim, Heon-Jung; Kim, Ki-Seok; Wang, J-F; Sasaki, M; Satoh, N; Ohnishi, A; Kitaura, M; Yang, M; Li, L
2013-12-13
Dirac metals (gapless semiconductors) are believed to turn into Weyl metals when perturbations, which break either time reversal symmetry or inversion symmetry, are employed. However, no experimental evidence has been reported for the existence of Weyl fermions in three dimensions. Applying magnetic fields near the topological phase transition from a topological insulator to a band insulator in Bi1-xSbx we observe not only the weak antilocalization phenomenon in magnetoconductivity near zero magnetic fields (B<0.4 T), but also its upturn above 0.4 T only for E//B. This "incompatible" coexistence between weak antilocalization and "negative" magnetoresistivity is attributed to the Adler-Bell-Jackiw anomaly ("topological" E·B term) in the presence of weak antilocalization corrections.
Un-equivalency theorem between deformed and undeformed Heisenberg-Weyl's algebras
International Nuclear Information System (INIS)
Zhang Jianzu
2006-01-01
Two fundamental issues about the relation between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed one in commutative space are elucidated. First the un-equivalency theorem between two algebras is proved: the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation is explored; furthermore, non-existence of a unitary similarity transformation which transforms the deformed algebra to the undeformed one is demonstrated. Secondly the uniqueness of realizing the deformed phase space variables via the undeformed ones is elucidated: both the deformed Heisenberg-Weyl algebra and the deformed bosonic algebra should be maintained under a linear transformation between two sets of phase space variables which fixes that such a linear transformation is unique. Elucidation of this un-equivalency theorem has basic meaning both in theory and experiment
Shot noise and electronic properties in the inversion-symmetric Weyl semimetal resonant structure
Yang, Yanling; Bai, Chunxu; Xu, Xiaoguang; Jiang, Yong
2018-02-01
Using the transfer matrix method, the authors combine the analytical formula with numerical calculation to explore the shot noise and conductance of massless Weyl fermions in the Weyl semimetal resonant junction. By varying the barrier strength, the structure of the junction, the Fermi energy, and the crystallographic angle, the shot noise and conductance can be tuned efficiently. For a quasiperiodic superlattice, in complete contrast to the conventional junction case, the effect of the disorder strength on the shot noise and conductance depends on the competition of classical tunneling and Klein tunneling. Moreover, the delta barrier structure is also vital in determining the shot noise and conductance. In particular, a universal Fano factor has been found in a single delta potential case, whereas the resonant structure of the Fano factor perfectly matches with the number of barriers in a delta potential superlattice. These results are crucial for engineering nanoelectronic devices based on this topological semimetal material.
Tuning the Drude weight of Dirac-Weyl fermions in one-dimensional ring traps
Bischoff, Manon; Jünemann, Johannes; Polini, Marco; Rizzi, Matteo
2017-12-01
We study the response to an applied flux of an interacting system of Dirac-Weyl fermions confined in a one-dimensional (1D) ring. Combining analytical calculations with density-matrix renormalization group results, we show that tuning of the interactions leads to a unique many-body system that displays either a suppression or an enhancement of the Drude weight—the zero-frequency peak in the ac conductivity—with respect to the noninteracting value. An asymmetry in the interaction strength between same- and different-pseudospin Dirac-Weyl fermions leads to Drude weight enhancement. Vice versa, symmetric interactions lead to Drude weight suppression. Our predictions can be tested in mixtures of ultracold fermions in 1D ring traps.
Signature of type-II Weyl semimetal phase in MoTe2
Jiang, J.; Liu, Z. K.; Sun, Y.; Yang, H. F.; Rajamathi, C. R.; Qi, Y. P.; Yang, L. X.; Chen, C.; Peng, H.; Hwang, C.-C.; Sun, S. Z.; Mo, S.-K.; Vobornik, I.; Fujii, J.; Parkin, S. S. P.; Felser, C.; Yan, B. H.; Chen, Y. L.
2017-01-01
Topological Weyl semimetal (TWS), a new state of quantum matter, has sparked enormous research interest recently. Possessing unique Weyl fermions in the bulk and Fermi arcs on the surface, TWSs offer a rare platform for realizing many exotic physical phenomena. TWSs can be classified into type-I that respect Lorentz symmetry and type-II that do not. Here, we directly visualize the electronic structure of MoTe2, a recently proposed type-II TWS. Using angle-resolved photoemission spectroscopy (ARPES), we unravel the unique surface Fermi arcs, in good agreement with our ab initio calculations that have nontrivial topological nature. Our work not only leads to new understandings of the unusual properties discovered in this family of compounds, but also allows for the further exploration of exotic properties and practical applications of type-II TWSs, as well as the interplay between superconductivity (MoTe2 was discovered to be superconducting recently) and their topological order.
Zhou, Jianhui; Chang, Hao-Ran
2018-02-01
We present a unified derivation of the dynamical correlation functions including density-density, density-current and current-current, of three-dimensional Weyl/Dirac semimetals by use of the Passarino-Veltman reduction scheme at zero temperature. The generalized Kramers-Kronig relations with arbitrary order of subtraction are established to verify these correlation functions. Our results lead to the exact chiral magnetic conductivity and directly recover the previous ones in several limits. We also investigate the magnetic susceptibilities, the orbital magnetization, and briefly discuss the impact of electron interactions on these physical quantities within the random phase approximation. Our work could provide a starting point for the investigation of the nonlocal transport and optical properties due to the higher-order spatial dispersion in three-dimensional Weyl/Dirac semimetals.
Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2
Belopolski, Ilya; Sanchez, Daniel S.; Ishida, Yukiaki; Pan, Xingchen; Yu, Peng; Xu, Su-Yang; Chang, Guoqing; Chang, Tay-Rong; Zheng, Hao; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Huang, Shin-Ming; Lee, Chi-Cheng; Song, You; Bu, Haijun; Wang, Guanghou; Li, Shisheng; Eda, Goki; Jeng, Horng-Tay; Kondo, Takeshi; Lin, Hsin; Liu, Zheng; Song, Fengqi; Shin, Shik; Hasan, M. Zahid
2016-01-01
The recent discovery of a Weyl semimetal in TaAs offers the first Weyl fermion observed in nature and dramatically broadens the classification of topological phases. However, in TaAs it has proven challenging to study the rich transport phenomena arising from emergent Weyl fermions. The series MoxW1−xTe2 are inversion-breaking, layered, tunable semimetals already under study as a promising platform for new electronics and recently proposed to host Type II, or strongly Lorentz-violating, Weyl fermions. Here we report the discovery of a Weyl semimetal in MoxW1−xTe2 at x=25%. We use pump-probe angle-resolved photoemission spectroscopy (pump-probe ARPES) to directly observe a topological Fermi arc above the Fermi level, demonstrating a Weyl semimetal. The excellent agreement with calculation suggests that MoxW1−xTe2 is a Type II Weyl semimetal. We also find that certain Weyl points are at the Fermi level, making MoxW1−xTe2 a promising platform for transport and optics experiments on Weyl semimetals. PMID:27917858
Multispectral image fusion based on fractal features
Tian, Jie; Chen, Jie; Zhang, Chunhua
2004-01-01
Imagery sensors have been one indispensable part of the detection and recognition systems. They are widely used to the field of surveillance, navigation, control and guide, et. However, different imagery sensors depend on diverse imaging mechanisms, and work within diverse range of spectrum. They also perform diverse functions and have diverse circumstance requires. So it is unpractical to accomplish the task of detection or recognition with a single imagery sensor under the conditions of different circumstances, different backgrounds and different targets. Fortunately, the multi-sensor image fusion technique emerged as important route to solve this problem. So image fusion has been one of the main technical routines used to detect and recognize objects from images. While, loss of information is unavoidable during fusion process, so it is always a very important content of image fusion how to preserve the useful information to the utmost. That is to say, it should be taken into account before designing the fusion schemes how to avoid the loss of useful information or how to preserve the features helpful to the detection. In consideration of these issues and the fact that most detection problems are actually to distinguish man-made objects from natural background, a fractal-based multi-spectral fusion algorithm has been proposed in this paper aiming at the recognition of battlefield targets in the complicated backgrounds. According to this algorithm, source images are firstly orthogonally decomposed according to wavelet transform theories, and then fractal-based detection is held to each decomposed image. At this step, natural background and man-made targets are distinguished by use of fractal models that can well imitate natural objects. Special fusion operators are employed during the fusion of area that contains man-made targets so that useful information could be preserved and features of targets could be extruded. The final fused image is reconstructed from the
On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello; Pravda, Vojtěch; Pravdová, Alena
2018-01-01
Roč. 35, č. 7 (2018), č. článku 075004. ISSN 0264-9381 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * WANDs * Weyl tensor Subject RIV: BA - General Mathematics Impact factor: 3.119, year: 2016 http://iopscience.iop.org/ article /10.1088/1361-6382/aaae25
A partial solution for Feynman's problem: A new derivation of the Weyl equation
Directory of Open Access Journals (Sweden)
Atsushi Inoue
2000-07-01
Full Text Available Associating classical mechanics to a system of partial differential equations, we give a procedure for Feynman-type quantization of a "Schrodinger-type equation with spin." Mathematically, we construct a "good parametrix" for the Weyl equation with an external electromagnetic field. Main ingredients are (i a new interpretation of the matrix structure using superanalysis and (ii another interpretation of the method of characteristics as a quantization procedure of Feynman type.
The geometry of a space-time with Kottler, Weyl and Trefftz Metric
International Nuclear Information System (INIS)
Geyer, K.H.
1980-01-01
The space-time manifold with the metric tensor of Kottler, Weyl and Trefftz (KWT) is analytically extended for all the three ranges 2m/a √ (2/3) 3 and the transformations into Kruskal-coordinates are given. The conformal infinity is represented by Penrose-diagrams. Finally embeddings in three-space are shown of surfaces with KWT-metric in cylindrical and spherical coordinates. (author)
International Nuclear Information System (INIS)
Namgung, W.
1991-01-01
The well known requirement that physical theories should be gauge independent is not so apparent in the actual calculation of gauge theories, especially in the perturbative approach. In this paper the authors show that the Weyl, Coulomb, and unitary gauges of the scalar QED are manifestly equivalent in the context of the functional Schrodinger picture. Further, the three gauge conditions are shown equivalent to the covariant gauge in the way that they correspond to some specific cases of the latter
Quantum critical matter. Quantum phase transitions with multiple dynamics and Weyl superconductors
International Nuclear Information System (INIS)
Meng, Tobias
2012-01-01
In this PhD thesis, the physics of quantum critical matter and exotic quantum state close to quantum phase transitions is investigated. We will focus on three different examples that highlight some of the interesting phenomena related to quantum phase transitions. Firstly, we discuss the physics of quantum phase transitions in quantum wires as a function of an external gate voltage when new subbands are activated. We find that at these transitions, strong correlations lead to the formation of an impenetrable gas of polarons, and identify criteria for possible instabilities in the spin- and charge sectors of the model. Our analysis is based on the combination of exact resummations, renormalization group techniques and Luttinger liquid approaches. Secondly, we turn to the physics of multiple divergent time scales close to a quantum critical point. Using an appropriately generalized renormalization group approach, we identify that the presence of multiple dynamics at a quantum phase transition can lead to the emergence of new critical scaling exponents and thus to the breakdown of the usual scaling schemes. We calculate the critical behavior of various thermodynamic properties and detail how unusual physics can arise. It is hoped that these results might be helpful for the interpretation of experimental scaling puzzles close to quantum critical points. Thirdly, we turn to the physics of topological transitions, and more precisely the physics of Weyl superconductors. The latter are the superconducting variant of the topologically non-trivial Weyl semimetals, and emerge at the quantum phase transition between a topological superconductor and a normal insulator upon perturbing the transition with a time reversal symmetry breaking perturbation, such as magnetism. We characterize the topological properties of Weyl superconductors and establish a topological phase diagram for a particular realization in heterostructures. We discuss the physics of vortices in Weyl
Anomalous transport phenomena in Weyl metal beyond the Drude model for Landau's Fermi liquids.
Kim, Ki-Seok; Kim, Heon-Jung; Sasaki, M; Wang, J-F; Li, L
2014-12-01
Landau's Fermi-liquid theory is the standard model for metals, characterized by the existence of electron quasiparticles near a Fermi surface as long as Landau's interaction parameters lie below critical values for instabilities. Recently this fundamental paradigm has been challenged by the physics of strong spin-orbit coupling, although the concept of electron quasiparticles remains valid near the Fermi surface, where Landau's Fermi-liquid theory fails to describe the electromagnetic properties of this novel metallic state, referred to as Weyl metal. A novel ingredient is that such a Fermi surface encloses a Weyl point with definite chirality, referred to as a chiral Fermi surface, which can arise from breaking of either time reversal or inversion symmetry in systems with strong spin-orbit coupling, responsible for both the Berry curvature and the chiral anomaly. As a result, electromagnetic properties of the Weyl metallic state are described not by conventional Maxwell equations but by axion electrodynamics, where Maxwell equations are modified with a topological-in-origin spatially modulated [Formula: see text] term. This novel metallic state was realized recently in Bi[Formula: see text]Sb x around [Formula: see text] under magnetic fields, where the Dirac spectrum appears around the critical point between the normal semiconducting ([Formula: see text]) and topological semiconducting phases ([Formula: see text]) and the time reversal symmetry breaking perturbation causes the Dirac point to split into a pair of Weyl points along the direction of the applied magnetic field for a very strong spin-orbit coupled system. In this review article, we discuss how the topological structure of both the Berry curvature and the chiral anomaly (axion electrodynamics) gives rise to anomalous transport phenomena in [Formula: see text]Sb x around [Formula: see text] under magnetic fields, thus modifying the Drude model of Landau's Fermi liquids.
Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients
International Nuclear Information System (INIS)
Zielinski, Lech
1999-01-01
The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients
Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients
Energy Technology Data Exchange (ETDEWEB)
Zielinski, Lech [Universite Paris 7 (D. Diderot), Institut de Mathematiques de Paris-Jussieu UMR9994 (France)
1999-09-15
The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hoermander''s type for the spectral function of pseudo differential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.
On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction
Czech Academy of Sciences Publication Activity Database
Ortaggio, Marcello; Pravda, Vojtěch; Pravdová, Alena
2018-01-01
Roč. 35, č. 7 (2018), č. článku 075004. ISSN 0264-9381 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : higher-dimensional gravity * WANDs * Weyl tensor Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 3.119, year: 2016 http://iopscience.iop.org/article/10.1088/1361-6382/aaae25
The distance-decay function of geographical gravity model: Power law or exponential law?
International Nuclear Information System (INIS)
Chen, Yanguang
2015-01-01
Highlights: •The distance-decay exponent of the gravity model is a fractal dimension. •Entropy maximization accounts for the gravity model based on power law decay. •Allometric scaling relations relate gravity models with spatial interaction models. •The four-parameter gravity models have dual mathematical expressions. •The inverse power law is the most probable distance-decay function. -- Abstract: The distance-decay function of the geographical gravity model is originally an inverse power law, which suggests a scaling process in spatial interaction. However, the distance exponent of the model cannot be reasonably explained with the ideas from Euclidean geometry. This results in a dimension dilemma in geographical analysis. Consequently, a negative exponential function was used to replace the inverse power function to serve for a distance-decay function. But a new puzzle arose that the exponential-based gravity model goes against the first law of geography. This paper is devoted for solving these kinds of problems by mathematical reasoning and empirical analysis. New findings are as follows. First, the distance exponent of the gravity model is demonstrated to be a fractal dimension using the geometric measure relation. Second, the similarities and differences between the gravity models and spatial interaction models are revealed using allometric relations. Third, a four-parameter gravity model possesses a symmetrical expression, and we need dual gravity models to describe spatial flows. The observational data of China's cities and regions (29 elements indicative of 841 data points) in 2010 are employed to verify the theoretical inferences. A conclusion can be reached that the geographical gravity model based on power-law decay is more suitable for analyzing large, complex, and scale-free regional and urban systems. This study lends further support to the suggestion that the underlying rationale of fractal structure is entropy maximization. Moreover
Localization and mass spectra of various matter fields on Weyl thin brane
Energy Technology Data Exchange (ETDEWEB)
Sui, Tao-Tao; Zhao, Li; Zhang, Yu-Peng [Lanzhou University, Institute of Theoretical Physics, Lanzhou (China); Xie, Qun-Ying [Lanzhou University, School of Information Science and Engineering, Lanzhou (China)
2017-06-15
It has been shown that the thin brane model in a five-dimensional Weyl gravity can deal with the wrong-signed Friedmann-like equation in the Randall-Sundrum-1 (RS1) model. In the Weyl brane model, there are also two branes with opposite brane tensions, but the four-dimensional graviton (the gravity zero mode) is localized near the negative tension brane, while our four-dimensional universe is localized on the positive tension brane. In this paper, we consider the mass spectra of various bulk matter fields (i.e., scalar, vector, and fermion fields) on the Weyl brane. It is shown that the zero modes of those matter fields can be localized on the positive tension brane under some conditions. The mass spectra of the bulk matter fields are equidistant for the higher excited states, and relatively sparse for the lower excited states. The size of the extra dimension determines the gap of the mass spectra. We also consider the correction to the Newtonian potential in this model and it is proportional to 1/r{sup 3}. (orig.)
You, Yizhi; Cho, Gil Young; Hughes, Taylor L.
2016-08-01
In this paper, we investigate the theory of dynamical axion strings emerging from chiral symmetry breaking in three-dimensional Weyl semimetals. The chiral symmetry is spontaneously broken by a charge density wave (CDW) order which opens an energy gap and converts the Weyl semimetal into an axion insulator. Indeed, the phase fluctuations of the CDW order parameter act as a dynamical axion field θ (x ⃗,t ) and couple to electromagnetic field via Lθ=θ/(x ⃗,t ) 32 π2 ɛσ τ ν μFσ τFν μ. Additionally, when the axion insulator is coupled to deformations of the background geometry/strain fields via torsional defects, e.g., screw dislocations, there is interesting interplay between the crystal dislocations and dynamical axion strings. For example, the screw dislocation traps axial charge, and there is a Berry phase accumulation when an axion string (which carries axial flux) is braided with a screw dislocation. In addition, a cubic coupling between the axial current and the geometry fields is nonvanishing and indicates a Berry phase accumulation during a particular three-loop braiding procedure where a dislocation loop is braided with another dislocation and they are both threaded by an axion string. We also observe a chiral magnetic effect induced by a screw dislocation density in the absence of a nodal energy imbalance between Weyl points and describe an additional chiral geometric effect and a geometric Witten effect.
Functional renormalization group approach to interacting three-dimensional Weyl semimetals
Sharma, Anand; Scammell, Arthur; Krieg, Jan; Kopietz, Peter
2018-03-01
We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes—cutoff in fermionic or bosonic propagators—in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavskiĭ [Sov. Phys. JETP 32, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.
A Note on the Problem of Proper Time in Weyl Space-Time
Avalos, R.; Dahia, F.; Romero, C.
2018-01-01
We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space-time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space-time is investigated. Our starting point is the well known axiomatic approach to space-time given by Elhers, Pirani and Schild (EPS). In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called "second clock effect". We take the view that if, based on experience, we were to reject space-time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable space-time as the most general structure that would be suitable to model space-time.
Spinless Weyl semimetals and Z2 topological crystalline insulator with glide symmetry
Kim, Heejae; Murakami, Shuichi
A topological crystalline insulator (TCI) is one of the symmetry protected topological phases protected by crystalline symmetries such as rotational symmetry, mirror symmetry etc. In recent works, a new class of three-dimensional (3D) Z2 TCI with a nonsymmorphic glide plane symmetry is theoretically predicted both for spinless and spinfull systems. Our study shows that a spinless Weyl semimetal (WSM) phase always emerges between a normal insulator (NI) and TCI phases transition in general glide symmetric spinless systems. In particular, we find how the Z2 topological invariant is changed by pair creations and pair annihilations of Weyl nodes in general phase transition. To confirm this scenario, we introduce a simple spinless tight-binding model on a 3D rectangular lattice with two sublattices and two orbitals with glide plane symmetry. Using this model, we show that the spinless WSM phase emerges between the NI and TCI phases, and the changing of Z2 topological invariant comes from the behavior of Weyl nodes. Our numerical calculation also shows that surface Fermi arcs in the spinless WSM phase evolve into a surface Dirac cone in the TCI phase.
Weyl semimetal and superconductor designed in an orbital-selective superlattice
Das, Tanmoy
2013-07-01
We propose two complementary design principles for engineering three-dimensional (3D) Weyl semimetals and superconductors in a layer-by-layer setup which includes even- and odd-parity orbitals in alternating layers—dubbed an orbital selective superlattice. Such a structure breaks mirror symmetry along the superlattice growth axis which, with the help of either a basal plane spin-orbit coupling or spinless p+ip superconductivity, stabilizes a 3D Dirac node. To explore this idea, we develop a 3D generalization of the Haldane model and a Bogoliubov-de Gennes Hamiltonian for the two cases, respectively, and show that tunable single or multiple Weyl nodes with linear dispersion in all spatial directions can be engineered desirably in a widespread parameter space. We also demonstrate that a single helical Weyl band can be created at the Γ point at the Fermi level in the superconducting case via gapping out either of the orbital states by violating its particle-hole symmetry but not any other symmetries. Finally, implications of our results for the realization of an anomalous Hall effect and Majorana bound state are discussed.
A Note on the Problem of Proper Time in Weyl Space-Time
Avalos, R.; Dahia, F.; Romero, C.
2018-02-01
We discuss the question of whether or not a general Weyl structure is a suitable mathematical model of space-time. This is an issue that has been in debate since Weyl formulated his unified field theory for the first time. We do not present the discussion from the point of view of a particular unification theory, but instead from a more general standpoint, in which the viability of such a structure as a model of space-time is investigated. Our starting point is the well known axiomatic approach to space-time given by Elhers, Pirani and Schild (EPS). In this framework, we carry out an exhaustive analysis of what is required for a consistent definition for proper time and show that such a definition leads to the prediction of the so-called "second clock effect". We take the view that if, based on experience, we were to reject space-time models predicting this effect, this could be incorporated as the last axiom in the EPS approach. Finally, we provide a proof that, in this case, we are led to a Weyl integrable space-time as the most general structure that would be suitable to model space-time.
DEFF Research Database (Denmark)
Langsted, Lars Bo; Garde, Peter; Greve, Vagn
<> book contains a thorough description of Danish substantive criminal law, criminal procedure and execution of sanctions. The book was originally published as a monograph in the International Encyclopaedia of Laws/Criminal Law....... book contains a thorough description of Danish substantive criminal law, criminal procedure and execution of sanctions. The book was originally published as a monograph in the International Encyclopaedia of Laws/Criminal Law....