Nuclear multifragmentation critical exponents
International Nuclear Information System (INIS)
Bauer, W.; Friedman, W.A.; Univ. of Wisconsin, Madison, WI
1995-01-01
In a recent Letter, cited in a reference, the EoS collaboration presented data of fragmentation of 1 A GeV gold nuclei incident on carbon. By analyzing moments of the fragment charge distribution, the authors claim to determine the values of the critical exponents γ, β, and τ for finite nuclei. These data represent a crucial step forward in the understanding of the physics of nuclear fragmentation. However, as shown in this paper, the analysis presented in the cited reference is not sufficient to support the claim that the critical exponents for nuclear fragmentation have been unambiguously determined
Quantum critical Hall exponents
Lütken, C A
2014-01-01
We investigate a finite size "double scaling" hypothesis using data from an experiment on a quantum Hall system with short range disorder [1-3]. For Hall bars of width w at temperature T the scaling form is w(-mu)T(-kappa), where the critical exponent mu approximate to 0.23 we extract from the data is comparable to the multi-fractal exponent alpha(0) - 2 obtained from the Chalker-Coddington (CC) model [4]. We also use the data to find the approximate location (in the resistivity plane) of seven quantum critical points, all of which closely agree with the predictions derived long ago from the modular symmetry of a toroidal sigma-model with m matter fields [5]. The value nu(8) = 2.60513 ... of the localisation exponent obtained from the m = 8 model is in excellent agreement with the best available numerical value nu(num) = 2.607 +/- 0.004 derived from the CC-model [6]. Existing experimental data appear to favour the m = 9 model, suggesting that the quantum Hall system is not in the same universality class as th...
Critical exponents from the effective average action
International Nuclear Information System (INIS)
Tetradis, N.; Wetterich, C.
1993-07-01
We compute the critical behaviour of three-dimensional scalar theories using a new exact non-perturbative evolution equation. Our values for the critical exponents agree well with previous precision estimates. (orig.)
Critical exponents of extremal Kerr perturbations
Gralla, Samuel E.; Zimmerman, Peter
2018-05-01
We show that scalar, electromagnetic, and gravitational perturbations of extremal Kerr black holes are asymptotically self-similar under the near-horizon, late-time scaling symmetry of the background metric. This accounts for the Aretakis instability (growth of transverse derivatives) as a critical phenomenon associated with the emergent symmetry. We compute the critical exponent of each mode, which is equivalent to its decay rate. It follows from symmetry arguments that, despite the growth of transverse derivatives, all generally covariant scalar quantities decay to zero.
Beyond Critical Exponents in Neuronal Avalanches
Friedman, Nir; Butler, Tom; Deville, Robert; Beggs, John; Dahmen, Karin
2011-03-01
Neurons form a complex network in the brain, where they interact with one another by firing electrical signals. Neurons firing can trigger other neurons to fire, potentially causing avalanches of activity in the network. In many cases these avalanches have been found to be scale independent, similar to critical phenomena in diverse systems such as magnets and earthquakes. We discuss models for neuronal activity that allow for the extraction of testable, statistical predictions. We compare these models to experimental results, and go beyond critical exponents.
Critical exponents for diluted resistor networks.
Stenull, O; Janssen, H K; Oerding, K
1999-05-01
An approach by Stephen [Phys. Rev. B 17, 4444 (1978)] is used to investigate the critical properties of randomly diluted resistor networks near the percolation threshold by means of renormalized field theory. We reformulate an existing field theory by Harris and Lubensky [Phys. Rev. B 35, 6964 (1987)]. By a decomposition of the principal Feynman diagrams, we obtain diagrams which again can be interpreted as resistor networks. This interpretation provides for an alternative way of evaluating the Feynman diagrams for random resistor networks. We calculate the resistance crossover exponent phi up to second order in epsilon=6-d, where d is the spatial dimension. Our result phi=1+epsilon/42+4epsilon(2)/3087 verifies a previous calculation by Lubensky and Wang, which itself was based on the Potts-model formulation of the random resistor network.
The Critical Exponent is Computable for Automatic Sequences
Directory of Open Access Journals (Sweden)
Jeffrey Shallit
2011-08-01
Full Text Available The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. This generalizes or recovers previous results of Krieger and others. Our technique is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.
Inverted rank distributions: Macroscopic statistics, universality classes, and critical exponents
Eliazar, Iddo; Cohen, Morrel H.
2014-01-01
An inverted rank distribution is an infinite sequence of positive sizes ordered in a monotone increasing fashion. Interlacing together Lorenzian and oligarchic asymptotic analyses, we establish a macroscopic classification of inverted rank distributions into five “socioeconomic” universality classes: communism, socialism, criticality, feudalism, and absolute monarchy. We further establish that: (i) communism and socialism are analogous to a “disordered phase”, feudalism and absolute monarchy are analogous to an “ordered phase”, and criticality is the “phase transition” between order and disorder; (ii) the universality classes are characterized by two critical exponents, one governing the ordered phase, and the other governing the disordered phase; (iii) communism, criticality, and absolute monarchy are characterized by sharp exponent values, and are inherently deterministic; (iv) socialism is characterized by a continuous exponent range, is inherently stochastic, and is universally governed by continuous power-law statistics; (v) feudalism is characterized by a continuous exponent range, is inherently stochastic, and is universally governed by discrete exponential statistics. The results presented in this paper yield a universal macroscopic socioeconophysical perspective of inverted rank distributions.
Lyapunov exponent and criticality in the Hamiltonian mean field model
Filho, L. H. Miranda; Amato, M. A.; Rocha Filho, T. M.
2018-03-01
We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.
Nature of exponents found in the critical regime of YBCO
International Nuclear Information System (INIS)
Marhas, Manmeet Kaur; Saravanan, P.; Balakrishnan, K.; Srinivasan, R.; Kanjilal, D.; Metha, G.K.; Pai, S.P.; Pinto, R.; Vedvyas, M.; Ogale, S.B.; Mohan Rao, G.; Nathan, Senthil; Mohan, S.
1997-01-01
Full text: Fluctuation effects in electrical conductivity near T c is an important tool for studying the nature of phase transition in high T c ceramics. Probing critical regime by way of experiments demand data of good precision. Measurements were carried out on well characterised high T c films prepared by laser ablation and high pressure oxygen sputtering. High energy ion irradiation carried out to see the effect of disorder. Precise electrical resistivity measurements were carried out near T c with a temperature control accuracy better than 10 mK and large number of data points were collected in this regime. 100 MeV oxygen and 200 MeV Ag ions were used with varying fluences for irradiation at 77K. The data was analysed using existing models of critical fluctuation effects. The exponent of electrical conductivity in laser ablated thin films whose transition widths are less than 1 K was 1.33 and is independent of disorder caused by high energy ion irradiation and this could be identified as the exponent for excess conductivity in the critical intermediate charged fluctuation regime as proposed by Fisher. The exponent is around 2.7 in those films whose transition widths are greater than 1 K and also was independent of disorder and this could be identified as exponent in the para coherence regime
Determination of critical exponents of inhomogeneous Gd films
Energy Technology Data Exchange (ETDEWEB)
Rosales-Rivera, A., E-mail: arosalesr@unal.edu.co [Laboratorio de Magnetismo y Materiales Avanzados, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Colombia, Sede Manizales, Manizales (Colombia); Salazar, N.A. [Laboratorio de Magnetismo y Materiales Avanzados, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Colombia, Sede Manizales, Manizales (Colombia); Hovorka, O.; Idigoras, O.; Berger, A. [CIC nanoGUNE Consolider, Tolosa Hiribidea 76, E-20018 Donostia-San Sebastian (Spain)
2012-08-15
The role of inhomogeneity on the critical behavior is studied for non-epitaxial Gd films. For this purpose, the film inhomogeneity was varied experimentally by annealing otherwise identical samples at different temperatures T{sub AN}=200, 400, and 500 Degree-Sign C. Vibrating sample magnetometry (VSM) was used for magnetization M vs. T measurements at different external fields H. A method based upon the linear superposition of different sample parts having different Curie temperatures T{sub C} was used to extract the critical exponents and the intrinsic distribution of Curie temperatures. We found that this method allows extracting reliable values of the critical exponents for all annealing temperatures, which enabled us to study the effects of disorder onto the universality class of Gd films.
Determination of critical exponents of inhomogeneous Gd films
International Nuclear Information System (INIS)
Rosales-Rivera, A.; Salazar, N.A.; Hovorka, O.; Idigoras, O.; Berger, A.
2012-01-01
The role of inhomogeneity on the critical behavior is studied for non-epitaxial Gd films. For this purpose, the film inhomogeneity was varied experimentally by annealing otherwise identical samples at different temperatures T AN =200, 400, and 500 °C. Vibrating sample magnetometry (VSM) was used for magnetization M vs. T measurements at different external fields H. A method based upon the linear superposition of different sample parts having different Curie temperatures T C was used to extract the critical exponents and the intrinsic distribution of Curie temperatures. We found that this method allows extracting reliable values of the critical exponents for all annealing temperatures, which enabled us to study the effects of disorder onto the universality class of Gd films.
Critical exponents for the Reggeon quantum spin model
International Nuclear Information System (INIS)
Brower, R.C.; Furman, M.A.
1978-01-01
The Reggeon quantum spin (RQS) model on the transverse lattice in D dimensional impact parameter space has been conjectured to have the same critical behaviour as the Reggeon field theory (RFT). Thus from a high 'temperature' series of ten (D=2) and twenty (D=1) terms for the RQS model the authors extrapolate to the critical temperature T=Tsub(c) by Pade approximants to obtain the exponents eta=0.238 +- 0.008, z=1.16 +- 0.01, γ=1.271 +- 0.007 for D=2 and eta=0.317 +- 0.002, z=1.272 +- 0.007, γ=1.736 +- 0.001, lambda=0.57 +- 0.03 for D=1. These exponents naturally interpolate between the D=0 and D=4-epsilon results for RFT as expected on the basis of the universality conjecture. (Auth.)
New relation for critical exponents in the Ising model
International Nuclear Information System (INIS)
Pishtshev, A.
2007-01-01
The Ising model in a transverse field is considered at T=0. From the analysis of the power low behaviors of the energy gap and the order parameter as functions of the field a new relation between the respective critical exponents, β>=1/(8s 2 ), is derived. By using the Suzuki equivalence from this inequality a new relation for critical exponents in the Ising model, β>=1/(8ν 2 ), is obtained. A number of numerical examples for different cases illustrates the generality and validity of the relation. By applying this relation the estimation ν=(1/4) 1/3 ∼0.62996 for the 3D-Ising model is proposed
Magnetic entropy change and critical exponents in double perovskite Y2NiMnO6
Sharma, G.; Tripathi, T. S.; Saha, J.; Patnaik, S.
2014-11-01
We report the magnetic entropy change (ΔSM) and the critical exponents in the double perovskite manganite Y2NiMnO6 with a ferromagnetic to paramagnetic transition TC~85 K. For a magnetic field change ΔH=80 kOe, a maximum magnetic entropy change ΔSM=-6.57 J/kg K is recorded around TC. The critical exponents β=0.363±0.05 and γ=1.331±0.09 obtained from power law fitting to spontaneous magnetization MS(T) and the inverse initial susceptibility χ0-1(T) satisfy well to values derived for a 3D-Heisenberg ferromagnet. The critical exponent δ=4.761±0.129 is determined from the isothermal magnetization at TC. The scaling exponents corresponding to second order phase transition are consistent with the exponents from Kouvel-Fisher analysis and satisfy Widom's scaling relation δ=1+(γ/β). Additionally, they also satisfy the single scaling equation M(H,ɛ)=ɛβf±(H/ɛ) according to which the magnetization-field-temperature data around TC should collapse into two curves for temperatures below and above TC.
International Nuclear Information System (INIS)
Sanders, Sören; Holthaus, Martin
2017-01-01
We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose–Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems. (paper)
Sanders, Sören; Holthaus, Martin
2017-10-01
We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.
Wilson's theory of critical phenomena. Higher order corrections to critical exponents
International Nuclear Information System (INIS)
Zinn-Justin, J.
1973-01-01
The Wilson's theory of critical phenomena is presented, in the context of renormalized field theory in d dimension and of the Callan-Symanzik equations. This theory allows in particular to compute critical exponents that govern the behavior of some correlation functions near the critical temperature, as power series in epsilon=4-d, using the standard perturbation theory. Owing to the large value of the expansion parameter epsilon, whose physical value is one, it is very important to perform higher order calculations [fr
Critical behavior of the Lyapunov exponent in type-III intermittency
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Llamoza, O. [Departamento de Fisica, FACYT, Universidad de Carabobo, Valencia (Venezuela); Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela)], E-mail: llamoza@ula.ve; Cosenza, M.G. [Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela); Ponce, G.A. [Departamento de Fisica, Universidad Nacional Autonoma de Honduras (Honduras); Departamento de Ciencias Naturales, Universidad Pedagogica Nacional Francisco Morazan, Tegucigalpa (Honduras)
2008-04-15
The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent {beta} expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that {beta} varies on the interval 0 {<=} {beta} < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent {beta} implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition.
Thickness dependence of effective critical exponents in three-dimensional Ising plates
International Nuclear Information System (INIS)
Marques, M.I.; Gonzalo, J.A.
2000-01-01
Phase transitions in ising plates of equal area and different thickness have been studied by the Monte Carlo approach. The evolution of the critical temperature and of the effective critical exponents with the thickness of the lattice has been numerically determined. The thickness dependence of the maximum value of the effective critical exponents is well described by an exponential decay towards the respective three-dimensional value. (author)
Truncatable bootstrap equations in algebraic form and critical surface exponents
Energy Technology Data Exchange (ETDEWEB)
Gliozzi, Ferdinando [Dipartimento di Fisica, Università di Torino andIstituto Nazionale di Fisica Nucleare - sezione di Torino,Via P. Giuria 1, Torino, I-10125 (Italy)
2016-10-10
We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space dimensions provides algebraic identities among conformal block derivatives which generate the exact spectrum of the infinitely many primary operators contributing to it. In boundary conformal field theories, we point out that the appearance of free parameters in the solutions of bootstrap equations is not an artifact of truncations, rather it reflects a physical property of permeable conformal interfaces which are described by the same equations. Surface transitions correspond to isolated points in the parameter space. We are able to locate them in the case of 3d Ising model, thanks to a useful algebraic form of 3d boundary bootstrap equations. It turns out that the low-lying spectra of the surface operators in the ordinary and the special transitions of 3d Ising model form two different solutions of the same polynomial equation. Their interplay yields an estimate of the surface renormalization group exponents, y{sub h}=0.72558(18) for the ordinary universality class and y{sub h}=1.646(2) for the special universality class, which compare well with the most recent Monte Carlo calculations. Estimates of other surface exponents as well as OPE coefficients are also obtained.
Condensation and critical exponents of an ideal non-Abelian gas
Talaei, Zahra; Mirza, Behrouz; Mohammadzadeh, Hosein
2017-11-01
We investigate an ideal gas obeying non-Abelian statistics and derive the expressions for some thermodynamic quantities. It is found that thermodynamic quantities are finite at the condensation point where their derivatives diverge and, near this point, they behave as \\vert T-Tc\\vert^{-ρ} in which Tc denotes the condensation temperature and ρ is a critical exponent. The critical exponents related to the heat capacity and compressibility are obtained by fitting numerical results and others are obtained using the scaling law hypothesis for a three-dimensional non-Abelian ideal gas. This set of critical exponents introduces a new universality class.
Numerical difficulties to obtain 3-d critical exponents from platonic solids
International Nuclear Information System (INIS)
Alcaraz, F.C.; Herrmann, H.J.
1985-01-01
The possibility to extract critical exponents of 3-d systems exploring the mass gap amplitudes of platonic solids is tested. For the Ising model the proposed method does not work for numerical reasons. (Author) [pt
High-accuracy critical exponents for O(N) hierarchical 3D sigma models
International Nuclear Information System (INIS)
Godina, J. J.; Li, L.; Meurice, Y.; Oktay, M. B.
2006-01-01
The critical exponent γ and its subleading exponent Δ in the 3D O(N) Dyson's hierarchical model for N up to 20 are calculated with high accuracy. We calculate the critical temperatures for the measure δ(φ-vector.φ-vector-1). We extract the first coefficients of the 1/N expansion from our numerical data. We show that the leading and subleading exponents agree with Polchinski equation and the equivalent Litim equation, in the local potential approximation, with at least 4 significant digits
Critical exponents predicted by grouping of Feynman diagrams in φ4 model
International Nuclear Information System (INIS)
Kaupuzs, J.
2001-01-01
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams of φ 4 model with O(n) symmetry. As a result, equations for calculation of the two-point correlation function are obtained which allow to predict possible exact values of critical exponents in two and three dimensions by proving relevant scaling properties of the asymptotic solution at (and near) the criticality. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments. (orig.)
International Nuclear Information System (INIS)
Kiskis, J.; Narayanan, R.; Vranas, P.
1993-01-01
The authors study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, the authors show that the critical exponent v describing the vanishing of the physical mass at the critical point is equal to v θ /d w , where d w is the Hausdorff dimension of the walk, and v θ = var-phi, where var-phi is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is var-phi/v for O(N) models. 3 refs
Critical behavior of the Lyapunov exponent in type-III intermittency
International Nuclear Information System (INIS)
Alvarez-Llamoza, O.; Cosenza, M.G.; Ponce, G.A.
2008-01-01
The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent β expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that β varies on the interval 0 ≤ β < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent β implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition
Rigorous lower bound on the dynamic critical exponent of some multilevel Swendsen-Wang algorithms
International Nuclear Information System (INIS)
Li, X.; Sokal, A.D.
1991-01-01
We prove the rigorous lower bound z exp ≥α/ν for the dynamic critical exponent of a broad class of multilevel (or ''multigrid'') variants of the Swendsen-Wang algorithm. This proves that such algorithms do suffer from critical slowing down. We conjecture that such algorithms in fact lie in the same dynamic universality class as the stanard Swendsen-Wang algorithm
The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice
Heydenreich, Markus; Kolesnikov, Leonid
2018-04-01
We consider the ferromagnetic nearest-neighbor Ising model on regular trees (Bethe lattice), which is well-known to undergo a phase transition in the absence of an external magnetic field. The behavior of the model at critical temperature can be described in terms of various critical exponents; one of them is the critical 1-arm exponent ρ which characterizes the rate of decay of the (root) magnetization as a function of the distance to the boundary. The crucial quantity we analyze in this work is the thermal expectation of the root spin on a finite subtree, where the expected value is taken with respect to a probability measure related to the corresponding finite-volume Hamiltonian with a fixed boundary condition. The spontaneous magnetization, which is the limit of this thermal expectation in the distance between the root and the boundary (i.e., in the height of the subtree), is known to vanish at criticality. We are interested in a quantitative analysis of the rate of this convergence in terms of the critical 1-arm exponent ρ. Therefore, we rigorously prove that ⟨σ0⟩ n +, the thermal expectation of the root spin at the critical temperature and in the presence of the positive boundary condition, decays as ⟨σ0 ⟩ n +≈n-1/2 (in a rather sharp sense), where n is the height of the tree. This establishes the 1-arm critical exponent for the Ising model on regular trees (ρ =1/2 ).
International Nuclear Information System (INIS)
Gauzzi, A.
1993-01-01
The Aslamazov-Larkin paraconductivity term is calculated in the case of sufficiently small superconducting coherence length. It is found that the critical exponent of paraconductivity depends on the short-wavelength cut-off of the fluctuation spectrum in the whole Ginzburg-Landau mean-field region. Hence, it is predicted that the Aslamazov-Larkin universal relation between the critical exponent of paraconductivity and the dimensionality of the superconducting state is no longer valid in short-coherence-length superconductors. This prediction is confirmed by paraconductivity measurements on cuprate superconductors. (orig.)
Magnetic entropy change and critical exponents in double perovskite Y{sub 2}NiMnO{sub 6}
Energy Technology Data Exchange (ETDEWEB)
Sharma, G. [School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067 (India); Tripathi, T.S. [Inter-University Accelerator Centre, New Delhi-110067 (India); Saha, J. [School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067 (India); Patnaik, S., E-mail: spatnaik@mail.jnu.ac.in [School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067 (India)
2014-11-15
We report the magnetic entropy change (ΔS{sub M}) and the critical exponents in the double perovskite manganite Y{sub 2}NiMnO{sub 6} with a ferromagnetic to paramagnetic transition T{sub C}∼85K. For a magnetic field change ΔH=80kOe, a maximum magnetic entropy change ΔS{sub M}=−6.57J/kgK is recorded around T{sub C}. The critical exponents β=0.363±0.05 and γ=1.331±0.09 obtained from power law fitting to spontaneous magnetization M{sub S}(T) and the inverse initial susceptibility χ{sub 0}{sup −1}(T) satisfy well to values derived for a 3D-Heisenberg ferromagnet. The critical exponent δ=4.761±0.129 is determined from the isothermal magnetization at T{sub C}. The scaling exponents corresponding to second order phase transition are consistent with the exponents from Kouvel–Fisher analysis and satisfy Widom's scaling relation δ=1+(γ/β). Additionally, they also satisfy the single scaling equation M(H,ϵ)=ϵ{sup β}f±(H/ϵ{sup β+γ}) according to which the magnetization-field-temperature data around T{sub C} should collapse into two curves for temperatures below and above T{sub C}. - Highlights: • The magneto-caloric (MC) effect and the critical exponent analysis in Y{sub 2}NiMnO{sub 6} are studied. • Methods such as Kouvel–Fisher, Widom's and Mean-Field scaling are used. • The magnetic ground state in Y{sub 2}NiMnO{sub 6} is based on isotropic 3D Heisenberg model. • The large MC effect can be utilized towards magnetic refrigeration around 77 K. • The nearest neighbor interaction in Y{sub 2}NiMnO{sub 6} rules out ferroelectricity.
Critical exponents in the transition to chaos in one-dimensional
Indian Academy of Sciences (India)
We report the numerically evaluated critical exponents associated with the scaling of generalized fractal dimensions during the transition from order to chaos. The analysis is carried out in detail in the context of unimodal and bimodal maps representing typical one-dimensional discrete dynamical systems. The behavior of ...
Singular elliptic systems involving concave terms and critical Caffarelli-Kohn-Nirenberg exponents
Directory of Open Access Journals (Sweden)
Mohammed E. O. El Mokhtar
2012-03-01
Full Text Available In this article, we establish the existence of at least four solutions to a singular system with a concave term, a critical Caffarelli-Kohn-Nirenberg exponent, and sign-changing weight functions. Our main tools are the Nehari manifold and the mountain pass theorem.
Four-loop critical exponents for the Gross-Neveu-Yukawa models
International Nuclear Information System (INIS)
Zerf, Nikolai; Mihaila, Luminita N.; Herbut, Igor F.; Scherer, Michael M.
2017-09-01
We study the chiral Ising, the chiral XY and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4-ε dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order O(ε 4 ). Further, we provide Pade estimates for the correlation length exponent, the boson and fermion anomalous dimension as well as the leading correction to scaling exponent in 2+1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N=1/4 and N=1/2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.
Four-loop critical exponents for the Gross-Neveu-Yukawa models
Energy Technology Data Exchange (ETDEWEB)
Zerf, Nikolai; Mihaila, Luminita N. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; Marquard, Peter [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Herbut, Igor F. [Simon Fraser Univ., Burnaby, BC (Canada). Dept. of Physics; Scherer, Michael M. [Koeln Univ. (Germany). Inst. for Theoretical Physics
2017-09-15
We study the chiral Ising, the chiral XY and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in 4-ε dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order O(ε{sup 4}). Further, we provide Pade estimates for the correlation length exponent, the boson and fermion anomalous dimension as well as the leading correction to scaling exponent in 2+1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with N=1/4 and N=1/2 fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.
Directory of Open Access Journals (Sweden)
Jie-Xiong Mo
2014-01-01
Full Text Available We investigate the phase transitions of black holes with conformal anomaly in canonical ensemble. Some interesting and novel phase transition phenomena have been discovered. It is shown that there are striking differences in both Hawking temperature and phase structure between black holes with conformal anomaly and those without it. Moreover, we probe in detail the dependence of phase transitions on the choice of parameters. The results show that black holes with conformal anomaly have much richer phase structure than those without it. There would be two, only one, or no phase transition points depending on the parameters. The corresponding parameter regions are derived both numerically and graphically. Geometrothermodynamics are built up to examine the phase structure we have discovered. It is shown that Legendre invariant thermodynamic scalar curvature diverges exactly where the specific heat diverges. Furthermore, critical behaviors are investigated by calculating the relevant critical exponents. And we prove that these critical exponents satisfy the thermodynamic scaling laws.
Some existence results for a fourth order equation involving critical exponent
Ben-Ayed, M; Hammami, M
2003-01-01
In this paper a fourth order equation involving critical growth is considered under the Navier boundary condition: DELTA sup 2 u = Ku sup p , u > 0 in OMEGA, u = DELTA u = 0 on partial deriv OMEGA, where K is a positive function, OMEGA is a bounded smooth domain in R sup n , n >= 5 and p + 1 2n/(n - 4) is the critical Sobolev exponent. We give some topological conditions on K to ensure the existence of solutions. Our methods involve the study of the critical points at infinity and their contribution to the topology of the level sets of the associated Euler Lagrange functional.
International Nuclear Information System (INIS)
Basnarkov, Lasko; Urumov, Viktor
2009-01-01
We consider an analytically solvable version of the Winfree model of synchronization of phase oscillators (proposed by Ariaratnam and Strogatz 2001 Phys. Rev. Lett. 86 4278). It is obtained that the transition from incoherence to a partial death state is characterized by third-order or higher phase transitions according to the Ehrenfest classification. The order of the transition depends on the shape of the distribution function for natural frequencies of oscillators in the vicinity of their lowest frequency. The corresponding critical exponents are found analytically and verified with numerical simulations of equations of motion. We also consider the generalized Winfree model with the interaction strength proportional to a power of the Kuramoto order parameter and find the domain where the critical exponent remains unchanged by this modification
Ogawa, Shun; Yamaguchi, Yoshiyuki Y
2015-06-01
An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two nonclassical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends the universality class of the nonclassical exponents to spatially periodic one-dimensional systems and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.
Critical exponents for square lattice trails with a fixed number of vertices of degree 4
International Nuclear Information System (INIS)
James, E W; Soteros, C E
2002-01-01
We prove several previously conjectured results about the number of n-edge trails and n-edge embeddings of Eulerian graphs, each with a fixed number, k, of degree 4 vertices, in the lattice Z 2 . In particular, under the assumption that the relevant critical exponents exist, we prove that the difference between the critical exponent for closed trails (Eulerian graph embeddings) and that for self-avoiding circuits (polygons) is exactly k, the number of degree 4 vertices. Similarly, we prove that the difference between the critical exponent for either open trails or open Eulerian graph embeddings and that for self-avoiding walks is also k. These results are proved by establishing upper and lower bounds for the number of n-edge embeddings of closed (open) Eulerian graphs with k vertices of degree 4 in terms of the number of n-edge self-avoiding polygons (walks). The lower bounds are proved using a Kesten pattern theorem argument and the upper bounds are established by developing (based on a detailed case analysis) a method for removing vertices of degree 4 from an embedding by altering at most a constant (independent of n) number of vertices and edges of the embedding. The work presented here extends and improves the arguments first given in the work of Zhao and Lookman (1993 J. Phys. A: Math. Gen. 26 1067-76)
International Nuclear Information System (INIS)
Riera, R.; Oliveira, P.M.C. de; Chaves, C.M.G.F.; Queiroz, S.L.A. de.
1980-04-01
A real-space renormalization group approach for the bond percolation problem in a square lattice with first- and second- neighbour bonds is proposed. The respective probabilities are treated, as independent variables. Two types of cells are constructed. In one of them the lattice is considered as two interpenetrating sublattices, first-neighbour bonds playing the role of intersublattice links. This allows the calculation of both critical exponents ν and γ, without resorting to any external field. Values found for the critical indices are in good agreement with data available in the literature. The phase diagram in parameter space is also obtained in each case. (Author) [pt
International Nuclear Information System (INIS)
Qin Shaojin; Yu Lu.
1996-03-01
The critical exponent of the momentum distribution near k F , 3k F and 5k F are studied numerically for one-dimensional U → ∞ Hubbard model, using finite size systems and extrapolating them to the thermodynamic limit. Results at k F agree with earlier calculations, while at 3k F exponents less than 1 are obtained for finite size systems with extrapolation to 1 (regular behaviour) in the thermodynamic limit, in contrast to earlier analytic prediction 9/8. The distribution is regular at 5k F even for finite systems. The singularity near 3k F is interpreted as due to low energy excitations near 3k F in finite systems. (author). 18 refs, 4 figs, 1 tab
Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class
Gracey, J. A.
2018-01-01
We compute the large N critical exponents η, ηϕ and 1/ν in d dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of 1/N. For instance, the large N conformal bootstrap method is used to determine η at O(1/N3) while the other exponents are computed to O(1/N2). Estimates of the exponents for a phase transition in graphene are given which are shown to be commensurate with other approaches. In particular the behavior of the exponents in 2
Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.
Leibovich, N; Dechant, A; Lutz, E; Barkai, E
2016-11-01
The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.
Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model
Liu, Maoxin; Chesi, Stefano; Ying, Zu-Jian; Chen, Xiaosong; Luo, Hong-Gang; Lin, Hai-Qing
2017-12-01
We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N >1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N =1 up to the thermodynamic limit.
International Nuclear Information System (INIS)
Boulatov, D.V.; Kazakov, V.A.
1987-01-01
We investigate the critical properties of a recently proposed exactly soluble Ising model on a planar random dynamical lattice representing a regularization of the zero-dimensional string with internal fermions. The sum over all lattices gives rise to a new quantum degree of freedom - fluctuation of the metric. The whole system of critical exponents is found: α = -1, β = 1/2, γ = 2, δ = 5, v . D = 3. To test the universality we have used the planar graphs with the coordination number equal to 4 (Φ 4 theory graphs) as well as with the equal to 3 (Φ 3 theory graphs or triangulations). The critical exponents coincide for both cases. (orig.)
Landau-Ginzburg Limit of Black Hole's Quantum Portrait: Self Similarity and Critical Exponent
Dvali, Gia
2012-01-01
Recently we have suggested that the microscopic quantum description of a black hole is an overpacked self-sustained Bose-condensate of N weakly-interacting soft gravitons, which obeys the rules of 't Hooft's large-N physics. In this note we derive an effective Landau-Ginzburg Lagrangian for the condensate and show that it becomes an exact description in a semi-classical limit that serves as the black hole analog of 't Hooft's planar limit. The role of a weakly-coupled Landau-Ginzburg order parameter is played by N. This description consistently reproduces the known properties of black holes in semi-classical limit. Hawking radiation, as the quantum depletion of the condensate, is described by the slow-roll of the field N. In the semiclassical limit, where black holes of arbitrarily small size are allowed, the equation of depletion is self similar leading to a scaling law for the black hole size with critical exponent 1/3.
On the curve of critical exponents for nonlinear elliptic problems in the case of a zero mass
Il'yasov, Ya. Sh.
2017-03-01
For semilinear elliptic equations -Δ u = λ| u| p-2 u-| u| q-2 u, boundary value problems in bounded and unbounded domains are considered. In the plane of exponents p × q, the so-called curves of critical exponents are defined that divide this plane into domains with qualitatively different properties of the boundary value problems and the corresponding parabolic equations. New solvability conditions for boundary value problems, conditions for the stability and instability of stationary solutions, and conditions for the existence of global solutions to parabolic equations are found.
Critical exponents of a fluid mixture in the presence of isotope exchange: Isobutyric acid/D2O
International Nuclear Information System (INIS)
Gulari, E.; Chu, B.; Woermann, D.
1980-01-01
Experiments on phase diagrams and critical opalescence of a fluid mixture, isobutyric acid in D 2 O, indicate that the presence of isotope exchange reactions can change the critical behavior of such a system from that of a simple binary fluid mixture. Appreciable amounts of additional species due to isotope exchange distort the coexistence curve, shift the critical solution concentration y/sub c/ away from the concentration (y/sub I/*) where the maximal phase separation temperature T/sub p/,max occurs, and make the critical exponents γ and ν in the one-phase region (T>T/sub c/) different from those of the coexisting two-phase region (T 0 C differing from y/sub I/*=0.310 at T/sub p/,max=45.11 0 C. In the one-phase region, γ=1.25, ν=0.633, and xi 0 =3.13 A, in excellent agreement with γ=1.24 and ν=0.633 of simple fluid systems. However, in the coexisting two-phase region, the critical exponents appear to be renormalized with γ/sub x/ =1.39, ν/sub x/approx. =0.76, and xi 0 approx. =0.6 A. These results are in agreement with the renormalized critical exponents γ/sub x/=1.40 +- 0.02 and ν/sub x/ =0.73 +- 0.04 near the plait point of a ternary liquid mixture: ethanol--water--chloroform
The relation between mass-gap amplitudes and critical exponents in the Heisenberg model
International Nuclear Information System (INIS)
Alcaraz, F.C.; Felicio, J.R.D. de
1985-01-01
A recent result concerning the universality of the ratio of mass-gap amplitudes using the well known 1-D Heisenberg model which is the quantum version of the two-dimensional eight-vertex model is discussed. The believed extended scaling relation (x sub(p) = x sub(is an element of)/4) relating the polarization and energy anomalous dimensions is confirmed. The exponent, α, ν, γ sub(m) and γ sub(p) is also obtained by usual phenomenological renormalization group methods. (Author) [pt
Energy Technology Data Exchange (ETDEWEB)
Park, Miok [Korea Institute for Advanced Study, Seoul (Korea, Republic of); Park, Jiwon; Oh, Jae-Hyuk [Hanyang University, Department of Physics, Seoul (Korea, Republic of)
2017-11-15
Einstein-scalar-U(2) gauge field theory is considered in a spacetime characterized by α and z, which are the hyperscaling violation factor and the dynamical critical exponent, respectively. We consider a dual fluid system of such a gravity theory characterized by temperature T and chemical potential μ. It turns out that there is a superfluid phase transition where a vector order parameter appears which breaks SO(3) global rotation symmetry of the dual fluid system when the chemical potential becomes a certain critical value. To study this system for arbitrary z and α, we first apply Sturm-Liouville theory and estimate the upper bounds of the critical values of the chemical potential. We also employ a numerical method in the ranges of 1 ≤ z ≤ 4 and 0 ≤ α ≤ 4 to check if the Sturm-Liouville method correctly estimates the critical values of the chemical potential. It turns out that the two methods are agreed within 10 percent error ranges. Finally, we compute free energy density of the dual fluid by using its gravity dual and check if the system shows phase transition at the critical values of the chemical potential μ{sub c} for the given parameter region of α and z. Interestingly, it is observed that the anisotropic phase is more favored than the isotropic phase for relatively small values of z and α. However, for large values of z and α, the anisotropic phase is not favored. (orig.)
Crauel, Hans; Eckmann, Jean-Pierre
1991-01-01
Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: The upper Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the problem of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant me...
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Ivanov, Alexei
2000-08-01
A model system, described by the consistent Vlasov-Poisson equations under periodical boundary conditions, has been studied numerically near the point of a marginal stability. The power laws, typical for a system, undergoing a second-order phase transition, hold in a vicinity of the critical point: (i) A ∝ -θ β , β=1.907±0.006 for θ ≤ 0, where A is the saturated amplitude of the marginally-stable mode; (ii) χ ∝ θ -γ as θ → 0, γ=γ - =1.020±0.008 for θ + =0.995±0.020 for θ > 0, where χ=∂A/∂F 1 at F 1 → 0 is the susceptibility to external drive of the strain F 1 ; (iii) at θ=0 the system responds to external drive as A ∝ F 1 1/δ , and δ=1.544±0.002. θ=( 2 >- cr 2 >)/ cr 2 > is the dimensionless reduced velocity dispersion. Within the error of computation these critical exponents satisfy to equality γ=β(δ-1), known in thermodynamics as the Widom equality, which is direct consequence of scaling invariance of the Fourier components f m of the distribution function f at |θ| m (λ at t, λ av v, λ aθ θ, λ aA0 A 0 , λ aF F 1 )=λf m (t, v, θ, A 0 , F 1 ) at θ approx. = 0. On the contrary to thermodynamics these critical indices indicate to a very wide critical area. In turn, it means that critical phenomena may determine macroscopic dynamics of a large fraction of systems. (author)
Sire, Clément
2004-09-24
We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.
International Nuclear Information System (INIS)
Mookerjee, A.
1984-09-01
The problem of spin-glass to ferromagnetic transition with increasing concentration is then one of the familiar nearest neighbour percolation but on the background of IIC. In the regime p<=psub(c) at T=Tsub(g)(p), the IIC forms a fractal background on which ferromagnetic percolation takes place. The equivalent statement is that the mobility edge Jsub(c)(p) moves outwards as p increases and at a critical psub(c) coincides with the band edge Jsub(B). At and above these concentrations the mode with highest energy is extended and we have the familiar paramagnetic to ferromagnetic transition as temperature is lowered across Jsub(B)/ksub(B). The physical justification of this picture is not at all transparent as in the case of the cluster percolation ideas. To this date no reliable estimates of the behaviour of Jsub(c)(p) as a function of p, for a purely off diagonal random matrix J(R) have been made
Fidelity susceptibility as holographic PV-criticality
Energy Technology Data Exchange (ETDEWEB)
Momeni, Davood, E-mail: davoodmomeni78@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Faizal, Mir, E-mail: mirfaizalmir@googlemail.com [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); Irving K. Barber School of Arts and Sciences, University of British Columbia – Okanagan, 3333 University Way, Kelowna, British Columbia V1V 1V7 (Canada); Myrzakulov, Kairat, E-mail: kairatmyrzakul@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Myrzakulov, Ratbay, E-mail: rmyrzakulov@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan)
2017-02-10
It is well known that entropy can be used to holographically establish a connection among geometry, thermodynamics and information theory. In this paper, we will use complexity to holographically establish a connection among geometry, thermodynamics and information theory. Thus, we will analyze the relation among holographic complexity, fidelity susceptibility, and thermodynamics in extended phase space. We will demonstrate that fidelity susceptibility (which is the informational complexity dual to a maximum volume in AdS) can be related to the thermodynamical volume (which is conjugate to the cosmological constant in the extended thermodynamic phase space). Thus, this letter establishes a relation among geometry, thermodynamics, and information theory, using complexity.
Energy Technology Data Exchange (ETDEWEB)
Lvanov, Alexei [Theory and Computer Simulation Center, National Inst. for Fusion Science, Toki, Gifu (Japan)
2000-08-01
A model system, described by the consistent Vlasov-Poisson equations under periodical boundary conditions, has been studied numerically near the point of a marginal stability. The power laws, typical for a system, undergoing a second-order phase transition, hold in a vicinity of the critical point: (i) A {proportional_to} -{theta}{sup {beta}}, {beta}=1.907{+-}0.006 for {theta} {<=} 0, where A is the saturated amplitude of the marginally-stable mode; (ii) {chi} {proportional_to} {theta}{sup -{gamma}} as {theta} {yields} 0, {gamma}={gamma}{sub -}=1.020{+-}0.008 for {theta} < 0, and {gamma}={gamma}{sub +}=0.995{+-}0.020 for {theta} > 0, where {chi}={partial_derivative}A/{partial_derivative}F{sub 1} at F{sub 1} {yields} 0 is the susceptibility to external drive of the strain F{sub 1}; (iii) at {theta}=0 the system responds to external drive as A {proportional_to} F{sub 1}{sup 1/{delta}}, and {delta}=1.544{+-}0.002. {theta}=(
Barreira, Luís
2017-01-01
This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.
Janssen, S.; Schwahn, D.; Springer, T.
1992-05-01
The critical behavior of the polymer blend d-PB/PS was investigated by small-angle neutron scattering experiments. 3D Ising behavior was clearly observed with the critical exponents γ=1.26+/-0.01, ν=0.59+/-0.01, and η=0.047+/-0.004. The crossover to mean-field behavior occurs at T*=Tc+5.4 K. This is compared with the results of other experiments and the Landau-Ginzburg criterion. The Q dependence of the structure factor S(Q) follows the Ornstein-Zernike form in both regimes.
Landslide Susceptibility Statistical Methods: A Critical and Systematic Literature Review
Mihir, Monika; Malamud, Bruce; Rossi, Mauro; Reichenbach, Paola; Ardizzone, Francesca
2014-05-01
Landslide susceptibility assessment, the subject of this systematic review, is aimed at understanding the spatial probability of slope failures under a set of geomorphological and environmental conditions. It is estimated that about 375 landslides that occur globally each year are fatal, with around 4600 people killed per year. Past studies have brought out the increasing cost of landslide damages which primarily can be attributed to human occupation and increased human activities in the vulnerable environments. Many scientists, to evaluate and reduce landslide risk, have made an effort to efficiently map landslide susceptibility using different statistical methods. In this paper, we do a critical and systematic landslide susceptibility literature review, in terms of the different statistical methods used. For each of a broad set of studies reviewed we note: (i) study geography region and areal extent, (ii) landslide types, (iii) inventory type and temporal period covered, (iv) mapping technique (v) thematic variables used (vi) statistical models, (vii) assessment of model skill, (viii) uncertainty assessment methods, (ix) validation methods. We then pulled out broad trends within our review of landslide susceptibility, particularly regarding the statistical methods. We found that the most common statistical methods used in the study of landslide susceptibility include logistic regression, artificial neural network, discriminant analysis and weight of evidence. Although most of the studies we reviewed assessed the model skill, very few assessed model uncertainty. In terms of geographic extent, the largest number of landslide susceptibility zonations were in Turkey, Korea, Spain, Italy and Malaysia. However, there are also many landslides and fatalities in other localities, particularly India, China, Philippines, Nepal and Indonesia, Guatemala, and Pakistan, where there are much fewer landslide susceptibility studies available in the peer-review literature. This
International Nuclear Information System (INIS)
Gulpinar, Gul; Vatansever, Erol
2012-01-01
In this study, the temperature variations of the equilibrium and the non-equilibrium antiferromagnetic and ferromagnetic susceptibilities of a metamagnetic system are examined near the critical point. The kinetic equations describing the time dependencies of the total and staggered magnetizations are derived by utilizing linear response theory. In order to obtain dynamic magnetic relaxation behavior of the system, the stationary solutions of the kinetic equations in existence of sinusoidal staggered and physical external magnetic fields are performed. In addition, the static and dynamical mean field critical exponents are calculated in order to formulate the critical behavior of antiferromagnetic and ferromagnetic magnetic response of a metamagnetic system. Finally, a comparison of the findings of this study with previous theoretical and experimental studies is represented and it is shown that a good agreement is found with our results. - Highlights: ► Staggered dynamic susceptibility diverges as T→T N in the low frequency region. ► Dynamic total susceptibility exhibits a finite jump discontinuity as T→T N while wτ 2 ⪡1. ► The slope of the staggered magnetic dispersion curve chances in sign as T→T N .
El-Showk, Sheer; Poland, David; Rychkov, Slava; Simmons-Duffin, David; Vichi, Alessandro
2014-01-01
We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z2-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Delta_sigma=0.518154(15), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.
Evolution of dynamic susceptibility in molecular glass formers-a critical assessment
International Nuclear Information System (INIS)
Brodin, A; Gainaru, C; Porokhonskyy, V; Roessler, E A
2007-01-01
Dielectric, depolarized light scattering (LS) and optical Kerr effect (OKE) data are critically discussed in an attempt to achieve a common interpretation of the evolution of dynamic susceptibility in molecular glass formers at temperatures down to the glass transition T g . The so-called intermediate power-law, observed in OKE data below a certain temperature T x , is identified with the excess wing, long since known from dielectric spectroscopy, with a temperature-independent exponent. This is in contrast with several recent analyses that concluded a considerable temperature dependence of spectral shapes. We introduce a new approach to disentangle α-peak and excess wing contributions in the dielectric spectra, which allows for frequency-temperature superposition (FTS) of the α-process at all temperatures above T g . From the LS spectra we conclude, in particular, that FTS holds even at temperatures well above the melting point, i.e. in normal equilibrium liquids. Attempting to correlate the fragility and stretching, our conclusions are opposite to those made previously. Specifically, we observe that a high fragility is associated with a less stretched relaxation function
Directory of Open Access Journals (Sweden)
H. Yurtseven
2015-09-01
Full Text Available Using Landau mean field model, the spontaneous polarization and the dielectric susceptibility are analyzed as functions of temperature and pressure close to the cubic–tetragonal (ferroelectric–paraelectric transition in BaTiO3. From the analysis of the dielectric susceptibility and the spontaneous polarization, the critical exponents are deduced in the classical and quantum limits for BaTiO3. From the critical behavior of the dielectric susceptibility, the spontaneous polarization can be described for the ferroelectric–paraelectric (cubic to tetragonal transition between 4 and 8 GPa at constant temperatures of 0 to 200 K in BaTiO3 within the Landau mean field model given here.
Critical exponents in nucleus breakup
International Nuclear Information System (INIS)
Campi, X.
1987-01-01
In recent years the study of cluster formation has become a new field in statistical physics. Nuclear reactions with particle number change can be viewed as a cluster formation processes. Multifragmentation decay produces a power law distribution of medium size clusters. These two cluster size distributions resemble that of many others statistical cluster formation processes. We discuss now these analogies in some details
International Nuclear Information System (INIS)
Takada, T.; Watanabe, T.
1980-01-01
The specific heat under saturated vapor pressure of pure 4 He and of six 3 He- 4 He mixtures up to X=0.545 was measured in the temperature range 3 x 10 -6 -2 K. The critical exponents α/sub phi/ and α'/sub phi/ along the path phi=phi/sub lambda/ are independent of X up to X=0.545, where phi(=μ 3 -μ 4 ) is the difference between chemical potentials. If we take account of higher order terms, the exponent α/sub phi/(=α'/sub phi/) and the amplitude ratio A/sub //A'are independent of X up to X=0.545. The values of α/sub phi/ and A/sub //A'/sub phi/ are -0.023 and 1.090, respectively. The critical-tricriticall crossover effect was observed for X=0.545 and the boundary of crossover region closest to the critical region was at theta/T/sub lambda/1(times)=10 -4 , where theta is the distance Vertical BarT-T/sub lambda/Vertical Bar along the path phi=phi/sub lambda/. This value is in good agreement with the estimated value by Riedel et al. But, remarkably, in the case of X=0.439 this effect was not observed
Observation of unusual critical region behavior in the magnetic susceptibility of EuSe
Bykovetz, N.; Klein, J.; Lin, C. L.
2018-05-01
The Europium Chalcogenides (EuCh: EuO, EuS, EuSe, and EuTe) have been regarded as model examples of simple, cubic, Heisenberg exchange coupled magnetic systems, with a ferromagnetic nearest-neighbor exchange constant J1 and an antiferromagnetic next-nearest-neighbor constant J2. Unlike the other EuCh, EuSe exhibits a range of complex magnetic behaviors, the latter being attributed to EuSe being near the point where J2=-J1, where its magnetism appears to consist of nearly de-coupled 2D ferromagnetic sheets. Analysis of precision SQUID measurements of the magnetic susceptibility χ in EuSe showed that in the region from ˜Tc to ˜2Tc, a fit of the data to the critical equation χ = χ2Tc(T/Tc-1)-γ gives γ=2.0, an exponent not predicted by any current theory. Additionally, this fit predicts that Tc should be ˜0K. We tentatively interpret this by saying that in the paramagnetic region the system "thinks" EuSe should not order above T=0. Tc=0K is predicted by the Mermin-Wagner theorem (MW) for Heisenberg-coupled 2D magnetic systems, and we can show that when J2=-J1, MW can also be applied to the J1, J2 exchange model of the EuCh to give a rigorous Tc=0 prediction. Under 10 kbar applied pressure EuSe exhibits a different γ and fitted Tc. An additional, and rather strange, critical-region effect was discovered. The EuSe sample was found to exhibit a relaxation effect in a small range of temperatures, just above and just below the actual Tc of 4.7K, with time constants of up to 5 minutes. We cannot yet fully explain this observed macroscopic effect.
Bera, Anindita; Mishra, Utkarsh; Singha Roy, Sudipto; Biswas, Anindya; Sen(De), Aditi; Sen, Ujjwal
2018-06-01
Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments.
Lyapunov, attractors and exponents
International Nuclear Information System (INIS)
Oliveira, C.R. de.
1987-01-01
Based on the fundamental principles of statistical mechanics and ergodic theory a definition is given to atractor, as an invariant measure. Many results which reinforce this definition are demonstrated. Chaos is related to the presence of an atractor with entropy above zero. The role of Lyapunov exponents is analyzed. (A.C.A.S.) [pt
DEFF Research Database (Denmark)
Li, Xiao-Fen; Grivel, Jean-Claude; Abrahamsen, Asger B.
2012-01-01
We have numerically proved that the dependence of AC susceptibility χ of a E(J) power law superconducting thin disc on many parameters can be reduced to one penetration parameter h, with E the electric field and J the current density. Based on this result, we propose a way of measuring the critical...... current density Jc of superconducting thin films by AC susceptibility. Compared with the normally used method based on the peak of the imaginary part, our method uses a much larger range of the AC susceptibility curve, thus allowing determination of the temperature (T) dependence of Jc from a normally...
Susceptibilities from a black hole engineered EoS with a critical point
International Nuclear Information System (INIS)
Portillo, Israel
2017-01-01
Currently at the Beam Energy Scan at RHIC experimental efforts are being made to find the QCD critical point. On the theoretical side, the behavior of higher-order susceptibilities of the net-baryon charge from Lattice QCD at µ B = 0 may allow us to estimate the position of the critical point in the QCD phase diagram. However, even if the series expansion continues to higher-orders, there is always the possibility to miss the critical point behavior due to truncation errors. An alternative approach is to use a black hole engineered holographic model, which displays a critical point at large densities and matches lattice susceptibilities at µB = 0. Using the thermodynamic data from this black hole model, we obtain the freeze-out points extracted from the net-protons distribution measured at STAR and explore higher order fluctuations at the lowest energies at the beam energy scan to investigate signatures of the critical point. (paper)
On the critical behavior of the inverse susceptibility of a model of structural phase transitions
International Nuclear Information System (INIS)
Pisanova, E.S.; Ivanov, S.I.
2013-01-01
An exactly solvable lattice model describing structural phase transitions in an anharmonic crystal with long-range interaction is considered in the neighborhoods of the quantum and classical critical points at the corresponding upper critical dimensions. In a broader neighborhood of the critical region the inverse susceptibility of the model is exactly calculated in terms of the Lambert W-function and graphically presented as a function of the deviation from the critical point and the upper critical dimension. For quantum and classical systems with real physical dimensions (chains, thin layers and three-dimensional systems) the exact results are compared with the asymptotic ones on the basis of some numerical data for their ratio. Relative errors are also provided
Analysis of critical state response in thin films by AC susceptibility measurements
Czech Academy of Sciences Publication Activity Database
Youssef, A.; Švindrych, Z.; Hadač, J.; Janů, Zdeněk
2008-01-01
Roč. 18, č. 2 (2008), s. 1589-1592 ISSN 1051-8223 R&D Projects: GA ČR GA102/05/0942 Institutional research plan: CEZ:AV0Z10100520 Keywords : AC susceptibility * critical state * harmonics * thin film * axial magnetic-field * superconductor disks * cylinders Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.919, year: 2008
Energy Technology Data Exchange (ETDEWEB)
Pallas, Norman R., E-mail: Sam-7-iam@hotmail.com [BP Research Centre Warrensville, 4440 Warrensville Center Road, Cleveland, Ohio 44128 (United States)
2016-03-21
The three-phase contact angle (θ) for the system cyclohexane/aniline/quartz has been measured from drop shapes as a function of temperature on approach to the cyclohexane/aniline upper consolute solution temperature T{sub c}. The experiments employed exacting criteria previously established for thermodynamic-quality measurements at fluid interfaces. A first-order wetting transition from partial wetting to complete wetting was observed at a temperature T{sub w}, 2.12 K below T{sub c}. The contact angle vanishes at T{sub w}, scaling as cos θ ∼ |T − T{sub c}|{sup β{sub 1}−μ} for T < T{sub w} and cos θ = 1.0 for T{sub w} < T < T{sub c}. The experimental results give a value for β{sub 1} = 0.74 ± 0.03, in agreement with theoretical calculations. The data clearly rule out higher order contributions to the change in the contact angle near the critical point for this system. These results are in marked contrast to previous measurements on this system from measurements of capillary rise and meniscus curvature.
Critical behavior of ferromagnetic Ising thin films
International Nuclear Information System (INIS)
Cossio, P.; Mazo-Zuluaga, J.; Restrepo, J.
2006-01-01
In the present work, we study the magnetic properties and critical behavior of simple cubic ferromagnetic thin films. We simulate LxLxd films with semifree boundary conditions on the basis of the Monte Carlo method and the Ising model with nearest neighbor interactions. A Metropolis dynamics was implemented to carry out the energy minimization process. For different film thickness, in the nanometer range, we compute the temperature dependence of the magnetization, the magnetic susceptibility and the fourth order Binder's cumulant. Bulk and surface contributions of these quantities are computed in a differentiated fashion. Additionally, according to finite size scaling theory, we estimate the critical exponents for the correlation length, magnetic susceptibility, and magnetization. Results reveal a strong dependence of critical temperature and critical exponents on the film thickness. The obtained critical exponents are finally compared to those reported in literature for thin films
N. Duarte; L.H. Pardo; M.J. Robin-Abbott
2013-01-01
The objectives of this study were to assess susceptibility to acidification and nitrogen (N) saturation caused by atmospheric deposition to northeastern US forests, evaluate the benefits and shortcomings of making critical load assessments using regional data, and assess the relationship between expected risk (exceedance) and forest health. We calculated the critical...
Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
Klein, Avraham; Lederer, Samuel; Chowdhury, Debanjan; Berg, Erez; Chubukov, Andrey
2018-04-01
We study the dynamic response of a two-dimensional system of itinerant fermions in the vicinity of a uniform (Q =0 ) Ising nematic quantum critical point of d - wave symmetry. The nematic order parameter is not a conserved quantity, and this permits a nonzero value of the fermionic polarization in the d - wave channel even for vanishing momentum and finite frequency: Π (q =0 ,Ωm)≠0 . For weak coupling between the fermions and the nematic order parameter (i.e., the coupling is small compared to the Fermi energy), we perturbatively compute Π (q =0 ,Ωm)≠0 over a parametrically broad range of frequencies where the fermionic self-energy Σ (ω ) is irrelevant, and use Eliashberg theory to compute Π (q =0 ,Ωm) in the non-Fermi-liquid regime at smaller frequencies, where Σ (ω )>ω . We find that Π (q =0 ,Ω ) is a constant, plus a frequency-dependent correction that goes as |Ω | at high frequencies, crossing over to |Ω| 1 /3 at lower frequencies. The |Ω| 1 /3 scaling holds also in a non-Fermi-liquid regime. The nonvanishing of Π (q =0 ,Ω ) gives rise to additional structure in the imaginary part of the nematic susceptibility χ″(q ,Ω ) at Ω >vFq , in marked contrast to the behavior of the susceptibility for a conserved order parameter. This additional structure may be detected in Raman scattering experiments in the d - wave geometry.
Non-universal spreading exponents in a catalytic reaction model
International Nuclear Information System (INIS)
De Andrade, Marcelo F; Figueiredo, W
2011-01-01
We investigated the dependence of the spreading critical exponents and the ultimate survival probability exponent on the initial configuration of a nonequilibrium catalytic reaction model. The model considers the competitive reactions between two different monomers, A and B, where we take into account the energy couplings between nearest neighbor monomers, and the adsorption energies, as well as the temperature T of the catalyst. For each value of T the model shows distinct absorbing states, with different concentrations of the two monomers. Employing an epidemic analysis, we established the behavior of the spreading exponents as we started the Monte Carlo simulations with different concentrations of the monomers. The exponents were determined as a function of the initial concentration ρ A, ini of A monomers. We have also considered initial configurations with correlations for a fixed concentration of A monomers. From the determination of three spreading exponents, and the ultimate survival probability exponent, we checked the validity of the generalized hyperscaling relation for a continuous set of initial states, random and correlated, which are dependent on the temperature of the catalyst
Lojasiewicz exponents and Newton polyhedra
International Nuclear Information System (INIS)
Pham Tien Son
2006-07-01
In this paper we obtain the exact value of the Lojasiewicz exponent at the origin of analytic map germs on K n (K = R or C under the Newton non-degeneracy condition, using information from their Newton polyhedra. We also give some conclusions on Newton non-degenerate analytic map germs. As a consequence, we obtain a link between Newton non-degenerate ideals and their integral closures, thus leading to a simple proof of a result of Saia. Similar results are also considered to polynomial maps which are Newton non-degenerate at infinity. (author)
Crossover phenomena in the critical range near magnetic ordering transition
Köbler, U.
2018-05-01
Among the most important issues of Renormalization Group (RG) theory are crossover events and relevant (or non-relevant) interactions. These terms are unknown to atomistic theories but they will be decisive for future field theories of magnetism. In this experimental study the importance of these terms for the critical dynamics above and below magnetic ordering transition is demonstrated on account of new analyses of published data. When crossover events are overlooked and critical data are fitted by a single power function of temperature over a temperature range including a crossover event, imprecise critical exponents result. The rather unsystematic and floating critical exponents reported in literature seem largely to be due to this problem. It is shown that for appropriate data analyses critical exponents are obtained that are to a good approximation rational numbers. In fact, rational critical exponents can be expected when spin dynamics is controlled by the bosons of the continuous magnetic medium (Goldstone bosons). The bosons are essentially magnetic dipole radiation generated by the precessing spins. As a result of the here performed data analyses, critical exponents for the magnetic order parameter of β = 1/2, 1/3, 1/4 and 1/6 are obtained. For the critical paramagnetic susceptibility the exponents are γ = 1 and γ = 4/3.
Critical behavior of the magnetic susceptibility of the uniaxial ferromagnet LiHoF4
DEFF Research Database (Denmark)
Beauvillain, P.; Renard, J. P.; Laursen, Ib
1978-01-01
The magnetic susceptibility of two LiHoF4 single crystals has been measured in the range 1.2-4.2 K. Ferromagnetic order occurs at Tc=1.527 K. Above 2.5 K, the susceptibilities parallel and perpendicular to the fourfold c axis are well interpreted by the molecular-field approximation, taking...
Finite-time braiding exponents
Budišić, Marko; Thiffeault, Jean-Luc
2015-08-01
Topological entropy of a dynamical system is an upper bound for the sum of positive Lyapunov exponents; in practice, it is strongly indicative of the presence of mixing in a subset of the domain. Topological entropy can be computed by partition methods, by estimating the maximal growth rate of material lines or other material elements, or by counting the unstable periodic orbits of the flow. All these methods require detailed knowledge of the velocity field that is not always available, for example, when ocean flows are measured using a small number of floating sensors. We propose an alternative calculation, applicable to two-dimensional flows, that uses only a sparse set of flow trajectories as its input. To represent the sparse set of trajectories, we use braids, algebraic objects that record how trajectories exchange positions with respect to a projection axis. Material curves advected by the flow are represented as simplified loop coordinates. The exponential rate at which a braid stretches loops over a finite time interval is the Finite-Time Braiding Exponent (FTBE). We study FTBEs through numerical simulations of the Aref Blinking Vortex flow, as a representative of a general class of flows having a single invariant component with positive topological entropy. The FTBEs approach the value of the topological entropy from below as the length and number of trajectories is increased; we conjecture that this result holds for a general class of ergodic, mixing systems. Furthermore, FTBEs are computed robustly with respect to the numerical time step, details of braid representation, and choice of initial conditions. We find that, in the class of systems we describe, trajectories can be re-used to form different braids, which greatly reduces the amount of data needed to assess the complexity of the flow.
Error exponents for entanglement concentration
International Nuclear Information System (INIS)
Hayashi, Masahito; Koashi, Masato; Matsumoto, Keiji; Morikoshi, Fumiaki; Winter, Andreas
2003-01-01
Consider entanglement concentration schemes that convert n identical copies of a pure state into a maximally entangled state of a desired size with success probability being close to one in the asymptotic limit. We give the distillable entanglement, the number of Bell pairs distilled per copy, as a function of an error exponent, which represents the rate of decrease in failure probability as n tends to infinity. The formula fills the gap between the least upper bound of distillable entanglement in probabilistic concentration, which is the well-known entropy of entanglement, and the maximum attained in deterministic concentration. The method of types in information theory enables the detailed analysis of the distillable entanglement in terms of the error rate. In addition to the probabilistic argument, we consider another type of entanglement concentration scheme, where the initial state is deterministically transformed into a (possibly mixed) final state whose fidelity to a maximally entangled state of a desired size converges to one in the asymptotic limit. We show that the same formula as in the probabilistic argument is valid for the argument on fidelity by replacing the success probability with the fidelity. Furthermore, we also discuss entanglement yield when optimal success probability or optimal fidelity converges to zero in the asymptotic limit (strong converse), and give the explicit formulae for those cases
Critical behavior of spin systems with quenched disorder
International Nuclear Information System (INIS)
Murtazaev, Akai K.; Kamilov, Ibragimkhan K.; Babaev, Albert B.
2006-01-01
A static critical behavior of three-dimensional diluted quenched Ising model on a cubic lattice is studied by Monte-Carlo methods. The static critical exponents of a specific heat α, susceptibility γ, magnetization β and exponent of correlation radius ν in a wide interval of change the values of spin concentrations p are calculated on the basis of the finite-size scaling theory using the common technique. The problem about universality classes of critical behavior for three-dimensional diluted systems is considered
Fujita Exponent for a Nonlinear Degenerate Parabolic Equation with Localized Source
Directory of Open Access Journals (Sweden)
Yulan Wang
2014-01-01
Full Text Available This paper is devoted to understand the blow-up properties of reaction-diffusion equations which combine a localized reaction term with nonlinear diffusion. In particular, we study the critical exponent of a p-Laplacian equation with a localized reaction. We obtain the Fujita exponent qc of the equation.
DEFF Research Database (Denmark)
Benfield, Thomas; Ejrnæs, Karen; Juul, Klaus
2010-01-01
ABSTRACT: INTRODUCTION: Disturbance of the pro-coagulatant and anti-coagulant balance is associated with a poor outcome from critical illness. The objective of this study is to determine whether the Factor V Leiden (FVL) mutation is associated with susceptibility to or death from critical illness....... METHODS: A genetic association study involving four case cohorts comprising two Gram negative sepsis, one invasive pneumococcal disease and one intensive care unit cohort with a total of 1,249 patients. Controls were derived from a population-based cohort study (N = 8,147). DNA from patients and controls...... not appear to increase the risk of admission due to severe invasive infections. Nevertheless, in the subgroup of patients admitted to intensive care an increased risk and a poorer long-term outcome for individuals with critical illness were observed for FVL mutation carriers....
Multiscale Lyapunov exponent for 2-microlocal functions
International Nuclear Information System (INIS)
Dhifaoui, Zouhaier; Kortas, Hedi; Ammou, Samir Ben
2009-01-01
The Lyapunov exponent is an important indicator of chaotic dynamics. Using wavelet analysis, we define a multiscale representation of this exponent which we demonstrate the scale-wise dependence for functions belonging to C x 0 s,s ' spaces. An empirical study involving simulated processes and financial time series corroborates the theoretical findings.
Cryptanalysis of 'less short' RSA secret exponents
Verheul, E.R.; Tilborg, van H.C.A.
1997-01-01
In some applications of RSA, it is desirable to have a short secret exponent d. Wiener [6], describes a technique to use continued fractions (CF) in a cryptanalytic attack on an RSA cryptosystem having a ‘short’ secret exponent. Let n=p¿·¿q be the modulus of the system. In the typical case that
Diophantine exponents for mildly restricted approximation
DEFF Research Database (Denmark)
Bugeaud, Yann; Kristensen, Simon
We are studying the Diophantine exponent defined for integers and a vector by letting , where is the scalar product and denotes the distance to the nearest integer and is the generalised cone consisting of all vectors with the height attained among the first coordinates. We show that the exponent...
Monte Carlo-based tail exponent estimator
Barunik, Jozef; Vacha, Lukas
2010-11-01
In this paper we propose a new approach to estimation of the tail exponent in financial stock markets. We begin the study with the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations, we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce a Monte Carlo-based method of estimation for the tail exponent. Our proposed method is not sensitive to the choice of tail size and works well also on small data samples. The new estimator also gives unbiased results with symmetrical confidence intervals. Finally, we demonstrate the power of our estimator on the international world stock market indices. On the two separate periods of 2002-2005 and 2006-2009, we estimate the tail exponent.
Warren, Joshua L; Son, Ji-Young; Pereira, Gavin; Leaderer, Brian P; Bell, Michelle L
2018-05-01
Identifying periods of increased vulnerability to air pollution during pregnancy with respect to the development of adverse birth outcomes can improve understanding of possible mechanisms of disease development and provide guidelines for protection of the child. Exposure to air pollution during pregnancy is typically based on the mother's residence at delivery, potentially resulting in exposure misclassification and biasing the estimation of critical windows of pregnancy. In this study, we determined the impact of maternal residential mobility during pregnancy on defining weekly exposure to particulate matter less than or equal to 10 μm in aerodynamic diameter (PM10) and estimating windows of susceptibility to term low birth weight. We utilized data sets from 4 Connecticut birth cohorts (1988-2008) that included information on all residential addresses between conception and delivery for each woman. We designed a simulation study to investigate the impact of increasing levels of mobility on identification of critical windows. Increased PM10 exposure during pregnancy weeks 16-18 was associated with an increased probability of term low birth weight. Ignoring residential mobility when defining weekly exposure had only a minor impact on the identification of critical windows for PM10 and term low birth weight in the data application and simulation study. Identification of critical pregnancy windows was robust to exposure misclassification caused by ignoring residential mobility in these Connecticut birth cohorts.
Tate, Kevin B; Kohl, Zachary F; Eme, John; Rhen, Turk; Crossley, Dane A
2015-01-01
Environmental conditions fluctuate dramatically in some reptilian nests. However, critical windows of environmental sensitivity for cardiovascular development have not been identified. Continuous developmental hypoxia has been shown to alter cardiovascular form and function in embryonic snapping turtles (Chelydra serpentina), and we used this species to identify critical periods during which hypoxia modifies the cardiovascular phenotype. We hypothesized that incubation in 10% O2 during specific developmental periods would have differential effects on the cardiovascular system versus overall somatic growth. Two critical windows were identified with 10% O2 from 50% to 70% of incubation, resulting in relative heart enlargement, either via preservation of or preferential growth of this tissue, while exposure to 10% O2 from 20% to 70% of incubation resulted in a reduction in arterial pressure. The deleterious or advantageous aspects of these embryonic phenotypes in posthatching snapping turtles have yet to be explored. However, identification of these critical windows has provided insight into how the developmental environment alters the phenotype of reptiles and will also be pivotal in understanding its impact on the fitness of egg-laying reptiles.
Adolescent but not adult-born neurons are critical for susceptibility to chronic social defeat
Directory of Open Access Journals (Sweden)
Greer S Kirshenbaum
2014-08-01
Full Text Available Recent evidence implicates adult hippocampal neurogenesis in regulating behavioral and physiologic responses to stress. Hippocampal neurogenesis occurs across the lifespan, however the rate of cell birth is up to 300% higher in adolescent mice compared to adults. Adolescence is a sensitive period in development where emotional circuitry and stress reactivity undergo plasticity establishing life-long set points. Therefore neurogenesis occurring during adolescence may be particularly important for emotional behavior. However, little is known about the function of hippocampal neurons born during adolescence. In order to assess the contribution of neurons born in adolescence to the adult stress response and depression-related behavior, we transiently reduced cell proliferation either during adolescence, or during adulthood in GFAP-Tk mice. We found that the intervention in adolescence did not change baseline behavioral responses in the forced swim test, sucrose preference test or social affiliation test, and did not change corticosterone responses to an acute stressor. However following chronic social defeat, adult mice with reduced adolescent neurogenesis showed a resilient phenotype. A similar transient reduction in adult neurogenesis did not affect depression-like behaviors or stress induced corticosterone. Our study demonstrates that hippocampal neurons born during adolescence, but not in adulthood are important to confer susceptibility to chronic social defeat.
Evaluating Lyapunov exponent spectra with neural networks
International Nuclear Information System (INIS)
Maus, A.; Sprott, J.C.
2013-01-01
Highlights: • Cross-correlation is employed to remove spurious Lyapunov exponents from a spectrum. • Neural networks are shown to accurately model Lyapunov exponent spectra. • Neural networks compare favorably to local linear fits in modeling Lyapunov exponents. • Numerical experiments are performed with time series of varying length and noise. • Methods perform reasonably well on discrete time series. -- Abstract: A method using discrete cross-correlation for identifying and removing spurious Lyapunov exponents when embedding experimental data in a dimension greater than the original system is introduced. The method uses a distribution of calculated exponent values produced by modeling a single time series many times or multiple instances of a time series. For this task, global models are shown to compare favorably to local models traditionally used for time series taken from the Hénon map and delayed Hénon map, especially when the time series are short or contaminated by noise. An additional merit of global modeling is its ability to estimate the dynamical and geometrical properties of the original system such as the attractor dimension, entropy, and lag space, although consideration must be taken for the time it takes to train the global models
Lyapunov exponents and smooth ergodic theory
Barreira, Luis
2001-01-01
This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). The authors consider several non-trivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory. This book is self-contained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field.
Lyapunov exponents for infinite dimensional dynamical systems
Mhuiris, Nessan Mac Giolla
1987-01-01
Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
Lai, Ying-Cheng; Harrison, Mary Ann F; Frei, Mark G; Osorio, Ivan
2004-09-01
Lyapunov exponents are a set of fundamental dynamical invariants characterizing a system's sensitive dependence on initial conditions. For more than a decade, it has been claimed that the exponents computed from electroencephalogram (EEG) or electrocorticogram (ECoG) signals can be used for prediction of epileptic seizures minutes or even tens of minutes in advance. The purpose of this paper is to examine the predictive power of Lyapunov exponents. Three approaches are employed. (1) We present qualitative arguments suggesting that the Lyapunov exponents generally are not useful for seizure prediction. (2) We construct a two-dimensional, nonstationary chaotic map with a parameter slowly varying in a range containing a crisis, and test whether this critical event can be predicted by monitoring the evolution of finite-time Lyapunov exponents. This can thus be regarded as a "control test" for the claimed predictive power of the exponents for seizure. We find that two major obstacles arise in this application: statistical fluctuations of the Lyapunov exponents due to finite time computation and noise from the time series. We show that increasing the amount of data in a moving window will not improve the exponents' detective power for characteristic system changes, and that the presence of small noise can ruin completely the predictive power of the exponents. (3) We report negative results obtained from ECoG signals recorded from patients with epilepsy. All these indicate firmly that, the use of Lyapunov exponents for seizure prediction is practically impossible as the brain dynamical system generating the ECoG signals is more complicated than low-dimensional chaotic systems, and is noisy. Copyright 2004 American Institute of Physics
Statistical-mechanical formulation of Lyapunov exponents
International Nuclear Information System (INIS)
Tanase-Nicola, Sorin; Kurchan, Jorge
2003-01-01
We show how the Lyapunov exponents of a dynamic system can, in general, be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive concepts and techniques of approximation can hence be borrowed
Tang, Huadong; Hussain, Azher; Leal, Mauricio; Fluhler, Eric; Mayersohn, Michael
2011-02-01
This commentary is a reply to a recent article by Mahmood commenting on the authors' article on the use of fixed-exponent allometry in predicting human clearance. The commentary discusses eight issues that are related to criticisms made in Mahmood's article and examines the controversies (fixed-exponent vs. varying-exponent allometry) from the perspective of statistics and mathematics. The key conclusion is that any allometric method, which is to establish a power function based on a limited number of animal species and to extrapolate the resulting power function to human values (varying-exponent allometry), is infused with fundamental statistical errors. Copyright © 2010 Wiley-Liss, Inc.
Behaviour of Lyapunov exponents near crisis points in the dissipative standard map
Pompe, B.; Leven, R. W.
1988-11-01
We numerically study the behaviour of the largest Lyapunov characteristic exponent λ1 in dependence on a control parameter in the 2D standard map with dissipation. In order to investigate the system's motion in parameter intervals slightly above crisis points we introduce "partial" Lyapunov exponents which characterize the average exponential divergence of nearby orbits on a semi-attractor at a boundary crisis and on distinct parts of a "large" chaotic attractor near an interior crisis. In the former case we find no significant difference between λ1 in the pre-crisis regime and the partial Lyapunov exponent describing transient chaotic motions slightly above the crisis. For the latter case we give a quantitative description of the drastic increase of λ1. Moreover, a formula which connects the critical exponent of a chaotic transient above a boundary crisis with a pointwise dimension is derived.
Relating Lagrangian passive scalar scaling exponents to Eulerian scaling exponents in turbulence
Schmitt , François G
2005-01-01
Intermittency is a basic feature of fully developed turbulence, for both velocity and passive scalars. Intermittency is classically characterized by Eulerian scaling exponent of structure functions. The same approach can be used in a Lagrangian framework to characterize the temporal intermittency of the velocity and passive scalar concentration of a an element of fluid advected by a turbulent intermittent field. Here we focus on Lagrangian passive scalar scaling exponents, and discuss their p...
Intermittency exponent of the turbulent energy cascade
International Nuclear Information System (INIS)
Cleve, J.; Greiner, M.; Pearson, B.R.; Sreenivasan, K.R.
2006-12-01
We consider the turbulent energy dissipation from one-dimensional records in experiments using air and gaseous helium at cryogenic temperatures, and obtain the intermittency exponent via the two-point correlation function of the energy dissipation. The air data are obtained in a number of flows in a wind tunnel and the atmospheric boundary layer at a height of about 35 m above the ground. The helium data correspond to the centerline of a jet exhausting into a container. The air data on the intermittency exponent are consistent with each other and with a trend that increases with the Taylor microscale Reynolds number, R λ , of up to about 1000 and saturates thereafter. On the other hand, the helium data cluster around a constant value at nearly all R λ , this being about half of the asymptotic value for the air data. Some possible explanation is offered for this anomaly. (author)
Local Lyapunov exponents for dissipative continuous systems
International Nuclear Information System (INIS)
Grond, Florian; Diebner, Hans H.
2005-01-01
We analyze a recently proposed algorithm for computing Lyapunov exponents focusing on its capability to calculate reliable local values for chaotic attractors. The averaging process of local contributions to the global measure becomes interpretable, i.e. they are related to the local topological structure in phase space. We compare the algorithm with the commonly used Wolf algorithm by means of analyzing correlations between coordinates of the chaotic attractor and local values of the Lyapunov exponents. The correlations for the new algorithm turn out to be significantly stronger than those for the Wolf algorithm. Since the usage of scalar measures to capture complex structures can be questioned we discuss these entities along with a more phenomenological description of scatter plots
Monte Carlo-Based Tail Exponent Estimator
Czech Academy of Sciences Publication Activity Database
Baruník, Jozef; Vácha, Lukáš
2010-01-01
Roč. 2010, č. 6 (2010), s. 1-26 R&D Projects: GA ČR GA402/09/0965; GA ČR GD402/09/H045; GA ČR GP402/08/P207 Institutional research plan: CEZ:AV0Z10750506 Keywords : Hill estimator * α-stable distributions * tail exponent estimation Subject RIV: AH - Economics http://library.utia.cas.cz/separaty/2010/E/barunik-0342493.pdf
Higgs Critical Exponents and Conformal Bootstrap in Four Dimensions
DEFF Research Database (Denmark)
Antipin, Oleg; Mølgaard, Esben; Sannino, Francesco
2015-01-01
We investigate relevant properties of composite operators emerging in nonsupersymmetric, four-dimensional gauge-Yukawa theories with interacting conformal fixed points within a precise framework. The theories investigated in this work are structurally similar to the standard model of particle int...... bootstrap results are then compared to precise four dimensional conformal field theoretical results. To accomplish this, it was necessary to calculate explicitly the crossing symmetry relations for the global symmetry group SU($N$)$\\times$SU($N$)....
International Nuclear Information System (INIS)
Nayak, P.K.; Ravi, S. . sravi@iitg.ernet.in
2008-01-01
We have prepared a series of compounds (La 1-x Y x ) 2 Ba 2 CaCu 5 O 2 for x = 0 to 0.5 by adding a CaCuO 2 layer to the parent compound La 2 Ba 2 Cu 4 O 2 and by doping Y in place of La. These materials are also prepared by adding 5 wt% of Ag to enhance the intergranular coupling and critical current density. X-ray diffraction measurements show that all the samples are essentially in single phase form and the patterns could be refined using P4/mmm space group in tetragonal cell. The typical lattice parameters are found to be a = b 3.856 A, c = 11.576 A for x = 0.5 sample. Temperature variations of dc electrical resistivity measured on the above samples show that they exhibit superconductivity with T c ranging from 60 to 75 K. Temperature and ac field amplitude variation of ac susceptibility have been measured on the above samples. The field variation of ac susceptibility data has been analyzed by using Bean critical state model. Using both temperature and field variations of ac susceptibility data, the material dependent parameters, such as critical current density as a function of temperature and effective volume fraction grains have been estimated. The Ag doped samples show relatively large critical current density compared to pure samples due to improved intergranular coupling. (author)
International Nuclear Information System (INIS)
Hara, T.; Tasaki, H.
1987-01-01
Continuing the analysis started in Part I of this work, they investigate critical phenomena in weakly coupled phi 4 spin systems in four dimensions. Concerning the critical behavior of the susceptibility and the correlation length (in the high-temperature phase), the existence of logarithmic corrections to their mean field type behavior is rigorously shown (i.e., they prove chi(t) ∼ t -1 absolute value 1n t/sup 1/3/, zeta(t) ∼ t/sup -1/2/ absolute value of ln t/sup 1/6/)
Extraction of the power law exponent for 1 GeV/nucleon Au + C projectile multifragmentation
International Nuclear Information System (INIS)
Gilkes, M.L.; Elliott, J.B.; Huager, A.; Hirsch, A.S.; Hjort, E.
1993-01-01
Using moments of the measured charge distribution in exclusive gold multifragmentation events, we present a preliminary determination of the power law exponent τ. For a system undergoing a phase transition near the critical point, τ governs the cluster size distribution and is expected on rather general grounds to lie in the range 2 < τ < 3
Geodesic stability, Lyapunov exponents, and quasinormal modes
International Nuclear Information System (INIS)
Cardoso, Vitor; Miranda, Alex S.; Berti, Emanuele; Witek, Helvi; Zanchin, Vilson T.
2009-01-01
Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d≥6.
Merit exponents and control area diagrams in materials selection
International Nuclear Information System (INIS)
Zander, Johan; Sandstroem, Rolf
2011-01-01
Highlights: → Merit exponents are introduced to generalise the merit indices commonly used in materials selection. → The merit exponents can rank materials in general design situations. → To allow identification of the active merit exponent(s), control area diagrams are used. → Principles for generating the control area diagrams are presented. -- Abstract: Merit indices play a fundamental role in materials selection, since they enable ranking of materials. However, the conventional formulation of merit indices is associated with severe limitations. They are dependent on the explicit solution of the variables in the equations for the constraints from the design criteria. Furthermore, it is not always easy to determine which the controlling merit index is. To enable the ranking of materials in more general design cases, merit exponents are introduced as generalisations of the merit indices. Procedures are presented for how to compute the merit exponents numerically without having to solve equations algebraically. Merit exponents (and indices) are only valid in a certain range of property values. To simplify the identification of the controlling merit exponent, it is suggested that so called control area diagrams are used. These diagrams consist of a number of domains, each showing the active constraints and the controlling merit exponent. It is shown that the merit exponents play a crucial role when the control area diagram (CAD) is set up. The principles in the paper are developed for mechanically loaded components and are illustrated for engineering beams with two or three geometric variables.
Can the bivariate Hurst exponent be higher than an average of the separate Hurst exponents?
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2015-01-01
Roč. 431, č. 1 (2015), s. 124-127 ISSN 0378-4371 R&D Projects: GA ČR(CZ) GP14-11402P Institutional support: RVO:67985556 Keywords : Correlations * Power- law cross-correlations * Bivariate Hurst exponent * Spectrum coherence Subject RIV: AH - Economics Impact factor: 1.785, year: 2015 http://library.utia.cas.cz/separaty/2015/E/kristoufek-0452314.pdf
The Hurst exponent in energy futures prices
Serletis, Apostolos; Rosenberg, Aryeh Adam
2007-07-01
This paper extends the work in Elder and Serletis [Long memory in energy futures prices, Rev. Financial Econ., forthcoming, 2007] and Serletis et al. [Detrended fluctuation analysis of the US stock market, Int. J. Bifurcation Chaos, forthcoming, 2007] by re-examining the empirical evidence for random walk type behavior in energy futures prices. In doing so, it uses daily data on energy futures traded on the New York Mercantile Exchange, over the period from July 2, 1990 to November 1, 2006, and a statistical physics approach-the ‘detrending moving average’ technique-providing a reliable framework for testing the information efficiency in financial markets as shown by Alessio et al. [Second-order moving average and scaling of stochastic time series, Eur. Phys. J. B 27 (2002) 197-200] and Carbone et al. [Time-dependent hurst exponent in financial time series. Physica A 344 (2004) 267-271; Analysis of clusters formed by the moving average of a long-range correlated time series. Phys. Rev. E 69 (2004) 026105]. The results show that energy futures returns display long memory and that the particular form of long memory is anti-persistence.
Directory of Open Access Journals (Sweden)
Joel Lavinsky
2015-04-01
Full Text Available In the United States, roughly 10% of the population is exposed daily to hazardous levels of noise in the workplace. Twin studies estimate heritability for noise-induced hearing loss (NIHL of approximately 36%, and strain specific variation in sensitivity has been demonstrated in mice. Based upon the difficulties inherent to the study of NIHL in humans, we have turned to the study of this complex trait in mice. We exposed 5 week-old mice from the Hybrid Mouse Diversity Panel (HMDP to a 10 kHz octave band noise at 108 dB for 2 hours and assessed the permanent threshold shift 2 weeks post exposure using frequency specific stimuli. These data were then used in a genome-wide association study (GWAS using the Efficient Mixed Model Analysis (EMMA to control for population structure. In this manuscript we describe our GWAS, with an emphasis on a significant peak for susceptibility to NIHL on chromosome 17 within a haplotype block containing NADPH oxidase-3 (Nox3. Our peak was detected after an 8 kHz tone burst stimulus. Nox3 mutants and heterozygotes were then tested to validate our GWAS. The mutants and heterozygotes demonstrated a greater susceptibility to NIHL specifically at 8 kHz both on measures of distortion product otoacoustic emissions (DPOAE and on auditory brainstem response (ABR. We demonstrate that this sensitivity resides within the synaptic ribbons of the cochlea in the mutant animals specifically at 8 kHz. Our work is the first GWAS for NIHL in mice and elucidates the power of our approach to identify tonotopic genetic susceptibility to NIHL.
How We Tend To Overestimate Powerlaw Tail Exponents
Nassim N. Taleb
2012-01-01
In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan" effects, i.e., why measurements tend to chronically underestimate tail contributions, rather than merely deliver imprecise but unbiased estimates.
Critical behavior in graphene with Coulomb interactions.
Wang, Jianhui; Fertig, H A; Murthy, Ganpathy
2010-05-07
We demonstrate that, in the presence of Coulomb interactions, electrons in graphene behave like a critical system, supporting power law correlations with interaction-dependent exponents. An asymptotic analysis shows that the origin of this behavior lies in particle-hole scattering, for which the Coulomb interaction induces anomalously close approaches. With increasing interaction strength the relevant power law changes from real to complex, leading to an unusual instability characterized by a complex-valued susceptibility in the thermodynamic limit. Measurable quantities, as well as the connection to classical two-dimensional systems, are discussed.
Critical Behaviour of a Two-Dimensional Random Antiferromagnet
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Birgeneau, R. J.; Guggenheim, H. J.
1976-01-01
A neutron scattering study of the order parameter, correlation length and staggered susceptibility of the two-dimensional random antiferromagnet Rb2Mn0.5Ni0.5F4 is reported. The system is found to exhibit a well-defined phase transition with critical exponents identical to those of the isomorphou...... pure materials K2NiF4 and K2MnF4. Thus, in these systems, which have the asymptotic critical behaviour of the two-dimensional Ising model, randomness has no measurable effect on the phase-transition behaviour....
Energy Technology Data Exchange (ETDEWEB)
Allard, L.T.; Elerath, J.G.
1976-02-01
This document presents a common cause failure analysis for Critical LMFBR Shutdown Heat Removal Systems. The report is intended to outline a systematic approach to defining areas with significant potential for common causes of failure, and ultimately provide inputs to the reliability prediction model. A preliminary evaluation of postulatd single initiating causes resulting in multiple failures of LMFBR-SHRS items is presented in Appendix C. This document will be periodically updated to reflect new information and activity.
On the Lojasiewicz exponent at infinity of real polynomials
International Nuclear Information System (INIS)
Ha Huy Vui; Pham Tien Son
2007-07-01
Let f : R n → R be a nonconstant polynomial function. In this paper, using the information from 'the curve of tangency' of f, we provide a method to determine the Lojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Lojasiewicz exponent at infinity is finite or not. Then, we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Lojasiewicz exponent at infinity of f with the problem of computing the global optimum of f is also established. (author)
ACCURATE ESTIMATES OF CHARACTERISTIC EXPONENTS FOR SECOND ORDER DIFFERENTIAL EQUATION
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, a second order linear differential equation is considered, and an accurate estimate method of characteristic exponent for it is presented. Finally, we give some examples to verify the feasibility of our result.
A MONTE-CARLO METHOD FOR ESTIMATING THE CORRELATION EXPONENT
MIKOSCH, T; WANG, QA
We propose a Monte Carlo method for estimating the correlation exponent of a stationary ergodic sequence. The estimator can be considered as a bootstrap version of the classical Hill estimator. A simulation study shows that the method yields reasonable estimates.
On some properties of the discrete Lyapunov exponent
International Nuclear Information System (INIS)
Amigo, Jose M.; Kocarev, Ljupco; Szczepanski, Janusz
2008-01-01
One of the possible by-products of discrete chaos is the application of its tools, in particular of the discrete Lyapunov exponent, to cryptography. In this Letter we explore this question in a very general setting
Full spectrum of Lyapunov exponents in gauge field theories
International Nuclear Information System (INIS)
Biro, T.S.; Markum, H.; Pullirsch, R.
2003-01-01
Full text: Results are presented for the full spectrum of Lyapunov exponents of the compact U(1) gauge system in classical field theory. Instead of the determination of the largest Lyapunov exponent by the rescaling method we now use the monodromy matrix approach. The Lyapunov spectrum L i is expressed in terms of the eigenvalues Λ i of the monodromy matrix M. In the confinement phase the eigenvalues lie on either the real or on the imaginary axes. This is a nice illustration of a strange attractor of a chaotic system. Positive Lyapunov exponents eject the trajectories from oscillating orbits provided by the imaginary eigenvalues. Negative Lyapunov exponents attract the trajectories keeping them confined in the basin. Latest studies concern the time (in)dependence of the monodromy matrix. Further, we show that monopoles are created and annihilated in pairs as a function of real time in access to a fixed average monopole number. (author)
What is the cementation exponent? A new differential interpretation
Glover, P. W. J.
2009-04-01
Between 1950 and 2002 the total volume of reserves discovered has run to over 1500 Bbbl. for oil and 7.5 Tcf. for gas. Over half of these resources has already been produced, and has driven the global economy for the last fifty years. All of the assessments of the volume of hydrocarbon reserves were made using Archie's relationships (1942). It would be difficult, therefore, to overestimate the impact of either the petrophysical techniques or Archie's relationships on the worldwide economy. Archie's laws link the electrical resistivity of a rock to its porosity, to the resistivity of the water that saturates its pores, and to the fractional saturation of the pore space with the water, and are used to calculate the hydrocarbon saturation of the reservoir rock from which the reserves are then calculated. Archie's laws contain two exponents, m and n, which Archie called the cementation exponent and the saturation exponent, respectively. The conductivity of the hydrocarbon saturated rock is highly sensitive to changes in either exponent. However, despite the importance of the cementation exponent, few petrophysicists, commercial or academic, are able to describe its real physical meaning. The purpose of this contribution is to investigate the elusive physical meaning of the cementation exponent. We review the traditional interpretation of the cementation exponent and consider the extension of Archie's first law to two conducting phases. Consequently, we develop a new differential interpretation of the cementation exponent that is based on a new definition for the connectedness of the conducting phases in a porous medium. In this interpretation the connectedness of a porous medium is defined as the availability of pathways for transport, where the connectedness is the inverse of the formation resistivity factor, G = σo σw = 1 F (and may also be called the conductivity formation factor). Porosity is defined as the fractional amount of pore space in the usual manner
A new exponent in self-avoiding walks
International Nuclear Information System (INIS)
Srivastava, V.
1983-06-01
Existence of a new exponent is reported in the problem of nonintersecting self-avoiding random walks. It is connected with the asymptotic behaviour of the growth of number of such walks of larger and larger length. The value of the exponent is found to be nearly 0.90 for all two-dimensional and nearly 0.96 for all three-dimensional lattices studied here. (author)
Anomalous roughness of turbulent interfaces with system size dependent local roughness exponent
International Nuclear Information System (INIS)
Balankin, Alexander S.; Matamoros, Daniel Morales
2005-01-01
In a system far from equilibrium the system size can play the role of control parameter that governs the spatiotemporal dynamics of the system. Accordingly, the kinetic roughness of interfaces in systems far from equilibrium may depend on the system size. To get an insight into this problem, we performed a detailed study of rough interfaces formed in paper combustion experiments. Using paper sheets of different width λ, we found that the turbulent flame fronts display anomalous multi-scaling characterized by non-universal global roughness exponent α and by the system size dependent spectrum of local roughness exponents, ζ q (λ)=ζ 1 (1)q -ω λ φ q =0.93q -0.15 . The structure factor of turbulent flame fronts also exhibits unconventional scaling dependence on λ. These results are expected to apply to a broad range of far from equilibrium systems when the kinetic energy fluctuations exceed a certain critical value.
International Nuclear Information System (INIS)
Murtazaev, A.K.; Ramazanov, M.K.; Badiev, M.K.
2009-01-01
The critical properties of the 3D frustrated antiferromagnetic Heisenberg model on a triangular lattice are investigated by the replica Monte Carlo method. The static magnetic and chiral critical exponents of heat capacity a = 0.05(2), magnetization Β 0.30(1), Β k = 0.52(2), susceptibility Γ = 1.36(2), Γ k = 0.93(3), and correlation radius Ν 0.64(1), Ν k = 0.64(2) are calculated by using the finitesize scaling theory. The critical Fisher exponents η = - 0.06(3), η k = 0.63(4) for this model are estimated for the first time. A new universality class of the critical behavior is shown to be formed by the 3D frustrated Heisenberg model on the triangular lattice. A type of the interlayer exchange interaction is found to influence the universality class of antiferromagnetic Heisenberg model on the a triangular lattice.
St-Onge, Guillaume; Young, Jean-Gabriel; Laurence, Edward; Murphy, Charles; Dubé, Louis J.
2018-02-01
We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework on a given degree distribution, we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the SIS process. This analysis is suitable for the characterization of the phase transition and leads to three main contributions: (1) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation. (2) We recover the predictions of a number of existing approaches as limiting cases of our analysis, providing thereby a unifying point of view for the SIS dynamics on random networks. (3) We obtain bounds for the critical exponents of a number of quantities in the stationary state. This allows us to reinterpret the concept of hub-dominated phase transition. Within our framework, it appears as a heterogeneous critical phenomenon: observables for different degree classes have a different scaling with the infection rate. This phenomenon is followed by the successive activation of the degree classes beyond the epidemic threshold.
A new theoretical interpretation of Archie's saturation exponent
Directory of Open Access Journals (Sweden)
P. W. J. Glover
2017-07-01
Full Text Available This paper describes the extension of the concepts of connectedness and conservation of connectedness that underlie the generalized Archie's law for n phases to the interpretation of the saturation exponent. It is shown that the saturation exponent as defined originally by Archie arises naturally from the generalized Archie's law. In the generalized Archie's law the saturation exponent of any given phase can be thought of as formally the same as the phase (i.e. cementation exponent, but with respect to a reference subset of phases in a larger n-phase medium. Furthermore, the connectedness of each of the phases occupying a reference subset of an n-phase medium can be related to the connectedness of the subset itself by Gi = GrefSini. This leads naturally to the idea of the term Sini for each phase i being a fractional connectedness, where the fractional connectednesses of any given reference subset sum to unity in the same way that the connectednesses sum to unity for the whole medium. One of the implications of this theory is that the saturation exponent of any phase can be now be interpreted as the rate of change of the fractional connectedness with saturation and connectivity within the reference subset.
OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.
Ott, William; Rivas, Mauricio A; West, James
2015-12-01
Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).
Anisotropies in magnetic field evolution and local Lyapunov exponents
International Nuclear Information System (INIS)
Tang, X.Z.; Boozer, A.H.
2000-01-01
The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic field embedded in a conducting flow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian flow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrangian coordinates and time, which are completely determined once the flow field is specified. The characteristic directions that are associated with the spatial anisotropy of the problem, are prescribed in both Lagrangian and Eulerian frames. Coordinate transformation techniques are employed to relate the spatial distributions of the magnetic field, the induced current density, and the Lorentz force, which are usually followed in Eulerian frame, to those of the local Lyapunov exponents, which are naturally defined in Lagrangian coordinates
The hurst exponent and long-time correlation
International Nuclear Information System (INIS)
Wang, G.; Antar, G.; Devynck, P.
1999-10-01
The rescaled range statistics (R/S) method is applied to the ion saturation current fluctuations measured by Langmuir probe at edge on Tore Supra to evaluate the Hurst exponent. Data block randomization is carried out to the data sets in order to investigate the relationship between the Hurst exponent and long time correlation. It is observed that h is well above 0.5 in the long time self-similar range. However, it is found that the information which leads to H > 0.5 is totally contained in the short-time correlation and no link to long times is found. (authors)
Quantum computation of multifractal exponents through the quantum wavelet transform
International Nuclear Information System (INIS)
Garcia-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand
2009-01-01
We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum algorithms for multifractal exponents with a polynomial gain compared to classical simulations. Numerical results indicate that a rough estimate of fractality could be obtained exponentially fast. Our findings are relevant, e.g., for quantum simulations of multifractal quantum maps and of the Anderson model at the metal-insulator transition.
Lyapunov exponent of the random frequency oscillator: cumulant expansion approach
International Nuclear Information System (INIS)
Anteneodo, C; Vallejos, R O
2010-01-01
We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, λ and λ* respectively. We discuss the numerical difficulties that arise in the numerical calculation of λ* in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically λ* by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.
Lyapunov exponent for aging process in induction motor
Bayram, Duygu; Ünnü, Sezen Yıdırım; Şeker, Serhat
2012-09-01
Nonlinear systems like electrical circuits and systems, mechanics, optics and even incidents in nature may pass through various bifurcations and steady states like equilibrium point, periodic, quasi-periodic, chaotic states. Although chaotic phenomena are widely observed in physical systems, it can not be predicted because of the nature of the system. On the other hand, it is known that, chaos is strictly dependent on initial conditions of the system [1-3]. There are several methods in order to define the chaos. Phase portraits, Poincaré maps, Lyapunov Exponents are the most common techniques. Lyapunov Exponents are the theoretical indicator of the chaos, named after the Russian mathematician Aleksandr Lyapunov (1857-1918). Lyapunov Exponents stand for the average exponential divergence or convergence of nearby system states, meaning estimating the quantitive measure of the chaotic attractor. Negative numbers of the exponents stand for a stable system whereas zero stands for quasi-periodic systems. On the other hand, at least if one of the exponents is positive, this situation is an indicator of the chaos. For estimating the exponents, the system should be modeled by differential equation but even in that case mathematical calculation of Lyapunov Exponents are not very practical and evaluation of these values requires a long signal duration [4-7]. For experimental data sets, it is not always possible to acquire the differential equations. There are several different methods in literature for determining the Lyapunov Exponents of the system [4, 5]. Induction motors are the most important tools for many industrial processes because they are cheap, robust, efficient and reliable. In order to have healthy processes in industrial applications, the conditions of the machines should be monitored and the different working conditions should be addressed correctly. To the best of our knowledge, researches related to Lyapunov exponents and electrical motors are mostly
Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model
Pan, Xue; Zhang, Yanhua; Chen, Lizhu; Xu, Mingmei; Wu, Yuanfang
2018-01-01
We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class. Supported by Fund Project of National Natural Science Foundation of China (11647093, 11405088, 11521064), Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University (2016RC004) and the Major State Basic Research Development Program of China (2014CB845402)
Quantum criticality and first-order transitions in the extended periodic Anderson model
Hagymási, I.; Itai, K.; Sólyom, J.
2013-03-01
We investigate the behavior of the periodic Anderson model in the presence of d-f Coulomb interaction (Udf) using mean-field theory, variational calculation, and exact diagonalization of finite chains. The variational approach based on the Gutzwiller trial wave function gives a critical value of Udf and two quantum critical points (QCPs), where the valence susceptibility diverges. We derive the critical exponent for the valence susceptibility and investigate how the position of the QCP depends on the other parameters of the Hamiltonian. For larger values of Udf, the Kondo regime is bounded by two first-order transitions. These first-order transitions merge into a triple point at a certain value of Udf. For even larger Udf valence skipping occurs. Although the other methods do not give a critical point, they support this scenario.
First-passage exponents of multiple random walks
International Nuclear Information System (INIS)
Ben-Naim, E; Krapivsky, P L
2010-01-01
We investigate first-passage statistics of an ensemble of N noninteracting random walks on a line. Starting from a configuration in which all particles are located in the positive half-line, we study S n (t), the probability that the nth rightmost particle remains in the positive half-line up to time t. This quantity decays algebraically, S n (t)∼t -β n , in the long-time limit. Interestingly, there is a family of nontrivial first-passage exponents, β 1 2 N-1 ; the only exception is the two-particle case where β 1 = 1/3. In the N → ∞ limit, however, the exponents attain a scaling form, β n (N) → β(z) with z=(n-N/2)/√N. We also demonstrate that the smallest exponent decays exponentially with N. We deduce these results from first-passage kinetics of a random walk in an N-dimensional cone and confirm them using numerical simulations. Additionally, we investigate the family of exponents that characterizes leadership statistics of multiple random walks and find that in this case, the cone provides an excellent approximation.
Density-scaling exponents and virial potential-energy correlation ...
Indian Academy of Sciences (India)
This paper investigates the relation between the density-scaling exponent γ and the virial potential energy correlation coefficient R at several thermodynamic state points in three dimensions for the generalized (2n, n) Lennard-Jones (LJ) system for n = 4, 9, 12, 18, as well as for the standard n = 6 LJ system in two,three, and ...
Analysis of Human Standing Balance by Largest Lyapunov Exponent
Directory of Open Access Journals (Sweden)
Kun Liu
2015-01-01
Full Text Available The purpose of this research is to analyse the relationship between nonlinear dynamic character and individuals’ standing balance by the largest Lyapunov exponent, which is regarded as a metric for assessing standing balance. According to previous study, the largest Lyapunov exponent from centre of pressure time series could not well quantify the human balance ability. In this research, two improvements were made. Firstly, an external stimulus was applied to feet in the form of continuous horizontal sinusoidal motion by a moving platform. Secondly, a multiaccelerometer subsystem was adopted. Twenty healthy volunteers participated in this experiment. A new metric, coordinated largest Lyapunov exponent was proposed, which reflected the relationship of body segments by integrating multidimensional largest Lyapunov exponent values. By using this metric in actual standing performance under sinusoidal stimulus, an obvious relationship between the new metric and the actual balance ability was found in the majority of the subjects. These results show that the sinusoidal stimulus can make human balance characteristics more obvious, which is beneficial to assess balance, and balance is determined by the ability of coordinating all body segments.
Nonlinear anisotropic elliptic equations with variable exponents and degenerate coercivity
Directory of Open Access Journals (Sweden)
Hocine Ayadi
2018-02-01
Full Text Available In this article, we prove the existence and the regularity of distributional solutions for a class of nonlinear anisotropic elliptic equations with $p_i(x$ growth conditions, degenerate coercivity and $L^{m(\\cdot}$ data, with $m(\\cdot$ being small, in appropriate Lebesgue-Sobolev spaces with variable exponents. The obtained results extend some existing ones [8,10].
Bayesian Estimation of the Logistic Positive Exponent IRT Model
Bolfarine, Heleno; Bazan, Jorge Luis
2010-01-01
A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…
Fermat's Last Theorem for Factional and Irrational Exponents
Morgan, Frank
2010-01-01
Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.
International Nuclear Information System (INIS)
Kawashima, N.; Katori, M.; Tsallis, C.; Suzuki, M.
1989-01-01
A general procedure to study critical phenomena of magnetic systems is discussed. It consists of systematic series of Landau-like approximations (Extended Variational Method) and the coherent-anomaly method (CAM). As for susceptibility, the present method is equivalent to the power-series CAM theory. On the other hand, the EVM gives a set of new approximants for other physical quantities. Applications to d-dimensional Ising ferromagnets are also described. The critical points and exponents are estimated with high accuracy. (author) [pt
Lyapunov exponents a tool to explore complex dynamics
Pikovsky, Arkady
2016-01-01
Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers...
Scaling exponents for fracture surfaces in opal glass
International Nuclear Information System (INIS)
Chavez-Guerrero, L.; Garza, F.J.; Hinojosa, M.
2010-01-01
We have investigated the scaling properties of fracture surfaces in opal glass. Specimens with two different opacifying particle sizes (1 μm and 0.4 μm) were broken by three-point bending test and the resulting fracture surfaces were analyzed using Atomic Force Microscopy. The analysis of the self-affine behavior was performed using the Variable Bandwidth and Height-Height Correlation Methods, and both the roughness exponent, ζ, and the correlation length, ξ, were determined. It was found that the roughness exponent obtained in both samples is ζ ∼ 0.8; whereas the correlation length in both fractures is of the order of the particle size, demonstrating the dependence of this self-affine parameter on the microstructure of opal glass.
Scaling exponents for fracture surfaces in opal glass
Energy Technology Data Exchange (ETDEWEB)
Chavez-Guerrero, L., E-mail: guerreroleo@hotmail.com [Facultad de Ingenieria Mecanica y Electrica. Cd. Universitaria s/n, C.P. 66450, Universidad Autonoma de Nuevo Leon, Nuevo Leon (Mexico); Center of Innovation, Research and Development on Engineering and Technology, Universidad Autonoma de Nuevo Leon Monterrey, C.P. 66600, Apodaca, Nuevo Leon (Mexico); Garza, F.J., E-mail: fjgarza@gama.fime.uanl.mx [Facultad de Ciencias Quimicas, Cd. Universitaria s/n, C.P. 66450, Universidad Autonoma de Nuevo Leon, Nuevo Leon (Mexico); Hinojosa, M., E-mail: hinojosa@gama.fime.uanl.mx [Facultad de Ingenieria Mecanica y Electrica. Cd. Universitaria s/n, C.P. 66450, Universidad Autonoma de Nuevo Leon, Nuevo Leon (Mexico); Center of Innovation, Research and Development on Engineering and Technology, Universidad Autonoma de Nuevo Leon Monterrey, C.P. 66600, Apodaca, Nuevo Leon (Mexico)
2010-09-25
We have investigated the scaling properties of fracture surfaces in opal glass. Specimens with two different opacifying particle sizes (1 {mu}m and 0.4 {mu}m) were broken by three-point bending test and the resulting fracture surfaces were analyzed using Atomic Force Microscopy. The analysis of the self-affine behavior was performed using the Variable Bandwidth and Height-Height Correlation Methods, and both the roughness exponent, {zeta}, and the correlation length, {xi}, were determined. It was found that the roughness exponent obtained in both samples is {zeta} {approx} 0.8; whereas the correlation length in both fractures is of the order of the particle size, demonstrating the dependence of this self-affine parameter on the microstructure of opal glass.
On generalized scaling laws with continuously varying exponents
International Nuclear Information System (INIS)
Sittler, Lionel; Hinrichsen, Haye
2002-01-01
Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the parameters. However, some systems do not obey power-law scaling, instead there is numerical evidence for a logarithmic scaling form, in which the scaling function depends on ratios of the logarithms of the parameters. Based on previous ideas by Tang we propose that this type of logarithmic scaling can be explained by a concept of local scaling invariance with continuously varying exponents. The functional dependence of the exponents is constrained by a homomorphism which can be expressed as a set of partial differential equations. Solving these equations we obtain logarithmic scaling as a special case. The other solutions lead to scaling forms where logarithmic and power-law scaling are mixed
Estimation of Hurst Exponent for the Financial Time Series
Kumar, J.; Manchanda, P.
2009-07-01
Till recently statistical methods and Fourier analysis were employed to study fluctuations in stock markets in general and Indian stock market in particular. However current trend is to apply the concepts of wavelet methodology and Hurst exponent, see for example the work of Manchanda, J. Kumar and Siddiqi, Journal of the Frankline Institute 144 (2007), 613-636 and paper of Cajueiro and B. M. Tabak. Cajueiro and Tabak, Physica A, 2003, have checked the efficiency of emerging markets by computing Hurst component over a time window of 4 years of data. Our goal in the present paper is to understand the dynamics of the Indian stock market. We look for the persistency in the stock market through Hurst exponent and fractal dimension of time series data of BSE 100 and NIFTY 50.
Lyapunov exponent and topological entropy plateaus in piecewise linear maps
International Nuclear Information System (INIS)
Botella-Soler, V; Oteo, J A; Ros, J; Glendinning, P
2013-01-01
We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory. (paper)
Spectrum-based estimators of the bivariate Hurst exponent
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2014-01-01
Roč. 90, č. 6 (2014), art. 062802 ISSN 1539-3755 R&D Projects: GA ČR(CZ) GP14-11402P Institutional support: RVO:67985556 Keywords : bivariate Hurst exponent * power- law cross-correlations * estimation Subject RIV: AH - Economics Impact factor: 2.288, year: 2014 http://library.utia.cas.cz/separaty/2014/E/kristoufek-0436818.pdf
On Hurst exponent estimation under heavy-tailed distributions
Czech Academy of Sciences Publication Activity Database
Baruník, Jozef; Krištoufek, Ladislav
2010-01-01
Roč. 389, č. 18 (2010), s. 3844-3855 ISSN 0378-4371 R&D Projects: GA ČR GA402/09/0965 Grant - others:GA UK(CZ) 118310; GA UK(CZ) 46108 Institutional research plan: CEZ:AV0Z10750506 Keywords : high frequency data analysis * heavy tails * Hurst exponent Subject RIV: AH - Economics Impact factor: 1.521, year: 2010 http://library.utia.cas.cz/separaty/2010/E/barunik-0343525.pdf
On nonlinear evolution variational inequalities involving variable exponent
Directory of Open Access Journals (Sweden)
Mingqi Xiang
2013-12-01
Full Text Available In this paper, we discuss a class of quasilinear evolution variational inequalities with variable exponent growth conditions in a generalized Sobolev space. We obtain the existence of weak solutions by means of penalty method. Moreover, we study the extinction properties of weak solutions to parabolic inequalities and provide a sufficient condition that makes the weak solutions vanish in a finite time. The existence of global attractors for weak solutions is also obtained via the theories of multi-valued semiflow.
Energy Technology Data Exchange (ETDEWEB)
Bałanda, Maria [Institute of Nuclear Physics, Polish Academy of Science, PL-31-342 Kraków (Poland); Dubiel, Stanisław M., E-mail: Stanislaw.Dubiel@fis.agh.edu.pl [AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, PL-30-059 Kraków (Poland); Pełka, Robert [Institute of Nuclear Physics, Polish Academy of Science, PL-31-342 Kraków (Poland)
2017-06-15
Highlights: • Sigma-phase Fe{sub 60}V{sub 40} alloy was studied by means of AC and DC magnetic susceptibilities. • Re-entrant character of the magnetism has been evidenced. • Curie temperature was found as ∼169 K and the spin-freezing temperature as ∼164 K. • Critical exponents β = 0.6, γ = 1.0 and Δ = 1.6 were determined. • Magnetocaloric effect was investigated. - Abstract: Magnetic properties of a sigma-phase Fe{sub 60}V{sub 40} intermetallic compound were studied by means of ac and dc magnetic susceptibility and magnetocaloric effect measurements. The compound is a soft magnet yet it was found to behave like a re-entrant spin-glass system. The magnetic ordering temperature was found to be T{sub C} ≈ 170 K, while the spin-freezing temperature was ∼164 K. Its relative shift per decade of ac frequency was 0.002, a value smaller than that typical of canonical spin-glasses. Magnetic entropy change, ΔS, in the vicinity of T{sub C} was determined for magnetic field, H, ranging between 5 and 50 kOe. Analysis of ΔS in terms of the power law yielded the critical exponent, n, vs. temperature with the minimum value of 0.75 at T{sub C}, while from the analysis of a relative shift of the maximum value of ΔS with the field a critical exponent Δ = 1.7 was obtained. Based on scaling laws relationships values of other two exponents viz. β = 0.6 and γ = 1 were determined.
International Nuclear Information System (INIS)
Decroux, M.; Junod, A.; Bezinge, A.
1987-01-01
The temperature dependence of the resistivity, the magnetic properties and the specific heat were investigated on sintered samples of La 1.85 Sr 0.15 CuO 4 having zero resistance below 35 K. The crystal structure at 300K (tetragonal K 2 NiF 4 -type) was refined from X-ray powder diffraction data. The d.c. susceptibility shows no indication for the existence of localized Cu 2+ moments. The observation of a 60% Meissner effect and a smeared jump at T c in the specific-heat curve prove the intrinsic character of this superconducting state. The amplitude of this jump is compatible with the DOS estimated from the Pauli susceptibility. With a critical magnetic field slope dH c2 /dT| Tc = - 2.5 T/K, the orbital critical field is expected to be of the order of 64 T
Critical point inequalities and scaling limits
International Nuclear Information System (INIS)
Newman, C.M.
1979-01-01
A refined and extended version of the Buckingham-Gunton inequality relating various pairs of critical exponents is shown to be valid for a large class of statistical mechanical models. If this inequality is an equality (in the refined sense) and one of the critical exponents has a non-Gaussian value, then any scaling limit must be non-Gaussian. This result clarifies the relationships between the nontriviality of triviality of the scaling limit for ordinary critical points in four dimensions (or tricritical points in three dimensions) and the existence of logarithmic factors in the asymptotics which define the two critical exponents. (orig.) [de
Zipf exponent of trajectory distribution in the hidden Markov model
Bochkarev, V. V.; Lerner, E. Yu
2014-03-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.
Zipf exponent of trajectory distribution in the hidden Markov model
International Nuclear Information System (INIS)
Bochkarev, V V; Lerner, E Yu
2014-01-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different
Tateiwa, Naoyuki; Pospíšil, Jiří; Haga, Yoshinori; Yamamoto, Etsuji
2018-02-01
The critical behavior of dc magnetization in the uranium ferromagnet URhAl with the hexagonal ZrNiAl-type crystal structure has been studied around the ferromagnetic transition temperature TC. The critical exponent β for the temperature dependence of the spontaneous magnetization below TC,γ for the magnetic susceptibility, and δ for the magnetic isotherm at TC, have been obtained with a modified Arrott plot, a Kouvel-Fisher plot, the critical isotherm analysis, and the scaling analysis. We have determined the critical exponents as β =0.287 ±0.005 , γ =1.47 ±0.02 , and δ =6.08 ±0.04 by the scaling analysis and the critical isotherm analysis. These critical exponents satisfy the Widom scaling law δ =1 +γ /β . URhAl has strong uniaxial magnetic anisotropy, similar to its isostructural UCoAl that has been regarded as a three-dimensional (3D) Ising system in previous studies. However, the universality class of the critical phenomenon in URhAl does not belong to the 3D Ising model (β =0.325 , γ =1.241 , and δ =4.82 ) with short-range exchange interactions between magnetic moments. The determined exponents can be explained with the results of the renormalization group approach for a two-dimensional (2D) Ising system coupled with long-range interactions decaying as J (r ) ˜r-(d +σ ) with σ =1.44 . We suggest that the strong hybridization between the uranium 5 f and rhodium 4 d electrons in the U-RhI layer in the hexagonal crystal structure is a source of the low-dimensional magnetic property. The present result is contrary to current understandings of the physical properties in a series of isostructural UTX uranium ferromagnets (T: transition metals, X: p -block elements) based on the 3D Ising model.
Soriano, Diogo C.; Santos, Odair V. dos; Suyama, Ricardo; Fazanaro, Filipe I.; Attux, Romis
2018-03-01
This work has a twofold aim: (a) to analyze an alternative approach for computing the conditional Lyapunov exponent (λcmax) aiming to evaluate the synchronization stability between nonlinear oscillators without solving the classical variational equations for the synchronization error dynamical system. In this first framework, an analytic reference value for λcmax is also provided in the context of Duffing master-slave scenario and precisely evaluated by the proposed numerical approach; (b) to apply this technique to the study of synchronization stability in chaotic Hindmarsh-Rose (HR) neuronal models under uni- and bi-directional resistive coupling and different excitation bias, which also considered the root mean square synchronization error, information theoretic measures and asymmetric transfer entropy in order to offer a better insight of the synchronization phenomenon. In particular, statistical and information theoretical measures were able to capture similarity increase between the neuronal oscillators just after a critical coupling value in accordance to the largest conditional Lyapunov exponent behavior. On the other hand, transfer entropy was able to detect neuronal emitter influence even in a weak coupling condition, i.e. under the increase of conditional Lyapunov exponent and apparently desynchronization tendency. In the performed set of numerical simulations, the synchronization measures were also evaluated for a two-dimensional parameter space defined by the neuronal coupling (emitter to a receiver neuron) and the (receiver) excitation current. Such analysis is repeated for different feedback couplings as well for different (emitter) excitation currents, revealing interesting characteristics of the attained synchronization region and conditions that facilitate the emergence of the synchronous behavior. These results provide a more detailed numerical insight of the underlying behavior of a HR in the excitation and coupling space, being in accordance
Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement
Energy Technology Data Exchange (ETDEWEB)
Ayati, Moosa [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: Ayati@dena.kntu.ac.ir; Khaki-Sedigh, Ali [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: sedigh@kntu.ac.ir
2009-08-30
This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.
Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement
International Nuclear Information System (INIS)
Ayati, Moosa; Khaki-Sedigh, Ali
2009-01-01
This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.
Exponent and scrambling index of double alternate circular snake graphs
Rahmayanti, Sri; Pasaribu, Valdo E.; Nasution, Sawaluddin; Liani Salnaz, Sishi
2018-01-01
A graph is primitive if it contains a cycle of odd length. The exponent of a primitive graph G, denoted by exp(G), is the smallest positive integer k such that for each pair of vertices u and v in G there is a uv-walk length k. The scrambling index of a primitive graph G, denoted by k(G), is the smallest positive integer k such that for each pair of vertices u and v in G there is a uv-walk of length 2k. For an even positive integer n and an odd positive integer r, a (n,r)-double alternate circular snake graph, denoted by DA(C r,n ), is a graph obtained from a path u 1 u 2 ... u n by replacing each edge of the form u 2i u 2i+1 by two different r-cycles. We study the exponent and scrambling index of DA(C r,n ) and show that exp(DA(C r,n )) = n + r - 4 and k(DA(C r,n )) = (n + r - 3)/2.
Riemannian theory of Hamiltonian chaos and Lyapunov exponents
Casetti, Lapo; Clementi, Cecilia; Pettini, Marco
1996-12-01
A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.
... Marker Bicarbonate (Total CO2) Bilirubin Blood Culture Blood Gases Blood Ketones Blood Smear Blood Typing Blood Urea ... hours depending on the method used. There are commercial tests available that offer rapid susceptibility testing and ...
Marginalism, quasi-marginalism and critical phenomena in micellar solutions
International Nuclear Information System (INIS)
Reatto, L.
1986-01-01
The observed nonuniversal critical behaviour of some micellar solutions is interpreted in terms of quasi-marginalism, i.e. the presence of a coupling which scales with an exponent very close to the spatial dimensionality. This can give rise to a preasymptotic region with varying effective critical exponents with a final crossover to the Ising ones. The reduced crossover temperature is estimated to be below 10 -6 . The exponents β and γ measured in C 12 e 5 are in good agreement with the scaling law expected to hold for the effective exponents. The model considered by Shnidman is found unable to explain the nonuniversal critical behaviour
Dynamic dilution exponent in monodisperse entangled polymer solutions
DEFF Research Database (Denmark)
Shahid, T.; Huang, Qian; Oosterlinck, F.
2017-01-01
of concentration but also depends on the molar mass of the chains. While the proposed approach successfully explains the viscoelastic properties of a large number of semi-dilute solutions of polymers in their own oligomers, important discrepancies are found for semi-dilute entangled polymers in small-molecule......We study and model the linear viscoelastic properties of several entangled semi-dilute and concentrated solutions of linear chains of different molar masses and at different concentrations dissolved in their oligomers. We discuss the dilution effect of the oligomers on the entangled long chains....... In particular, we investigate the influence of both concentration and molar mass on the value of the effective dynamic dilution exponent determined from the level of the storage plateau at low and intermediate frequencies. We show that the experimental results can be quantitatively explained by considering...
Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents
Cho, Y. S.; Lee, J. S.; Herrmann, H. J.; Kahng, B.
2016-01-01
Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of g fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a more unusual phase transition, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent τ in the range 2 power-law behavior of the avalanche size distribution arising in models with link-deleting processes in interdependent networks.
A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents
International Nuclear Information System (INIS)
Guo-Si, Hu
2009-01-01
There are many hyperchaotic systems, but few systems can generate hyperchaotic attractors with more than three PLEs (positive Lyapunov exponents). A new hyperchaotic system, constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system, is presented. With the increasing number of phase-shift units used in this system, the number of PLEs also steadily increases. Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units. The sum of the PLEs will reach the maximum value when 23 phase-shift units are used. A simple electronic circuit, consisting of 16 operational amplifiers and two analogy multipliers, is presented for confirming hyperchaos of order 5, i.e., with 5 PLEs
Generalized Hurst exponent approach to efficiency in MENA markets
Sensoy, A.
2013-10-01
We study the time-varying efficiency of 15 Middle East and North African (MENA) stock markets by generalized Hurst exponent analysis of daily data with a rolling window technique. The study covers a time period of six years from January 2007 to December 2012. The results reveal that all MENA stock markets exhibit different degrees of long-range dependence varying over time and that the Arab Spring has had a negative effect on market efficiency in the region. The least inefficient market is found to be Turkey, followed by Israel, while the most inefficient markets are Iran, Tunisia, and UAE. Turkey and Israel show characteristics of developed financial markets. Reasons and implications are discussed.
The critical behavior of PHI41
International Nuclear Information System (INIS)
Isaacson, D.
1977-01-01
The eigenvalues, eigenfunctions, and Schwinger functions of the ordinary differential operator H(Λ,m) = 1/2[p 2 + Λq 4 + (m 2 - Λm -1 )q 2 ] are studied as Λ → infinity. It is shown that the scaling limit of the Schwinger functions equals the scaling limit of a one dimensional Ising model. Critical exponents of H(Λ,m) are shown to equal critical exponents of the Ising model, while critical exponents of the renormalized theory are shown to agree with those of a harmonic oscillator. (orig.) [de
Nonlinearity exponent of ac conductivity in disordered systems
International Nuclear Information System (INIS)
Nandi, U N; Sircar, S; Karmakar, A; Giri, S
2012-01-01
We measured the real part of ac conductance Σ(x,f) or Σ(T,f) of iron-doped mixed-valent polycrystalline manganite oxides LaMn 1-x Fe x O 3 as a function of frequency f by varying initial conductance Σ 0 by quenched disorder x at a fixed temperature T (room) and by temperature T at a fixed quenched disorder x. At a fixed temperature T, Σ(x,f) of a sample with fixed x remains almost constant at its zero-frequency dc value Σ 0 at lower frequency. With increase in f, Σ(x,f) increases slowly from Σ 0 and finally increases rapidly following a power law with an exponent s at high frequency. Scaled appropriately, the data for Σ(T,f) and Σ(x,f) fall on the same universal curve, indicating the existence of a general scaling formalism for the ac conductivity in disordered systems. The characteristic frequency f c at which Σ(x,f) or Σ(T,f) increases for the first time from Σ 0 scales with initial conductance Σ 0 as f c ∼ Σ 0 x f , where x f is the onset exponent. The value of x f is nearly equal to one and is found to be independent of x and T. Further, an inverse relationship between x f and s provides a self-consistency check of the systematic description of Σ(x,f) or Σ(T,f). This apparent universal value of x f is discussed within the framework of existing theoretical models and scaling theories. The relevance to other similar disordered systems is also highlighted. (paper)
On the upper critical dimension of Bernoulli percolation
International Nuclear Information System (INIS)
Chayes, J.T.; Chayes, L.
1987-01-01
Derived is a set of inequalities for the d-dimensional independent percolation problem. Assuming the existence of critical exponents, these inequalities imply: f + nu ≥ 1 + β/sub Q/, μ + nu ≥ 1 + β/sub Q/, zeta ≥ min (1, nu'/nu), where the above exponents are f: the flow constant exponent, nu (nu'): the correlation length exponent below (above) threshold, μ: the surface tension exponent, β/sub Q/: the backbone density exponent and zeta: the chemical distance exponent. Note that all of these inequalities are mean-field bounds, and that they relate the exponent nu defined from below the percolation threshold to exponents defined from above threshold. Furthermore, we combine the strategy of the proofs these inequalities with notions of finite-size scaling to derive: max (d nu, d nu') ≥ 1 + β/sub Q/, where d is the lattice dimension. Since β/sub Q/ ≥ 2β, where β is the percolation density exponent, the final bound implies that, below six dimensions, the standard order parameter and correlation length exponents cannot simultaneously assume their mean-field values; hence an implicit bound on the upper critical dimension: d/sub c/ ≥ 6
Critical properties of the SIS model dynamics on the Apollonian network
International Nuclear Information System (INIS)
Da Silva, L F; Costa Filho, R N; Cunha, A R; Macedo-Filho, A; Serva, M; Fulco, U L; Albuquerque, E L
2013-01-01
We present an analysis of the classical SIS (susceptible–infected–susceptible) model on the Apollonian network which is scale free and displays the small word effect. Numerical simulations show a continuous absorbing-state phase transition at a finite critical value λ c of the control parameter λ. Since the coordination number k of the vertices of the Apollonian network is cumulatively distributed according to a power-law P(k) ∝ 1/k η−1 , with exponent η ≃ 2.585, finite size effects are large and the infinite network limit cannot be reached in practice. Consequently, our study requires the application of finite size scaling theory, allowing us to characterize the transition by a set of critical exponents β/ν ⊥ , γ/ν ⊥ , ν ⊥ , β. We found that the phase transition belongs to the mean-field directed percolation universality class in regular lattices but, very peculiarly, is associated with a short-range distribution whose power-law distribution of k is defined by an exponent η larger than 3. (paper)
Spacetime dependence of the anomalous exponent of electric transport in the disorder model
International Nuclear Information System (INIS)
Egami, Takeshi; Suzuki, Koshiro; Watanabe, Katsuhiro
2012-01-01
Spacetime dependence of the anomalous exponent of electric transport in the disorder model is investigated. We show that the anomalous exponent evolves with time, according to the time evolution of the number of the effective neighbouring sites. Transition from subdiffusive to normal transport is recovered at macroscopic timescales. Plateaus appear in the history of the anomalous exponent due to the discreteness of the hopping sites, which is compatible with the conventional treatment to regard the anomalous exponent as a constant. We also show that, among various microscopic spatial structures, the number of the effective neighbouring sites is the only element which determines the anomalous exponent. This is compatible with the mesoscopic model of Scher–Montroll. These findings are verified by means of Monte Carlo simulation. The well-known expression of the anomalous exponent in the conventional multiple trapping model is derived by deducing it as a special case of the disorder model. (paper)
A new combined approach on Hurst exponent estimate and its applications in realized volatility
Luo, Yi; Huang, Yirong
2018-02-01
The purpose of this paper is to propose a new estimator of Hurst exponent based on the combined information of the conventional rescaled range methods. We demonstrate the superiority of the proposed estimator by Monte Carlo simulations, and the applications in estimating the Hurst exponent of daily volatility series in Chinese stock market. Moreover, we indicate the impact of the type of estimator and structural break on the estimating results of Hurst exponent.
Partial differential equations with variable exponents variational methods and qualitative analysis
Radulescu, Vicentiu D
2015-01-01
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive meth
Universal Postquench Prethermalization at a Quantum Critical Point
Gagel, Pia; Orth, Peter P.; Schmalian, Jörg
2014-11-01
We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive nonequilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are: (i) a power law rise of order and correlations after an initial collapse of the equilibrium state and (ii) a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.
Microscopic processes controlling the Herschel-Bulkley exponent
Lin, Jie; Wyart, Matthieu
2018-01-01
The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent n =1 /β . A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to β =2 in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to β =1 with logarithmic correction. This result supports that HL is not a suitable explanation for the value of β , which is instead significantly affected by finite-dimensional effects. From considerations on elastoplastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that β =1 +1 /(d -df) , where df is the fractal dimension of avalanches and d the spatial dimension. Measurements of df then supports that β ≈2.1 and β ≈1.7 in two and three dimensions, respectively. We discuss theoretical arguments leading to approximations of β in finite dimensions.
Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents
Athanassoulis, Agissilaos; Katsaounis, Theodoros; Kyza, Irene
2016-01-01
Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.
Regularized semiclassical limits: Linear flows with infinite Lyapunov exponents
Athanassoulis, Agissilaos
2016-08-30
Semiclassical asymptotics for Schrödinger equations with non-smooth potentials give rise to ill-posed formal semiclassical limits. These problems have attracted a lot of attention in the last few years, as a proxy for the treatment of eigenvalue crossings, i.e. general systems. It has recently been shown that the semiclassical limit for conical singularities is in fact well-posed, as long as the Wigner measure (WM) stays away from singular saddle points. In this work we develop a family of refined semiclassical estimates, and use them to derive regularized transport equations for saddle points with infinite Lyapunov exponents, extending the aforementioned recent results. In the process we answer a related question posed by P.L. Lions and T. Paul in 1993. If we consider more singular potentials, our rigorous estimates break down. To investigate whether conical saddle points, such as -|x|, admit a regularized transport asymptotic approximation, we employ a numerical solver based on posteriori error control. Thus rigorous upper bounds for the asymptotic error in concrete problems are generated. In particular, specific phenomena which render invalid any regularized transport for -|x| are identified and quantified. In that sense our rigorous results are sharp. Finally, we use our findings to formulate a precise conjecture for the condition under which conical saddle points admit a regularized transport solution for the WM. © 2016 International Press.
Percolation systems away from the critical point
Indian Academy of Sciences (India)
DEEPAK DHAR. Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India ... There is more to percolation theory than the critical exponents. Of course, an experi- .... simple qualitative arguments. In the summation ...
Critical exponents in the transition to chaos in one-dimensional ...
Indian Academy of Sciences (India)
The transition from periodic to chaotic behavior in one-dimensional discrete dynamical systems .... consider the reverse sequence from µb to µ∞, a ... at which the change from one scaling region to another takes place, with the higher order. 12.
Directory of Open Access Journals (Sweden)
Guanwei Chen
2014-01-01
Full Text Available We study the existence of positive solutions and multiplicity of nontrivial solutions for a class of quasilinear elliptic equations by using variational methods. Our obtained results extend some existing ones.
A critical blow-up exponent in a chemotaxis system with nonlinear signal production
Winkler, Michael
2018-05-01
This paper is concerned with radially symmetric solutions of the Keller–Segel system with nonlinear signal production, as given by in the ball for and R > 0, where f is a suitably regular function generalizing the prototype determined by the choice , , with . The main results assert that if in this setting the number κ satisfies then for any prescribed mass level m > 0, there exist initial data u 0 with , for which the solution of the corresponding Neumann initial-boundary value problem blows up in finite time. The condition in () is essentially optimal and is indicated by a complementary result according to which in the case , for widely arbitrary initial data, a global bounded classical solution can always be found.
Two-dimensional critical phenomena
International Nuclear Information System (INIS)
Saleur, H.
1987-09-01
Two dimensional critical systems are studied using transformation to free fields and conformal invariance methods. The relations between the two approaches are also studied. The analytical results obtained generally depend on universality hypotheses or on renormalization group trajectories which are not established rigorously, so numerical verifications, mainly using the transfer matrix approach, are presented. The exact determination of critical exponents; the partition functions of critical models on toruses; and results as the critical point is approached are discussed [fr
International Nuclear Information System (INIS)
Junod, A.; Bezinge, A.; Graf, T.
1987-01-01
YBa 2 Cu 3 O 7 superconductors with inductive transitions as narrows as 0.45 K above 90 K were synthetized. Samples were characterized by thermogravimetry, differential thermal analysis, X-ray and neutron diffraction. The structure is characterized by a two-dimensional Cu-O network with square-pyramidal and square-planar coordinated Cu atoms. Results show a clear metallic behaviour of the resistivity. An orbital critical field as high as 300 T is extrapolated. Meissner flux expulsion up to 40% is observed. Small amounts of magnetic Cu 2+ ions are correlated with the presence of the impurity phase BaCuO 2 . The Pauli susceptibility and the specific-heat jump at T c are consistent with γ ≅ 2mJ/(K 2 gat) (9mJ/(K 2 mole-Cu)), neglecting all renormalizations
Variation of Zipf's exponent in one hundred live languages: A study of the Holy Bible translations
Mehri, Ali; Jamaati, Maryam
2017-08-01
Zipf's law, as a power-law regularity, confirms long-range correlations between the elements in natural and artificial systems. In this article, this law is evaluated for one hundred live languages. We calculate Zipf's exponent for translations of the holy Bible to several languages, for this purpose. The results show that, the average of Zipf's exponent in studied texts is slightly above unity. All studied languages in some families have Zipf's exponent lower/higher than unity. It seems that geographical distribution impresses the communication between speakers of different languages in a language family, and affect similarity between their Zipf's exponent. The Bible has unique concept regardless of its language, but the discrepancy in grammatical rules and syntactic regularities in applying stop words to make sentences and imply a certain concept, lead to difference in Zipf's exponent for various languages.
Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets
Eom, Cheoljun; Choi, Sunghoon; Oh, Gabjin; Jung, Woo-Sung
2008-07-01
We empirically investigated the relationships between the degree of efficiency and the predictability in financial time-series data. The Hurst exponent was used as the measurement of the degree of efficiency, and the hit rate calculated from the nearest-neighbor prediction method was used for the prediction of the directions of future price changes. We used 60 market indexes of various countries. We empirically discovered that the relationship between the degree of efficiency (the Hurst exponent) and the predictability (the hit rate) is strongly positive. That is, a market index with a higher Hurst exponent tends to have a higher hit rate. These results suggested that the Hurst exponent is useful for predicting future price changes. Furthermore, we also discovered that the Hurst exponent and the hit rate are useful as standards that can distinguish emerging capital markets from mature capital markets.
The Evolution of the Exponent of Zipf's Law in Language Ontogeny
Baixeries, Jaume; Elvevåg, Brita; Ferrer-i-Cancho, Ramon
2013-01-01
It is well-known that word frequencies arrange themselves according to Zipf's law. However, little is known about the dependency of the parameters of the law and the complexity of a communication system. Many models of the evolution of language assume that the exponent of the law remains constant as the complexity of a communication systems increases. Using longitudinal studies of child language, we analysed the word rank distribution for the speech of children and adults participating in conversations. The adults typically included family members (e.g., parents) or the investigators conducting the research. Our analysis of the evolution of Zipf's law yields two main unexpected results. First, in children the exponent of the law tends to decrease over time while this tendency is weaker in adults, thus suggesting this is not a mere mirror effect of adult speech. Second, although the exponent of the law is more stable in adults, their exponents fall below 1 which is the typical value of the exponent assumed in both children and adults. Our analysis also shows a tendency of the mean length of utterances (MLU), a simple estimate of syntactic complexity, to increase as the exponent decreases. The parallel evolution of the exponent and a simple indicator of syntactic complexity (MLU) supports the hypothesis that the exponent of Zipf's law and linguistic complexity are inter-related. The assumption that Zipf's law for word ranks is a power-law with a constant exponent of one in both adults and children needs to be revised. PMID:23516390
The anomalous scaling exponents of turbulence in general dimension from random geometry
Energy Technology Data Exchange (ETDEWEB)
Eling, Christopher [Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP (United Kingdom); Oz, Yaron [Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978 (Israel)
2015-09-22
We propose an analytical formula for the anomalous scaling exponents of inertial range structure functions in incompressible fluid turbulence. The formula is a Knizhnik-Polyakov-Zamolodchikov (KPZ)-type relation and is valid in any number of space dimensions. It incorporates intermittency in a novel way by dressing the Kolmogorov linear scaling via a coupling to a lognormal random geometry. The formula has one real parameter γ that depends on the number of space dimensions. The scaling exponents satisfy the convexity inequality, and the supersonic bound constraint. They agree with the experimental and numerical data in two and three space dimensions, and with numerical data in four space dimensions. Intermittency increases with γ, and in the infinite γ limit the scaling exponents approach the value one, as in Burgers turbulence. At large n the nth order exponent scales as √n. We discuss the relation between fluid flows and black hole geometry that inspired our proposal.
Variation of CRE with exponents of time and number of fractions
International Nuclear Information System (INIS)
Supe, S.J.; Rao, S.M.; Sawant, S.G.; Bisht, J.S.
1976-01-01
The concept of NSD has been modified into TDF's by Orton and Ellis and CRE's by Kirk et al. It was aimed to study the variability of these new concepts on the exponents of time and number of fractions. It was found that TDF has larger variation with the exponents compared to that of CRE. The use of CRE and NSD for solving the treatment scheduling problems or for intercomparison of various regimes has been simplified by providing readymade estimation of CRE for various doses/fraction with increasing number of fractions. As there is increasing evidence for the change of exponents J and H, nomograms are presented to determine the CRE for various values of J and H. The variation of decay correction factors with the exponent H is also evaluated and is presented. This will help various radiotherapists to use CRE and the decay correction factors consistent with their clinical findings. (orig.) [de
A comment on measuring the Hurst exponent of financial time series
Couillard, Michel; Davison, Matt
2005-03-01
A fundamental hypothesis of quantitative finance is that stock price variations are independent and can be modeled using Brownian motion. In recent years, it was proposed to use rescaled range analysis and its characteristic value, the Hurst exponent, to test for independence in financial time series. Theoretically, independent time series should be characterized by a Hurst exponent of 1/2. However, finite Brownian motion data sets will always give a value of the Hurst exponent larger than 1/2 and without an appropriate statistical test such a value can mistakenly be interpreted as evidence of long term memory. We obtain a more precise statistical significance test for the Hurst exponent and apply it to real financial data sets. Our empirical analysis shows no long-term memory in some financial returns, suggesting that Brownian motion cannot be rejected as a model for price dynamics.
High-resolution satellite image segmentation using Hölder exponents
Indian Academy of Sciences (India)
Keywords. High resolution image; texture analysis; segmentation; IKONOS; Hölder exponent; cluster. ... are that. • it can be used as a tool to measure the roughness ... uses reinforcement learning to learn the reward values of ..... The numerical.
Hyperchaos of four state autonomous system with three positive Lyapunov exponents
International Nuclear Information System (INIS)
Ge Zhengming; Yang, C-H.
2009-01-01
This Letter gives the results of numerical simulations of Quantum Cellular Neural Network (Quantum-CNN) autonomous system with four state variables. Three positive Lyapunov exponents confirm hyperchaotic nature of its dynamics
Einstein, T. L.; Morales-Cifuentes, Josue; Pimpinelli, Alberto
2015-03-01
Analyzing capture-zone distributions (CZD) using the generalized Wigner distribution (GWD) has proved a powerful way to access the critical nucleus size i. Of the several systems to which the GWD has been applied, we consider 6P on mica, for which Winkler's group found i ~ 3 . Subsequently they measured the growth exponent α (island density ~Fα , for flux F) of this system and found good scaling but different values at small and large F, which they attributed to DLA and ALA dynamics, but with larger values of i than found from the CZD analysis. We investigate this result in some detail. The third talk of this group describes a new universal relation between α and the characteristic exponent β of the GWD. The second talk reports the results of a proposed model that takes long-known transient ballistic adsorption into account, for the first time in a quantitative way. We find several intermediate scaling regimes, with distinctive values of α and an effective activation energy. One of these, rather than ALA, gives the best fit of the experimental data and a value of i consistent with the CZD analysis. Work at UMD supported by NSF CHE 13-05892.
Phong, P. T.; Ngan, L. T. T.; Dang, N. V.; Nguyen, L. H.; Nam, P. H.; Thuy, D. M.; Tuan, N. D.; Bau, L. V.; Lee, I. J.
2018-03-01
In this work, we report the structural and magnetic properties of La0.75Ca0.25MnO3 nanoparticles synthesized by the sol-gel route. Rietvield refinement of X-ray powder diffraction confirms that our sample is single phase and crystallizes in orthorhombic system with Pnma space group. The facts that effective magnetic moment is large and the inverse susceptibility deviates from the Curie Weiss lawn indicate the presence of Griffiths-like cluster phase. The critical exponents have been estimated using different techniques such as modified Arrott plot, Kouvel-Fisher plot and critical isotherm technique. The critical exponents values of La0.75Ca0.25MnO3 are very close to those found out by the mean-field model, and this can be explained by the existence of a long-range interactions between spins in this system. These results were in good agreement with those obtained using the critical exponents of magnetic entropy change. The self-consistency and reliability of the critical exponent was verified by the Widom scaling law and the universal scaling hypothesis. Using the Harris criterion, we deduced that the disorder is relevant in our case. The maximum magnetic entropy change (ΔSM) calculated from the M-H measurements is 3.47 J/kg K under an external field change of 5 T. The ΔSM-T curves collapsed onto a single master curve regardless of the composition and the applied field, confirming the magnetic ordering is of second order nature. The obtained result was compared to ones calculated based on the Arrott plot and a good concordance is observed. Moreover, the spontaneous magnetization obtained from the entropy change is in excellent agreement with that deduced by classically extrapolation the Arrott curves. This result confirms the validity of the estimation of the spontaneous magnetization using the magnetic entropy change.
Experimental mathematics on the magnetic susceptibility of the square lattice Ising model
Energy Technology Data Exchange (ETDEWEB)
Boukraa, S [LPTHIRM and Departement d' Aeronautique, Universite de Blida (Algeria); Guttmann, A J; Jensen, I [ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia); Hassani, S; Zenine, N [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Maillard, J-M [LPTMC, Universite de Paris, Tour 24, 4eme etage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Nickel, B [Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)], E-mail: boukraa@mail.univ-blida.dz, E-mail: tonyg@ms.unimelb.edu.au, E-mail: I.Jensen@ms.unimelb.edu.au, E-mail: maillard@lptmc.jussieu.fr, E-mail: maillard@lptl.jussieu.fr, E-mail: njzenine@yahoo.com
2008-11-14
We calculate very long low- and high-temperature series for the susceptibility {chi} of the square lattice Ising model as well as very long series for the five-particle contribution {chi}{sup (5)} and six-particle contribution {chi}{sup (6)}. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 CPU hours on computer clusters. The series for {chi} (low- and high-temperature regimes), {chi}{sup (5)} and {chi}{sup (6)} are now extended to 2000 terms. In addition, for {chi}{sup (5)}, 10 000 terms of the series are calculated modulo a single prime, and have been used to find the linear ODE satisfied by {chi}{sup (5)} modulo a prime. A diff-Pade analysis of the 2000 terms series for {chi}{sup (5)} and {chi}{sup (6)} confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the n-particle components of the susceptibility, up to a small set of 'additional' singularities. The exponents at all the singularities of the Fuchsian linear ODE of {chi}{sup (5)} and the (as yet unknown) ODE of {chi}{sup (6)} are given: they are all rational numbers. We find the presence of singularities at w = 1/2 for the linear ODE of {chi}{sup (5)}, and w{sup 2} = 1/8 for the ODE of {chi}{sup (6)}, which are not singularities of the 'physical' {chi}{sup (5)} and {chi}{sup (6)}, that is to say the series solutions of the ODE's which are analytic at w = 0. Furthermore, analysis of the long series for {chi}{sup (5)} (and {chi}{sup (6)}) combined with the corresponding long series for the full susceptibility {chi} yields previously conjectured singularities in some {chi}{sup (n)}, n {>=} 7. The exponents at all these singularities are also seen to be rational numbers. We also present a mechanism of resummation of the logarithmic singularities of the {chi}{sup (n)} leading to the known power-law critical behaviour occurring in
Critical behavior in a stochastic model of vector mediated epidemics
Alfinito, E.; Beccaria, M.; Macorini, G.
2016-06-01
The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.
Laminar Flame Velocity and Temperature Exponent of Diluted DME-Air Mixture
Naseer Mohammed, Abdul; Anwar, Muzammil; Juhany, Khalid A.; Mohammad, Akram
2017-03-01
In this paper, the laminar flame velocity and temperature exponent diluted dimethyl ether (DME) air mixtures are reported. Laminar premixed mixture of DME-air with volumetric dilutions of carbon dioxides (CO2) and nitrogen (N2) are considered. Experiments were conducted using a preheated mesoscale high aspect-ratio diverging channel with inlet dimensions of 25 mm × 2 mm. In this method, flame velocities are extracted from planar flames that were stabilized near adiabatic conditions inside the channel. The flame velocities are then plotted against the ratio of mixture temperature and the initial reference temperature. A non-linear power law regression is observed suitable. This regression analysis gives the laminar flame velocity at the initial reference temperature and temperature exponent. Decrease in the laminar flame velocity and increase in temperature exponent is observed for CO2 and N2 diluted mixtures. The addition of CO2 has profound influence when compared to N2 addition on both flame velocity and temperature exponent. Numerical prediction of the similar mixture using a detailed reaction mechanism is obtained. The computational mechanism predicts higher magnitudes for laminar flame velocity and smaller magnitudes of temperature exponent compared to experimental data.
The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance
Directory of Open Access Journals (Sweden)
Kun Liu
2015-01-01
Full Text Available The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body’s standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age.
Subdiffusive master equation with space-dependent anomalous exponent and structural instability
Fedotov, Sergei; Falconer, Steven
2012-03-01
We derive the fractional master equation with space-dependent anomalous exponent. We analyze the asymptotic behavior of the corresponding lattice model both analytically and by Monte Carlo simulation. We show that the subdiffusive fractional equations with constant anomalous exponent μ in a bounded domain [0,L] are not structurally stable with respect to the nonhomogeneous variations of parameter μ. In particular, the Gibbs-Boltzmann distribution is no longer the stationary solution of the fractional Fokker-Planck equation whatever the space variation of the exponent might be. We analyze the random distribution of μ in space and find that in the long-time limit, the probability distribution is highly intermediate in space and the behavior is completely dominated by very unlikely events. We show that subdiffusive fractional equations with the nonuniform random distribution of anomalous exponent is an illustration of a “Black Swan,” the low probability event of the small value of the anomalous exponent that completely dominates the long-time behavior of subdiffusive systems.
Critical lengths of error events in convolutional codes
DEFF Research Database (Denmark)
Justesen, Jørn
1994-01-01
If the calculation of the critical length is based on the expurgated exponent, the length becomes nonzero for low error probabilities. This result applies to typical long codes, but it may also be useful for modeling error events in specific codes......If the calculation of the critical length is based on the expurgated exponent, the length becomes nonzero for low error probabilities. This result applies to typical long codes, but it may also be useful for modeling error events in specific codes...
Critical Lengths of Error Events in Convolutional Codes
DEFF Research Database (Denmark)
Justesen, Jørn; Andersen, Jakob Dahl
1998-01-01
If the calculation of the critical length is based on the expurgated exponent, the length becomes nonzero for low error probabilities. This result applies to typical long codes, but it may also be useful for modeling error events in specific codes......If the calculation of the critical length is based on the expurgated exponent, the length becomes nonzero for low error probabilities. This result applies to typical long codes, but it may also be useful for modeling error events in specific codes...
International Nuclear Information System (INIS)
Zhikov, Vasilii V; Pastukhova, Svetlana E
2008-01-01
Elliptic equations of p(x)-Laplacian type are investigated. There is a well-known logarithmic condition on the modulus of continuity of the nonlinearity exponent p(x), which ensures that a Laplacian with variable order of nonlinearity inherits many properties of the usual p-Laplacian of constant order. One of these is the so-called improved integrability of the gradient of the solution. It is proved in this paper that this property holds also under a slightly more general condition on the exponent p(x), although then the improvement of integrability is logarithmic rather than power-like. The method put forward is based on a new generalization of Gehring's lemma, which relies upon the reverse Hoelder inequality 'with increased support and exponent on the right-hand side'. A counterexample is constructed that reveals the extent to which the condition on the modulus of continuity obtained is sharp. Bibliography: 28 titles.
Stochastic model of Zipf's law and the universality of the power-law exponent.
Yamamoto, Ken
2014-04-01
We propose a stochastic model of Zipf's law, namely a power-law relation between rank and size, and clarify as to why a specific value of its power-law exponent is quite universal. We focus on the successive total of a multiplicative stochastic process. By employing properties of a well-known stochastic process, we concisely show that the successive total follows a stationary power-law distribution, which is directly related to Zipf's law. The formula of the power-law exponent is also derived. Finally, we conclude that the universality of the rank-size exponent is brought about by symmetry between an increase and a decrease in the random growth rate.
International Nuclear Information System (INIS)
Kari, R.E.; Mezey, P.G.; Csizmadia, I.G.
1975-01-01
Expressions are given for calculating the energy gradient vector in the exponent space of Gaussian basis sets and a technique to optimize orbital exponents using the method of conjugate gradients is described. The method is tested on the (9/sups/5/supp/) Gaussian basis space and optimum exponents are determined for the carbon atom. The analysis of the results shows that the calculated one-electron properties converge more slowly to their optimum values than the total energy converges to its optimum value. In addition, basis sets approximating the optimum total energy very well can still be markedly improved for the prediction of one-electron properties. For smaller basis sets, this improvement does not warrant the necessary expense
Effect of density of state on isotope effect exponent of two-band superconductors
International Nuclear Information System (INIS)
Udomsamuthirun, P.; Kumvongsa, C.; Burakorn, A.; Changkanarth, P.; Yoksan, S.
2005-01-01
The exact formula of T c 's equation and the isotope effect exponent of two-band s-wave superconductors in weak-coupling limit are derived by considering the influence of two kinds of density of state: constant and van Hove singularity. The paring interaction in each band consisted of two parts: the electron-phonon interaction and non-electron-phonon interaction are included in our model. We find that the interband interaction of electron-phonon show more effect on isotope exponent than the intraband interaction and the isotope effect exponent with constant density of state can fit to experimental data, MgB 2 and high-T c superconductor, better than van Hove singularity density of state
Identification of exponent from load-deformation relation for soft materials from impact tests
Ciornei, F. C.; Alaci, S.; Romanu, I. C.; Ciornei, M. C.; Sopon, G.
2018-01-01
When two bodies are brought into contact, the magnitude of occurring reaction forces increase together with the amplitude of deformations. The load-deformation dependency of two contacting bodies is described by a function having the form F = Cxα . An accurate illustration of this relationship assumes finding the precise coefficient C and exponent α. This representation proved to be very useful in hardness tests, in dynamic systems modelling or in considerations upon the elastic-plastic ratio concerning a Hertzian contact. The classical method for identification of the exponent consists in finding it from quasi-static tests. The drawback of the method is the fact that the accurate estimation of the exponent supposes precise identification of the instant of contact initiation. To overcome this aspect, the following observation is exploited: during an impact process, the dissipated energy is converted into heat released by internal friction in the materials and energy for plastic deformations. The paper is based on the remark that for soft materials the hysteresis curves obtained for a static case are similar to the ones obtained for medium velocities. Furthermore, utilizing the fact that for the restitution phase the load-deformation dependency is elastic, a method for finding the α exponent for compression phase is proposed. The maximum depth of the plastic deformations obtained for a series of collisions, by launching, from different heights, a steel ball in free falling on an immobile prism made of soft material, is evaluated by laser profilometry method. The condition that the area of the hysteresis loop equals the variation of kinetical energy of the ball is imposed and two tests are required for finding the exponent. Five collisions from different launching heights of the ball were taken into account. For all the possible impact-pair cases, the values of the exponent were found and close values were obtained.
Relation between the Hurst Exponent and the Efficiency of Self-organization of a Deformable System
Alfyorova, E. A.; Lychagin, D. V.
2018-04-01
We have established the degree of self-organization of a system under plastic deformation at different scale levels. Using fractal analysis, we have determined the Hurst exponent and correlation lengths in the region of formation of a corrugated (wrinkled) structure in [111] nickel single crystals under compression. This has made it possible to single out two (micro-and meso-) levels of self-organization in the deformable system. A qualitative relation between the values of the Hurst exponent and the stages of the stress-strain curve has been established.
Hunt, Allen G.
2016-04-01
Percolation theory can be used to find water flow paths of least resistance. Application of percolation theory to drainage networks allows identification of the range of exponent values that describe the tortuosity of rivers in real river networks, which is then used to generate the observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on an assessment of the heterogeneity of the substrate.
Explanation of the values of Hack's drainage basin, river length scaling exponent
Hunt, A. G.
2015-08-01
Percolation theory can be used to find water flow paths of least resistance. The application of percolation theory to drainage networks allows identification of the range of exponent values that describe the tortuosity of rivers in real river networks, which is then used to generate the observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law allows interpretation of the range of exponent values based on an assessment of the heterogeneity of the substrate.
Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise
Morita, Satoru
2018-05-01
Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. For discrete-time systems, the power-law exponent is known to decrease as the autocorrelation time of the multiplier increases. However, for continuous-time systems, it is not yet clear how the temporal correlation affects the power-law behavior. Herein, we analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.
An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity
Energy Technology Data Exchange (ETDEWEB)
Friedland, Gerald [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Metere, Alfredo [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2017-06-07
We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches to the calculation of related quantities, such as the Kolmogorov Sinai entropy which has been linked to thermodynamic entropy. This work provides a bridge between fundamental physics and information theory. It suggests, among other things, that machine learning and other information theory methods can be employed at the core of physics simulations.
New prediction of chaotic time series based on local Lyapunov exponent
International Nuclear Information System (INIS)
Zhang Yong
2013-01-01
A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically. (general)
On the relation between Lyapunov exponents and exponential decay of correlations
International Nuclear Information System (INIS)
Slipantschuk, Julia; Bandtlow, Oscar F; Just, Wolfram
2013-01-01
Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and exponential decay rates, are related. More specifically, for piecewise linear expanding Markov maps observed via piecewise analytic functions, we show that the decay rate is bounded above by twice the Lyapunov exponent, that is, we establish lower bounds for the subleading eigenvalue of the corresponding Perron–Frobenius operator. In addition, we comment on similar relations for general piecewise smooth expanding maps. (paper)
Parachors in terms of critical temperature, critical pressure and acentric factor
Energy Technology Data Exchange (ETDEWEB)
Broseta, D.; Ragil, K.
1995-12-31
The method of parachors is widely used in conventional thermodynamic codes and reservoir simulators to calculate oil/gas interfacial tensions of complex hydrocarbon mixtures. In the low-to-moderate interfacial tension regime, a value p{approx}11/3 has previously been shown to be the {open_quotes}best{close_quotes} parachor exponent. This exponent is a critical exponent and its value is consistent with the values of critical exponents characterizing the liquid/vapor critical behavior. Therefore parachors may be viewed as critical amplitudes. By using critical scaling theory, parachors are related to other critical amplitudes and critical parameters that describe the bulk thermodynamic behavior of fluids. A simple expression relating the parachor of a pure compound to its critical temperature T{sub c}, critical pressure P{sub c}, and acentric factor {omega} is proposed: P= (0.85-0.19{omega})T{sub c}{sup 12/11}/P{sub c}{sup 9/11} where the parachor P is in units of (dyn/cm){sup 3/11}cm{sup 3}/mol, T{sub c} in K and P{sub c} in MPa. This equation matches (within experimental error) the known parachor values of normal fluids (e.g. alkanes, aromatics, CO{sub 2}, N{sub 2}, H{sub 2}S, etc...).
Lee, Hyun-Jung; Kim, Ki-Seok
2018-04-01
We investigate the role of Coulomb interaction in the multifractality of Anderson metal-insulator transition, where the Coulomb interaction is treated within the Hartree-Fock approximation, but disorder effects are taken into account exactly. An innovative technical aspect in our simulation is to utilize the Ewald-sum technique, which allows us to introduce the long-range nature of the Coulomb interaction into Hartree-Fock self-consistent equations of order parameters more accurately. This numerical simulation reproduces the Altshuler-Aronov correction in a metallic state and the Efros-Shklovskii pseudogap in an insulating phase, where the density of states ρ (ω ) is evaluated in three dimensions. Approaching the quantum critical point of a metal-insulator transition from either the metallic or insulting phase, we find that the density of states is given by ρ (ω ) ˜|ω| 1 /2 , which determines one critical exponent of the McMillan-Shklovskii scaling theory. Our main result is to evaluate the eigenfunction multifractal scaling exponent αq, given by the Legendre transformation of the fractal dimension τq, which characterizes the scaling behavior of the inverse participation ratio with respect to the system size L . Our multifractal analysis leads us to identify two kinds of mobility edges, one of which occurs near the Fermi energy and the other of which appears at a high energy, where the density of states at the Fermi energy shows the Coulomb-gap feature. We observe that the multifractal exponent at the high-energy mobility edge remains to be almost identical to that of the Anderson localization transition in the absence of Coulomb interactions. On the other hand, we find that the multifractal exponent near the Fermi energy is more enhanced than that at the high-energy mobility edge, suspected to result from interaction effects. However, both the multifractal exponents do not change even if the strength of the Coulomb interaction varies. We also show that the
GAO Hongying; WU Kangping
2007-01-01
This paper estimates the Pareto exponent of the city size (population size and economy size) distribution, all provinces, and three regions in China in 1997, 2000 and 2003 by OLS, comparatively analyzes the Pareto exponent cross section and times, and empirically analyzes the factors which impacts on the Pareto exponents of provinces. Our analyses show that the size distributions of cities in China follow the Pareto distribution and are of structural features. Variations in the value of the P...
Griffith, Leah
2016-01-01
Classroom teachers try to provide opportunities for students to practice and use the algebra skills they are learning in ways that are nonroutine. They also want to help students connect the big ideas of math with the skills they are learning as part of the balance between understanding concepts and procedures. Math games can be used to accomplish…
On the Topological Changes of Local Hurst Exponent in Polar Regions
Consolini, G.; De Michelis, P.
2014-12-01
Geomagnetic activity during magnetic substorms and storms is related to the dinamical and topological changes of the current systems flowing in the Earth's magnetosphere-ionosphere. This is particularly true in the case of polar regions where the enhancement of auroral electrojet current system is responsible for the observed geomagnetic perturbations. Here, using the DMA-technique we evaluate the local Hurst exponent (H"older exponent) for a set of 46 geomagnetic observatories, widely distributed in the northern hemisphere, during one of the most famous and strong geomagnetic storm, the Bastille event, and reconstruct a sequence of polar maps showing the dinamical changes of the topology of the local Hurst exponent with the geomagnetic activity level. The topological evolution of local Hurst exponent maps is discussed in relation to the dinamical changes of the current systems flowing in the polar ionosphere. G. Consolini has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant agreement no. 313038/STORM for this research.
Fast and unbiased estimator of the time-dependent Hurst exponent
Pianese, Augusto; Bianchi, Sergio; Palazzo, Anna Maria
2018-03-01
We combine two existing estimators of the local Hurst exponent to improve both the goodness of fit and the computational speed of the algorithm. An application with simulated time series is implemented, and a Monte Carlo simulation is performed to provide evidence of the improvement.
A new interpretation of zero Lyapunov exponents in BKL time for Mixmaster cosmology
International Nuclear Information System (INIS)
Wu Xin
2010-01-01
A global relationship between cosmological time and Belinskii-Khalatnikov-Lifshitz (BKL) time during the entire evolution of the Mixmaster Bianchi IX universe is used to explain why all the Lyapunov exponents are zero at the BKL time. The actual reason is that the domain of the cosmological time is finite as the BKL time runs from minus infinity to infinity.
Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data
Energy Technology Data Exchange (ETDEWEB)
Josiński, Henryk [Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Świtoński, Adam [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland); Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Michalczuk, Agnieszka; Wojciechowski, Konrad [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland)
2015-03-10
The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.
Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data
Pathak, Jaideep; Lu, Zhixin; Hunt, Brian R.; Girvan, Michelle; Ott, Edward
2017-12-01
We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system and the large number of Lyapunov exponents yield a challenging test of our method, which we find the method successfully passes.
Adiabatic invariants and asymptotic behavior of Lyapunov exponents of the Schrodinger equation
International Nuclear Information System (INIS)
Delyon, F.; Foulon, P.
1986-01-01
We give an upper bound for the high-energy behavior of the Lyapunov exponent of the one-dimensional Schrodinger equation. We relate this behavior to the diffrentiability properties of the potential. As an application, this result provides an upper bound for the asymptotic length of the gaps of the Schrodinger equation
Directional maximum likelihood self-estimation of the path-loss exponent
Hu, Y.; Leus, G.J.T.; Dong, Min; Zheng, Thomas Fang
2016-01-01
The path-loss exponent (PLE) is a key parameter in wireless propagation channels. Therefore, obtaining the knowledge of the PLE is rather significant for assisting wireless communications and networking to achieve a better performance. Most existing methods for estimating the PLE not only require
Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent
Directory of Open Access Journals (Sweden)
Yan Liu
2016-01-01
Full Text Available The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs, are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase space, and a reduced dynamic system is obtained from the dynamic system viewpoint. Then, a numerical method for computing the largest Lyapunov exponent of the low-dimensional dynamic system is presented. Further, the longest predictable time, which is related to chaotic behaviors in the system, is studied using the largest Lyapunov exponent, and the Wolf method is used to predict the evolution of the traffic in a local area network by both Dot and Interval predictions, and a reliable result is obtained by the presented method. As the conclusion, the results show that the largest Lyapunov exponent can be used to describe the sensitivity of the trajectory in the reconstructed phase space to the initial values. Moreover, Dot Prediction can effectively predict the flow burst. The numerical simulation also shows that the presented method is feasible and efficient for predicting the complex dynamic behaviors in LAN traffic, especially for congestion and attack in networks, which are the main two complex phenomena behaving as chaos in networks.
On identifying relationships between the flood scaling exponent and basin attributes.
Medhi, Hemanta; Tripathi, Shivam
2015-07-01
Floods are known to exhibit self-similarity and follow scaling laws that form the basis of regional flood frequency analysis. However, the relationship between basin attributes and the scaling behavior of floods is still not fully understood. Identifying these relationships is essential for drawing connections between hydrological processes in a basin and the flood response of the basin. The existing studies mostly rely on simulation models to draw these connections. This paper proposes a new methodology that draws connections between basin attributes and the flood scaling exponents by using observed data. In the proposed methodology, region-of-influence approach is used to delineate homogeneous regions for each gaging station. Ordinary least squares regression is then applied to estimate flood scaling exponents for each homogeneous region, and finally stepwise regression is used to identify basin attributes that affect flood scaling exponents. The effectiveness of the proposed methodology is tested by applying it to data from river basins in the United States. The results suggest that flood scaling exponent is small for regions having (i) large abstractions from precipitation in the form of large soil moisture storages and high evapotranspiration losses, and (ii) large fractions of overland flow compared to base flow, i.e., regions having fast-responding basins. Analysis of simple scaling and multiscaling of floods showed evidence of simple scaling for regions in which the snowfall dominates the total precipitation.
Effect of interband interaction on isotope effect exponent of MgB2 ...
Indian Academy of Sciences (India)
The interband interaction of the electron–phonon interaction shows more effect on the isotope exponent than on the non-phonon interaction. Acknowledgement. The authors would like to thank Thailand Research Fund for financial support and the University of the Thai Chamber of Commerce for partial financial support and.
PHYSIOLOGICAL RESPONSES DURING MATCHES AND PROFILE OF ELITE PENCAK SILAT EXPONENTS
Directory of Open Access Journals (Sweden)
Benedict Tan
2002-12-01
Full Text Available This is a descriptive, cross-sectional study describing the physiological responses during competitive matches and profile of elite exponents of an emerging martial art sport, pencak silat. Thirty exponents (21 males and 9 females were involved in the study. Match responses (i.e. heart rate (HR throughout match and capillary blood lactate concentration, [La], at pre-match and at the end of every round were obtained during actual competitive duels. Elite silat exponents' physiological attributes were assessed via anthropometry, vertical jump, isometric grip strength, maximal oxygen uptake, and the Wingate 30 s anaerobic test of the upper and lower body, in the laboratory. The match response data showed that silat competitors' mean HR was > 84% of estimated HR maximum and levels of [La] ranged from 6.7 - 18.7 mMol-1 during matches. This suggests that competitive silat matches are characterised by high aerobic and anaerobic responses. In comparison to elite taekwondo and judo athletes' physiological characteristics, elite silat exponents have lower aerobic fitness and grip strength, but greater explosive leg power (vertical jump. Generally, they also possessed a similar anaerobic capability in the lower but markedly inferior anaerobic capability in the upper body
Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series
Morales, Raffaello; Di Matteo, T.; Gramatica, Ruggero; Aste, Tomaso
2012-06-01
We investigate the use of the Hurst exponent, dynamically computed over a weighted moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007-2008 credit crisis show a neat increase with time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. We find that the multifractality of the bailed-out firms increase at the crisis suggesting that the multi fractal properties of the time series are changing. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce a method to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past. We also investigate the scaling associated with the tails of the log-returns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling.
Kiuchi, R.; Mori, J. J.
2015-12-01
As a way to understand the characteristics of the earthquake source, studies of source parameters (such as radiated energy and stress drop) and their scaling are important. In order to estimate source parameters reliably, often we must use appropriate source spectrum models and the omega-square model is most frequently used. In this model, the spectrum is flat in lower frequencies and the falloff is proportional to the angular frequency squared. However, Some studies (e.g. Allmann and Shearer, 2009; Yagi et al., 2012) reported that the exponent of the high frequency falloff is other than -2. Therefore, in this study we estimate the source parameters using a spectral model for which the falloff exponent is not fixed. We analyze the mainshock and larger aftershocks of the 2008 Iwate-Miyagi Nairiku earthquake. Firstly, we calculate the P wave and SH wave spectra using empirical Green functions (EGF) to remove the path effect (such as attenuation) and site effect. For the EGF event, we select a smaller earthquake that is highly-correlated with the target event. In order to obtain the stable results, we calculate the spectral ratios using a multitaper spectrum analysis (Prieto et al., 2009). Then we take a geometric mean from multiple stations. Finally, using the obtained spectra ratios, we perform a grid search to determine the high frequency falloffs, as well as corner frequency of both of events. Our results indicate the high frequency falloff exponent is often less than 2.0. We do not observe any regional, focal mechanism, or depth dependencies for the falloff exponent. In addition, our estimated corner frequencies and falloff exponents are consistent between the P wave and SH wave analysis. In our presentation, we show differences in estimated source parameters using a fixed omega-square model and a model allowing variable high-frequency falloff.
Inter-relationship between scaling exponents for describing self-similar river networks
Yang, Soohyun; Paik, Kyungrock
2015-04-01
Natural river networks show well-known self-similar characteristics. Such characteristics are represented by various power-law relationships, e.g., between upstream length and drainage area (exponent h) (Hack, 1957), and in the exceedance probability distribution of upstream area (exponent É) (Rodriguez-Iturbe et al., 1992). It is empirically revealed that these power-law exponents are within narrow ranges. Power-law is also found in the relationship between drainage density (the total stream length divided by the total basin area) and specified source area (the minimum drainage area to form a stream head) (exponent η) (Moussa and Bocquillon, 1996). Considering that above three scaling relationships all refer to fundamental measures of 'length' and 'area' of a given drainage basin, it is natural to hypothesize plausible inter-relationship between these three scaling exponents. Indeed, Rigon et al. (1996) demonstrated the relationship between É and h. In this study, we expand this to a more general É-η-h relationship. We approach É-η relationship in an analytical manner while η-h relationship is demonstrated for six study basins in Korea. Detailed analysis and implications will be presented. References Hack, J. T. (1957). Studies of longitudinal river profiles in Virginia and Maryland. US, Geological Survey Professional Paper, 294. Moussa, R., & Bocquillon, C. (1996). Fractal analyses of tree-like channel networks from digital elevation model data. Journal of Hydrology, 187(1), 157-172. Rigon, R., Rodriguez-Iturbe, I., Maritan, A., Giacometti. A., Tarboton, D. G., & Rinaldo, A. (1996). On Hack's Law. Water Resources Research, 32(11), 3367-3374. Rodríguez-Iturbe, I., Ijjasz-Vasquez, E. J., Bras, R. L., & Tarboton, D. G. (1992). Power law distributions of discharge mass and energy in river basins. Water Resources Research, 28(4), 1089-1093.
An analysis of the financial crisis in the KOSPI market using Hurst exponents
Yim, Kyubin; Oh, Gabjin; Kim, Seunghwan
2014-09-01
Recently, the study of the financial crisis has progressed to include the concept of the complex system, thereby improving the understanding of this extreme event from a neoclassical economic perspective. To determine which variables are related to the financial event caused by the 2008 US subprime crisis using temporal correlations, we investigate the diverse variables that may explain the financial system. These variables include return, volatility, trading volume and inter-trade duration data sets within the TAQ data for 27 highly capitalized individual companies listed on the KOSPI stock market. During 2008 and 2009, the Hurst exponent for the return time series over the whole period was less than 0.5, and the Hurst exponents for other variables, such as the volatility, trading volume and inter-trade duration, were greater than 0.5. Additionally, we analyze the relationships between the variation of temporal correlation and market instability based on these Hurst exponents and the degree of multifractality. We find that for the data related to trading volume, the Hurst exponents do not allow us to detect changes in market status, such as changes from normal to abnormal status, whereas other variables, including the return, volatility and weekly inter-trade duration, indicate a significant change in market status after the Lehman Brothers' bankruptcy. In addition, the multifractality and the measurement defined by subtracting the Hurst exponent of the return time series from that of the volatility time series decrease sharply after the US subprime event and recover approximately 50 days after the Lehman Brothers' collapse. Our findings suggest that the temporal features of financial quantities in the TAQ data set and the market complexity perform very well at diagnosing financial market stability.
Critical composition fluctuations in artificial and cell-derived lipid membranes
Honerkamp-Smith, Aurelia
2014-03-01
Cell plasma membranes contain a mixture of lipid types which can segregate into coexisting liquids, a thermodynamic phenomenon which may contribute to biological functions. Simplified, artificial three-component lipid vesicles can be prepared which display a critical miscibility transition near room temperature. We found that such vesicles exhibit concentration fluctuations whose size, composition, and timescales vary consistently with critical exponents for two-dimensional conserved order parameter systems. However, the critical miscibility transition is also observed in vesicles formed directly from the membranes of living cells, despite their more complex composition and the presence of membrane proteins. I will describe our critical fluctuation measurements and also review a variety of more recent work by other researchers. Proximity to a critical point alters the spatial distribution and aggregation tendencies of proteins, and makes lipid mixtures more susceptible to domain formation by protein-mediated interactions, such as adhesion zones. Recent work suggests that critical temperature depression may also be relevant to the mechanism of anaesthetic action.
Electron spin resonance and quantum critical phenomena in VOx multiwall nanotubes
International Nuclear Information System (INIS)
Demishev, S.V.; Chernobrovkin, A.L.; Glushkov, V.V.; Samarin, N.A.; Sluchanko, N.E.; Semeno, A.V.; Goodilin, E.A.; Grigorieva, A.V.; Tretyakov, Yu.D.
2008-01-01
Basing on the high frequency (60 GHz) electron spin resonance study of the VO x multiwall nanotubes (VO x -NTs) carried out in the temperature range 4.2-200 K we report: (i) the first direct experimental evidence of the presence of the antiferromagnetic dimers in VO x -NTs and (ii) the observation of an anomalous low temperature growth of the magnetic susceptibility for quasi-free spins, which obey the power law χ(T)∝1/T α with the exponent α∼0.6 in a wide temperature range 4.2-50 K. We argue that the observed departures from the Curie-Weiss behaviour manifest the onset of the quantum critical regime and formation of the Griffiths phase as a magnetic ground state of these spin species. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Directory of Open Access Journals (Sweden)
Emlyn Flint
2017-03-01
Full Text Available Background: Contingent claims on underlying assets are typically priced under a framework that assumes, inter alia, that the log returns of the underlying asset are normally distributed. However, many researchers have shown that this assumption is violated in practice. Such violations include the statistical properties of heavy tails, volatility clustering, leptokurtosis and long memory. This paper considers the pricing of contingent claims when the underlying is assumed to display long memory, an issue that has heretofore not received much attention. Aim: We address several theoretical and practical issues in option pricing and implied volatility calibration in a fractional Black–Scholes market. We introduce a novel eight-parameter fractional Black–Scholes-inspired (FBSI model for the implied volatility surface, and consider in depth the issue of calibration. One of the main benefits of such a model is that it allows one to decompose implied volatility into an independent long-memory component – captured by an implied Hurst exponent – and a conditional implied volatility component. Such a decomposition has useful applications in the areas of derivatives trading, risk management, delta hedging and dynamic asset allocation. Setting: The proposed FBSI volatility model is calibrated to South African equity index options data as well as South African Rand/American Dollar currency options data. However, given the focus on the theoretical development of the model, the results in this paper are applicable across all financial markets. Methods: The FBSI model essentially combines a deterministic function form of the 1-year implied volatility skew with a separate deterministic function for the implied Hurst exponent, thus allowing one to model both observed implied volatility surfaces as well as decompose them into independent volatility and long-memory components respectively. Calibration of the model makes use of a quasi-explicit weighted
Dynamical critical phenomena in driven-dissipative systems.
Sieberer, L M; Huber, S D; Altman, E; Diehl, S
2013-05-10
We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the Keldysh framework, we characterize the dynamical critical behavior that governs decoherence and an effective thermalization of the low frequency dynamics. We identify a critical exponent special to the driven system, showing that it defines a new dynamical universality class. Hence critical points in driven systems lie beyond the standard classification of equilibrium dynamical phase transitions. We show how the new critical exponent can be probed in experiments with driven cold atomic systems and exciton-polariton condensates.
Quantum criticality in Einstein-Maxwell-dilaton gravity
International Nuclear Information System (INIS)
Wen, Wen-Yu
2012-01-01
We investigate the quantum Lifshitz criticality in a general background of Einstein-Maxwell-dilaton gravity. In particular, we demonstrate the existence of critical point with dynamic critical exponent z by tuning a nonminimal coupling to its critical value. We also study the effect of nonminimal coupling and exponent z to the Efimov states and holographic RG flow in the overcritical region. We have found that the nonminimal coupling increases the instability for a probe scalar to condensate and its back reaction is discussed. At last, we give a quantum mechanics treatment to a solvable system with z=2, and comment for generic z>2.
Geometrical critical phenomena on a random surface of arbitrary genus
International Nuclear Information System (INIS)
Duplantier, B.; Kostov, I.K.
1990-01-01
The statistical mechanics of self-avoiding walks (SAW) or of the O(n)-loop model on a two-dimensional random surface are shown to be exactly solvable. The partition functions of SAW and surface configurations (possibly in the presence of vacuum loops) are calculated by planar diagram enumeration techniques. Two critical regimes are found: a dense phase where the infinite walks and loops fill the infinite surface, the non-filled part staying finite, and a dilute phase where the infinite surface singularity on the one hand, and walk and loop singularities on the other, merge together. The configuration critical exponents of self-avoiding networks of any fixed topology G, on a surface with arbitrary genus H, are calculated as universal functions of G and H. For self-avoiding walks, the exponents are built from an infinite set of basic conformal dimensions associated with central charges c = -2 (dense phase) and c = 0 (dilute phase). The conformal spectrum Δ L , L ≥ 1 associated with L-leg star polymers is calculated exactly, for c = -2 and c = 0. This is generalized to the set of L-line 'watermelon' exponents Δ L of the O(n) model on a random surface. The divergences of the partition functions of self-avoiding networks on the random surface, possibly in the presence of vacuum loops, are shown to satisfy a factorization theorem over the vertices of the network. This provides a proof, in the presence of a fluctuating metric, of a result conjectured earlier in the standard plane. From this, the value of the string susceptibility γ str (H,c) is extracted for a random surface of arbitrary genus H, bearing a field theory of central charge c, or equivalently, embedded in d=c dimensions. Lastly, by enumerating spanning trees on a random lattice, we solve the similar problem of hamiltonian walks on the (fluctuating) Manhattan covering lattice. We also obtain new results for dilute trees on a random surface. (orig./HSI)
Garcin, Matthieu
2017-10-01
Hurst exponents depict the long memory of a time series. For human-dependent phenomena, as in finance, this feature may vary in the time. It justifies modelling dynamics by multifractional Brownian motions, which are consistent with time-dependent Hurst exponents. We improve the existing literature on estimating time-dependent Hurst exponents by proposing a smooth estimate obtained by variational calculus. This method is very general and not restricted to the sole Hurst framework. It is globally more accurate and easier than other existing non-parametric estimation techniques. Besides, in the field of Hurst exponents, it makes it possible to make forecasts based on the estimated multifractional Brownian motion. The application to high-frequency foreign exchange markets (GBP, CHF, SEK, USD, CAD, AUD, JPY, CNY and SGD, all against EUR) shows significantly good forecasts. When the Hurst exponent is higher than 0.5, what depicts a long-memory feature, the accuracy is higher.
International Nuclear Information System (INIS)
Solano, Yully P; Uribe, Rodolfo; Frydman, Marcelo; Saavedra, Nestor F; Calderon, Zuly H
2007-01-01
The methodology for the pore pressure prediction known as an exponent is o function of an exponent of adjustment that was originally defined for the Gulf of Mexico (Jorden and Shirley, 1966; Eaton, 1972). A limiting factor of this methodology is the definition of the normal compaction trend (NCT), which needs to be interpreted from the data (Mouchet and Mitchell, 1989). In this study, the D exponent methodology was modified to make it applicable to the Oligocene Carbonera Formation in an oil field of the llanos foothills Colombia. The approach consisted of calculating the ratio between affective stress and the D exponent of each wall, in order to find a robust NCT for the entire field, thus reducing subjectivity in the traditional d exponent methodology. Pore pressure determinations from Measured Direct Tests (MDT) at one wall confirm the predictive capability of our approach
Interplay of quantum and classical fluctuations near quantum critical points
International Nuclear Information System (INIS)
Continentino, Mucio Amado
2011-01-01
For a system near a quantum critical point (QCP), above its lower critical dimension d L , there is in general a critical line of second-order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, d eff = d + z (d is the Euclidean dimension of the system and z the dynamic quantum critical exponent) is above its upper critical dimension d c there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation ψ = νz between the shift exponent ψ of the critical line and the crossover exponent νz, for d + z > d c by a dangerous irrelevant interaction. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP. (author)
Universal post-quench prethermalization at a quantum critical point
Orth, Peter P.; Gagel, Pia; Schmalian, Joerg
2015-03-01
We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive non-equilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are a powerlaw rise of order and correlations after an initial collapse of the equilibrium state and a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches. [1] P. Gagel, P. P. Orth, J. Schmalian, Phys.Rev. Lett. (in press) arXiv:1406.6387
Directory of Open Access Journals (Sweden)
Rui Wang
2014-01-01
Full Text Available A modified multiple structural changes model is built to test structural breaks of the financial system based on calculating the largest Lyapunov exponents of the financial time series. Afterwards, the Lorenz system is used as a simulation example to inspect the new model. As the Lorenz system has strong nonlinearity, the verification results show that the new model has good capability in both finding the breakpoint and revealing the changes in nonlinear characteristics of the time series. The empirical study based on the model used daily data from the S&P 500 stock index during the global financial crisis from 2005 to 2012. The results provide four breakpoints of the period, which divide the contagion into four stages: stationary, local outbreak, global outbreak, and recovery period. An additional significant result is the obvious chaos characteristic difference in the largest Lyapunov exponents and the standard deviation at various stages, particularly at the local outbreak stage.
Dependence of exponents on text length versus finite-size scaling for word-frequency distributions
Corral, Álvaro; Font-Clos, Francesc
2017-08-01
Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of this scaling law, using both careful statistical tests and analytical arguments based on the generalized central-limit theorem applied to the moments of the distribution (and obtaining a novel derivation of Heaps' law as a by-product). We also find that the picture of word-frequency distributions with power-law exponents that decrease with text length [X. Yan and P. Minnhagen, Physica A 444, 828 (2016), 10.1016/j.physa.2015.10.082] does not stand with rigorous statistical analysis. Instead, we show that the distributions are perfectly described by power-law tails with stable exponents, whose values are close to 2, in agreement with the classical Zipf's law. Some misconceptions about scaling are also clarified.
Directory of Open Access Journals (Sweden)
L.F.P. Franca
2003-01-01
Full Text Available This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.
The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system
International Nuclear Information System (INIS)
Waldner, Franz; Hoover, William G.; Hoover, Carol G.
2014-01-01
Highlights: •We consider the local Lyapunov spectrum for a four-dimensional Hamilton system. •Its stable periodic motion can be reversed for long times. •In the chaotic motion, time reversal occurs only for a short time. •Perturbations will change this short unstable case into a different stable case. •These observations might relate chaos to the Second Law of Thermodynamics. - Abstract: We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed
Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents.
Salceanu, Paul L
2011-07-01
This paper extends the work of Salceanu and Smith [12, 13] where Lyapunov exponents were used to obtain conditions for uniform persistence ina class of dissipative discrete-time dynamical systems on the positive orthant of R(m), generated by maps. Here a united approach is taken, for both discrete and continuous time, and the dissipativity assumption is relaxed. Sufficient conditions are given for compact subsets of an invariant part of the boundary of R(m+) to be robust uniform weak repellers. These conditions require Lyapunov exponents be positive on such sets. It is shown how this leads to robust uniform persistence. The results apply to the investigation of robust uniform persistence of the disease in host populations, as shown in an application.
Application of the Lyapunov exponent to detect noise-induced chaos in oscillating microbial cultures
International Nuclear Information System (INIS)
Patnaik, P.R.
2005-01-01
Oscillating microbial processes can, under certain conditions, gravitate into chaotic behavior induced by external noise. Detection and control of chaos are important for the survival of the microorganisms and to operate a process usefully. In this study the largest Lyapunov exponent is recommended as a convenient and reliable index of chaos in continuous oscillating cultures. For the growth of Saccharomyces cerevisiae as a model system, the exponents increase with the oxygen mass transfer coefficient and decrease as the dilution rate increases. By comparing with the corresponding time-domain oscillations determined earlier, it is inferred that weakly oscillating cultures are less likely to be driven to chaotic behavior. The main carbon source, glucose, is quite robust to chaotic destabilization, thus enhancing its suitability as a manipulated variable for bioreactor control
Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors
International Nuclear Information System (INIS)
Gavilian-Moreno, Carlos; Espinosa-Paredes, Gilberto
2016-01-01
The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution
Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors
Energy Technology Data Exchange (ETDEWEB)
Gavilian-Moreno, Carlos [Iberdrola Generacion, S.A., Cofrentes Nuclear Power Plant, Project Engineering Department, Paraje le Plano S/N, Valencia (Spain); Espinosa-Paredes, Gilberto [Area de ingeniera en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Mexico city (Mexico)
2016-04-15
The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.
The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange
Domino, Krzysztof
2011-01-01
The local properties of the time series of the evolution of share prices of 126 significant companies traded on the Warsaw Stock Exchange during the period between 1991-2008 have been investigated. The analysis was applied to daily financial returns. I have used the local DFA to obtain the Hurst exponent (diffusion coefficient) while searching for negative correlations by which changes of long-term trends would be effected. A certain evidence, proving that after the signature of anti-correlation-the drop in the Hurst exponent-the change in the trend and in the return rate of an investment is probable, was pointed out. Hence after further investigation this method may be useful as a part of an investment strategy. As the Warsaw Stock Exchange is relatively smaller and younger than other significant world Stock Exchanges-and as the developing market is less efficient-the generalization for others markets needs further investigation.
Cajueiro, Daniel O.; Tabak, Benjamin M.
2004-05-01
This paper is concerned with the assertion found in the financial literature that emerging markets are becoming more efficient over time. To verify whether this assertion is true or not, we propose the calculation of the Hurst exponent over time using a time window with 4 years of data. The data used here comprises the bulk of emerging markets for Latin America and Asia. Our empirical results show that this assertion seems to be true for most countries, but it does not hold for countries such as Brazil, The Philippines and Thailand. Moreover, in order to check whether or not these results depend on the short term memory and the volatility of returns common in such financial asset return data, we filter the data by an AR-GARCH procedure and present the Hurst exponents for this filtered data.
Using Largest Lyapunov Exponent to Confirm the Intrinsic Stability of Boiling Water Reactors
Directory of Open Access Journals (Sweden)
Carlos J. Gavilán-Moreno
2016-04-01
Full Text Available The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs. Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.
The path integral formulation of fractional Brownian motion for the general Hurst exponent
International Nuclear Information System (INIS)
Calvo, I; Sanchez, R
2008-01-01
In 1995, Sebastian (1995 J. Phys. A: Math. Gen. 28 4305) gave a path integral computation of the propagator of subdiffusive fractional Brownian motion (fBm), i.e. fBm with a Hurst or self-similarity exponent H element of (0, 1/2). The extension of Sebastian's calculation to superdiffusion, H element of (1/2, 1], becomes however quite involved due to the appearance of additional boundary conditions on fractional derivatives of the path. In this communication, we address the construction of the path integral representation in a different fashion, which allows us to treat both subdiffusion and superdiffusion on an equal footing. The derivation of the propagator of fBm for the general Hurst exponent is then performed in a neat and unified way. (fast track communication)
Perturbation theory for Lyapunov exponents of an Anderson model on a strip
Schulz-Baldes, H
2003-01-01
It is proven that the localization length of an Anderson model on a strip of width $L$ is bounded above by $L/\\lambda^2$ for small values of the coupling constant $\\lambda$ of the disordered potential. For this purpose, a new formalism is developed in order to calculate the bottom Lyapunov exponent associated with random products of large symplectic matrices perturbatively in the coupling constant of the randomness.
Bolgorian, Meysam; Raei, Reza
In this paper using the global Hurst exponent, the impact of privatization of public companies in Iran on the degree of efficiency in Tehran Stock Exchange is assessed. The results show that selling public companies' share in Tehran Stock Exchange (TSE) leads to a structural break in degree of market development. To model this phenomenon a catastrophe approach is used and it is demonstrated that this structural break can be better explained by a cusp catastrophe model.
Randomness confidence bands of fractal scaling exponents for financial price returns
International Nuclear Information System (INIS)
Ibarra-Valdez, C.; Alvarez, J.; Alvarez-Ramirez, J.
2016-01-01
Highlights: • A robust test for randomness of price returns is proposed. • The DFA scaling exponent is contrasted against confidence bands for random sequences. • The size of the band depends of the sequence length. • Crude oil and USA stock markets have been rarely inefficient. - Abstract: The weak-form of the efficient market hypothesis (EMH) establishes that price returns behave as a pure random process and so their outcomes cannot be forecasted. The detrended fluctuation analysis (DFA) has been widely used to test the weak-form of the EMH by showing that time series of price returns are serially uncorrelated. In this case, the DFA scaling exponent exhibits deviations from the theoretical value of 0.5. This work considers the test of the EMH for DFA implementation on a sliding window, which is an approach that is intended to monitor the evolution of markets. Under these conditions, the scaling exponent exhibits important variations over the scrutinized period that can offer valuable insights in the behavior of the market provided the estimated scaling value is kept within strict statistical tests to verify the presence or not of serial correlations in the price returns. In this work, the statistical tests are based on comparing the estimated scaling exponent with the values obtained from pure Gaussian sequences with the length of the real time series. In this way, the presence of serial correlations can be guaranteed only in terms of the confidence bands of a pure Gaussian process. The crude oil (WTI) and the USA stock (DJIA) markets are used to illustrate the methodology.
Niu, Q.; Zhang, C.
2017-12-01
Archie's law is an important empirical relationship linking the electrical resistivity of geological materials to their porosity. It has been found experimentally that the porosity exponent m in Archie's law in sedimentary rocks might be related to the degree of cementation, and therefore m is termed as "cementation factor" in most literatures. Despite it has been known for many years, there is lack of well-accepted physical interpretations of the porosity exponent. Some theoretical and experimental evidences have also shown that m may be controlled by the particle and/or pore shape. In this study, we conduct a pore-scale modeling of the porosity exponent that incorporates different geological processes. The evolution of m of eight synthetic samples with different particle sizes and shapes are calculated during two geological processes, i.e., compaction and cementation. The numerical results show that in dilute conditions, m is controlled by the particle shape. As the samples deviate from dilute conditions, m increases gradually due to the strong interaction between particles. When the samples are at static equilibrium, m is noticeably larger than its values at dilution condition. The numerical simulation results also show that both geological compaction and cementation induce a significant increase in m. In addition, the geometric characteristics of these samples (e.g., pore space/throat size, and their distributions) during compaction and cementation are also calculated. Preliminary analysis shows a unique correlation between the pore size broadness and porosity exponent for all eight samples. However, such a correlation is not found between m and other geometric characteristics.
Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System.
Rozenbaum, Efim B; Ganeshan, Sriram; Galitski, Victor
2017-02-24
It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because, in the semiclassical limit ℏ→0, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator C(t) for the classical and quantum kicked rotor-a textbook driven chaotic system-and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are, in general, distinct quantities, corresponding to the logarithm of the phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength K, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as K→0, while the OTOC's growth rate may decrease much slower, showing a higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time t_{E}: transitioning from a time-independent value of t^{-1}lnC(t) at ttime at t>t_{E}. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996)PRBMDO0163-182910.1103/PhysRevB.54.14423; Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.124101] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.
Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies
Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.
2015-01-01
Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.
Critical behavior from Schrodinger representation
International Nuclear Information System (INIS)
Suranyi, P.
1992-01-01
In this paper, the Schrodinger equation for φ 4 field theory is reduced to an infinite set of integral equations. A systematic truncation scheme is proposed and it is solved in second order to obtain the approximate critical behavior of the renormalized mass. The correlation exponent is given as a solution of a transcendental equation. It is in good agreement with the Ising model in all physical dimensions
Gaussian fluctuation of the diffusion exponent of virus capsid in a living cell nucleus
Itto, Yuichi
2018-05-01
In their work [4], Bosse et al. experimentally showed that virus capsid exhibits not only normal diffusion but also anomalous diffusion in nucleus of a living cell. There, it was found that the distribution of fluctuations of the diffusion exponent characterizing them takes the Gaussian form, which is, quite remarkably, the same form for two different types of the virus. This suggests high robustness of such fluctuations. Here, the statistical property of local fluctuations of the diffusion exponent of the virus capsid in the nucleus is studied. A maximum-entropy-principle approach (originally proposed for a different virus in a different cell) is applied for obtaining the fluctuation distribution of the exponent. Largeness of the number of blocks identified with local areas of interchromatin corrals is also examined based on the experimental data. It is shown that the Gaussian distribution of the local fluctuations can be derived, in accordance with the above form. In addition, it is quantified how the fluctuation distribution on a long time scale is different from the Gaussian distribution.
Sensitivity of TDF and CRE to variations in exponents of N and T
International Nuclear Information System (INIS)
Orton, C.G.
1976-01-01
A typical example is given of the calculation by two methods of the value of the radiation dose given in 20 treatments at 5 fractions per week to be equivalent to 6000 rad given in 30 treatments also at 5 fractions per week. The solutions obtained were identical and demonstrated that, in normal clinical practice, whatever values are chosen for the exponents of N and T in the basic NSD equation, the CRE (Kirk, J., Gray, W.M., and Watson, E.R., 1971, Clinical Radiology, vol. 22, 145) and TDF (Orton, C.G., and Ellis, F., 1973, Br. J. Radiol., vol. 46, 529) methods are exactly equivalent. The variations in the values calculated by the TDF method of the dose/fraction in the same example for differing values of the exponents of N and T were typically less than +- 3%, and even for more drastic changes a variation of less than 5% resulted. The TDF and CRE methods are not therefore very sensitive to changes in these exponents. It is emphasized that since CREs are not linearly additive, application of the TDF method greatly reduces the probability of arithmetical error, particularly for more complex treatment regimes. The TDF method should however be applied with great caution if the time, dose or fractionation differ significantly from that used in conventional radiotherapeutic practice, since the theory was based on clinical evidence obtained by retrospective analysis of typical radiotherapy data. (U.K.)
An accurate algorithm to calculate the Hurst exponent of self-similar processes
International Nuclear Information System (INIS)
Fernández-Martínez, M.; Sánchez-Granero, M.A.; Trinidad Segovia, J.E.; Román-Sánchez, I.M.
2014-01-01
In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Lévy stable motions are considered. We conclude the paper with a dynamic study of the Hurst exponent evolution in the S and P500 index stocks. - Highlights: • We provide a new approach to properly calculate the Hurst exponent. • This generalizes FD algorithms and GM2, introduced previously by the authors. • This method (FD4) results especially appropriate for short time series. • FD4 may be used in both unifractal and multifractal contexts. • As an empirical application, we show that S and P500 stocks improved their efficiency
Fractal characters and hurst exponent of radon exhalation rate from uranium Tailings
International Nuclear Information System (INIS)
Hu Hanqiao; Tan Kaixuan; Li Chunguang; Lv Junwen; Liu Dong
2010-01-01
The uranium tailings radon exhalation is an important environmental problem. The change of the radon exhalation rate of uranium tailings with the time through laboratory experiments is measured, and the results show that the radon exhalation rate of the tailings change obviously with time in non-periodic oscillations. Applying fractal analysis to the radon exhalation rate time-series data by R/S method, the Hurst exponent of the entire time series data is 0.83, the fractal dimension is 1.17. Mobile Hurst exponent is between 0.5 and 0.8 in most cases. The Hurst exponent of the experiments in the later part are below 0.5. The exhalation rate of uranium tailings radon does not meet the long-term trend of random walk theory, the radon exhalation rate has long-term memory, but the short-term memory is not distinct. The radon exhalation from uranium tailings is a deterministic chaotic dynamics. (authors)
Scaling exponent and dispersity of polymers in solution by diffusion NMR.
Williamson, Nathan H; Röding, Magnus; Miklavcic, Stanley J; Nydén, Magnus
2017-05-01
Molecular mass distribution measurements by pulsed gradient spin echo nuclear magnetic resonance (PGSE NMR) spectroscopy currently require prior knowledge of scaling parameters to convert from polymer self-diffusion coefficient to molecular mass. Reversing the problem, we utilize the scaling relation as prior knowledge to uncover the scaling exponent from within the PGSE data. Thus, the scaling exponent-a measure of polymer conformation and solvent quality-and the dispersity (M w /M n ) are obtainable from one simple PGSE experiment. The method utilizes constraints and parametric distribution models in a two-step fitting routine involving first the mass-weighted signal and second the number-weighted signal. The method is developed using lognormal and gamma distribution models and tested on experimental PGSE attenuation of the terminal methylene signal and on the sum of all methylene signals of polyethylene glycol in D 2 O. Scaling exponent and dispersity estimates agree with known values in the majority of instances, leading to the potential application of the method to polymers for which characterization is not possible with alternative techniques. Copyright © 2017 Elsevier Inc. All rights reserved.
An accurate algorithm to calculate the Hurst exponent of self-similar processes
Energy Technology Data Exchange (ETDEWEB)
Fernández-Martínez, M., E-mail: fmm124@ual.es [Department of Mathematics, Faculty of Science, Universidad de Almería, 04120 Almería (Spain); Sánchez-Granero, M.A., E-mail: misanche@ual.es [Department of Mathematics, Faculty of Science, Universidad de Almería, 04120 Almería (Spain); Trinidad Segovia, J.E., E-mail: jetrini@ual.es [Department of Accounting and Finance, Faculty of Economics and Business, Universidad de Almería, 04120 Almería (Spain); Román-Sánchez, I.M., E-mail: iroman@ual.es [Department of Accounting and Finance, Faculty of Economics and Business, Universidad de Almería, 04120 Almería (Spain)
2014-06-27
In this paper, we introduce a new approach which generalizes the GM2 algorithm (introduced in Sánchez-Granero et al. (2008) [52]) as well as fractal dimension algorithms (FD1, FD2 and FD3) (first appeared in Sánchez-Granero et al. (2012) [51]), providing an accurate algorithm to calculate the Hurst exponent of self-similar processes. We prove that this algorithm performs properly in the case of short time series when fractional Brownian motions and Lévy stable motions are considered. We conclude the paper with a dynamic study of the Hurst exponent evolution in the S and P500 index stocks. - Highlights: • We provide a new approach to properly calculate the Hurst exponent. • This generalizes FD algorithms and GM2, introduced previously by the authors. • This method (FD4) results especially appropriate for short time series. • FD4 may be used in both unifractal and multifractal contexts. • As an empirical application, we show that S and P500 stocks improved their efficiency.
Sensitivity of TDF and CRE to variations in exponents of N and T
Energy Technology Data Exchange (ETDEWEB)
Orton, C G [Rhode Island Hospital, Providence (USA). Dept. of Radiation Oncology
1976-10-01
A typical example is given of the calculation by two methods of the value of the radiation dose given in 20 treatments at 5 fractions per week to be equivalent to 6000 rad given in 30 treatments also at 5 fractions per week. The solutions obtained were identical and demonstrated that, in normal clinical practice, whatever values are chosen for the exponents of N and T in the basic NSD equation, the CRE (Kirk, J., Gray, W.M., and Watson, E.R., 1971, Clinical Radiology, vol. 22, 145) and TDF (Orton, C.G., and Ellis, F., 1973, Br. J. Radiol., vol. 46, 529) methods are exactly equivalent. The variations in the values calculated by the TDF method of the dose/fraction in the same example for differing values of the exponents of N and T were typically less than +- 3%, and even for more drastic changes a variation of less than 5% resulted. The TDF and CRE methods are not therefore very sensitive to changes in these exponents. It is emphasized that since CREs are not linearly additive, application of the TDF method greatly reduces the probability of arithmetical error, particularly for more complex treatment regimes. The TDF method should however be applied with great caution if the time, dose or fractionation differ significantly from that used in conventional radiotherapeutic practice, since the theory was based on clinical evidence obtained by retrospective analysis of typical radiotherapy data.
Asymmetric fluid criticality. II. Finite-size scaling for simulations.
Kim, Young C; Fisher, Michael E
2003-10-01
The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions L focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded "complete" thermodynamic (L--> infinity) scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling [Phys. Rev. E 67, 061506 (2003)] is extended to finite L, initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when L--> infinity, the second temperature derivative (d2musigma/dT2) of the chemical potential along the phase boundary musigmaT diverges when T-->Tc-. The finite-size behavior of various special critical loci in the temperature-density or (T,rho) plane, in particular, the k-inflection susceptibility loci and the Q-maximal loci--derived from QL(T,L) is identical with 2L/L where m is identical with rho-L--is carefully elucidated and shown to be of value in estimating Tc and rhoc. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent nu that confirms Ising-type character. The treatment is extended to the canonical representation where further complications appear.
Dashti-Naserabadi, H.; Najafi, M. N.
2017-10-01
We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension Du=4 . After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions. We found that the exponent of the distribution function of avalanche mass is the same for the d -dimensional cross sections and the d -dimensional BTW model for d =2 and 3. The geometrical quantities, however, have completely different behaviors with respect to the same-dimensional BTW model. By analyzing the FSS theory for the geometrical exponents of the two-dimensional cross sections, we propose that the 2D induced models have degrees of similarity with the Gaussian free field (GFF). Although some local exponents are slightly different, this similarity is excellent for the fractal dimensions. The most important one showing this feature is the fractal dimension of loops df, which is found to be 1.50 ±0.02 ≈3/2 =dfGFF .
Hurst's Exponent Determination for Radial Distribution Functions of In, Sn and In-40 wt%Sn Melt
International Nuclear Information System (INIS)
Zhou Yong-Zhi; Li Mei; Geng Hao-Ran; Yang Zhong-Xi; Sun Chun-Jing
2011-01-01
Hurst's exponent of radial distribution functions (RDFs) within the short-range scope of In, Sn and In-40 wt % Sn melts are determined by the rescaled range analysis method. Hurst's exponents H are between 0.94 and 0.97, which display long-range dependence. Within short-range scope, the number of particles from a reference particle belongs to fractional Brownian motion. After RDF serials are randomly scrambled, Hurst's exponents all dramatically dropped, which proves long-range dependence. H irregularly varies as the temperature rises, but the change tendency is not consistent with the correlation radius r c . (general)
Directory of Open Access Journals (Sweden)
Li Wang
2016-12-01
Full Text Available In this article, we show the existence of infinitely many solutions for the fractional p-Laplacian equations of Schrodinger-Kirchhoff type equation $$ M([u]_{s, p}^p (-\\Delta _p^s u+V(x|u|^{p-2}u= \\alpha |u|^{ p_s^{*}-2 }u+\\beta k(x|u|^{q-2}u \\quad x\\in \\mathbb{R}^N, $$ where $(-\\Delta ^s_p$ is the fractional p-Laplacian operator, $[u]_{s,p}$ is the Gagliardo p-seminorm, $0 sp$, $1
Critical behaviour in very pure Ni-Ta systems
International Nuclear Information System (INIS)
Oddou, J.L.; Berthier, J.; Peretto, P.
1978-01-01
The authors use the perturbed angular correlation technique to follow the behaviour of the magnetic hyperfine field on 181 Ta in nickel in the critical region of the matrix. Contrary to what is expected, it is observed that the critical exponent associated to the hyperfine field is different from the critical exponent associated to the bulk magnetization. Because the concentrations of the various impurities are very low, the authors think that the explanation of the phenomenon is to be found in the framework of a one-impurity model interacting with the surrounding spins via an isotropic exchange energy
Critical behaviors of gravity under quantum perturbations
Directory of Open Access Journals (Sweden)
ZHANG Hongsheng
2014-02-01
Full Text Available Phase transition and critical phenomenon is a very interesting topic in thermodynamics and statistical mechanics. Gravity is believed to have deep and inherent relation to thermodynamics. Near the critical point,the perturbation becomes significant. Thus for ordinary matter (governed by interactions besides gravity the critical behavior will become very different if we ignore the perturbations around the critical point,such as mean field theory. We find that the critical exponents for RN-AdS spacetime keep the same values even when we consider the full quantum perturbations. This indicates a key difference between gravity and ordinary thermodynamic system.
An effective field study of the magnetic properties and critical behaviour at the surface Ising film
International Nuclear Information System (INIS)
Bengrine, M.; Benyoussef, A.; Ez-Zahraouy, H.; Mhirech, F.
1998-09-01
The influence of corrugation and disorder at the surface on the critical behaviour of a ferromagnetic spin-1/2 Ising film is investigated using mean-field theory and finite cluster approximation. It is found that the critical surface exponent β 1 follows closely the one of a perfect surface, in the two cases: corrugated surface and random equiprobable coupling surface. However, in the case of flat surface with random interactions the surface critical exponent β 1 depends on the concentration p of the strong interaction for p>p c =0,5, while for p≤p c , such critical exponent is independent on the value of p and is equal to the one of the perfect surface. Moreover, in the case of corrugated surface, the effective exponent for a layer z, β eff J(z,n), is calculated as a function of the number of steps at the surface. (author)
Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles
Dai, Xiongping
Consider in this paper a linear skew-product system (θ,Θ) :T×W×R→W×R; (t,w,x)↦(tw,Θ(t,w)ṡx) where T=R or Z, and θ :(t,w)↦tw is a topological dynamical system on a compact metrizable space W, and where Θ(t,w)∈GL(n,R) satisfies the cocycle condition based on θ and is continuously differentiable in t if T=R. We show that 'semi λ-exponential dichotomy' of (θ,Θ) implies ' λ-exponential dichotomy.' Precisely, if Θ has no Lyapunov exponent λ and is almost uniformly λ-contracting along the λ-stable direction E(w;λ) and if dimE(w;λ) is constant a.e., then Θ is almost λ-exponentially dichotomous. To prove this, we first use Liao's spectrum theorem, which gives integral expression of the Lyapunov exponents, and then use the semi-uniform ergodic theorem by Sturman and Stark, which allows one to derive uniform estimates from nonuniform ones. As a consequence, we obtain the open-and-dense hyperbolicity of eventual GL(2,R)-cocycles based on a uniquely ergodic endomorphism, and of GL(2,R)-cocycles based on a uniquely ergodic equi-continuous endomorphism, respectively. On the other hand, in the sense of C-topology we obtain the density of SL(2,R)-cocycles having positive Lyapunov exponent based on a minimal subshift satisfying the Boshernitzan condition.
Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement
Energy Technology Data Exchange (ETDEWEB)
Ataei, Mohammad, E-mail: ataei@eng.ui.ac.i [Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Hezar-Jerib St., Postal Code 8174673441, Isfahan (Iran, Islamic Republic of); Kiyoumarsi, Arash, E-mail: kiyoumarsi@eng.ui.ac.i [Department of Electrical Engineering, Faculty of Engineering, University of Isfahan, Hezar-Jerib St., Postal Code 8174673441, Isfahan (Iran, Islamic Republic of); Ghorbani, Behzad, E-mail: behzad.ghorbani63@gmail.co [Department of Control Engineering, Najafabad Azad University, Najafabad, Isfahan (Iran, Islamic Republic of)
2010-09-13
Permanent Magnet Synchronous Motor (PMSM) experiences chaotic behavior for a certain range of its parameters. In this case, since the performance of the PMSM degrades, the chaos should be eliminated. In this Letter, the control of the undesirable chaos in PMSM using Lyapunov exponents (LEs) placement is proposed that is also improved by choosing optimal locations of the LEs in the sense of predefined cost function. Moreover, in order to provide the physical realization of the method, nonlinear parameter estimator for the system is suggested. Finally, to show the effectiveness of the proposed methodology, the simulation results for applying this control strategy are provided.
The high exponent limit $p \\to \\infty$ for the one-dimensional nonlinear wave equation
Tao, Terence
2009-01-01
We investigate the behaviour of solutions $\\phi = \\phi^{(p)}$ to the one-dimensional nonlinear wave equation $-\\phi_{tt} + \\phi_{xx} = -|\\phi|^{p-1} \\phi$ with initial data $\\phi(0,x) = \\phi_0(x)$, $\\phi_t(0,x) = \\phi_1(x)$, in the high exponent limit $p \\to \\infty$ (holding $\\phi_0, \\phi_1$ fixed). We show that if the initial data $\\phi_0, \\phi_1$ are smooth with $\\phi_0$ taking values in $(-1,1)$ and obey a mild non-degeneracy condition, then $\\phi$ converges locally uniformly to a piecewis...
Uniform persistence and upper Lyapunov exponents for monotone skew-product semiflows
International Nuclear Information System (INIS)
Novo, Sylvia; Obaya, Rafael; Sanz, Ana M
2013-01-01
Several results of uniform persistence above and below a minimal set of an abstract monotone skew-product semiflow are obtained. When the minimal set has a continuous separation the results are given in terms of the principal spectrum. In the case that the semiflow is generated by the solutions of a family of non-autonomous differential equations of ordinary, delay or parabolic type, the former results are strongly improved. A method of calculus of the upper Lyapunov exponent of the minimal set is also determined. (paper)
Jitomirskaya, S.; Marx, C. A.
2012-11-01
We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic {M_2({C})}-cocycles. This includes rational approximation of the frequency, which so far has not been available.
Estimating the density-scaling exponent of a monatomic liquid from its pair potential
DEFF Research Database (Denmark)
Bøhling, Lasse; Bailey, Nicholas; Schrøder, Thomas
2014-01-01
This paper investigates two conjectures for calculating the density dependence of the density-scaling exponent γ of a single-component, pair-potential liquid with strong virial potential-energy correlations. The first conjecture gives an analytical expression for γ directly in terms of the pair...... potential. The second conjecture is a refined version of this involving the most likely nearest-neighbor distance determined from the pair-correlation function. The conjectures are tested by simulations of three systems, one of which is the standard Lennard-Jones liquid. While both expressions give...
Modulational estimate for the maximal Lyapunov exponent in Fermi-Pasta-Ulam chains
Dauxois, Thierry; Ruffo, Stefano; Torcini, Alessandro
1997-12-01
In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the modulational instability growth rates associated to unstable modes. Moreover, we show that the strong stochasticity threshold found in the β-FPU system is closely related to a transition in tangent space, the Lyapunov eigenvector being more localized in space at high energy.
Some comments on Hurst exponent and the long memory processes on capital markets
Sánchez Granero, M. A.; Trinidad Segovia, J. E.; García Pérez, J.
2008-09-01
The analysis of long memory processes in capital markets has been one of the topics in finance, since the existence of the market memory could implicate the rejection of an efficient market hypothesis. The study of these processes in finance is realized through Hurst exponent and the most classical method applied is R/S analysis. In this paper we will discuss the efficiency of this methodology as well as some of its more important modifications to detect the long memory. We also propose the application of a classical geometrical method with short modifications and we compare both approaches.
Exponence, allomorphy and haplology in the number and State morphology of Modern Hebrew
Faust, Noam
2018-01-01
This paper provides an account of the regularities of plural exponence in Modern Hebrew. There are two genders in Modern Hebrew, each with its specific plural marker. Nouns can appear in the Construct or Free states, and the State of a noun also has an effect on the plural marking, though only in the case of masculine nouns. Finally, in nouns with possessive suffixes and in newly-formed dual nouns, plural number seems to be marked twice in the feminine noun, but only once in the masculine nou...
Estimation of Spectral Exponent Parameter of 1/f Process in Additive White Background Noise
Directory of Open Access Journals (Sweden)
Semih Ergintav
2007-01-01
Full Text Available An extension to the wavelet-based method for the estimation of the spectral exponent, γ, in a 1/fγ process and in the presence of additive white noise is proposed. The approach is based on eliminating the effect of white noise by a simple difference operation constructed on the wavelet spectrum. The γ parameter is estimated as the slope of a linear function. It is shown by simulations that the proposed method gives reliable results. Global positioning system (GPS time-series noise is analyzed and the results provide experimental verification of the proposed method.
Criticality in Neuronal Networks
Friedman, Nir; Ito, Shinya; Brinkman, Braden A. W.; Shimono, Masanori; Deville, R. E. Lee; Beggs, John M.; Dahmen, Karin A.; Butler, Tom C.
2012-02-01
In recent years, experiments detecting the electrical firing patterns in slices of in vitro brain tissue have been analyzed to suggest the presence of scale invariance and possibly criticality in the brain. Much of the work done however has been limited in two ways: 1) the data collected is from local field potentials that do not represent the firing of individual neurons; 2) the analysis has been primarily limited to histograms. In our work we examine data based on the firing of individual neurons (spike data), and greatly extend the analysis by considering shape collapse and exponents. Our results strongly suggest that the brain operates near a tuned critical point of a highly distinctive universality class.
Magnetocaloric effect and its implementation in critical behaviour ...
Indian Academy of Sciences (India)
Model; manganites; magnetization; magnetocaloric effect; critical exponent. 1. Introduction. Large number of magnetocaloric effect (MCE) materials have attracted much ... external magnetic field, which is advantageous for applica- tion as magnetic ... of the magnetic phase transition and critical behaviour can be obtained by ...
Determination of the Lyapunov exponents and the information dimension in some dynamical systems
International Nuclear Information System (INIS)
Ziar, A.
1992-01-01
Classical phase space for some dynamical systems relevant in nuclear physics are studied. The nuclei is described by convex billiards or in the mean field theory. In both cases, besides the Poincare surface of sections which gives a qualitative description, each trajectory is characterized by its maximum Lyapunov exponent. The analytic monodromy matrix for a free particle in convex billiards rotating around an axis perpendicular to the plan of billiards, is determined, generalizing a previous result obtained for static billiards. In the frame of the mean field theory, it is shown an interesting alternative to the Lyapunov exponent, which is the dimension of the manifold in the phase space associated to the trajectory, leading to the evaluation of the relative chaotic volume in phase space as a function of the different parameters. The dimension appears as a character which could be determined easily for the rotating mean field, where the dimension of the manifold on which the trajectory is lying could be equal to 5 or 4 for chaotic trajectories, and less or equal to 3 for regular ones
Relationship between deficiency of vitamin D and exponents of metabolic syndrome.
Kramkowska, M; Grzelak, T; Walczak, M; Bogdanski, P; Pupek-Musialik, D; Czyzewska, K
2015-06-01
Widespread hypovitaminosis D and an increased incidence of metabolic syndrome (MetS) represent significant problems of contemporary medicine but link between them remain unresolved. We aimed to define relationship between vitamin D serum concentration and exponents of MetS. The studies were conducted on 70 individuals (51 with and 19 without MetS). Concentrations of 25(OH)D (25-hydroxyergocalciferol and 25-hydroxycholecalciferol), calcium, cholesterol, HDL, cholesterol LDL, triglycerides, fasting glucose, blood pressure and anthropometric parameters were measured. Median concentration of vitamin D in the research population amounted to 41.46 nmol/L. Concentration of 25(OH)D in MetS group was lower than in remainder participants (38.45 nmol/L vs. 58.50 nmol/L, p = 0.0104). An inverse correlation was demonstrated between 25(OH)D level on one hand and body weight, waist and hips circumference, adipose body weight, Body Mass Index, Waist to Height Ratio (WHtR), glycaemia and number of MetS components on the other in persons free of MetS. No such relationships could be documented in MetS group. In the entire population values of Waist to Hip Ratio (WHpR) and WHtR indices manifested correlation with hyperglycaemia, hypertriglyceridaemia, low HDL concentrations. In persons without MetS a relationship was detected between vitamin D concentration and exponents of metabolic syndrome, although further studies on this problem are required.
Adhi, H. A.; Wijaya, S. K.; Prawito; Badri, C.; Rezal, M.
2017-03-01
Stroke is one of cerebrovascular diseases caused by the obstruction of blood flow to the brain. Stroke becomes the leading cause of death in Indonesia and the second in the world. Stroke also causes of the disability. Ischemic stroke accounts for most of all stroke cases. Obstruction of blood flow can cause tissue damage which results the electrical changes in the brain that can be observed through the electroencephalogram (EEG). In this study, we presented the results of automatic detection of ischemic stroke and normal subjects based on the scaling exponent EEG obtained through detrended fluctuation analysis (DFA) using extreme learning machine (ELM) as the classifier. The signal processing was performed with 18 channels of EEG in the range of 0-30 Hz. Scaling exponents of the subjects were used as the input for ELM to classify the ischemic stroke. The performance of detection was observed by the value of accuracy, sensitivity and specificity. The result showed, performance of the proposed method to classify the ischemic stroke was 84 % for accuracy, 82 % for sensitivity and 87 % for specificity with 120 hidden neurons and sine as the activation function of ELM.
International Nuclear Information System (INIS)
Zhang Jiangang; Li Xianfeng; Chu Yandong; Yu Jianning; Chang Yingxiang
2009-01-01
In this paper, complex dynamical behavior of a class of centrifugal flywheel governor system is studied. These systems have a rich variety of nonlinear behavior, which are investigated here by numerically integrating the Lagrangian equations of motion. A tiny change in parameters can lead to an enormous difference in the long-term behavior of the system. Bubbles of periodic orbits may also occur within the bifurcation sequence. Hyperchaotic behavior is also observed in cases where two of the Lyapunov exponents are positive, one is zero, and one is negative. The routes to chaos are analyzed using Poincare maps, which are found to be more complicated than those of nonlinear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincare sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. This paper proposes a parametric open-plus-closed-loop approach to controlling chaos, which is capable of switching from chaotic motion to any desired periodic orbit. The theoretical work and numerical simulations of this paper can be extended to other systems. Finally, the results of this paper are of practical utility to designers of rotational machines.
Scaling exponents of the velocity structure functions in the interplanetary medium
Directory of Open Access Journals (Sweden)
V. Carbone
Full Text Available We analyze the scaling exponents of the velocity structure functions, obtained from the velocity fluctuations measured in the interplanetary space plasma. Using the expression for the energy transfer rate which seems the most relevant in describing the evolution of the pseudo-energy densities in the interplanetary medium, we introduce an energy cascade model derived from a simple fragmentation process, which takes into account the intermittency effect. In the absence and in the presence of the large-scale magnetic field decorrelation effect the model reduces to the fluid and the hydromagnetic p-model, respectively. We show that the scaling exponents of the q-th power of the velocity structure functions, as obtained by the model in the absence of the decorrelation effect, furnishes the best-fit to the data analyzed from the Voyager 2 velocity field measurements at 8.5 AU. Our results allow us to hypothesize a new kind of scale-similarity for magnetohydrodynamic turbulence when the decorrelation effect is at work, related to the fourth-order velocity structure function.
Predicting the long tail of book sales: Unearthing the power-law exponent
Fenner, Trevor; Levene, Mark; Loizou, George
2010-06-01
The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression techniques on the assumption that the data obeys a power-law distribution. Here we propose a different technique for estimation based on a generative model of book sales that results in an asymptotic power-law distribution of sales, but which does not suffer from the problems related to power-law regression techniques. We show that the proportion of tail sales predicted is very sensitive to the estimated power-law exponent. In particular, if we assume that the power-law exponent of the cumulative distribution is closer to 1.1 rather than to 1.2 (estimates published in 2003, calculated using regression by two groups of researchers), then our computations suggest that the tail sales of Amazon.com, rather than being 40% as estimated by Brynjolfsson, Hu and Smith in 2003, are actually closer to 20%, the proportion estimated by its CEO.
Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series
Directory of Open Access Journals (Sweden)
A. M. López Jiménez
2002-01-01
Full Text Available The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation of λ starting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.
Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data
Buonocore, R. J.; Aste, T.; Di Matteo, T.
2017-04-01
We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.
Relation Between Hertz Stress-Life Exponent, Ball-Race Conformity, and Ball Bearing Life
Zaretsky, Erwin V.; Poplawski, Joseph V.; Root, Lawrence E.
2008-01-01
ANSI/ABMA and ISO standards based on Lundberg-Palmgren bearing life theory are normalized for ball bearings having inner- and outerrace conformities of 52 percent (0.52) and made from pre-1940 bearing steel. The Lundberg-Palmgren theory incorporates an inverse 9th power relation between Hertz stress and fatigue life for ball bearings. The effect of race conformity on ball set life independent of race life is not incorporated into the Lundberg-Palmgren theory. In addition, post-1960 vacuum-processed bearing steel exhibits a 12th power relation between Hertz stress and life. The work reported extends the previous work of Zaretsky, Poplawski, and Root to calculate changes in bearing life--that includes the life of the ball set--caused by race conformity, Hertz stress-life exponent, ball bearing type and bearing series. The bearing fatigue life in actual application will usually be equal to or greater than that calculated using the ANSI/ABMA and ISO standards that incorporate the Lundberg-Palmgren theory. The relative fatigue life of an individual race is more sensitive to changes in race conformity for Hertz stress-life exponent n of 12 than where n = 9. However, when the effects are combined to predict actual bearing life for a specified set of conditions and bearing geometry, the predicted life of the bearing will be greater for a value of n = 12 than n = 9.
a Comparison of Three Hurst Exponent Approaches to Predict Nascent Bubbles in S&P500 Stocks
Fernández-Martínez, M.; Sánchez-Granero, M. A.; Muñoz Torrecillas, M. J.; McKelvey, Bill
Since the pioneer contributions due to Vandewalle and Ausloos, the Hurst exponent has been applied by econophysicists as a useful indicator to deal with investment strategies when such a value is above or below 0.5, the Hurst exponent of a Brownian motion. In this paper, we hypothesize that the self-similarity exponent of financial time series provides a reliable indicator for herding behavior (HB) in the following sense: if there is HB, then the higher the price, the more the people will buy. This will generate persistence in the stocks which we shall measure by their self-similarity exponents. Along this work, we shall explore whether there is some connections between the self-similarity exponent of a stock (as a HB indicator) and the stock’s future performance under the assumption that the HB will last for some time. With this aim, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which performs best to identify the transition from random efficient market behavior to HB and hence, to detect the beginning of a bubble. Generalized Hurst Exponent, Detrended Fluctuation Analysis, and GM2 algorithms have been tested. Traditionally, researchers have focused on identifying the beginning of a crash. We study the beginning of the transition from efficient market behavior to a market bubble, instead. Our empirical results support that the higher (respectively the lower) the self-similarity index, the higher (respectively the lower) the mean of the price change, and hence, the better (respectively the worse) the performance of the corresponding stock. This would imply, as a consequence, that the transition process from random efficient market to HB has started. For experimentation purposes, S&P500 stock Index constituted our main data source.
Magnetic susceptibilities of integrable quantum ladders
International Nuclear Information System (INIS)
Park, Soo A; Lee, K.
2001-01-01
As an extension of previous studies, we consider the magnetic susceptibilities of a coupled spin chain model at low temperature and of a more realistic model at low temperature and of a more realistic model having a t-J ladder structure at zero temperature. The magnetic susceptibilities for both models are obtained numerically when the coupling constant is greater than its critical value. In this region, the ladders behave as a single chain for H c and as two independent chains for H>H c , showing a divergence at H c . This divergence is expected to smear out at a finite temperature
International Nuclear Information System (INIS)
Look, Nicole; Arellano, Christopher J.; Grabowski, Alena M.; Kram, Rodger; McDermott, William J.; Bradley, Elizabeth
2013-01-01
In this paper, we study dynamic stability during running, focusing on the effects of speed, and the use of a leg prosthesis. We compute and compare the maximal Lyapunov exponents of kinematic time-series data from subjects with and without unilateral transtibial amputations running at a wide range of speeds. We find that the dynamics of the affected leg with the running-specific prosthesis are less stable than the dynamics of the unaffected leg and also less stable than the biological legs of the non-amputee runners. Surprisingly, we find that the center-of-mass dynamics of runners with two intact biological legs are slightly less stable than those of runners with amputations. Our results suggest that while leg asymmetries may be associated with instability, runners may compensate for this effect by increased control of their center-of-mass dynamics
Decrease in Hurst exponent of human gait with aging and neurodegenerative diseases
International Nuclear Information System (INIS)
Zhauang Jianjun; Ning Xinbao; Yang Xiaodong; Huo Chengyu; Hou Fengzhen
2008-01-01
In this paper the decrease in the Hurst exponent of human gait with aging and neurodegenerative diseases was observed by using an improved rescaled range (R/S) analysis method. It indicates that the long-range correlations of gait rhythm from young healthy people are stronger than those from the healthy elderly and the diseased. The result further implies that fractal dynamics in human gait will be altered due to weakening or impairment of neural control on locomotion resulting from aging and neurodegenerative diseases. Due to analysing short-term data sequences rather than long datasets required by most nonlinear methods, the algorithm has the characteristics of simplicity and sensitivity, most importantly, fast calculation as well as powerful anti-noise capacities. These findings have implications for modelling locomotor control and also for quantifying gait dynamics in varying physiologic and pathologic states
On the improvement of Wiener attack on RSA with small private exponent.
Wu, Mu-En; Chen, Chien-Ming; Lin, Yue-Hsun; Sun, Hung-Min
2014-01-01
RSA system is based on the hardness of the integer factorization problem (IFP). Given an RSA modulus N = pq, it is difficult to determine the prime factors p and q efficiently. One of the most famous short exponent attacks on RSA is the Wiener attack. In 1997, Verheul and van Tilborg use an exhaustive search to extend the boundary of the Wiener attack. Their result shows that the cost of exhaustive search is 2r + 8 bits when extending the Weiner's boundary r bits. In this paper, we first reduce the cost of exhaustive search from 2r + 8 bits to 2r + 2 bits. Then, we propose a method named EPF. With EPF, the cost of exhaustive search is further reduced to 2r - 6 bits when we extend Weiner's boundary r bits. It means that our result is 2(14) times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits.
Fractality Evidence and Long-Range Dependence on Capital Markets: a Hurst Exponent Evaluation
Oprean, Camelia; Tănăsescu, Cristina
2014-07-01
Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is the market efficiency hypothesis.
Importance sampling with imperfect cloning for the computation of generalized Lyapunov exponents
Anteneodo, Celia; Camargo, Sabrina; Vallejos, Raúl O.
2017-12-01
We revisit the numerical calculation of generalized Lyapunov exponents, L (q ) , in deterministic dynamical systems. The standard method consists of adding noise to the dynamics in order to use importance sampling algorithms. Then L (q ) is obtained by taking the limit noise-amplitude → 0 after the calculation. We focus on a particular method that involves periodic cloning and pruning of a set of trajectories. However, instead of considering a noisy dynamics, we implement an imperfect (noisy) cloning. This alternative method is compared with the standard one and, when possible, with analytical results. As a workbench we use the asymmetric tent map, the standard map, and a system of coupled symplectic maps. The general conclusion of this study is that the imperfect-cloning method performs as well as the standard one, with the advantage of preserving the deterministic dynamics.
Connection of optimum temporal exponents with a principle of least action
Sergeev, E. V.; Karzanov, A. V.; Tremaskin, A. V.
2008-06-01
The principle of the least action states, that the motion of objects on optimum trajectories conjugates to the underload expenditure of activity. In the canonical approach this statement is reduced to searching extreme activity. For the immediate proof of the underload expenditure of activity on optimum trajectories the relevant mathematical algorithm in the basis of which bottom the concept of optimum time exponents lays is offered. Using this algorithm, various modes of a motion of charged particles are explored: the harmonic motion, a motion in the homogeneous force field, a motion in a central force field and a motion on inertia. The terrain clearance minimum under the rate of flux of activity for the harmonic motions is detected.
Detection of the onset of numerical chaotic instabilities by lyapunov exponents
Directory of Open Access Journals (Sweden)
Alicia Serfaty De Markus
2001-01-01
Full Text Available It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. We present a procedure that establishes a criterion to select the largest possible step size before the onset of chaotic numerical instabilities, based upon the observation that computational chaos does not occur in a smooth, continuous way, but rather abruptly, as detected by examining the largest Lyapunov exponent as a function of the step size. For completeness, examination of the bifurcation diagrams with the step reveals the complexity imposed by the algorithmic discretization, showing the robustness of a scheme to numerical instabilities, illustrated here for explicit and implicit Euler schemes. An example of numerical suppression of chaos is also provided.
Uehara, Erica; Deguchi, Tetsuo
2017-12-07
We show that the average size of self-avoiding polygons (SAPs) with a fixed knot is much larger than that of no topological constraint if the excluded volume is small and the number of segments is large. We call it topological swelling. We argue an "enhancement" of the scaling exponent for random polygons with a fixed knot. We study them systematically through SAP consisting of hard cylindrical segments with various different values of the radius of segments. Here we mean by the average size the mean-square radius of gyration. Furthermore, we show numerically that the topological balance length of a composite knot is given by the sum of those of all constituent prime knots. Here we define the topological balance length of a knot by such a number of segments that topological entropic repulsions are balanced with the knot complexity in the average size. The additivity suggests the local knot picture.
On the Improvement of Wiener Attack on RSA with Small Private Exponent
Directory of Open Access Journals (Sweden)
Mu-En Wu
2014-01-01
Full Text Available RSA system is based on the hardness of the integer factorization problem (IFP. Given an RSA modulus N=pq, it is difficult to determine the prime factors p and q efficiently. One of the most famous short exponent attacks on RSA is the Wiener attack. In 1997, Verheul and van Tilborg use an exhaustive search to extend the boundary of the Wiener attack. Their result shows that the cost of exhaustive search is 2r+8 bits when extending the Weiner's boundary r bits. In this paper, we first reduce the cost of exhaustive search from 2r+8 bits to 2r+2 bits. Then, we propose a method named EPF. With EPF, the cost of exhaustive search is further reduced to 2r-6 bits when we extend Weiner's boundary r bits. It means that our result is 214 times faster than Verheul and van Tilborg's result. Besides, the security boundary is extended 7 bits.
Spectral analysis of structure functions and their scaling exponents in forced isotropic turbulence
Linkmann, Moritz; McComb, W. David; Yoffe, Samuel; Berera, Arjun
2014-11-01
The pseudospectral method, in conjunction with a new technique for obtaining scaling exponents ζn from the structure functions Sn (r) , is presented as an alternative to the extended self-similarity (ESS) method and the use of generalized structure functions. We propose plotting the ratio | Sn (r) /S3 (r) | against the separation r in accordance with a standard technique for analysing experimental data. This method differs from the ESS technique, which plots the generalized structure functions Gn (r) against G3 (r) , where G3 (r) ~ r . Using our method for the particular case of S2 (r) we obtain the new result that the exponent ζ2 decreases as the Taylor-Reynolds number increases, with ζ2 --> 0 . 679 +/- 0 . 013 as Rλ --> ∞ . This supports the idea of finite-viscosity corrections to the K41 prediction for S2, and is the opposite of the result obtained by ESS. The pseudospectral method permits the forcing to be taken into account exactly through the calculation of the energy input in real space from the work spectrum of the stirring forces. The combination of the viscous and the forcing corrections as calculated by the pseudospectral method is shown to account for the deviation of S3 from Kolmogorov's ``four-fifths''-law at all scales. This work has made use of the resources provided by the UK supercomputing service HECToR, made available through the Edinburgh Compute and Data Facility (ECDF). A. B. is supported by STFC, S. R. Y. and M. F. L. are funded by EPSRC.
Critical behavior of electrical resistivity in amorphous Fe–Zr alloys
Indian Academy of Sciences (India)
Analysis of the resistivity data particularly in the critical region reveals that these systems have a much wider range of critical region compared to other crystalline ferromagnetic materials. The value of and speciﬁc heat critical exponent, has the same values as those determined from our earlier magnetic measurements ...
International Nuclear Information System (INIS)
Markos, P; Schweitzer, L; Weyrauch, M
2004-01-01
In a recent publication, Kuzovkov et al (2002 J. Phys.: Condens. Matter. 14 13777) announced an analytical solution of the two-dimensional Anderson localization problem via the calculation of a generalized Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalized states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy of using a generalized Lyapunov exponent for studying Anderson localization. (comment)
Stock markets and criticality in the current economic crisis
da Silva, Roberto; Zembrzuski, Marcelo; Correa, Fabio C.; Lamb, Luis C.
2010-12-01
We show that the current economic crisis has led the market to exhibit a non-critical behavior. We do so by analyzing the quantitative parameters of time series from the main assets of the Brazilian Stock Market BOVESPA. By monitoring global persistence we show a deviation of power law behavior during the crisis in a strong analogy with spin systems (from where this concept was originally conceived). Such behavior is corroborated by an emergent heavy tail of absolute return distribution and also by the magnitude autocorrelation exponent. Comparisons with universal exponents obtained in the international stock markets are also performed. This suggests how a thorough analysis of suitable exponents can bring a possible way of forecasting market crises characterized by non-criticality.
DEFF Research Database (Denmark)
Kjellberg, Caspar Mølholt; Meredith, David
2014-01-01
. Since the comments are not input sequentially, with regard to position, but in arbitrary order, this list must be sorted by copy/pasting the rows into place—an error-prone and time-consuming process. Scholars who produce critical editions typically use off-the-shelf music notation software......The best text method is commonly applied among music scholars engaged in producing critical editions. In this method, a comment list is compiled, consisting of variant readings and editorial emendations. This list is maintained by inserting the comments into a document as the changes are made......, consisting of a Sibelius plug-in, a cross-platform application, called CriticalEd, and a REST-based solution, which handles data storage/retrieval. A prototype has been tested at the Danish Centre for Music Publication, and the results suggest that the system could greatly improve the efficiency...
Metallic magnets without inversion symmetry and antiferromagnetic quantum critical points
Energy Technology Data Exchange (ETDEWEB)
Fischer, I.A.
2006-07-01
This thesis focusses on two classes of systems that exhibit non-Fermi liquid behaviour in experiments: we investigated aspects of chiral ferromagnets and of antiferromagnetic metals close to a quantum critical point. In chiral ferromagnets, the absence of inversion symmetry makes spin-orbit coupling possible, which leads to a helical modulation of the ferromagnetically ordered state. We studied the motion of electrons in the magnetically ordered state of a metal without inversion symmetry by calculating their generic band-structure. We found that spin-orbit coupling, although weak, has a profound effect on the shape of the Fermi surface: On a large portion of the Fermi surface the electron motion parallel to the helix practically stops. Signatures of this effect can be expected to show up in measurements of the anomalous Hall effect. Recent neutron scattering experiments uncovered the existence of a peculiar kind of partial order in a region of the phase diagram adjacent to the ordered state of the chiral ferromagnet MnSi. Starting from the premise that this partially ordered state is a thermodynamically distinct phase, we investigated an extended Ginzburg-Landau theory for chiral ferromagnets. In a certain parameter regime of the Ginzburg-Landau theory we identified crystalline phases that are reminiscent of the so-called blue phases in liquid crystals. Many antiferromagnetic heavy-fermion systems can be tuned into a regime where they exhibit non-Fermi liquid exponents in the temperature dependence of thermodynamic quantities such as the specific heat capacity; this behaviour could be due to a quantum critical point. If the quantum critical behaviour is field-induced, the external field does not only suppress antiferromagnetism but also induces spin precession and thereby influences the dynamics of the order parameter. We investigated the quantum critical behavior of clean antiferromagnetic metals subject to a static, spatially uniform external magnetic field. We
Genetic susceptibility of periodontitis
Laine, M.L.; Crielaard, W.; Loos, B.G.
2012-01-01
In this systematic review, we explore and summarize the peer-reviewed literature on putative genetic risk factors for susceptibility to aggressive and chronic periodontitis. A comprehensive literature search on the PubMed database was performed using the keywords ‘periodontitis’ or ‘periodontal
Energy Technology Data Exchange (ETDEWEB)
Restrepo-Parra, E., E-mail: erestrepopa@unal.edu.c [Departamento de Fisica y Quimica, Universidad Nacional de Colombia-Sede Manizales, A.A. 127 Manizales (Colombia); Bedoya-Hincapie, C.M.; Jurado, F.J.; Riano-Rojas, J.C. [Departamento de Fisica y Quimica, Universidad Nacional de Colombia-Sede Manizales, A.A. 127 Manizales (Colombia); Restrepo, J. [Grupo de Magnetismo y Simulacion G, Instituto de Fisica, Universidad de Antioquia, A.A. 1226 Medellin (Colombia)
2010-11-15
Critical exponents offer important information concerning the interaction mechanisms near the paramagnetic to ferromagnetic transition. In this work a Monte Carlo-Metropolis simulation of the critical behavior in La{sub 2/3}Ca{sub 1/3}MnO{sub 3} thin films is addressed. Canonical ensemble averages for magnetization per site, magnetic susceptibility and specific heat of stoichiometric manganite within a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions are computed. The La{sub 2/3}Ca{sub 1/3}MnO{sub 3} thin films were simulated addressing the thickness influence and thermal dependence. In the model, Mn magnetic ions are distributed on a simple cubic lattice according to the perovskite structure of this manganite. Ferromagnetic coupling for the bonds Mn{sup 3+}-Mn{sup 3+}(e{sub g}-e{sub g}'), Mn{sup 3+}-Mn{sup 4+}(e{sub g}-d{sup 3}) and Mn{sup 3+}-Mn{sup 4+}(e{sub g}'-d{sup 3}) were taken into account. On the basis of finite-size scaling theory, our best estimates of critical exponents, linked to the ferromagnetic to paramagnetic transition, for the correlation length, specific heat, magnetization and susceptibility are, respectively: v=0.56{+-}0.01, {alpha}=0.16{+-}0.03, {beta}=0.34{+-}0.04{gamma} and {gamma}=1.17{+-}0.05. These theoretical results are consistent with the Rushbrooke equalitiy {alpha}+2{beta}+{gamma}=2.
CISH and Susceptibility to Infectious Diseases
Khor, CC; Vannberg, FO; Chapman, SJ; Guo, H; Wong, SH; Walley, AJ; Vukcevic, D; Rautanen, A; Mills, TC; Chang, K-C; Kam, K-M; Crampin, AC; Ngwira, B; Leung, C-C; Tam, C-M
2010-01-01
BACKGROUND The interleukin-2-mediated immune response is critical for host defense against infectious pathogens. Cytokine-inducible SRC homology 2 (SH2) domain protein (CISH), a suppressor of cytokine signaling, controls interleukin-2 signaling. METHODS Using a case-control design, we tested for an association between CISH polymorphisms and susceptibility to major infectious diseases (bacteremia, tuberculosis, and severe malaria) in blood samples from 8402 persons in Gambia, Hong Kong, Kenya,...
The critical thermal expansion of gadolinium
International Nuclear Information System (INIS)
Robinson, K.; Lanchester, P.C.
1978-01-01
Measurements have been made of the critical thermal expansion of single crystals of gadolinium, prepared by solid state electrotransport processing. Although the expansion data can be fitted to a simple power law with exponents lambda + =-0.25, lambda - =-0.33, these values are not predicted by theory and a discontinuity remains at Tsub(c)=293.620 K. It is suggested that the results relate to a region of crossover to uniaxial dipolar behaviour. (Auth.)
Wavefunctions, quantum diffusion, and scaling exponents in golden-mean quasiperiodic tilings.
Thiem, Stefanie; Schreiber, Michael
2013-02-20
We study the properties of wavefunctions and the wavepacket dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider fairly large systems numerically. We show that the wavefunctions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wavepackets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wavepacket with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wavepacket and propose a modified lower bound for the absolute continuous regime.
Generalized Hurst exponent estimates differentiate EEG signals of healthy and epileptic patients
Lahmiri, Salim
2018-01-01
The aim of our current study is to check whether multifractal patterns of the electroencephalographic (EEG) signals of normal and epileptic patients are statistically similar or different. In this regard, the generalized Hurst exponent (GHE) method is used for robust estimation of the multifractals in each type of EEG signals, and three powerful statistical tests are performed to check existence of differences between estimated GHEs from healthy control subjects and epileptic patients. The obtained results show that multifractals exist in both types of EEG signals. Particularly, it was found that the degree of fractal is more pronounced in short variations of normal EEG signals than in short variations of EEG signals with seizure free intervals. In contrary, it is more pronounced in long variations of EEG signals with seizure free intervals than in normal EEG signals. Importantly, both parametric and nonparametric statistical tests show strong evidence that estimated GHEs of normal EEG signals are statistically and significantly different from those with seizure free intervals. Therefore, GHEs can be efficiently used to distinguish between healthy and patients suffering from epilepsy.
Wavefunctions, quantum diffusion, and scaling exponents in golden-mean quasiperiodic tilings
International Nuclear Information System (INIS)
Thiem, Stefanie; Schreiber, Michael
2013-01-01
We study the properties of wavefunctions and the wavepacket dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider fairly large systems numerically. We show that the wavefunctions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wavepackets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wavepacket with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wavepacket and propose a modified lower bound for the absolute continuous regime.
Benettin, G.; Pasquali, S.; Ponno, A.
2018-05-01
FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual β -model, perturbations of Toda include the usual α +β model. In this paper we explore and compare two families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each model, the maximal Lyapunov exponent χ . More precisely, we consider statistically typical trajectories and study the asymptotics of χ for large N (the number of particles) and small ɛ (the specific energy E / N), and find, for all models, asymptotic power laws χ ˜eq Cɛ ^a, C and a depending on the model. The asymptotics turns out to be, in general, rather slow, and producing accurate results requires a great computational effort. We also revisit and extend the analytic computation of χ introduced by Casetti, Livi and Pettini, originally formulated for the β -model. With great evidence the theory extends successfully to all models of the linear hierarchy, but not to models close to Toda.
International Nuclear Information System (INIS)
Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
2014-01-01
We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics
Mancilla Canales, M. A.; Leguto, A. J.; Riquelme, B. D.; León, P. Ponce de; Bortolato, S. A.; Korol, A. M.
2017-12-01
Ektacytometry techniques quantifies red blood cells (RBCs) deformability by measuring the elongation of suspended RBCs subjected to shear stress. Raw shear stress elongation plots are difficult to understand, thus most research papers apply data reduction methods characterizing the relationship between curve fitting. Our approach works with the naturally generated photometrically recorded time series of the diffraction pattern of several million of RBCs subjected to shear stress, and applies nonlinear quantifiers to study the fluctuations of these elongations. The development of new quantitative methods is crucial for restricting the subjectivity in the study of the cells behavior, mainly if they are capable of analyze at the same time biological and mechanical aspects of the cells in flowing conditions and compare their dynamics. A patented optical system called Erythrocyte Rheometer was used to evaluate viscoelastic properties of erythrocytes by Ektacytometry. To analyze cell dynamics we used the technique of Time Delay Coordinates, False Nearest Neighbors, the forecasting procedure proposed by Sugihara and May, and Hurst exponent. The results have expressive meaning on comparing healthy samples with parasite treated samples, suggesting that apparent noise associated with deterministic chaos can be used not only to distinguish but also to characterize biological and mechanical aspects of cells at the same time in flowing conditions.
Influence of finite-time Lyapunov exponents on winter precipitation over the Iberian Peninsula
Garaboa-Paz, Daniel; Lorenzo, Nieves; Pérez-Muñuzuri, Vicente
2017-05-01
Seasonal forecasts have improved during the last decades, mostly due to an increase in understanding of the coupled ocean-atmosphere dynamics, and the development of models able to predict the atmosphere variability. Correlations between different teleconnection patterns and severe weather in different parts of the world are constantly evolving and changing. This paper evaluates the connection between winter precipitation over the Iberian Peninsula and the large-scale tropospheric mixing over the eastern Atlantic Ocean. Finite-time Lyapunov exponents (FTLEs) have been calculated from 1979 to 2008 to evaluate this mixing. Our study suggests that significant negative correlations exist between summer FTLE anomalies and winter precipitation over Portugal and Spain. To understand the mechanisms behind this correlation, summer anomalies of the FTLE have also been correlated with other climatic variables such as the sea surface temperature (SST), the sea level pressure (SLP) or the geopotential. The East Atlantic (EA) teleconnection index correlates with the summer FTLE anomalies, confirming their role as a seasonal predictor for winter precipitation over the Iberian Peninsula.
International Nuclear Information System (INIS)
Xia Xiangao
2011-01-01
Using aerosol loading data from 79 Aerosol Robotic Network (AERONET) stations with observations from more than six years, changes in aerosol optical depth (AOD) and Angstrom wavelength exponent (AWE) were studied. A statistical method was developed to determine whether AOD changes were due to increased background AOD values and/or an increased number of high AOD events. AOD decreased significantly at AERONET sites in northeastern North American and in Western Europe, which was accompanied by decreased AWE. Reduction of AOD there was mainly due to a decreased frequency of high AOD events and an increased frequency of background AOD events. In addition, decreased AOD values for high AOD events also accounted for ∼ 16–32% of the AOD reduction. This is indicative of significant meteorological effects on AOD variability. AOD trends in other regions were marginal and most were not significant; however, AOD increased significantly at one site in the Sahel and another in Saudi Arabia, predominantly due to the increased frequency of high AOD events and their average AOD.
Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents.
Hua, Zhongyun; Yi, Shuang; Zhou, Yicong; Li, Chengqing; Wu, Yue
2018-02-01
Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an -dimensional ( -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic -D Cat matrices iteratively and then constructs the final -D Cat matrix by performing similarity transformation on one basic -D Cat matrix by the other. Given any number of positive LEs, it can generate an -D HCM with desired hyperchaotic complexity. Two illustrative examples of -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.
Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent
Nec, Yana
2018-01-01
Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).
Black Carbon, Aerosol optical depth and Angstrom Exponent in São Paulo, Brazil
Miranda, R. M.; Perez-Martinez, P. J.; Andrade, M. D. F.
2017-12-01
Black carbon (BC) is a major absorber of solar radiation, and its impact on the radiative balance is therefore considered important. Fossil fuel combustion processes and biomass burning result in the emission of BC. Black carbon is being monitored since 2014 with a Multi-Angle Absorption Photometer-MAAP (5012; Thermo Scientific) in the East Zone of São Paulo, Brazil. São Paulo Metropolitan Area with more than 19 million inhabitants, 7 million vehicles, has high concentrations of air pollutants, especially in the winter. Vehicles can be considered the principal source of particles emitted to the atmosphere. Concentration of the pollutant had an average of 1.95 ug.m-3 ± 2.06 and a maximum value of 19.93 ug.m-3. These large variations were due to meteorological effects and to the influence of anthropogenic activities, since samples were collected close to important highways. Winds coming from the East part predominate. Higher concentrations were found in the winter months (June, July and August). Optical data from AERONET (Aerosol Optical Depth-AOD 550 nm and Angstrom Exponent 440-675 nm) were related to BC concentrations for the period from August, 2016. Average values of AOD at 500 nm and Angstrom Parameter (440-675nm) were 0.16±0.11 and 1.44±0.23, respectively. Higher BC concentrations were related to lower Angstrom values.
Reliability of Lyapunov characteristic exponents computed by the two-particle method
Mei, Lijie; Huang, Li
2018-03-01
For highly complex problems, such as the post-Newtonian formulation of compact binaries, the two-particle method may be a better, or even the only, choice to compute the Lyapunov characteristic exponent (LCE). This method avoids the complex calculations of variational equations compared with the variational method. However, the two-particle method sometimes provides spurious estimates to LCEs. In this paper, we first analyze the equivalence in the definition of LCE between the variational and two-particle methods for Hamiltonian systems. Then, we develop a criterion to determine the reliability of LCEs computed by the two-particle method by considering the magnitude of the initial tangent (or separation) vector ξ0 (or δ0), renormalization time interval τ, machine precision ε, and global truncation error ɛT. The reliable Lyapunov characteristic indicators estimated by the two-particle method form a V-shaped region, which is restricted by d0, ε, and ɛT. Finally, the numerical experiments with the Hénon-Heiles system, the spinning compact binaries, and the post-Newtonian circular restricted three-body problem strongly support the theoretical results.
A perturbation method to the tent map based on Lyapunov exponent and its application
Cao, Lv-Chen; Luo, Yu-Ling; Qiu, Sen-Hui; Liu, Jun-Xiu
2015-10-01
Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).
The Tail Exponent for Stock Returns in Bursa Malaysia for 2003-2008
Rusli, N. H.; Gopir, G.; Usang, M. D.
2010-07-01
A developed discipline of econophysics that has been introduced is exhibiting the application of mathematical tools that are usually applied to the physical models for the study of financial models. In this study, an analysis of the time series behavior of several blue chip and penny stock companies in Main Market of Bursa Malaysia has been performed. Generally, the basic quantity being used is the relative price changes or is called the stock price returns, contains daily-sampled data from the beginning of 2003 until the end of 2008, containing 1555 trading days recorded. The aim of this paper is to investigate the tail exponent in tails of the distribution for blue chip stocks and penny stocks financial returns in six years period. By using a standard regression method, it is found that the distribution performed double scaling on the log-log plot of the cumulative probability of the normalized returns. Thus we calculate α for a small scale return as well as large scale return. Based on the result obtained, it is found that the power-law behavior for the probability density functions of the stock price absolute returns P(z)˜z-α with values lying inside and outside the Lévy stable regime with values α>2. All the results were discussed in detail.
DEFF Research Database (Denmark)
Friisberg, Ida Marie; Costigliola, Lorenzo; Dyre, Jeppe C.
2017-01-01
This paper investigates the relation between the density-scaling exponent γ and the virial potentialenergy coefficient R at several thermodynamic state points in three dimensions for the generalized (2n, n) Lennard-Jones (LJ) system for n = 4, 9, 12, 18, as well as for the standard n = 6 LJ syste...
Magnasco, Valerio
2008-01-01
Orbital exponent optimization in the elementary ab-initio VB calculation of the ground states of H[subscript 2][superscript +], H[subscript 2], He[subscript 2][superscript +], He[subscript 2] gives a fair description of the exchange-overlap component of the interatomic interaction that is important in the bond region. Correct bond lengths and…
Sikora, Grzegorz; Teuerle, Marek; Wyłomańska, Agnieszka; Grebenkov, Denis
2017-08-01
The most common way of estimating the anomalous scaling exponent from single-particle trajectories consists of a linear fit of the dependence of the time-averaged mean-square displacement on the lag time at the log-log scale. We investigate the statistical properties of this estimator in the case of fractional Brownian motion (FBM). We determine the mean value, the variance, and the distribution of the estimator. Our theoretical results are confirmed by Monte Carlo simulations. In the limit of long trajectories, the estimator is shown to be asymptotically unbiased, consistent, and with vanishing variance. These properties ensure an accurate estimation of the scaling exponent even from a single (long enough) trajectory. As a consequence, we prove that the usual way to estimate the diffusion exponent of FBM is correct from the statistical point of view. Moreover, the knowledge of the estimator distribution is the first step toward new statistical tests of FBM and toward a more reliable interpretation of the experimental histograms of scaling exponents in microbiology.
International Nuclear Information System (INIS)
Guerrieri, A.
2009-01-01
In this report the largest Lyapunov characteristic exponent of a high dimensional atmospheric global circulation model of intermediate complexity has been estimated numerically. A sensitivity analysis has been carried out by varying the equator-to-pole temperature difference, the space resolution and the value of some parameters employed by the model. Chaotic and non-chaotic regimes of circulation have been found. [it
Cluster tails for critical power-law inhomogeneous random graphs
van der Hofstad, R.; Kliem, S.; van Leeuwaarden, J.S.H.
2018-01-01
Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299–2361, 2012). It was proved that when the degrees obey a power law with exponent τ∈ (3 , 4)
International Nuclear Information System (INIS)
Goldfarb, R.B.; Clark, A.F.
1985-01-01
Magnetization and ac susceptibility of a standard NbTi superconductor were measured as a function of longitudinal dc magnetic field. The ac-field-amplitude and frequency dependences of the complex susceptibility are examined. The magnetization is related to the susceptibility by means of a theoretical derivation based on the field dependence of the critical current density. Hysteresis losses, obtained directly from dc hysteresis loops and derived theoretically from ac susceptibility and critical current density, were in reasonable agreement
Critical behavior of ferromagnetic La0.7Sr0.3CoO3 thin films
International Nuclear Information System (INIS)
Schwarz, T.
2007-07-01
The present thesis concentrates on the critical behavior of ferromagnetic La 0.7 Sr 0.3 CoO 3 thin films (LSCO) close to the magnetic phase transition. The LSCO thin films were prepared by pulsed laser deposition and optimized with respect to their structural and magnetic properties. For the characterization of the structural and magnetic characteristics various methods were used. By means of X-ray diffraction and electron microscopy the crystallinity and microstructure of the epitaxial films were examined, respectively. The analysis of the chemical composition was accomplished by Rutherford backscattering and energy dispersive X-ray diffraction (EDX). Parallel to the investigations of the LSCO films a low-temperature measuring system for electrical measurements in magnetic fields up to 8 T in a temperature range from 1.5 K to 300 K was developed and built up including the necessary control and measuring software. The central point of this work was dedicated to the characterization of the magnetic characteristics of the LSCO films. In comparison, single crystals and polycrystalline bulk samples were also available. At these samples temperature-dependent and isothermal magnetization measurements were accomplished by a SQUID magnetometer. To determine the critical behavior of the samples the critical exponents of the susceptibility and the spontaneous magnetization in the proximity of the ferromagnetic phase transition were determined. For the exact determination of the critical exponents from the experimental data an evaluation routine in Matlab on basis of the Arrott representation method was used. In addition to the investigations of the critical behavior, electrical transportation measurements and neutron reflection measurements with spin-polarized neutrons were performed. The investigations of this work show that, in contrast to the critical behavior of single-crystal LSCO volume samples where a three-dimensional Heisenberg behavior could be observed, the
Mehdizadeh, Sina; Sanjari, Mohammad Ali
2017-11-07
This study aimed to determine the effect of added noise, filtering and time series length on the largest Lyapunov exponent (LyE) value calculated for time series obtained from a passive dynamic walker. The simplest passive dynamic walker model comprising of two massless legs connected by a frictionless hinge joint at the hip was adopted to generate walking time series. The generated time series was used to construct a state space with the embedding dimension of 3 and time delay of 100 samples. The LyE was calculated as the exponential rate of divergence of neighboring trajectories of the state space using Rosenstein's algorithm. To determine the effect of noise on LyE values, seven levels of Gaussian white noise (SNR=55-25dB with 5dB steps) were added to the time series. In addition, the filtering was performed using a range of cutoff frequencies from 3Hz to 19Hz with 2Hz steps. The LyE was calculated for both noise-free and noisy time series with different lengths of 6, 50, 100 and 150 strides. Results demonstrated a high percent error in the presence of noise for LyE. Therefore, these observations suggest that Rosenstein's algorithm might not perform well in the presence of added experimental noise. Furthermore, findings indicated that at least 50 walking strides are required to calculate LyE to account for the effect of noise. Finally, observations support that a conservative filtering of the time series with a high cutoff frequency might be more appropriate prior to calculating LyE. Copyright © 2017 Elsevier Ltd. All rights reserved.
ANTHIM THE IVIRITE AN EXPONENT OF CAUCASIAN AND ROMANIAN SPIRITUALITY IN THE 18TH CENTURY
Directory of Open Access Journals (Sweden)
Angela BOTEZ
2016-10-01
Full Text Available The paper approaches the theme about Anthim the Ivirite is an exponent of Romanian and Caucasian spirituality. Honouring this personality we start from the observation that his spiritual heritage remains relevant over the ages. Some biographers claim that Anthim the Ivirite was from a noble family. His life was as well dramatic, as noble. Anthim the Ivirite remains in Romanian history as a deeply religious man and a man of many talents. He spoke several foreign languages among which Romanian, Greek, Arabic and Turkish. Saint Anthim was a scholar, a printer of religious writings, he wrote religious literature and succeeded to leave a deep mark in the Romanian culture that times undimmed. We consider relevant also that among the important anniversaries of the year 2016 along with the anniversary of Saint Anthim the Ivirite the Romanian Orthodox Church celebrates all the Romanian Church typographers who have contributed fundamentally to a rich religious culture in Romanian. A religious journalist notice for a specialized publication that The fact that the Romanian Orthodox Church, under the clear vision of His Beatitude Patriarch Daniel has chosen to inscribe amongst the paramount holidays of the year 2016 the Church typographers represents a memorable and soul-uplifting gesture, a gesture of conscience in agreement with all who wanted and succeeded to conquer time through the eternity of the typed letter, taking the Word of God in all the four skies and seeding the values of Christian faith and Christian moral in the hearts and thoughts of all Romanians. Posterity’s judgment was warm, respectful and fair in what concerns Saint Hierarch Anthim, and the Holy Synod of the Romanian Orthodox Church glorified him, as a saint and martyr of our Romanian Orthodox Church and this is the reason why the final part of the paper is dedicated to the identification of a string of interesting Anthim anniversaries over the times.
Hurst Exponent Analysis of Resting-State fMRI Signal Complexity across the Adult Lifespan
Directory of Open Access Journals (Sweden)
Jianxin Dong
2018-02-01
Full Text Available Exploring functional information among various brain regions across time enables understanding of healthy aging process and holds great promise for age-related brain disease diagnosis. This paper proposed a method to explore fractal complexity of the resting-state functional magnetic resonance imaging (rs-fMRI signal in the human brain across the adult lifespan using Hurst exponent (HE. We took advantage of the examined rs-fMRI data from 116 adults 19 to 85 years of age (44.3 ± 19.4 years, 49 females from NKI/Rockland sample. Region-wise and voxel-wise analyses were performed to investigate the effects of age, gender, and their interaction on complexity. In region-wise analysis, we found that the healthy aging is accompanied by a loss of complexity in frontal and parietal lobe and increased complexity in insula, limbic, and temporal lobe. Meanwhile, differences in HE between genders were found to be significant in parietal lobe (p = 0.04, corrected. However, there was no interaction between gender and age. In voxel-wise analysis, the significant complexity decrease with aging was found in frontal and parietal lobe, and complexity increase was found in insula, limbic lobe, occipital lobe, and temporal lobe with aging. Meanwhile, differences in HE between genders were found to be significant in frontal, parietal, and limbic lobe. Furthermore, we found age and sex interaction in right parahippocampal gyrus (p = 0.04, corrected. Our findings reveal HE variations of the rs-fMRI signal across the human adult lifespan and show that HE may serve as a new parameter to assess healthy aging process.
A Brainnetome Atlas Based Mild Cognitive Impairment Identification Using Hurst Exponent
Directory of Open Access Journals (Sweden)
Zhuqing Long
2018-04-01
Full Text Available Mild cognitive impairment (MCI, which generally represents the transition state between normal aging and the early changes related to Alzheimer’s disease (AD, has drawn increasing attention from neuroscientists due that efficient AD treatments need early initiation ahead of irreversible brain tissue damage. Thus effective MCI identification methods are desperately needed, which may be of great importance for the clinical intervention of AD. In this article, the range scaled analysis, which could effectively detect the temporal complexity of a time series, was utilized to calculate the Hurst exponent (HE of functional magnetic resonance imaging (fMRI data at a voxel level from 64 MCI patients and 60 healthy controls (HCs. Then the average HE values of each region of interest (ROI in brainnetome atlas were extracted and compared between MCI and HC. At last, the abnormal average HE values were adopted as the classification features for a proposed support vector machine (SVM based identification algorithm, and the classification performance was estimated with leave-one-out cross-validation (LOOCV. Our results indicated 83.1% accuracy, 82.8% sensitivity and 83.3% specificity, and an area under curve of 0.88, suggesting that the HE index could serve as an effective feature for the MCI identification. Furthermore, the abnormal HE brain regions in MCI were predominately involved in left middle frontal gyrus, right hippocampus, bilateral parahippocampal gyrus, bilateral amygdala, left cingulate gyrus, left insular gyrus, left fusiform gyrus, left superior parietal gyrus, left orbital gyrus and left basal ganglia.
Diamagnetic susceptibility of a confined donor in inhomogeneous quantum dots
International Nuclear Information System (INIS)
Rahmani, K; Zorkani, I; Jorio, A
2011-01-01
The binding energy and diamagnetic susceptibility χ dia are estimated for a shallow donor confined to move in GaAs-GaAlAs inhomogeneous quantum dots. The calculation was performed within the effective mass approximation and using the variational method. The results show that the binding energy and the diamagnetic susceptibility χ dia depend strongly on the core radius and the shell radius. We have demonstrated that there is a critical value of the ratio of the inner radius to the outer radius which may be important for nanofabrication techniques. The binding energy E b shows a minimum for a critical value of this ratio depending on the value of the outer radius and shows a maximum when the donor is placed at the center of the spherical layer. The diamagnetic susceptibility is more sensitive to variations of the radius for a large spherical layer. The binding energy and diamagnetic susceptibility depend strongly on the donor position.
Temporal percolation of the susceptible network in an epidemic spreading.
Valdez, Lucas Daniel; Macri, Pablo Alejandro; Braunstein, Lidia Adriana
2012-01-01
In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity ΦS(t), namely, the probability that a given neighbor of a node is susceptible at time t, is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time t(c) above which the giant susceptible component is destroyed. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time t(c). Our theoretical results are confirmed by extensive simulations of the SIR process.
A-site deficiency effects on the critical behavior of La0.6Ca0.15·0.05Ba0.2MnO3
Debbebi, I. Sfifir; Omrani, H.; Cheikhrouhou-Koubaa, W.; Cheikhrouhou, A.
2018-02-01
The aim of the present work is to study the critical behavior of calcium deficient La0.6Ca0.15·0.05Ba0.2MnO3 (LCBMO), synthetized by the conventional solid-state reaction method, around the paramagnetic (PM)-ferromagnetic (FM) phase transition. X-ray diffraction revealed that these manganites crystallized in the orthorhombic structure with Pbnm space group. Then, the magnetic properties of this compound are discussed in detail, building on the magnetization and the susceptibility. The temperature dependence of magnetic susceptibility at higher temperature confirms the presence of the Griffiths phase above the Curie temperature which proves the existence of ferromagnetic clusters in the paramagnetic domain. Experimental results revealed that our sample exhibit a second-order magnetic phase transition. The estimated critical exponents derived from the magnetic data were estimated using various techniques such as modified Arrott plot, Kouvel-Fisher method, and critical magnetization isotherms M(TC, H). The obtained values are very close to those representative of the mean-field model (β = 0.547, γ = 1.23, and δ = 3.092 at an average TC = 201.74 K).
International Nuclear Information System (INIS)
Christensen, K.; Olami, Z.
1992-01-01
We present a two-dimensional continuous cellular automaton that is equivalent to a driven spring-block model. Both the conservation and the anisotropy in the model are controllable quantities. Above a critical level of conservation, the model exhibits self-organized criticality. The self-organization of this system and hence the critical exponents depend on the conservation and the boundary conditions. In the critical isotropic nonconservative phase, the exponents change continuously as a function of conservation. Furthermore, the exponents vary continuously when changing the boundary conditions smoothly. Consequently, there is no universality of the critical exponents. We discuss the relevance of this for earthquakes. Introducing anisotropy changes the scaling of the distribution function, but not the power-law exponent. We explore the phase diagram of this model. We find that at low conservation levels a localization transition occurs. We see two additional phase transitions. The first is seen when moving from the conservative into the nonconservative model. The second appears when passing from the anisotropic two-dimensional system to the purely one-dimensional system
Defect production in nonlinear quench across a quantum critical point.
Sen, Diptiman; Sengupta, K; Mondal, Shreyoshi
2008-07-04
We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.
Struzik, Zbigniew R.; van Wijngaarden, Willem J.
We introduce a special purpose cumulative indicator, capturing in real time the cumulative deviation from the reference level of the exponent h (local roughness, Hölder exponent) of the fetal heartbeat during labour. We verify that the indicator applied to the variability component of the heartbeat coincides with the fetal outcome as determined by blood samples. The variability component is obtained from running real time decomposition of fetal heartbeat into independent components using an adaptation of an oversampled Haar wavelet transform. The particular filters used and resolutions applied are motivated by obstetricial insight/practice. The methodology described has the potential for real-time monitoring of the fetus during labour and for the prediction of the fetal outcome, allerting the attending staff in the case of (threatening) hypoxia.
Directory of Open Access Journals (Sweden)
Gontijo Guilherme L.
2017-01-01
Full Text Available We report results concerning the fractal dimension of a air/fluid interface formed during the capillary rising of a fluid into a dense granular media. The system consists in a modified Hele-Shaw cell filled with grains at different granulometries and confined in a narrow gap between the glass plates. The system is then placed onto a water reservoir, and the liquid penetrates the medium due to capillary forces. We measure the Hurst exponent of the liquid/air interface with help of image processing, and follow the temporal evolution of the profiles. We observe that the Hurst exponent can be related with the granulometry, but the range of values are odd to the predicted values from models or theory.
Hu, D. L.; Liu, X. B.
Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non-Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.
Using the Hurst's exponent as a monitor and predictor of BWR reactor instabilities
International Nuclear Information System (INIS)
Gavilan Moreno, Carlos J.
2010-01-01
Since the decade of the 1950s, when the development of boiling water reactor technology began, unstable situations have existed, which involve a high amplitude self-oscillatory process in the reactor's thermal power. As the development progressed and the reactors increased power density, the possibility of instability under certain circumstances increased. Thus, in 1985, Caorso nuclear plant (Italy) reported the first event of this type, and in 1988, such an event was reported at La Salle as well. Since then, multiple instability events have been reported. The danger of these unstable power situations resides in the possibility of exceeding a thermal limit, as expressed in Appendix A of 10FR50. Thus, the need arises to monitor and correct these situations in the industry. The most common way to monitor and control these instability situations involves the use of Decay Ratio (DR) and Resonance Frequency (RF). The use of these parameters is polemical, because their use involves certain simplifications and operations prior to the calculation which question how well they represent the reality. The most important simplifications are those which lead to the interpretation of the power time series as the result of a second order system. With regard to the previous operations, the time series needs to be standardized and filtered. The result is loss of information during prediction, due to the operations, and the results, therefore, lack accuracy. In this paper, the system is considered without simplifications, that is to say that it is treated as dynamic and, as we shall see, chaotic, in the mathematical sense of the term. The series will be used in pure form without manipulations. The parameter used for monitoring and prediction of the core's behaviour will be the Hurst's exponent (H). The concept used for this proposal is that the response of a complex dynamic system depends not only on the last excitation, but on the prior history. The processes and systems are
International Nuclear Information System (INIS)
El-Nabulsi, Ahmad Rami
2009-01-01
Multidimensional fractional actionlike variational problem with time-dependent dynamical fractional exponents is constructed. Fractional Euler-Lagrange equations are derived and discussed in some details. The results obtained are used to explore some novel aspects of fractional quantum field theory where many interesting consequences are revealed, in particular the complexification of quantum field theory, in particular Dirac operators and the novel notion of 'mass without mass'.
P. E. S. N. Krishna Prasad; Pavan Kumar K; M. V. Ramakrishna; B. D. C. N. Prasad
2013-01-01
Biometrics is one of the primary key concepts of real application domains such as aadhar card, passport, pan card, etc. In such applications user can provide two to three biometrics patterns like face, finger, palm, signature, iris data, and so on. We considered face and finger patterns for encoding and then also for verification. Using this data we proposed a novel model for authentication in multimodal biometrics often called Context-Sensitive Exponent Associative Memory Mode...
Estimating the small-x exponent of the structure function g1NS from the Bjorken sum rule
International Nuclear Information System (INIS)
Knauf, Anke; Meyer-Hermann, Michael; Soff, Gerhard
2002-01-01
We present a new estimate of the exponent governing the small-x behavior of the nonsinglet structure function g 1 p-n derived under the assumption that the Bjorken sum rule is valid. We use the world wide average of α s and the NNNLO QCD corrections to the Bjorken sum rule. The structure function g 1 NS is found to be clearly divergent for small x
Nigmatullin, R. R.; Arbuzov, A. A.; Salehli, F.; Giz, A.; Bayrak, I.; Catalgil-Giz, H.
2007-01-01
For the first time we achieved incontestable evidence that the real process of dielectric relaxation during the polymerization reaction of polyvinylpyrrolidone (PVP) is described in terms of the fractional kinetic equations containing complex-power-law exponents. The possibility of the existence of the fractional kinetics containing non-integer complex-power-law exponents follows from the general theory of dielectric relaxation that has been suggested recently by one of the authors (R.R.N). Based on the physical/geometrical meaning of the fractional integral with complex exponents there is a possibility to develop a general theory of dielectric relaxation based on the self-similar (fractal) character of the reduced (averaged) microprocesses that take place in the mesoscale region. This theory contains some essential predictions related to existence of the non-integer power-law kinetics and the results of this paper can be considered as the first confirmation of existence of the kinetic phenomena that are described by fractional derivatives with complex-power-law exponents. We want to stress here that with the help of a new complex fitting function for the complex permittivity it becomes possible to describe the whole process for real and imaginary parts simultaneously throughout the admissible frequency range (30 Hz-13 MHz). The fitting parameters obtained for the complex permittivity function for three temperatures (70, 90 and 110 °C) confirm in general the picture of reaction that was known qualitatively before. They also reveal some new features, which improve the interpretation of the whole polymerization process. We hope that these first results obtained in the paper will serve as a good stimulus for other researches to find the traces of the existence of new fractional kinetics in other relaxation processes unrelated to the dielectric relaxation. These results should lead to the reconsideration and generalization of irreversibility and kinetic phenomena that
Competition-induced criticality in a model of meme popularity.
Gleeson, James P; Ward, Jonathan A; O'Sullivan, Kevin P; Lee, William T
2014-01-31
Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at criticality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent α<2, unlike preferential-attachment models), similar to those seen in empirical data.
Competition-Induced Criticality in a Model of Meme Popularity
Gleeson, James P.; Ward, Jonathan A.; O'Sullivan, Kevin P.; Lee, William T.
2014-01-01
Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at criticality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent α <2, unlike preferential-attachment models), similar to those seen in empirical data.
Monte Carlo computation of correlation times of independent relaxation modes at criticality
Bloete, H.W.J.; Nightingale, M.P.
2000-01-01
We investigate aspects of universality of Glauber critical dynamics in two dimensions. We compute the critical exponent $z$ and numerically corroborate its universality for three different models in the static Ising universality class and for five independent relaxation modes. We also present
Criticality of the anisotropic quantum Heisenberg model on a simple cubic lattice
International Nuclear Information System (INIS)
Mariz, A.M.; Santos, R.M.Z. dos; Tsallis, C.; Santos, R.R. dos.
1984-01-01
Within a Real Space Renormalization group framework, the criticality (phase diagram, and critical thermal and crossover exponents) of the spin 1/2 - anisotropic quantum Heisenberg ferromagnet on a simple cubic lattice is studied. The results obtained are in satisfactory agreement with known results whenever available. (Author) [pt
Criticality of the anisotropic quantum Heisenberg model on a simple cubic lattice
International Nuclear Information System (INIS)
Mariz, A.M.; Tsallis, C.; Santos, R.M.Z. dos; Santos, Raimundo R. dos.
1984-11-01
Within a Real Space Renormalization Group Framework, the criticality (phase diagram, and critical thermal and crossover exponents) of the spin 1/2 - anisotropic quantum Heisenberg ferromagnet on a simple cubic lattice is studied. The results obtained are in antisfactory agreement with known results whenever available. (Author) [pt
Apparent anomalous critical behaviour of superfluid helium 4 in porous medium
International Nuclear Information System (INIS)
Maynard, R.; Deutscher, G.
1989-01-01
The anomalous critical exponents of the superfluid 4 He density in silica aerogels is analysed by a simple model where the distribution of pore size is assumed to be very broad. The strong modification of the critical behaviour is related to the structure of the aerogels skeleton which is discussed in terms of a percolation or alternatively a hierarchical sponge model
Makarava, Natallia; Menz, Stephan; Theves, Matthias; Huisinga, Wilhelm; Beta, Carsten; Holschneider, Matthias
2014-10-01
Amoebae explore their environment in a random way, unless external cues like, e.g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.
Nastac, Gabriel; Labahn, Jeffrey W.; Magri, Luca; Ihme, Matthias
2017-09-01
Metrics used to assess the quality of large-eddy simulations commonly rely on a statistical assessment of the solution. While these metrics are valuable, a dynamic measure is desirable to further characterize the ability of a numerical simulation for capturing dynamic processes inherent in turbulent flows. To address this issue, a dynamic metric based on the Lyapunov exponent is proposed which assesses the growth rate of the solution separation. This metric is applied to two turbulent flow configurations: forced homogeneous isotropic turbulence and a turbulent jet diffusion flame. First, it is shown that, despite the direct numerical simulation (DNS) and large-eddy simulation (LES) being high-dimensional dynamical systems with O (107) degrees of freedom, the separation growth rate qualitatively behaves like a lower-dimensional dynamical system, in which the dimension of the Lyapunov system is substantially smaller than the discretized dynamical system. Second, a grid refinement analysis of each configuration demonstrates that as the LES filter width approaches the smallest scales of the system the Lyapunov exponent asymptotically approaches a plateau. Third, a small perturbation is superimposed onto the initial conditions of each configuration, and the Lyapunov exponent is used to estimate the time required for divergence, thereby providing a direct assessment of the predictability time of simulations. By comparing inert and reacting flows, it is shown that combustion increases the predictability of the turbulent simulation as a result of the dilatation and increased viscosity by heat release. The predictability time is found to scale with the integral time scale in both the reacting and inert jet flows. Fourth, an analysis of the local Lyapunov exponent is performed to demonstrate that this metric can also determine flow-dependent properties, such as regions that are sensitive to small perturbations or conditions of large turbulence within the flow field. Finally
Critical scaling of a jammed system after a quench of temperature.
Otsuki, Michio; Hayakawa, Hisao
2012-09-01
Critical behavior of soft repulsive particles after quench of temperature near the jamming transition is numerically investigated. It is found that the plateau of the mean-square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.
de Sousa, J. Ricardo; de Albuquerque, Douglas F.
1997-02-01
By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one ( N‧ = 1) and two ( N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and ε-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.
Local quantum thermal susceptibility
de Pasquale, Antonella; Rossini, Davide; Fazio, Rosario; Giovannetti, Vittorio
2016-09-01
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties originate from averaging procedures which smoothen out local details. While undoubtedly successful, elegant and formally correct, this approach carries over an operational problem, namely determining the precision at which such variables are inferred, when technical/practical limitations restrict our capabilities to local probing. Here we introduce the local quantum thermal susceptibility, a quantifier for the best achievable accuracy for temperature estimation via local measurements. Our method relies on basic concepts of quantum estimation theory, providing an operative strategy to address the local thermal response of arbitrary quantum systems at equilibrium. At low temperatures, it highlights the local distinguishability of the ground state from the excited sub-manifolds, thus providing a method to locate quantum phase transitions.
Topological Susceptibility from Slabs
Bietenholz, Wolfgang; Gerber, Urs
2015-01-01
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.
Topological susceptibility from slabs
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Forcrand, Philippe de [Institute for Theoretical Physics, ETH Zürich,CH-8093 Zürich (Switzerland); CERN, Physics Department, TH Unit, CH-1211 Geneva 23 (Switzerland); Gerber, Urs [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo,Edificio C-3, Apdo. Postal 2-82, Morelia, Michoacán, C.P. 58040 (Mexico)
2015-12-14
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ{sub t}. In principle it seems straightforward to measure χ{sub t} by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ{sub t} even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ{sub t}, as we demonstrate with numerical results for non-linear σ-models.
Local quantum thermal susceptibility
De Pasquale, Antonella; Rossini, Davide; Fazio, Rosario; Giovannetti, Vittorio
2016-01-01
Thermodynamics relies on the possibility to describe systems composed of a large number of constituents in terms of few macroscopic variables. Its foundations are rooted into the paradigm of statistical mechanics, where thermal properties originate from averaging procedures which smoothen out local details. While undoubtedly successful, elegant and formally correct, this approach carries over an operational problem, namely determining the precision at which such variables are inferred, when technical/practical limitations restrict our capabilities to local probing. Here we introduce the local quantum thermal susceptibility, a quantifier for the best achievable accuracy for temperature estimation via local measurements. Our method relies on basic concepts of quantum estimation theory, providing an operative strategy to address the local thermal response of arbitrary quantum systems at equilibrium. At low temperatures, it highlights the local distinguishability of the ground state from the excited sub-manifolds, thus providing a method to locate quantum phase transitions. PMID:27681458
Susceptibility to anchoring effects
Directory of Open Access Journals (Sweden)
Todd McElroy
2007-02-01
Full Text Available Previous research on anchoring has shown this heuristic to be a very robust psychological phenomenon ubiquitous across many domains of human judgment and decision-making. Despite the prevalence of anchoring effects, researchers have only recently begun to investigate the underlying factors responsible for how and in what ways a person is susceptible to them. This paper examines how one such factor, the Big-Five personality trait of openness-to-experience, influences the effect of previously presented anchors on participants' judgments. Our findings indicate that participants high in openness-to-experience were significantly more influenced by anchoring cues relative to participants low in this trait. These findings were consistent across two different types of anchoring tasks providing convergent evidence for our hypothesis.
Power spectral density and scaling exponent of high frequency global solar radiation sequences
Calif, Rudy; Schmitt, François G.; Huang, Yongxiang
2013-04-01
invariance: Iq(f) ~ f-?(q) , ?(q) is the scaling exponent. This allows to characterize the scaling behavior of a process: fractal or multifractal with intermittent properties. For q = 2, the Hilbert spectrum is defined. In this work, The data are collected at the University site of Guadeloupe, an island in the West Indies, located at 16°15 N latitude 60°30 W longitude. Our measurements sampled at 1 Hz were performed during one year period. The analyzed data present a power spectral density E(f) displaying a power law of the form E(f) ~ f-β with 1.6 ˜ β ˜ 2.2 for frequencies f ˜ 0.1 Hz, corresponding to time scales T × 10 s. Furthermore, global solar radiation data possesses multifractal properties. For comparison, other multifractal analysis techniques such as structure functions, MDFA, wavelet leaders are also used. This preliminary work set the basis for further investigation dedicated to simulate and forecast a sequence of solar energy fluctuation under different meteorological conditions, in the multifractal framework.
The critical properties of magnetic films
International Nuclear Information System (INIS)
Saber, M.; Ainane, A.; Essaoudi, I.; Miguel, J.J. de
2010-01-01
Within the framework of the transverse spin-1/2 Ising model and by using the effective field theory with a probability distribution technique that accounts for the self spin correlations, we have studied the critical properties of an L-layer film of simple cubic symmetry in which the exchanges strength are assumed to be different from the bulk values in N S surface layers. We derive and illustrate the expressions for the phase diagrams, order parameter profiles and susceptibility. In such films, the critical temperature can shift to either lower or higher temperature compared with the corresponding bulk value. We calculate also some magnetic properties of the film, such as the layer magnetizations, their averages and their profiles and the longitudinal susceptibility of the film. The film longitudinal susceptibility still diverges at the film critical temperature as does the bulk longitudinal susceptibility.
Thinking Critically about Critical Thinking
Mulnix, Jennifer Wilson
2012-01-01
As a philosophy professor, one of my central goals is to teach students to think critically. However, one difficulty with determining whether critical thinking can be taught, or even measured, is that there is widespread disagreement over what critical thinking actually is. Here, I reflect on several conceptions of critical thinking, subjecting…
New estimates on various critical/universal quantities of the 3d Ising model
International Nuclear Information System (INIS)
Hasenbusch, M.
1998-01-01
We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude σ 0 in the critical law σ=ρ 0 t μ , and for the universal combination R - =σξ 2 . Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A + /A - , together with the exponent α, the nonsingular background of energy and specific heat at criticality, together with the exponent ν. There are also results for the universal combination f s ξ 3 , where f s is the singular part of the free energy. (orig.)
1997-01-01
The objective of this work was to determine the three dimensional volumetric stress field, surface pressure distribution and actual contact area between a 0.50" square roller with different crown profiles and a flat raceway surface using Finite Element Analysis. The 3-dimensional stress field data was used in conjunction with several bearing fatigue life theories to extract appropriate values for stress-life exponents. Also, results of the FEA runs were used to evaluate the laminated roller model presently used for stress and life prediction.
Cleve, J.; Greiner, M.; Sreenivasan, K. R.
2003-03-01
The two-point correlation function of the energy dissipation, obtained from a one-point time record of an atmospheric boundary layer, reveals a rigorous power law scaling with intermittency exponent μ approx 0.20 over almost the entire inertial range of scales. However, for the related integral moment, the power law scaling is restricted to the upper part of the inertial range only. This observation is explained in terms of the operational surrogacy of the construction of energy dissipation, which influences the behaviour of the correlation function for small separation distances.
Discussion of Various Susceptibilities within Thermal and Dense Quantum Chromodynamics
International Nuclear Information System (INIS)
Xu Shu-Sheng; Shi Yuan-Mei; Yang You-Chang; Cui Zhu-Fang; Zong Hong-Shi
2015-01-01
It is commonly accepted that the system undergoes a crossover at high temperature and low chemical potential beyond the chiral limit case, and the properties of the crossover region are important for researchers to understand the nature of strong interacting matters of quantum chromodynamics (QCD). Since at present there is no exact order of parameters of the phase transitions beyond the chiral limit, QCD susceptibilities are widely used as indicators. In this work various susceptibilities are discussed in the framework of Dyson–Schwinger equations. The results show that different kinds of susceptibilities give the same critical end point, which is the bifurcation point of the crossover region and the first order phase transition line of QCD. Nevertheless, different pseudocritical points are found in the temperature axis. We think that defining a critical band is more suitable in the crossover region. (paper)
Nonlinear AC susceptibility, surface and bulk shielding
van der Beek, C. J.; Indenbom, M. V.; D'Anna, G.; Benoit, W.
1996-02-01
We calculate the nonlinear AC response of a thin superconducting strip in perpendicular field, shielded by an edge current due to the geometrical barrier. A comparison with the results for infinite samples in parallel field, screened by a surface barrier, and with those for screening by a bulk current in the critical state, shows that the AC response due to a barrier has general features that are independent of geometry, and that are significantly different from those for screening by a bulk current in the critical state. By consequence, the nonlinear (global) AC susceptibility can be used to determine the origin of magnetic irreversibility. A comparison with experiments on a Bi 2Sr 2CaCu 2O 8+δ crystal shows that in this material, the low-frequency AC screening at high temperature is mainly due to the screening by an edge current, and that this is the unique source of the nonlinear magnetic response at temperatures above 40 K.
Critical care helps people with life-threatening injuries and illnesses. It might treat problems such as complications from surgery, ... attention by a team of specially-trained health care providers. Critical care usually takes place in an ...
International Nuclear Information System (INIS)
Rentzsch, R.; Reich, Ch.; Ionov, A.N.; Ginodman, V.; Slimak, I.; Fozooni, P.; Lea, M.J.
1999-01-01
We present a critical review of the present status of the critical exponent puzzle of the metal-insulator transition of doped semiconductors with the emphasis on the role of meso- and macroscopy inhomogeneity caused by the disorder of acceptors and donors in the crystals. By using the isotopic and engineering and the neutron transmutation doping of germanium we found for low compensations (at K = 1.4 and 12%) that the critical exponents of the localization length and the dielectric constant are nearly ν = 1/2 and ξ = 1, which double for medium compensations (at K = 39 and 54%) to ν 1 and ξ = 2, respectively
Gene susceptibility in Iranian asthmatic patients: a narrative review ...
African Journals Online (AJOL)
As environmental factors are important in the development of asthma, genetic factors could have a critical role in the expression of the disease. Hence, we carried out a systematic review to assess the susceptible genes for asthma in Iranian population. We conducted a literature search by using the electronic database ...
CISH and susceptibility to infectious diseases.
Khor, Chiea C; Vannberg, Fredrik O; Chapman, Stephen J; Guo, Haiyan; Wong, Sunny H; Walley, Andrew J; Vukcevic, Damjan; Rautanen, Anna; Mills, Tara C; Chang, Kwok-Chiu; Kam, Kai-Man; Crampin, Amelia C; Ngwira, Bagrey; Leung, Chi-Chiu; Tam, Cheuk-Ming; Chan, Chiu-Yeung; Sung, Joseph J Y; Yew, Wing-Wai; Toh, Kai-Yee; Tay, Stacey K H; Kwiatkowski, Dominic; Lienhardt, Christian; Hien, Tran-Tinh; Day, Nicholas P; Peshu, Nobert; Marsh, Kevin; Maitland, Kathryn; Scott, J Anthony; Williams, Thomas N; Berkley, James A; Floyd, Sian; Tang, Nelson L S; Fine, Paul E M; Goh, Denise L M; Hill, Adrian V S
2010-06-03
The interleukin-2-mediated immune response is critical for host defense against infectious pathogens. Cytokine-inducible SRC homology 2 (SH2) domain protein (CISH), a suppressor of cytokine signaling, controls interleukin-2 signaling. Using a case-control design, we tested for an association between CISH polymorphisms and susceptibility to major infectious diseases (bacteremia, tuberculosis, and severe malaria) in blood samples from 8402 persons in Gambia, Hong Kong, Kenya, Malawi, and Vietnam. We had previously tested 20 other immune-related genes in one or more of these sample collections. We observed associations between variant alleles of multiple CISH polymorphisms and increased susceptibility to each infectious disease in each of the study populations. When all five single-nucleotide polymorphisms (SNPs) (at positions -639, -292, -163, +1320, and +3415 [all relative to CISH]) within the CISH-associated locus were considered together in a multiple-SNP score, we found an association between CISH genetic variants and susceptibility to bacteremia, malaria, and tuberculosis (P=3.8x10(-11) for all comparisons), with -292 accounting for most of the association signal (P=4.58x10(-7)). Peripheral-blood mononuclear cells obtained from adult subjects carrying the -292 variant, as compared with wild-type cells, showed a muted response to the stimulation of interleukin-2 production--that is, 25 to 40% less CISH expression. Variants of CISH are associated with susceptibility to diseases caused by diverse infectious pathogens, suggesting that negative regulators of cytokine signaling have a role in immunity against various infectious diseases. The overall risk of one of these infectious diseases was increased by at least 18% among persons carrying the variant CISH alleles. 2010 Massachusetts Medical Society
Polymyxins: Antimicrobial susceptibility concerns and therapeutic options
Directory of Open Access Journals (Sweden)
V Balaji
2011-01-01
Full Text Available The increasing prevalence of multidrug-resistant nosocomial pathogens such as Acinetobacter baumannii, Pseudomonas aeruginosa and Klebsiella pneumoniae poses a great challenge to the treating physicians. The paucity of newer effective antimicrobials has led to renewed interest in the polymyxin group of drugs, as a last resort for treatment of gram-negative bacterial infections. There is a dearth of information on the pharmacological properties of colistin, leading to difficulties in selecting the right dose, dosing interval, and route of administration for treatment, especially in critically-ill patients. The increasing use of colistin over the last few years necessitates the need for accurate and reliable in vitro susceptibility testing methods. Development of heteroresistant strains as a result of colistin monotherapy is also a growing concern. There is a compelling need from the clinicians to provide options for probable and possible colistin combination therapy for multidrug-resistant bacterial infections in the ICU setting. Newer combination drug synergy determination tests are being developed and reported. There are no standardized recommendations from antimicrobial susceptibility testing reference agencies for the testing and interpretation of these drug combinations. Comparison and analysis of these reported methodologies may help to understand and assist the microbiologist to choose the best method that produces accurate results at the earliest. This will help clinicians to select the appropriate combination therapy. In this era of multidrug resistance it is important for the microbiology laboratory to be prepared, by default, to provide timely synergistic susceptibility results in addition to routine susceptibility, if warranted. Not as a favour or at request, but as a responsibility.
CISH and Susceptibility to Infectious Diseases
Khor, Chiea C.; Vannberg, Fredrik O.; Chapman, Stephen J.; Guo, Haiyan; Wong, Sunny H.; Walley, Andrew J.; Vukcevic, Damjan; Rautanen, Anna; Mills, Tara C.; Chang, Kwok-Chiu; Kam, Kai-Man; Crampin, Amelia C.; Ngwira, Bagrey; Leung, Chi-Chiu; Tam, Cheuk-Ming; Chan, Chiu-Yeung; Sung, Joseph J.Y.; Yew, Wing-Wai; Toh, Kai-Yee; Tay, Stacey K.H.; Kwiatkowski, Dominic; Lienhardt, Christian; Hien, Tran-Tinh; Day, Nicholas P.; Peshu, Nobert; Marsh, Kevin; Maitland, Kathryn; Scott, J. Anthony; Williams, Thomas N.; Berkley, James A.; Floyd, Sian; Tang, Nelson L.S.; Fine, Paul E.M.; Goh, Denise L.M.; Hill, Adrian V.S.
2013-01-01
Background The interleukin-2 (IL2)-mediated immune response is critical for host defence against infectious pathogens. CISH, a suppressor of cytokine signalling, controls IL2 signalling. Methods We tested for association between CISH polymorphisms and susceptibility to major infectious diseases (bacteremia, tuberculosis and severe malaria) in 8402 persons from the Gambia, Hong Kong, Kenya, Malawi, and Vietnam using a case-control design. We have previously tested twenty other immune-related genes in one or more of these sample collections. Results We observed associations between variant alleles of multiple CISH polymorphisms and increased susceptibility to each infectious disease in each of the study populations. When all five SNPs (CISH −639, −292, −163, +1320 and +3415) within the CISH-associated locus were considered together in a multi-SNP score, we found substantial support for an effect of CISH genetic variants on susceptibility to bacteremia, malaria, and tuberculosis (overall P=3.8 × 10−11) with CISH −292 being “responsible” for the majority of the association signal (P=4.58×10−7). Peripheral blood mononuclear cells of adult volunteers carrying the CISH −292 variant showed a muted response to IL2 stimulation — in the form of 25-40% less CISH — when compared with “control” cells lacking the −292 variant. Conclusions Variants of CISH are associated with susceptibility to diseases caused by diverse infectious pathogens, suggesting that negative regulators of cytokine signalling may play a major role in immunity against various infectious diseases. The overall risk of having one of these infectious diseases was found to be increased by at least 18 percent in individuals carrying the variant CISH alleles. PMID:20484391
International Nuclear Information System (INIS)
Gritli, Hassène; Belghith, Safya
2015-01-01
Highlights: • A numerical calculation method of the Lyapunov exponents in the compass-gait model under OGY control is proposed. • A new linearization method of the impulsive hybrid dynamics around a one-periodic hybrid limit cycle is achieved. • We develop a simple analytical expression of a controlled hybrid Poincaré map. • A dimension reduction of the hybrid Poincaré map is realized. • We describe the numerical computation procedure of the Lyapunov exponents via the designed hybrid Poincaré map. - Abstract: This paper aims at providing a numerical calculation method of the spectrum of Lyapunov exponents in a four-dimensional impulsive hybrid nonlinear dynamics of a passive compass-gait model under the OGY control approach by means of a controlled hybrid Poincaré map. We present a four-dimensional simplified analytical expression of such hybrid map obtained by linearizing the uncontrolled impulsive hybrid nonlinear dynamics around a desired one-periodic passive hybrid limit cycle. In order to compute the spectrum of Lyapunov exponents, a dimension reduction of the controlled hybrid Poincaré map is realized. The numerical calculation of the spectrum of Lyapunov exponents using the reduced-dimension controlled hybrid Poincaré map is given in detail. In order to show the effectiveness of the developed method, the spectrum of Lyapunov exponents is calculated as the slope (bifurcation) parameter varies and hence used to predict the walking dynamics behavior of the compass-gait model under the OGY control.
Engineering Surface Critical Behavior of (2 +1 )-Dimensional O(3) Quantum Critical Points
Ding, Chengxiang; Zhang, Long; Guo, Wenan
2018-06-01
Surface critical behavior (SCB) refers to the singularities of physical quantities on the surface at the bulk phase transition. It is closely related to and even richer than the bulk critical behavior. In this work, we show that three types of SCB universality are realized in the dimerized Heisenberg models at the (2 +1 )-dimensional O(3) quantum critical points by engineering the surface configurations. The ordinary transition happens if the surface is gapped in the bulk disordered phase, while the gapless surface state generally leads to the multicritical special transition, even though the latter is precluded in classical phase transitions because the surface is in the lower critical dimension. An extraordinary transition is induced by the ferrimagnetic order on the surface of the staggered Heisenberg model, in which the surface critical exponents violate the results of the scaling theory and thus seriously challenge our current understanding of extraordinary transitions.
International Nuclear Information System (INIS)
Tao, Xiaoyi; Yin, Tianxiang; Xu, Chen; Shen, Weiguo
2017-01-01
Highlights: • Coexistence curve, heat capacity and turbidity measurements were performed. • RTIL solution showed solvophobic criticality. • Universal critical amplitude ratios were testified. • Asymmetric behavior of the diameter of coexistence curve was discussed. - Abstract: The liquid-liquid coexistence curve, heat capacity, and turbidity of binary solution {ethanol + butylpyridinium tetrafluoroborate]} have been precisely measured. The critical exponents and critical amplitudes corresponding to the heat capacity, width of coexistence curve, osmotic compressibility, and correlation length were obtained. The critical exponents and critical amplitude ratios showed well agreements with the theoretical values of the 3D-Ising universality class. The asymmetric behavior of the coexistence curve diameter was found to be well described by the complete scaling theory with the consideration of the heat capacity related term.
Directory of Open Access Journals (Sweden)
Pablo César Rodríguez Gómez
2017-05-01
Full Text Available Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis. Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior. Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed. Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system. Language: English
International Nuclear Information System (INIS)
Wang Jianzhou; Jia Ruiling; Zhao Weigang; Wu Jie; Dong Yao
2012-01-01
Highlights: ► The maximal predictive step size is determined by the largest Lyapunov exponent. ► A proper forecasting step size is applied to load demand forecasting. ► The improved approach is validated by the actual load demand data. ► Non-linear fractal extrapolation method is compared with three forecasting models. ► Performance of the models is evaluated by three different error measures. - Abstract: Precise short-term load forecasting (STLF) plays a key role in unit commitment, maintenance and economic dispatch problems. Employing a subjective and arbitrary predictive step size is one of the most important factors causing the low forecasting accuracy. To solve this problem, the largest Lyapunov exponent is adopted to estimate the maximal predictive step size so that the step size in the forecasting is no more than this maximal one. In addition, in this paper a seldom used forecasting model, which is based on the non-linear fractal extrapolation (NLFE) algorithm, is considered to develop the accuracy of predictions. The suitability and superiority of the two solutions are illustrated through an application to real load forecasting using New South Wales electricity load data from the Australian National Electricity Market. Meanwhile, three forecasting models: the gray model, the seasonal autoregressive integrated moving average approach and the support vector machine method, which received high approval in STLF, are selected to compare with the NLFE algorithm. Comparison results also show that the NLFE model is outstanding, effective, practical and feasible.
[Antimicrobial susceptibility in Chile 2012].
Cifuentes-D, Marcela; Silva, Francisco; García, Patricia; Bello, Helia; Briceño, Isabel; Calvo-A, Mario; Labarca, Jaime
2014-04-01
Bacteria antimicrobial resistance is an uncontrolled public health problem that progressively increases its magnitude and complexity. The Grupo Colaborativo de Resistencia, formed by a join of experts that represent 39 Chilean health institutions has been concerned with bacteria antimicrobial susceptibility in our country since 2008. In this document we present in vitro bacterial susceptibility accumulated during year 2012 belonging to 28 national health institutions that represent about 36% of hospital discharges in Chile. We consider of major importance to report periodically bacteria susceptibility so to keep the medical community updated to achieve target the empirical antimicrobial therapies and the control measures and prevention of the dissemination of multiresistant strains.
Kwon, Sungchul; Kim, Yup
2013-01-01
We investigate epidemic spreading in annealed directed scale-free networks with the in-degree (k) distribution P(in)(k)~k(-γ(in)) and the out-degree (ℓ) distribution, P(out)(ℓ)~ℓ(-γ(out)). The correlation of each node on the networks is controlled by the probability r(0≤r≤1) in two different algorithms, the so-called k and ℓ algorithms. For r=1, the k algorithm gives =, whereas the ℓ algorithm gives =. For r=0, = for both algorithms. As the prototype of epidemic spreading, the susceptible-infected-susceptible model and contact process on the networks are analyzed using the heterogeneous mean-field theory and Monte Carlo simulations. The directedness of links and the correlation of the network are found to play important roles in the spreading, so that critical behaviors of both models are distinct from those on undirected scale-free networks.
Low-temperature approach to the renormalization-group study of critical phenomena
International Nuclear Information System (INIS)
Suranyi, P.
1977-01-01
A new method of exploring the contents of the renormalization-group equations for discrete spins is introduced. The equations are expanded in low-temperature series and the truncated series are used to obtain the critical exponents and critical temperature of a system. The method is demonstrated on the planar triangular Ising lattice and the critical parameters are found to be within a few percent of the exactly known values in third nonvanishing order of approximation
How Critical Is Critical Thinking?
Shaw, Ryan D.
2014-01-01
Recent educational discourse is full of references to the value of critical thinking as a 21st-century skill. In music education, critical thinking has been discussed in relation to problem solving and music listening, and some researchers suggest that training in critical thinking can improve students' responses to music. But what exactly is…
Critical behavior in a microcanonical multifragmentation model
International Nuclear Information System (INIS)
Raduta, A.H.; Raduta, A.R.; Chomaz, Ph.; Raduta, A.H.; Raduta, A.R.; Gulminelli, F.
2001-01-01
Scaling properties of the fragment size distributions are studied in a microcanonical multifragmentation model. A new method based on the global quality of the scaling function is presented. Scaling is not washed out by the long range Coulomb interaction nor by secondary decays for a wide range of source masses, densities and deposited energies. However, the influence of these factors on precise value of the critical exponents as well as the finite size corrections to scaling are shown to be important and to affect the possible determination of a specific universality class. (authors)
Critical acceleration of finite temperature SU(2) gauge simulations
International Nuclear Information System (INIS)
Ben-Av, R.; Marcu, M.; Hamburg Univ.; Solomon, S.
1991-04-01
We present a cluster algorithm that strongly reduces critical slowing down for the SU(2) gauge theory on one time slice. The idea that underlies the new algorithm is to perform efficient flips for the signs of Polyakov loops. Ergodicity is ensured by combining it with a standard local algorithm. We show how to quantify critical slowing down for such a mixed algorithm. At the finite temperature transition, the dynamical critical exponent z is ≅0.5, whereas for the purely local algoirthm z ≅ 2. (orig.)
Square-lattice random Potts model: criticality and pitchfork bifurcation
International Nuclear Information System (INIS)
Costa, U.M.S.; Tsallis, C.
1983-01-01
Within a real space renormalization group framework based on self-dual clusters, the criticality of the quenched bond-mixed q-state Potts ferromagnet on square lattice is discussed. On qualitative grounds it is exhibited that the crossover from the pure fixed point to the random one occurs, while q increases, through a pitchfork bifurcation; the relationship with Harris criterion is analyzed. On quantitative grounds high precision numerical values are presented for the critical temperatures corresponding to various concentrations of the coupling constants J 1 and J 2 , and various ratios J 1 /J 2 . The pure, random and crossover critical exponents are discussed as well. (Author) [pt
Einstein, Theodore L.; Pimpinelli, Alberto; González, Diego Luis; Morales-Cifuentes, Josue R.
2015-09-01
In studies of epitaxial growth, analysis of the distribution of the areas of capture zones (i.e. proximity polygons or Voronoi tessellations with respect to island centers) is often the best way to extract the critical nucleus size i. For non-random nucleation the normalized areas s of these Voronoi cells are well described by the generalized Wigner distribution (GWD) Pβ(s) = asβ exp(-bs2), particularly in the central region 0.5 < s < 2 where data are least noisy. Extensive Monte Carlo simulations reveal inadequacies of our earlier mean field analysis, suggesting β = i + 2 for diffusion-limited aggregation (DLA). Since simulations generate orders of magnitude more data than experiments, they permit close examination of the tails of the distribution, which differ from the simple GWD form. One refinement is based on a fragmentation model. We also compare island-size distributions. We compare analysis by island-size distribution and by scaling of island density with flux. Modifications appear for attach-limited aggregation (ALA). We focus on the experimental system para-hexaphenyl on amorphous mica, comparing the results of the three analysis techniques and reconciling their results via a novel model of hot precursors based on rate equations, pointing out the existence of intermediate scaling regimes between DLA and ALA.
Ancestral susceptibility to colorectal cancer
Czech Academy of Sciences Publication Activity Database
Huhn, S.; Pardini, Barbara; Naccarati, Alessio; Vodička, Pavel (ed.); Hemminki, K.; Försti, A.
2012-01-01
Roč. 27, č. 2 (2012), s. 197-204 ISSN 0267-8357 R&D Projects: GA ČR GA310/07/1430; GA ČR GAP304/10/1286 Grant - others:EU FP7(XE) HEALTH-F4-2007-200767 Institutional research plan: CEZ:AV0Z50390512 Keywords : cancer susceptibility * molecular epidemiology * genetic susceptibility Subject RIV: EB - Genetics ; Molecular Biology Impact factor: 3.500, year: 2012
Directory of Open Access Journals (Sweden)
Pippin Barr
2016-11-01
Full Text Available Games can serve a critical function in many different ways, from serious games about real world subjects to self-reflexive commentaries on the nature of games themselves. In this essay we discuss critical possibilities stemming from the area of critical design, and more specifically Carl DiSalvo’s adversarial design and its concept of reconfiguring the remainder. To illustrate such an approach, we present the design and outcomes of two games, Jostle Bastard and Jostle Parent. We show how the games specifically engage with two previous games, Hotline Miami and Octodad: Dadliest Catch, reconfiguring elements of those games to create interactive critical experiences and extensions of the source material. Through the presentation of specific design concerns and decisions, we provide a grounded illustration of a particular critical function of videogames and hope to highlight this form as another valuable approach in the larger area of videogame criticism.
Simon, Jane
2010-01-01
This essay considers how written language frames visual objects. Drawing on Michel Foucault’s response to Raymond Roussel’s obsessive description, the essay proposes a model of criticism where description might press up against its objects. This critical closeness is then mapped across the conceptual art practice and art criticism of Ian Burn. Burn attends to the differences between seeing and reading, and considers the conditions which frame how we look at images, including how w...
International Nuclear Information System (INIS)
Alsaed, A.
2004-01-01
The ''Disposal Criticality Analysis Methodology Topical Report'' (YMP 2003) presents the methodology for evaluating potential criticality situations in the monitored geologic repository. As stated in the referenced Topical Report, the detailed methodology for performing the disposal criticality analyses will be documented in model reports. Many of the models developed in support of the Topical Report differ from the definition of models as given in the Office of Civilian Radioactive Waste Management procedure AP-SIII.10Q, ''Models'', in that they are procedural, rather than mathematical. These model reports document the detailed methodology necessary to implement the approach presented in the Disposal Criticality Analysis Methodology Topical Report and provide calculations utilizing the methodology. Thus, the governing procedure for this type of report is AP-3.12Q, ''Design Calculations and Analyses''. The ''Criticality Model'' is of this latter type, providing a process evaluating the criticality potential of in-package and external configurations. The purpose of this analysis is to layout the process for calculating the criticality potential for various in-package and external configurations and to calculate lower-bound tolerance limit (LBTL) values and determine range of applicability (ROA) parameters. The LBTL calculations and the ROA determinations are performed using selected benchmark experiments that are applicable to various waste forms and various in-package and external configurations. The waste forms considered in this calculation are pressurized water reactor (PWR), boiling water reactor (BWR), Fast Flux Test Facility (FFTF), Training Research Isotope General Atomic (TRIGA), Enrico Fermi, Shippingport pressurized water reactor, Shippingport light water breeder reactor (LWBR), N-Reactor, Melt and Dilute, and Fort Saint Vrain Reactor spent nuclear fuel (SNF). The scope of this analysis is to document the criticality computational method. The criticality
Evidence for criticality in financial data
Ruiz, G.; de Marcos, A. F.
2018-01-01
We provide evidence that cumulative distributions of absolute normalized returns for the 100 American companies with the highest market capitalization, uncover a critical behavior for different time scales Δt. Such cumulative distributions, in accordance with a variety of complex - and financial - systems, can be modeled by the cumulative distribution functions of q-Gaussians, the distribution function that, in the context of nonextensive statistical mechanics, maximizes a non-Boltzmannian entropy. These q-Gaussians are characterized by two parameters, namely ( q, β), that are uniquely defined by Δt. From these dependencies, we find a monotonic relationship between q and β, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality.
Characterizing critical phenomena via the Purcell effect
Silva Neto, M. B.; Szilard, D.; Rosa, F. S. S.; Farina, C.; Pinheiro, F. A.
2017-12-01
We investigate the role of phase transitions into the spontaneous-emission rate of a single quantum emitter embedded in a critical medium. Using a Landau-Ginzburg approach, we find that in the broken symmetry phase, the emission rate is reduced, or even suppressed, due to the photon mass generated by the Higgs mechanism. Remarkably, its sensitivity to the critical exponents of the phase transition allows for an optical determination of universality classes. When applied to the cases of superconductivity and superfluidity, we show that the Purcell effect also provides valuable information on spectroscopic and thermodynamic quantities, such as the size of the superconducting gap and the discontinuity in the specific heat at the transition. By unveiling that a deeper connection between the Purcell effect and phase transitions exists, we demonstrate that the former is an efficient optical probe of distinct critical phenomena and their associated observables.
Universal signatures of fractionalized quantum critical points.
Isakov, Sergei V; Melko, Roger G; Hastings, Matthew B
2012-01-13
Ground states of certain materials can support exotic excitations with a charge equal to a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive unusual quantum phase transitions. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly nonclassical critical exponent η = 1.493 and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z(2) gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.
Healthcare disparities in critical illness.
Soto, Graciela J; Martin, Greg S; Gong, Michelle Ng
2013-12-01
To summarize the current literature on racial and gender disparities in critical care and the mechanisms underlying these disparities in the course of acute critical illness. MEDLINE search on the published literature addressing racial, ethnic, or gender disparities in acute critical illness, such as sepsis, acute lung injury, pneumonia, venous thromboembolism, and cardiac arrest. Clinical studies that evaluated general critically ill patient populations in the United States as well as specific critical care conditions were reviewed with a focus on studies evaluating factors and contributors to health disparities. Study findings are presented according to their association with the prevalence, clinical presentation, management, and outcomes in acute critical illness. This review presents potential contributors for racial and gender disparities related to genetic susceptibility, comorbidities, preventive health services, socioeconomic factors, cultural differences, and access to care. The data are organized along the course of acute critical illness. The literature to date shows that disparities in critical care are most likely multifactorial involving individual, community, and hospital-level factors at several points in the continuum of acute critical illness. The data presented identify potential targets as interventions to reduce disparities in critical care and future avenues for research.
Adolescent Susceptibility to Peer Influence in Sexual Situations.
Widman, Laura; Choukas-Bradley, Sophia; Helms, Sarah W; Prinstein, Mitchell J
2016-03-01
One consistent predictor of adolescents' engagement in sexual risk behavior is their belief that peers are engaging in similar behavior; however, not all youth are equally susceptible to these peer influence effects. Understanding individual differences in susceptibility to peer influence is critical to identifying adolescents at risk for negative health outcomes. The purpose of this project was to identify predictors of susceptibility to peer influence using a novel performance-based measure of sexual risk taking. Participants were 300 early adolescents (Mage = 12.6 years; 53% female; 44% Caucasian) who completed (1) a pretest assessment of demographics, sexual attitudes, and hypothetical scenarios measuring the likelihood of engaging in sexual risk behavior and (2) a subsequent experimental procedure that simulated an Internet chat room in which youth believed that they were communicating with peers regarding these same hypothetical scenarios. In reality, these "peers" were computer-programmed e-confederates. Changes in responses to the sexual scenarios in the private pretest versus during the public chat room provided a performance-based measure of peer influence susceptibility. In total, 78% of youth provided more risky responses in the chat room than those in pretest. The most robust predictor of this change was gender, with boys significantly more susceptible to peer influence than girls. Significant interactions also were noted, with greater susceptibility among boys with later pubertal development and African-American boys. Results confirm that not all youth are equally susceptible to peer influence. Consistent with sexual script theory, boys evidence greater susceptibility to social pressure regarding sexual behavior than girls. Copyright © 2016 Society for Adolescent Health and Medicine. Published by Elsevier Inc. All rights reserved.
Susceptibility analysis of landslide in Chittagong City Corporation Area, Bangladesh
Directory of Open Access Journals (Sweden)
Sourav Das
2015-06-01
Full Text Available In Chittagong city, landslide phenomena is the most burning issue which causes great problems to the life and properties and it is increasing day by day and becoming one of the main problems of city life. On 11 June 2007, a massive landslide happened in Chittagong City Corporation (CCC area, a large number of foothill settlements and slums were demolished; more than 90 people died and huge resource destruction took place. It is therefore essential to analyze the landslide susceptibility for CCC area to prepare mitigation strategies as well as assessing the impacts of climate change. To assess community susceptibility of landslide hazard, a landslide susceptibility index map has been prepared using analytical hierarchy process (AHP model based on geographic information system (GIS and remote sensing (RS and its susceptibility is analyzed through community vulnerability assessment tool (CVAT. The major findings of the research are 27% of total CCC area which is susceptible to landslide hazard and whereas 6.5 sq.km areas are found very highly susceptible. The landslide susceptible areas of CCC have also been analyzed in respect of physical, social, economic, environmental and critical facilities and it is found that the overall CCC area is highly susceptible to landslide hazard. So the findings of the research can be utilized to prioritize risk mitigation investments, measures to strengthen the emergency preparedness and response mechanisms for reducing the losses and damages due to future landslide events. DOI: http://dx.doi.org/10.3126/ije.v4i2.12635 International Journal of Environment Vol.4(2 2015: 157-181
Quantum criticality of one-dimensional multicomponent Fermi gas with strongly attractive interaction
International Nuclear Information System (INIS)
He, Peng; Jiang, Yuzhu; Guan, Xiwen; He, Jinyu
2015-01-01
Quantum criticality of strongly attractive Fermi gas with SU(3) symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations. The phase transitions driven by the chemical potential μ, effective magnetic field H 1 , H 2 (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the TBA equations in the zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent z=2 and correlation length exponent ν=1/2 read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multicomponent Fermi gases with SU(N) symmetry. (paper)
The U(1)-Higgs model: critical behaviour in the confining-Higgs region
International Nuclear Information System (INIS)
Alonso, J.L.; Azcoiti, V.; Campos, I.; Ciria, J.C.; Cruz, A.; Iniguez, D.; Lesmes, F.; Piedrafita, C.; Rivero, A.; Tarancon, A.; Badoni, D.; Fernandez, L.A.; Munoz Sudupe, A.; Ruiz-Lorenzo, J.J.; Gonzalez-Arroyo, A.; Martinez, P.; Pech, J.; Tellez, P.
1993-01-01
We study numerically the critical properties of the U(1)-Higgs lattice model, with fixed Higgs modulus, in the region of small gauge coupling where the Higgs and confining phases merge. We find evidence for a first-order transition line that ends in a second-order point. By means of a rotation in parameter space we introduce thermodynamic magnitudes and critical exponents in close resemblance with simple models that show analogous critical behaviour. The measured data allow us to fit the critical exponents finding values in agreement with the mean-field prediction. The location of the critical point and the slope of the first-order line are accurately measured. (orig.)
Niu, Qifei; Zhang, Chi
2018-02-01
The empirical Archie's law has been widely used in geosciences and engineering to explain the measured electrical resistivity of many geological materials, but its physical basis has not been fully understood yet. In this study, we use a pore-scale numerical approach combining discrete element-finite difference methods to study Archie's porosity exponent m of granular materials over a wide porosity range. Numerical results reveal that at dilute states (e.g., porosity ϕ > 65%), m is exclusively related to the particle shape and orientation. As the porosity decreases, the electric flow in pore space concentrates progressively near particle contacts and m increases continuously in response to the intensified nonuniformity of the local electrical field. It is also found that the increase in m is universally correlated with the volume fraction of pore throats for all the samples regardless of their particle shapes, particle size range, and porosities.
Directory of Open Access Journals (Sweden)
Ana-Maria CALOMFIR (METESCU
2015-12-01
Full Text Available In recent years, research in the capital markets and management of portfolios has been producing more questions than it has been answering: the need for a new paradigm or a new way of looking at things has become more and more concludent. The existing and classical view of capital markets, based on efficient market hypothesis, has a definite theory for the last six decades, but it is still not capable of significantly increase the understanding of how capital markets function. The purpose of this article is to theoretically describe a less used statistic coefficient, having a vast area of applicability due to its robustness, and which can easily divide the random series from a non-random series, even if the random series is non-Gaussian: the Hurst exponent.
Directory of Open Access Journals (Sweden)
Saša Horvat
2018-02-01
Full Text Available The aim of this study was evaluation of cognitive complexity of tasks for the topic hydrogen exponent in the solutions of acids and bases and its validation. The created procedure included an assessment of the difficulty of concepts and an assessment of their interactivity. There were 48 freshmen students enrolled in the study program Basic academic studies in chemistry. As a research instrument for assessing performance, test of knowledge was specifically constructed for this research. Each task in the test was followed by a seven-point Likert scale for the evaluation of invested mental effort. The evaluation of cognitive complexity was confirmed by a series of linear regression analysis where high values of correlation coefficients are obtained among the examined variables: student’s performance and invested mental effort (dependent variables and cognitive complexity (independent variable.
Cristescu, Constantin P.; Stan, Cristina; Scarlat, Eugen I.; Minea, Teofil; Cristescu, Cristina M.
2012-04-01
We present a novel method for the parameter oriented analysis of mutual correlation between independent time series or between equivalent structures such as ordered data sets. The proposed method is based on the sliding window technique, defines a new type of correlation measure and can be applied to time series from all domains of science and technology, experimental or simulated. A specific parameter that can characterize the time series is computed for each window and a cross correlation analysis is carried out on the set of values obtained for the time series under investigation. We apply this method to the study of some currency daily exchange rates from the point of view of the Hurst exponent and the intermittency parameter. Interesting correlation relationships are revealed and a tentative crisis prediction is presented.
Cook, G C
2002-06-01
The "pavilion plan" for hospital design originated in France in the 18th century and was popularised in England by John Roberton and George Godwin in the mid-19th century; the underlying rationale was that with improved ventilation the mortality rate (at that time exceedingly high) was significantly reduced. Among the enthusiasts for this new style was Florence Nightingale (herself a miasmatist)--who had experienced astronomically high death rates in the hospital at Scutari during the Crimean War (1854-6). One of the leading exponents of this style of hospital architecture was Henry Currey (1820-1900) whose greatest achievement was undoubtedly the design for the new St Thomas's Hospital on the Lambeth Palace Road.
Energy Technology Data Exchange (ETDEWEB)
Kamei, T [Kiso Jiban Consultants Co. Ltd., Tokyo (Japan); Tokida, M [Nagano National College of Technology, Nagano (Japan)
1994-12-21
Because there is a report example that the yield stress of a landslide clay increases along with a decrease of a hydrogen-ion concentration exponent, it is thought that a shear strength of the landslide clay depends on the hydrogen-ion concentration exponent. Furthermore, when the soil stabilization method by lime is applied to the soft ground and high organic earth, it is pointed out that the hydrogen-ion concentration exponent will become one of the harmful factors. Accordingly, it is understood that revealing an influence of a hydrogen-ion concentration exponent affects on the characteristics of an earth is one of the important factors, to evaluate a strength, deformation and so forth of the viscous ground. In this study, in order to examine an influence of a hydrogen-ion concentration exponent affecting on an undrained shear behavior of the bentonites, for the artificially adjusted bentonite specimens with 5 kinds of different pH, the isotropic consolidated undrained triaxial compression tests were performed, and consequently an influence of pH affecting on the engineering characteristics of the bentonites was made clear quantitatively. 28 refs., 16 figs., 5 tabs.
DEFF Research Database (Denmark)
Rosenbaum, Ralph K.; Olsen, Stig Irving
2018-01-01
Manipulation and mistakes in LCA studies are as old as the tool itself, and so is its critical review. Besides preventing misuse and unsupported claims, critical review may also help identifying mistakes and more justifiable assumptions as well as generally improve the quality of a study. It thus...... supports the robustness of an LCA and increases trust in its results and conclusions. The focus of this chapter is on understanding what a critical review is, how the international standards define it, what its main elements are, and what reviewer qualifications are required. It is not the objective...... of this chapter to learn how to conduct a critical review, neither from a reviewer nor from a practitioner perspective. The foundation of this chapter and the basis for any critical review of LCA studies are the International Standards ISO 14040:2006, ISO 14044:2006 and ISO TS 14071:2014....
Natural hazards and self-organized criticality
International Nuclear Information System (INIS)
Krenn, R.
2012-01-01
Several natural hazards exhibit power-law behavior on their frequency-size distributions. Self-organized criticality has become a promising candidate that could offer a more in-depth understanding of the origin of temporal and spatial scaling in dissipative nonequilibrium systems. The outcomes of this thesis are presented in three scientific papers followed by a concluding summary and an appendix.In paper (A) we present a semi-phenomenological approach to explain the complex scaling behavior of the Drossel-Schwabl forest-fire model (DS-FFM) in two dimensions. We derive the scaling exponent solely from the scaling exponent of the clusters' accessible perimeter. Furthermore, the unusual transition to an exponential decay is explained both qualitatively and quantitatively. The exponential decay itself could be reproduced at least qualitatively. In paper (B) we extend the DS-FFM towards anthropogenic ignition factors. The main outcomes are an increase of the scaling exponent with decreasing lightning probability as well as a splitting of the partial frequency-size distributions of lightning induced and man made fires. Lightning is identified as the dominant mechanism in the regime of the largest fires. The results could be validated through an analysis of the Canadian Large Fire Database.In paper (C) we obtain an almost complete theory of the Olami-Feder-Christensen (OFC) model's complex spatio-temporal behavior. Synchronization pushes the system towards a critical state and generates the Gutenberg-Richter law. Desynchronization prevents the system from becoming overcritical and generates foreshocks and aftershocks. Our approach also provides a simple explanation of Omori's law. Beyond this, it explains the phenomena of foreshock migration and aftershock diffusion and the occurrence of large earthquakes without any foreshocks. A novel integer algorithm for the numerics is presented in appendix (A).(author) [de
Study on non-universal critical behaviour in Ising model with defects
International Nuclear Information System (INIS)
Guimaraes, L.G.
1986-01-01
One-dimensional quantum analogous of two-dimensional Ising models with line and step type linear defects are studied. The phenomenological renormalization group was approached using conformal invariance for relating critical exponent N sup(*) sub(H). Aiming to obtain the Hamiltonian diagonal, Lanczos tridiagonal method was used. (H.C.K.)
Susceptibility Genes in Thyroid Autoimmunity
Directory of Open Access Journals (Sweden)
Yoshiyuki Ban
2005-01-01
Full Text Available The autoimmune thyroid diseases (AITD are complex diseases which are caused by an interaction between susceptibility genes and environmental triggers. Genetic susceptibility in combination with external factors (e.g. dietary iodine is believed to initiate the autoimmune response to thyroid antigens. Abundant epidemiological data, including family and twin studies, point to a strong genetic influence on the development of AITD. Various techniques have been employed to identify the genes contributing to the etiology of AITD, including candidate gene analysis and whole genome screening. These studies have enabled the identification of several loci (genetic regions that are linked with AITD, and in some of these loci, putative AITD susceptibility genes have been identified. Some of these genes/loci are unique to Graves' disease (GD and Hashimoto's thyroiditis (HT and some are common to both the diseases, indicating that there is a shared genetic susceptibility to GD and HT. The putative GD and HT susceptibility genes include both immune modifying genes (e.g. HLA, CTLA-4 and thyroid specific genes (e.g. TSHR, Tg. Most likely, these loci interact and their interactions may influence disease phenotype and severity.
Thermal-neutron multiple scattering: critical double scattering
International Nuclear Information System (INIS)
Holm, W.A.
1976-01-01
A quantum mechanical formulation for multiple scattering of thermal-neutrons from macroscopic targets is presented and applied to single and double scattering. Critical nuclear scattering from liquids and critical magnetic scattering from ferromagnets are treated in detail in the quasielastic approximation for target systems slightly above their critical points. Numerical estimates are made of the double scattering contribution to the critical magnetic cross section using relevant parameters from actual experiments performed on various ferromagnets. The effect is to alter the usual Lorentzian line shape dependence on neutron wave vector transfer. Comparison with corresponding deviations in line shape resulting from the use of Fisher's modified form of the Ornstein-Zernike spin correlations within the framework of single scattering theory leads to values for the critical exponent eta of the modified correlations which reproduce the effect of double scattering. In addition, it is shown that by restricting the range of applicability of the multiple scattering theory from the outset to critical scattering, Glauber's high energy approximation can be used to provide a much simpler and more powerful description of multiple scattering effects. When sufficiently close to the critical point, it provides a closed form expression for the differential cross section which includes all orders of scattering and has the same form as the single scattering cross section with a modified exponent for the wave vector transfer
Myopes show increased susceptibility to nearwork aftereffects.
Ciuffreda, K J; Wallis, D M
1998-09-01
Some aspects of accommodation may be slightly abnormal (or different) in myopes, compared with accommodation in emmetropes and hyperopes. For example, the initial magnitude of accommodative adaptation in the dark after nearwork is greatest in myopes. However, the critical test is to assess this initial accommodative aftereffect and its subsequent decay in the light under more natural viewing conditions with blur-related visual feedback present, if a possible link between this phenomenon and clinical myopia is to be considered. Subjects consisted of adult late- (n = 11) and early-onset (n = 13) myopes, emmetropes (n = 11), and hyperopes (n = 9). The distance-refractive state was assessed objectively using an autorefractor immediately before and after a 10-minute binocular near task at 20 cm (5 diopters [D]). Group results showed that myopes were most susceptible to the nearwork aftereffect. It averaged 0.35 D in initial magnitude, with considerably faster posttask decay to baseline in the early-onset (35 seconds) versus late-onset (63 seconds) myopes. There was no myopic aftereffect in the remaining two refractive groups. The myopes showed particularly striking accommodatively related nearwork aftereffect susceptibility. As has been speculated and found by many others, transient pseudomyopia may cause or be a precursor to permanent myopia or myopic progression. Time-integrated increased retinal defocus causing axial elongation is proposed as a possible mechanism.
High-order nonlinear susceptibilities of He
International Nuclear Information System (INIS)
Liu, W.C.; Clark, C.W.
1996-01-01
High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. The authors have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s, within the framework of Rayleigh=Schroedinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Ponte and Shakeshaft, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used; the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals
African Journals Online (AJOL)
both formal and informal) in culture and social theory. CRITICAL ARTS aims to challenge and ... Book Review: Brian McNair, An Introduction to Political Communication (3rd edition), London: Routledge, 2003, ISBN 0415307082, 272pp. Phil Joffe ...
Directory of Open Access Journals (Sweden)
Jane Simon
2010-09-01
Full Text Available This essay considers how written language frames visual objects. Drawing on Michel Foucault’s response to Raymond Roussel’s obsessive description, the essay proposes a model of criticism where description might press up against its objects. This critical closeness is then mapped across the conceptual art practice and art criticism of Ian Burn. Burn attends to the differences between seeing and reading, and considers the conditions which frame how we look at images, including how we look at, and through words. The essay goes on to consider Meaghan Morris’s writing on Lynn Silverman’s photographs. Both Morris and Burn offer an alternative to a parasitic model of criticism and enact a patient way of looking across and through visual landscapes.
Directory of Open Access Journals (Sweden)
Simon, Jane
2010-01-01
Full Text Available This essay considers how written language frames visual objects. Drawing on Michel Foucault’s response to Raymond Roussel’s obsessive description, the essay proposes a model of criticism where description might press up against its objects. This critical closeness is then mapped across the conceptual art practice and art criticism of Ian Burn. Burn attends to the differences between seeing and reading, and considers the conditions which frame how we look at images, including how we look at, and through words. The essay goes on to consider Meaghan Morris’s writing on Lynn Silverman’s photographs. Both Morris and Burn offer an alternative to a parasitic model of criticism and enact a patient way of looking across and through visual landscapes.
Two-dimensional fractal geometry, critical phenomena and conformal invariance
International Nuclear Information System (INIS)
Duplantier, B.
1988-01-01
The universal properties of critical geometrical systems in two-dimensions (2D) like the O (n) and Potts models, are described in the framework of Coulomb gas methods and conformal invariance. The conformal spectrum of geometrical critical systems obtained is made of a discrete infinite series of scaling dimensions. Specific applications involve the fractal properties of self-avoiding walks, percolation clusters, and also some non trivial critical exponents or fractal dimensions associated with subsets of the planar Brownian motion. The statistical mechanics of the same critical models on a random 2D lattice (namely in presence of a critically-fluctuating metric, in the so-called 2D quantum gravity) is also addressed, and the above critical geometrical systems are shown to be exactly solvable in this case. The new ''gravitational'' conformal spectrum so derived is found to satisfy the recent Knizhnik, Polyakov and Zamolodchikov quadratic relation which links it to the standard conformal spectrum in the plane
Critical Behavior of Light in Mode-Locked Lasers
Weill, Rafi; Rosen, Amir; Gordon, Ariel; Gat, Omri; Fischer, Baruch
2005-06-01
Light is shown to exhibit critical and tricritical behavior in passively mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many-body light-mode system. The phase diagrams consist of regimes with continuous wave, driven parapulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines that terminate with critical or tricritical points. Enhanced non-Gaussian fluctuations and collective dynamics are present at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.
Cerebral malaria: susceptibility weighted MRI
Directory of Open Access Journals (Sweden)
Vinit Baliyan
2015-03-01
Full Text Available Cerebral malaria is one of the fatal complications of Plasmodium falciparum infection. Pathogenesis involves cerebral microangiopathy related to microvascular plugging by infected red blood cells. Conventional imaging with MRI and CT do not reveal anything specific in case of cerebral malaria. Susceptibility weighted imaging, a recent advance in the MRI, is very sensitive to microbleeds related to microangiopathy. Histopathological studies in cerebral malaria have revealed microbleeds in brain parenchyma secondary to microangiopathy. Susceptibility weighted imaging, being exquisitely sensitive to microbleeds may provide additional information and improve the diagnostic accuracy of MRI in cerebral malaria.
Topological susceptibility from the overlap
DEFF Research Database (Denmark)
Del Debbio, Luigi; Pica, Claudio
2003-01-01
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge....... Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study...
International Nuclear Information System (INIS)
Shimansky, Yu.I.; Shimanskaya, E.T.
1996-01-01
The temperature dependence of the density along the coexistence curve of benzene in the vicinity of the critical point and in a wide temperature range down to the triple point was investigated. The original results as well as literature data were statistically treated. A regression analysis of data on the critical exponents and critical amplitudes used as fitting parameters in a model equations was carried out. An adequate description of the order parameter by the three-term scaling equation in the entire two-phase (liquid-gas) region of benzene was obtained with experimental values of Β O -0.352 ±0.003 and δ = 1.3 ± 0.2, which are inconsistent with the Ising model (Β O = 0.325) and the Wegner exponent (δ = 0.5), respectively. It is shown that the equation with fixed classical exponents does not adequately describe the experimental data even far from the critical point
International Nuclear Information System (INIS)
Walker, G.
1983-01-01
When a sufficient quantity of fissile material is brought together a self-sustaining neutron chain reaction will be started in it and will continue until some change occurs in the fissile material to stop the chain reaction. The quantity of fissile material required is the 'Critical Mass'. This is not a fixed quantity even for a given type of fissile material but varies between quite wide limits depending on a number of factors. In a nuclear reactor the critical mass of fissile material is assembled under well-defined condition to produce a controllable chain reaction. The same materials have to be handled outside the reactor in all stages of fuel element manufacture, storage, transport and irradiated fuel reprocessing. At any stage it is possible (at least in principle) to assemble a critical mass and thus initiate an accidental and uncontrollable chain reaction. Avoiding this is what criticality safety is all about. A system is just critical when the rate of production of neutrons balances the rate of loss either by escape or by absorption. The factors affecting criticality are, therefore, those which effect neutron production and loss. The principal ones are:- type of nuclide and enrichment (or isotopic composition), moderation, reflection, concentration (density), shape and interaction. Each factor is considered in detail. (author)
Interventions on Metabolism: Making Antibiotic-Susceptible Bacteria
Directory of Open Access Journals (Sweden)
Fernando Baquero
2017-11-01
Full Text Available Antibiotics act on bacterial metabolism, and antibiotic resistance involves changes in this metabolism. Interventions on metabolism with drugs might therefore modify drug susceptibility and drug resistance. In their recent article, Martin Vestergaard et al. (mBio 8:e01114-17, 2017, https://doi.org/10.1128/mBio.01114-17 illustrate the possibility of converting intrinsically resistant bacteria into susceptible ones. They reported that inhibition of a central metabolic enzyme, ATP synthase, allows otherwise ineffective polymyxin antibiotics to act on Staphylococcus aureus. The study of the intrinsic resistome of bacterial pathogens has shown that several metabolic genes, including multigene transcriptional regulators, contribute to antibiotic resistance. In some cases, these genes only marginally increase antibiotic resistance, but reduced levels of susceptibility might be critical in the evolution or resistance under low antibiotic concentrations or in the clinical response of highly resistant bacteria. Drug interventions on bacterial metabolism might constitute a critical adjuvant therapy in combination with antibiotics to ensure susceptibility of pathogens with intrinsic or acquired antimicrobial resistance.
Nanotoxicity overview: nano-threat to susceptible populations.
Li, Yang; Zhang, Yi; Yan, Bing
2014-02-28
Due to the increasing applications of nanomaterials and nanotechnology, potential danger of nanoparticle exposure has become a critical issue. However, recent nanotoxicity studies have mainly focused on the health risks to healthy adult population. The nanotoxicity effects on susceptible populations (such as pregnant, neonate, diseased, and aged populations) have been overlooked. Due to the alterations in physiological structures and functions in susceptible populations, they often suffer more damage from the same exposure. Thus, it is urgent to understand the effects of nanoparticle exposure on these populations. In order to fill this gap, the potential effects of nanoparticles to pregnant females, neonate, diseased, and aged population, as well as the possible underlying mechanisms are reviewed in this article. Investigations show that responses from susceptible population to nanoparticle exposure are often more severe. Reduced protection mechanism, compromised immunity, and impaired self-repair ability in these susceptible populations may contribute to the aggravated toxicity effects. This review will help minimize adverse effects of nanoparticles to susceptible population in future nanotechnology applications.
Nanotoxicity Overview: Nano-Threat to Susceptible Populations
Directory of Open Access Journals (Sweden)
Yang Li
2014-02-01
Full Text Available Due to the increasing applications of nanomaterials and nanotechnology, potential danger of nanoparticle exposure has become a critical issue. However, recent nanotoxicity studies have mainly focused on the health risks to healthy adult population. The nanotoxicity effects on susceptible populations (such as pregnant, neonate, diseased, and aged populations have been overlooked. Due to the alterations in physiological structures and functions in susceptible populations, they often suffer more damage from the same exposure. Thus, it is urgent to understand the effects of nanoparticle exposure on these populations. In order to fill this gap, the potential effects of nanoparticles to pregnant females, neonate, diseased, and aged population, as well as the possible underlying mechanisms are reviewed in this article. Investigations show that responses from susceptible population to nanoparticle exposure are often more severe. Reduced protection mechanism, compromised immunity, and impaired self-repair ability in these susceptible populations may contribute to the aggravated toxicity effects. This review will help minimize adverse effects of nanoparticles to susceptible population in future nanotechnology applications.
Polymyxin susceptibility testing, interpretative breakpoints and resistance mechanisms: An update.
Bakthavatchalam, Yamuna Devi; Pragasam, Agila Kumari; Biswas, Indranil; Veeraraghavan, Balaji
2018-03-01
Emerging multidrug-resistant (MDR) nosocomial pathogens are a great threat. Polymyxins, an old class of cationic polypeptide antibiotic, are considered as last-resort drugs in treating infections caused by MDR Gram-negative bacteria. Increased use of polymyxins in treating critically ill patients necessitates routine polymyxin susceptibility testing. However, susceptibility testing both of colistin and polymyxin B (PMB) is challenging. In this review, currently available susceptibility testing methods are briefly discussed. The multicomponent composition of colistin and PMB significantly influences susceptibility testing. In addition, poor diffusion in the agar medium, adsorption to microtitre plates and the synergistic effect of the surfactant polysorbate 80 with polymyxins have a great impact on the performance of susceptibility testing methods This review also describes recently identified chromosomal resistance mechanisms, including modification of lipopolysaccharide (LPS) with 4-amino-4-deoxy-l-arabinose (L-Ara4-N) and phosphoethanolamine (pEtN) resulting in alteration of the negative charge, as well as the plasmid-mediated colistin resistance determinants mcr-1, mcr-1.2, mcr-2 and mcr-3. Copyright © 2017 International Society for Chemotherapy of Infection and Cancer. Published by Elsevier Ltd. All rights reserved.
Critical slowing down of spin fluctuations in BiFeO3
International Nuclear Information System (INIS)
Scott, J F; Singh, M K; Katiyar, R S
2008-01-01
In earlier work we reported the discovery of phase transitions in BiFeO 3 evidenced by divergences in the magnon light-scattering cross-sections at 140 and 201 K (Singh et al 2008 J. Phys.: Condens. Matter 20 252203) and fitted these intensity data to critical exponents α = 0.06 and α' = 0.10 (Scott et al 2008 J. Phys.: Condens. Matter 20 322203), under the assumption that the transitions are strongly magnetoelastic (Redfern et al 2008 at press) and couple to strain divergences through the Pippard relationship (Pippard 1956 Phil. Mag. 1 473). In the present paper we extend those criticality studies to examine the magnon linewidths, which exhibit critical slowing down (and hence linewidth narrowing) of spin fluctuations. The linewidth data near the two transitions are qualitatively different and we cannot reliably extract a critical exponent ν, although the mean field value ν = 1/2 gives a good fit near the lower transition.
Critical Phenomena in Higher Curvature Charged AdS Black Holes
Directory of Open Access Journals (Sweden)
Arindam Lala
2013-01-01
Full Text Available In this paper, we have studied the critical phenomena in higher curvature charged AdS black holes. We have considered Lovelock-Born-Infeld-AdS black hole as an example. The thermodynamics of the black hole have been studied which reveals the onset of a higher-order phase transition in the black hole in the canonical ensemble (fixed charge ensemble framework. We have analytically derived the critical exponents associated with these thermodynamic quantities. We find that our results fit well with the thermodynamic scaling laws and consistent with the mean field theory approximation. The suggestive values of the other two critical exponents associated with the correlation function and correlation length on the critical surface have been derived.
Prion protein and scrapie susceptibility
Smits, M.A.; Bossers, A.; Schreuder, B.E.C.
1997-01-01
This article presents briefly current views on the role of prion protein (PrP) in Transmissible Spongiform Encephalopathies or prion diseases and the effect of PrP polymoryhisms on the susceptibility to these diseases, with special emphasis on sheep scrapie. The PrP genotype of sheep apears to be a
Antifungal susceptibilities of Cryptococcus neoformans.
Archibald, Lennox K; Tuohy, Marion J; Wilson, Deborah A; Nwanyanwu, Okey; Kazembe, Peter N; Tansuphasawadikul, Somsit; Eampokalap, Boonchuay; Chaovavanich, Achara; Reller, L Barth; Jarvis, William R; Hall, Gerri S; Procop, Gary W
2004-01-01
Susceptibility profiles of medically important fungi in less-developed countries remain uncharacterized. We measured the MICs of amphotericin B, 5-flucytosine, fluconazole, itraconazole, and ketoconazole for Cryptococcus neoformans clinical isolates from Thailand, Malawi, and the United States and found no evidence of resistance or MIC profile differences among the countries.
India, Genomic diversity & Disease susceptibility
Indian Academy of Sciences (India)
Table of contents. India, Genomic diversity & Disease susceptibility · India, a paradise for Genetic Studies · Involved in earlier stages of Immune response protecting us from Diseases, Responsible for kidney and other transplant rejections Inherited from our parents · PowerPoint Presentation · Slide 5 · Slide 6 · Slide 7.
Energy Technology Data Exchange (ETDEWEB)
Ding, L.J., E-mail: dinglinjie82@126.com; Zhong, Y.
2017-07-15
Highlights: • The quantum critical scaling is investigated by Green’s function theory. • The obtained power-law critical exponents (β, δ and α) obey the critical scaling relation α + β(1 + δ) = 2. • The scaling hypothesis equations are proposed to verify the scaling analysis. - Abstract: The quantum phase transition and thermodynamics of a periodic Anderson-like polymer chain in a magnetic field are investigated by Green’s function theory. The T-h phase diagram is explored, wherein a crossover temperature T{sup ∗} denoting the gapless phase crossover into quantum critical regimes, smoothly connects near the critical fields to the universal linear line T{sup ∗} ∼ (h − h{sub c,s}), and ends at h{sub c,s}, providing a new route to capture quantum critical point (QCP). The quantum critical scaling around QCPs is demonstrated by analyzing magnetization, specific heat and Grüneisen parameter Γ{sub h}, which provide direct access to distill the power-law critical exponents (β, δ and α) obeying the critical scaling relation α + β(1 + δ) = 2, analogous to the quantum spin system. Furthermore, scaling hypothesis equations are proposed to check the scaling analysis, for which all the data collapse onto a single curve or two independent branches for the plot against an appropriate scaling variable, indicating the self-consistency and reliability of the obtained critical exponents.
Dynamical Response near Quantum Critical Points.
Lucas, Andrew; Gazit, Snir; Podolsky, Daniel; Witczak-Krempa, William
2017-02-03
We study high-frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz invariance, powerful methods from quantum field theory allow us to fix the high-frequency response in terms of universal coefficients. We test our predictions analytically in the large-N O(N) model and using the gauge-gravity duality and numerically via quantum Monte Carlo simulations on a lattice model hosting the interacting superfluid-insulator QCP. In superfluid phases, interacting Goldstone bosons qualitatively change the high-frequency optical conductivity and the corresponding sum rule.
Impact of network topology on self-organized criticality
Hoffmann, Heiko
2018-02-01
The general mechanisms behind self-organized criticality (SOC) are still unknown. Several microscopic and mean-field theory approaches have been suggested, but they do not explain the dependence of the exponents on the underlying network topology of the SOC system. Here, we first report the phenomena that in the Bak-Tang-Wiesenfeld (BTW) model, sites inside an avalanche area largely return to their original state after the passing of an avalanche, forming, effectively, critically arranged clusters of sites. Then, we hypothesize that SOC relies on the formation process of these clusters, and present a model of such formation. For low-dimensional networks, we show theoretically and in simulation that the exponent of the cluster-size distribution is proportional to the ratio of the fractal dimension of the cluster boundary and the dimensionality of the network. For the BTW model, in our simulations, the exponent of the avalanche-area distribution matched approximately our prediction based on this ratio for two-dimensional networks, but deviated for higher dimensions. We hypothesize a transition from cluster formation to the mean-field theory process with increasing dimensionality. This work sheds light onto the mechanisms behind SOC, particularly, the impact of the network topology.
Electromigration kinetics and critical current of Pb-free interconnects
Energy Technology Data Exchange (ETDEWEB)
Lu, Minhua; Rosenberg, Robert [IBM T. J. Watson Research Center, Yorktown Heights, New York 10598 (United States)
2014-04-07
Electromigration kinetics of Pb-free solder bump interconnects have been studied using a single bump parameter sweep technique. By removing bump to bump variations in structure, texture, and composition, the single bump sweep technique has provided both activation energy and power exponents that reflect atomic migration and interface reactions with fewer samples, shorter stress time, and better statistics than standard failure testing procedures. Contact metallurgies based on Cu and Ni have been studied. Critical current, which corresponds to the Blech limit, was found to exist in the Ni metallurgy, but not in the Cu metallurgy. A temperature dependence of critical current was also observed.
Exact renormalization group equation for the Lifshitz critical point
Bervillier, C.
2004-10-01
An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.
Spherically symmetric random walks. II. Dimensionally dependent critical behavior
International Nuclear Information System (INIS)
Bender, C.M.; Boettcher, S.; Meisinger, P.N.
1996-01-01
A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state distributions of random walkers are obtained for all dimensions D approx-gt 0 by solving a discrete eigenvalue problem. These distributions exhibit dimensionally dependent critical behavior as a function of the birth rate. This remarkably simple model exhibits a second-order phase transition with a universal, nontrivial critical exponent for all dimensions D approx-gt 0. copyright 1996 The American Physical Society
A critical scattering study of the helical antiferromagnets Ho and Dy
International Nuclear Information System (INIS)
Gaulin, B.D.; Hagen, M.; Child, H.R.
1988-01-01
We have measured the frequency integrated magnetic critical scattering of neutrons from paramagnetic Dy and Ho. Analysis of these data show the paramagnetic to helical antiferromagnetic phase transitions are characterized by the critical exponents ν = 0.57 +- 0.05 and γ = 1.05 = +- .07 for Dy and ν = 0.57 +- .04 and γ = 1.14 = +- .10 for Ho. 3 refs., 2 figs., 1 tab
Some remarks concerning the equation of state near a critical point
International Nuclear Information System (INIS)
Lebrun, J.P.
1977-01-01
The thermodynamical scaling hypothesis is referred to in terms of SLsub(2,R) representations. The Josephson-Schofield proposal to avoid non-analyticity on the critical isotherm is shown to conflict with the Lebowitz-Penrose theorem in the one-phase region. One proposes to uniformize the critical region using e.g. Beltrami's equations and derives from the implicit function theorem a simple relation between the exponents (β, delta)
Criticality of the D=2 quantum Heisenberg ferromagnet with quenched random anisotropic
International Nuclear Information System (INIS)
Mariz, A.M.; Tsallis, C.
1985-01-01
The square-lattice spin 1/2 anisotropic Heisenberg ferromagnet is considered, with interactions whose symmetry can independently (quenched model) and randomly be of two competing types, namely the isotropic Heisenberg type and the Ising one. Within a real space renormalization group framework, a quite precise numerical calculation of the critical frontier is performed, and its main asymptotic behaviour are established. The relevant universality classes are also characterized, through the analysis of the correlation length critical exponent. (Author) [pt
Susceptible-infected-recovered and susceptible-exposed-infected models
International Nuclear Information System (INIS)
Tome, Tania; De Oliveira, Mario J
2011-01-01
Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than b c = k/2(k - 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than p c = 1/(k - 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k - (k - 1)b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.
Mukherjee, Sandipan
2017-09-01
Due to heterogeneous nonlinear forcing of complex geomorphological features, predictability of monsoon rainfall 10-90-day intra-seasonal oscillations (ISO) over the complex terrain of northeastern and western Himalayan region (NEH and WH) remained poorly quantified. Using 72 and 61 number of station observations of monsoon rainfall ISOs of NEH and WH, respectively, this study attempts to investigate variation in the regional scale predictability of monsoon rainfall ISOs with respect to changing geomorphological features and monsoon rainfall characteristics. In view of the bimodal nonlinear dynamical structure of monsoon rainfall ISO, the fractal dynamical Hurst exponent-based predictability indices are estimated as an indicator of predictability for station observations of NEH and WH, and relationships with elevations, slopes, aspects, and average numbers of occurrences of long (short) spell of active (break) phases are investigated. Results show 10-90-day ISOs are anti-persistent throughout the IHR, although, predictability of 10-90-day ISOs is higher over the NEH region than WH. Predictabilities of ISOs are found to decrease with increasing elevation and slope for both NEH and WH regions. Predictabilities of ISOs over both regions are also found to increase linearly as the number of occurrences of monsoon rainfall ISO phases (active/break) increases.
International Nuclear Information System (INIS)
Feng Guolin; Zhang Daquan; Gong Zhiqiang; Zhi Rong
2008-01-01
Precipitation sequence is a typical nonlinear and chaotic observational series, and studies on precipitation forecasts are restricted to the use of traditional linear statistical methods, especially when analysing the regional characteristics of precipitation. In the context of 20 stations' daily precipitation series (from 1956 to 2000) in South China (SC) and North China (NC), we divide each precipitation series into many self-stationary segments by using the heuristic segmentation algorithm (briefly BG algorithm). For each station's precipitation series, we calculate the exponent of power-law tail (EPT) of the cumulative probability distribution of segments with a length larger than l for precipitation and temperature series. Our results show that the power-law decay of the cumulative probability distribution of stationary segments might be a common attribution for precipitation and other nonstationary time series; the EPT somewhat indicates the precipitation duration and its spatial distribution that might be different from area to area. The EPT in NC is larger than in SC; Meanwhile, EPT might be another effective way to study the abrupt changes in nonlinear and nonstationary time series. (geophysics, astronomy and astrophysics)
Ausloos, M.
2012-09-01
A nonlinear dynamics approach can be used in order to quantify complexity in written texts. As a first step, a one-dimensional system is examined: two written texts by one author (Lewis Carroll) are considered, together with one translation into an artificial language (i.e., Esperanto) are mapped into time series. Their corresponding shuffled versions are used for obtaining a baseline. Two different one-dimensional time series are used here: one based on word lengths (LTS), the other on word frequencies (FTS). It is shown that the generalized Hurst exponent h(q) and the derived f(α) curves of the original and translated texts show marked differences. The original texts are far from giving a parabolic f(α) function, in contrast to the shuffled texts. Moreover, the Esperanto text has more extreme values. This suggests cascade model-like, with multiscale time-asymmetric features as finally written texts. A discussion of the difference and complementarity of mapping into a LTS or FTS is presented. The FTS f(α) curves are more opened than the LTS ones.
Carasso, Alfred S; Vladár, András E
2012-01-01
Helium ion microscopes (HIM) are capable of acquiring images with better than 1 nm resolution, and HIM images are particularly rich in morphological surface details. However, such images are generally quite noisy. A major challenge is to denoise these images while preserving delicate surface information. This paper presents a powerful slow motion denoising technique, based on solving linear fractional diffusion equations forward in time. The method is easily implemented computationally, using fast Fourier transform (FFT) algorithms. When applied to actual HIM images, the method is found to reproduce the essential surface morphology of the sample with high fidelity. In contrast, such highly sophisticated methodologies as Curvelet Transform denoising, and Total Variation denoising using split Bregman iterations, are found to eliminate vital fine scale information, along with the noise. Image Lipschitz exponents are a useful image metrology tool for quantifying the fine structure content in an image. In this paper, this tool is applied to rank order the above three distinct denoising approaches, in terms of their texture preserving properties. In several denoising experiments on actual HIM images, it was found that fractional diffusion smoothing performed noticeably better than split Bregman TV, which in turn, performed slightly better than Curvelet denoising.
Bailey, Nicholas P; Bøhling, Lasse; Veldhorst, Arno A; Schrøder, Thomas B; Dyre, Jeppe C
2013-11-14
We derive exact results for the rate of change of thermodynamic quantities, in particular, the configurational specific heat at constant volume, CV, along configurational adiabats (curves of constant excess entropy Sex). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. The slope of the isomorphs in a double logarithmic representation of the density-temperature phase diagram, γ, can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where γ increases (decreases) with density, the contours of CV have smaller (larger) slope than configurational adiabats. We clarify also the connection between γ and the pair potential. A fluctuation formula for the slope of the CV-contours is derived. The theoretical results are supported with data from computer simulations of two systems, the Lennard-Jones fluid, and the Girifalco fluid. The sign of dγ∕dρ is thus a third key parameter in characterizing Roskilde liquids, after γ and the virial-potential energy correlation coefficient R. To go beyond isomorph theory we compare invariance of a dynamical quantity, the self-diffusion coefficient, along adiabats and CV-contours, finding it more invariant along adiabats.
Shang, Xiang; Xia, Haiyun; Dou, Xiankang; Shangguan, Mingjia; Li, Manyi; Wang, Chong
2018-07-01
An eye-safe 1 . 5 μm visibility lidar is presented in this work considering in situ particle size distribution, which can be deployed in crowded places like airports. In such a case, the measured extinction coefficient at 1 . 5 μm should be converted to that at 0 . 55 μm for visibility retrieval. Although several models have been established since 1962, the accurate wavelength conversion remains a challenge. An adaptive inversion algorithm for 1 . 5 μm visibility lidar is proposed and demonstrated by using the in situ Angstrom wavelength exponent, which is derived from an aerosol spectrometer. The impact of the particle size distribution of atmospheric aerosols and the Rayleigh backscattering of atmospheric molecules are taken into account. Using the 1 . 5 μm visibility lidar, the visibility with a temporal resolution of 5 min is detected over 48 h in Hefei (31 . 83∘ N, 117 . 25∘ E). The average visibility error between the new method and a visibility sensor (Vaisala, PWD52) is 5.2% with the R-square value of 0.96, while the relative error between another reference visibility lidar at 532 nm and the visibility sensor is 6.7% with the R-square value of 0.91. All results agree with each other well, demonstrating the accuracy and stability of the algorithm.
International Nuclear Information System (INIS)
Franchi, M; Ricci, L
2014-01-01
The embedding of time series provides a valuable, and sometimes indispensable, tool in order to analyze the dynamical properties of a chaotic system. To this purpose, the choice of the embedding dimension and lag is decisive. The scientific literature describes several methods for selecting the most appropriate parameter pairs. Unfortunately, no conclusive criterion to decide which method – and thus which embedding pair – is the best has been so far devised. A widely employed quantity to compare different methods is the maximum Lyapunov exponent (MLE) because, for chaotic systems that have explicit analytic representations, MLE can be numerically evaluated independently of the embedding dimension and lag. Within this framework, we investigated the dependence on the calculated MLE on the embedding dimension and lag in the case of three dynamical systems that are also widespreadly used as reference systems, namely the Lorenz, Rössler and Mackey-Glass attractors. By also taking into account the statistical fluctuations of the calculated MLE, we propose a new method to assess which systems provide suitable test benches for the comparison of different embedding methods via MLE calculation. For example we found that, despite of its popularity in this scientific context, the Rössler attractor is not a reliable workbench to test the validity of an embedding method
Vrazic, Sacha
2015-08-01
Preventing car accidents by monitoring the driver's physiological parameters is of high importance. However, existing measurement methods are not robust to driver's body movements. In this paper, a system that estimates the heartbeat from the seat embedded piezoelectric sensors, and that is robust to strong body movements is presented. Multifractal q-Hurst exponents are used within a classifier to predict the most probable best sensor signal to be used in an Interactive Multi-Model Extended Kalman Filter pulsation estimation procedure. The car vibration noise is reduced using an autoregressive exogenous model to predict the noise on sensors. The performance of the proposed system was evaluated on real driving data up to 100 km/h and with slaloms at high speed. It is shown that this method improves by 36.7% the pulsation estimation under strong body movement compared to static sensor pulsation estimation and appears to provide reliable pulsation variability information for top-level analysis of drowsiness or other conditions.
International Nuclear Information System (INIS)
Chen, Zhiyun; Shi, Aiqin; Liu, Shixia; Yin, Tianxiang; Shen, Weiguo
2014-01-01
Highlights: • Coexistence curves of dimethyl carbonate + n-undecane (or + n-tridecane) were measured. • Isobaric heat capacity per unit volume of critical binary solutions dimethyl carbonate + n-undecane (or + n-tridecane) were determined. • The critical exponent β are consistent with the 3D-Ising value. • The asymmetry of the coexistence curves were discussed by the complete scaling theory. - Abstract: The (liquid + liquid) coexistences and the critical behavior of isobaric heat capacity per unit volume for critical binary solutions {dimethyl carbonate + n-undecane, or n-tridecane} have been studied. The critical exponents β and α were deduced and found to be consistent with the 3D-Ising values. The critical amplitudes were determined and used to test the asymmetric criticality of coexistence curves. It was found that the heat capacity does play an important role in describing the asymmetric criticality of the coexistence curves
Nonlinear electromagnetic susceptibilities of unmagnetized plasmas
International Nuclear Information System (INIS)
Yoon, Peter H.
2005-01-01
Fully electromagnetic nonlinear susceptibilities of unmagnetized plasmas are analyzed in detail. Concrete expressions of the second-order nonlinear susceptibility are found in various forms in the literature, usually in connection with the discussions of various three-wave decay processes, but the third-order susceptibilities are rarely discussed. The second-order susceptibility is pertinent to nonlinear wave-wave interactions (i.e., the decay/coalescence), whereas the third-order susceptibilities affect nonlinear wave-particle interactions (i.e., the induced scattering). In the present article useful approximate analytical expressions of these nonlinear susceptibilities that can be readily utilized in various situations are derived
DEFF Research Database (Denmark)
Svegaard, Robin Sebastian Kaszmarczyk
2015-01-01
This article will introduce and take a look at a specific subset of the fan created remix videos known as vids, namely those that deal with feminist based critique of media. Through examples, it will show how fans construct and present their critique, and finally broach the topic of the critical ...
International Nuclear Information System (INIS)
Chen Zhiyun; Cai Li; Huang Meijun; Yin Tianxiang; An Xueqin; Shen Weiguo
2012-01-01
Highlights: ► Coexistence curves of (dimethyl adipate + n-hexane) (+n-heptane) were measured. ► The critical exponent β are consistent with the 3D-Ising value. ► The asymmetry of the coexistence curves were discussed by complete scaling theory. - Abstract: The liquid–liquid coexistence curves for (dimethyl adipate + n-hexane), (dimethyl adipate + n-heptane) have been measured, from which the critical amplitudes and the critical exponents are deduced. The critical exponent β corresponding to the coexistence curves are consistent with the 3D-Ising value. The experimental results have also been analyzed to determine the critical amplitudes of Wegner-correction terms when β and Δ are fixed at their theoretical values, and to examine the asymmetry of the diameters for the coexistence curves.
Two critical tests for the Critical Point earthquake
Tzanis, A.; Vallianatos, F.
2003-04-01
It has been credibly argued that the earthquake generation process is a critical phenomenon culminating with a large event that corresponds to some critical point. In this view, a great earthquake represents the end of a cycle on its associated fault network and the beginning of a new one. The dynamic organization of the fault network evolves as the cycle progresses and a great earthquake becomes more probable, thereby rendering possible the prediction of the cycle’s end by monitoring the approach of the fault network toward a critical state. This process may be described by a power-law time-to-failure scaling of the cumulative seismic release rate. Observational evidence has confirmed the power-law scaling in many cases and has empirically determined that the critical exponent in the power law is typically of the order n=0.3. There are also two theoretical predictions for the value of the critical exponent. Ben-Zion and Lyakhovsky (Pure appl. geophys., 159, 2385-2412, 2002) give n=1/3. Rundle et al. (Pure appl. geophys., 157, 2165-2182, 2000) show that the power-law activation associated with a spinodal instability is essentially identical to the power-law acceleration of Benioff strain observed prior to earthquakes; in this case n=0.25. More recently, the CP model has gained support from the development of more dependable models of regional seismicity with realistic fault geometry that show accelerating seismicity before large events. Essentially, these models involve stress transfer to the fault network during the cycle such, that the region of accelerating seismicity will scale with the size of the culminating event, as for instance in Bowman and King (Geophys. Res. Let., 38, 4039-4042, 2001). It is thus possible to understand the observed characteristics of distributed accelerating seismicity in terms of a simple process of increasing tectonic stress in a region already subjected to stress inhomogeneities at all scale lengths. Then, the region of
Reducing Susceptibility to Courtesy Stigma.
Bachleda, Catherine L; El Menzhi, Leila
2018-06-01
In light of the chronic shortage of health professionals willing to care for HIV/AIDS patients, and rising epidemics in many Muslim countries, this qualitative study examined susceptibility and resistance to courtesy stigma as experienced by nurses, doctors, and social workers in Morocco. Forty-nine in-depth interviews provided rich insights into the process of courtesy stigma and how it is managed, within the context of interactions with Islam, interactions within the workplace (patients, other health professionals), and interactions outside the workplace (the general public, friends, and family). Theoretically, the findings extend understanding of courtesy stigma and the dirty work literature. The findings also offer practical suggestions for the development of culturally appropriate strategies to reduce susceptibility to courtesy stigmatization. This study represents the first to explore courtesy stigma as a process experienced by health professionals providing HIV/AIDS care in an Islamic country.
Genetic susceptibility to Grave's disease.
Li, Hong; Chen, Qiuying
2013-06-01
The variety of clinical presentations of eye changes in patients with Graves' disease (GD) suggests that complex interactions between genetic, environmental, endogenous and local factors influence the severity of Graves' ophthalmopathy (GO). It is thought that the development of GO might be influenced by genetic factors and environmental factors, such as cigarette smoking. At present, however, the role of genetic factors in the development of GO is not known. On the basis of studies with candidate genes and other genetic approaches, several susceptibility loci in GO have been proposed, including immunological genes, human leukocyte antigen (HLA), cytotoxic T-lymphocyte antigen-4 (CTLA-4), regulatory T-cell genes and thyroid-specific genes. This review gives a brief overview of the current range of major susceptibility genes found for GD.
Critical reading and critical thinking Critical reading and critical thinking
Directory of Open Access Journals (Sweden)
Loni Kreis Taglieber
2008-04-01
Full Text Available The purpose of this paper is to provide, for L1 and L2 reading and writing teachers, a brief overview of the literature about critical reading and higher level thinking skills. The teaching of these skills is still neglected in some language classes in Brazil, be it in L1 or in L2 classes. Thus, this paper may also serve as a resource guide for L1 and/or L2 reading and writing teachers who want to incorporate critical reading and thinking into their classes. In modern society, even in everyday life people frequently need to deal with complicated public and political issues, make decisions, and solve problems. In order to do this efficiently and effectively, citizens must be able to evaluate critically what they see, hear, and read. Also, with the huge amount of printed material available in all areas in this age of “information explosion” it is easy to feel overwhelmed. But often the information piled up on people’s desks and in their minds is of no use due to the enormous amount of it. The purpose of this paper is to provide, for L1 and L2 reading and writing teachers, a brief overview of the literature about critical reading and higher level thinking skills. The teaching of these skills is still neglected in some language classes in Brazil, be it in L1 or in L2 classes. Thus, this paper may also serve as a resource guide for L1 and/or L2 reading and writing teachers who want to incorporate critical reading and thinking into their classes. In modern society, even in everyday life people frequently need to deal with complicated public and political issues, make decisions, and solve problems. In order to do this efficiently and effectively, citizens must be able to evaluate critically what they see, hear, and read. Also, with the huge amount of printed material available in all areas in this age of “information explosion” it is easy to feel overwhelmed. But often the information piled up on people’s desks and in their minds is of
Antibiotic susceptibility of Atopobium vaginae
Directory of Open Access Journals (Sweden)
Verschraegen Gerda
2006-03-01
Full Text Available Abstract Background Previous studies have indicated that a recently described anaerobic bacterium, Atopobium vaginae is associated with bacterial vaginosis (BV. Thus far the four isolates of this fastidious micro-organism were found to be highly resistant to metronidazole and susceptible for clindamycin, two antibiotics preferred for the treatment of BV. Methods Nine strains of Atopobium vaginae, four strains of Gardnerella vaginalis, two strains of Lactobacillus iners and one strain each of Bifidobacterium breve, B. longum, L. crispatus, L. gasseri and L. jensenii were tested against 15 antimicrobial agents using the Etest. Results All nine strains of A. vaginae were highly resistant to nalidixic acid and colistin while being inhibited by low concentrations of clindamycin (range: G. vaginalis strains were also susceptible for clindamycin ( 256 μg/ml but susceptible to clindamycin (0.023 – 0.125 μg/ml. Conclusion Clindamycin has higher activity against G. vaginalis and A. vaginae than metronidazole, but not all A. vaginae isolates are metronidazole resistant, as seemed to be a straightforward conclusion from previous studies on a more limited number of strains.
Antimicrobial Susceptibility Patterns Of Salmonella Species In ...
African Journals Online (AJOL)
% susceptible to cefepime and carbapenem, 91% to azithromycin, 82.1% to cefixime and 73% to quinolones. Also susceptibility to chloramphenicol, erythromycin, streptomycin, ampicillin, gentamicin, co-trimoxazole, augmentin and amikacin ...
Antibiotic susceptibility profiles for mastitis treatment.
Hinckley, L S; Benson, R H; Post, J E; DeCloux, J C
1985-10-01
Susceptibility tests were performed on milk samples representing prevalent mastitis infections in certain herds. Susceptibility patterns of the same bacterial species from several mastitis infections in the same herd were consistent. The herd antibiotic susceptibility profiles were used as a basis for selecting antibiotics for treatment of all such mastitis cases in that herd. A high degree of correlation was seen between the susceptibility test results and treatment results. Susceptibility patterns of the same bacterial species from mastitis infections in different herds varied greatly, which indicated that any one antibiotic would not work equally well against the same bacterial infection in every herd. Therefore, treatment should be selected on the basis of susceptibility test results. When both Streptococcus and Staphylococcus mastitis occurred in the same herd, the susceptibility patterns for the 2 bacterial species varied widely. Therefore, for herds that experienced both streptococcal and staphylococcal mastitis, antibiotics to which both bacterial species were susceptible were used for treatment.
International Nuclear Information System (INIS)
Canavese, Susana I.
2000-01-01
A criticality accident occurred at 10:35 on September 30, 1999. It occurred in a precipitation tank in a Conversion Test Building at the JCO Tokai Works site in Tokaimura (Tokai Village) in the Ibaraki Prefecture of Japan. STA provisionally rated this accident a 4 on the seven-level, logarithmic International Nuclear Event Scale (INES). The September 30, 1999 criticality accident at the JCO Tokai Works Site in Tokaimura, Japan in described in preliminary, technical detail. Information is based on preliminary presentations to technical groups by Japanese scientists and spokespersons, translations by technical and non-technical persons of technical web postings by various nuclear authorities, and English-language non-technical reports from various news media and nuclear-interest groups. (author)
International Nuclear Information System (INIS)
Dekker, H.
1980-01-01
It is shown how to solve the master equation for a Markov process including a critical point by means of successive approximations in terms of a small parameter. A critical point occurs if, by adjusting an externally controlled quantity, the system shows a transition from normal monostable to bistable behaviour. The fundamental idea of the theory is to separate the master equation into its proper irreducible part and a corrective remainder. The irreducible or zeroth order stochastic approximation will be a relatively simple Fokker-Planck equation that contains the essential features of the process. Once the solution of this irreducible equation is known, the higher order corrections in the original master equation can be incorporated in a systematic manner. (Auth.)
International Nuclear Information System (INIS)
Stirling, W.G.; Perry, S.C.
1996-01-01
We outline the theoretical and experimental background to neutron scattering studies of critical phenomena at magnetic and structural phase transitions. The displacive phase transition of SrTiO 3 is discussed, along with examples from recent work on magnetic materials from the rare-earth (Ho, Dy) and actinide (NpAs, NpSb, USb) classes. The impact of synchrotron X-ray scattering is discussed in conclusion. (author) 13 figs., 18 refs
International Nuclear Information System (INIS)
Chen, Zhiyun; Bai, Yongliang; Yin, Tianxiang; An, Xueqin; Shen, Weiguo
2012-01-01
Highlights: ► Coexistence curves of (benzonitrile + n-pentadecane) and (benzonitrile + n-heptadecane) were measured. ► The values of the critical exponent β are consistent with that predicted by the 3D-Ising model. ► The coexistence curves are well described by the critical crossover model. ► The asymmetry of the diameters of the coexistence curves were discussed by the complete scaling theory. - Abstract: Liquid + liquid coexistence curves for the binary solutions of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} have been measured in the critical region. The critical exponent β and the critical amplitudes have been deduced and the former is consistent with the theoretic prediction. It was found that the coexistence curves may be well described by the crossover model proposed by Gutkowski et al. The asymmetries of the diameters of the coexistence curves were also discussed in the frame of the complete scaling theory.
International Nuclear Information System (INIS)
Kim, J.-T.
1998-01-01
The effect of columnar defects on the critical dynamics of superconducting Tl 2 Ba 2 CaCu 2 O 8 (Tl-2212) film has been investigated. The Tl-2212 film was irradiated at 0 C by 1.3 GeV U-ions along the normal of the film surface. The dose of 6.0 x 10 10 ions/cm 2 of the U-ion irradiation corresponds to a matching field of 1.2 T. The in-plane longitudinal resistivity of the irradiated Tl-2212 has been measured as a function of magnetic field H and temperature T. The extracted fluctuation part of the conductivity σ xx (T, H) of the unirradiated sample exhibits 3D-XY scaling behavior that reveals dynamic critical exponent z = 1.8 ± 0.1 and static critical exponent v ∼ 1.338. The results indicate that the weak interlayer coupling along the c-axis of Tl-2212 significantly influences static critical exponent v and does not change dynamical critical exponent. After the irradiation, the fluctuation conductivities are enhanced by the strong pinnings and do not exhibit the same 3D-XY scaling behavior as for the unirradiated Tl-2212. Particularly at the low magnetic field values near the matching field of 1.2 T, the fluctuation conductivities show a clear deviation from the critical dynamics, suggesting that the pinning effect on the critical dynamics is significant
International Nuclear Information System (INIS)
Bettencourt, João H; López, Cristóbal; Hernández-García, Emilio
2013-01-01
In this paper, we use the finite-size Lyapunov exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3D) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. 3D FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by the numerical solution of the primitive equations where two-dimensional (2D) turbulence dominates. In the channel flow, autocorrelations of the FSLE field show that the structure is substantially different from the near wall to the mid-channel region and relates well to the more widely studied Eulerian coherent structure of the turbulent channel flow. The ridges of the FSLE field have complex shapes due to the 3D character of the turbulent fluctuations. In the oceanic flow, strong horizontal stirring is present and the flow regime is similar to that of 2D turbulence where the domain is populated by coherent eddies that interact strongly. This in turn results in the presence of high FSLE lines throughout the domain leading to strong non-local mixing. The ridges of the FSLE field are quasi-vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, due to rotation and stratification, vertical motions in the ocean are much less intense than horizontal ones. This suppression is absent in the channel flow, as the 3D character of the FSLE ridges shows. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Susceptibility Tensor Imaging (STI) of the Brain
Li, Wei; Liu, Chunlei; Duong, Timothy Q.; van Zijl, Peter C.M.; Li, Xu
2016-01-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility (MMS) and magnetic susceptibility anisotropy (MSA) can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping (QSM) to remove such dependence. Similar to diffusion tensor imaging (DTI), STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of susceptibility anisotropy in brain white matter is myelin. Another unique feature of susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. PMID:27120169
Measurements of temperature dependence of 'localized susceptibility'
Shiozawa, H; Ishii, H; Takayama, Y; Obu, K; Muro, T; Saitoh, Y; Matsuda, T D; Sugawara, H; Sato, H
2003-01-01
The magnetic susceptibility of some rare-earth compounds is estimated by measuring magnetic circular dichroism (MCD) of rare-earth 3d-4f absorption spectra. The temperature dependence of the magnetic susceptibility obtained by the MCD measurement is remarkably different from the bulk susceptibility in most samples, which is attributed to the strong site selectivity of the core MCD measurement.
Critical behaviors of half-metallic ferromagnet Co3Sn2S2
Yan, Weinian; Zhang, Xiao; Shi, Qi; Yu, Xiaoyun; Zhang, Zhiqing; Wang, Qi; Li, Si; Lei, Hechang
2018-01-01
We have investigated the critical behavior of a shandite-type half-metal ferromagnet Co3Sn2S2. It exhibits a second-order paramagnetic-ferromagnetic phase transition with TC = 174 K. To investigate the nature of the magnetic phase transition, a detailed critical exponent study has been performed. The critical components beta, gamma, and delta determined using the modified Arrott plot, the Kouvel-Fisher method as well as the critical isotherm analysis are match reasonably well and follow the s...
Renormalization group critical frontier of the three-dimensional bond-dilute Ising ferromagnet
International Nuclear Information System (INIS)
Chao, N.-C.; Schwaccheim, G.; Tsallis, C.
1981-01-01
The critical frontier (as well as the thermal type critical exponents) associated to the quenched bond-dilute spin - 1/2 Ising ferromagnet in the simple cubic lattice is approximately calculated within a real space renormalization group framework in two different versions. Both lead to qualitatively satisfactory critical frontiers, although one of them provides an unphysical fixed point (which seem to be related to the three-dimensionality of the system) besides the expected pure ones; its effects tend to disappear for increasingly large clusters. Through an extrapolation procedure the (unknown) critical frontier is approximately located. (Author) [pt
Quantum influence in the criticality of the spin- {1}/{2} anisotropic Heisenberg model
Ricardo de Sousa, J.; Araújo, Ijanílio G.
1999-07-01
We study the spin- {1}/{2} anisotropic Heisenberg antiferromagnetic model using the effective field renormalization group (EFRG) approach. The EFRG method is illustrated by employing approximations in which clusters with one ( N'=1) and two ( N=2) spins are used. The dependence of the critical temperature Tc (ferromagnetic-F case) and TN (antiferromagnetic-AF case) and thermal critical exponent, Yt, are obtained as a function of anisotropy parameter ( Δ) on a simple cubic lattice. We find that, in our results, TN is higher than Tc for the quantum anisotropic Heisenberg limit and TN= Tc for the Ising and quantum XY limits. We have also shown that the thermal critical exponent Yt for the isotropic Heisenberg model shows a small dependence on the type of interaction (F or AF) due to finite size effects.
Criticality in the configuration-mixed interacting boson model: (1) U(5)-Q(χ)Q(χ) mixing
International Nuclear Information System (INIS)
Hellemans, V.; Van Isacker, P.; De Baerdemacker, S.; Heyde, K.
2007-01-01
The case of U(5)-Q(χ)Q(χ) mixing in the configuration-mixed interacting boson model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively
Energy Technology Data Exchange (ETDEWEB)
Pawlak, A., E-mail: pawlak@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61–614 Poznań (Poland); Gülpınar, G. [Department of Physics, Dokuz Eylül University, 35160 İzmir (Turkey); Erdem, R. [Department of Physics, Akdeniz University, 07058 Antalya (Turkey); Ağartıoğlu, M. [Institute of Science, Dokuz Eylül University, 35160 İzmir (Turkey)
2015-12-01
The expressions for the dipolar and quadrupolar susceptibilities are obtained within the mean-field approximation in the Blume–Emery–Griffiths model. Temperature as well as crystal field dependences of the susceptibilities are investigated for two different phase diagram topologies which take place for K/J=3 and K/J=5.0.Their behavior near the second and first order transition points as well as multi-critical points such as tricritical, triple and critical endpoint is presented. It is found that in addition to the jumps connected with the phase transitions there are broad peaks in the quadrupolar susceptibility. It is indicated that these broad peaks lie on a prolongation of the first-order line from a triple point to a critical point ending the line of first-order transitions between two distinct paramagnetic phases. It is argued that the broad peaks are a reminiscence of very strong quadrupolar fluctuations at the critical point. The results reveal the fact that near ferromagnetic–paramagnetic phase transitions the quadrupolar susceptibility generally shows a jump whereas near the phase transition between two distinct paramagnetic phases it is an edge-like. - Highlights: • MFA calculation of the quadrupolar and dipolar susceptibility in BEG model is given • The crystal-field variation of susceptibilities near the multi-critical points is examined • There are broad peaks in the quadrupolar susceptibility in the vicinity of CP • These maxima are remembrances of the very strong quadrupolar Fluctuations.
Random-fractal Ansatz for the configurations of two-dimensional critical systems.
Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki
2016-12-01
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.
AUTHOR|(CDS)2070299
2017-01-01
Critical Mass is a cycling event typically held on the last Friday of every month; its purpose is not usually formalized beyond the direct action of meeting at a set location and time and traveling as a group through city or town streets on bikes. The event originated in 1992 in San Francisco; by the end of 2003, the event was being held in over 300 cities around the world. At CERN it is held once a year in conjunction with the national Swiss campaing "Bike to work".
van der Waals criticality in AdS black holes: A phenomenological study
Bhattacharya, Krishnakanta; Majhi, Bibhas Ranjan; Samanta, Saurav
2017-10-01
Anti-de Sitter black holes exhibit van der Waals-type phase transition. In the extended phase-space formalism, the critical exponents for any spacetime metric are identical to the standard ones. Motivated by this fact, we give a general expression for the Helmholtz free energy near the critical point, which correctly reproduces these exponents. The idea is similar to the Landau model, which gives a phenomenological description of the usual second-order phase transition. Here, two main inputs are taken into account for the analysis: (a) black holes should have van der Waals-like isotherms, and (b) free energy can be expressed solely as a function of thermodynamic volume and horizon temperature. Resulting analysis shows that the form of Helmholtz free energy correctly encapsulates the features of the Landau function. We also discuss the isolated critical point accompanied by nonstandard values of critical exponents. The whole formalism is then extended to two other criticalities, namely, Y -X and T -S (based on the standard; i.e., nonextended phase space), where X and Y are generalized force and displacement, whereas T and S are the horizon temperature and entropy. We observe that in the former case Gibbs free energy plays the role of Landau function, whereas in the later case, that role is played by the internal energy (here, it is the black hole mass). Our analysis shows that, although the existence of a van der Waals phase transition depends on the explicit form of the black hole metric, the values of the critical exponents are universal in nature.
Magnetic susceptibility of functional groups
International Nuclear Information System (INIS)
Herr, T.; Ferraro, M.B.; Contreras, R.H.
1990-01-01
Proceeding with a series of works where new criteria are applied to the the calculation of the contribution of molecular fragments to certain properties, results are presented for a group of 1-X-benzenes and 1-X-naphtalenes for the magnetic susceptibility constant. Both the diamagnetic and paramagnetic parts are taken into account. To reduce the problems associated with the Gauge dependence originated in the approximations made, Gauge independent atomic orbitals (GIAO) orbitals are used in the atomic orbital basis. Results are discussed in terms of functional groups. (Author). 17 refs., 1 fig., 3 tabs
Magnetic susceptibility of curium pnictides
International Nuclear Information System (INIS)
Nave, S.E.; Huray, P.G.; Peterson, J.R.; Damien, D.A.; Haire, R.G.
1981-09-01
The magnetic susceptibility of microgram quantities of 248 CmP and 248 CmSb has been determined with the use of a SQUID micromagnetic susceptometer over the temperature range 4.2 to 340 K and in the applied magnetic field range of 0.45 to 1600 G. The fcc (NaCl-type) samples yield magnetic transitions at 73K and 162 K for the phosphide and antimonide, respectively. Together with published magnetic data for CmN and CmAs, these results indicate spatially extended exchange interactions between the relatively localized 5f electrons of the metallic actinide atoms
Polygenic susceptibility to testicular cancer
DEFF Research Database (Denmark)
Litchfield, Kevin; Mitchell, Jonathan S; Shipley, Janet
2015-01-01
BACKGROUND: The increasing incidence of testicular germ cell tumour (TGCT) combined with its strong heritable basis suggests that stratified screening for the early detection of TGCT may be clinically useful. We modelled the efficiency of such a personalised screening approach, based on genetic...... known TGCT susceptibility variants. The diagnostic performance of testicular biopsy and non-invasive semen analysis was also assessed, within a simulated combined screening programme. RESULTS: The area under the curve for the TGCT PRS model was 0.72 with individuals in the top 1% of the PRS having...
Universal postquench coarsening and aging at a quantum critical point
Gagel, Pia; Orth, Peter P.; Schmalian, Jörg
2015-09-01
The nonequilibrium dynamics of a system that is located in the vicinity of a quantum critical point is affected by the critical slowing down of order-parameter correlations with the potential for novel out-of-equilibrium universality. After a quantum quench, i.e., a sudden change of a parameter in the Hamiltonian, such a system is expected to almost instantly fall out of equilibrium and undergo aging dynamics, i.e., dynamics that depends on the time passed since the quench. Investigating the quantum dynamics of an N -component φ4 model coupled to an external bath, we determine this universal aging and demonstrate that the system undergoes a coarsening, governed by a critical exponent that is unrelated to the equilibrium exponents of the system. We analyze this behavior in the large-N limit, which is complementary to our earlier renormalization-group analysis, allowing in particular the direct investigation of the order-parameter dynamics in the symmetry-broken phase and at the upper critical dimension. By connecting the long-time limit of fluctuations and response, we introduce a distribution function that shows that the system remains nonthermal and exhibits quantum coherence even on long time scales.
Universal Critical Dynamics in High Resolution Neuronal Avalanche Data
Friedman, Nir; Ito, Shinya; Brinkman, Braden A. W.; Shimono, Masanori; DeVille, R. E. Lee; Dahmen, Karin A.; Beggs, John M.; Butler, Thomas C.
2012-05-01
The tasks of neural computation are remarkably diverse. To function optimally, neuronal networks have been hypothesized to operate near a nonequilibrium critical point. However, experimental evidence for critical dynamics has been inconclusive. Here, we show that the dynamics of cultured cortical networks are critical. We analyze neuronal network data collected at the individual neuron level using the framework of nonequilibrium phase transitions. Among the most striking predictions confirmed is that the mean temporal profiles of avalanches of widely varying durations are quantitatively described by a single universal scaling function. We also show that the data have three additional features predicted by critical phenomena: approximate power law distributions of avalanche sizes and durations, samples in subcritical and supercritical phases, and scaling laws between anomalous exponents.
Pham, A J; Schilling, M W; Yoon, Y; Kamadia, V V; Marshall, D L
2008-05-01
The objectives of this study were to characterize volatile compounds and to determine the characteristic aromas associated with impact compounds in 4 fish sauces using solid-phase micro-extraction, gas chromatography-mass spectrometry, Osme, and gas chromatography olfactometry (SPME-Osme-GCO) coupled with Stevens' Power Law. Compounds were separated using GCMS and GCO and were identified with the mass spectral database, aroma perceived at the sniffing port, retention indices, and verification of compounds by authentic standards in the GCMS and GCO. Aromas that were isolated and present in all 4 fish sauce samples at all concentrations included fishy (trimethylamine), pungent and dirty socks (combination of butanoic, pentanoic, hexanoic, and heptanoic acids), cooked rice and buttery popcorn (2,6-dimethyl pyrazine), and sweet and cotton candy (benzaldehyde). All fish sauces contained the same aromas as determined by GCO and GCMS (verified using authentic standard compounds), but the odor intensity associated with each compound or group of compounds was variable for different fish sauce samples. Stevens' Power Law exponents were also determined using this analytical technique, but exponents were not consistent for the same compounds that were found in all fish sauces. Stevens' Power Law exponents ranged from 0.14 to 0.37, 0.24 to 0.34, 0.09 to 0.21, and 0.10 to 0.35 for dirty socks, fishy, buttery popcorn, and sweet aromas, respectively. This demonstrates that there is variability in Stevens' Power Law exponents for odorants within fish sauce samples.
Efektivita kapitálových trhů: Fraktální dimenze, Hurstův exponent a entropie
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav; Vošvrda, Miloslav
2012-01-01
Roč. 60, č. 2 (2012), s. 208-221 ISSN 0032-3233 R&D Projects: GA ČR GA402/09/0965 Institutional support: RVO:67985556 Keywords : capital markets efficiency * fractal dimension * long-range dependence * entropy Subject RIV: AH - Economics Impact factor: 0.722, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kristoufek-capital markets efficiency fractal dimension hurst exponent and entropy.pdf
International Nuclear Information System (INIS)
Zamani, Najmeh; Ataei, Mohammad; Niroomand, Mehdi
2015-01-01
Highlights: • Applying nonlinear analysis of complex dynamics displayed by current-mode controlled boost converter. • The ramp compensation method is used to control bifurcation and chaos in these converters based on bifurcation diagram and Lyapunov exponents assignment. • A discrete-time iterative nonlinear mapping model has been derived by inserting the ramp compensation parameter in the dynamical equations of the system. • A design methodology for chaos control is provided in this converter based on Lyapunov exponents assignment in desired values theoretically by proper selection of compensator slope. • Practical results are provided to confirm the theoretical analysis and simulations. - Abstract: Nonlinear analysis of complex dynamics displayed by current mode dc–dc converter and idea of Lyapunov exponents assignment by ramp compensator in order to control chaotic behavior is proposed in this article. A discrete-time iterative nonlinear mapping model is derived. The occurrence of the complex behaviors of bifurcation and chaos generated by varying the circuit parameters are investigated through numerical analysis and software implementation of the circuit. Next, in order to control bifurcation and chaos in these converters, the ramp compensation method is used. By inserting the ramp compensation parameter in the dynamical equations of the system, these complex behaviors are examined theoretically and numerically as well. It is proved that through this method, the stable period-one operation of the converter can be extended. By evaluating the Lyapunov exponents (LEs) of the system, the impact of the slope on the location of LEs are determined analytically. This leads to a design methodology for control of chaos in this converter based on LEs assignment in desired values by proper selection of compensator slope. By developing an experimental set up, practical results are obtained to confirm the theoretical analysis and simulations.
Topological susceptibility from the overlap
International Nuclear Information System (INIS)
Del Debbio, Luigi; Pica, Claudio
2004-01-01
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge. Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study the topology of the gauge configurations. The topological charge is obtained from the zero modes of the overlap and using a new algorithm for the spectral flow analysis. A detailed comparison with cooling techniques is presented. Particular care is taken in assessing the systematic errors. Relatively high statistics (500 to 1000 independent configurations) yield an extrapolated continuum limit with errors that are comparable with other methods. Our current value from the overlap is χ 1/4 = 188±12±5MeV (author)
DEFF Research Database (Denmark)
Nielsen, Sandro
2018-01-01
Dictionary criticism is part of the lexicographical universe and reviewing of electronic and printed dictionaries is not an exercise in linguistics or in subject fields but an exercise in lexicography. It does not follow from this that dictionary reviews should not be based on a linguistic approach......, but that the linguistic approach is only one of several approaches to dictionary reviewing. Similarly, the linguistic and factual competences of reviewers should not be relegated to an insignificant position in the review process. Moreover, reviewers should define the object of their reviews, the dictionary, as a complex...... information tool with several components and in terms of significant lexicographical features: lexicographical functions, data and structures. This emphasises the fact that dictionaries are much more than mere vessels of linguistic categories, namely lexicographical tools that have been developed to fulfil...
Directory of Open Access Journals (Sweden)
F. Masci
2013-09-01
Full Text Available Many papers document the observation of earthquake-related precursory signatures in geomagnetic field data. However, the significance of these findings is ambiguous because the authors did not adequately take into account that these signals could have been generated by other sources, and the seismogenic origin of these signals have not been validated by comparison with independent datasets. Thus, they are not reliable examples of magnetic disturbances induced by the seismic activity. Hayakawa et al. (2004 claim that at the time of the 2000 Izu swarm the Hurst exponent of the Ultra-Low-Frequency (ULF: 0.001–10 Hz band of the geomagnetic field varied in accord with the energy released by the seismicity. The present paper demonstrates that the behaviour of the Hurst exponent was insufficiently investigated and also misinterpreted by the authors. We clearly show that during the Izu swarm the changes of the Hurst exponent were strongly related to the level of global geomagnetic activity and not to the increase of the local seismic activity.
Keylock, Christopher J.
2018-04-01
A technique termed gradual multifractal reconstruction (GMR) is formulated. A continuum is defined from a signal that preserves the pointwise Hölder exponent (multifractal) structure of a signal but randomises the locations of the original data values with respect to this (φ = 0), to the original signal itself(φ = 1). We demonstrate that this continuum may be populated with synthetic time series by undertaking selective randomisation of wavelet phases using a dual-tree complex wavelet transform. That is, the φ = 0 end of the continuum is realised using the recently proposed iterated, amplitude adjusted wavelet transform algorithm (Keylock, 2017) that fully randomises the wavelet phases. This is extended to the GMR formulation by selective phase randomisation depending on whether or not the wavelet coefficient amplitudes exceeds a threshold criterion. An econophysics application of the technique is presented. The relation between the normalised log-returns and their Hölder exponents for the daily returns of eight financial indices are compared. One particularly noticeable result is the change for the two American indices (NASDAQ 100 and S&P 500) from a non-significant to a strongly significant (as determined using GMR) cross-correlation between the returns and their Hölder exponents from before the 2008 crash to afterwards. This is also reflected in the skewness of the phase difference distributions, which exhibit a geographical structure, with Asian markets not exhibiting significant skewness in contrast to those from elsewhere globally.