Critical exponents of extremal Kerr perturbations

Science.gov (United States)

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

Science.gov (United States)

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.

Universal post-quench prethermalization at a quantum critical point

Science.gov (United States)

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

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.)

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

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

The Ising model on a random planar lattice: The structure of the phase transition and the exact critical exponents

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.)

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

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

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

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.

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.)

The critical 1-arm exponent for the ferromagnetic Ising model on the Bethe lattice

Science.gov (United States)

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 ).

Stochastic model of Zipf's law and the universality of the power-law exponent.

Science.gov (United States)

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.

Lyapunov exponent and criticality in the Hamiltonian mean field model

Science.gov (United States)

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.

Magnetic entropy change and critical exponents in double perovskite Y2NiMnO6

Science.gov (United States)

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.

Universal signatures of fractionalized quantum critical points.

Science.gov (United States)

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.

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

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 ...

Universal postquench coarsening and aging at a quantum critical point

Science.gov (United States)

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.

Phase Transitions, Geometrothermodynamics, and Critical Exponents of Black Holes with Conformal Anomaly

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.

Critical exponents for diluted resistor networks.

Science.gov (United States)

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 Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory

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

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.

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.

Some existence results for a fourth order equation involving critical exponent

CERN Document Server

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.

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.

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

Critical exponents of the transition from incoherence to partial oscillation death in the Winfree model

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

Universal Critical Dynamics in High Resolution Neuronal Avalanche Data

Science.gov (United States)

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.

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)

Universal critical wrapping probabilities in the canonical ensemble

Directory of Open Access Journals (Sweden)

Hao Hu

2015-09-01

Full Text Available Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in the random-cluster representation, under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We derive that, in the limit L→∞, the critical values of the wrapping probability are different from those of the unconstrained model, i.e. the model in the grand-canonical ensemble, but still universal, for systems with 2yt−d>0 where yt=1/ν is the thermal renormalization exponent and d is the spatial dimension. Similar modifications apply to other dimensionless quantities, such as Binder ratios. For systems with 2yt−d≤0, these quantities share same critical universal values in the two ensembles. It is also derived that new finite-size corrections are induced. These findings apply more generally to systems in the canonical ensemble, e.g. the dilute Potts model with a fixed total number of vacancies. Finally, we formulate an efficient cluster-type algorithm for the canonical ensemble, and confirm these predictions by extensive simulations.

Momentum distribution critical exponents for one dimensional large U hubbard model in thermodynamic limit

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

Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.

Science.gov (United States)

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.

On the curve of critical exponents for nonlinear elliptic problems in the case of a zero mass

Science.gov (United States)

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.

Specific heat near the Lambda point in 4He and 3He- 4He mixtures: test of universality of the critical exponent and the amplitude ratio, and observation of the critical-tricritical crossover effect

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

Universality hypothesis breakdown at one-loop order

Science.gov (United States)

Carvalho, P. R. S.

2018-05-01

We probe the universality hypothesis by analytically computing the at least two-loop corrections to the critical exponents for q -deformed O (N ) self-interacting λ ϕ4 scalar field theories through six distinct and independent field-theoretic renormalization group methods and ɛ -expansion techniques. We show that the effect of q deformation on the one-loop corrections to the q -deformed critical exponents is null, so the universality hypothesis is broken down at this loop order. Such an effect emerges only at the two-loop and higher levels, and the validity of the universality hypothesis is restored. The q -deformed critical exponents obtained through the six methods are the same and, furthermore, reduce to their nondeformed values in the appropriated limit.

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

Percolation with first-and-second neighbour bonds: a renormalization-group calculation of critical exponents

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

Some Aspects of Scaling and Universality in Magnetocaloric Materials

DEFF Research Database (Denmark)

Smith, Anders; Nielsen, Kaspar Kirstein; Bahl, Christian R.H.

2014-01-01

The magnetocaloric effect of a magnetic material is characterized by two quantities, the isothermal entropy change and the adiabatic temperature change, both of which are functions of temperature and applied magnetic field. We discuss the scaling properties of these quantities close to a second...... order phase transition within the context of critical scaling theory. In the critical region the isothermal entropy change will exhibit universal scaling exponents. However, this is only true close to Tc and for small fields; we show that for finite fields the scaling exponents in general become field...... dependent, even at Tc. Furthermore, the scaling exponents at finite fields are not universal: Two models with the same critical exponents can exhibit markedly different scaling behaviour even at relatively low fields. Turning to the adiabatic temperature change, we argue that it is not determined...

Universality classes and critical phenomena in confined liquid systems

Directory of Open Access Journals (Sweden)

A.V. Chalyi

2013-06-01

Full Text Available It is well known that the similar universal behavior of infinite-size (bulk systems of different nature requires the same basic conditions: space dimensionality; number components of order parameter; the type (short- or long-range of the intermolecular interaction; symmetry of the fluctuation part of thermodynamical potential. Basic conditions of similar universal behavior of confined systems needs the same supplementary conditions such as the number of monolayers for a system confinement; low crossover dimensionality, i.e., geometric form of restricted volume; boundary conditions on limiting surfaces; physical properties under consideration. This review paper is aimed at studying all these conditions of similar universal behavior for diffusion processes in confined liquid systems. Special attention was paid to the effects of spatial dispersion and low crossover dimensionality. This allowed us to receive receiving correct nonzero expressions for the diffusion coefficient at the critical point and to take into account the specific geometric form of the confined liquid volume. The problem of 3D⇔2D dimensional crossover was analyzed. To receive a smooth crossover for critical exponents, the Kawasaki-like approach from the theory of mode coupling in critical dynamics was proposed. This ensured a good agreement between data of computer experiment and theoretical calculations of the size dependence of the critical temperature Tc(H of water in slitlike pores. The width of the quasi-elastic scattering peak of slow neutrons near the structural phase transition in the aquatic suspensions of plasmatic membranes (mesostructures with the typical thickness up to 10 nm was studied. It was shown that the width of quasi-elastic peak of neutron scattering decreases due to the process of cell proliferation, i.e., with an increase of the membrane size (including the membrane thickness. Thus, neutron studies could serve as an additional diagnostic test for the

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

Monte Carlo computation of correlation times of independent relaxation modes at criticality

NARCIS (Netherlands)

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

Dynamical critical phenomena in driven-dissipative systems.

Science.gov (United States)

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.

Thermodynamic behavior of {ethanol + butylpyridinium tetrafluoroborate} binary solution in the critical region

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.

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

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.

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.

Scaling, phase transitions, and nonuniversality in a self-organized critical cellular-automaton model

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

Lyapunov Exponents

CERN Document Server

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...

Stock markets and criticality in the current economic crisis

Science.gov (United States)

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.

Landau-Ginzburg Limit of Black Hole's Quantum Portrait: Self Similarity and Critical Exponent

CERN Document Server

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.

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.)

Phase transition in anisotropic holographic superfluids with arbitrary dynamical critical exponent z and hyperscaling violation factor α

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.)

Asymmetric criticality of ionic solution containing 1-hexyl-3-methylimidazolium tetrafluoroborate and 2-propanol

International Nuclear Information System (INIS)

Zhang, Xianshuo; Xu, Chen; Zheng, Peizhu; Yin, Tianxiang; Shen, Weiguo

2016-01-01

Highlights: • Liquid–liquid equilibrium of {2-propanol + RTIL} binary solution was measured. • The critical exponents were deduced and showed well agreements with 3D-Ising universality. • Asymmetry of the coexistence curve was analyzed by the complete scaling theory. • RPM-rescaled critical parameters were calculated. - Abstract: The liquid–liquid coexistence curve for binary solution {2-propanol + 1-hexyl-3-methylimidazolium tetrafluoroborate ([C_6mim][BF_4])} has been measured. The isobaric heat capacities per unit volume were obtained in both critical and non-critical regions. The critical exponents α and β were deduced and showed good agreement with those predicted for the 3D-Ising universality class. The asymmetric behaviour of the diameter of the coexistence curve was analysed based on the complete scaling theory, which indicated that the heat capacity related term plays an important role in describing the asymmetric behaviour of the coexistence curve. Furthermore, the RPM (restricted primitive model)-rescaled critical parameters were calculated and suggested the solvophobic criticality for this system.

Behaviour of Lyapunov exponents near crisis points in the dissipative standard map

Science.gov (United States)

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.

Critical properties of the classical XY and classical Heisenberg models: A renormalization group study

Science.gov (United States)

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.

Universality class of the two-dimensional polymer collapse transition

Science.gov (United States)

Nahum, Adam

2016-05-01

The nature of the θ point for a polymer in two dimensions has long been debated, with a variety of candidates put forward for the critical exponents. This includes those derived by Duplantier and Saleur for an exactly solvable model. We use a representation of the problem via the CPN -1σ model in the limit N →1 to determine the stability of this critical point. First we prove that the Duplantier-Saleur (DS) critical exponents are robust, so long as the polymer does not cross itself: They can arise in a generic lattice model and do not require fine-tuning. This resolves a longstanding theoretical question. We also address an apparent paradox: Two different lattice models, apparently both in the DS universality class, show different numbers of relevant perturbations, apparently leading to contradictory conclusions about the stability of the DS exponents. We explain this in terms of subtle differences between the two models, one of which is fine-tuned (and not strictly in the DS universality class). Next we allow the polymer to cross itself, as appropriate, e.g., to the quasi-two-dimensional case. This introduces an additional independent relevant perturbation, so we do not expect the DS exponents to apply. The exponents in the case with crossings will be those of the generic tricritical O (n ) model at n =0 and different from the case without crossings. We also discuss interesting features of the operator content of the CPN -1 model. Simple geometrical arguments show that two operators in this field theory, with very different symmetry properties, have the same scaling dimension for any value of N (or, equivalently, any value of the loop fugacity). Also we argue that for any value of N the CPN -1 model has a marginal odd-parity operator that is related to the winding angle.

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...).

Controversy in the allometric application of fixed- versus varying-exponent models: a statistical and mathematical perspective.

Science.gov (United States)

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.

Mean-field Ising crossover and the critical exponents γ, ν, and η for a polymer blend: d-PB/PS studied by small-angle neutron scattering

Science.gov (United States)

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.

Perturbative Field-Theoretical Renormalization Group Approach to Driven-Dissipative Bose-Einstein Criticality

Directory of Open Access Journals (Sweden)

Uwe C. Täuber

2014-04-01

Full Text Available The universal critical behavior of the driven-dissipative nonequilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex-valued Landau-Ginzburg functional, which captures the near critical nonequilibrium dynamics, and generalizes model A for classical relaxational dynamics with nonconserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest nontrivial order in the dimensional ε expansion about the upper critical dimension d_{c}=4 and establish the emergence of a novel universal scaling exponent associated with the nonequilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (subdiffusive model B with complex coefficients.

Critical initial-slip scaling for the noisy complex Ginzburg–Landau equation

International Nuclear Information System (INIS)

Liu, Weigang; Täuber, Uwe C

2016-01-01

We employ the perturbative fieldtheoretic renormalization group method to investigate the universal critical behavior near the continuous non-equilibrium phase transition in the complex Ginzburg–Landau equation with additive white noise. This stochastic partial differential describes a remarkably wide range of physical systems: coupled nonlinear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose–Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics, such as cold atomic gases and exciton-polaritons in pumped semiconductor quantum wells in optical cavities. Our starting point is a noisy, dissipative Gross–Pitaevski or nonlinear Schrödinger equation, or equivalently purely relaxational kinetics originating from a complex-valued Landau–Ginzburg functional, which generalizes the standard equilibrium model A critical dynamics of a non-conserved complex order parameter field. We study the universal critical behavior of this system in the early stages of its relaxation from a Gaussian-weighted fully randomized initial state. In this critical aging regime, time translation invariance is broken, and the dynamics is characterized by the stationary static and dynamic critical exponents, as well as an independent ‘initial-slip’ exponent. We show that to first order in the dimensional expansion about the upper critical dimension, this initial-slip exponent in the complex Ginzburg–Landau equation is identical to its equilibrium model A counterpart. We furthermore employ the renormalization group flow equations as well as construct a suitable complex spherical model extension to argue that this conclusion likely remains true to all orders in the perturbation expansion. (paper)

Phase diagram and universality of the Lennard-Jones gas-liquid system

KAUST Repository

Watanabe, Hiroshi

2012-01-01

The gas-liquid phase transition of the three-dimensional Lennard-Jones particles system is studied by molecular dynamics simulations. The gas and liquid densities in the coexisting state are determined with high accuracy. The critical point is determined by the block density analysis of the Binder parameter with the aid of the law of rectilinear diameter. From the critical behavior of the gas-liquid coexisting density, the critical exponent of the order parameter is estimated to be β = 0.3285(7). Surface tension is estimated from interface broadening behavior due to capillary waves. From the critical behavior of the surface tension, the critical exponent of the correlation length is estimated to be ν = 0.63(4). The obtained values of β and ν are consistent with those of the Ising universality class. © 2012 American Institute of Physics.

Controlled test for predictive power of Lyapunov exponents: their inability to predict epileptic seizures.

Science.gov (United States)

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

Critical behaviour of the randomly stirred dynamical Potts model: novel universality class and effects of compressibility

International Nuclear Information System (INIS)

Antonov, N V; Kapustin, A S

2012-01-01

Critical behaviour of the dynamical Potts model, subjected to vivid turbulent mixing, is studied by means of the renormalization group. The advecting velocity field is modelled by Kraichnan’s rapid-change ensemble: Gaussian statistics with a given pair correlator 〈vv〉∝δ(t − t′) k −d−ξ , where k is the wave number, d is the dimension of space and 0 < ξ < 2 is an arbitrary exponent. The system exhibits different types of infrared scaling behaviour, associated with four infrared attractors of the renormalization group equations. In addition to the known asymptotic regimes (equilibrium Potts model and passive scalar field), the existence of a new, strongly non-equilibrium type of critical behaviour (universality class) is established, where the self-interaction of the order parameter and the turbulent mixing are equally important. The corresponding critical dimensions and the regions of stability for all the regimes are calculated in the leading order of the double expansion in ξ and ε = 6 − d. Special attention is paid to the effects of compressibility of the fluid, because they lead to interesting crossover phenomena. (paper)

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)

Critical behavior of binary mixture of {x C6H5CN + (1 - x) CH3(CH2)12CH3}: Measurements of coexistence curves, turbidity, and heat capacity

International Nuclear Information System (INIS)

Yin Tianxiang; Lei Yuntao; Huang Meijun; Chen Zhiyun; Mao Chunfeng; An Xueqin; Shen Weiguo

2011-01-01

Research highlights: → Coexistence curve, turbidity and heat capacity of critical solution were measured. → Critical amplitudes were determined to test universal ratios. → Complete scaling theory was verified. → Monotonic critical crossover behavior was demonstrated. - Abstract: (Liquid + liquid) coexistence curve, turbidity, and isobaric heat capacity per unit volume for the critical solution of {benzonitrile + n-tetradecane} have been measured. The critical exponents β, ν, γ, and α and system-dependent critical amplitudes B, ξ 0 , χ 0 , and A ± , corresponding to the difference of the general density variable of two coexisting phases Δρ, the correlation length ξ, the osmotic compressibility χ, and the isobaric heat capacity per unit volume C p V -1 , have been deduced and were used to test some universal ratios. The behavior of the diameter of the coexistence curves showed good agreement with the complete scaling theory. The analysis of effective critical exponent β eff , which was well described by the crossover model proposed by Anisimov and Sengers, and effective critical exponent α eff indicated monotonic crossover phenomena from 3D-Ising behavior to mean-field one as the temperature departed from the critical point.

Relating Lagrangian passive scalar scaling exponents to Eulerian scaling exponents in turbulence

OpenAIRE

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...

van der Waals criticality in AdS black holes: A phenomenological study

Science.gov (United States)

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.

Study into critical properties of 3D frustrated Heisenberg model on triangular lattice by the use of Monte Carlo methods

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.

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

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

Quantum criticality around metal-insulator transitions of strongly correlated electron systems

Science.gov (United States)

Misawa, Takahiro; Imada, Masatoshi

2007-03-01

Quantum criticality of metal-insulator transitions in correlated electron systems is shown to belong to an unconventional universality class with violation of the Ginzburg-Landau-Wilson (GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square lattices are capable of such metal-insulator transitions with unusual criticality under a preexisting symmetry breaking. The obtained universality is consistent with the scaling theory formulated for Mott transitions and with a number of numerical results beyond the mean-field level, implying that preexisting symmetry breaking is not necessarily required for the emergence of this unconventional universality. Examinations of fluctuation effects indicate that the obtained critical exponents remain essentially exact beyond the mean-field level. It further clarifies the whole structure of singularities by a unified treatment of the bandwidth-control and filling-control transitions. Detailed analyses of the criticality, containing diverging carrier density fluctuations around the marginal quantum critical point, are presented from microscopic calculations and reveal the nature as quantum critical “opalescence.” The mechanism of emerging marginal quantum critical point is ascribed to a positive feedback and interplay between the preexisting gap formation present even in metals and kinetic energy gain (loss) of the metallic carrier. Analyses of crossovers between GLW type at nonzero temperature and topological type at zero temperature show that the critical exponents observed in (V,Cr)2O3 and κ-ET -type organic conductors provide us with evidence for the existence of the present marginal

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)

Criticality in Neuronal Networks

Science.gov (United States)

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.

Engineering Surface Critical Behavior of (2 +1 )-Dimensional O(3) Quantum Critical Points

Science.gov (United States)

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.

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.

Universal Properties of Many-Body Delocalization Transitions

Directory of Open Access Journals (Sweden)

Andrew C. Potter

2015-09-01

Full Text Available We study the dynamical melting of “hot” one-dimensional many-body localized systems. As disorder is weakened below a critical value, these nonthermal quantum glasses melt via a continuous dynamical phase transition into classical thermal liquids. By accounting for collective resonant tunneling processes, we derive and numerically solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow subdiffusive equilibration dynamics and energy transport. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. Our approach elucidates the universal long-distance, low-energy scaling structure of many-body delocalization transitions in one dimension, in a way that is transparently connected to the underlying microscopic physics. We discuss experimentally testable signatures of the predicted scaling properties.

Crossover phenomena in the critical range near magnetic ordering transition

Science.gov (United States)

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.

Monte Carlo-based tail exponent estimator

Science.gov (United States)

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.

Quantum critical scaling for field-induced quantum phase transition in a periodic Anderson-like model polymer chain

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.

Scaling and universality in magnetocaloric materials

DEFF Research Database (Denmark)

Smith, Anders; Nielsen, Kaspar Kirstein; Bahl, Christian R. H.

2014-01-01

-order phase transition within the context of the theory of critical phenomena. Sufficiently close to the critical temperature of a second-order material, the scaling of the isothermal entropy change will be determined by the critical exponents and will be the same as that of the singular part of the entropy......The magnetocaloric effect of a magnetic material is characterized by two quantities, the isothermal entropy change and the adiabatic temperature change, both of which are functions of temperature and applied magnetic field. We discuss the scaling properties of these quantities close to a second...... fields are not universal, showing significant variation for models in the same universality class. As regards the adiabatic temperature change, it is not determined exclusively by the singular part of the free energy and its derivatives. We show that the field dependence of the adiabatic temperature...

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

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

Critical Capability Pedagogies and University Education

Science.gov (United States)

Walker, Melanie

2010-01-01

The article argues for an alliance of the capability approach developed by Amartya Sen with ideas from critical pedagogy for undergraduate university education which develops student agency and well being on the one hand, and social change towards greater justice on the other. The purposes of a university education in this article are taken to…

Bak-Tang-Wiesenfeld model in the upper critical dimension: Induced criticality in lower-dimensional subsystems

Science.gov (United States)

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 .

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...

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

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.

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

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

Exact critical properties of two-dimensional polymer networks from conformal invariance

International Nuclear Information System (INIS)

Duplantier, B.

1988-03-01

An infinity of exact critical exponents for two-dimensional self-avoiding walks can be derived from conformal invariance and Coulomb gas techniques applied to the O(n) model and to the Potts model. They apply to polymer networks of any topology, for which a general scaling theory is given, valid in any dimension d. The infinite set of exponents has also been calculated to O(ε 2 ), for d=4-ε. The 2D study also includes other universality classes like the dense polymers, the Hamiltonian walks, the polymers at their θ-point. Exact correlation functions can be further given for Hamiltonian walks, and exact winding angle probability distributions for the self-avoiding walks

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)

Critical behavior of magnetization in URhAl: Quasi-two-dimensional Ising system with long-range interactions

Science.gov (United States)

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.

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

Characterizing Submonolayer Growth of 6P on Mica: Capture Zone Distributions vs. Growth Exponents and the Role of Hot Precursors

Science.gov (United States)

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.

Universality in random-walk models with birth and death

International Nuclear Information System (INIS)

Bender, C.M.; Boettcher, S.; Meisinger, P.N.

1995-01-01

Models of random walks are considered in which walkers are born at one site and die at all other sites. Steady-state distributions of walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions D≠2, 4. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. This work elucidates the adsorption transition of polymers at curved interfaces. copyright 1995 The American Physical Society

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)

Scaling of the distribution function and the critical exponents near the point of a marginal stability under the Vlasov-Poisson equations

International Nuclear Information System (INIS)

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)

Weightless experiments to probe universality of fluid critical behavior

Science.gov (United States)

Lecoutre, C.; Guillaument, R.; Marre, S.; Garrabos, Y.; Beysens, D.; Hahn, I.

2015-06-01

Near the critical point of fluids, critical opalescence results in light attenuation, or turbidity increase, that can be used to probe the universality of critical behavior. Turbidity measurements in SF6 under weightlessness conditions on board the International Space Station are performed to appraise such behavior in terms of both temperature and density distances from the critical point. Data are obtained in a temperature range, far (1 K) from and extremely close (a few μ K ) to the phase transition, unattainable from previous experiments on Earth. Data are analyzed with renormalization-group matching classical-to-critical crossover models of the universal equation of state. It results that the data in the unexplored region, which is a minute deviant from the critical density value, still show adverse effects for testing the true asymptotic nature of the critical point phenomena.

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.

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.

Lyapunov exponents and smooth ergodic theory

CERN Document Server

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.

Dynamical Response near Quantum Critical Points.

Science.gov (United States)

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.

Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime

International Nuclear Information System (INIS)

Visser, A de; Ponomarenko, L A; Galistu, G; Lang, D T N de; Pruisken, A M M; Zeitler, U; Maude, D

2006-01-01

High-field magnetotransport experiments provide an excellent tool to investigate the plateau-insulator phase transition in the integral quantum Hall effect. Here we review recent low-temperature high-field magnetotransport studies carried out on several InGaAs/InP heterostructures and an InGaAs/GaAs quantum well. We find that the longitudinal resistivity ρ xx near the critical filling factor ν c ∼ 0.5 follows the universal scaling law ρ xx (ν, T) ∝ exp(-Δν/(T/T 0 ) κ ), where Δν = ν-ν c . The critical exponent κ equals 0.56 ± 0.02, which indicates that the plateau-insulator transition falls in a non-Fermi liquid universality class

Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

International Nuclear Information System (INIS)

Borisenko, O.; Chelnokov, V.; Cortese, G.; Gravina, M.; Papa, A.; Surzhikov, I.

2014-01-01

Three-dimensional Z(N) lattice gauge theories at zero temperature are studied for various values of N. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized Z(N) model for N=2,3,4,5,6,8. Numerical computations are used to simulate vector models for N=2,3,4,5,6,8,13,20 for lattices with linear extension up to L=96. We locate the critical points of phase transitions and establish their scaling with N. The values of the critical indices indicate that the models with N>4 belong to the universality class of the three-dimensional XY model. However, the exponent α derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle

Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

Energy Technology Data Exchange (ETDEWEB)

Borisenko, O., E-mail: oleg@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine); Chelnokov, V., E-mail: chelnokov@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine); Cortese, G., E-mail: cortese@unizar.es [Instituto de Física Teórica UAM/CSIC, Cantoblanco, E-28049 Madrid (Spain); Departamento de Física Teórica, Universidad de Zaragoza, E-50009 Zaragoza (Spain); Gravina, M., E-mail: gravina@cs.infn.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy); Papa, A., E-mail: papa@cs.infn.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy); Surzhikov, I., E-mail: i_van_go@inbox.ru [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine)

2014-02-15

Three-dimensional Z(N) lattice gauge theories at zero temperature are studied for various values of N. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized Z(N) model for N=2,3,4,5,6,8. Numerical computations are used to simulate vector models for N=2,3,4,5,6,8,13,20 for lattices with linear extension up to L=96. We locate the critical points of phase transitions and establish their scaling with N. The values of the critical indices indicate that the models with N>4 belong to the universality class of the three-dimensional XY model. However, the exponent α derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle.

Cryptanalysis of 'less short' RSA secret exponents

NARCIS (Netherlands)

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

Lyapunov exponent for aging process in induction motor

Science.gov (United States)

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

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)

Scaling of the distribution function and the critical exponents near the point of a marginal stability under the Vlasov-Poisson equations

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}=(-)/ is the dimensionless reduced velocity dispersion. Within the error of computation these critical exponents satisfy to equality {gamma}={beta}({delta}-1), known in thermodynamics as the Widom equality, which is direct consequence of scaling invariance of the Fourier components f{sub m} of the distribution function f at |{theta}| << 1, i.e. f{sub m}({lambda}{sup at}t, {lambda}{sup av}v, {lambda}{sup a{theta}}{theta}, {lambda}{sup aA0}A{sub 0}, {lambda}{sup aF}F{sub 1})={lambda}f{sub m}(t, v, {theta}, A{sub 0}, F{sub 1}) at {theta} 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)

Nuclear criticality research at the University of New Mexico

International Nuclear Information System (INIS)

Busch, R.D.

1997-01-01

Two projects at the University of New Mexico are briefly described. The university's Chemical and Nuclear Engineering Department has completed the final draft of a primer for MCNP4A, which it plans to publish soon. The primer was written to help an analyst who has little experience with the MCNP code to perform criticality safety analyses. In addition, the department has carried out a series of approach-to-critical experiments on the SHEBA-II, a UO 2 F 2 solution critical assembly at Los Alamos National Laboratory. The results obtained differed slightly from what was predicted by the TWODANT code

Singularity of the London penetration depth at quantum critical points in superconductors.

Science.gov (United States)

Chowdhury, Debanjan; Swingle, Brian; Berg, Erez; Sachdev, Subir

2013-10-11

We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents and ratios of amplitudes on the two sides of the transition are universal, an overall sign depends upon the interplay between the critical theory and the underlying Fermi surface. We determine these features for critical points to spin density wave and nematic ordering, and for a topological transition between a superconductor with Z2 fractionalization and a conventional superconductor. We note implications for recent measurements of the London penetration depth in BaFe2(As(1-x)P(x))2 [K. Hashimoto et al., Science 336, 1554 (2012)].

Molecular dynamics simulation of a binary mixture near the lower critical point

Energy Technology Data Exchange (ETDEWEB)

Pousaneh, Faezeh; Edholm, Olle, E-mail: oed@kth.se [Theoretical Biological Physics, Department of Theoretical Physics, Royal Institute of Technology (KTH), AlbaNova University Center, SE-106 91 Stockholm (Sweden); Maciołek, Anna [Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw (Poland); Max-Planck-Institut für Intelligente Systeme, Heisenbergstrasse 3, D-70569 Stuttgart (Germany)

2016-07-07

2,6-lutidine molecules mix with water at high and low temperatures but in a wide intermediate temperature range a 2,6-lutidine/water mixture exhibits a miscibility gap. We constructed and validated an atomistic model for 2,6-lutidine and performed molecular dynamics simulations of 2,6-lutidine/water mixture at different temperatures. We determined the part of demixing curve with the lower critical point. The lower critical point extracted from our data is located close to the experimental one. The estimates for critical exponents obtained from our simulations are in a good agreement with the values corresponding to the 3D Ising universality class.

Criticality of Parasitic Disease Transmission in a Diffusive Population

International Nuclear Information System (INIS)

He Minhua; Zhang Duanming; Yin Yanping; Chen Zhiyuan; Pan Guijun

2008-01-01

Through using the methods of finite-size effect and short time dynamic scaling, we study the critical behavior of parasitic disease spreading process in a diffusive population mediated by a static vector environment. Through comprehensive analysis of parasitic disease spreading we find that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. We determine the critical population density, above which the system reaches an epidemic spreading stationary state. We also perform a scaling analysis to determine the order parameter and critical relaxation exponents. The results show that the model does not belong to the usual directed percolation universality class and is compatible with the class of directed percolation with diffusive and conserved fields

(Liquid + liquid) phase equilibrium and critical behavior of binary solution {heavy water + 2,6-dimethylpyridine}

International Nuclear Information System (INIS)

Xu, Chen; Chai, Shouning; Yin, Tianxiang; Chen, Zhiyun; Shen, Weiguo

2015-01-01

Highlights: • Coexistence curves, heat capacities and turbidities were measured. • Deuterium effect on coexistence curves was discussed. • Universal critical amplitude ratios were tested. • Asymmetry of coexistence curves was analyzed by the complete scaling theory. - Abstract: The (liquid + liquid) coexistence curves, the isobaric heat capacities per unit volume and the turbidities for the binary solution of {heavy water + 2,6-dimethylpyridine} have been precisely measured. The values of the critical exponents were obtained, which confirmed the 3D-Ising universality. It was found that the critical temperature dropped by 5.9 K and the critical amplitude of the coexistence curve significantly increased as compared to the binary solution of {water + 2,6-dimethylpyridine}. The complete scaling theory was applied to well describe the asymmetric behavior of the diameter of the coexistence curve as the heat capacity contribution was considered. Moreover, the values of the critical amplitudes of the correlation length and the osmotic compressibility were deduced, which together with the critical amplitudes of the coexistence curve and the heat capacity to test universal amplitude ratios

What is the cementation exponent? A new differential interpretation

Science.gov (United States)

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

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.

Universality and the Renormalisation Group

CERN Document Server

Litim, D F

2005-01-01

Several functional renormalisation group (RG) equations including Polchinski flows and Exact RG flows are compared from a conceptual point of view and in given truncations. Similarities and differences are highlighted with special emphasis on stability properties. The main observations are worked out at the example of O(N) symmetric scalar field theories where the flows, universal critical exponents and scaling potentials are compared within a derivative expansion. To leading order, it is established that Polchinski flows and ERG flows - despite their inequivalent derivative expansions - have identical universal content, if the ERG flow is amended by an adequate optimisation. The results are also evaluated in the light of stability and minimum sensitivity considerations. Extensions to higher order and further implications are emphasized.

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

Critical behavior and dimension crossover of pion superfluidity

Science.gov (United States)

Wang, Ziyue; Zhuang, Pengfei

2016-09-01

We investigate the critical behavior of pion superfluidity in the framework of the functional renormalization group (FRG). By solving the flow equations in the SU(2) linear sigma model at finite temperature and isospin density, and making comparison with the fixed point analysis of a general O (N ) system with continuous dimension, we find that the pion superfluidity is a second order phase transition subject to an O (2 ) universality class with a dimension crossover from dc=4 to dc=3 . This phenomenon provides a concrete example of dimension reduction in thermal field theory. The large-N expansion gives a temperature independent critical exponent β and agrees with the FRG result only at zero temperature.

Critical behavior at the deconfinement phase phase transition of SU(2) lattice gauge theory in (2+1) dimensions

International Nuclear Information System (INIS)

Christensen, J.; Damgaard, P.H.

1991-01-01

The finite-temperature deconfinement phase transition of SU(2) lattice gauge theory in (2+1) dimensions is studied by Monte Carlo methods. Comparison is made with the expected form of correlation functions on both sides of the critical point. The critical behavior is compared with expectations based on universality arguments. Attempts are made to extract unbiased values of critical exponents on several lattices sizes. The behavior of Polyakov loops in higher representations of the gauge group is studied close to the phase transition. (orig.)

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.

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)

Adapting the Critical Thinking Assessment Test for Palestinian Universities

Science.gov (United States)

Basha, Sami; Drane, Denise; Light, Gregory

2016-01-01

Critical thinking is a key learning outcome for Palestinian students. However, there are no validated critical thinking tests in Arabic. Suitability of the US developed Critical Thinking Assessment Test (CAT) for use in Palestine was assessed. The test was piloted with university students in English (n = 30) and 4 questions were piloted in Arabic…

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.

How We Tend To Overestimate Powerlaw Tail Exponents

OpenAIRE

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.

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

The Evolution of the Exponent of Zipf's Law in Language Ontogeny

Science.gov (United States)

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

Exploring Finnish university students' perceived level of critical thinking

OpenAIRE

Orszag, Aaron

2015-01-01

Critical thinking is believed to be a 21 st century skill that many employers consider crucial when hiring recent graduates. However, it is debated whether critical thinking should be taught in academic foreign language courses at the tertiary level, which primarily aim to develop students’ language and communication skills. This localized, exploratory research examines Finnish university students’ self-reported critical thinking skills a...

Characterizing critical phenomena via the Purcell effect

Science.gov (United States)

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.

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

Scaling functions for the Inverse Compressibility near the QCD critical point

Science.gov (United States)

Lacey, Roy

2017-09-01

The QCD phase diagram can be mapped out by studying fluctuations and their response to changes in the temperature and baryon chemical potential. Theoretical studies indicate that the cumulant ratios Cn /Cm used to characterize the fluctuation of conserved charges, provide a valuable probe of deconfinement and chiral dynamics, as well as for identifying the position of the critical endpoint (CEP) in the QCD phase diagram. The ratio C1 /C2 , which is linked to the inverse compressibility, vanishes at the CEP due to the divergence of the net quark number fluctuations at the critical point belonging to the Z(2) universality class. Therefore, it's associated scaling function can give insight on the location of the critical end point, as well as the critical exponents required to assign its static universality class. Scaling functions for the ratio C1 /C2 , obtained from net-proton multiplicity distributions for a broad range of collision centralities in Au+Au (√{sNN} = 7.7 - 200 GeV) collisions will be presented and discussed.

Lyapunov exponents

CERN Document Server

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.

Critical behavior of the contact process on small-world networks

Science.gov (United States)

Ferreira, Ronan S.; Ferreira, Silvio C.

2013-11-01

We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a homogeneous cluster-approximation for the limit of vanishing clustering ( p → 1). The critical exponents and dimensionless moment ratios of the CP are in agreement with those predicted by the mean-field theory for any p > 0. This independence on the network clustering shows that the small-world property is a sufficient condition for the mean-field theory to correctly predict the universality of the model. Moreover, we compare the CP dynamics on WS networks with rewiring probability p = 1 and random regular networks and show that the weak heterogeneity of the WS network slightly changes the critical point but does not alter other critical quantities of the model.

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)

Crowding of Interacting Fluid Particles in Porous Media through Molecular Dynamics: Breakdown of Universality for Soft Interactions

Science.gov (United States)

Schnyder, Simon K.; Horbach, Jürgen

2018-02-01

Molecular dynamics simulations of interacting soft disks confined in a heterogeneous quenched matrix of soft obstacles show dynamics which is fundamentally different from that of hard disks. The interactions between the disks can enhance transport when their density is increased, as disks cooperatively help each other over the finite energy barriers in the matrix. The system exhibits a transition from a diffusive to a localized state, but the transition is strongly rounded. Effective exponents in the mean-squared displacement can be observed over three decades in time but depend on the density of the disks and do not correspond to asymptotic behavior in the vicinity of a critical point, thus, showing that it is incorrect to relate them to the critical exponents in the Lorentz model scenario. The soft interactions are, therefore, responsible for a breakdown of the universality of the dynamics.

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)

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

Insulating phase in Sr{sub 2}IrO{sub 4}: An investigation using critical analysis and magnetocaloric effect

Energy Technology Data Exchange (ETDEWEB)

Bhatti, Imtiaz Noor; Pramanik, A.K., E-mail: akpramanik@mail.jnu.ac.in

2017-01-15

The nature of insulating phase in 5d based Sr{sub 2}IrO{sub 4} is quite debated as the theoretical as well as experimental investigations have put forward evidences in favor of both magnetically driven Slater-type and interaction driven Mott-type insulator. To understand this insulating behavior, we have investigated the nature of magnetic state in Sr{sub 2}IrO{sub 4} through studying critical exponents, low temperature thermal demagnetization and magnetocaloric effect. The estimated critical exponents do not exactly match with any universality class, however, the values obey the scaling behavior. The exponent values suggest that spin interaction in present material is close to mean-field model. The analysis of low temperature thermal demagnetization data, however, shows dual presence of localized- and itinerant-type of magnetic interaction. Moreover, field dependent change in magnetic entropy indicates magnetic interaction is close to mean-field type. While this material shows an insulating behavior across the magnetic transition, yet a distinct change in slope in resistivity is observed around T{sub c}. We infer that though the insulating phase in Sr{sub 2}IrO{sub 4} is more close to be Slater-type but the simultaneous presence of both Slater- and Mott-type is the likely scenario for this material. - Highlights: • Critical analysis shows Sr{sub 2}IrO{sub 4} has ferromagnetic ordering temperature T{sub c}~225 K. • Obtained critical exponents imply spin interaction is close to mean-field model. • Analysis of magneto-entropy data also supports mean-field type interaction. • However, the presence of both itinerant and localized spin interaction is evident. • Sr{sub 2}IrO{sub 4} has simultaneous presence of both Slater- and Mott-type insulating phase.

Data collapse and critical dynamics in neuronal avalanche data

Science.gov (United States)

Butler, Thomas; Friedman, Nir; Dahmen, Karin; Beggs, John; Deville, Lee; Ito, Shinya

2012-02-01

The tasks of information processing, computation, and response to stimuli require neural computation to be remarkably flexible and diverse. To optimally satisfy the demands of neural computation, neuronal networks have been hypothesized to operate near a non-equilibrium critical point. In spite of their importance for neural dynamics, experimental evidence for critical dynamics has been primarily limited to power law statistics that can also emerge from non-critical mechanisms. By tracking the firing of large numbers of synaptically connected cortical neurons and comparing the resulting data to the predictions of critical phenomena, we show that cortical tissues in vitro can function near criticality. Among the most striking predictions of critical dynamics is that the mean temporal profiles of avalanches of widely varying durations are quantitatively described by a single universal scaling function (data collapse). We show for the first time that this prediction is confirmed in neuronal networks. 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.

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...

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

Science.gov (United States)

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).

Critical cooperation range to improve spatial network robustness.

Directory of Open Access Journals (Sweden)

Vitor H P Louzada

Full Text Available A robust worldwide air-transportation network (WAN is one that minimizes the number of stranded passengers under a sequence of airport closures. Building on top of this realistic example, here we address how spatial network robustness can profit from cooperation between local actors. We swap a series of links within a certain distance, a cooperation range, while following typical constraints of spatially embedded networks. We find that the network robustness is only improved above a critical cooperation range. Such improvement can be described in the framework of a continuum transition, where the critical exponents depend on the spatial correlation of connected nodes. For the WAN we show that, except for Australia, all continental networks fall into the same universality class. Practical implications of this result are also discussed.

Lyapunov exponents for infinite dimensional dynamical systems

Science.gov (United States)

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.

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)

Subdiffusive master equation with space-dependent anomalous exponent and structural instability

Science.gov (United States)

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.

Introduction to the critical and multicritical phenomena

International Nuclear Information System (INIS)

Salinas, S.R.A.

1982-09-01

The behavior of matter in the neighborhood of simple critical points is treated. The concepts of critical exponents and universality is introduced and the classical theories of the critical behavior and the phenomenological scaling theories of the thermodynamic functions and the critical correlations are described. Finally, a description of the theory of the renormalization group, which gives the microscopic bases of the scaling laws is ended . Four types of multicritical points which have already been detected in solid crystals tricritical, bicritical, tetracritical, and Lifshitz points are studied. Landa's theory and the formulation of the scaling laws in the neighborhood of these points is described. Also, the main features of some theoretical models which produce multicritical points-the Ising metamagnet and BEG model, which exhibit tricritical points, and the ANNNI model, which exhibits a Lifshitz point are described. The renormalization group approach in the Fourier space to the Ising metamagnet, and the new techniques of partial differential aproximants to analyze the scaling behavior in the neighborhood of the multicritical points are presented. (Author) [pt

Benford analysis of quantum critical phenomena: First digit provides high finite-size scaling exponent while first two and further are not much better

Science.gov (United States)

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.

Critical behaviour of binary mixture of {xC6H5CN + (1 - x)CH3(CH2)7CH3}: Measurements of coexistence curves, light scattering, and heat capacity

International Nuclear Information System (INIS)

Lei Yuntao; Chen Zhiyun; Wang Nong; Mao Chunfeng; An Xueqin; Shen Weiguo

2010-01-01

Liquid + liquid coexistence, light scattering, and isobaric heat capacity per unit volume for the critical solutions of (benzonitrile + n-nonane) have been measured. The critical exponents relating to the coexistence curve β, the osmotic compressibility γ, the correlation length ν, and the heat capacity α have been deduced and the values are consistent with the 3D-Ising values in the range close to the critical point. The experimental results of the liquid + liquid coexistence were analyzed to examine the Wegner correction terms and the behaviour of the diameter of the coexistence curves. The light scattering data were well described by the crossover model proposed by Anisimov and Sengers, and showed a tendency of monotonic crossover of the critical exponents γ and ν from the 3D-Ising values to the mean-field values as the temperature departures from the critical point. From calorimetric measurements, the amplitude A ± and the critical background B cr of the heat capacity in the critical region have been deduced and some universal ratios are tested.

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.

Critical phases in the raise and peel model

Science.gov (United States)

Jara, D. A. C.; Alcaraz, F. C.

2018-05-01

The raise and peel model (RPM) is a nonlocal stochastic model describing the space and time fluctuations of an evolving one dimensional interface. Its relevant parameter u is the ratio between the rates of local adsorption and nonlocal desorption processes (avalanches) The model at u  =  1 is the first example of a conformally invariant stochastic model. For small values u    u 0 it is critical. Although previous studies indicate that u 0  =  1, a determination of u 0 with a reasonable precision is still missing. By calculating numerically the structure function of the height profiles in the reciprocal space we confirm with good precision that indeed u 0  =  1. We establish that at the conformal invariant point u  =  1 the RPM has a roughening transition with dynamical and roughness critical exponents z  =  1 and , respectively. For u  >  1 the model is critical with a u-dependent dynamical critical exponent that tends towards zero as . However at 1/u  =  0 the RPM is exactly mapped into the totally asymmetric exclusion problem. This last model is known to be noncritical (critical) for open (periodic) boundary conditions. Our numerical studies indicate that the RPM as , due to its nonlocal dynamical processes, has the same large-distance physics no matter what boundary condition we chose. For u  >  1, our numerical analysis shows that in contrast to previous predictions, the region is composed of two distinct critical phases. For the height profiles are rough (), and for the height profiles are flat at large distances (). We also observed that in both critical phases (u  >  1) the RPM at short length scales, has an effective behavior in the Kardar–Parisi–Zhang critical universality class, that is not the true behavior of the system at large length scales.

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)

Self-organized Criticality Model for Ocean Internal Waves

International Nuclear Information System (INIS)

Wang Gang; Hou Yijun; Lin Min; Qiao Fangli

2009-01-01

In this paper, we present a simple spring-block model for ocean internal waves based on the self-organized criticality (SOC). The oscillations of the water blocks in the model display power-law behavior with an exponent of -2 in the frequency domain, which is similar to the current and sea water temperature spectra in the actual ocean and the universal Garrett and Munk deep ocean internal wave model [Geophysical Fluid Dynamics 2 (1972) 225; J. Geophys. Res. 80 (1975) 291]. The influence of the ratio of the driving force to the spring coefficient to SOC behaviors in the model is also discussed. (general)

Partial differential equations with variable exponents variational methods and qualitative analysis

CERN Document Server

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

Introduction to critical and multicritical phenomena

International Nuclear Information System (INIS)

Salinas, S.R.A.

1984-01-01

The behavior of matter in the neighborhood of simple critical points is treated. The concepts of critical exponents and universality are introduced, and the classical theories of the critical behavior and the phenomenological scaling theories of the thermodynamic functions and the critical correlations are described. Finally the first part is ended with a discription of the theory of the renormalization group, which gives the microscopic bases of the scaling laws. In the second part of these notes four types of multicritical points which have already been detected in solid crystals; tricritical, bicritical, tetracritical, and Lifshitz points are studied. Landau's theory and the formulation of the scaling laws in the neighborhood of these points is described. The main features of some theoretical models which produce multicritical points - the Ising metamagnet and the BEG model which exhibit tricritical points, and the ANNNI model, which exhibits a Lifshitz point are also described. The renormalization group approach in the Fourier space to the Ising metamagnet, and the new techniques of partial differential approximants to analyze the scaling behavior in the neighborhood of the multicritical points is presented. (Author) [pt

Critical adsorption profiles around a sphere and a cylinder in a fluid at criticality: Local functional theory

Science.gov (United States)

Yabunaka, Shunsuke; Onuki, Akira

2017-09-01

We study universal critical adsorption on a solid sphere and a solid cylinder in a fluid at bulk criticality, where preferential adsorption occurs. We use a local functional theory proposed by Fisher et al. [M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Paris Ser. B 287, 207 (1978); M. E. Fisher and H. Au-Yang, Physica A 101, 255 (1980), 10.1016/0378-4371(80)90112-0]. We calculate the mean order parameter profile ψ (r ) , where r is the distance from the sphere center and the cylinder axis, respectively. The resultant differential equation for ψ (r ) is solved exactly around a sphere and numerically around a cylinder. A strong adsorption regime is realized except for very small surface field h1, where the surface order parameter ψ (a ) is determined by h1 and is independent of the radius a . If r considerably exceeds a , ψ (r ) decays as r-(1 +η ) for a sphere and r-(1 +η )/2 for a cylinder in three dimensions, where η is the critical exponent in the order parameter correlation at bulk criticality.

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

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.

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)

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

Laminar Flame Velocity and Temperature Exponent of Diluted DME-Air Mixture

Science.gov (United States)

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 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.)

A comment on measuring the Hurst exponent of financial time series

Science.gov (United States)

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.

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

Universal Nonequilibrium Signatures of Majorana Zero Modes in Quench Dynamics

Directory of Open Access Journals (Sweden)

R. Vasseur

2014-10-01

Full Text Available The quantum evolution that occurs after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of “quantum quench” to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo L(t=|⟨ψ(0|ψ(t⟩|^{2}∼t^{-α} for large times after the quench, with a universal critical exponent α=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels, or the presence of bound levels between the lead and the superconductor. As in recent quantum-dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.

On universal procrastination

Science.gov (United States)

Eliazar, Iddo

2017-09-01

This paper presents a general stochastic model for procrastination with respect to a deadline. The model establishes a universal procrastination pattern that follows an inverse power-law: if the time remaining to the deadline is r then the response is 1/rε , where ɛ is a positive exponent. The model further establishes that the exponent value ε =1 , which yields the harmonic response 1/r , stands out as special and distinguishable. The theoretical results of the model are shown to be in perfect accord with recent empirical findings.

Griffiths-like phase, critical behavior near the paramagnetic-ferromagnetic phase transition and magnetic entropy change of nanocrystalline La0.75Ca0.25MnO3

Science.gov (United States)

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.

Critical behavior of two- and three-dimensional ferromagnetic and antiferromagnetic spin-ice systems using the effective-field renormalization group technique

Science.gov (United States)

Garcia-Adeva, Angel J.; Huber, David L.

2001-07-01

In this work we generalize and subsequently apply the effective-field renormalization-group (EFRG) technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagomé and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin-ice model can be exactly mapped to the standard Ising model, but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated and does not order. Antiferromagnetic spin ice (in both two and three dimensions) is found to undergo a transition to a long-range-ordered state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in these systems. In addition, the recently introduced generalized constant coupling method is also applied to the calculation of the critical points and ground-state configurations. Again, a very good agreement is found with exact, Monte Carlo, and renormalization-group calculations for the critical points. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest-order limit of the EFRG technique, in which correlations outside a frustrated unit are neglected, and scaling is substituted by strict equality of the thermodynamic quantities.

Critical Success Factors for Knowledge Transfer Collaborations between University and Industry

Science.gov (United States)

Schofield, Tatiana

2013-01-01

In a fast moving business environment university-industry collaborations play a critical role in contributing to national economies and furthering a competitive advantage. Knowledge transfer from university to industry is supported by national governments as part of their innovation, national growth and competitiveness agenda. A…

Universality and Quantum Criticality of the One-Dimensional Spinor Bose Gas

Science.gov (United States)

PâÅ£u, Ovidiu I.; Klümper, Andreas; Foerster, Angela

2018-06-01

We investigate the universal thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. We find that the quantum critical region belongs to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case and identify its boundaries with the peaks of the specific heat. In addition, we show that the compressibility Wilson ratio, which quantifies the relative strength of thermal and quantum fluctuations, serves as a good discriminator of the quantum regimes near the quantum critical point. Remarkably, in the Tonks-Girardeau regime, the universal contact develops a pronounced minimum, reflected in a counterintuitive narrowing of the momentum distribution as we increase the temperature. This momentum reconstruction, also present at low and intermediate momenta, signals the transition from the ferromagnetic to the spin-incoherent Luttinger liquid phase and can be detected in current experiments with ultracold atomic gases in optical lattices.

On the Topological Changes of Local Hurst Exponent in Polar Regions

Science.gov (United States)

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.

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

Effective and fundamental quantum fields at criticality

Energy Technology Data Exchange (ETDEWEB)

Scherer, Michael

2010-10-28

We employ Wetterich's approach to functional renormalization as a suitable method to investigate universal phenomena in non-perturbative quantum field theories both qualitatively and quantitatively. Therefore we derive and investigate flow equations for a class of chiral Yukawa models with and without gauge bosons and reveal fixed-point mechanisms. In four dimensions chiral Yukawa systems serve as toy models for the standard model Higgs sector and show signatures of asymptotically safe fixed points by a balancing of bosonic and fermionic contributions. In the approximations investigated this renders the theory fundamental and solves the triviality problem. Further, we obtain predictions for the Higgs mass and even for the top mass of our toy model. In three dimensions we compute the critical exponents which define new universality classes and provide benchmark values for systems of strongly correlated chiral fermions. In a Yukawa system of non-relativistic two-component fermions a fixed point dominates the renormalization flow giving rise to universality in the BCS-BEC crossover. We push the functional renormalization method to a quantitative level and we compute the critical temperature and the single-particle gap with a considerable precision for the whole crossover. Finally, we provide further evidence for the asymptotic safety scenario in quantum gravity by confirming the existence of an ultraviolet fixed point under inclusion of a curvature-ghost coupling. (orig.)

Effective and fundamental quantum fields at criticality

International Nuclear Information System (INIS)

Scherer, Michael

2010-01-01

We employ Wetterich's approach to functional renormalization as a suitable method to investigate universal phenomena in non-perturbative quantum field theories both qualitatively and quantitatively. Therefore we derive and investigate flow equations for a class of chiral Yukawa models with and without gauge bosons and reveal fixed-point mechanisms. In four dimensions chiral Yukawa systems serve as toy models for the standard model Higgs sector and show signatures of asymptotically safe fixed points by a balancing of bosonic and fermionic contributions. In the approximations investigated this renders the theory fundamental and solves the triviality problem. Further, we obtain predictions for the Higgs mass and even for the top mass of our toy model. In three dimensions we compute the critical exponents which define new universality classes and provide benchmark values for systems of strongly correlated chiral fermions. In a Yukawa system of non-relativistic two-component fermions a fixed point dominates the renormalization flow giving rise to universality in the BCS-BEC crossover. We push the functional renormalization method to a quantitative level and we compute the critical temperature and the single-particle gap with a considerable precision for the whole crossover. Finally, we provide further evidence for the asymptotic safety scenario in quantum gravity by confirming the existence of an ultraviolet fixed point under inclusion of a curvature-ghost coupling. (orig.)

Random-fractal Ansatz for the configurations of two-dimensional critical systems.

Science.gov (United States)

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.

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.

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

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 ...

Safety considerations of new critical assembly for the Research Reactor Institute, Kyoto University

International Nuclear Information System (INIS)

Umeda, Iwao; Matsuoka, Naomi; Harada, Yoshihiko; Miyamoto, Keiji; Kanazawa, Takashi

1975-01-01

The new critical assembly type of nuclear reactor having three cores for the first time in the world was completed successfully at the Research Reactor Institute of Kyoto University in autumn of 1974. It is called KUCA (Kyoto University Critical Assembly). Safety of the critical assembly was considered sufficiently in consequence of discussions between the researchers of the institute and the design group of our company, and then many bright ideas were created through the discussions. This paper is described the new safety design of main equipments - oil pressure type center core drive mechanism, removable water overflow mechanism, core division mechanism, control rod drive mechansim, protection instrumentation system and interlock key system - for the critical assembly. (author)

Critical Thinking in the University Curriculum--The Impact on Engineering Education

Science.gov (United States)

Ahern, A.; O'Connor, T.; McRuairc, G.; McNamara, M.; O'Donnell, D.

2012-01-01

Critical thinking is a graduate attribute that many courses, including engineering courses, claim to produce in students. As a graduate attribute it is seen by academics as a particularly desirable outcome of student learning and is said by researchers to be a defining characteristic of university education. However, how critical thinking is…

Catastrophic Failure and Critical Scaling Laws of Fiber Bundle Material

Directory of Open Access Journals (Sweden)

Shengwang Hao

2017-05-01

Full Text Available This paper presents a spring-fiber bundle model used to describe the failure process induced by energy release in heterogeneous materials. The conditions that induce catastrophic failure are determined by geometric conditions and energy equilibrium. It is revealed that the relative rates of deformation of, and damage to the fiber bundle with respect to the boundary controlling displacement ε0 exhibit universal power law behavior near the catastrophic point, with a critical exponent of −1/2. The proportion of the rate of response with respect to acceleration exhibits a linear relationship with increasing displacement in the vicinity of the catastrophic point. This allows for the prediction of catastrophic failure immediately prior to failure by extrapolating the trajectory of this relationship as it asymptotes to zero. Monte Carlo simulations are completed and these two critical scaling laws are confirmed.

Critical magnetic behaviour in one and two dimensions

International Nuclear Information System (INIS)

Koebler, U.; Hoser, A.

2007-01-01

Critical magnetic data of magnets in which the phase transition is driven by one-dimensional (1D) or two-dimensional (2D) interactions are examined. Characteristic for 1D (2D) phase transitions is that only the longitudinal (in plane) correlation length diverges. The transverse (inter-layer) interactions are then not relevant although they may be finite. The condition for 1D (2D) phase transitions is that the ratio of transverse (inter-layer) to longitudinal (in plane) interactions is below some threshold value. This threshold defines the bandwidth of the 1D (2D) universality class. On the other hand, three-dimensional (3D) magnetic Bragg scattering relies on a finite transverse (inter-layer) correlation length. If this correlation length is relatively long the spin structure appears 3D. For materials with a pure spin moment the dimensionality can now conveniently be inferred from the universal power function by which the order parameter approaches saturation at the stable fixed point T=0. Using this criterion it is concluded that the critical behaviour of 2D magnets is essentially of the 2D Ising type but for 1D magnets of the 3D Ising type. Slight deviations from the ideal model exponents are, however, frequently observed. Universality for T->0 is not of the Ising type in the investigated magnets with a 3D spin

Conditional Lyapunov exponents and transfer entropy in coupled bursting neurons under excitation and coupling mismatch

Science.gov (United States)

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

Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets

Science.gov (United States)

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.

Universities scale like cities.

Directory of Open Access Journals (Sweden)

Anthony F J van Raan

Full Text Available Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to all cities, with similar power law exponents. These findings mean that the larger the city, the more disproportionally they are places of wealth and innovation. Local properties of cities cause a deviation from the expected behavior as predicted by the power law scaling. In this paper we demonstrate that universities show a similar behavior as cities in the distribution of the 'gross university income' in terms of total number of citations over 'size' in terms of total number of publications. Moreover, the power law exponents for university scaling are comparable to those for urban scaling. We find that deviations from the expected behavior can indeed be explained by specific local properties of universities, particularly the field-specific composition of a university, and its quality in terms of field-normalized citation impact. By studying both the set of the 500 largest universities worldwide and a specific subset of these 500 universities--the top-100 European universities--we are also able to distinguish between properties of universities with as well as without selection of one specific local property, the quality of a university in terms of its average field-normalized citation impact. It also reveals an interesting observation concerning the working of a crucial property in networked systems, preferential attachment.

Universities scale like cities.

Science.gov (United States)

van Raan, Anthony F J

2013-01-01

Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to all cities, with similar power law exponents. These findings mean that the larger the city, the more disproportionally they are places of wealth and innovation. Local properties of cities cause a deviation from the expected behavior as predicted by the power law scaling. In this paper we demonstrate that universities show a similar behavior as cities in the distribution of the 'gross university income' in terms of total number of citations over 'size' in terms of total number of publications. Moreover, the power law exponents for university scaling are comparable to those for urban scaling. We find that deviations from the expected behavior can indeed be explained by specific local properties of universities, particularly the field-specific composition of a university, and its quality in terms of field-normalized citation impact. By studying both the set of the 500 largest universities worldwide and a specific subset of these 500 universities--the top-100 European universities--we are also able to distinguish between properties of universities with as well as without selection of one specific local property, the quality of a university in terms of its average field-normalized citation impact. It also reveals an interesting observation concerning the working of a crucial property in networked systems, preferential attachment.

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)

Quantum theories of the early universe - a critical appraisal

International Nuclear Information System (INIS)

Hu, B.L.

1988-01-01

A critical appraisal of certain general problems in the study of quantum processes in curved space as applied to the construction of theories of the early universe is presented. Outstanding issues in different cosmological models and the degree of success of different quantum processes in addressing these issues are summarized. (author)

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.

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.

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.

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

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.

Effects of mixing and stirring on the critical behaviour

International Nuclear Information System (INIS)

Antonov, N V; Hnatich, Michal; Honkonen, Juha

2006-01-01

Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field-theoretic renormalization group. The stirring and mixing are modelled by a random external Gaussian noise with the correlation function ∼δ(t - t')k 4-d-y and the divergence-free (due to incompressibility) velocity field, governed by the stochastic Navier-Stokes equation with a random Gaussian force with the correlation function ∝ δ(t-t')k 4-d-y' . Depending on the relations between the exponents y and y' and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there are three new non-equilibrium regimes (universality classes) associated with new nontrivial fixed points of the renormalization group equations. The corresponding critical dimensions are calculated in the two-loop approximation (second order of the triple expansion in y, y' and ε = 4 - d)

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 ...

Hartree-Fock study of the Anderson metal-insulator transition in the presence of Coulomb interaction: Two types of mobility edges and their multifractal scaling exponents

Science.gov (United States)

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

Analytical description of critical dynamics for two-dimensional dissipative nonlinear maps

International Nuclear Information System (INIS)

Méndez-Bermúdez, J.A.; Oliveira, Juliano A. de; Leonel, Edson D.

2016-01-01

The critical dynamics near the transition from unlimited to limited action diffusion for two families of well known dissipative nonlinear maps, namely the dissipative standard and dissipative discontinuous maps, is characterized by the use of an analytical approach. The approach is applied to explicitly obtain the average squared action as a function of the (discrete) time and the parameters controlling nonlinearity and dissipation. This allows to obtain a set of critical exponents so far obtained numerically in the literature. The theoretical predictions are verified by extensive numerical simulations. We conclude that all possible dynamical cases, independently on the map parameter values and initial conditions, collapse into the universal exponential decay of the properly normalized average squared action as a function of a normalized time. The formalism developed here can be extended to many other different types of mappings therefore making the methodology generic and robust. - Highlights: • We analytically approach scaling properties of a family of two-dimensional dissipative nonlinear maps. • We derive universal scaling functions that were obtained before only approximately. • We predict the unexpected condition where diffusion and dissipation compensate each other exactly. • We find a new universal scaling function that embraces all possible dissipative behaviors.

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

A new combined approach on Hurst exponent estimate and its applications in realized volatility

Science.gov (United States)

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.

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 thinking, nurse education and universities: some thoughts on current issues and implications for nursing practice.

Science.gov (United States)

Morrall, Peter; Goodman, Benny

2013-09-01

When in the latter part of the 20th century nurse 'training' in the UK left the old schools of nursing (based within the health delivery system) and entered universities, the promise was not just a change of focus from training to education but an embracement of 'higher' education. Specifically, nurses were to be exposed to the demands of thinking rather than just doing - and critical thinking at that. However, despite a history of critical perspectives informing nursing theory, that promise may be turning sour. The insidious saturation of the university system in bureaucracy and managerialism has, we argue, undermined critical thinking. A major funding restructuring of higher education in the UK, coinciding with public concern about the state of nursing practice, is undermining further the viability of critical thinking in nursing and potentially the acceptability of university education for nurses. Nevertheless, while critical thinking in universities has decayed, there is no obvious educational alternative that can provide this core attribute, one that is even more necessary to understand health and promote competent nursing practice in an increasingly complex and globalising world. We propose that nurse academics and their colleagues from many other academic and professional disciplines engage in collegiate 'moral action' to re-establish critical thinking in UK universities. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

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

Research on the reactor physics using the Kyoto University Critical Assembly (KUCA)

International Nuclear Information System (INIS)

1986-10-01

The Kyoto University Critical Assembly [KUCA] is a multi-core type critical assembly established in 1974, as a facility for the joint use study by researchers of all universities in Japan. Thereafter, many reactor physics experiments have been carried out using three cores (A-, B-, and C-cores) in the KUCA. In the A- and B-cores, solid moderator such as polyethylene or graphite is used, whereas light-water is utilized as moderator in the C-core. The A-core has been employed mainly in connection with the Cockcroft-Walton type accelerator installed in the KUCA, to measure (1) the subcriticality by the pulsed neutron technique for the critical safety research and (2) the neutron spectrum by the time-of-flight technique. Recently, a basic study on the tight lattice core has also launched using the A-core. The B-core has been employed for the research on the thorium fuel cycle ever since. The C-core has been employed (1) for the basic studies on the nuclear characteristics of light-water moderated high-flux research reactors, including coupled-cores, and (2) for a research related to reducing enrichment of uranium fuel used in research reactors. The C-core is being utilized in the reactor laboratory course experiment for students of ten universities in Japan. The data base of the KUCA critical experiments is generated so far on the basis of approximately 350 experimental reports accumulated in the KUCA. Besides, the assessed KUCA code system has been established through analyses on the various KUCA experiments. In addition to the KUCA itself, both of them are provided for the joint use study by researchers of all universities in Japan. (author)

Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

International Nuclear Information System (INIS)

Yang Bo; Li Xiao-Teng; Chen Xiao-Song; Chen Wei; Liu Jian

2016-01-01

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents v, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model. (paper)

Defect production in nonlinear quench across a quantum critical point.

Science.gov (United States)

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.

Finite-time braiding exponents

Science.gov (United States)

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.

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)

Towards a Gravity Dual for the Large Scale Structure of the Universe

CERN Document Server

Kehagias, A.

2016-01-01

The dynamics of the large-scale structure of the universe enjoys at all scales, even in the highly non-linear regime, a Lifshitz symmetry during the matter-dominated period. In this paper we propose a general class of six-dimensional spacetimes which could be a gravity dual to the four-dimensional large-scale structure of the universe. In this set-up, the Lifshitz symmetry manifests itself as an isometry in the bulk and our universe is a four-dimensional brane moving in such six-dimensional bulk. After finding the correspondence between the bulk and the brane dynamical Lifshitz exponents, we find the intriguing result that the preferred value of the dynamical Lifshitz exponent of our observed universe, at both linear and non-linear scales, corresponds to a fixed point of the RGE flow of the dynamical Lifshitz exponent in the dual system where the symmetry is enhanced to the Schrodinger group containing a non-relativistic conformal symmetry. We also investigate the RGE flow between fixed points of the Lifshitz...

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

Inter-relationship between scaling exponents for describing self-similar river networks

Science.gov (United States)

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 ɛ) (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 ɛ and h. In this study, we expand this to a more general ɛ-η-h relationship. We approach ɛ-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.

Phase transition universality classes of classical, nonequilibrium systems

CERN Document Server

Ódor, G

2004-01-01

In the first chapter I summarize the most important critical exponents and relations used in this work. In the second chapter I briefly address the question of scaling behavior at first order phase transitions.In chapter three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and percolation behavior. The main body of this work is given in chapter four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In chapter five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of known transitions in low dimensional systems are between active and absorbing states of reaction-diffusion type systems, but I briefly introduce related classes that appear in interface growth models in chapter six. Some of them are related to critical behavior of coupled, multi-component systems. Finally in chapter seven I summarize families of absorbing state system classes, mean-field classes and the most freq...

On identifying relationships between the flood scaling exponent and basin attributes.

Science.gov (United States)

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.

Impact of network topology on self-organized criticality

Science.gov (United States)

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.

Short-time dynamics of random-bond Potts ferromagnet with continuous self-dual quenched disorders

OpenAIRE

Pan, Z. Q.; Ying, H. P.; Gu, D. W.

2001-01-01

We present Monte Carlo simulation results of random-bond Potts ferromagnet with the Olson-Young self-dual distribution of quenched disorders in two-dimensions. By exploring the short-time scaling dynamics, we find universal power-law critical behavior of the magnetization and Binder cumulant at the critical point, and thus obtain estimates of the dynamic exponent $z$ and magnetic exponent $\\eta$, as well as the exponent $\\theta$. Our special attention is paid to the dynamic process for the $q...

Fermat's Last Theorem for Factional and Irrational Exponents

Science.gov (United States)

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.

Lyapunov exponents a tool to explore complex dynamics

CERN Document Server

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...

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

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.

Critical behavior of the contact process in a multiscale network

Science.gov (United States)

Ferreira, Silvio C.; Martins, Marcelo L.

2007-09-01

Inspired by dengue and yellow fever epidemics, we investigated the contact process (CP) in a multiscale network constituted by one-dimensional chains connected through a Barabási-Albert scale-free network. In addition to the CP dynamics inside the chains, the exchange of individuals between connected chains (travels) occurs at a constant rate. A finite epidemic threshold and an epidemic mean lifetime diverging exponentially in the subcritical phase, concomitantly with a power law divergence of the outbreak’s duration, were found. A generalized scaling function involving both regular and SF components was proposed for the quasistationary analysis and the associated critical exponents determined, demonstrating that the CP on this hybrid network and nonvanishing travel rates establishes a new universality class.

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)

Data base of reactor physics experimental results in Kyoto University critical assembly experimental facilities

International Nuclear Information System (INIS)

Ichihara, Chihiro; Fujine, Shigenori; Hayashi, Masatoshi

1986-01-01

The Kyoto University critical assembly experimental facilities belong to the Kyoto University Research Reactor Institute, and are the versatile critical assembly constructed for experimentally studying reactor physics and reactor engineering. The facilities are those for common utilization by universities in whole Japan. During more than ten years since the initial criticality in 1974, various experiments on reactor physics and reactor engineering have been carried out using many experimental facilities such as two solidmoderated cores, a light water-moderated core and a neutron generator. The kinds of the experiment carried out were diverse, and to find out the required data from them is very troublesome, accordingly it has become necessary to make a data base which can be processed by a computer with the data accumulated during the past more than ten years. The outline of the data base, the data base CAEX using personal computers, the data base supported by a large computer and so on are reported. (Kako, I.)

Turbulent mixing of a critical fluid: The non-perturbative renormalization

Directory of Open Access Journals (Sweden)

M. Hnatič

2018-01-01

Full Text Available Non-perturbative Renormalization Group (NPRG technique is applied to a stochastical model of a non-conserved scalar order parameter near its critical point, subject to turbulent advection. The compressible advecting flow is modeled by a random Gaussian velocity field with zero mean and correlation function 〈υjυi〉∼(Pji⊥+αPji∥/kd+ζ. Depending on the relations between the parameters ζ, α and the space dimensionality d, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow, but there is a new nonequilibrium regime (universality class associated with new nontrivial fixed points of the renormalization group equations. We have obtained the phase diagram (d, ζ of possible scaling regimes in the system. The physical point d=3, ζ=4/3 corresponding to three-dimensional fully developed Kolmogorov's turbulence, where critical fluctuations are irrelevant, is stable for α≲2.26. Otherwise, in the case of “strong compressibility” α≳2.26, the critical fluctuations of the order parameter become relevant for three-dimensional turbulence. Estimations of critical exponents for each scaling regime are presented.

Variation of Zipf's exponent in one hundred live languages: A study of the Holy Bible translations

Science.gov (United States)

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.

Identification of exponent from load-deformation relation for soft materials from impact tests

Science.gov (United States)

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.

Universal role of correlation entropy in critical phenomena

International Nuclear Information System (INIS)

Gu Shijian; Sun Changpu; Lin Haiqing

2008-01-01

In statistical physics, if we divide successively an equilibrium system into two parts, we will face a situation that, to a certain length ξ, the physics of a subsystem is no longer the same as the original one. The extensive property of the thermal entropy S(A union B) = S(A) + S(B) is then violated. This observation motivates us to introduce a concept of correlation entropy between two points, as measured by the mutual information in information theory, to study the critical phenomena. A rigorous relation is established to display some drastic features of the non-vanishing correlation entropy of a subsystem formed by any two distant particles with long-range correlation. This relation actually indicates a universal role played by the correlation entropy for understanding the critical phenomena. We also verify these analytical studies in terms of two well-studied models for both the thermal and quantum phase transitions: the two-dimensional Ising model and the one-dimensional transverse-field Ising model. Therefore, the correlation entropy provides us with a new physical intuition of the critical phenomena from the point of view of information theory

Universal conductance and conductivity at critical points in integer quantum Hall systems.

Science.gov (United States)

Schweitzer, L; Markos, P

2005-12-16

The sample averaged longitudinal two-terminal conductance and the respective Kubo conductivity are calculated at quantum critical points in the integer quantum Hall regime. In the limit of large system size, both transport quantities are found to be the same within numerical uncertainty in the lowest Landau band, and , respectively. In the second-lowest Landau band, a critical conductance is obtained which indeed supports the notion of universality. However, these numbers are significantly at variance with the hitherto commonly believed value . We argue that this difference is due to the multifractal structure of critical wave functions, a property that should generically show up in the conductance at quantum critical points.

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

Casimir amplitudes in topological quantum phase transitions.

Science.gov (United States)

Griffith, M A; Continentino, M A

2018-01-01

Topological phase transitions constitute a new class of quantum critical phenomena. They cannot be described within the usual framework of the Landau theory since, in general, the different phases cannot be distinguished by an order parameter, neither can they be related to different symmetries. In most cases, however, one can identify a diverging length at these topological transitions. This allows us to describe them using a scaling approach and to introduce a set of critical exponents that characterize their universality class. Here we consider some relevant models of quantum topological transitions associated with well-defined critical exponents that are related by a quantum hyperscaling relation. We extend to these models a finite-size scaling approach based on techniques for calculating the Casimir force in electromagnetism. This procedure allows us to obtain universal Casimir amplitudes at their quantum critical points. Our results verify the validity of finite-size scaling in these systems and confirm the values of the critical exponents obtained previously.

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.

Scaling analysis of [Fe(pyrazole)4]2[Nb(CN)8] molecular magnet

International Nuclear Information System (INIS)

Konieczny, P.; Pełka, R.; Zieliński, P.M.; Pratt, F.L.; Pinkowicz, D.; Sieklucka, B.; Wasiutyński, T.

2013-01-01

The critical behaviour of the three dimensional (3D) molecular magnet {[Fe II (pirazol) 4 ] 2 [Nb IV (CN) 8 ]·4H 2 O} n has been studied with the use of experimental techniques such as ac magnetometry and zero field μSR spectroscopy. The sample orders magnetically below T c =7.8 K. The measurements allowed to determine static exponents β, γ, and the dynamic exponent w. The resulting exponent values indicate that the studied system belongs to the universality class of the 3D Heisenberg model. - Highlights: • The critical behaviour of {[Fe II (pirazol) 4 ] 2 [Nb IV (CN) 8 ]∙4H 2 O} n has been studied. • Critical exponents β, γ, and w were obtained from ac magnetometry and ZF µSR data. • All obtained values of critical exponents are close to the 3D Heisenberg model

Prior Education of Open University Students Contributes to Their Capability in Critical Thinking

Science.gov (United States)

Repo, Saara; Lehtinen, Taina; Rusanen, Erja; Hyytinen, Heidi

2017-01-01

The focus of this study is on Open University students' entry-level critical thinking skills. The research questions were: how are students' age, and level and discipline of previous education related to critical thinking skills; is the level and discipline of previous education connected to the accuracy of students' self-evaluation of their…

Estimation of Hurst Exponent for the Financial Time Series

Science.gov (United States)

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.

Pinning effect on critical dynamics in Tl2Ba2CaCu2O8 films before and after introducing columnar defects

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

Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

Science.gov (United States)

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.

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)

The liquid–liquid coexistence curves of {x dimethyl adipate + (1 − x) n-hexane} and {x dimethyl adipate + (1 − x) n-heptane} in the critical region

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.

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.

Scaling exponent and dispersity of polymers in solution by diffusion NMR.

Science.gov (United States)

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.

The measurements of coexistence curves and light scattering for {xC6H5CN + (1 - x)CH3(CH2)10CH3} in the critical region

International Nuclear Information System (INIS)

Mao Chunfeng; Wang Nong; Peng Xuhong; An Xueqin; Shen Weiguo

2008-01-01

The coexistence curves and light scattering data for a critical solution of (benzonitrile + dodecane) have been reported. The critical exponents relating to the difference in density variables of two coexisting phases β, the correlation length ν, and the osmotic compressibility γ have been determined. The experimental results of the coexistence curves have also been analyzed to examine the Wegner correction terms and the behavior of the diameter of the coexistence curves. The data analysis shows that the 3D-Ising behavior is valid in a temperature range close to the critical point. However, in a wide temperature range the exponential values of ν and γ change with the temperature significantly, clearly exhibiting the critical crossover from the 3D-Ising universality class to the classical one

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.

Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates

Science.gov (United States)

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.

Critical Discourse Analysis of Moderated Discussion Board of Virtual University of Pakistan

Directory of Open Access Journals (Sweden)

Ayesha Perveen

2015-07-01

Full Text Available The paper critically evaluated the discursive practices on the Moderated Discussion Board (MDB of Virtual University of Pakistan (VUP. The paramount objective of the study was to conduct a critical discourse analysis (CDA of the MDB on the Learning Management System (LMS of VUP. For this purpose, the academic power relations of the students and instructors were evaluated by analyzing whose discourse was dominant in communication with each other on MDB. The researcher devised a model based on the blended theoretical framework of Norman Fairclough and Teun van Dijk to critically analyze the linguistics, ideological, semiotic and socio cognitive-cultural undercurrents in the production and reception processes of MDB discourse. The primary data of the MDB of English Comprehension (ENG101 course was randomly selected to be qualitatively analyzed for this research study. The findings demonstrated that the learners were at a disadvantage because of their lack of command of the English language. However, quick and pertinent replies from instructors revealed students’ empowerment in an educational discursive practice. The results indicated a balance of power relations amongst instructors, students and the University. However, the need to improve the critical thinking of the students to further empower them was strongly felt.

Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

Science.gov (United States)

Yang, Bo; Li, Xiao-Teng; Chen, Wei; Liu, Jian; Chen, Xiao-Song

2016-10-01

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents v, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model. Supported by the National Natural Science Foundation of China under Grant Nos. 11121403 and 11504384

Slow Movement/Slow University: Critical Engagements. Introduction to the Thematic Section

Directory of Open Access Journals (Sweden)

Maggie O'Neill

2014-09-01

Full Text Available This thematic section emerged from two seminars that took place at Durham University in England in November 2013 and March 2014 on the possibilities for thinking through what a change movement towards slow might mean for the University. Slow movements have emerged in relation to a number of topics: Slow food, Citta slow and more recently, slow science. What motivated us in the seminars was to explore how far these movements could help us address the acceleration and intensification of work within our own and other universities, and indeed, what new learning, research, philosophies, practices, structures and governance might emerge. This editorial introduction presents the concept of the "slow university" and introduces our critical engagements with slow. The articles presented here interrogate the potentialities, challenges, problems and pitfalls of the slow university in an era of corporate culture and management rationality. URN: http://nbn-resolving.de/urn:nbn:de:0114-fqs1403166

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.

Scaling, crossover, and classical behavior in the order parameter equation for coexisting phases of benzene from triple point to critical point

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

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.

Universality for the parameter-mismatching effect on weak synchronization in coupled chaotic systems

International Nuclear Information System (INIS)

Lim, Woochang; Kim, Sang-Yoon

2004-01-01

To examine the universality for the parameter-mismatching effect on weak chaotic synchronization, we study coupled multidimensional invertible systems such as the coupled Henon maps and coupled pendula. By generalizing the method proposed in coupled one-dimensional (1D) noninvertible maps, we introduce the parameter sensitivity exponent δ to measure the degree of the parameter sensitivity of a weakly stable synchronous chaotic attractor. In terms of the parameter sensitivity exponents, we characterize the effect of the parameter mismatch on the intermittent bursting and the basin riddling occurring in the regime of weak synchronization. It is thus found that the scaling exponent μ for the average characteristic time (i.e., the average interburst time and the average chaotic transient lifetime) for both the bubbling and riddling cases is given by the reciprocal of the parameter sensitivity exponent, as in the simple system of coupled 1D maps. Hence, the reciprocal relation (i.e., μ = 1/δ) seems to be 'universal', in the sense that it holds in typical coupled chaotic systems of different nature

Phase transitions and critical behaviour for charged black holes

International Nuclear Information System (INIS)

Carlip, S; Vaidya, S

2003-01-01

We investigate the thermodynamics of a four-dimensional charged black hole in a finite cavity in asymptotically flat and asymptotically de Sitter spaces. In each case, we find a Hawking-Page-like phase transition between a black hole and a thermal gas very much like the known transition in asymptotically anti-de Sitter space. For a 'supercooled' black hole - a thermodynamically unstable black hole below the critical temperature for the Hawking-Page phase transition - the phase diagram has a line of first-order phase transitions that terminates in a second-order point. For the asymptotically flat case, we calculate the critical exponents at the second-order phase transition and find that they exactly match the known results for a charged black hole in anti-de Sitter space. We find strong evidence for similar phase transitions for the de Sitter black hole as well. Thus many of the thermodynamic features of charged anti-de Sitter black holes do not really depend on asymptotically anti-de Sitter boundary conditions; the thermodynamics of charged black holes is surprisingly universal

Scaling analysis of [Fe(pyrazole){sub 4}]{sub 2}[Nb(CN){sub 8}] molecular magnet

Energy Technology Data Exchange (ETDEWEB)

Konieczny, P., E-mail: piotr.konieczny@ifj.edu.pl [Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Kraków (Poland); Pełka, R.; Zieliński, P.M. [Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Kraków (Poland); Pratt, F.L. [ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX (United Kingdom); Pinkowicz, D.; Sieklucka, B. [Department of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow (Poland); Wasiutyński, T. [Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Kraków (Poland)

2013-10-15

The critical behaviour of the three dimensional (3D) molecular magnet {[Fe"I"I(pirazol)_4]_2[Nb"I"V(CN)_8]·4H_2O}{sub n} has been studied with the use of experimental techniques such as ac magnetometry and zero field μSR spectroscopy. The sample orders magnetically below T{sub c}=7.8 K. The measurements allowed to determine static exponents β, γ, and the dynamic exponent w. The resulting exponent values indicate that the studied system belongs to the universality class of the 3D Heisenberg model. - Highlights: • The critical behaviour of {[Fe"I"I(pirazol)_4]_2[Nb"I"V(CN)_8]∙4H_2O}{sub n} has been studied. • Critical exponents β, γ, and w were obtained from ac magnetometry and ZF µSR data. • All obtained values of critical exponents are close to the 3D Heisenberg model.

Industry-University SBIR NDT Projects — A Critical Assessment

Science.gov (United States)

Reinhart, Eugene R.

2007-03-01

The Small Business Innovative Research (SBIR) program, funded by various United States government agencies (DOD, DOE, NSF, etc.), provides funds for Research and Development (R&D) of nondestructive testing (NDT) techniques and equipment, thereby supplying valuable money for NDT development by small businesses and stimulating cooperative university programs. A review and critical assessment of the SBIR program as related to NDT is presented and should provide insight into reasons for or against pursuing this source of R&D funding.

A MONTE-CARLO METHOD FOR ESTIMATING THE CORRELATION EXPONENT

NARCIS (Netherlands)

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.

Integrating Critical Thinking Instruction and Assessment into Online University Courses: An Action Research Study

Science.gov (United States)

Mason Heinrichs, Kim R.

2016-01-01

Universities claim that improved critical thinking ability is an educational outcome for their graduates, but they seldom create a path for students to achieve that outcome. In this practitioner action research study, the author created a job aid, entitled "Critical Thinking as a Differentiator for Distinguished Performance," to help…

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)

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

Quantum influence in the criticality of the spin- {1}/{2} anisotropic Heisenberg model

Science.gov (United States)

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.

Critical applied stresses for a crack initiation from a sharp V-notch

Directory of Open Access Journals (Sweden)

L. Náhlík

2014-10-01

Full Text Available The aim of the paper is to estimate a value of the critical applied stress for a crack initiation from a sharp V-notch tip. The classical approach of the linear elastic fracture mechanics (LELM was generalized, because the stress singularity exponent differs from 0.5 in the studied case. The value of the stress singularity exponent depends on the V-notch opening angle. The finite element method was used for a determination of stress distribution in the vicinity of the sharp V-notch tip and for the estimation of the generalized stress intensity factor depending on the V-notch opening angle. Critical value of the generalized stress intensity factor was obtained using stability criteria based on the opening stress component averaged over a critical distance d from the V-notch tip and generalized strain energy density factor. Calculated values of the critical applied stresses were compared with experimental data from the literature and applicability of the LEFM concept is discussed.

Explanation of the values of Hack's drainage basin, river length scaling exponent

Science.gov (United States)

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.

Nuclear criticality safety program at the University of Tennessee-Knoxville

International Nuclear Information System (INIS)

Basoglu, B.; Bentley, C.; Brewer, R.; Dunn, M.; Haught, C.; Plaster, M.; Wilkinson, A.; Dodds, H.; Elliott, E.; Waddell, W.

1993-01-01

This paper presents an overview of the nuclear criticality safety (NCS) educational program at the University of Tennessee-Knoxville. The program is an academic specialization for nuclear engineering graduate students pursuing either the MS or PhD degree and includes special NCS courses and NCS research projects. Both the courses and the research projects serve as partial fulfillment of the requirements for the degree being pursued

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 ...

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

Recovering the Power Inside: A Qualitative Study of Critical Reading in an Iranian University

Directory of Open Access Journals (Sweden)

Sue-san Ghahremani Ghajar

2011-07-01

Full Text Available A fundamental goal of critical literacy approaches is to bring a change and empower students as critical agents and subjects of decision making. Students are expected to do more than simply accumulate information; they are encouraged to challenge their ‘taken for granted’ belief structures and transform themselves as well as their immediate social environment. In this article, we present a qualitative enquiry in a university reading course based on critical literacy. We explored how learners reflected on their individual/community and word/world concerns through critical understanding of texts and how they challenged and shattered their ‘taken for granted’ beliefs and started to transform into critical agents of voice and position. The data consists of 400 concept maps, called webs, and personal journals by fifty undergraduate English literature students at an Iranian University, as well as oral and written interviews. The data was qualitatively analyzed in search of themes that could illustrate students’ early thinking structures and their empowerment and transformations into subjects of decisions. The study revealed that, through webbing words/worlds and critically challenging texts, students took the opportunity to approach the knowledge and information presented to them analytically and critically. On this basis, we discuss how students were able to gain the power of critiquing, freeing their thoughts, finding and expressing their voice and position, discovering personal meanings in texts and contexts, cooperating and participating, and understanding learning for meaning through the critical act of reading.

Critical scaling of a jammed system after a quench of temperature.

Science.gov (United States)

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.

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)

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.

Observation of structural universality in disordered systems using bulk diffusion measurement

Science.gov (United States)

Papaioannou, Antonios; Novikov, Dmitry S.; Fieremans, Els; Boutis, Gregory S.

2017-12-01

We report on an experimental observation of classical diffusion distinguishing between structural universality classes of disordered systems in one dimension. Samples of hyperuniform and short-range disorder were designed, characterized by the statistics of the placement of micrometer-thin parallel permeable barriers, and the time-dependent diffusion coefficient was measured by NMR methods over three orders of magnitude in time. The relation between the structural exponent, characterizing disorder universality class, and the dynamical exponent of the diffusion coefficient is experimentally verified. The experimentally established relation between structure and transport exemplifies the hierarchical nature of structural complexity—dynamics are mainly determined by the universality class, whereas microscopic parameters affect the nonuniversal coefficients. These results open the way for noninvasive characterization of structural correlations in porous media, complex materials, and biological tissues via a bulk diffusion measurement.

a Comparison of Three Hurst Exponent Approaches to Predict Nascent Bubbles in S&P500 Stocks

Science.gov (United States)

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.

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.

An analysis of the financial crisis in the KOSPI market using Hurst exponents

Science.gov (United States)

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.

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

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.

Critical and Scientific Thinking Assessment in Preservice Teachers at a Chilean University

Directory of Open Access Journals (Sweden)

Carlos Ossa-Cornejo

2018-03-01

Full Text Available This paper describes a research project focused on identifying student-teachers’ critical thinking performance levels in scientific reasoning and, secondly, on analyzing the reliability level of the Critical Thinking Tasks test (CTT. As part of the methodology, a non-probabilistic sample of 129 teacher education students from different majors at Bio-Bio University was considered, and the Critical Thinking Task test was applied to collect data. The data analysis was conducted using descriptive statistics, reliability measures and mean score differences. The data showed that the instrument is reliable (α=0,79; there is also a relatively low performance in the global test and its dimensions; and there are differences between the different teacher education programs. It is concluded that the instrument is reliable, and findings support the idea that knowledge-based areas influence critical thinking. Finally, it is necessary to strengthen specific sub-skills to enhance critical thinking as a contribution for scientific reasoning.

Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data

Science.gov (United States)

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.

Heat capacities and asymmetric criticality of the (liquid + liquid) coexistence curves for {dimethyl carbonate + n-undecane, or n-tridecane}

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

Zipf's law and influential factors of the Pareto exponent of the city size distribution: Evidence from China

OpenAIRE

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...

Critical Behavior of Light in Mode-Locked Lasers

Science.gov (United States)

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.

Analysis of kyoto university reactor physics critical experiments using NCNSRC calculation methodology

International Nuclear Information System (INIS)

Amin, E.; Hathout, A.M.; Shouman, S.

1997-01-01

The kyoto university reactor physics experiments on the university critical assembly is used to benchmark validate the NCNSRC calculations methodology. This methodology has two lines, diffusion and Monte Carlo. The diffusion line includes the codes WIMSD4 for cell calculations and the two dimensional diffusion code DIXY2 for core calculations. The transport line uses the MULTIKENO-Code vax Version. Analysis is performed for the criticality, and the temperature coefficients of reactivity (TCR) for the light water moderated and reflected cores, of the different cores utilized in the experiments. The results of both Eigen value and TCR approximately reproduced the experimental and theoretical Kyoto results. However, some conclusions are drawn about the adequacy of the standard wimsd4 library. This paper is an extension of the NCNSRC efforts to assess and validate computer tools and methods for both Et-R R-1 and Et-MMpr-2 research reactors. 7 figs., 1 tab

Benchmarks of subcriticality in accelerator-driven system at Kyoto University Critical Assembly

Directory of Open Access Journals (Sweden)

Cheol Ho Pyeon

2017-09-01

Full Text Available Basic research on the accelerator-driven system is conducted by combining 235U-fueled and 232Th-loaded cores in the Kyoto University Critical Assembly with the pulsed neutron generator (14 MeV neutrons and the proton beam accelerator (100 MeV protons with a heavy metal target. The results of experimental subcriticality are presented with a wide range of subcriticality level between near critical and 10,000 pcm, as obtained by the pulsed neutron source method, the Feynman-α method, and the neutron source multiplication method.

Statistical properties of the anomalous scaling exponent estimator based on time-averaged mean-square displacement

Science.gov (United States)

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.

Influence of the disorder in doped germanium changed by compensation on the critical indices of the metal-insulator transition

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

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

Universal Design for Learning: Critical Need Areas for People with Learning Disabilities

Science.gov (United States)

Strobel, Wendy; Arthanat, Sajay; Bauer, Stephen; Flagg, Jennifer

2007-01-01

The primary market research outlined in this paper was conducted by the Rehabilitation Engineering Research Center on Technology Transfer to identify critical technology needs for people with learning disabilities. Based on the research conducted, the underlying context of these technology needs is Universal Design for Learning (UDL). The paper…

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)

Bayesian Estimation of the Logistic Positive Exponent IRT Model

Science.gov (United States)

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…

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.)

Student research in criticality safety at the University of Arizona

International Nuclear Information System (INIS)

Hetrick, D.L.

1997-01-01

A very brief progress report on four University of Arizona student projects is given. Improvements were made in simulations of power pulses in aqueous solutions, including the TWODANT model. TWODANT calculations were performed to investigate the effect of assembly shape on the expansion coefficient of reactivity for solutions. Preliminary calculations were made of critical heights for the Los Alamos SHEBA assembly. Calculations to support French experiments to measure temperature coefficients of dilute plutonium solutions confirmed feasibility

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

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

Observing golden-mean universality class in the scaling of thermal transport

Science.gov (United States)

Xiong, Daxing

2018-02-01

We address the issue of whether the golden-mean [ψ =(√{5 }+1 ) /2 ≃1.618 ] universality class, as predicted by several theoretical models, can be observed in the dynamical scaling of thermal transport. Remarkably, we show strong evidence that ψ appears to be the scaling exponent of heat mode correlation in a purely quartic anharmonic chain. This observation seems to somewhat deviate from the previous expectation and we explain it by the unusual slow decay of the cross correlation between heat and sound modes. Whenever the cubic anharmonicity is included, this cross correlation gradually dies out and another universality class with scaling exponent γ =5 /3 , as commonly predicted by theories, seems recovered. However, this recovery is accompanied by two interesting phase transition processes characterized by a change of symmetry of the potential and a clear variation of the dynamic structure factor, respectively. Due to these transitions, an additional exponent close to γ ≃1.580 emerges. All this evidence suggests that, to gain a full prediction of the scaling of thermal transport, more ingredients should be taken into account.

Dynamical effects and the critical behavior of random-field systems

International Nuclear Information System (INIS)

Shapir, Y.

1985-01-01

A variety of phenomena is observed experimentally in random-field (RF) systems realized by the application of an external field to diluted antiferromagnets. At low temperatures, infinitely long hysteretic effects are manifested by the history dependence of the final states: long-range order is observed if the field is applied after cooling, while domain states are reached when field cooled. While no indications for critical fluctuations are detected in 2-D systems, scaling behavior, for both the correlation length and the specific heat, is observed in 3-D systems over an intermediate range of temperatures. The related critical properties seem to be well described by the corresponding ones in the 2-D pure Ising model. The renormalization-group approach, which yields for the equilibrium critical exponents their values of the pure model in d-2 dimensions, is reviewed. A generalization of the dimensional-reduction approach, which accounts self-consistently for renormalized responses of the RF system, is presented. The dynamical effects are implicitly incorporated through the variation in the critical response between the local and the global regimes, associated with short- and long-time scales, respectively. In both regimes the lower critical dimension is found to be d = 2 in accordance with stability arguments. The short-time critical behavior indicates a dimensional reduction by one for the 3-D thermal exponents, in agreement with the experimental results. 37 references

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

The liquid–liquid coexistence curves of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} in the critical region

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.

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

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

Cut-off scaling and multiplicative reformalization in the theory of critical phenomena

International Nuclear Information System (INIS)

Forgacs, G.; Solyom, J.; Zawadowski, A.

1976-03-01

In the paper a new method to study the critical fluctuations in systems of 4-epsilon dimensions around the phase transition point is developed. This method unifies the Kadanoff scaling hypothesis as formulated by Wilson by help of his renormalization group technique and the simple mathematical structure of the Lie equations of the Gell-Mann-Low multiplicative renormalization. The basic idea of the new method is that a change in the physical cut-off can be compensated by an effective coupling in such a way that the Green's function and vertex in the original and transformed system differ only by a multiplicative factor. The critical indices, the anomalous dimensions and the critical exponent describing the correction to scaling are determined to second order in epsilon. The specific heat exponent is also calculated, in four dimensions the effect of fluctuations appears in the form of logarithmic corrections. In the last sections the new method is compared to other ones and the differences are discussed. (Sz.N.Z.)

A modified approach to predict pore pressure using the D exponent method: An example from the Carbonera Formation, Colombia

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

Fast and unbiased estimator of the time-dependent Hurst exponent

Science.gov (United States)

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.

Directional maximum likelihood self-estimation of the path-loss exponent

NARCIS (Netherlands)

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

Evidence for criticality in financial data

Science.gov (United States)

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.

Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent

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.

The Exponent of High-frequency Source Spectral Falloff and Contribution to Source Parameter Estimates

Science.gov (United States)

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.

The origin of the criticality in meme popularity distribution on complex networks.

Science.gov (United States)

Kim, Yup; Park, Seokjong; Yook, Soon-Hyung

2016-03-24

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks.

The origin of the criticality in meme popularity distribution on complex networks

Science.gov (United States)

Kim, Yup; Park, Seokjong; Yook, Soon-Hyung

2016-03-01

Previous studies showed that the meme popularity distribution is described by a heavy-tailed distribution or a power-law, which is a characteristic feature of the criticality. Here, we study the origin of the criticality on non-growing and growing networks based on the competition induced criticality model. From the direct Mote Carlo simulations and the exact mapping into the position dependent biased random walk (PDBRW), we find that the meme popularity distribution satisfies a very robust power- law with exponent α = 3/2 if there is an innovation process. On the other hand, if there is no innovation, then we find that the meme popularity distribution is bounded and highly skewed for early transient time periods, while it satisfies a power-law with exponent α ≠ 3/2 for intermediate time periods. The exact mapping into PDBRW clearly shows that the balance between the creation of new memes by the innovation process and the extinction of old memes is the key factor for the criticality. We confirm that the balance for the criticality sustains for relatively small innovation rate. Therefore, the innovation processes with significantly influential memes should be the simple and fundamental processes which cause the critical distribution of the meme popularity in real social networks.

Static critical phenomena in Co-Ni-Ga ferromagnetic shape memory alloy

International Nuclear Information System (INIS)

Sethi, Brahmananda; Sarma, S.; Srinivasan, A.; Santra, S. B.

2014-01-01

Ferromagnetic shape memory alloys are smart materials because they exhibit temperature driven shape memory effect and magnetic field induced strain. Thus two types of energy, i.e. thermal and magnetic, are used to control their shape memory behaviour. Study of critical phenomenon in such materials has received increased experimental and theoretical attention for better understanding of the magnetic phase transition behavior as well as further development of ferromagnetic shape memory materials. In the present study we report the preparation and characterization of bulk Co 45 Ni 25 Ga 30 alloy, prepared by a sequence of arc melting technique followed by homogenization at 1150 °C for 24 hours and ice-water quenching. Structural and magnetic properties of the alloys were studied by means of X-ray diffraction and vibrating sample magnetometer in an applied field range of ±18 kOe equipped with a high temperature oven. We have determined the critical temperature T C (∼375.5 K) and the critical exponents viz; β=0.40, γ=1.68 and δ=5.2. Asymptotic critical exponents β, γ, and δ obey Widom scaling relation, γ+β=βδ, and the magnetization data satisfy the scaling equation of state for second-order phase transition in the asymptotic critical region

Critical behaviors of half-metallic ferromagnet Co3Sn2S2

OpenAIRE

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...

The threshold of coexistence and critical behaviour of a predator-prey cellular automaton

International Nuclear Information System (INIS)

Arashiro, Everaldo; Tome, Tania

2007-01-01

We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out mean-field approximations and numerical simulations we obtain the phase boundaries (thresholds) related to the transition between an active state, where prey and predators present a stable coexistence, and a prey absorbing state. The numerical estimates for the critical exponents show that the transition belongs to the directed percolation universality class. In the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class. Patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed

Educational use of research reactor (KUR) and critical assembly (KUCA) at Kyoto University

International Nuclear Information System (INIS)

Misawa, Tsuyoshi; Unesaki, Hironobu; Ichihara, Chihiro; Pyeon, Cheol Ho; Shiroya, Seiji

2005-01-01

At Kyoto University Research Reactor Institute, a research reactor of 5MW (KUR) and a critical assembly (KUCA) have been used for educational purpose to train undergraduate or graduate students. Using KUR, basic experiments for neutron applications have been carried out, and KUCA has been used for the education of nuclear engineering and technology. Especially, using KUCA, a joint reactor laboratory course of graduate level is offered every summer since 1975 by nine associated Japanese universities, and more than 2200 students attended this course

Investigating textural controls on Archie's porosity exponent using process-based, pore-scale modelling

Science.gov (United States)

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.

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)

Quality of Gaussian basis sets: direct optimization of orbital exponents by the method of conjugate gradients

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

Structural, transport, magnetic, magnetocaloric properties and critical analysis of Ni-Co-Mn-Ga Heusler alloys

Science.gov (United States)

Arumugam, S.; Devarajan, U.; Esakki Muthu, S.; Singh, Sanjay; Thiyagarajan, R.; Raja, M. Manivel; Rama Rao, N. V.; Banerjee, Alok

2017-11-01

In this work, we have investigated structural, transport, magnetic, magnetocaloric (MC) properties and critical exponents analysis of the (Ni2.1-xCox)Mn0.9 Ga (x = 0, 0.04, 0.12 and 0.2) Heusler alloys. For all compositions, cubic austenite (A) phase with metallic character is observed at room temperature (RT). With increasing of Co content, magnitude of resistivity decreases, whereas residual resistivity (ρ0) and electron scattering factor (A) increases linearly. Magnetic measurements exhibit that ferromagnetic (FM) Curie temperature (TCA) increases towards RT by increasing Co concentration. All samples show conventional MC and maximum magnetic entropy change (ΔSMpeak) of -2.8 Jkg-1 K-1 is observed for x = 0.12 at 147 K under 5 T. Further, hysteresis is observed between cooling and warming cycles around FM-PM (TCA) transition in x = 0, 0.04 samples, which suggests that first order nature of transition. However, there is no hysteresis across TCA for x = 0.12 and 0.2 samples suggesting second-order nature of the transition. The critical exponents are calculated for x = 0.12 sample around TCA using Arrott plot and Kouvel-Fisher method, the estimated critical exponents are found closer to the mean-field model reveals the long range ferromagnetic ordering in this composition.

Weakly interacting topological insulators: Quantum criticality and the renormalization group approach

Science.gov (United States)

Chen, Wei

2018-03-01

For D -dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D - or (D +1 ) -dimensional integration over a certain curvature function that is expressed in terms of single-particle Green's functions. Based on the divergence of curvature function at the topological phase transition, we demonstrate how a renormalization group approach circumvents these integrations and reduces the necessary calculation to that for the Green's function alone, rendering a numerically efficient tool to identify topological phase transitions in a large parameter space. The method further unveils a number of statistical aspects related to the quantum criticality in weakly interacting topological insulators, including correlation function, critical exponents, and scaling laws, that can be used to characterize the topological phase transitions driven by either interacting or noninteracting parameters. We use 1D class BDI and 2D class A Dirac models with electron-electron and electron-phonon interactions to demonstrate these principles and find that interactions may change the critical exponents of the topological insulators.

Dynamical effects and the critical behavior of random-field systems (invited)

International Nuclear Information System (INIS)

Shapir, Y.

1985-01-01

A variety of phenomena is observed experimentally in random-field (RF) systems realized by the application of an external field to diluted antiferromagnets. At low temperatures, infinitely long hysteretic effects are manifested by the history dependence of the final states: long-range order is observed if the field is applied after cooling, while domain states are reached when field cooled. While no indications for critical fluctuations are detected in 2-D systems, scaling behavior, for both the correlation length and the specific heat, is observed in 3-D systems over an intermediate range of temperatures. The related critical properties seem to be well described by the corresponding ones in the 2-D pure Ising model. The renormalization-group approach, which yields for the equilibrium critical exponents their values of the pure model in d-2 dimensions, is reviewed. A generalization of the dimensional-reduction approach, which accounts self-consistently for renormalized responses of the RF system, is presented. The dynamical effects are implicitly incorporated through the variation in the critical response between the local and the global regimes, associated with short- and long-time scales, respectively. In both regimes the lower critical dimension is found to be d = 2 in accordance with stability arguments. The short-time critical behavior indicates a dimensional reduction by one for the 3-D thermal exponents, in agreement with the experimental results

Competition-induced criticality in a model of meme popularity.

Science.gov (United States)

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

Science.gov (United States)

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.

Teaching and Learning Critical Reading with Transnational Texts at a Mexican University: An Emergentist Case Study

Science.gov (United States)

Perales Escudero, Moises Damian

2011-01-01

This dissertation project examines the implementation of a critical reading intervention in a Mexican university, and the emergence of target critical reading processes in Mexican college-level EFL readers. It uses a Complexity Theory-inspired, qualitative methodology. Orienting the selection and design of materials is a deep view of culture that…

Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles

Science.gov (United States)

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.

Universities and Regional Development: A Critical Assessment of Tensions and Contradictions. International Studies in Higher Education

Science.gov (United States)

Pinheiro, Romulo, Ed.; Benneworth, Paul, Ed.; Jones, Glen A., Ed.

2012-01-01

Universities are under increasing pressure to help promote socio-economic growth in their local communities. However until now, no systematic, critical attention has been paid to the factors and mechanisms that currently make this process so daunting. In Universities and Regional Development, scholars from Europe, the Americas, Africa, and Asia…

Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series

Science.gov (United States)

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.

Building Social Inclusion through Critical Arts-Based Pedagogies in University Classroom Communities

Science.gov (United States)

Chappell, Sharon Verner; Chappell, Drew

2016-01-01

In humanities and education university classrooms, the authors facilitated counter-narrative arts-based inquiry projects in order to build critical thought and social inclusion. The first author examines public performance installations created by graduate students in elementary and bilingual education on needs-based and dignity-based rights of…

Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

Science.gov (United States)

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.

Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents.

Science.gov (United States)

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.

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.

University Applicants' Critical Thinking Skills: The Case of the Finnish Educational Sciences

Science.gov (United States)

Utriainen, Jukka; Marttunen, Miika; Kallio, Eeva; Tynjälä, Päivi

2017-01-01

This study investigates the quality of the critical thinking skills of applicants (n = 77) seeking entry to the faculty of educational sciences in a Finnish university and how these skills are associated with the applicant's age, previous higher education experience, and matriculation and entrance examination scores. The data consist of the…

On the Relationship among Critical Thinking, Language Learning Strategy Use and University Achievement of Iranian English as a Foreign Language Majors

Science.gov (United States)

Afshar, Hassan Soodmand; Movassagh, Hossein

2017-01-01

The study investigated the relationship among critical thinking, strategy use and university achievement. To this end, 76 English major students sat the California Critical Thinking Skills Test and filled out Oxford's Strategy Inventory for Language Learning. Participants' Grade Point Averages were regarded as their university achievement. The…

Designing a model for critical thinking development in AJA University of Medical Sciences

Science.gov (United States)

MAFAKHERI LALEH, MAHYAR; MOHAMMADIMEHR, MOJGAN; ZARGAR BALAYE JAME, SANAZ

2016-01-01

Introduction: In the new concept of medical education, creativity development is an important goal. The aim of this research was to identify a model for developing critical thinking among students with the special focus on learning environment and learning style. Methods: This applied and cross-sectional study was conducted among all students studying in undergraduate and professional doctorate programs in Fall Semester 2013-2014 in AJA University of Medical Sciences (N=777). The sample consisted of 257 students selected based on the proportional stratified random sampling method. To collect data, three questionnaires including Critical Thinking, Perception of Learning Environment and Learning Style were employed. The data were analyzed using Pearson's correlation statistical test, and one-sample t-test. The Structural Equation Model (SEM) was used to test the research model. SPSS software, version 14 and the LISREL software were used for data analysis. Results: The results showed that students had significantly assessed the teaching-learning environment and two components of "perception of teachers" and "perception of emotional-psychological climate" at the desirable level (pcritical thinking among students in terms of components of "commitment", "creativity" and "cognitive maturity" was at the relatively desirable level (pcritical thinking through learning style. Conclusion: One of the factors which can significantly impact the quality improvement of the teaching and learning process in AJA University of Medical Sciences is to develop critical thinking among learners. This issue requires providing the proper situation for teaching and learning critical thinking in the educational environment. PMID:27795968

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

Cluster tails for critical power-law inhomogeneous random graphs

NARCIS (Netherlands)

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)

Critical Success Factors in Crafting Strategic Architecture for E-Learning at HP University

Science.gov (United States)

Sharma, Kunal; Pandit, Pallvi; Pandit, Parul

2011-01-01

Purpose: The purpose of this paper is to outline the critical success factors for crafting a strategic architecture for e-learning at HP University. Design/methodology/approach: A descriptive survey type of research design was used. An empirical study was conducted on students enrolled with the International Centre for Distance and Open Learning…

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....

Exponent and scrambling index of double alternate circular snake graphs

Science.gov (United States)

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.

University of New Mexico short course in nuclear criticality safety: Training for new NCS [nuclear criticality safety] specialists

International Nuclear Information System (INIS)

Busch, R.D.

1990-01-01

Since 1973, the University of New Mexico (UNM) has given ten short courses in nuclear criticality safety (NCS). Generally, thee have been given every other year, although in 1989 it was decided to offer the course on an annual basis. This decision was primarily based on the large demand for NCS specialists and a large turnover rate in the industry. The purpose of the course is to provide a 1-week overview of NCS. The typical student has been involved in NCS for <1 yr, although it many cases they have been associated with the nuclear industry in other capacities for many years. The short course is conducted at several levels. Carefully prepared lectures provide the information framework for selected topics. The following topics are covered in the course: basic reactor theory, criticality accidents and consequences, hand calculations, administration of a criticality safety program, regulators and their processes, computer methods and applications, experimental methods and correlations, overview of some process operations, and transportation and storage issues in NCS

Universal asymptotics in hyperbolicity breakdown

International Nuclear Information System (INIS)

Bjerklöv, Kristian; Saprykina, Maria

2008-01-01

We study a scenario for the disappearance of hyperbolicity of invariant tori in a class of quasi-periodic systems. In this scenario, the system loses hyperbolicity because two invariant directions come close to each other, losing their regularity. In a recent paper, based on numerical results, Haro and de la Llave (2006 Chaos 16 013120) discovered a quantitative universality in this scenario, namely, that the minimal angle between the two invariant directions has a power law dependence on the parameters and the exponents of the power law are universal. We present an analytic proof of this result

Mindfulness as an Alternative for Supporting University Student Mental Health: Cognitive-Emotional and Depressive Self-Criticism Measures

Science.gov (United States)

Azam, Muhammad Abid; Mongrain, Myriam; Vora, Khushboo; Pirbaglou, Meysam; Azargive, Saam; Changoor, Tina; Wayne, Noah; Guglietti, Crissa; Macpherson, Alison; Irvine, Jane; Rotondi, Michael; Smith, Dawn; Perez, Daniel; Ritvo, Paul

2016-01-01

Increases in university-based mental health problems require alternative mental health programs, applicable to students with elevated psychological risks due to personality traits. This study examined the cognitive-emotional outcomes of a university mindfulness meditation (MM) program and their relationship with Self-Criticism (SC), a personality…

Gaussian fluctuation of the diffusion exponent of virus capsid in a living cell nucleus

Science.gov (United States)

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.

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.)

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].

The role of critical thinking skills and learning styles of university students in their academic performance

Directory of Open Access Journals (Sweden)

ZOHRE GHAZIVAKILI

2014-07-01

Full Text Available Introduction: The current world needs people who have a lot of different abilities such as cognition and application of different ways of thinking, research, problem solving, critical thinking skills and creativity. In addition to critical thinking, learning styles is another key factor which has an essential role in the process of problem solving. This study aimed to determine the relationship between learning styles and critical thinking of students and their academic performance in Alborz University of Medical Sciences. Methods: This cross-correlation study was performed in 2012, on 216 students of Alborz University who were selected randomly by the stratified method. The data was obtained via a three-part questionnaire included demographic data, Kolb standardized questionnaire of learning style and California critical thinking standardized questionnaire. The academic performance of the students was extracted by the school records. The validity of the instruments was determined in terms of content validity, and the reliability was gained through internal consistency methods. Cronbach's alpha coefficient was found to be 0.78 for the California critical thinking questionnaire. The Chi Square test, Independent T-test, one way ANOVA and Pearson Correlation test were used to determine relationship between variables. The Package SPSS14 statistical software was used to analyze data with a significant level of p<0.05. Results: Our findings indicated the significant difference of mean score in four learning style, suggesting university students with convergent learning style have better performance than other groups. Also learning style had a relationship with age, gender, field of study, semester and job. The results about the critical thinking of the students showed that the mean of deductive reasoning and evaluation skills were higher than that of other skills and analytical skills had the lowest mean and there was a positive significant

Reactor laboratory course for Korean under-graduate students in Kyoto University Critical Assembly (KUGSiKUCA)

International Nuclear Information System (INIS)

Pyeon, Cheol Ho; Misawa, Tsuyoshi; Unesaki, Hironobu; Ichihara, Chihiro; Shiroya, Seiji; Whang, Joo Ho; Kim, Myung Hyun

2005-01-01

The Reactor Laboratory Course for Korean Under-Graduate Students has been carried out at Kyoto University Critical Assembly of Japan. This course has been launched from fiscal year 2003 and has been founded by Ministry of Science and Technology of Korean Government. Since then, the total number of 43 Korean under-graduate students, who have majored in nuclear engineering of 6 universities in all over the Korea, has been taken part in this course. The reactor physics experiments have been performed in this course, such as Approach to criticality, Control rod calibration, Measurement of neutron flux and power calibration, and Educational reactor operation. As technical tour of Japan, nuclear site tour has been taken during their stay in Japan, such as PWR, FBR, nuclear fuel company and some institutes

Computation of the Lyapunov exponents in the compass-gait model under OGY control via a hybrid Poincaré map

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.

Critical dynamics of the Potts model: short-time Monte Carlo simulations

International Nuclear Information System (INIS)

Silva, Roberto da; Drugowich de Felicio, J.R.

2004-01-01

We calculate the new dynamic exponent θ of the 4-state Potts model, using short-time simulations. Our estimates θ1=-0.0471(33) and θ2=-0.0429(11) obtained by following the behavior of the magnetization or measuring the evolution of the time correlation function of the magnetization corroborate the conjecture by Okano et al. [Nucl. Phys. B 485 (1997) 727]. In addition, these values agree with previous estimate of the same dynamic exponent for the two-dimensional Ising model with three-spin interactions in one direction, that is known to belong to the same universality class as the 4-state Potts model. The anomalous dimension of initial magnetization x0=zθ+β/ν is calculated by an alternative way that mixes two different initial conditions. We have also estimated the values of the static exponents β and ν. They are in complete agreement with the pertinent results of the literature

Critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model

Science.gov (United States)

Sousa, J. Ricardo de

A two-step renormalization group approach - a decimation followed by an effective field renormalization group (EFRG) - is proposed in this work to study the critical behavior of the quantum spin- {1}/{2} anisotropic Heisenberg model. The new method is illustrated by employing approximations in which clusters with one, two and three spins are used. The values of the critical parameter and critical exponent, in two- and three-dimensional lattices, for the Ising and isotropic Heisenberg limits are calculated and compared with other renormalization group approaches and exact (or series) results.

Brief communication: Possible explanation of the values of Hack's drainage basin, river length scaling exponent

Science.gov (United States)

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.

Aging and coarsening in isolated quantum systems after a quench: Exact results for the quantum O(N) model with N → ∞.

Science.gov (United States)

Maraga, Anna; Chiocchetta, Alessio; Mitra, Aditi; Gambassi, Andrea

2015-10-01

The nonequilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with O(N) symmetry, starting from a ground state in the disordered phase. In the limit of infinite N, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.

Criticality of the D=2 bond-dilute anisotropic Heisenberg ferromagnet

International Nuclear Information System (INIS)

Mariz, A.M.; Tsallis, C.; Caride, A.O.

1984-01-01

The critical frontier and critical exponents associated with the quenched bond-dilute quantum anisotropic spin 1/2 Heisenberg ferromagnet in square lattice are described. To perform the calculations, an approximate real-space renormalization-group framework recently developed by some of us for the pure model (and analysed with some detail) is extended. Whenever comparison with available exact results is possible, the agreement is either perfect or quite satisfactory. Some effort has been dedicated to extract the main asymptotic behaviours of the critical frontier. Also several interesting quantum effects appearing in the composition laws of (Heisenberg) bond arrays are exhibited. (Author) [pt

Universality in driven-dissipative quantum many-body systems

International Nuclear Information System (INIS)

Sieberer, L.M.

2015-01-01

Recent experimental investigations of condensation phenomena in driven-dissipative quantum many-body systems raise the question of what kind of novel universal behavior can emerge under non-equilibrium conditions. We explore various aspects of universality in this context. Our results are of relevance for a variety of open quantum systems on the interface of quantum optics and condensed matter physics, ranging from exciton-polariton condensates to cold atomic gases. In Part I we characterize the dynamical critical behavior at the Bose-Einstein condensation phase transition in driven open quantum systems in three spatial dimensions. Although thermodynamic equilibrium conditions are emergent at low frequencies, the approach to this thermalized low-frequency regime is described by a critical exponent which is specific to the non-equilibrium transition, and places the latter beyond the standard classification of equilibrium dynamical critical behavior. Our theoretical approach is based on the functional renormalization group within the framework of Keldysh non-equilibrium field theory, which is equivalent to a microscopic description of the open system dynamics in terms of a many-body quantum master equation. Universal behavior in the coherence properties of driven-dissipative condensates in reduced dimensions is investigated in Part II. We show that driven two-dimensional Bose systems cannot exhibit algebraic order as in thermodynamic equilibrium, unless they are sufficiently anisotropic. However, we find evidence that even isotropic systems may have a finite superfluidity fraction. In one-dimensional systems, non-equilibrium conditions are traceable in the behavior of the autocorrelation function. We obtain these results by mapping the long-wavelength condensate dynamics onto the Kardar-Parisi-Zhang equation. In Part III we show that systems in thermodynamic equilibrium have a specific symmetry, which makes them distinct from generic driven open systems. The novel

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

Relation between the Hurst Exponent and the Efficiency of Self-organization of a Deformable System

Science.gov (United States)

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.

Dynamic phase transition in diffusion-limited reactions

International Nuclear Information System (INIS)

Tauber, U.C.

2002-01-01

Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means of the renormalization group. The resulting universality classes for single-species systems are reviewed here. Generically, the critical exponents are those of directed percolation (Reggeon field theory), with critical dimension d c = 4. Yet local particle number parity conservation in even-offspring branching and annihilating random walks implies an inactive phase (emerging below d c = 4/3) that is characterized by the power laws of the pair annihilation reaction, and leads to different critical exponents at the transition. For local processes without memory, the pair contact process with diffusion represents the only other non-trivial universality class. The consistent treatment of restricted site occupations and quenched random reaction rates are important open issues (Author)

Exact renormalization group equation for the Lifshitz critical point

Science.gov (United States)

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.

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

Realization of the mean-field universality class in spin-crossover materials

Science.gov (United States)

Miyashita, Seiji; Konishi, Yusuké; Nishino, Masamichi; Tokoro, Hiroko; Rikvold, Per Arne

2008-01-01

In spin-crossover materials, the volume of a molecule changes depending on whether it is in the high-spin (HS) or low-spin (LS) state. This change causes distortion of the lattice. Elastic interactions among these distortions play an important role for the cooperative properties of spin-transition phenomena. We find that the critical behavior caused by this elastic interaction belongs to the mean-field universality class, in which the critical exponents for the spontaneous magnetization and the susceptibility are β=1/2 and γ=1 , respectively. Furthermore, the spin-spin correlation function is a constant at long distances, and it does not show an exponential decay in contrast to short-range models. The value of the correlation function at long distances shows different size dependences: O(1/N) , O(1/N) , and constant for temperatures above, at, and below the critical temperature, respectively. The model does not exhibit clusters, even near the critical point. We also found that cluster growth is suppressed in the present model and that there is no critical opalescence in the coexistence region. During the relaxation process from a metastable state at the end of a hysteresis loop, nucleation phenomena are not observed, and spatially uniform configurations are maintained during the change of the fraction of HS and LS. These characteristics of the mean-field model are expected to be found not only in spin-crossover materials, but also generally in systems where elastic distortion mediates the interaction among local states.

Self-Organized Criticality in an Anisotropic Earthquake Model

Science.gov (United States)

Li, Bin-Quan; Wang, Sheng-Jun

2018-03-01

We have made an extensive numerical study of a modified model proposed by Olami, Feder, and Christensen to describe earthquake behavior. Two situations were considered in this paper. One situation is that the energy of the unstable site is redistributed to its nearest neighbors randomly not averagely and keeps itself to zero. The other situation is that the energy of the unstable site is redistributed to its nearest neighbors randomly and keeps some energy for itself instead of reset to zero. Different boundary conditions were considered as well. By analyzing the distribution of earthquake sizes, we found that self-organized criticality can be excited only in the conservative case or the approximate conservative case in the above situations. Some evidence indicated that the critical exponent of both above situations and the original OFC model tend to the same result in the conservative case. The only difference is that the avalanche size in the original model is bigger. This result may be closer to the real world, after all, every crust plate size is different. Supported by National Natural Science Foundation of China under Grant Nos. 11675096 and 11305098, the Fundamental Research Funds for the Central Universities under Grant No. GK201702001, FPALAB-SNNU under Grant No. 16QNGG007, and Interdisciplinary Incubation Project of SNU under Grant No. 5

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

Science.gov (United States)

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.

Universal rescaling of flow curves for yield-stress fluids close to jamming

Science.gov (United States)

Dinkgreve, M.; Paredes, J.; Michels, M. A. J.; Bonn, D.

2015-07-01

The experimental flow curves of four different yield-stress fluids with different interparticle interactions are studied near the jamming concentration. By appropriate scaling with the distance to jamming all rheology data can be collapsed onto master curves below and above jamming that meet in the shear-thinning regime and satisfy the Herschel-Bulkley and Cross equations, respectively. In spite of differing interactions in the different systems, master curves characterized by universal scaling exponents are found for the four systems. A two-state microscopic theory of heterogeneous dynamics is presented to rationalize the observed transition from Herschel-Bulkley to Cross behavior and to connect the rheological exponents to microscopic exponents for the divergence of the length and time scales of the heterogeneous dynamics. The experimental data and the microscopic theory are compared with much of the available literature data for yield-stress systems.

Magnetocaloric properties and critical behavior of high relative cooling power FeNiB nanoparticles

Energy Technology Data Exchange (ETDEWEB)

Chaudhary, V. [Interdisciplinary Graduate School, Nanyang Technological University, Singapore 639798 (Singapore); Energy Research Institute @NTU, Nanyang Technological University, Singapore 637553 (Singapore); School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798 (Singapore); Maheswar Repaka, D. V.; Chaturvedi, A.; Ramanujan, R. V., E-mail: ramanujan@ntu.edu.sg [School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798 (Singapore); Sridhar, I. [School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798 (Singapore)

2014-10-28

Low cost magnetocaloric nanomaterials have attracted considerable attention for energy efficient applications. We report a very high relative cooling power (RCP) in a study of the magnetocaloric effect in quenched FeNiB nanoparticles. RCP increases from 89.8 to 640 J kg{sup −1} for a field change of 1 and 5 T, respectively, these values are the largest for rare earth free iron based magnetocaloric nanomaterials. To investigate the magnetocaloric behavior around the Curie temperature (T{sub C}), the critical behavior of these quenched nanoparticles was studied. Detailed analysis of the magnetic phase transition using the modified Arrott plot, Kouvel-Fisher method, and critical isotherm plots yields critical exponents of β = 0.364, γ = 1.319, δ = 4.623, and α = −0.055, which are close to the theoretical exponents obtained from the 3D-Heisenberg model. Our results indicate that these FeNiB nanoparticles are potential candidates for magnetocaloric fluid based heat pumps and low grade waste heat recovery.

Intermittency-induced criticality in a resistor-inductor-diode circuit.

Science.gov (United States)

Potirakis, Stelios M; Contoyiannis, Yiannis; Diakonos, Fotios K; Hanias, Michael P

2017-04-01

The current fluctuations of a driven resistor-inductor-diode circuit are investigated here looking for signatures of critical behavior monitored by the driving frequency. The experimentally obtained time series of the voltage drop across the resistor (as directly proportional to the current flowing through the circuit) were analyzed by means of the method of critical fluctuations in analogy to thermal critical systems. Intermittent criticality was revealed for a critical frequency band signifying the transition between the normal rectifier phase in the low frequencies and a full-wave conducting, capacitorlike phase in the high frequencies. The transition possesses critical characteristics with a characteristic exponent p_{l}=1.65. A fractal analysis in terms of the rescale range (R/RSS) and detrended fluctuation analysis methods yielded results fully compatible with the critical dynamics analysis. Suggestions for the interpretation of the observed behavior in terms of p-n junction operation are discussed.

Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System.

Science.gov (United States)

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.

Physical Explanation of Archie's Porosity Exponent in Granular Materials: A Process-Based, Pore-Scale Numerical Study

Science.gov (United States)

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.

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.

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)

Fractional Black–Scholes option pricing, volatility calibration and implied Hurst exponents in South African context

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

Low-dimensional chiral physics. Gross-Neveu universality and magnetic catalysis

Energy Technology Data Exchange (ETDEWEB)

Scherer, Daniel David

2012-09-27

In this thesis, we investigate the 3-dimensional, chirally symmetric Gross-Neveu model with functional renormalization group methods. This low-dimensional quantum field theory describes the continuum limit of the low-energy sector in certain lattice systems. The functional renormalization group allows to study in a nonperturbative way the physical properties of many-body systems and quantum field theories. The starting point is a formally exact flow equation with 1-loop structure for the generating functional of 1-particle irreducible vertices. Within a gradient expansion - tailor-made for extracting the infrared asymptotics of the momentum and frequency dependent vertices of the theory - we study the strong-coupling fixed point of the Gross-Neveu model even beyond the formal limit of infinite flavor number. This fixed point controls a 2nd order quantum phase transition from a massless phase to a phase with massive Dirac fermions. After a first analysis of the purely fermionic theory, a Hubbard-Stratonovich transformation is used to partially bosonize the theory. Within this bosonized description, we find universal critical exponents that are in excellent quantitative agreement with available results from 1/N{sub f}-expansions and Monte Carlo simulations and are expected to improve upon earlier results. The renormalization group flow allows us to gain insights into the global and local structure of the critical manifold within given truncations and better understanding of the relevant directions in the space of couplings, which in general do not coincide with the Gaussian classification. Within the framework of the so-called ''asymptotic safety''-scenario relevant for the construction of proper field theories, the fixed-point theory could be determined exactly in the limit of infinite flavor number. Here, the Gross-Neveu model yields a simple and intuitive example for how to define a nonperturbatively renormalizable quantum field theory. Going

Low-dimensional chiral physics. Gross-Neveu universality and magnetic catalysis

International Nuclear Information System (INIS)

Scherer, Daniel David

2012-01-01

In this thesis, we investigate the 3-dimensional, chirally symmetric Gross-Neveu model with functional renormalization group methods. This low-dimensional quantum field theory describes the continuum limit of the low-energy sector in certain lattice systems. The functional renormalization group allows to study in a nonperturbative way the physical properties of many-body systems and quantum field theories. The starting point is a formally exact flow equation with 1-loop structure for the generating functional of 1-particle irreducible vertices. Within a gradient expansion - tailor-made for extracting the infrared asymptotics of the momentum and frequency dependent vertices of the theory - we study the strong-coupling fixed point of the Gross-Neveu model even beyond the formal limit of infinite flavor number. This fixed point controls a 2nd order quantum phase transition from a massless phase to a phase with massive Dirac fermions. After a first analysis of the purely fermionic theory, a Hubbard-Stratonovich transformation is used to partially bosonize the theory. Within this bosonized description, we find universal critical exponents that are in excellent quantitative agreement with available results from 1/N f -expansions and Monte Carlo simulations and are expected to improve upon earlier results. The renormalization group flow allows us to gain insights into the global and local structure of the critical manifold within given truncations and better understanding of the relevant directions in the space of couplings, which in general do not coincide with the Gaussian classification. Within the framework of the so-called ''asymptotic safety''-scenario relevant for the construction of proper field theories, the fixed-point theory could be determined exactly in the limit of infinite flavor number. Here, the Gross-Neveu model yields a simple and intuitive example for how to define a nonperturbatively renormalizable quantum field theory. Going beyond the determination

Exploring the Relationship between Burnout and Critical Thinking Skills among Iranian University Professors Teaching TEFL

Directory of Open Access Journals (Sweden)

Hossein Khodabakhshzadeh

2017-10-01

Full Text Available The profession as a teacher involves experiencing a number of challenges which naturally lead to emotional tiredness and lack of reward, technically known as burnout (Colomeischi, 2015. The goal of the present study was to investigate the relationship between burnout and critical thinking ability. To this end, a sample of 40 professors of Teaching English as a Foreign Language (TEFL filed at a number of universities in Iran was chosen. Maslach Burnout Inventory (MBI was employed to assess the participants' burnout level, which is specifically evaluated by measuring three subscales of emotional exhaustion, depersonalization, and personal achievement. In addition, the measures of the participants' critical thinking skills were obtained via Watson-Glaser Critical Thinking Appraisal (WGCTA. The Pearson correlation coefficient analysis indicated that emotional exhaustion and depersonalization strongly and negatively correlated with critical thinking ability. However, a strong and positive relationship was found between personal achievement and critical thinking skills.

Universal Critical Power for Nonlinear Schroedinger Equations with a Symmetric Double Well Potential

International Nuclear Information System (INIS)

Sacchetti, Andrea

2009-01-01

Here we consider stationary states for nonlinear Schroedinger equations in any spatial dimension n with symmetric double well potentials. These states may bifurcate as the strength of the nonlinear term increases and we observe two different pictures depending on the value of the nonlinearity power: a supercritical pitchfork bifurcation, and a subcritical pitchfork bifurcation with two asymmetric branches occurring as the result of saddle-node bifurcations. We show that in the semiclassical limit, or for a large barrier between the two wells, the first kind of bifurcation always occurs when the nonlinearity power is less than a critical value; in contrast, when the nonlinearity power is larger than such a critical value then we always observe the second scenario. The remarkable fact is that such a critical value is a universal constant in the sense that it does not depend on the shape of the double well potential and on the dimension n.

Scaling identity connects human mobility and social interactions.

Science.gov (United States)

Deville, Pierre; Song, Chaoming; Eagle, Nathan; Blondel, Vincent D; Barabási, Albert-László; Wang, Dashun

2016-06-28

Massive datasets that capture human movements and social interactions have catalyzed rapid advances in our quantitative understanding of human behavior during the past years. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws, each characterized by its specific critical exponents. Although human mobility and social networks develop concomitantly as two prolific yet largely separated fields, we lack any known relationships between the critical exponents explored by them, despite the fact that they often study the same datasets. Here, by exploiting three different mobile phone datasets that capture simultaneously these two aspects, we discovered a new scaling relationship, mediated by a universal flux distribution, which links the critical exponents characterizing the spatial dependencies in human mobility and social networks. Therefore, the widely studied scaling laws uncovered in these two areas are not independent but connected through a deeper underlying reality.

Restoration of dimensional reduction in the random-field Ising model at five dimensions

Science.gov (United States)

Fytas, Nikolaos G.; Martín-Mayor, Víctor; Picco, Marco; Sourlas, Nicolas

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D equality at all studied dimensions.

Scaling analysis of [Fe(pyrazole)4]2[Nb(CN)8] molecular magnet

Science.gov (United States)

Konieczny, P.; Pełka, R.; Zieliński, P. M.; Pratt, F. L.; Pinkowicz, D.; Sieklucka, B.; Wasiutyński, T.

2013-10-01

The critical behaviour of the three dimensional (3D) molecular magnet {[FeII(pirazol)4]2[NbIV(CN)8]·4H2O}n has been studied with the use of experimental techniques such as ac magnetometry and zero field μSR spectroscopy. The sample orders magnetically below Tc=7.8 K. The measurements allowed to determine static exponents β, γ, and the dynamic exponent w. The resulting exponent values indicate that the studied system belongs to the universality class of the 3D Heisenberg model.

Reactor laboratory course for students majoring in nuclear engineering with the Kyoto University Critical Assembly (KUCA)

International Nuclear Information System (INIS)

Nishihara, H.; Shiroya, S.; Kanda, K.

1996-01-01

With the use of the Kyoto University Critical Assembly (KUCA), a joint reactor laboratory course of graduate level is offered every summer since 1975 by nine associated Japanese universities (Hokkaido University, Tohoku University, Tokyo Institute of Technology, Musashi Institute of Technology, Tokai University, Nagoya University, Osaka University, Kobe University of Mercantile Marine and Kyushu University) in addition to a reactor laboratory course of undergraduate level for Kyoto University. These courses are opened for three weeks (two weeks for the joint course and one week for the undergraduate course) to students majoring in nuclear engineering and a total of 1,360 students have taken the course in the last 21 years. The joint course has been institutionalized with the background that it is extremely difficult for a single university in Japan to have her own research or training reactor. By their effort, the united faculty team of the joint course have succeeded in giving an effective, unique one-week course, taking advantage of their collaboration. Last year, an enquete (questionnaire survey) was conducted to survey the needs for the educational experiments of graduate level and precious data have been obtained for promoting reactor laboratory courses. (author)

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.)

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.

Lyapunov exponent as a metric for assessing the dynamic content and predictability of large-eddy simulations

Science.gov (United States)

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

Citizenship Education: Cultivating a Critical Capacity to Implement Universal Values Nationally

Directory of Open Access Journals (Sweden)

Katarzyna Twarog

2017-04-01

Full Text Available Citizenship and citizenship education face challenges due to globalizing factors affecting modern liberal-democratic states. Earlier models of citizenship, which were based on assimilation into the dominant society, have been challenged by scholars seeking to create a fuller understanding of citizenship more inclusive of diversity. This paper addresses the works of Martha Nussbaum and James A. Banks who present two possibilities for citizenship education: purified patriotism (Nussbaum and transformative citizenship education (Banks. By considering values, identity and the national narrative, this paper compares their views in relation to these topics as well as gives supporting and opposing ideas from other scholars. It concludes by stating that these authors share a common commitment to the need for a critical civic culture, which in turn requires a willingness and openness on the part of all citizens to use their imagination and help foster the critical capacity to think anew. In this way, the traditional dichotomous debate over citizenship, values and identity within the nation and the world might be transformed. By utilizing what Freire refers to as deliberative dialogue, we can foster creative solutions to ensure that universal values of justice, tolerance, recognition and equality are not merely democratic ideals, but are practiced by all individuals and institutions. Furthermore, this paper addresses the need for a teacher training program which would teach educators how to promote and endorse a critical culture through dialogue within the classroom and create citizens who are capable of using their imagination and critical thinking to function cooperatively within a multicultural society.

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)

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

The role of critical thinking skills and learning styles of university students in their academic performance.

Science.gov (United States)

Ghazivakili, Zohre; Norouzi Nia, Roohangiz; Panahi, Faride; Karimi, Mehrdad; Gholsorkhi, Hayede; Ahmadi, Zarrin

2014-07-01

The Current world needs people who have a lot of different abilities such as cognition and application of different ways of thinking, research, problem solving, critical thinking skills and creativity. In addition to critical thinking, learning styles is another key factor which has an essential role in the process of problem solving. This study aimed to determine the relationship between learning styles and critical thinking of students and their academic performance in Alborz University of Medical Science. This cross-correlation study was performed in 2012, on 216 students of Alborz University who were selected randomly by the stratified random sampling. The data was obtained via a three-part questionnaire included demographic data, Kolb standardized questionnaire of learning style and California critical thinking standardized questionnaire. The academic performance of the students was extracted by the school records. The validity of the instruments was determined in terms of content validity, and the reliability was gained through internal consistency methods. Cronbach's alpha coefficient was found to be 0.78 for the California critical thinking questionnaire. The Chi Square test, Independent t-test, one way ANOVA and Pearson correlation test were used to determine relationship between variables. The Package SPSS14 statistical software was used to analyze data with a significant level of pstudents with convergent learning style have better performance than other groups. Also learning style had a relationship with age, gender, field of study, semester and job. The results about the critical thinking of the students showed that the mean of deductive reasoning and evaluation skills were higher than that of other skills and analytical skills had the lowest mean and there was a positive significant relationship between the students' performance with inferential skill and the total score of critical thinking skills (pskills and deductive reasoning had significant

The role of critical thinking skills and learning styles of university students in their academic performance

Science.gov (United States)

GHAZIVAKILI, ZOHRE; NOROUZI NIA, ROOHANGIZ; PANAHI, FARIDE; KARIMI, MEHRDAD; GHOLSORKHI, HAYEDE; AHMADI, ZARRIN

2014-01-01

Introduction: The Current world needs people who have a lot of different abilities such as cognition and application of different ways of thinking, research, problem solving, critical thinking skills and creativity. In addition to critical thinking, learning styles is another key factor which has an essential role in the process of problem solving. This study aimed to determine the relationship between learning styles and critical thinking of students and their academic performance in Alborz University of Medical Science. Methods: This cross-correlation study was performed in 2012, on 216 students of Alborz University who were selected randomly by the stratified random sampling. The data was obtained via a three-part questionnaire included demographic data, Kolb standardized questionnaire of learning style and California critical thinking standardized questionnaire. The academic performance of the students was extracted by the school records. The validity of the instruments was determined in terms of content validity, and the reliability was gained through internal consistency methods. Cronbach's alpha coefficient was found to be 0.78 for the California critical thinking questionnaire. The Chi Square test, Independent t-test, one way ANOVA and Pearson correlation test were used to determine relationship between variables. The Package SPSS14 statistical software was used to analyze data with a significant level of pcritical thinking of the students showed that the mean of deductive reasoning and evaluation skills were higher than that of other skills and analytical skills had the lowest mean and there was a positive significant relationship between the students’ performance with inferential skill and the total score of critical thinking skills (pcritical thinking had significant difference between different learning styles. Conclusion: The results of this study showed that the learning styles, critical thinking and academic performance are significantly associated

Two critical tests for the Critical Point earthquake

Science.gov (United States)

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

Adiabatic physics of an exchange-coupled spin-dimer system: Magnetocaloric effect, zero-point fluctuations, and possible two-dimensional universal behavior

International Nuclear Information System (INIS)

Brambleby, J.; Goddard, P. A.; Singleton, John; Jaime, Marcelo; Lancaster, T.

2017-01-01

We present the magnetic and thermal properties of the bosonic-superfluid phase in a spin-dimer network using both quasistatic and rapidly changing pulsed magnetic fields. The entropy derived from a heat-capacity study reveals that the pulsed-field measurements are strongly adiabatic in nature and are responsible for the onset of a significant magnetocaloric effect (MCE). In contrast to previous predictions we show that the MCE is not just confined to the critical regions, but occurs for all fields greater than zero at sufficiently low temperatures. We explain the MCE using a model of the thermal occupation of exchange-coupled dimer spin states and highlight that failure to take this effect into account inevitably leads to incorrect interpretations of experimental results. In addition, the heat capacity in our material is suggestive of an extraordinary contribution from zero-point fluctuations and appears to indicate universal behavior with different critical exponents at the two field-induced critical points. Finally, the data at the upper critical point, combined with the layered structure of the system, are consistent with a two-dimensional nature of spin excitations in the system.

Bose-Einstein condensation in chains with power-law hoppings: Exact mapping on the critical behavior in d-dimensional regular lattices.

Science.gov (United States)

Dias, W S; Bertrand, D; Lyra, M L

2017-06-01

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d>4.

Bose-Einstein condensation in chains with power-law hoppings: Exact mapping on the critical behavior in d -dimensional regular lattices

Science.gov (United States)

Dias, W. S.; Bertrand, D.; Lyra, M. L.

2017-06-01

Recent experimental progress on the realization of quantum systems with highly controllable long-range interactions has impelled the study of quantum phase transitions in low-dimensional systems with power-law couplings. Long-range couplings mimic higher-dimensional effects in several physical contexts. Here, we provide the exact relation between the spectral dimension d at the band bottom and the exponent α that tunes the range of power-law hoppings of a one-dimensional ideal lattice Bose gas. We also develop a finite-size scaling analysis to obtain some relevant critical exponents and the critical temperature of the BEC transition. In particular, an irrelevant dangerous scaling field has to be taken into account when the hopping range is sufficiently large to make the effective dimensionality d >4 .

On self-organized criticality in nonconserving systems

International Nuclear Information System (INIS)

Socolar, J.E.S.; Grinstein, G.; Jayaprakash, C.

1993-01-01

Two models with nonconserving dynamics and slow continuous deterministic driving, a stick-slip model (SSM) of earthquake dynamics and a toy forest-fire model (FFM), have recently been argued to show numerical evidence of self-organized criticality (generic, scale-invariant steady states). To determine whether the observed criticality is indeed generic, we study these models as a function of a parameter γ which was implicitly tuned to a special value, γ=1, in their original definitions. In both cases, the maximum Lyapunov exponent vanishes at γ=1. We find that the FFM does not exhibit self-organized criticality for any γ, including γ=1; nor does the SSM with periodic boundary conditions. Both models show evidence of macroscopic periodic oscillations in time for some range of γ values. We suggest that such oscillations may provide a mechanism for the generation of scale-invariant structure in nonconserving systems, and, in particular, that they underlie the criticality previously observed in the SSM with open boundary conditions

Mastering Leadership Concepts through Utilizing Critical Thinking Strategies within Educational Administration Courses at Kuwait University

Science.gov (United States)

Alqahtani, Abdulmuhsen Ayedh; Al-Enezi, Mutlaq M.

2012-01-01

The current study aims at exploring the students' perceptions of mastering leadership concepts and critical thinking strategies implemented by faculty members in the college of education at Kuwait University, and the impact of the later on former. The data was collected using a questionnaire on a sample consisting of 411 students representing…

Comment on 'Exact analytical solution for the generalized Lyapunov exponent of the two-dimensional Anderson localization'

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)

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

Science.gov (United States)

Grassberger, Peter

2018-05-01

Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).

Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition

CERN Document Server

Ódor, G

2003-01-01

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.

Random walks, critical phenomena, and triviality in quantum field theory

International Nuclear Information System (INIS)

Fernandez, R.; Froehlich, J.; Sokal, A.D.

1992-01-01

The subject of this book is equilibrium statistical mechanics - in particular the theory of critical phenomena - and quantum field theory. A general review of the theory of critical phenomena in spin systems, field theories, and random-walk and random-surface models is presented. Among the more technical topics treated in this book, the central theme is the use of random-walk representations as a tool to derive correlation inequalities. The consequences of these inequalities for critical-exponent theory and the triviality question in quantum field theory are expounded in detail. The book contains some previously unpublished results. It addresses both the researcher and the graduate student in modern statistical mechanics and quantum field theory. (orig.)

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

Finite size scaling analysis of disordered electron systems

International Nuclear Information System (INIS)

Markos, P.

2012-01-01

We demonstrated the application of the finite size scaling method to the analysis of the transition of the disordered system from the metallic to the insulating regime. The method enables us to calculate the critical point and the critical exponent which determines the divergence of the correlation length in the vicinity of the critical point. The universality of the metal-insulator transition was verified by numerical analysis of various physical parameters and the critical exponent was calculated with high accuracy for different disordered models. Numerically obtained value of the critical exponent for the three dimensional disordered model (1) has been recently supported by the semi-analytical work and verified by experimental optical measurements equivalent to the three dimensional disordered model (1). Another unsolved problem of the localization is the disagreement between numerical results and predictions of the analytical theories. At present, no analytical theory confirms numerically obtained values of critical exponents. The reason for this disagreement lies in the statistical character of the process of localization. The theory must consider all possible scattering processes on randomly distributed impurities. All physical variables are statistical quantities with broad probability distributions. It is in general not know how to calculate analytically their mean values. We believe that detailed numerical analysis of various disordered systems bring inspiration for the formulation of analytical theory. (authors)

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

Criticality of the Potts ferromagnet in Midgal-Kadanoff - like hierarchical lattices

International Nuclear Information System (INIS)

Silva, L.R. da; Tsallis, C.

1987-01-01

Within the real space renormalisation group framework, we discuss the critical point and exponent υ of the Potts ferromagnet in b-sized Migdal-Kadanoff-like hierarchical lattices. Both b → ∞ and b → 1 limits are exhibited. The important discrepancies that might exist between the exact results for d-dimensional hierarchical lattices and d-dimensional Bravais lattices are illustrated. (Author) [pt

Non-equilibrium relaxation in a stochastic lattice Lotka-Volterra model

Science.gov (United States)

Chen, Sheng; Täuber, Uwe C.

2016-04-01

We employ Monte Carlo simulations to study a stochastic Lotka-Volterra model on a two-dimensional square lattice with periodic boundary conditions. If the (local) prey carrying capacity is finite, there exists an extinction threshold for the predator population that separates a stable active two-species coexistence phase from an inactive state wherein only prey survive. Holding all other rates fixed, we investigate the non-equilibrium relaxation of the predator density in the vicinity of the critical predation rate. As expected, we observe critical slowing-down, i.e., a power law dependence of the relaxation time on the predation rate, and algebraic decay of the predator density at the extinction critical point. The numerically determined critical exponents are in accord with the established values of the directed percolation universality class. Following a sudden predation rate change to its critical value, one finds critical aging for the predator density autocorrelation function that is also governed by universal scaling exponents. This aging scaling signature of the active-to-absorbing state phase transition emerges at significantly earlier times than the stationary critical power laws, and could thus serve as an advanced indicator of the (predator) population’s proximity to its extinction threshold.

Fractal dimension of cantori

International Nuclear Information System (INIS)

Li, W.; Bak, P.

1986-01-01

At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D = 1 to the cantorus is governed by an exponent ν = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent

Phase transitions in scale-free neural networks: Departure from the standard mean-field universality class

International Nuclear Information System (INIS)

Aldana, Maximino; Larralde, Hernan

2004-01-01

We investigate the nature of the phase transition from an ordered to a disordered state that occurs in a family of neural network models with noise. These models are closely related to the majority voter model, where a ferromagneticlike interaction between the elements prevails. Each member of the family is distinguished by the network topology, which is determined by the probability distribution of the number of incoming links. We show that for homogeneous random topologies, the phase transition belongs to the standard mean-field universality class, characterized by the order parameter exponent β=1/2. However, for scale-free networks we obtain phase transition exponents ranging from 1/2 to infinity. Furthermore, we show the existence of a phase transition even for values of the scale-free exponent in the interval (1.5,2], where the average network connectivity diverges

Relationship between Female Pre University Students' Critical Thinking Skills and Their Mental Health

Directory of Open Access Journals (Sweden)

Y. Maroofi

2012-04-01

Full Text Available Introduction & Objective: Critical thinking is simply defined as ability for analysis and evaluation of information. Today, this skill is considered as an undeniable necessity for social life. So fostering critical thinking ability is one of the basic goals of different levels of education from primary school to higher education. Each conscious behavior is related to the theoretical and intellectual foundation and origin. Therefore, the quality and types of thought play an important role in human mental health. This research studies the relationship between female pre-university students' critical thinking skills and their mental health in the academic year 2009-2010 in Hamadan city. Materials & Methods: This study is a cross sectional research and our method is based on correlation. Using random multiple stages clustering method, we selected 331 students as statistical sample. The data gathering instruments are two standard questionnaires: California form b critical thinking questionnaire and 28-question Goldberg and Hilier general health questionnaire. The data were analyzed using descriptive statistic indexes such as frequency, percent, mean and standard deviation and inferential tests such as Pearson correlation coefficient and multiple regressions. Results: Research findings show that the average point of students' critical thinking skills is (6.51 out of 34 and their average point of mental health is (31.52 .About 61 persons(18.4 percent have not any psychological disorder, about 270 person (81.6 percent seemed to have psychological disorder symptoms. There are negative and significant differences between critical thinking skills and disorder in mental health. Multiple regression analysis show that: there is negative and significant differences between critical analysis and deductive rational skills with psychological disorder symptoms, that is when students' critical thinking skills increases, the psychological disorder symptoms decrease

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.

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.

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.

Critical Analysis of Management and Transformation in University Education, from Various Postulates

Directory of Open Access Journals (Sweden)

Josseilin Jasenka Marcano Ortega

2017-02-01

Full Text Available The Venezuelan university transformation is guided by principles of Latin American and Caribbean integration, whose priority is to overcome the evolutionary and progressive need of societies; In this sense, to manage it, it becomes the primary tool to overcome numerous challenges in terms of technological education political social education. The present research has as an incentive the critical analysis of postulates on the subject, issued by authors such as: Berrios, Castillo and Castro (2009, Morales (2012, Muro and Picón (2005, to Rivero and Goyo (2012. From a qualitative methodology, using hermeneutics as a general method of understanding, located in a documentary design, directed to the discourse analysis, one uses the technique of the triad model, where diverse categories and subcategories emerge, to form an assumption with the vision proposal. Among the outstanding findings: university transformation requires leaders committed to the new paradigmatic changes that humanity demands; The university management, must make the knowledge towards the construction and operation of a national productive model towards the development of the country; And, within the complexity of political, social and economic interactions and interrelations, to make a sustained effort in conceiving and founding a reform of thought for the evolution of society.

Small angle neutron scattering study on a phase separation in a 3-component microemulsion system

DEFF Research Database (Denmark)

Seto, H.; Yokoi, E.; Komura, S.

1993-01-01

In literature, the 3-component microemulsion system consisting of AOT, water and n-decane is known to belong to 3D-Ising universality class so far. Recently, we have found that the critical exponent of the susceptibility is the meanfield value at near-critical region, and at the same time we have...

The University of the Third Age in the UK: An Interpretive and Critical Study

Science.gov (United States)

Huang, Chin-Shan

2006-01-01

The idea of the University of the Third Age (U3A) in the UK was originated from France. However, the British formed their own model of U3As, which is different from that of French U3As. What are the reasons that the British U3As developed in a different way? The purpose of this article is to interpret and criticize in-depth the reasons why British…

A perturbation method to the tent map based on Lyapunov exponent and its application

Science.gov (United States)

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).

Cumulative Effective Hölder Exponent Based Indicator for Real-Time Fetal Heartbeat Analysis during Labour

Science.gov (United States)

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.

The nature of the continuous non-equilibrium phase transition of Axelrod's model

Science.gov (United States)

Peres, Lucas R.; Fontanari, José F.

2015-09-01

Axelrod's model in the square lattice with nearest-neighbors interactions exhibits culturally homogeneous as well as culturally fragmented absorbing configurations. In the case in which the agents are characterized by F = 2 cultural features and each feature assumes k states drawn from a Poisson distribution of parameter q, these regimes are separated by a continuous transition at qc = 3.10 +/- 0.02 . Using Monte Carlo simulations and finite-size scaling we show that the mean density of cultural domains μ is an order parameter of the model that vanishes as μ ∼ (q - q_c)^β with β = 0.67 +/- 0.01 at the critical point. In addition, for the correlation length critical exponent we find ν = 1.63 +/- 0.04 and for Fisher's exponent, τ = 1.76 +/- 0.01 . This set of critical exponents places the continuous phase transition of Axelrod's model apart from the known universality classes of non-equilibrium lattice models.

Universality of P−V criticality in horizon thermodynamics

Energy Technology Data Exchange (ETDEWEB)

Hansen, Devin; Kubizňák, David [Perimeter Institute,31 Caroline St. N., Waterloo, Ontario, N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo,Waterloo, Ontario, N2L 3G1 (Canada); Mann, Robert B. [Department of Physics and Astronomy, University of Waterloo,Waterloo, Ontario, N2L 3G1 (Canada)

2017-01-11

We study P−V criticality of black holes in Lovelock gravities in the context of horizon thermodynamics. The corresponding first law of horizon thermodynamics emerges as one of the Einstein-Lovelock equations and assumes the universal (independent of matter content) form δE=TδS−PδV, where P is identified with the total pressure of all matter in the spacetime (including a cosmological constant Λ if present). We compare this approach to recent advances in extended phase space thermodynamics of asymptotically AdS black holes where the ‘standard’ first law of black hole thermodynamics is extended to include a pressure-volume term, where the pressure is entirely due to the (variable) cosmological constant. We show that both approaches are quite different in interpretation. Provided there is sufficient non-linearity in the gravitational sector, we find that horizon thermodynamics admits the same interesting black hole phase behaviour seen in the extended case, such as a Hawking-Page transition, Van der Waals like behaviour, and the presence of a triple point. We also formulate the Smarr formula in horizon thermodynamics and discuss the interpretation of the quantity E appearing in the horizon first law.

Universality of P−V criticality in horizon thermodynamics

International Nuclear Information System (INIS)

Hansen, Devin; Kubizňák, David; Mann, Robert B.

2017-01-01

We study P−V criticality of black holes in Lovelock gravities in the context of horizon thermodynamics. The corresponding first law of horizon thermodynamics emerges as one of the Einstein-Lovelock equations and assumes the universal (independent of matter content) form δE=TδS−PδV, where P is identified with the total pressure of all matter in the spacetime (including a cosmological constant Λ if present). We compare this approach to recent advances in extended phase space thermodynamics of asymptotically AdS black holes where the ‘standard’ first law of black hole thermodynamics is extended to include a pressure-volume term, where the pressure is entirely due to the (variable) cosmological constant. We show that both approaches are quite different in interpretation. Provided there is sufficient non-linearity in the gravitational sector, we find that horizon thermodynamics admits the same interesting black hole phase behaviour seen in the extended case, such as a Hawking-Page transition, Van der Waals like behaviour, and the presence of a triple point. We also formulate the Smarr formula in horizon thermodynamics and discuss the interpretation of the quantity E appearing in the horizon first law.

Universality of collapsing two-dimensional self-avoiding trails

International Nuclear Information System (INIS)

Foster, D P

2009-01-01

Results of a numerically exact transfer matrix calculation for the model of interacting self-avoiding trails are presented. The results lead to the conclusion that at the collapse transition, self-avoiding trails are in the same universality class as the O(n = 0) model of Bloete and Nienhuis (or vertex-interacting self-avoiding walk), which has thermal exponent ν = 12/23, contrary to previous conjectures. (fast track communication)

Beyond the Young-Laplace model for cluster growth during dewetting of thin films: effective coarsening exponents and the role of long range dewetting interactions.

Science.gov (United States)

Constantinescu, Adi; Golubović, Leonardo; Levandovsky, Artem

2013-09-01

Long range dewetting forces acting across thin films, such as the fundamental van der Waals interactions, may drive the formation of large clusters (tall multilayer islands) and pits, observed in thin films of diverse materials such as polymers, liquid crystals, and metals. In this study we further develop the methodology of the nonequilibrium statistical mechanics of thin films coarsening within continuum interface dynamics model incorporating long range dewetting interactions. The theoretical test bench model considered here is a generalization of the classical Mullins model for the dynamics of solid film surfaces. By analytic arguments and simulations of the model, we study the coarsening growth laws of clusters formed in thin films due to the dewetting interactions. The ultimate cluster growth scaling laws at long times are strongly universal: Short and long range dewetting interactions yield the same coarsening exponents. However, long range dewetting interactions, such as the van der Waals forces, introduce a distinct long lasting early time scaling behavior characterized by a slow growth of the cluster height/lateral size aspect ratio (i.e., a time-dependent Young angle) and by effective coarsening exponents that depend on cluster size. In this study, we develop a theory capable of analytically calculating these effective size-dependent coarsening exponents characterizing the cluster growth in the early time regime. Such a pronounced early time scaling behavior has been indeed seen in experiments; however, its physical origin has remained elusive to this date. Our theory attributes these observed phenomena to ubiquitous long range dewetting interactions acting across thin solid and liquid films. Our results are also applicable to cluster growth in initially very thin fluid films, formed by depositing a few monolayers or by a submonolayer deposition. Under this condition, the dominant coarsening mechanism is diffusive intercluster mass transport while the

New Type of Quantum Criticality in the Pyrochlore Iridates

Directory of Open Access Journals (Sweden)

Lucile Savary

2014-11-01

Full Text Available Magnetic fluctuations and electrons couple in intriguing ways in the vicinity of zero-temperature phase transitions—quantum critical points—in conducting materials. Quantum criticality is implicated in non-Fermi liquid behavior of diverse materials and in the formation of unconventional superconductors. Here, we uncover an entirely new type of quantum critical point describing the onset of antiferromagnetism in a nodal semimetal engendered by the combination of strong spin-orbit coupling and electron correlations, and which is predicted to occur in the iridium oxide pyrochlores. We formulate and solve a field theory for this quantum critical point by renormalization group techniques and show that electrons and antiferromagnetic fluctuations are strongly coupled and that both these excitations are modified in an essential way. This quantum critical point has many novel features, including strong emergent spatial anisotropy, a vital role for Coulomb interactions, and highly unconventional critical exponents. Our theory motivates and informs experiments on pyrochlore iridates and constitutes a singular realistic example of a nontrivial quantum critical point with gapless fermions in three dimensions.

Exposing Ideology within University Policies: A Critical Discourse Analysis of Faculty Hiring, Promotion and Remuneration Practices

Science.gov (United States)

Uzuner-Smith, Sedef; Englander, Karen

2015-01-01

Using critical discourse analysis (CDA), this paper exposes the neoliberal ideology of the knowledge-based economy embedded within university policies, specifically those that regulate faculty hiring, promotion, and remuneration in two national contexts: Turkey and Mexico. The paper follows four stages of CDA: (1) focus upon a social wrong in its…

Critical composition fluctuations in artificial and cell-derived lipid membranes

Science.gov (United States)

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.

How many universes are in the multiverse?

International Nuclear Information System (INIS)

Linde, Andrei; Vanchurin, Vitaly

2010-01-01

We argue that the total number of distinguishable locally Friedmann 'universes' generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by e e 3N , where N is the number of e-folds of slow-roll posteternal inflation. For simplest models of chaotic inflation, N is approximately equal to de Sitter entropy at the end of eternal inflation; it can be exponentially large. However, not all of these universes can be observed by a local observer. In the presence of a cosmological constant Λ the number of distinguishable universes is bounded by e |Λ| -3/4 . In the context of the string theory landscape, the overall number of different universes is expected to be exponentially greater than the total number of vacua in the landscape. We discuss the possibility that the strongest constraint on the number of distinguishable universes may be related not to the properties of the multiverse but to the properties of observers.

Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench.

Science.gov (United States)

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.

Critical reflexivity in financial markets: a Hawkes process analysis

Science.gov (United States)

Hardiman, Stephen J.; Bercot, Nicolas; Bouchaud, Jean-Philippe

2013-10-01

We model the arrival of mid-price changes in the E-mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to -1.15 at short times, less than ≈ 103 s, and crosses over to a second power-law regime with a larger decay exponent ≈-1.45 for longer times scales in the range [ 103,106 ] seconds. More importantly, we find that the Hawkes kernel integrates to unity independently of the analysed period, from 1998 to 2011. This suggests that markets are and have always been close to criticality, challenging a recent study which indicates that reflexivity (endogeneity) has increased in recent years as a result of increased automation of trading. However, we note that the scale over which market events are correlated has decreased steadily over time with the emergence of higher frequency trading.

Systematic approach to critical phenomena by the extended variational method and coherent-anomaly method

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

Critical behavior in graphene with Coulomb interactions.

Science.gov (United States)

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.

Zipf exponent of trajectory distribution in the hidden Markov model

Science.gov (United States)

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

Predicting the long tail of book sales: Unearthing the power-law exponent

Science.gov (United States)

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.

Characterization of fish sauce aroma-impact compounds using GC-MS, SPME-Osme-GCO, and Stevens' power law exponents.

Science.gov (United States)

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.

Dependence of exponents on text length versus finite-size scaling for word-frequency distributions

Science.gov (United States)

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.

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

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.

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.

Science.gov (United States)

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.

Critical behavior of the ideal-gas Bose-Einstein condensation in the Apollonian network.

Science.gov (United States)

de Oliveira, I N; dos Santos, T B; de Moura, F A B F; Lyra, M L; Serva, M

2013-08-01

We show that the ideal Boson gas displays a finite-temperature Bose-Einstein condensation transition in the complex Apollonian network exhibiting scale-free, small-world, and hierarchical properties. The single-particle tight-binding Hamiltonian with properly rescaled hopping amplitudes has a fractal-like energy spectrum. The energy spectrum is analytically demonstrated to be generated by a nonlinear mapping transformation. A finite-size scaling analysis over several orders of magnitudes of network sizes is shown to provide precise estimates for the exponents characterizing the condensed fraction, correlation size, and specific heat. The critical exponents, as well as the power-law behavior of the density of states at the bottom of the band, are similar to those of the ideal Boson gas in lattices with spectral dimension d(s)=2ln(3)/ln(9/5)~/=3.74.

Analysis of Multiple Structural Changes in Financial Contagion Based on the Largest Lyapunov Exponents

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.

Generalized Hurst exponent approach to efficiency in MENA markets

Science.gov (United States)

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 Hurst exponent over time: testing the assertion that emerging markets are becoming more efficient

Science.gov (United States)

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.

Perturbation theory for Lyapunov exponents of an Anderson model on a strip

CERN Document Server

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.

What Kind of Critical University Education for Sustainable Development? A Comparative Study of European Students and Social Representations

Directory of Open Access Journals (Sweden)

Agnieszka Jeziorski

2012-12-01

Full Text Available In the course of the institutional integration of education for sustainable development (ESD, university courses have been going through rapid changes, but this process can be blocked or aided by each country’s peculiar features, whether institutional, financial, cultural or other. This article proposes an examination of the specific socio-educational characteristics of the implementation of ESD based on a study of the social representations of students in three European countries (Germany, France and Poland, and in two types of Master’s level university education. The paper initially focuses on the differences and similarities in the student research groups. It then analyses the representational components in terms of the possible impacts on the implementation of ESD at the university from a critical, citizenship perspective. Despite the differences in the students’ representational structures in the various countries, we can see that, in the three national groups, the social representations of sustainable development are highly focused and have a highly fragmented character. The lack of systematization of the different elements of the representation poses barriers to critical education, although this takes different forms in the different countries.

Quantum criticality and first-order transitions in the extended periodic Anderson model

Science.gov (United States)

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.

Activation barrier scaling and crossover for noise-induced switching in micromechanical parametric oscillators.

Science.gov (United States)

Chan, H B; Stambaugh, C

2007-08-10

We explore fluctuation-induced switching in parametrically driven micromechanical torsional oscillators. The oscillators possess one, two, or three stable attractors depending on the modulation frequency. Noise induces transitions between the coexisting attractors. Near the bifurcation points, the activation barriers are found to have a power law dependence on frequency detuning with critical exponents that are in agreement with predicted universal scaling relationships. At large detuning, we observe a crossover to a different power law dependence with an exponent that is device specific.

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...

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)

Reactor Physics Experiments by Korean Under-Graduate Students in Kyoto University Critical Assembly Program (KUGSiKUCA Program)

International Nuclear Information System (INIS)

Pyeon, Cheol Ho; Misawa, Tsuyoshi; Unesaki, Hironobu; Ichihara, Chihiro; Shiroya, Seiji; Whang, Joo Ho; Kim, Myung Hyun

2006-01-01

The Reactor Laboratory Course for Korean Under-Graduate Students in Kyoto University Critical Assembly (KUGSiKUCA) program has been launched from 2003, as one of international collaboration programs of Kyoto University Research Reactor Institute (KURRI). This program was suggested by Department of Nuclear Engineering, College of Advanced Technology, Kyunghee University (KHU), and was adopted by Ministry of Science and Technology of Korean Government as one of among Nuclear Human Resources Education and Training Programs. On the basis of her suggestion for KURRI, memorandum for academic corporation and exchange between KHU and KURRI was concluded on July 2003. The program has been based on the background that it is extremely difficult for any single university in Korea to have her own research or training reactor. Up to this 2006, total number of 61 Korean under-graduate school students, who have majored in nuclear engineering of Kyunghee University, Hanyang University, Seoul National University, Korea Advanced Institute of Science and Technology, Chosun University and Cheju National University in all over the Korea, has taken part in this program. In all the period, two professors and one teaching assistant on the Korean side led the students and helped their successful experiments, reports and discussions. Due to their effort, the program has succeeded in giving an effective and unique course, taking advantage of their collaboration

Conceptions of Critical Thinking from University EFL Teachers

Science.gov (United States)

Marin, Matias A.; de la Pava, Luisa

2017-01-01

Critical Thinking has become an educational and social ideal. English as a Foreign Language (EFL) teaching has not been apart from the discussion on the importance of implementing Critical Thinking into the educational process. However, research on Critical Thinking has broadly been carried out in other fields of knowledge rather than in EFL.…

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

dc Resistivity of Quantum Critical, Charge Density Wave States from Gauge-Gravity Duality.

Science.gov (United States)

Amoretti, Andrea; Areán, Daniel; Goutéraux, Blaise; Musso, Daniele

2018-04-27

In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high T_{c} superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.