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

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

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.

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 ).

Non-universality of critical exponents in the paraconductivity of short-coherence-length superconductors

International Nuclear Information System (INIS)

Gauzzi, A.

1993-01-01

The Aslamazov-Larkin paraconductivity term is calculated in the case of sufficiently small superconducting coherence length. It is found that the critical exponent of paraconductivity depends on the short-wavelength cut-off of the fluctuation spectrum in the whole Ginzburg-Landau mean-field region. Hence, it is predicted that the Aslamazov-Larkin universal relation between the critical exponent of paraconductivity and the dimensionality of the superconducting state is no longer valid in short-coherence-length superconductors. This prediction is confirmed by paraconductivity measurements on cuprate superconductors. (orig.)

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.

Landau-like theory for universality of critical exponents in quasistationary states of isolated mean-field systems.

Science.gov (United States)

Ogawa, Shun; Yamaguchi, Yoshiyuki Y

2015-06-01

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two nonclassical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends the universality class of the nonclassical exponents to spatially periodic one-dimensional systems and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.

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 ...

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.

Critical behavior of the spontaneous polarization and the dielectric susceptibility close to the cubic-tetragonal transition in BaTiO3

Directory of Open Access Journals (Sweden)

H. Yurtseven

2015-09-01

Full Text Available Using Landau mean field model, the spontaneous polarization and the dielectric susceptibility are analyzed as functions of temperature and pressure close to the cubic–tetragonal (ferroelectric–paraelectric transition in BaTiO3. From the analysis of the dielectric susceptibility and the spontaneous polarization, the critical exponents are deduced in the classical and quantum limits for BaTiO3. From the critical behavior of the dielectric susceptibility, the spontaneous polarization can be described for the ferroelectric–paraelectric (cubic to tetragonal transition between 4 and 8 GPa at constant temperatures of 0 to 200 K in BaTiO3 within the Landau mean field model given here.

Critical 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

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.

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.

Critical behavior of AC antiferromagnetic and ferromagnetic susceptibilities of a spin-1/2 metamagnetic Ising system

International Nuclear Information System (INIS)

Gulpinar, Gul; Vatansever, Erol

2012-01-01

In this study, the temperature variations of the equilibrium and the non-equilibrium antiferromagnetic and ferromagnetic susceptibilities of a metamagnetic system are examined near the critical point. The kinetic equations describing the time dependencies of the total and staggered magnetizations are derived by utilizing linear response theory. In order to obtain dynamic magnetic relaxation behavior of the system, the stationary solutions of the kinetic equations in existence of sinusoidal staggered and physical external magnetic fields are performed. In addition, the static and dynamical mean field critical exponents are calculated in order to formulate the critical behavior of antiferromagnetic and ferromagnetic magnetic response of a metamagnetic system. Finally, a comparison of the findings of this study with previous theoretical and experimental studies is represented and it is shown that a good agreement is found with our results. - Highlights: ► Staggered dynamic susceptibility diverges as T→T N in the low frequency region. ► Dynamic total susceptibility exhibits a finite jump discontinuity as T→T N while wτ 2 ⪡1. ► The slope of the staggered magnetic dispersion curve chances in sign as T→T N .

Rigorous lower bound on the dynamic critical exponent of some multilevel Swendsen-Wang algorithms

International Nuclear Information System (INIS)

Li, X.; Sokal, A.D.

1991-01-01

We prove the rigorous lower bound z exp ≥α/ν for the dynamic critical exponent of a broad class of multilevel (or ''multigrid'') variants of the Swendsen-Wang algorithm. This proves that such algorithms do suffer from critical slowing down. We conjecture that such algorithms in fact lie in the same dynamic universality class as the stanard Swendsen-Wang algorithm

Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class

OpenAIRE

Gracey, J. A.

2018-01-01

We compute the large N critical exponents η, ηϕ and 1/ν in d dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of 1/N. For instance, the large N conformal bootstrap method is used to determine η at O(1/N3) while the other exponents are computed to O(1/N2). Estimates of the exponents for a phase transition in graphene are given which are shown to be commensurate with other approaches. In particular the behavior of the exponents in 2

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

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)

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.)

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

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.

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.

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

Evolution of dynamic susceptibility in molecular glass formers-a critical assessment

International Nuclear Information System (INIS)

Brodin, A; Gainaru, C; Porokhonskyy, V; Roessler, E A

2007-01-01

Dielectric, depolarized light scattering (LS) and optical Kerr effect (OKE) data are critically discussed in an attempt to achieve a common interpretation of the evolution of dynamic susceptibility in molecular glass formers at temperatures down to the glass transition T g . The so-called intermediate power-law, observed in OKE data below a certain temperature T x , is identified with the excess wing, long since known from dielectric spectroscopy, with a temperature-independent exponent. This is in contrast with several recent analyses that concluded a considerable temperature dependence of spectral shapes. We introduce a new approach to disentangle α-peak and excess wing contributions in the dielectric spectra, which allows for frequency-temperature superposition (FTS) of the α-process at all temperatures above T g . From the LS spectra we conclude, in particular, that FTS holds even at temperatures well above the melting point, i.e. in normal equilibrium liquids. Attempting to correlate the fragility and stretching, our conclusions are opposite to those made previously. Specifically, we observe that a high fragility is associated with a less stretched relaxation function

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model

Science.gov (United States)

Liu, Maoxin; Chesi, Stefano; Ying, Zu-Jian; Chen, Xiaosong; Luo, Hong-Gang; Lin, Hai-Qing

2017-12-01

We investigate the quantum phase transition of the anisotropic quantum Rabi model, in which the rotating and counterrotating terms are allowed to have different coupling strengths. The model interpolates between two known limits with distinct universal properties. Through a combination of analytic and numerical approaches, we extract the phase diagram, scaling functions, and critical exponents, which determine the universality class at finite anisotropy (identical to the isotropic limit). We also reveal other interesting features, including a superradiance-induced freezing of the effective mass and discontinuous scaling functions in the Jaynes-Cummings limit. Our findings are extended to the few-body quantum phase transitions with N >1 spins, where we expose the same effective parameters, scaling properties, and phase diagram. Thus, a stronger form of universality is established, valid from N =1 up to the thermodynamic limit.

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)

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)

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

Magnetism of a sigma-phase Fe{sub 60}V{sub 40} alloy: Magnetic susceptibilities and magnetocaloric effect studies

Energy Technology Data Exchange (ETDEWEB)

Bałanda, Maria [Institute of Nuclear Physics, Polish Academy of Science, PL-31-342 Kraków (Poland); Dubiel, Stanisław M., E-mail: Stanislaw.Dubiel@fis.agh.edu.pl [AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, PL-30-059 Kraków (Poland); Pełka, Robert [Institute of Nuclear Physics, Polish Academy of Science, PL-31-342 Kraków (Poland)

2017-06-15

Highlights: • Sigma-phase Fe{sub 60}V{sub 40} alloy was studied by means of AC and DC magnetic susceptibilities. • Re-entrant character of the magnetism has been evidenced. • Curie temperature was found as ∼169 K and the spin-freezing temperature as ∼164 K. • Critical exponents β = 0.6, γ = 1.0 and Δ = 1.6 were determined. • Magnetocaloric effect was investigated. - Abstract: Magnetic properties of a sigma-phase Fe{sub 60}V{sub 40} intermetallic compound were studied by means of ac and dc magnetic susceptibility and magnetocaloric effect measurements. The compound is a soft magnet yet it was found to behave like a re-entrant spin-glass system. The magnetic ordering temperature was found to be T{sub C} ≈ 170 K, while the spin-freezing temperature was ∼164 K. Its relative shift per decade of ac frequency was 0.002, a value smaller than that typical of canonical spin-glasses. Magnetic entropy change, ΔS, in the vicinity of T{sub C} was determined for magnetic field, H, ranging between 5 and 50 kOe. Analysis of ΔS in terms of the power law yielded the critical exponent, n, vs. temperature with the minimum value of 0.75 at T{sub C}, while from the analysis of a relative shift of the maximum value of ΔS with the field a critical exponent Δ = 1.7 was obtained. Based on scaling laws relationships values of other two exponents viz. β = 0.6 and γ = 1 were determined.

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.

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...

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks

Science.gov (United States)

St-Onge, Guillaume; Young, Jean-Gabriel; Laurence, Edward; Murphy, Charles; Dubé, Louis J.

2018-02-01

We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework on a given degree distribution, we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the SIS process. This analysis is suitable for the characterization of the phase transition and leads to three main contributions: (1) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation. (2) We recover the predictions of a number of existing approaches as limiting cases of our analysis, providing thereby a unifying point of view for the SIS dynamics on random networks. (3) We obtain bounds for the critical exponents of a number of quantities in the stationary state. This allows us to reinterpret the concept of hub-dominated phase transition. Within our framework, it appears as a heterogeneous critical phenomenon: observables for different degree classes have a different scaling with the infection rate. This phenomenon is followed by the successive activation of the degree classes beyond the epidemic threshold.

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.

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....

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.

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

Science.gov (United States)

Pan, Xue; Zhang, Yanhua; Chen, Lizhu; Xu, Mingmei; Wu, Yuanfang

2018-01-01

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class. Supported by Fund Project of National Natural Science Foundation of China (11647093, 11405088, 11521064), Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University (2016RC004) and the Major State Basic Research Development Program of China (2014CB845402)

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 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)

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.)

Susceptibilities from a black hole engineered EoS with a critical point

International Nuclear Information System (INIS)

Portillo, Israel

2017-01-01

Currently at the Beam Energy Scan at RHIC experimental efforts are being made to find the QCD critical point. On the theoretical side, the behavior of higher-order susceptibilities of the net-baryon charge from Lattice QCD at µ B = 0 may allow us to estimate the position of the critical point in the QCD phase diagram. However, even if the series expansion continues to higher-orders, there is always the possibility to miss the critical point behavior due to truncation errors. An alternative approach is to use a black hole engineered holographic model, which displays a critical point at large densities and matches lattice susceptibilities at µB = 0. Using the thermodynamic data from this black hole model, we obtain the freeze-out points extracted from the net-protons distribution measured at STAR and explore higher order fluctuations at the lowest energies at the beam energy scan to investigate signatures of the critical point. (paper)

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.

Observation of unusual critical region behavior in the magnetic susceptibility of EuSe

Science.gov (United States)

Bykovetz, N.; Klein, J.; Lin, C. L.

2018-05-01

The Europium Chalcogenides (EuCh: EuO, EuS, EuSe, and EuTe) have been regarded as model examples of simple, cubic, Heisenberg exchange coupled magnetic systems, with a ferromagnetic nearest-neighbor exchange constant J1 and an antiferromagnetic next-nearest-neighbor constant J2. Unlike the other EuCh, EuSe exhibits a range of complex magnetic behaviors, the latter being attributed to EuSe being near the point where J2=-J1, where its magnetism appears to consist of nearly de-coupled 2D ferromagnetic sheets. Analysis of precision SQUID measurements of the magnetic susceptibility χ in EuSe showed that in the region from ˜Tc to ˜2Tc, a fit of the data to the critical equation χ = χ2Tc(T/Tc-1)-γ gives γ=2.0, an exponent not predicted by any current theory. Additionally, this fit predicts that Tc should be ˜0K. We tentatively interpret this by saying that in the paramagnetic region the system "thinks" EuSe should not order above T=0. Tc=0K is predicted by the Mermin-Wagner theorem (MW) for Heisenberg-coupled 2D magnetic systems, and we can show that when J2=-J1, MW can also be applied to the J1, J2 exchange model of the EuCh to give a rigorous Tc=0 prediction. Under 10 kbar applied pressure EuSe exhibits a different γ and fitted Tc. An additional, and rather strange, critical-region effect was discovered. The EuSe sample was found to exhibit a relaxation effect in a small range of temperatures, just above and just below the actual Tc of 4.7K, with time constants of up to 5 minutes. We cannot yet fully explain this observed macroscopic effect.

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

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

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.

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.

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.

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.

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 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.

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...

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

Landslide Susceptibility Statistical Methods: A Critical and Systematic Literature Review

Science.gov (United States)

Mihir, Monika; Malamud, Bruce; Rossi, Mauro; Reichenbach, Paola; Ardizzone, Francesca

2014-05-01

Landslide susceptibility assessment, the subject of this systematic review, is aimed at understanding the spatial probability of slope failures under a set of geomorphological and environmental conditions. It is estimated that about 375 landslides that occur globally each year are fatal, with around 4600 people killed per year. Past studies have brought out the increasing cost of landslide damages which primarily can be attributed to human occupation and increased human activities in the vulnerable environments. Many scientists, to evaluate and reduce landslide risk, have made an effort to efficiently map landslide susceptibility using different statistical methods. In this paper, we do a critical and systematic landslide susceptibility literature review, in terms of the different statistical methods used. For each of a broad set of studies reviewed we note: (i) study geography region and areal extent, (ii) landslide types, (iii) inventory type and temporal period covered, (iv) mapping technique (v) thematic variables used (vi) statistical models, (vii) assessment of model skill, (viii) uncertainty assessment methods, (ix) validation methods. We then pulled out broad trends within our review of landslide susceptibility, particularly regarding the statistical methods. We found that the most common statistical methods used in the study of landslide susceptibility include logistic regression, artificial neural network, discriminant analysis and weight of evidence. Although most of the studies we reviewed assessed the model skill, very few assessed model uncertainty. In terms of geographic extent, the largest number of landslide susceptibility zonations were in Turkey, Korea, Spain, Italy and Malaysia. However, there are also many landslides and fatalities in other localities, particularly India, China, Philippines, Nepal and Indonesia, Guatemala, and Pakistan, where there are much fewer landslide susceptibility studies available in the peer-review literature. This

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.

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.

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

Universal Postquench Prethermalization at a Quantum Critical Point

Science.gov (United States)

Gagel, Pia; Orth, Peter P.; Schmalian, Jörg

2014-11-01

We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive nonequilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are: (i) a power law rise of order and correlations after an initial collapse of the equilibrium state and (ii) a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.

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

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...

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.

Phase structure of the O(n) model on a random lattice for n > 2

DEFF Research Database (Denmark)

Durhuus, B.; Kristjansen, C.

1997-01-01

We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with diverging string susceptibility, then either γ = +1....../2 or there exists a dual critical point with negative string susceptibility exponent, γ̃, related to γ by γ = γ̃/γ̃-1. Exploiting the exact solution of the O(n) model on a random lattice we show that both situations are realized for n > 2 and that the possible dual pairs of string susceptibility exponents are given...... by (γ̃, γ) = (-1/m, 1/m+1), m = 2, 3, . . . We also show that at the critical points with positive string susceptibility exponent the average number of loops on the surface diverges while the average length of a single loop stays finite....

Analysis of critical state response in thin films by AC susceptibility measurements

Czech Academy of Sciences Publication Activity Database

Youssef, A.; Švindrych, Z.; Hadač, J.; Janů, Zdeněk

2008-01-01

Roč. 18, č. 2 (2008), s. 1589-1592 ISSN 1051-8223 R&D Projects: GA ČR GA102/05/0942 Institutional research plan: CEZ:AV0Z10100520 Keywords : AC susceptibility * critical state * harmonics * thin film * axial magnetic-field * superconductor disks * cylinders Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 0.919, year: 2008

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

Interplay of quantum and classical fluctuations near quantum critical points

International Nuclear Information System (INIS)

Continentino, Mucio Amado

2011-01-01

For a system near a quantum critical point (QCP), above its lower critical dimension d L , there is in general a critical line of second-order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, d eff = d + z (d is the Euclidean dimension of the system and z the dynamic quantum critical exponent) is above its upper critical dimension d c there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation ψ = νz between the shift exponent ψ of the critical line and the crossover exponent νz, for d + z > d c by a dangerous irrelevant interaction. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP. (author)

Universal post-quench prethermalization at a quantum critical point

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 current density measurement of thin films by AC susceptibility based on the penetration parameter h

DEFF Research Database (Denmark)

Li, Xiao-Fen; Grivel, Jean-Claude; Abrahamsen, Asger B.

2012-01-01

We have numerically proved that the dependence of AC susceptibility χ of a E(J) power law superconducting thin disc on many parameters can be reduced to one penetration parameter h, with E the electric field and J the current density. Based on this result, we propose a way of measuring the critical...... current density Jc of superconducting thin films by AC susceptibility. Compared with the normally used method based on the peak of the imaginary part, our method uses a much larger range of the AC susceptibility curve, thus allowing determination of the temperature (T) dependence of Jc from a normally...

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.

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.

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

On the critical behavior of the inverse susceptibility of a model of structural phase transitions

International Nuclear Information System (INIS)

Pisanova, E.S.; Ivanov, S.I.

2013-01-01

An exactly solvable lattice model describing structural phase transitions in an anharmonic crystal with long-range interaction is considered in the neighborhoods of the quantum and classical critical points at the corresponding upper critical dimensions. In a broader neighborhood of the critical region the inverse susceptibility of the model is exactly calculated in terms of the Lambert W-function and graphically presented as a function of the deviation from the critical point and the upper critical dimension. For quantum and classical systems with real physical dimensions (chains, thin layers and three-dimensional systems) the exact results are compared with the asymptotic ones on the basis of some numerical data for their ratio. Relative errors are also provided

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.

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

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

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.

Critical behavior in a stochastic model of vector mediated epidemics

Science.gov (United States)

Alfinito, E.; Beccaria, M.; Macorini, G.

2016-06-01

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

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.

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

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)

Monte Carlo study of the critical behavior and magnetic properties of La{sub 2/3}Ca{sub 1/3}MnO{sub 3} thin films

Energy Technology Data Exchange (ETDEWEB)

Restrepo-Parra, E., E-mail: erestrepopa@unal.edu.c [Departamento de Fisica y Quimica, Universidad Nacional de Colombia-Sede Manizales, A.A. 127 Manizales (Colombia); Bedoya-Hincapie, C.M.; Jurado, F.J.; Riano-Rojas, J.C. [Departamento de Fisica y Quimica, Universidad Nacional de Colombia-Sede Manizales, A.A. 127 Manizales (Colombia); Restrepo, J. [Grupo de Magnetismo y Simulacion G, Instituto de Fisica, Universidad de Antioquia, A.A. 1226 Medellin (Colombia)

2010-11-15

Critical exponents offer important information concerning the interaction mechanisms near the paramagnetic to ferromagnetic transition. In this work a Monte Carlo-Metropolis simulation of the critical behavior in La{sub 2/3}Ca{sub 1/3}MnO{sub 3} thin films is addressed. Canonical ensemble averages for magnetization per site, magnetic susceptibility and specific heat of stoichiometric manganite within a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions are computed. The La{sub 2/3}Ca{sub 1/3}MnO{sub 3} thin films were simulated addressing the thickness influence and thermal dependence. In the model, Mn magnetic ions are distributed on a simple cubic lattice according to the perovskite structure of this manganite. Ferromagnetic coupling for the bonds Mn{sup 3+}-Mn{sup 3+}(e{sub g}-e{sub g}'), Mn{sup 3+}-Mn{sup 4+}(e{sub g}-d{sup 3}) and Mn{sup 3+}-Mn{sup 4+}(e{sub g}'-d{sup 3}) were taken into account. On the basis of finite-size scaling theory, our best estimates of critical exponents, linked to the ferromagnetic to paramagnetic transition, for the correlation length, specific heat, magnetization and susceptibility are, respectively: v=0.56{+-}0.01, {alpha}=0.16{+-}0.03, {beta}=0.34{+-}0.04{gamma} and {gamma}=1.17{+-}0.05. These theoretical results are consistent with the Rushbrooke equalitiy {alpha}+2{beta}+{gamma}=2.

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.

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.

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.

Susceptibility of forests in the northeastern USA to nitrogen and sulfur deposition: critical load exceedance and forest health

Science.gov (United States)

N. Duarte; L.H. Pardo; M.J. Robin-Abbott

2013-01-01

The objectives of this study were to assess susceptibility to acidification and nitrogen (N) saturation caused by atmospheric deposition to northeastern US forests, evaluate the benefits and shortcomings of making critical load assessments using regional data, and assess the relationship between expected risk (exceedance) and forest health. We calculated the critical...

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

Fidelity susceptibility as holographic PV-criticality

Energy Technology Data Exchange (ETDEWEB)

Momeni, Davood, E-mail: davoodmomeni78@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Faizal, Mir, E-mail: mirfaizalmir@googlemail.com [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta T1K 3M4 (Canada); Irving K. Barber School of Arts and Sciences, University of British Columbia – Okanagan, 3333 University Way, Kelowna, British Columbia V1V 1V7 (Canada); Myrzakulov, Kairat, E-mail: kairatmyrzakul@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Myrzakulov, Ratbay, E-mail: rmyrzakulov@gmail.com [Eurasian International Center for Theoretical Physics and Department of General & Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan)

2017-02-10

It is well known that entropy can be used to holographically establish a connection among geometry, thermodynamics and information theory. In this paper, we will use complexity to holographically establish a connection among geometry, thermodynamics and information theory. Thus, we will analyze the relation among holographic complexity, fidelity susceptibility, and thermodynamics in extended phase space. We will demonstrate that fidelity susceptibility (which is the informational complexity dual to a maximum volume in AdS) can be related to the thermodynamical volume (which is conjugate to the cosmological constant in the extended thermodynamic phase space). Thus, this letter establishes a relation among geometry, thermodynamics, and information theory, using complexity.

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

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.

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)

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

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).

Experimental mathematics on the magnetic susceptibility of the square lattice Ising model

Energy Technology Data Exchange (ETDEWEB)

Boukraa, S [LPTHIRM and Departement d' Aeronautique, Universite de Blida (Algeria); Guttmann, A J; Jensen, I [ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, University of Melbourne, Victoria 3010 (Australia); Hassani, S; Zenine, N [Centre de Recherche Nucleaire d' Alger, 2 Bd. Frantz Fanon, BP 399, 16000 Alger (Algeria); Maillard, J-M [LPTMC, Universite de Paris, Tour 24, 4eme etage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05 (France); Nickel, B [Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)], E-mail: boukraa@mail.univ-blida.dz, E-mail: tonyg@ms.unimelb.edu.au, E-mail: I.Jensen@ms.unimelb.edu.au, E-mail: maillard@lptmc.jussieu.fr, E-mail: maillard@lptl.jussieu.fr, E-mail: njzenine@yahoo.com

2008-11-14

We calculate very long low- and high-temperature series for the susceptibility {chi} of the square lattice Ising model as well as very long series for the five-particle contribution {chi}{sup (5)} and six-particle contribution {chi}{sup (6)}. These calculations have been made possible by the use of highly optimized polynomial time modular algorithms and a total of more than 150 000 CPU hours on computer clusters. The series for {chi} (low- and high-temperature regimes), {chi}{sup (5)} and {chi}{sup (6)} are now extended to 2000 terms. In addition, for {chi}{sup (5)}, 10 000 terms of the series are calculated modulo a single prime, and have been used to find the linear ODE satisfied by {chi}{sup (5)} modulo a prime. A diff-Pade analysis of the 2000 terms series for {chi}{sup (5)} and {chi}{sup (6)} confirms to a very high degree of confidence previous conjectures about the location and strength of the singularities of the n-particle components of the susceptibility, up to a small set of 'additional' singularities. The exponents at all the singularities of the Fuchsian linear ODE of {chi}{sup (5)} and the (as yet unknown) ODE of {chi}{sup (6)} are given: they are all rational numbers. We find the presence of singularities at w = 1/2 for the linear ODE of {chi}{sup (5)}, and w{sup 2} = 1/8 for the ODE of {chi}{sup (6)}, which are not singularities of the 'physical' {chi}{sup (5)} and {chi}{sup (6)}, that is to say the series solutions of the ODE's which are analytic at w = 0. Furthermore, analysis of the long series for {chi}{sup (5)} (and {chi}{sup (6)}) combined with the corresponding long series for the full susceptibility {chi} yields previously conjectured singularities in some {chi}{sup (n)}, n {>=} 7. The exponents at all these singularities are also seen to be rational numbers. We also present a mechanism of resummation of the logarithmic singularities of the {chi}{sup (n)} leading to the known power-law critical behaviour occurring in

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.

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.

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

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.

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.

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)

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

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)

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)

Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling.

Science.gov (United States)

Nishikawa, Yoshihiko; Michel, Manon; Krauth, Werner; Hukushima, Koji

2015-12-01

We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.

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

A-site deficiency effects on the critical behavior of La0.6Ca0.15·0.05Ba0.2MnO3

Science.gov (United States)

Debbebi, I. Sfifir; Omrani, H.; Cheikhrouhou-Koubaa, W.; Cheikhrouhou, A.

2018-02-01

The aim of the present work is to study the critical behavior of calcium deficient La0.6Ca0.15·0.05Ba0.2MnO3 (LCBMO), synthetized by the conventional solid-state reaction method, around the paramagnetic (PM)-ferromagnetic (FM) phase transition. X-ray diffraction revealed that these manganites crystallized in the orthorhombic structure with Pbnm space group. Then, the magnetic properties of this compound are discussed in detail, building on the magnetization and the susceptibility. The temperature dependence of magnetic susceptibility at higher temperature confirms the presence of the Griffiths phase above the Curie temperature which proves the existence of ferromagnetic clusters in the paramagnetic domain. Experimental results revealed that our sample exhibit a second-order magnetic phase transition. The estimated critical exponents derived from the magnetic data were estimated using various techniques such as modified Arrott plot, Kouvel-Fisher method, and critical magnetization isotherms M(TC, H). The obtained values are very close to those representative of the mean-field model (β = 0.547, γ = 1.23, and δ = 3.092 at an average TC = 201.74 K).

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

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.

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.

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.

Electron spin resonance and quantum critical phenomena in VOx multiwall nanotubes

International Nuclear Information System (INIS)

Demishev, S.V.; Chernobrovkin, A.L.; Glushkov, V.V.; Samarin, N.A.; Sluchanko, N.E.; Semeno, A.V.; Goodilin, E.A.; Grigorieva, A.V.; Tretyakov, Yu.D.

2008-01-01

Basing on the high frequency (60 GHz) electron spin resonance study of the VO x multiwall nanotubes (VO x -NTs) carried out in the temperature range 4.2-200 K we report: (i) the first direct experimental evidence of the presence of the antiferromagnetic dimers in VO x -NTs and (ii) the observation of an anomalous low temperature growth of the magnetic susceptibility for quasi-free spins, which obey the power law χ(T)∝1/T α with the exponent α∼0.6 in a wide temperature range 4.2-50 K. We argue that the observed departures from the Curie-Weiss behaviour manifest the onset of the quantum critical regime and formation of the Griffiths phase as a magnetic ground state of these spin species. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

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

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.

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 ...

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.

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.

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)

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.

Study of critical current density from ac susceptibility measurements in (La1-xYx)2Ba2CaCu5O2 superconductors

International Nuclear Information System (INIS)

Nayak, P.K.; Ravi, S. . sravi@iitg.ernet.in

2008-01-01

We have prepared a series of compounds (La 1-x Y x ) 2 Ba 2 CaCu 5 O 2 for x = 0 to 0.5 by adding a CaCuO 2 layer to the parent compound La 2 Ba 2 Cu 4 O 2 and by doping Y in place of La. These materials are also prepared by adding 5 wt% of Ag to enhance the intergranular coupling and critical current density. X-ray diffraction measurements show that all the samples are essentially in single phase form and the patterns could be refined using P4/mmm space group in tetragonal cell. The typical lattice parameters are found to be a = b 3.856 A, c = 11.576 A for x = 0.5 sample. Temperature variations of dc electrical resistivity measured on the above samples show that they exhibit superconductivity with T c ranging from 60 to 75 K. Temperature and ac field amplitude variation of ac susceptibility have been measured on the above samples. The field variation of ac susceptibility data has been analyzed by using Bean critical state model. Using both temperature and field variations of ac susceptibility data, the material dependent parameters, such as critical current density as a function of temperature and effective volume fraction grains have been estimated. The Ag doped samples show relatively large critical current density compared to pure samples due to improved intergranular coupling. (author)

Influence of Factor V Leiden on susceptibility to and outcome from critical illness: a genetic association study

DEFF Research Database (Denmark)

Benfield, Thomas; Ejrnæs, Karen; Juul, Klaus

2010-01-01

ABSTRACT: INTRODUCTION: Disturbance of the pro-coagulatant and anti-coagulant balance is associated with a poor outcome from critical illness. The objective of this study is to determine whether the Factor V Leiden (FVL) mutation is associated with susceptibility to or death from critical illness....... METHODS: A genetic association study involving four case cohorts comprising two Gram negative sepsis, one invasive pneumococcal disease and one intensive care unit cohort with a total of 1,249 patients. Controls were derived from a population-based cohort study (N = 8,147). DNA from patients and controls...... not appear to increase the risk of admission due to severe invasive infections. Nevertheless, in the subgroup of patients admitted to intensive care an increased risk and a poorer long-term outcome for individuals with critical illness were observed for FVL mutation carriers....

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

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 ...

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

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.

Rigorous control of logarithmic corrections in four-dimensional phi4 spin systems. II. Critical behavior of susceptibility and correlation length

International Nuclear Information System (INIS)

Hara, T.; Tasaki, H.

1987-01-01

Continuing the analysis started in Part I of this work, they investigate critical phenomena in weakly coupled phi 4 spin systems in four dimensions. Concerning the critical behavior of the susceptibility and the correlation length (in the high-temperature phase), the existence of logarithmic corrections to their mean field type behavior is rigorously shown (i.e., they prove chi(t) ∼ t -1 absolute value 1n t/sup 1/3/, zeta(t) ∼ t/sup -1/2/ absolute value of ln t/sup 1/6/)

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)

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

Asymmetric fluid criticality. II. Finite-size scaling for simulations.

Science.gov (United States)

Kim, Young C; Fisher, Michael E

2003-10-01

The vapor-liquid critical behavior of intrinsically asymmetric fluids is studied in finite systems of linear dimensions L focusing on periodic boundary conditions, as appropriate for simulations. The recently propounded "complete" thermodynamic (L--> infinity) scaling theory incorporating pressure mixing in the scaling fields as well as corrections to scaling [Phys. Rev. E 67, 061506 (2003)] is extended to finite L, initially in a grand canonical representation. The theory allows for a Yang-Yang anomaly in which, when L--> infinity, the second temperature derivative (d2musigma/dT2) of the chemical potential along the phase boundary musigmaT diverges when T-->Tc-. The finite-size behavior of various special critical loci in the temperature-density or (T,rho) plane, in particular, the k-inflection susceptibility loci and the Q-maximal loci--derived from QL(T,L) is identical with 2L/L where m is identical with rho-L--is carefully elucidated and shown to be of value in estimating Tc and rhoc. Concrete illustrations are presented for the hard-core square-well fluid and for the restricted primitive model electrolyte including an estimate of the correlation exponent nu that confirms Ising-type character. The treatment is extended to the canonical representation where further complications appear.

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.

Critical behavior of ferromagnetic La0.7Sr0.3CoO3 thin films

International Nuclear Information System (INIS)

Schwarz, T.

2007-07-01

The present thesis concentrates on the critical behavior of ferromagnetic La 0.7 Sr 0.3 CoO 3 thin films (LSCO) close to the magnetic phase transition. The LSCO thin films were prepared by pulsed laser deposition and optimized with respect to their structural and magnetic properties. For the characterization of the structural and magnetic characteristics various methods were used. By means of X-ray diffraction and electron microscopy the crystallinity and microstructure of the epitaxial films were examined, respectively. The analysis of the chemical composition was accomplished by Rutherford backscattering and energy dispersive X-ray diffraction (EDX). Parallel to the investigations of the LSCO films a low-temperature measuring system for electrical measurements in magnetic fields up to 8 T in a temperature range from 1.5 K to 300 K was developed and built up including the necessary control and measuring software. The central point of this work was dedicated to the characterization of the magnetic characteristics of the LSCO films. In comparison, single crystals and polycrystalline bulk samples were also available. At these samples temperature-dependent and isothermal magnetization measurements were accomplished by a SQUID magnetometer. To determine the critical behavior of the samples the critical exponents of the susceptibility and the spontaneous magnetization in the proximity of the ferromagnetic phase transition were determined. For the exact determination of the critical exponents from the experimental data an evaluation routine in Matlab on basis of the Arrott representation method was used. In addition to the investigations of the critical behavior, electrical transportation measurements and neutron reflection measurements with spin-polarized neutrons were performed. The investigations of this work show that, in contrast to the critical behavior of single-crystal LSCO volume samples where a three-dimensional Heisenberg behavior could be observed, the

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.

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)

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.

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...

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.

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.

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.

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.

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

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.

Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter

Science.gov (United States)

Klein, Avraham; Lederer, Samuel; Chowdhury, Debanjan; Berg, Erez; Chubukov, Andrey

2018-04-01

We study the dynamic response of a two-dimensional system of itinerant fermions in the vicinity of a uniform (Q =0 ) Ising nematic quantum critical point of d - wave symmetry. The nematic order parameter is not a conserved quantity, and this permits a nonzero value of the fermionic polarization in the d - wave channel even for vanishing momentum and finite frequency: Π (q =0 ,Ωm)≠0 . For weak coupling between the fermions and the nematic order parameter (i.e., the coupling is small compared to the Fermi energy), we perturbatively compute Π (q =0 ,Ωm)≠0 over a parametrically broad range of frequencies where the fermionic self-energy Σ (ω ) is irrelevant, and use Eliashberg theory to compute Π (q =0 ,Ωm) in the non-Fermi-liquid regime at smaller frequencies, where Σ (ω )>ω . We find that Π (q =0 ,Ω ) is a constant, plus a frequency-dependent correction that goes as |Ω | at high frequencies, crossing over to |Ω| 1 /3 at lower frequencies. The |Ω| 1 /3 scaling holds also in a non-Fermi-liquid regime. The nonvanishing of Π (q =0 ,Ω ) gives rise to additional structure in the imaginary part of the nematic susceptibility χ″(q ,Ω ) at Ω >vFq , in marked contrast to the behavior of the susceptibility for a conserved order parameter. This additional structure may be detected in Raman scattering experiments in the d - wave geometry.

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.

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

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.

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.

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.

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)

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.

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)

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.)

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.

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

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.

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.

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.

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.

The critical properties of magnetic films

International Nuclear Information System (INIS)

Saber, M.; Ainane, A.; Essaoudi, I.; Miguel, J.J. de

2010-01-01

Within the framework of the transverse spin-1/2 Ising model and by using the effective field theory with a probability distribution technique that accounts for the self spin correlations, we have studied the critical properties of an L-layer film of simple cubic symmetry in which the exchanges strength are assumed to be different from the bulk values in N S surface layers. We derive and illustrate the expressions for the phase diagrams, order parameter profiles and susceptibility. In such films, the critical temperature can shift to either lower or higher temperature compared with the corresponding bulk value. We calculate also some magnetic properties of the film, such as the layer magnetizations, their averages and their profiles and the longitudinal susceptibility of the film. The film longitudinal susceptibility still diverges at the film critical temperature as does the bulk longitudinal susceptibility.

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

Magnetic properties of mixed Ni–Cu ferrites calculated using mean field approach

Energy Technology Data Exchange (ETDEWEB)

Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63, 46000 Safi (Morocco); LMPHE, URAC 12, Faculté des Sciences, Université Mohamed V-Agdal, Rabat (Morocco); Hamedoun, M. [Institute for Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE, URAC 12, Faculté des Sciences, Université Mohamed V-Agdal, Rabat (Morocco); Institute for Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Academie Hassan II des Sciences et Techniques, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France)

2014-08-01

The magnetic properties of spinel ferrites [Fe{sub 1−(1−x)y}{sup 3+}Cu{sub (1−x)y}{sup 2+}]{sub A}[Ni{sub x}{sup 2+}Cu{sub (1−x)(1−y)}{sup 2+}Fe{sub 1+(1−x)y}{sup 3+}]{sub B}O{sub 4} have been studied by the mean field theory (MFT) and high temperature series expansions (HTSEs) combined with the Padé approximants. The critical temperature, the saturation magnetisation (M{sub S}) and the intra-sublattice exchanges interactions (J{sub AA}(x,y), J{sub BB}(x,y) and J{sub AB}(x,y)) are obtained by using a probability distribution law. The critical exponents associate with the magnetic susceptibility have been obtained. The effect of copper doping on the magnetic properties of nickel ferrites has been examined. - Highlights: • The exchange and constants interactions of CuFe{sub 2}O{sub 4} material are obtained. • The saturation magnetisation, the critical temperature, the Curie Weiss temperature and the Curie constant of CuFe{sub 2}O{sub 4} are obtained. • The critical exponent associated with the magnetic susceptibility is given.

Interventions on Metabolism: Making Antibiotic-Susceptible Bacteria

Directory of Open Access Journals (Sweden)

Fernando Baquero

2017-11-01

Full Text Available Antibiotics act on bacterial metabolism, and antibiotic resistance involves changes in this metabolism. Interventions on metabolism with drugs might therefore modify drug susceptibility and drug resistance. In their recent article, Martin Vestergaard et al. (mBio 8:e01114-17, 2017, https://doi.org/10.1128/mBio.01114-17 illustrate the possibility of converting intrinsically resistant bacteria into susceptible ones. They reported that inhibition of a central metabolic enzyme, ATP synthase, allows otherwise ineffective polymyxin antibiotics to act on Staphylococcus aureus. The study of the intrinsic resistome of bacterial pathogens has shown that several metabolic genes, including multigene transcriptional regulators, contribute to antibiotic resistance. In some cases, these genes only marginally increase antibiotic resistance, but reduced levels of susceptibility might be critical in the evolution or resistance under low antibiotic concentrations or in the clinical response of highly resistant bacteria. Drug interventions on bacterial metabolism might constitute a critical adjuvant therapy in combination with antibiotics to ensure susceptibility of pathogens with intrinsic or acquired antimicrobial resistance.

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.

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

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.

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

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.)

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

Exact results on the one-dimensional Potts lattice gas

International Nuclear Information System (INIS)

Riera, R.; Chaves, C.M.G.F.

1982-12-01

An exact calculation of the Potts Lattice Gas in one dimension is presented. Close to T=O 0 K, the uniform susceptibility presents an essencial singularity, when the excharge parameter is positive, and a power law behaviour with critical exponent γ=1, when this parameter is negative. (Author) [pt

Exact results on the one-dimensional Potts lattice gas

International Nuclear Information System (INIS)

Riera, R.; Chaves, C.M.G.F.

1983-01-01

An exact calculation of the Potts Lattice Gas in one dimension is presented. Close to T=O 0 K, the uniform susceptibility presents an essential singularity, when the exchange parameter is positive, and a power law behaviour with critical exponent γ=1, when this parameter is negative. (Author) [pt

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

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.

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

Magnetic properties of magnetic Co1-xMgxFe2O4 spinel by HTSE method

International Nuclear Information System (INIS)

Hamedoun, M.; Benyoussef, A.; Bousmina, M.

2011-01-01

Magnetic properties and exchange-coupling interactions of diluted magnetic spinels A 1-x A' x B 2 X 4 , where A and B are magnetic ions, namely Co 1-x Mg x Fe 2 O 4 , were investigated using the high-temperature series expansion method (HTSE) and the distribution method of magnetic cations in the range 0≤x≤1. The magnetic phase diagram and transition temperature versus dilution x were determined using the Pade approximants method along with HTSE. The critical exponent associated with the magnetic susceptibility γ was then deduced. The obtained results are in good agreement with experimental results and critical exponent values are consistent with those suggested by the universality hypothesis.

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.

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.

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.

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...

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.

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.

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.

Static quadrupolar susceptibility for a Blume–Emery–Griffiths model based on the mean-field approximation

Energy Technology Data Exchange (ETDEWEB)

Pawlak, A., E-mail: pawlak@amu.edu.pl [Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61–614 Poznań (Poland); Gülpınar, G. [Department of Physics, Dokuz Eylül University, 35160 İzmir (Turkey); Erdem, R. [Department of Physics, Akdeniz University, 07058 Antalya (Turkey); Ağartıoğlu, M. [Institute of Science, Dokuz Eylül University, 35160 İzmir (Turkey)

2015-12-01

The expressions for the dipolar and quadrupolar susceptibilities are obtained within the mean-field approximation in the Blume–Emery–Griffiths model. Temperature as well as crystal field dependences of the susceptibilities are investigated for two different phase diagram topologies which take place for K/J=3 and K/J=5.0.Their behavior near the second and first order transition points as well as multi-critical points such as tricritical, triple and critical endpoint is presented. It is found that in addition to the jumps connected with the phase transitions there are broad peaks in the quadrupolar susceptibility. It is indicated that these broad peaks lie on a prolongation of the first-order line from a triple point to a critical point ending the line of first-order transitions between two distinct paramagnetic phases. It is argued that the broad peaks are a reminiscence of very strong quadrupolar fluctuations at the critical point. The results reveal the fact that near ferromagnetic–paramagnetic phase transitions the quadrupolar susceptibility generally shows a jump whereas near the phase transition between two distinct paramagnetic phases it is an edge-like. - Highlights: • MFA calculation of the quadrupolar and dipolar susceptibility in BEG model is given • The crystal-field variation of susceptibilities near the multi-critical points is examined • There are broad peaks in the quadrupolar susceptibility in the vicinity of CP • These maxima are remembrances of the very strong quadrupolar Fluctuations.

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.

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.

On the entropy of random surfaces with arbitrary genus

International Nuclear Information System (INIS)

Kostov, I.K.; Krzywicki, A.

1987-01-01

We calculate the susceptibility critical exponent γ for Polyakov random surfaces with arbitrary genus, using the Liouville theory to one-loop order. Some rigorous results obtained for special dimensionalities in a discrete version of the model are also noted. In all cases γ grows linearly with the genus of the surface. (orig.)

Temporal percolation of the susceptible network in an epidemic spreading.

Science.gov (United States)

Valdez, Lucas Daniel; Macri, Pablo Alejandro; Braunstein, Lidia Adriana

2012-01-01

In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity ΦS(t), namely, the probability that a given neighbor of a node is susceptible at time t, is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time t(c) above which the giant susceptible component is destroyed. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time t(c). Our theoretical results are confirmed by extensive simulations of the SIR process.

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.

Magnetic hysteresis and complex susceptibility as measures of ac losses in a multifilamentary NbTi superconductor

International Nuclear Information System (INIS)

Goldfarb, R.B.; Clark, A.F.

1985-01-01

Magnetization and ac susceptibility of a standard NbTi superconductor were measured as a function of longitudinal dc magnetic field. The ac-field-amplitude and frequency dependences of the complex susceptibility are examined. The magnetization is related to the susceptibility by means of a theoretical derivation based on the field dependence of the critical current density. Hysteresis losses, obtained directly from dc hysteresis loops and derived theoretically from ac susceptibility and critical current density, were in reasonable agreement

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.

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)

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.

Intrinsic and extrinsic geometry of random surfaces

International Nuclear Information System (INIS)

Jonsson, T.

1992-01-01

We prove that the extrinsic Hausdorff dimension is always greater than or equal to the intrinsic Hausdorff dimension in models of triangulated random surfaces with action which is quadratic in the separation of vertices. We furthermore derive a few naive scaling relations which relate the intrinsic Hausdorff dimension to other critical exponents. These relations suggest that the intrinsic Hausdorff dimension is infinite if the susceptibility does not diverge at the critical point. (orig.)

Finite-size scaling theory and quantum hamiltonian Field theory: the transverse Ising model

International Nuclear Information System (INIS)

Hamer, C.J.; Barber, M.N.

1979-01-01

Exact results for the mass gap, specific heat and susceptibility of the one-dimensional transverse Ising model on a finite lattice are generated by constructing a finite matrix representation of the Hamiltonian using strong-coupling eigenstates. The critical behaviour of the limiting infinite chain is analysed using finite-size scaling theory. In this way, excellent estimates (to within 1/2% accuracy) are found for the critical coupling and the exponents α, ν and γ

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.)

Investigating the Impact of Maternal Residential Mobility on Identifying Critical Windows of Susceptibility to Ambient Air Pollution During Pregnancy.

Science.gov (United States)

Warren, Joshua L; Son, Ji-Young; Pereira, Gavin; Leaderer, Brian P; Bell, Michelle L

2018-05-01

Identifying periods of increased vulnerability to air pollution during pregnancy with respect to the development of adverse birth outcomes can improve understanding of possible mechanisms of disease development and provide guidelines for protection of the child. Exposure to air pollution during pregnancy is typically based on the mother's residence at delivery, potentially resulting in exposure misclassification and biasing the estimation of critical windows of pregnancy. In this study, we determined the impact of maternal residential mobility during pregnancy on defining weekly exposure to particulate matter less than or equal to 10 μm in aerodynamic diameter (PM10) and estimating windows of susceptibility to term low birth weight. We utilized data sets from 4 Connecticut birth cohorts (1988-2008) that included information on all residential addresses between conception and delivery for each woman. We designed a simulation study to investigate the impact of increasing levels of mobility on identification of critical windows. Increased PM10 exposure during pregnancy weeks 16-18 was associated with an increased probability of term low birth weight. Ignoring residential mobility when defining weekly exposure had only a minor impact on the identification of critical windows for PM10 and term low birth weight in the data application and simulation study. Identification of critical pregnancy windows was robust to exposure misclassification caused by ignoring residential mobility in these Connecticut birth cohorts.

Diamagnetic susceptibility of a confined donor in inhomogeneous quantum dots

International Nuclear Information System (INIS)

Rahmani, K; Zorkani, I; Jorio, A

2011-01-01

The binding energy and diamagnetic susceptibility χ dia are estimated for a shallow donor confined to move in GaAs-GaAlAs inhomogeneous quantum dots. The calculation was performed within the effective mass approximation and using the variational method. The results show that the binding energy and the diamagnetic susceptibility χ dia depend strongly on the core radius and the shell radius. We have demonstrated that there is a critical value of the ratio of the inner radius to the outer radius which may be important for nanofabrication techniques. The binding energy E b shows a minimum for a critical value of this ratio depending on the value of the outer radius and shows a maximum when the donor is placed at the center of the spherical layer. The diamagnetic susceptibility is more sensitive to variations of the radius for a large spherical layer. The binding energy and diamagnetic susceptibility depend strongly on the donor position.

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].

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 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.

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.

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.

Structure, resistivity, critical field, specific-heat jump at Tc, Meissner effect, a.c. and d.c. Susceptibility of the high-temperature superconductor La2-xSrxCuO4

International Nuclear Information System (INIS)

Decroux, M.; Junod, A.; Bezinge, A.

1987-01-01

The temperature dependence of the resistivity, the magnetic properties and the specific heat were investigated on sintered samples of La 1.85 Sr 0.15 CuO 4 having zero resistance below 35 K. The crystal structure at 300K (tetragonal K 2 NiF 4 -type) was refined from X-ray powder diffraction data. The d.c. susceptibility shows no indication for the existence of localized Cu 2+ moments. The observation of a 60% Meissner effect and a smeared jump at T c in the specific-heat curve prove the intrinsic character of this superconducting state. The amplitude of this jump is compatible with the DOS estimated from the Pauli susceptibility. With a critical magnetic field slope dH c2 /dT| Tc = - 2.5 T/K, the orbital critical field is expected to be of the order of 64 T

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.)

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

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.

Critical behavior of the magnetic susceptibility of the uniaxial ferromagnet LiHoF4

DEFF Research Database (Denmark)

Beauvillain, P.; Renard, J. P.; Laursen, Ib

1978-01-01

The magnetic susceptibility of two LiHoF4 single crystals has been measured in the range 1.2-4.2 K. Ferromagnetic order occurs at Tc=1.527 K. Above 2.5 K, the susceptibilities parallel and perpendicular to the fourfold c axis are well interpreted by the molecular-field approximation, taking...

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.

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

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

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

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.

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.

Discussion of Various Susceptibilities within Thermal and Dense Quantum Chromodynamics

International Nuclear Information System (INIS)

Xu Shu-Sheng; Shi Yuan-Mei; Yang You-Chang; Cui Zhu-Fang; Zong Hong-Shi

2015-01-01

It is commonly accepted that the system undergoes a crossover at high temperature and low chemical potential beyond the chiral limit case, and the properties of the crossover region are important for researchers to understand the nature of strong interacting matters of quantum chromodynamics (QCD). Since at present there is no exact order of parameters of the phase transitions beyond the chiral limit, QCD susceptibilities are widely used as indicators. In this work various susceptibilities are discussed in the framework of Dyson–Schwinger equations. The results show that different kinds of susceptibilities give the same critical end point, which is the bifurcation point of the crossover region and the first order phase transition line of QCD. Nevertheless, different pseudocritical points are found in the temperature axis. We think that defining a critical band is more suitable in the crossover region. (paper)

Magnetic susceptibilities of integrable quantum ladders

International Nuclear Information System (INIS)

Park, Soo A; Lee, K.

2001-01-01

As an extension of previous studies, we consider the magnetic susceptibilities of a coupled spin chain model at low temperature and of a more realistic model at low temperature and of a more realistic model having a t-J ladder structure at zero temperature. The magnetic susceptibilities for both models are obtained numerically when the coupling constant is greater than its critical value. In this region, the ladders behave as a single chain for H c and as two independent chains for H>H c , showing a divergence at H c . This divergence is expected to smear out at a finite temperature

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.

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.

Nanotoxicity overview: nano-threat to susceptible populations.

Science.gov (United States)

Li, Yang; Zhang, Yi; Yan, Bing

2014-02-28

Due to the increasing applications of nanomaterials and nanotechnology, potential danger of nanoparticle exposure has become a critical issue. However, recent nanotoxicity studies have mainly focused on the health risks to healthy adult population. The nanotoxicity effects on susceptible populations (such as pregnant, neonate, diseased, and aged populations) have been overlooked. Due to the alterations in physiological structures and functions in susceptible populations, they often suffer more damage from the same exposure. Thus, it is urgent to understand the effects of nanoparticle exposure on these populations. In order to fill this gap, the potential effects of nanoparticles to pregnant females, neonate, diseased, and aged population, as well as the possible underlying mechanisms are reviewed in this article. Investigations show that responses from susceptible population to nanoparticle exposure are often more severe. Reduced protection mechanism, compromised immunity, and impaired self-repair ability in these susceptible populations may contribute to the aggravated toxicity effects. This review will help minimize adverse effects of nanoparticles to susceptible population in future nanotechnology applications.

Nanotoxicity Overview: Nano-Threat to Susceptible Populations

Directory of Open Access Journals (Sweden)

Yang Li

2014-02-01

Full Text Available Due to the increasing applications of nanomaterials and nanotechnology, potential danger of nanoparticle exposure has become a critical issue. However, recent nanotoxicity studies have mainly focused on the health risks to healthy adult population. The nanotoxicity effects on susceptible populations (such as pregnant, neonate, diseased, and aged populations have been overlooked. Due to the alterations in physiological structures and functions in susceptible populations, they often suffer more damage from the same exposure. Thus, it is urgent to understand the effects of nanoparticle exposure on these populations. In order to fill this gap, the potential effects of nanoparticles to pregnant females, neonate, diseased, and aged population, as well as the possible underlying mechanisms are reviewed in this article. Investigations show that responses from susceptible population to nanoparticle exposure are often more severe. Reduced protection mechanism, compromised immunity, and impaired self-repair ability in these susceptible populations may contribute to the aggravated toxicity effects. This review will help minimize adverse effects of nanoparticles to susceptible population in future nanotechnology applications.

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.

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

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

Quantum–classical transition in the Caldeira–Leggett model

Energy Technology Data Exchange (ETDEWEB)

Kovács, J. [Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen (Hungary); Institute of Nuclear Research, P.O. Box 51, H-4001 Debrecen (Hungary); Fazekas, B. [Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen (Hungary); Nagy, S., E-mail: nagys@phys.unideb.hu [Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen (Hungary); Sailer, K. [Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen (Hungary)

2017-01-15

The quantum–classical transition in the Caldeira–Leggett model is investigated in the framework of the functional renormalization group method. It is shown that a divergent quadratic term arises in the action due to the heat bath in the model. By removing the divergence with a frequency cutoff we considered the critical behavior of the model. The critical exponents belonging to the susceptibility and the correlation length are determined and their independence of the frequency cutoff and the renormalization scheme is shown.

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)

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.

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.

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

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

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)

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.

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

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

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

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)

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.)

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

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

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

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

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)].

On the criticality of inferred models

Science.gov (United States)

Mastromatteo, Iacopo; Marsili, Matteo

2011-10-01

Advanced inference techniques allow one to reconstruct a pattern of interaction from high dimensional data sets, from probing simultaneously thousands of units of extended systems—such as cells, neural tissues and financial markets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to singular values of parameters, akin to critical points in physics where phase transitions occur. These are points where the response of physical systems to external perturbations, as measured by the susceptibility, is very large and diverges in the limit of infinite size. We show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher information) are directly related to the susceptibility of the inferred model. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. This region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time scales naturally yield models which are close to criticality.

On the criticality of inferred models

International Nuclear Information System (INIS)

Mastromatteo, Iacopo; Marsili, Matteo

2011-01-01

Advanced inference techniques allow one to reconstruct a pattern of interaction from high dimensional data sets, from probing simultaneously thousands of units of extended systems—such as cells, neural tissues and financial markets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models which are close to singular values of parameters, akin to critical points in physics where phase transitions occur. These are points where the response of physical systems to external perturbations, as measured by the susceptibility, is very large and diverges in the limit of infinite size. We show that the reparameterization invariant metrics in the space of probability distributions of these models (the Fisher information) are directly related to the susceptibility of the inferred model. As a result, distinguishable models tend to accumulate close to critical points, where the susceptibility diverges in infinite systems. This region is the one where the estimate of inferred parameters is most stable. In order to illustrate these points, we discuss inference of interacting point processes with application to financial data and show that sensible choices of observation time scales naturally yield models which are close to criticality

Epidemic spreading in annealed directed networks: susceptible-infected-susceptible model and contact process.

Science.gov (United States)

Kwon, Sungchul; Kim, Yup

2013-01-01

We investigate epidemic spreading in annealed directed scale-free networks with the in-degree (k) distribution P(in)(k)~k(-γ(in)) and the out-degree (ℓ) distribution, P(out)(ℓ)~ℓ(-γ(out)). The correlation of each node on the networks is controlled by the probability r(0≤r≤1) in two different algorithms, the so-called k and ℓ algorithms. For r=1, the k algorithm gives =, whereas the ℓ algorithm gives =. For r=0, = for both algorithms. As the prototype of epidemic spreading, the susceptible-infected-susceptible model and contact process on the networks are analyzed using the heterogeneous mean-field theory and Monte Carlo simulations. The directedness of links and the correlation of the network are found to play important roles in the spreading, so that critical behaviors of both models are distinct from those on undirected scale-free networks.

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.

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.

Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

Science.gov (United States)

Biswas, Sounak; Damle, Kedar

2018-02-01

A transverse magnetic field Γ is known to induce antiferromagnetic three-sublattice order of the Ising spins σz in the triangular lattice Ising antiferromagnet at low enough temperature. This low-temperature order is known to melt on heating in a two-step manner, with a power-law ordered intermediate temperature phase characterized by power-law correlations at the three-sublattice wave vector Q : ˜cos(Q .R ⃗) /|R⃗| η (T ) with the temperature-dependent power-law exponent η (T )∈(1 /9 ,1 /4 ) . Here, we use a quantum cluster algorithm to study the ferromagnetic easy-axis susceptibility χu(L ) of an L ×L sample in this power-law ordered phase. Our numerical results are consistent with a recent prediction of a singular L dependence χu(L ) ˜L2 -9 η when η (T ) is in the range (1 /9 ,2 /9 ) . This finite-size result implies, via standard scaling arguments, that the ferromagnetic susceptibility χu(B ) to a uniform field B along the easy axis is singular at intermediate temperatures in the small B limit, χu(B ) ˜|B| -4/-18 η 4 -9 η for η (T )∈(1 /9 ,2 /9 ) , although there is no ferromagnetic long-range order in the low temperature state. Additionally we establish similar two-step melting behavior (via a study of the order parameter susceptibility χQ) in the case of the ferrimagnetic three-sublattice ordered phase which is stabilized by ferromagnetic next-neighbor couplings (J2) and confirm that the ferromagnetic susceptibility obeys the predicted singular form in the associated power-law ordered phase.

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.

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.

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.

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.

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.

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.

Summing Feynman graphs by Monte Carlo: Planar φ3-theory and dynamically triangulated random surfaces

International Nuclear Information System (INIS)

Boulatov, D.V.

1988-01-01

New combinatorial identities are suggested relating the ratio of (n-1)th and nth orders of (planar) perturbation expansion for any quantity to some average over the ensemble of all planar graphs of the nth order. These identities are used for Monte Carlo calculation of critical exponents γ str (string susceptibility) in planar φ 3 -theory and in the dynamically triangulated random surface (DTRS) model near the convergence circle for various dimensions. In the solvable case D=1 the exact critical properties of the theory are reproduced numerically. (orig.)

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.

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.

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)

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.

Antiferromagnetic spintronics of Mn{sub 2}Au: An experiment, first principle, mean field and series expansions calculations study

Energy Technology Data Exchange (ETDEWEB)

Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000, Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Boutahar, A.; Lassri, H. [LPMMAT, Université Hassan II-Casablanca, Faculté des Sciences, BP 5366 Maârif (Morocco)

2015-11-01

The self-consistent ab initio calculations, based on DFT (Density Functional Theory) approach and using FLAPW (Full potential Linear Augmented Plane Wave) method, are performed to investigate both electronic and magnetic properties of the Mn{sub 2}Au. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn plans. Magnetic moment considered to lie along (110) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Mn–Mn in Mn{sub 2}Au are given by using the experiment results and the mean field theory. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility with the magnetic moments in Mn{sub 2}Au (m{sub Mn}) is given up to tenth order series in, 1/k{sub B}T. The Néel temperature T{sub N} is obtained by HTSEs combined with the Padé approximant method. The critical exponent associated with the magnetic susceptibility is deduced as well. - Highlights: • The both electronic and magnetic properties of the Mn{sub 2}Au are studied. • The exchange interactions between the magnetic atoms Mn–Mn in Mn{sub 2}Au are given. • The Néel temperature T{sub N} of Mn{sub 2}Au is obtained by HTSEs method. • The critical exponent associated with the magnetic susceptibility is deduced.

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

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.

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

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.

CISH and Susceptibility to Infectious Diseases

OpenAIRE

Khor, CC; Vannberg, FO; Chapman, SJ; Guo, H; Wong, SH; Walley, AJ; Vukcevic, D; Rautanen, A; Mills, TC; Chang, K-C; Kam, K-M; Crampin, AC; Ngwira, B; Leung, C-C; Tam, C-M

2010-01-01

BACKGROUND The interleukin-2-mediated immune response is critical for host defense against infectious pathogens. Cytokine-inducible SRC homology 2 (SH2) domain protein (CISH), a suppressor of cytokine signaling, controls interleukin-2 signaling. METHODS Using a case-control design, we tested for an association between CISH polymorphisms and susceptibility to major infectious diseases (bacteremia, tuberculosis, and severe malaria) in blood samples from 8402 persons in Gambia, Hong Kong, Kenya,...

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.

Adolescent Susceptibility to Peer Influence in Sexual Situations.

Science.gov (United States)

Widman, Laura; Choukas-Bradley, Sophia; Helms, Sarah W; Prinstein, Mitchell J

2016-03-01

One consistent predictor of adolescents' engagement in sexual risk behavior is their belief that peers are engaging in similar behavior; however, not all youth are equally susceptible to these peer influence effects. Understanding individual differences in susceptibility to peer influence is critical to identifying adolescents at risk for negative health outcomes. The purpose of this project was to identify predictors of susceptibility to peer influence using a novel performance-based measure of sexual risk taking. Participants were 300 early adolescents (Mage = 12.6 years; 53% female; 44% Caucasian) who completed (1) a pretest assessment of demographics, sexual attitudes, and hypothetical scenarios measuring the likelihood of engaging in sexual risk behavior and (2) a subsequent experimental procedure that simulated an Internet chat room in which youth believed that they were communicating with peers regarding these same hypothetical scenarios. In reality, these "peers" were computer-programmed e-confederates. Changes in responses to the sexual scenarios in the private pretest versus during the public chat room provided a performance-based measure of peer influence susceptibility. In total, 78% of youth provided more risky responses in the chat room than those in pretest. The most robust predictor of this change was gender, with boys significantly more susceptible to peer influence than girls. Significant interactions also were noted, with greater susceptibility among boys with later pubertal development and African-American boys. Results confirm that not all youth are equally susceptible to peer influence. Consistent with sexual script theory, boys evidence greater susceptibility to social pressure regarding sexual behavior than girls. Copyright © 2016 Society for Adolescent Health and Medicine. Published by Elsevier Inc. All rights reserved.

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.

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.

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.

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.)

Critical properties of Sudden Quench Dynamics in the anisotropic XY Model

OpenAIRE

Guo, Hongli; Liu, Zhao; Fan, Heng; Chen, Shu

2010-01-01

We study the zero temperature quantum dynamical critical behavior of the anisotropic XY chain under a sudden quench in a transverse field. We demonstrate theoretically that both quench magnetic susceptibility and two-particle quench correlation can be used to describe the dynamical quantum phase transition (QPT) properties. Either the quench magnetic susceptibility or the derivative of correlation functions as a function of initial magnetic field $a$ exhibits a divergence at the critical poin...

New measurement technique of ductility curve for ductility-dip cracking susceptibility in Alloy 690 welds

Energy Technology Data Exchange (ETDEWEB)

Kadoi, Kota, E-mail: kadoi@hiroshima-u.ac.jp [Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527 (Japan); Uegaki, Takanori; Shinozaki, Kenji; Yamamoto, Motomichi [Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527 (Japan)

2016-08-30

The coupling of a hot tensile test with a novel in situ observation technique using a high-speed camera was investigated as a high-accuracy quantitative evaluation method for ductility-dip cracking (DDC) susceptibility. Several types of Alloy 690 filler wire were tested in this study owing to its susceptibility to DDC. The developed test method was used to directly measure the critical strain for DDC and high temperature ductility curves with a gauge length of 0.5 mm. Minimum critical strains of 1.3%, 4.0%, and 3.9% were obtained for ERNiCrFe-7, ERNiCrFe-13, and ERNiCrFe-15, respectively. The DDC susceptibilities of ERNiCrFe-13 and ERNiCrFe-15 were nearly the same and quite low compared with that of ERNiCrFe-7. This was likely caused by the tortuosity of the grain boundaries arising from the niobium content of around 2.5% in the former samples. Besides, ERNiCrFe-13 and ERNiCrFe-15 indicated higher minimum critical strains even though these specimens include higher content of sulfur and phosphorus than ERNiCrFe-7. Thus, containing niobium must be more effective to improve the susceptibility compared to sulfur and phosphorous in the alloy system.

New measurement technique of ductility curve for ductility-dip cracking susceptibility in Alloy 690 welds

International Nuclear Information System (INIS)

Kadoi, Kota; Uegaki, Takanori; Shinozaki, Kenji; Yamamoto, Motomichi

2016-01-01

The coupling of a hot tensile test with a novel in situ observation technique using a high-speed camera was investigated as a high-accuracy quantitative evaluation method for ductility-dip cracking (DDC) susceptibility. Several types of Alloy 690 filler wire were tested in this study owing to its susceptibility to DDC. The developed test method was used to directly measure the critical strain for DDC and high temperature ductility curves with a gauge length of 0.5 mm. Minimum critical strains of 1.3%, 4.0%, and 3.9% were obtained for ERNiCrFe-7, ERNiCrFe-13, and ERNiCrFe-15, respectively. The DDC susceptibilities of ERNiCrFe-13 and ERNiCrFe-15 were nearly the same and quite low compared with that of ERNiCrFe-7. This was likely caused by the tortuosity of the grain boundaries arising from the niobium content of around 2.5% in the former samples. Besides, ERNiCrFe-13 and ERNiCrFe-15 indicated higher minimum critical strains even though these specimens include higher content of sulfur and phosphorus than ERNiCrFe-7. Thus, containing niobium must be more effective to improve the susceptibility compared to sulfur and phosphorous in the alloy system.

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)

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.

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.

Continuous phase transition and critical behaviors of 3D black hole with torsion

International Nuclear Information System (INIS)

Ma, Meng-Sen; Liu, Fang; Zhao, Ren

2014-01-01

We study the phase transition and the critical behavior of the BTZ black hole with torsion obtained in (1 + 2)-dimensional Poincaré gauge theory. According to Ehrenfest’s classification, when the parameters in the theory are arranged properly, the BTZ black hole with torsion may possess the second-order phase transition which is also a smaller mass/larger mass black hole phase transition. Nevertheless, the critical behavior is different from the one in the van der Waals liquid/gas system. We also calculated the critical exponents of the relevant thermodynamic quantities, which are the same as the ones obtained in the Hořava-Lifshitz black hole and the Born–Infeld black hole. (paper)

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

2018-04-01

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 Tc superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.

Critical slowing down and error analysis in lattice QCD simulations

Energy Technology Data Exchange (ETDEWEB)

Schaefer, Stefan [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Sommer, Rainer; Virotta, Francesco [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2010-09-15

We study the critical slowing down towards the continuum limit of lattice QCD simulations with Hybrid Monte Carlo type algorithms. In particular for the squared topological charge we find it to be very severe with an effective dynamical critical exponent of about 5 in pure gauge theory. We also consider Wilson loops which we can demonstrate to decouple from the modes which slow down the topological charge. Quenched observables are studied and a comparison to simulations of full QCD is made. In order to deal with the slow modes in the simulation, we propose a method to incorporate the information from slow observables into the error analysis of physical observables and arrive at safer error estimates. (orig.)

Critical slowing down and error analysis in lattice QCD simulations

International Nuclear Information System (INIS)

Schaefer, Stefan; Sommer, Rainer; Virotta, Francesco

2010-09-01

We study the critical slowing down towards the continuum limit of lattice QCD simulations with Hybrid Monte Carlo type algorithms. In particular for the squared topological charge we find it to be very severe with an effective dynamical critical exponent of about 5 in pure gauge theory. We also consider Wilson loops which we can demonstrate to decouple from the modes which slow down the topological charge. Quenched observables are studied and a comparison to simulations of full QCD is made. In order to deal with the slow modes in the simulation, we propose a method to incorporate the information from slow observables into the error analysis of physical observables and arrive at safer error estimates. (orig.)

Type II critical phenomena of neutron star collapse

International Nuclear Information System (INIS)

Noble, Scott C.; Choptuik, Matthew W.

2008-01-01

We investigate spherically symmetric, general relativistic systems of collapsing perfect fluid distributions. We consider neutron star models that are driven to collapse by the addition of an initially 'ingoing' velocity profile to the nominally static star solution. The neutron star models we use are Tolman-Oppenheimer-Volkoff solutions with an initially isentropic, gamma law equation of state. The initial values of (1) the amplitude of the velocity profile, and (2) the central density of the star, span a parameter space, and we focus only on that region that gives rise to type II critical behavior, wherein black holes of arbitrarily small mass can be formed. In contrast to previously published work, we find that--for a specific value of the adiabatic index (Γ=2)--the observed type II critical solution has approximately the same scaling exponent as that calculated for an ultrarelativistic fluid of the same index. Further, we find that the critical solution computed using the ideal-gas equations of state asymptotes to the ultrarelativistic critical solution.

Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data

Science.gov (United States)

Buonocore, R. J.; Aste, T.; Di Matteo, T.

2017-04-01

We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.

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.

Influence of hydrogen-ion concentration exponent on undrained shear behaviour of bentonites; Bentonaito no hihaisui sendan kyodo ni oyobosu suiso ion nodo shisu no eikyo

Energy Technology Data Exchange (ETDEWEB)

Kamei, T [Kiso Jiban Consultants Co. Ltd., Tokyo (Japan); Tokida, M [Nagano National College of Technology, Nagano (Japan)

1994-12-21

Because there is a report example that the yield stress of a landslide clay increases along with a decrease of a hydrogen-ion concentration exponent, it is thought that a shear strength of the landslide clay depends on the hydrogen-ion concentration exponent. Furthermore, when the soil stabilization method by lime is applied to the soft ground and high organic earth, it is pointed out that the hydrogen-ion concentration exponent will become one of the harmful factors. Accordingly, it is understood that revealing an influence of a hydrogen-ion concentration exponent affects on the characteristics of an earth is one of the important factors, to evaluate a strength, deformation and so forth of the viscous ground. In this study, in order to examine an influence of a hydrogen-ion concentration exponent affecting on an undrained shear behavior of the bentonites, for the artificially adjusted bentonite specimens with 5 kinds of different pH, the isotropic consolidated undrained triaxial compression tests were performed, and consequently an influence of pH affecting on the engineering characteristics of the bentonites was made clear quantitatively. 28 refs., 16 figs., 5 tabs.

Critical phenomena at a first-order phase transition in a lattice of glow lamps: Experimental findings and analogy to neural activity

Energy Technology Data Exchange (ETDEWEB)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: ludovico.minati@ifj.edu [Center for Mind/Brain Sciences, University of Trento, 38123 Mattarello (Italy); Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Kraków (Poland); Candia, Antonio de [Department of Physics “E. Pancini,” University of Naples “Federico II,” Napoli (Italy); INFN Gr. Coll. Salerno, Unità di Napoli, Napoli (Italy); Scarpetta, Silvia [INFN Gr. Coll. Salerno, Unità di Napoli, Napoli (Italy); Department of Physics “E.R.Caianiello,” University of Salerno, Napoli (Italy)

2016-07-15

Networks of non-linear electronic oscillators have shown potential as physical models of neural dynamics. However, two properties of brain activity, namely, criticality and metastability, remain under-investigated with this approach. Here, we present a simple circuit that exhibits both phenomena. The apparatus consists of a two-dimensional square lattice of capacitively coupled glow (neon) lamps. The dynamics of lamp breakdown (flash) events are controlled by a DC voltage globally connected to all nodes via fixed resistors. Depending on this parameter, two phases having distinct event rate and degree of spatiotemporal order are observed. The transition between them is hysteretic, thus a first-order one, and it is possible to enter a metastability region, wherein, approaching a spinodal point, critical phenomena emerge. Avalanches of events occur according to power-law distributions having exponents ≈3/2 for size and ≈2 for duration, and fractal structure is evident as power-law scaling of the Fano factor. These critical exponents overlap observations in biological neural networks; hence, this circuit may have value as building block to realize corresponding physical models.

Microscopic processes controlling the Herschel-Bulkley exponent

Science.gov (United States)

Lin, Jie; Wyart, Matthieu

2018-01-01

The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent n =1 /β . A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to β =2 in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to β =1 with logarithmic correction. This result supports that HL is not a suitable explanation for the value of β , which is instead significantly affected by finite-dimensional effects. From considerations on elastoplastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that β =1 +1 /(d -df) , where df is the fractal dimension of avalanches and d the spatial dimension. Measurements of df then supports that β ≈2.1 and β ≈1.7 in two and three dimensions, respectively. We discuss theoretical arguments leading to approximations of β in finite dimensions.

Metallic magnets without inversion symmetry and antiferromagnetic quantum critical points

Energy Technology Data Exchange (ETDEWEB)

Fischer, I.A.

2006-07-01

This thesis focusses on two classes of systems that exhibit non-Fermi liquid behaviour in experiments: we investigated aspects of chiral ferromagnets and of antiferromagnetic metals close to a quantum critical point. In chiral ferromagnets, the absence of inversion symmetry makes spin-orbit coupling possible, which leads to a helical modulation of the ferromagnetically ordered state. We studied the motion of electrons in the magnetically ordered state of a metal without inversion symmetry by calculating their generic band-structure. We found that spin-orbit coupling, although weak, has a profound effect on the shape of the Fermi surface: On a large portion of the Fermi surface the electron motion parallel to the helix practically stops. Signatures of this effect can be expected to show up in measurements of the anomalous Hall effect. Recent neutron scattering experiments uncovered the existence of a peculiar kind of partial order in a region of the phase diagram adjacent to the ordered state of the chiral ferromagnet MnSi. Starting from the premise that this partially ordered state is a thermodynamically distinct phase, we investigated an extended Ginzburg-Landau theory for chiral ferromagnets. In a certain parameter regime of the Ginzburg-Landau theory we identified crystalline phases that are reminiscent of the so-called blue phases in liquid crystals. Many antiferromagnetic heavy-fermion systems can be tuned into a regime where they exhibit non-Fermi liquid exponents in the temperature dependence of thermodynamic quantities such as the specific heat capacity; this behaviour could be due to a quantum critical point. If the quantum critical behaviour is field-induced, the external field does not only suppress antiferromagnetism but also induces spin precession and thereby influences the dynamics of the order parameter. We investigated the quantum critical behavior of clean antiferromagnetic metals subject to a static, spatially uniform external magnetic field. We

Critical behavior of the system of two crossing self-avoiding walks on a family of three-dimensional fractal lattices

International Nuclear Information System (INIS)

Zivic, I.; Elezovic-Hadzic, S.; Milosevic, S.

2009-01-01

We study the polymer system consisting of two-polymer chains situated in a fractal container that belongs to the three-dimensional Sierpinski Gasket (3D SG) family of fractals. The two-polymer system is modeled by two interacting self-avoiding walks (SAW) immersed in a good solvent. To conceive the inter-chain interactions we apply the model of two crossing self-avoiding walks (CSAW) in which the chains can cross each other. By applying renormalization group (RG) method, we establish the relevant phase diagrams for b=2 and b=3 members of the 3D SG fractal family. Also, at the appropriate transition fixed points we calculate the contact critical exponents φ, associated with the number of contacts between monomers of different chains. For larger b(2≤b≤30) we apply Monte Carlo renormalization group (MCRG) method, and compare the obtained results for φ with phenomenological proposals for the contact critical exponent, as well as with results obtained for other similar models of two-polymer system.

Gene susceptibility in Iranian asthmatic patients: a narrative review ...

African Journals Online (AJOL)

As environmental factors are important in the development of asthma, genetic factors could have a critical role in the expression of the disease. Hence, we carried out a systematic review to assess the susceptible genes for asthma in Iranian population. We conducted a literature search by using the electronic database ...

Fermionic quantum critical point of spinless fermions on a honeycomb lattice

International Nuclear Information System (INIS)

Wang, Lei; Corboz, Philippe; Troyer, Matthias

2014-01-01

Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of the Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recent discovery (Huffman and Chandrasekharan 2014 Phys. Rev. B 89 111101) of the absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous-time quantum Monte Carlo method with a worm-sampling technique. We estimate the transition point V/t=1.356(1) with the critical exponents ν=0.80(3) and η=0.302(7). Compatible results for the transition point are also obtained with infinite projected entangled-pair states. (paper)

Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series

Directory of Open Access Journals (Sweden)

A. M. López Jiménez

2002-01-01

Full Text Available The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation of λ starting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.

Criticality in the configuration-mixed interacting boson model: (1) U(5)-Q(χ)Q(χ) mixing

International Nuclear Information System (INIS)

Hellemans, V.; Van Isacker, P.; De Baerdemacker, S.; Heyde, K.

2007-01-01

The case of U(5)-Q(χ)Q(χ) mixing in the configuration-mixed interacting boson model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively

Theoretical investigation of electronic and magnetic properties of MnAu layers

Energy Technology Data Exchange (ETDEWEB)

Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, BP 63, 46000, Sidi Bouzid, Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Neel, CNRS et Universite Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco); Mounkachi, O. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Bahmad, L. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco)

2013-01-15

Self-consistent ab initio calculations, based on the density functional theory (DFT) approach and using the full potential linear augmented plane wave (FLAPW) method, are performed to investigate both electronic and magnetic properties of the MnAu layers. Polarized spin and spin-orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn layers. Magnetic moment considered to lie along a axes are computed. The data obtained from the ab initio calculations are then used as input for the high temperature series expansions (HTSEs) calculation to compute other magnetic parameters. The exchange integrals between the magnetic atoms in the same layer and between the magnetic atoms in the bilayers adjacent are given by using mean field theory. The HTSEs of the magnetic susceptibility of MnAu antiferromagnetic spin-S through two model: Ising and XY layers consisting of l=2, 3, 4, 5, 6 and bulk ({infinity}) interacting layers, are studied to sixth order series in {beta}=1/k{sub B}T obtained for free-surface boundary conditions. The effects of finite size on critical-point behavior are studied by extrapolation of the high-temperature series. The Neel temperature T{sub N}(l) as a function of the number of l spin layers is obtained by HTSEs of the magnetic susceptibility series by using the Pade approximant method and by MFT theory. The critical exponent {gamma} associated with the magnetic susceptibility is deduced. T{sub N}(l) for the l-layers are estimated from the divergence of the staggered susceptibility with an exponent for Ising model of {gamma}(1)=2.96, and for XY model of {gamma}(2)=2.82, which is consistent with the basic assumptions of scaling laws. Our estimates for the shift exponent of the Neel temperature for the two models are obtained. - Highlights: Black-Right-Pointing-Pointer ab initio calculations is using to investigate both electronic and magnetic properties of the MnAu layers. Black

Theoretical investigation of electronic and magnetic properties of MnAu layers

International Nuclear Information System (INIS)

Masrour, R.; Hlil, E.K.; Hamedoun, M.; Benyoussef, A.; Mounkachi, O.; Bahmad, L.

2013-01-01

Self-consistent ab initio calculations, based on the density functional theory (DFT) approach and using the full potential linear augmented plane wave (FLAPW) method, are performed to investigate both electronic and magnetic properties of the MnAu layers. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Mn layers. Magnetic moment considered to lie along a axes are computed. The data obtained from the ab initio calculations are then used as input for the high temperature series expansions (HTSEs) calculation to compute other magnetic parameters. The exchange integrals between the magnetic atoms in the same layer and between the magnetic atoms in the bilayers adjacent are given by using mean field theory. The HTSEs of the magnetic susceptibility of MnAu antiferromagnetic spin-S through two model: Ising and XY layers consisting of l=2, 3, 4, 5, 6 and bulk (∞) interacting layers, are studied to sixth order series in β=1/k B T obtained for free-surface boundary conditions. The effects of finite size on critical-point behavior are studied by extrapolation of the high-temperature series. The Néel temperature T N (l) as a function of the number of l spin layers is obtained by HTSEs of the magnetic susceptibility series by using the Padé approximant method and by MFT theory. The critical exponent γ associated with the magnetic susceptibility is deduced. T N (l) for the l-layers are estimated from the divergence of the staggered susceptibility with an exponent for Ising model of γ(1)=2.96, and for XY model of γ(2)=2.82, which is consistent with the basic assumptions of scaling laws. Our estimates for the shift exponent of the Néel temperature for the two models are obtained. - Highlights: ► ab initio calculations is using to investigate both electronic and magnetic properties of the MnAu layers. ► Obtained data from ab initio calculations are used as input for the HTSEs

Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data

Energy Technology Data Exchange (ETDEWEB)

Josiński, Henryk [Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Świtoński, Adam [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland); Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Michalczuk, Agnieszka; Wojciechowski, Konrad [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland)

2015-03-10

The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.

Impact of a small amount of vacancy in both lanthanum and calcium on the physical properties of nanocrystalline La_0_._7Ca_0_._3MnO_3 manganite

International Nuclear Information System (INIS)

Makni-Chakroun, J.; Cheikhrouhou-Koubaa, W.; Koubaa, M.; Cheikhrouhou, A.

2015-01-01

In this paper, we report the effect of both lanthanum and calcium (1%) on the structural and magnetic properties of nanocrystalline La_0_._7Ca_0_._3MnO_3 manganite. Our powder specimens were synthesized using the sol–gel method with an annealing temperature of 850 °C. The X-ray diffraction patterns refined using Rietveld method confirms that our compounds are single phase and crystallize in the orthorhombic perovskite structure (Pbnm space group). The morphology of the samples, observed using a scanning electron microscope (SEM), reveals a spherical shape with an average grain size lower than 100 nm. Magnetization measurements versus temperature under low magnetic applied field (0.05T) show a paramagnetic–ferromagnetic transition for all compounds. The Curie temperature T_C is found to increase with lacuna in both cases. In addition, the inverse of the susceptibility (1/χ) as a function of temperature indicates a deviation from the Curie Weiss lawn, signature of Griffiths phase occurrence. Experimental results for the critical β and γ exponents are typical of a behavior governed by the tricritical mean-field theory model. Using magnetization measurements as a function of magnetic applied field at several temperatures, we have deduced the magnetic entropy change, which undergoes an enlargement for both lacuna sites. The obtained results are compared to calculated ones based on the Landau theory and a good concordance is observed. - Graphical abstract: (a) Spontaneous magnetization and inverse of susceptibility versus T for La_0_._7Ca_0_._2_9□_0_._0_1MnO_3 compound. Inset the Ln–Ln plot used to determine the critical exponents β and γ. (b) M vs μ_0H isotherm measured at T_C = 200 K. Inset the Ln–Ln plot for the critical exponent δ calculation as well as the modified Arrott plot for La_0_._7Ca_0_._2_9□_0_._0_1MnO_3 compound. - Highlights: • SEM images reveal a spherical shape with an average grain size lower than 100 nm. • Curie temperature T

Accurate Determination of the Quasiparticle and Scaling Properties Surrounding the Quantum Critical Point of Disordered Three-Dimensional Dirac Semimetals.

Science.gov (United States)

Fu, Bo; Zhu, Wei; Shi, Qinwei; Li, Qunxiang; Yang, Jinlong; Zhang, Zhenyu

2017-04-07

Exploiting the enabling power of the Lanczos method in momentum space, we determine accurately the quasiparticle and scaling properties of disordered three-dimensional Dirac semimetals surrounding the quantum critical point separating the semimetal and diffusive metal regimes. We unveil that the imaginary part of the quasiparticle self-energy obeys a common power law before, at, and after the quantum phase transition, but the power law is nonuniversal, whose exponent is dependent on the disorder strength. More intriguingly, whereas a common power law is also found for the real part of the self-energy before and after the phase transition, a distinctly different behavior is identified at the critical point, characterized by the existence of a nonanalytic logarithmic singularity. This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point. Our approach also allows the ready and reliable determination of the scaling properties of the correlation length and dynamical exponents. We further show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.

Electronic and magnetic structures of GdS layers investigated by first principle and series expansions calculations

International Nuclear Information System (INIS)

Masrour, R.; Hlil, E.K.; Hamedoun, M.; Benyoussef, A.

2014-01-01

Self-consistent ab initio calculations, based on Density Functional Theory (DFT) approach and using Full Potential Linear Augmented Plane Wave (FLAPW) method within GGA+U approximation, are performed to investigate both electronic and magnetic properties of the GdS layers. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Gd layers. Magnetic moment considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the High Temperature Series Expansions (HTSEs) calculations to compute other magnetic parameters. Using the Heisenberg model, the exchange interactions between the magnetic atoms Gd–Gd in the same layer and between the magnetic atoms in the adjacent bilayers are estimated. This estimate is obtained using the antiferromagnetic and ferromagnetic energies computed by abinitio calculations for GdS layers. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility of GdS with antiferromagnetic moment (m Gd ) is given up to sixth order series versus of (J 11 (Gd–Gd)/k B T). The Néel temperature T N is obtained by mean field theory and by HTSEs of the magnetic susceptibility series using the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is calculated for GdS layers. - Highlights: • Electronic and magnetic properties of GdS are investigated using the ab initio calculations. • Obtained data from abinitio calculations are used as input for HTSEs to compute other magnetic parameters. • Néel temperature and critical exponent are deduced using HTSE method

Polymyxin susceptibility testing, interpretative breakpoints and resistance mechanisms: An update.

Science.gov (United States)

Bakthavatchalam, Yamuna Devi; Pragasam, Agila Kumari; Biswas, Indranil; Veeraraghavan, Balaji

2018-03-01

Emerging multidrug-resistant (MDR) nosocomial pathogens are a great threat. Polymyxins, an old class of cationic polypeptide antibiotic, are considered as last-resort drugs in treating infections caused by MDR Gram-negative bacteria. Increased use of polymyxins in treating critically ill patients necessitates routine polymyxin susceptibility testing. However, susceptibility testing both of colistin and polymyxin B (PMB) is challenging. In this review, currently available susceptibility testing methods are briefly discussed. The multicomponent composition of colistin and PMB significantly influences susceptibility testing. In addition, poor diffusion in the agar medium, adsorption to microtitre plates and the synergistic effect of the surfactant polysorbate 80 with polymyxins have a great impact on the performance of susceptibility testing methods This review also describes recently identified chromosomal resistance mechanisms, including modification of lipopolysaccharide (LPS) with 4-amino-4-deoxy-l-arabinose (L-Ara4-N) and phosphoethanolamine (pEtN) resulting in alteration of the negative charge, as well as the plasmid-mediated colistin resistance determinants mcr-1, mcr-1.2, mcr-2 and mcr-3. Copyright © 2017 International Society for Chemotherapy of Infection and Cancer. Published by Elsevier Ltd. All rights reserved.

Quantum coherence and quantum phase transition in the XY model with staggered Dzyaloshinsky-Moriya interaction

Energy Technology Data Exchange (ETDEWEB)

Hui, Ning-Ju [Department of Applied Physics, Xi' an University of Technology, Xi' an 710054 (China); Xu, Yang-Yang; Wang, Jicheng; Zhang, Yixin [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China); Hu, Zheng-Da, E-mail: huyuanda1112@jiangnan.edu.cn [Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122 (China)

2017-04-01

We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.

Dynamic critical phenomena in two-dimensional fully frustrated Coulomb gas model with disorder

International Nuclear Information System (INIS)

Zhang Wei; Luo Mengbo

2008-01-01

The dynamic critical phenomena near depinning transition in two-dimensional fully frustrated square lattice Coulomb gas model with disorders was studied using Monte Carlo technique. The ground state of the model system with disorder σ=0.3 is a disordered state. The dependence of charge current density J on electric field E was investigated at low temperatures. The nonlinear J-E behavior near critical depinning field can be described by a scaling function proposed for three-dimensional flux line system [M.B. Luo, X. Hu, Phys. Rev. Lett. 98 (2007) 267002]. We evaluated critical exponents and found an Arrhenius creep motion for field region E c /2 c . The scaling law of the depinning transition is also obtained from the scaling function

Quantifying the degree of persistence in random amoeboid motion based on the Hurst exponent of fractional Brownian motion.

Science.gov (United States)

Makarava, Natallia; Menz, Stephan; Theves, Matthias; Huisinga, Wilhelm; Beta, Carsten; Holschneider, Matthias

2014-10-01

Amoebae explore their environment in a random way, unless external cues like, e.g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.

Susceptibility analysis of landslide in Chittagong City Corporation Area, Bangladesh

Directory of Open Access Journals (Sweden)

Sourav Das

2015-06-01

Full Text Available In Chittagong city, landslide phenomena is the most burning issue which causes great problems to the life and properties and it is increasing day by day and becoming one of the main problems of city life. On 11 June 2007, a massive landslide happened in Chittagong City Corporation (CCC area, a large number of foothill settlements and slums were demolished; more than 90 people died and huge resource destruction took place. It is therefore essential to analyze the landslide susceptibility for CCC area to prepare mitigation strategies as well as assessing the impacts of climate change. To assess community susceptibility of landslide hazard, a landslide susceptibility index map has been prepared using analytical hierarchy process (AHP model based on geographic information system (GIS and remote sensing (RS and its susceptibility is analyzed through community vulnerability assessment tool (CVAT. The major findings of the research are 27% of total CCC area which is susceptible to landslide hazard and whereas 6.5 sq.km areas are found very highly susceptible. The landslide susceptible areas of CCC have also been analyzed in respect of physical, social, economic, environmental and critical facilities and it is found that the overall CCC area is highly susceptible to landslide hazard. So the findings of the research can be utilized to prioritize risk mitigation investments, measures to strengthen the emergency preparedness and response mechanisms for reducing the losses and damages due to future landslide events. DOI: http://dx.doi.org/10.3126/ije.v4i2.12635 International Journal of Environment Vol.4(2 2015: 157-181

Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents

Science.gov (United States)

Cho, Y. S.; Lee, J. S.; Herrmann, H. J.; Kahng, B.

2016-01-01

Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of g fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a more unusual phase transition, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent τ in the range 2 power-law behavior of the avalanche size distribution arising in models with link-deleting processes in interdependent networks.

Monte Carlo analysis of critical phenomenon of the Ising model on memory stabilizer structures

International Nuclear Information System (INIS)

Viteri, C. Ricardo; Tomita, Yu; Brown, Kenneth R.

2009-01-01

We calculate the critical temperature of the Ising model on a set of graphs representing a concatenated three-bit error-correction code. The graphs are derived from the stabilizer formalism used in quantum error correction. The stabilizer for a subspace is defined as the group of Pauli operators whose eigenvalues are +1 on the subspace. The group can be generated by a subset of operators in the stabilizer, and the choice of generators determines the structure of the graph. The Wolff algorithm, together with the histogram method and finite-size scaling, is used to calculate both the critical temperature and the critical exponents of each structure. The simulations show that the choice of stabilizer generators, both the number and the geometry, has a large effect on the critical temperature.

The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange

Science.gov (United States)

Domino, Krzysztof

2011-01-01

The local properties of the time series of the evolution of share prices of 126 significant companies traded on the Warsaw Stock Exchange during the period between 1991-2008 have been investigated. The analysis was applied to daily financial returns. I have used the local DFA to obtain the Hurst exponent (diffusion coefficient) while searching for negative correlations by which changes of long-term trends would be effected. A certain evidence, proving that after the signature of anti-correlation-the drop in the Hurst exponent-the change in the trend and in the return rate of an investment is probable, was pointed out. Hence after further investigation this method may be useful as a part of an investment strategy. As the Warsaw Stock Exchange is relatively smaller and younger than other significant world Stock Exchanges-and as the developing market is less efficient-the generalization for others markets needs further investigation.

Work and power fluctuations in a critical heat engine

Science.gov (United States)

Holubec, Viktor; Ryabov, Artem

2017-09-01

We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close to a critical point where Carnot's efficiency may be attained at a finite power as reported by M. Campisi and R. Fazio [Nat. Commun. 7, 11895 (2016), 10.1038/ncomms11895]. We show that the variance of work output per cycle scales with the same critical exponent as the heat capacity of the working fluid. As a consequence, the relative work fluctuation diverges unless the output work obeys a rather strict scaling condition, which would be very hard to fulfill in practice. Even under this condition, the fluctuations of work and power do not vanish in the infinite system size limit. Large fluctuations of output work thus constitute inseparable and dominant element in performance of the macroscopic heat engines close to a critical point.

Work and power fluctuations in a critical heat engine.

Science.gov (United States)

Holubec, Viktor; Ryabov, Artem

2017-09-01

We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close to a critical point where Carnot's efficiency may be attained at a finite power as reported by M. Campisi and R. Fazio [Nat. Commun. 7, 11895 (2016)2041-172310.1038/ncomms11895]. We show that the variance of work output per cycle scales with the same critical exponent as the heat capacity of the working fluid. As a consequence, the relative work fluctuation diverges unless the output work obeys a rather strict scaling condition, which would be very hard to fulfill in practice. Even under this condition, the fluctuations of work and power do not vanish in the infinite system size limit. Large fluctuations of output work thus constitute inseparable and dominant element in performance of the macroscopic heat engines close to a critical point.

Modulational estimate for the maximal Lyapunov exponent in Fermi-Pasta-Ulam chains

Science.gov (United States)

Dauxois, Thierry; Ruffo, Stefano; Torcini, Alessandro

1997-12-01

In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the modulational instability growth rates associated to unstable modes. Moreover, we show that the strong stochasticity threshold found in the β-FPU system is closely related to a transition in tangent space, the Lyapunov eigenvector being more localized in space at high energy.

Study of multiparameter respiratory pattern complexity in surgical critically ill patients during weaning trials

Directory of Open Access Journals (Sweden)

Maglaveras Nikos K

2011-01-01

Full Text Available Abstract Background Separation from mechanical ventilation is a difficult task, whereas conventional predictive indices have not been proven accurate enough, so far. A few studies have explored changes of breathing pattern variability for weaning outcome prediction, with conflicting results. In this study, we tried to assess respiratory complexity during weaning trials, using different non-linear methods derived from theory of complex systems, in a cohort of surgical critically ill patients. Results Thirty two patients were enrolled in the study. There were 22 who passed and 10 who failed a weaning trial. Tidal volume and mean inspiratory flow were analyzed for 10 minutes during two phases: 1. pressure support (PS ventilation (15-20 cm H2O and 2. weaning trials with PS: 5 cm H2O. Sample entropy (SampEn, detrended fluctuation analysis (DFA exponent, fractal dimension (FD and largest lyapunov exponents (LLE of the two respiratory parameters were computed in all patients and during the two phases of PS. Weaning failure patients exhibited significantly decreased respiratory pattern complexity, reflected in reduced sample entropy and lyapunov exponents and increased DFA exponents of respiratory flow time series, compared to weaning success subjects (p 0.1, SampEn and LLE predicted better weaning outcome compared with RSBI, P0.1 and RSBI* P0.1 (conventional model, R2 = 0.874 vs 0.643, p Conclusions We suggest that complexity analysis of respiratory signals can assess inherent breathing pattern dynamics and has increased prognostic impact upon weaning outcome in surgical patients.

AC susceptibility of thin Pb films in intermediate and mixed state

Energy Technology Data Exchange (ETDEWEB)

Janu, Zdenek, E-mail: janu@fzu.cz [Institute of Physics of the AS CR, v.v.i., Na Slovance 2, CZ-182 21 Prague 8 (Czech Republic); Svindrych, Zdenek [Institute of Physics of the AS CR, v.v.i., Na Slovance 2, CZ-182 21 Prague 8 (Czech Republic); Trunecek, Otakar [Charles University in Prague, Faculty of Mathematics and Physics, Ke Karlovu 3, CZ-121 16 Prague 2 (Czech Republic); Kus, Peter; Plecenik, Andrej [Komenius University in Bratislava, Faculty of Mathematics, Physics, and Informatics, Mlynska dolina, 842 48 Bratislava 4 (Slovakia)

2011-12-15

Thickness dependent transition in AC susceptibility between intermediate and mixed state in type-I superconducting films. The temperature induced crossover between reversible and irreversible behavior was observed in the thicker film. The temperature dependence of the AC susceptibility in mixed state follows prediction of model based on Bean critical state. The temperature dependence of the harmonics of the complex AC susceptibility in the intermediate state is explained. Thin films of type I superconductors of a thickness comparable or less than a flux penetration length behave like type II superconductors in a mixed state. With decreasing film thickness normal domains carrying a magnetic flux get smaller with smaller number of flux quanta per domain and finally transform into single quantum flux lines, i.e. quantum vortices similar to those found in type II superconductors. We give an evidence of this behavior from the measurements of the nonlinear response of a total magnetic moment to an applied AC magnetic field, directly from the temperature dependence of an AC susceptibility.

The Hurst exponent in energy futures prices

Science.gov (United States)

Serletis, Apostolos; Rosenberg, Aryeh Adam

2007-07-01

This paper extends the work in Elder and Serletis [Long memory in energy futures prices, Rev. Financial Econ., forthcoming, 2007] and Serletis et al. [Detrended fluctuation analysis of the US stock market, Int. J. Bifurcation Chaos, forthcoming, 2007] by re-examining the empirical evidence for random walk type behavior in energy futures prices. In doing so, it uses daily data on energy futures traded on the New York Mercantile Exchange, over the period from July 2, 1990 to November 1, 2006, and a statistical physics approach-the ‘detrending moving average’ technique-providing a reliable framework for testing the information efficiency in financial markets as shown by Alessio et al. [Second-order moving average and scaling of stochastic time series, Eur. Phys. J. B 27 (2002) 197-200] and Carbone et al. [Time-dependent hurst exponent in financial time series. Physica A 344 (2004) 267-271; Analysis of clusters formed by the moving average of a long-range correlated time series. Phys. Rev. E 69 (2004) 026105]. The results show that energy futures returns display long memory and that the particular form of long memory is anti-persistence.

Automatic detection of ischemic stroke based on scaling exponent electroencephalogram using extreme learning machine

Science.gov (United States)

Adhi, H. A.; Wijaya, S. K.; Prawito; Badri, C.; Rezal, M.

2017-03-01

Stroke is one of cerebrovascular diseases caused by the obstruction of blood flow to the brain. Stroke becomes the leading cause of death in Indonesia and the second in the world. Stroke also causes of the disability. Ischemic stroke accounts for most of all stroke cases. Obstruction of blood flow can cause tissue damage which results the electrical changes in the brain that can be observed through the electroencephalogram (EEG). In this study, we presented the results of automatic detection of ischemic stroke and normal subjects based on the scaling exponent EEG obtained through detrended fluctuation analysis (DFA) using extreme learning machine (ELM) as the classifier. The signal processing was performed with 18 channels of EEG in the range of 0-30 Hz. Scaling exponents of the subjects were used as the input for ELM to classify the ischemic stroke. The performance of detection was observed by the value of accuracy, sensitivity and specificity. The result showed, performance of the proposed method to classify the ischemic stroke was 84 % for accuracy, 82 % for sensitivity and 87 % for specificity with 120 hidden neurons and sine as the activation function of ELM.

Inequality for the infinite-cluster density in Bernoulli percolation

International Nuclear Information System (INIS)

Chayes, J.T.; Chayes, L.

1986-01-01

Under a certain assumption (which is satisfied whenever there is a dense infinite cluster in the half-space), we prove a differential inequality for the infinite-cluster density, P/sub infinity/(p), in Bernoulli percolation. The principal implication of this result is that if P/sub infinity/(p) vanishes with critical exponent β, then β obeys the mean-field bound β< or =1. As a corollary, we also derive an inequality relating the backbone density, the truncated susceptibility, and the infinite-cluster density

Critical parameters and saturated density of trifluoroiodomethane (CF{sub 3}I)

Energy Technology Data Exchange (ETDEWEB)

Duan, Y.Y.; Shi, L.; Zhu, M.S.; Han, L.Z. [Tsinghua Univ., Beijing (China). Dept. of Thermal Engineering

1999-05-01

The vapor-liquid coexistence curve of trifluoroiodomethane (CF{sub 3}I) was measured by visual observation of the meniscus disappearance in an optical cell. Thirty-two saturated density data points were obtained along the vapor-liquid coexistence curve between 384.5 and 2024.9 kg/m{sup 3} in the temperature range from 301.02 K to the critical temperature. The experimental uncertainties in temperature and density were estimated to be within {+-}10 mK and {+-}0.5%, respectively. Measurements near the critical point were used to determine the critical temperature T{sub c} = 396.44 {+-} 0.01 K and the critical density {rho}{sub c} = 868 {+-} 3 kg/m{sup 3} for trifluoroiodomethane (CF{sub 3}I) on the basis of the meniscus disappearing level as well as the intensity of the critical opalescence. The critical pressure {rho}{sub c} = 3.953 {+-} 0.005 MPa was extrapolated from the existing vapor pressure equation proposed previously using the present {Tc} value. The critical exponent, {beta}, was also determined, and correlations of the saturated liquid and saturated vapor densities of CF{sub 3}I were developed.

Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

Directory of Open Access Journals (Sweden)

L.F.P. Franca

2003-01-01

Full Text Available This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

Critical behavior of mean-field spin glasses on a dilute random graph

Energy Technology Data Exchange (ETDEWEB)

De Sanctis, Luca [Dipartimento di Matematica e di Psicologia, Universita di Bologna, P.zza di Porta San Donato 5, 40126 Bologna (Italy); Barra, Adriano; Folli, Viola [Dipartimento di Fisica, Universita La Sapienza, P.le Aldo Moro 5, 00185 Roma (Italy)], E-mail: desanctis@dm.unibo.it, E-mail: adriano.barra@roma1.infn.it, E-mail: viola.folli@roma1.infn.it

2008-05-30

We provide a rigorous strategy to find the critical exponents of the overlaps for dilute spin glasses, in the absence of an external field. Such a strategy is based on the expansion of a suitably perturbed average of the overlaps, which is used in the formulation of the free energy as the difference between a cavity part and the derivative of the free energy itself, considered as a function of the connectivity of the model. We assume the validity of certain reasonable approximations, equivalent to assuming a second-order transition, e.g. that higher powers of overlap monomials are of smaller magnitude near the critical point, of which we do not provide a rigorous proof.

Critical behavior of mean-field spin glasses on a dilute random graph

International Nuclear Information System (INIS)

De Sanctis, Luca; Barra, Adriano; Folli, Viola

2008-01-01

We provide a rigorous strategy to find the critical exponents of the overlaps for dilute spin glasses, in the absence of an external field. Such a strategy is based on the expansion of a suitably perturbed average of the overlaps, which is used in the formulation of the free energy as the difference between a cavity part and the derivative of the free energy itself, considered as a function of the connectivity of the model. We assume the validity of certain reasonable approximations, equivalent to assuming a second-order transition, e.g. that higher powers of overlap monomials are of smaller magnitude near the critical point, of which we do not provide a rigorous proof

Critical phenomena in quasi-two-dimensional vibrated granular systems.

Science.gov (United States)

Guzmán, Marcelo; Soto, Rodrigo

2018-01-01

The critical phenomena associated to the liquid-to-solid transition of quasi-two-dimensional vibrated granular systems is studied using molecular dynamics simulations of the inelastic hard sphere model. The critical properties are associated to the fourfold bond-orientational order parameter χ_{4}, which measures the level of square crystallization of the system. Previous experimental results have shown that the transition of χ_{4}, when varying the vibration amplitude, can be either discontinuous or continuous, for two different values of the height of the box. Exploring the amplitude-height phase space, a transition line is found, which can be either discontinuous or continuous, merging at a tricritical point and the continuous branch ends in an upper critical point. In the continuous transition branch, the critical properties are studied. The exponent associated to the amplitude of the order parameter is β=1/2, for various system sizes, in complete agreement with the experimental results. However, the fluctuations of χ_{4} do not show any critical behavior, probably due to crossover effects by the close presence of the tricritical point. Finally, in quasi-one-dimensional systems, the transition is only discontinuous, limited by one critical point, indicating that two is the lower dimension for having a tricritical point.

Critical fluctuations of the proton density in A+A collisions at $158A$ GeV

CERN Document Server

Anticic, T.; Bartke, J.; Beck, H.; Betev, L.; Białkowska, H.; Blume, C.; Bogusz, M.; Boimska, B.; Book, J.; Botje, M.; Bunčić, P.; Cetner, T.; Christakoglou, P.; Chvala, O.; Cramer, J.; Eckardt, V.; Fodor, Z.; Foka, P.; Friese, V.; Gaździcki, M.; Grebieszkow, K.; Höhne, C.; Kadija, K.; Karev, A.; Kolesnikov, V.I.; Kowalski, M.; Kresan, D.; Laszlo, A.; Leeuwen, M.; Maćkowiak-Pawłowska, M.; Makariev, M.; Malakhov, A.I.; Mateev, M.; Melkumov, G.L.; Mitrovski, M.; Mrówczyński, St.; Pálla, G.; Panagiotou, A.D.; Peryt, W.; Pluta, J.; Prindle, D.; Pühlhofer, F.; Renfordt, R.; Roland, C.; Roland, G.; Rustamov, A.; Rybczyński, M.; Rybicki, A.; Sandoval, A.; Schmitz, N.; Schuster, T.; Seyboth, P.; Siklér, F.; Skrzypczak, E.; Slodkowski, M.; Stefanek, G.; Stock, R.; Ströbele, H.; Susa, T.; Szuba, M.; Varga, D.; Vassiliou, M.; Veres, G.I.; Vesztergombi, G.; Vranić, D.; Włodarczyk, Z.; Wojtaszek-Szwarć, A.; Antoniou, N.G.; Davis, N.; Diakonos, F.K.

2015-12-12

Studies of QCD suggest the existence of a critical point in the phase diagram of strongly interacting matter. Close to this point, according to recent theoretical investigations, the net-proton density carries the critical fluctuations of the chiral order parameter. Using intermittency analysis in the transverse momentum phase space of protons produced around midrapidity in the 12.5% most central C+C, Si+Si and Pb+Pb collisions at the maximum SPS energy of 158$A$ GeV we find evidence of power-law fluctuations for the Si+Si and Pb+Pb data. The fitted power-law exponent approaches the value expected for critical fluctuations. This suggests that the freeze-out states of these two systems are located in the phase diagram in the neighbourhood of the chiral critical point.

A birational mapping with a strange attractor: post-critical set and covariant curves

International Nuclear Information System (INIS)

Bouamra, M; Hassani, S; Maillard, J-M

2009-01-01

We consider some two-dimensional birational transformations. One of them is a birational deformation of the Henon map. For some of these birational mappings, the post-critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These covariant curves are used to build the preserved meromorphic 2-form. One may also have an infinite post-critical set yielding a covariant curve which is not algebraic (transcendental). For two of the birational mappings considered, the post-critical set is finite and we claim that there is no algebraic covariant curve and no preserved meromorphic 2-form. For these two mappings with finite post-critical sets, attracting sets occur and we show that they pass the usual tests (Lyapunov exponents and the fractal dimension) for being strange attractors. The strange attractor of one of these two mappings is unbounded.

Nonuniversal critical behaviour in a model for charge density wave dynamics

International Nuclear Information System (INIS)

Ritala, R.K.; Hertz, J.A.

1986-02-01

We have studied short range fluctuations around the infinite-range model of charge density wave (CDW) dynamics. We find that the inhomogeneity of the local field, which is neglected in the infinite-range approximation has a dramatic effect on the transition. In the Bethe approximation the critical behaviour is nonuniversal. In particular, the current exponent is ζ = 3/2 log(z-1)/[log(z)]+log(1+f/J)], where z is the number of neighbors, f the pinning strength, and J the elastic coupling. (orig.)

The theory of critical phenomena an introduction to the renormalization group

CERN Document Server

Binney, J J; Fisher, A J; Newman, M E J

1993-01-01

The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulation

Exchange integrals and magnetic short range order in the system CdCr2-xGaxSe4 (0=

International Nuclear Information System (INIS)

Bakrim, H.; Bouslykhane, K.; Hamedoun, M.; Hourmatallah, A.; Benzakour, N.

2005-01-01

High-temperature series expansions are derived for the magnetic susceptibility and two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random phase approximation and are given for both nearest and next-nearest neighbour exchange integrals J1 and J2, respectively. Our results are given up to order 6 in β=(kBT)-1 and are used to study the paramagnetic region of the ferromagnetic spinel CdCr 2-x Ga x Se 4 . The critical temperature Tc and the critical exponents γ and ν associated with the magnetic susceptibility χ(T) and the correlation length ξ(T), respectively are deduced by applying the Pade approximate methods. The results as a function of the dilution x obtained by the present approach are found to be in agreement with the experimental ones

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.

Pure Theory of Hans Kelsen and Criticism of Luis Alberto Warat

Directory of Open Access Journals (Sweden)

Thaisa Haber Faleiros

2015-12-01

building a new model for learning practices based on a remaking of old premises according to a critical and reflexive law, Warat aims at preventing law knowledge from being mummified and completely adapted to renewable and ceaseless situations and conflicts because of lack of critical reasoning. To contextualize this authors approach, this study presents previously the positivist theory of law, whose exponent is Hans Kelsen. After all, studying Warat means verifying the ways he followed to reach his approach. Besides, delaing with law teaching requires tracing back its legislation since its creation in 1827 to the present. For that, Kelsen laws pure theory, its influence on law teaching and Warat ideas on law and his pedagogical approach are unfolded in the context of law teaching history.

Relation Between Hertz Stress-Life Exponent, Ball-Race Conformity, and Ball Bearing Life

Science.gov (United States)

Zaretsky, Erwin V.; Poplawski, Joseph V.; Root, Lawrence E.

2008-01-01

ANSI/ABMA and ISO standards based on Lundberg-Palmgren bearing life theory are normalized for ball bearings having inner- and outerrace conformities of 52 percent (0.52) and made from pre-1940 bearing steel. The Lundberg-Palmgren theory incorporates an inverse 9th power relation between Hertz stress and fatigue life for ball bearings. The effect of race conformity on ball set life independent of race life is not incorporated into the Lundberg-Palmgren theory. In addition, post-1960 vacuum-processed bearing steel exhibits a 12th power relation between Hertz stress and life. The work reported extends the previous work of Zaretsky, Poplawski, and Root to calculate changes in bearing life--that includes the life of the ball set--caused by race conformity, Hertz stress-life exponent, ball bearing type and bearing series. The bearing fatigue life in actual application will usually be equal to or greater than that calculated using the ANSI/ABMA and ISO standards that incorporate the Lundberg-Palmgren theory. The relative fatigue life of an individual race is more sensitive to changes in race conformity for Hertz stress-life exponent n of 12 than where n = 9. However, when the effects are combined to predict actual bearing life for a specified set of conditions and bearing geometry, the predicted life of the bearing will be greater for a value of n = 12 than n = 9.

Antifungal susceptibility and phylogeny of opportunistic members of the order mucorales.

Science.gov (United States)

Vitale, Roxana G; de Hoog, G Sybren; Schwarz, Patrick; Dannaoui, Eric; Deng, Shuwen; Machouart, Marie; Voigt, Kerstin; van de Sande, Wendy W J; Dolatabadi, Somayeh; Meis, Jacques F; Walther, Grit

2012-01-01

The in vitro susceptibilities of 66 molecularly identified strains of the Mucorales to eight antifungals (amphotericin B, terbinafine, itraconazole, posaconazole, voriconazole, caspofungin, micafungin, and 5-fluorocytosine) were tested. Molecular phylogeny was reconstructed based on the nuclear ribosomal large subunit to reveal taxon-specific susceptibility profiles. The impressive phylogenetic diversity of the Mucorales was reflected in susceptibilities differing at family, genus, and species levels. Amphotericin B was the most active drug, though somewhat less against Rhizopus and Cunninghamella species. Posaconazole was the second most effective antifungal agent but showed reduced activity in Mucor and Cunninghamella strains, while voriconazole lacked in vitro activity for most strains. Genera attributed to the Mucoraceae exhibited a wide range of MICs for posaconazole, itraconazole, and terbinafine and included resistant strains. Cunninghamella also comprised strains resistant to all azoles tested but was fully susceptible to terbinafine. In contrast, the Lichtheimiaceae completely lacked strains with reduced susceptibility for these antifungals. Syncephalastrum species exhibited susceptibility profiles similar to those of the Lichtheimiaceae. Mucor species were more resistant to azoles than Rhizopus species. Species-specific responses were obtained for terbinafine where only Rhizopus arrhizus and Mucor circinelloides were resistant. Complete or vast resistance was observed for 5-fluorocytosine, caspofungin, and micafungin. Intraspecific variability of in vitro susceptibility was found in all genera tested but was especially high in Mucor and Rhizopus for azoles and terbinafine. Accurate molecular identification of etiologic agents is compulsory to predict therapy outcome. For species of critical genera such as Mucor and Rhizopus, exhibiting high intraspecific variation, susceptibility testing before the onset of therapy is recommended.

Harmonic and static susceptibilities of YBa2Cu3O7

International Nuclear Information System (INIS)

Ishida, T.; Goldfarb, R.B.; Okayasu, S.; Kazumata, Y.; Franz, J.; Arndt, T.; Schauer, W.

1993-01-01

Intergranular properties of the sintered superconductor YBa 2 Cu 3 O 7 have been studied in terms of complex harmonic magnetic susceptibility χ n χ n ' - iχ n '' (n integer) as well as DC susceptibility χ dc . As functions of temperature T, χ 1 ' and χ 1 '' depend on both the AC magnetic-field amplitude H ac and the magnitude of a superimposed DC field H dc . Only odd-harmonic susceptibilities are observed below the critical temperature, T c , for zero H dc while both odd and even harmonics are observed for nonzero H dc . With T constant, odd-harmonic susceptibilities are even functions of H dc , whereas even-harmonic susceptibilities are odd functions of H dc . Experimental intergranular characteristics of χ n ' and χ n '' are in good agreement with theoretical predictions from a simplified Kim model of magnetization. In contrast, even-harmonic susceptibilities measured for a GdBa 2 Cu 3 O 7 thin film and an YBa 2 Cu 3 O 7 single crystal are not prominent due to missing weak links, whereas odd-harmonic susceptibilities are remarkable. A survey of several models for the harmonic response of superconductors is presented. The DC susceptibility curve for the zero-field-cooled YBa 2 Cu 3 O 7 sample, χ ZFC (T), has a two-step structure arising from intra- and inter-granular components, similar to χ 1 '. DC susceptibility measured upon warming, χ FCW (T), shows a negative peak near T c for the sample cooled rapidly in small DC fields. DC susceptibility measured upon cooling, χ FCC (T), does not show a peak. A negative peak is not seen in measurements on a powdered sample. The negative peak can be explained by intergranular flux depinning upon warming. (orig.)

Moment Lyapunov Exponent and Stochastic Stability of Binary Airfoil under Combined Harmonic and Non-Gaussian Colored Noise Excitations

Science.gov (United States)

Hu, D. L.; Liu, X. B.

Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non-Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.

Susceptibility-Weighted Imaging and Quantitative Susceptibility Mapping in the Brain

Science.gov (United States)

Liu, Chunlei; Li, Wei; Tong, Karen A.; Yeom, Kristen W.; Kuzminski, Samuel

2015-01-01

Susceptibility-weighted imaging (SWI) is a magnetic resonance imaging (MRI) technique that enhances image contrast by using the susceptibility differences between tissues. It is created by combining both magnitude and phase in the gradient echo data. SWI is sensitive to both paramagnetic and diamagnetic substances which generate different phase shift in MRI data. SWI images can be displayed as a minimum intensity projection that provides high resolution delineation of the cerebral venous architecture, a feature that is not available in other MRI techniques. As such, SWI has been widely applied to diagnose various venous abnormalities. SWI is especially sensitive to deoxygenated blood and intracranial mineral deposition and, for that reason, has been applied to image various pathologies including intracranial hemorrhage, traumatic brain injury, stroke, neoplasm, and multiple sclerosis. SWI, however, does not provide quantitative measures of magnetic susceptibility. This limitation is currently being addressed with the development of quantitative susceptibility mapping (QSM) and susceptibility tensor imaging (STI). While QSM treats susceptibility as isotropic, STI treats susceptibility as generally anisotropic characterized by a tensor quantity. This article reviews the basic principles of SWI, its clinical and research applications, the mechanisms governing brain susceptibility properties, and its practical implementation, with a focus on brain imaging. PMID:25270052

Susceptibility-weighted imaging and quantitative susceptibility mapping in the brain.

Science.gov (United States)

Liu, Chunlei; Li, Wei; Tong, Karen A; Yeom, Kristen W; Kuzminski, Samuel

2015-07-01

Susceptibility-weighted imaging (SWI) is a magnetic resonance imaging (MRI) technique that enhances image contrast by using the susceptibility differences between tissues. It is created by combining both magnitude and phase in the gradient echo data. SWI is sensitive to both paramagnetic and diamagnetic substances which generate different phase shift in MRI data. SWI images can be displayed as a minimum intensity projection that provides high resolution delineation of the cerebral venous architecture, a feature that is not available in other MRI techniques. As such, SWI has been widely applied to diagnose various venous abnormalities. SWI is especially sensitive to deoxygenated blood and intracranial mineral deposition and, for that reason, has been applied to image various pathologies including intracranial hemorrhage, traumatic brain injury, stroke, neoplasm, and multiple sclerosis. SWI, however, does not provide quantitative measures of magnetic susceptibility. This limitation is currently being addressed with the development of quantitative susceptibility mapping (QSM) and susceptibility tensor imaging (STI). While QSM treats susceptibility as isotropic, STI treats susceptibility as generally anisotropic characterized by a tensor quantity. This article reviews the basic principles of SWI, its clinical and research applications, the mechanisms governing brain susceptibility properties, and its practical implementation, with a focus on brain imaging. © 2014 Wiley Periodicals, Inc.

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)

Critical quench dynamics in confined systems.

Science.gov (United States)

Collura, Mario; Karevski, Dragi

2010-05-21

We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system finally reaches or crosses a critical point. Under this protocol we derive general scaling laws for the density of excitations created during the nonadiabatic sweep of the confining potential. It is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. We confirm our scaling laws by first order adiabatic calculation and exact results on the Ising quantum chain with a varying transverse field.

CISH and susceptibility to infectious diseases.

Science.gov (United States)

Khor, Chiea C; Vannberg, Fredrik O; Chapman, Stephen J; Guo, Haiyan; Wong, Sunny H; Walley, Andrew J; Vukcevic, Damjan; Rautanen, Anna; Mills, Tara C; Chang, Kwok-Chiu; Kam, Kai-Man; Crampin, Amelia C; Ngwira, Bagrey; Leung, Chi-Chiu; Tam, Cheuk-Ming; Chan, Chiu-Yeung; Sung, Joseph J Y; Yew, Wing-Wai; Toh, Kai-Yee; Tay, Stacey K H; Kwiatkowski, Dominic; Lienhardt, Christian; Hien, Tran-Tinh; Day, Nicholas P; Peshu, Nobert; Marsh, Kevin; Maitland, Kathryn; Scott, J Anthony; Williams, Thomas N; Berkley, James A; Floyd, Sian; Tang, Nelson L S; Fine, Paul E M; Goh, Denise L M; Hill, Adrian V S

2010-06-03

The interleukin-2-mediated immune response is critical for host defense against infectious pathogens. Cytokine-inducible SRC homology 2 (SH2) domain protein (CISH), a suppressor of cytokine signaling, controls interleukin-2 signaling. Using a case-control design, we tested for an association between CISH polymorphisms and susceptibility to major infectious diseases (bacteremia, tuberculosis, and severe malaria) in blood samples from 8402 persons in Gambia, Hong Kong, Kenya, Malawi, and Vietnam. We had previously tested 20 other immune-related genes in one or more of these sample collections. We observed associations between variant alleles of multiple CISH polymorphisms and increased susceptibility to each infectious disease in each of the study populations. When all five single-nucleotide polymorphisms (SNPs) (at positions -639, -292, -163, +1320, and +3415 [all relative to CISH]) within the CISH-associated locus were considered together in a multiple-SNP score, we found an association between CISH genetic variants and susceptibility to bacteremia, malaria, and tuberculosis (P=3.8x10(-11) for all comparisons), with -292 accounting for most of the association signal (P=4.58x10(-7)). Peripheral-blood mononuclear cells obtained from adult subjects carrying the -292 variant, as compared with wild-type cells, showed a muted response to the stimulation of interleukin-2 production--that is, 25 to 40% less CISH expression. Variants of CISH are associated with susceptibility to diseases caused by diverse infectious pathogens, suggesting that negative regulators of cytokine signaling have a role in immunity against various infectious diseases. The overall risk of one of these infectious diseases was increased by at least 18% among persons carrying the variant CISH alleles. 2010 Massachusetts Medical Society

Criticality in the configuration-mixed interacting boson model (1) $U(5)-\\hat{Q}(\\chi)\\cdot\\hat{Q}(\\chi)$ mixing

CERN Document Server

Hellemans, V; De Baerdemacker, S; Heyde, K

2008-01-01

The case of U(5)--$\\hat{Q}(\\chi)\\cdot\\hat{Q}(\\chi)$ mixing in the configuration-mixed Interacting Boson Model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively.

Electronic and magnetic structures of GdS layers investigated by first principle and series expansions calculations

Energy Technology Data Exchange (ETDEWEB)

Masrour, R., E-mail: rachidmasrour@hotmail.com [Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, 63 46000 Safi (Morocco); LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Hlil, E.K. [Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble cedex 9 (France); Hamedoun, M. [Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Benyoussef, A. [LMPHE (URAC 12), Faculty of Science, Mohammed V-Agdal University, Rabat (Morocco); Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat (Morocco); Hassan II Academy of Science and Technology, Rabat (Morocco)

2014-04-01

Self-consistent ab initio calculations, based on Density Functional Theory (DFT) approach and using Full Potential Linear Augmented Plane Wave (FLAPW) method within GGA+U approximation, are performed to investigate both electronic and magnetic properties of the GdS layers. Polarized spin and spin–orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Gd layers. Magnetic moment considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the High Temperature Series Expansions (HTSEs) calculations to compute other magnetic parameters. Using the Heisenberg model, the exchange interactions between the magnetic atoms Gd–Gd in the same layer and between the magnetic atoms in the adjacent bilayers are estimated. This estimate is obtained using the antiferromagnetic and ferromagnetic energies computed by abinitio calculations for GdS layers. The High Temperature Series Expansions (HTSEs) of the magnetic susceptibility of GdS with antiferromagnetic moment (m{sub Gd}) is given up to sixth order series versus of (J{sub 11}(Gd–Gd)/k{sub B}T). The Néel temperature T{sub N} is obtained by mean field theory and by HTSEs of the magnetic susceptibility series using the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is calculated for GdS layers. - Highlights: • Electronic and magnetic properties of GdS are investigated using the ab initio calculations. • Obtained data from abinitio calculations are used as input for HTSEs to compute other magnetic parameters. • Néel temperature and critical exponent are deduced using HTSE method.

An in-depth characterization of the major psoriasis susceptibility locus identifies candidate susceptibility alleles within an HLA-C enhancer element.

Directory of Open Access Journals (Sweden)

Alex Clop

Full Text Available Psoriasis is an immune-mediated skin disorder that is inherited as a complex genetic trait. Although genome-wide association scans (GWAS have identified 36 disease susceptibility regions, more than 50% of the genetic variance can be attributed to a single Major Histocompatibility Complex (MHC locus, known as PSORS1. Genetic studies indicate that HLA-C is the strongest PSORS1 candidate gene, since markers tagging HLA-Cw*0602 consistently generate the most significant association signals in GWAS. However, it is unclear whether HLA-Cw*0602 is itself the causal PSORS1 allele, especially as the role of SNPs that may affect its expression has not been investigated. Here, we have undertaken an in-depth molecular characterization of the PSORS1 interval, with a view to identifying regulatory variants that may contribute to disease susceptibility. By analysing high-density SNP data, we refined PSORS1 to a 179 kb region encompassing HLA-C and the neighbouring HCG27 pseudogene. We compared multiple MHC sequences spanning this refined locus and identified 144 candidate susceptibility variants, which are unique to chromosomes bearing HLA-Cw*0602. In parallel, we investigated the epigenetic profile of the critical PSORS1 interval and uncovered three enhancer elements likely to be active in T lymphocytes. Finally we showed that nine candidate susceptibility SNPs map within a HLA-C enhancer and that three of these variants co-localise with binding sites for immune-related transcription factors. These data indicate that SNPs affecting HLA-Cw*0602 expression are likely to contribute to psoriasis susceptibility and highlight the importance of integrating multiple experimental approaches in the investigation of complex genomic regions such as the MHC.

Fidelity Susceptibility Made Simple: A Unified Quantum Monte Carlo Approach

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Lei Wang

2015-07-01

Full Text Available The fidelity susceptibility is a general purpose probe of phase transitions. With its origin in quantum information and in the differential geometry perspective of quantum states, the fidelity susceptibility can indicate the presence of a phase transition without prior knowledge of the local order parameter, as well as reveal the universal properties of a critical point. The wide applicability of the fidelity susceptibility to quantum many-body systems is, however, hindered by the limited computational tools to evaluate it. We present a generic, efficient, and elegant approach to compute the fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in a broad range of quantum Monte Carlo methods. It can be applied to both the ground-state and nonzero-temperature cases. The Monte Carlo estimator has a simple yet universal form, which can be efficiently evaluated in simulations. We demonstrate the power of this approach with applications to the Bose-Hubbard model, the spin-1/2 XXZ model, and use it to examine the hypothetical intermediate spin-liquid phase in the Hubbard model on the honeycomb lattice.

Gauss-Bonnet coupling constant as a free thermodynamical variable and the associated criticality

International Nuclear Information System (INIS)

Xu, Wei; Xu, Hao; Zhao, Liu

2014-01-01

The thermodynamic phase space of Gauss-Bonnet (GB) AdS black holes is extended, taking the inverse of the GB coupling constant as a new thermodynamic pressure P GB . We studied the critical behavior associated with P GB in the extended thermodynamic phase space at fixed cosmological constant and electric charge. The result shows that when the black holes are neutral, the associated critical points can only exist in five dimensional GB-AdS black holes with spherical topology, and the corresponding critical exponents are identical to those for the Van der Waals system. For charged GB-AdS black holes, it is shown that there can be only one critical point in five dimensions (for black holes with either spherical or hyperbolic topologies), which also requires the electric charge to be bounded within some appropriate range; while in d < 5 dimensions, there can be up to two different critical points at the same electric charge, and the phase transition can occur only at temperatures which are not in between the two critical values. (orig.)

Influence of granulometry in the Hurst exponent of air liquid interfaces formed during capillary rising in a granular media

Directory of Open Access Journals (Sweden)

Gontijo Guilherme L.

2017-01-01

Full Text Available We report results concerning the fractal dimension of a air/fluid interface formed during the capillary rising of a fluid into a dense granular media. The system consists in a modified Hele-Shaw cell filled with grains at different granulometries and confined in a narrow gap between the glass plates. The system is then placed onto a water reservoir, and the liquid penetrates the medium due to capillary forces. We measure the Hurst exponent of the liquid/air interface with help of image processing, and follow the temporal evolution of the profiles. We observe that the Hurst exponent can be related with the granulometry, but the range of values are odd to the predicted values from models or theory.

Healthcare disparities in critical illness.

Science.gov (United States)

Soto, Graciela J; Martin, Greg S; Gong, Michelle Ng

2013-12-01

To summarize the current literature on racial and gender disparities in critical care and the mechanisms underlying these disparities in the course of acute critical illness. MEDLINE search on the published literature addressing racial, ethnic, or gender disparities in acute critical illness, such as sepsis, acute lung injury, pneumonia, venous thromboembolism, and cardiac arrest. Clinical studies that evaluated general critically ill patient populations in the United States as well as specific critical care conditions were reviewed with a focus on studies evaluating factors and contributors to health disparities. Study findings are presented according to their association with the prevalence, clinical presentation, management, and outcomes in acute critical illness. This review presents potential contributors for racial and gender disparities related to genetic susceptibility, comorbidities, preventive health services, socioeconomic factors, cultural differences, and access to care. The data are organized along the course of acute critical illness. The literature to date shows that disparities in critical care are most likely multifactorial involving individual, community, and hospital-level factors at several points in the continuum of acute critical illness. The data presented identify potential targets as interventions to reduce disparities in critical care and future avenues for research.

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

Brittle Creep Failure, Critical Behavior, and Time-to-Failure Prediction of Concrete under Uniaxial Compression

Directory of Open Access Journals (Sweden)

Yingchong Wang

2015-01-01

Full Text Available Understanding the time-dependent brittle deformation behavior of concrete as a main building material is fundamental for the lifetime prediction and engineering design. Herein, we present the experimental measures of brittle creep failure, critical behavior, and the dependence of time-to-failure, on the secondary creep rate of concrete under sustained uniaxial compression. A complete evolution process of creep failure is achieved. Three typical creep stages are observed, including the primary (decelerating, secondary (steady state creep regime, and tertiary creep (accelerating creep stages. The time-to-failure shows sample-specificity although all samples exhibit a similar creep process. All specimens exhibit a critical power-law behavior with an exponent of −0.51 ± 0.06, approximately equal to the theoretical value of −1/2. All samples have a long-term secondary stage characterized by a constant strain rate that dominates the lifetime of a sample. The average creep rate expressed by the total creep strain over the lifetime (tf-t0 for each specimen shows a power-law dependence on the secondary creep rate with an exponent of −1. This could provide a clue to the prediction of the time-to-failure of concrete, based on the monitoring of the creep behavior at the steady stage.

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)

Connection of optimum temporal exponents with a principle of least action

Science.gov (United States)

Sergeev, E. V.; Karzanov, A. V.; Tremaskin, A. V.

2008-06-01

The principle of the least action states, that the motion of objects on optimum trajectories conjugates to the underload expenditure of activity. In the canonical approach this statement is reduced to searching extreme activity. For the immediate proof of the underload expenditure of activity on optimum trajectories the relevant mathematical algorithm in the basis of which bottom the concept of optimum time exponents lays is offered. Using this algorithm, various modes of a motion of charged particles are explored: the harmonic motion, a motion in the homogeneous force field, a motion in a central force field and a motion on inertia. The terrain clearance minimum under the rate of flux of activity for the harmonic motions is detected.

Possible individual variation in susceptibility to radiation-induced genetic changes

International Nuclear Information System (INIS)

Gentner, N.E.; Walker, J.A.

1990-01-01

Several studies have shown variation between individuals in radiosensitivity. A person could have a high level of cytogenetic indicator because of high exposure or high susceptibility. To relate spontaneous cytogenetic end-points to dose it is advisable to have a measure of both the spontaneous level and of induced susceptibility. These end points need to be compared in irradiated persons who have developed cancer versus those who have not, as a guide to what end points are appropriate for susceptibility to radiogenic cancer. The use of inbred rodent strains may not be appropriate to derive specific locus mutation data relevant to the human situation, in which large differences in susceptibility appear to exist. Variability in response because of differential DNA repair capacity should be kept in mind when evaluating existing human data. For accident situations, using acute exposures for testing susceptibility may be appropriate, but to be relevant to low dose, low dose rate exposures, more use of protracted dose delivery in testing is recommended. There is a need for international collaborative study where these different tests are done on the same donors at the same time. It might now be prudent for radiation protection to take into account the occurrence of critical groups in the population on the basis of their increased radiation sensitivity. (12 refs., 3 figs.)

Polymyxins: Antimicrobial susceptibility concerns and therapeutic options

Directory of Open Access Journals (Sweden)

V Balaji

2011-01-01

Full Text Available The increasing prevalence of multidrug-resistant nosocomial pathogens such as Acinetobacter baumannii, Pseudomonas aeruginosa and Klebsiella pneumoniae poses a great challenge to the treating physicians. The paucity of newer effective antimicrobials has led to renewed interest in the polymyxin group of drugs, as a last resort for treatment of gram-negative bacterial infections. There is a dearth of information on the pharmacological properties of colistin, leading to difficulties in selecting the right dose, dosing interval, and route of administration for treatment, especially in critically-ill patients. The increasing use of colistin over the last few years necessitates the need for accurate and reliable in vitro susceptibility testing methods. Development of heteroresistant strains as a result of colistin monotherapy is also a growing concern. There is a compelling need from the clinicians to provide options for probable and possible colistin combination therapy for multidrug-resistant bacterial infections in the ICU setting. Newer combination drug synergy determination tests are being developed and reported. There are no standardized recommendations from antimicrobial susceptibility testing reference agencies for the testing and interpretation of these drug combinations. Comparison and analysis of these reported methodologies may help to understand and assist the microbiologist to choose the best method that produces accurate results at the earliest. This will help clinicians to select the appropriate combination therapy. In this era of multidrug resistance it is important for the microbiology laboratory to be prepared, by default, to provide timely synergistic susceptibility results in addition to routine susceptibility, if warranted. Not as a favour or at request, but as a responsibility.

Matrix models with γstring>0

International Nuclear Information System (INIS)

Marzban, C.; Viswanathan, R.R.

1990-12-01

Within the framework of c = 1 matrix models, we consider multi-matrix models. A connection is established between a D-dimensional gas of fermions (bosons) for odd (even) values of D. A statistical mechanical analysis yields the scaling law for the free energy, and hence the susceptibility exponents for the various models. The exponents turn out to be positive for the multi-matrix models, suggesting that these could represent models of 2 d-gravity coupled to c>1 matter. Whereas in the c=1 case the density of states itself diverges as one approaches the critical point, in the D-matrix models various derivatives of the density of states diverge, with the order of the derivative depending on D. This qualitatively different behaviour of the density of states could be a signal of the conjectured ''phase transition'' at c=1. (author). 14 refs

Quantum critical singularities in two-dimensional metallic XY ferromagnets

Science.gov (United States)

Varma, Chandra M.; Gannon, W. J.; Aronson, M. C.; Rodriguez-Rivera, J. A.; Qiu, Y.

2018-02-01

An important problem in contemporary physics concerns quantum-critical fluctuations in metals. A scaling function for the momentum, frequency, temperature, and magnetic field dependence of the correlation function near a 2D-ferromagnetic quantum-critical point (QCP) is constructed, and its singularities are determined by comparing to the recent calculations of the correlation functions of the dissipative quantum XY model (DQXY). The calculations are motivated by the measured properties of the metallic compound YFe2Al10 , which is a realization of the DQXY model in 2D. The frequency, temperature, and magnetic field dependence of the scaling function as well as the singularities measured in the experiments are given by the theory without adjustable exponents. The same model is applicable to the superconductor-insulator transitions, classes of metallic AFM-QCPs, and as fluctuations of the loop-current ordered state in hole-doped cuprates. The results presented here lend credence to the solution found for the 2D-DQXY model and its applications in understanding quantum-critical properties of diverse systems.

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 the three-dimensional Heisenberg antiferromagnet RbMnF₃

DEFF Research Database (Denmark)

Coldea, R.; Cowley, R.A.; Perring, T.G.

1998-01-01

component evolves below T-N into the longitudinal susceptibility identified in an earlier polarized neutron experiment. The intensity and energy width of the longitudinal scattering decrease on cooling below T-N. Down to the lowest temperatures where the longitudinal susceptibility could be measured......The magnetic critical scattering of the near-ideal three-dimensional Heisenberg antiferromagnet (AF) RbMnF3 has been remeasured using neutron scattering. The critical dynamics has been studied in detail in the temperature range 0.77T(N)

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.

Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model

Science.gov (United States)

Yang, Shuo; Gu, Shi-Jian; Sun, Chang-Pu; Lin, Hai-Qing