Estimate of the critical exponents from the field-theoretical renormalization group: mathematical meaning of the 'Standard Values'

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pogorelov, A. A.; Suslov, I. M.

2008-06-15

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called standard values), but have lower uncertainty. It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions. The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions. The appropriate interpretation of the last contribution is necessary both for the estimation of the systematic errors of the standardmore » values and for a further increase in accuracy.« less

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

NASA Astrophysics Data System (ADS)

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.

Universality of crossover scaling for the adsorption transition of lattice polymers

NASA Astrophysics Data System (ADS)

Bradly, C. J.; Owczarek, A. L.; Prellberg, T.

2018-02-01

Recently, it has been proposed that the adsorption transition for a single polymer in dilute solution, modeled by lattice walks in three dimensions, is not universal with respect to intermonomer interactions. Moreover, it has been conjectured that key critical exponents ϕ , measuring the growth of the contacts with the surface at the adsorption point, and 1 /δ , which measures the finite-size shift of the critical temperature, are not the same. However, applying standard scaling arguments the two key critical exponents should rather be identical, hence pointing to a potential breakdown of these standard scaling arguments. Both of these conjectures are in contrast to the well-studied situation in two dimensions, where there are exact results from conformal field theory: these exponents are both accepted to be 1 /2 and universal. We use the flatPERM algorithm to simulate self-avoiding walks and trails on the hexagonal, square, and simple cubic lattices up to length 1024 to investigate these claims. Walks can be seen as a repulsive limit of intermonomer interaction for trails, allowing us to probe the universality of adsorption. For each lattice model we analyze several thermodynamic properties to produce different methods of estimating the critical temperature and the key exponents. We test our methodology on the two-dimensional cases, and the resulting spread in values for ϕ and 1 /δ indicates that there is a systematic error which can far exceed the statistical error usually reported. We further suggest a methodology for consistent estimation of the key adsorption exponents which gives ϕ =1 /δ =0.484 (4 ) in three dimensions. Hence, we conclude that in three dimensions these critical exponents indeed differ from the mean-field value of 1 /2 , as had previously been calculated, but cannot find evidence that they differ from each other. Importantly, we also find no substantive evidence of any nonuniversality in the polymer adsorption transition.

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

PubMed

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.

Effect of Zn doping on the magneto-caloric effect and critical constants of Mott insulator MnV{sub 2}O{sub 4}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shahi, Prashant; Kumar, A.; Shukla, K. K.

2014-09-15

X-ray absorption near edge spectra (XANES) and magnetization of Zn doped MnV{sub 2}O{sub 4} have been measured and from the magnetic measurement the critical exponents and magnetocaloric effect have been estimated. The XANES study indicates that Zn doping does not change the valence states in Mn and V. It has been shown that the obtained values of critical exponents β, γ and δ do not belong to universal class and the values are in between the 3D Heisenberg model and the mean field interaction model. The magnetization data follow the scaling equation and collapse into two branches indicating that themore » calculated critical exponents and critical temperature are unambiguous and intrinsic to the system. All the samples show large magneto-caloric effect. The second peak in magneto-caloric curve of Mn{sub 0.95}Zn{sub 0.05}V{sub 2}O{sub 4} is due to the strong coupling between orbital and spin degrees of freedom. But 10% Zn doping reduces the residual spins on the V-V pairs resulting the decrease of coupling between orbital and spin degrees of freedom.« less

Three dimensional finite temperature SU(3) gauge theory near the phase transition

NASA Astrophysics Data System (ADS)

Bialas, P.; Daniel, L.; Morel, A.; Petersson, B.

2013-06-01

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent ν has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.

5-D Choptuik critical exponent and holography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bland, J.; Kunstatter, G.

2007-05-15

Recently, a holographic argument was used to relate the saturation exponent, {gamma}{sub BFKL}, of 4-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, {gamma}{sub 5d}, in 5-dimensional black hole formation via scalar field collapse [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.]. Remarkably, the numerical value of the former agreed quite well with previous calculations of the latter. We present new results of an improved calculation of {gamma}{sub 5d} with substantially decreased numerical error. Our current result is {gamma}{sub 5d}=0.4131{+-}0.0001, which is close to, but not in strict agreement with, the value of {gamma}{sub BFKL}=0.409more » 552 quoted in [L. Alvarez-Gaume, C. Gomez, and M. A. Vazquez-Mozo, arXiv:hep-th/0611312.].« less

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

PubMed

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.

The fourth law of black-hole thermodynamics

NASA Astrophysics Data System (ADS)

Lousto, C. O.

1993-12-01

We show that black holes fulfill the scaling laws arising in critical transitions. In particular, we find that in the transition from negative to positive values the heat capacities CJQ, CΩQ and CJΦ give rise to critical exponents satisfying the scaling laws. The three transitions have the same critical exponents as predicted by the universality hypothesis. We also briefly discuss the implications of this result with regards to the connections among gravitation, quantum mechanics and statistical physics. Permanent address: Instituto de Astronomía y Física del Espacio, Casilla de Correo 67-Sucursal 28, 1428 Buenos Aires, Argentina.

Jamming criticality revealed by removing localized buckling excitations.

PubMed

Charbonneau, Patrick; Corwin, Eric I; Parisi, Giorgio; Zamponi, Francesco

2015-03-27

Recent theoretical advances offer an exact, first-principles theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small interparticle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the interparticle gaps is known to be constant in all spatial dimensions d-including the physically relevant d=2 and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II. Critical Exponents of Bond Percolation Model

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

1991-10-01

The critical exponents of the bond percolation model are calculated in the D(=2, 3, \\cdots)-dimensional simple cubic lattice on the basis of Suzuki’s coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

The critical crossover at the n-hexane-water interface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tikhonov, A. M., E-mail: tikhonov@kapitza.ras.r

According to estimates of the parameters of the critical crossover in monolayers of long-chain alcohol molecules adsorbed at the n-hexane-water interface, all systems in which this phenomenon is observed are characterized by the same value of the critical exponent {nu} {approx} 1.8.

Bootstrap percolation on spatial networks

NASA Astrophysics Data System (ADS)

Gao, Jian; Zhou, Tao; Hu, Yanqing

2015-10-01

Bootstrap percolation is a general representation of some networked activation process, which has found applications in explaining many important social phenomena, such as the propagation of information. Inspired by some recent findings on spatial structure of online social networks, here we study bootstrap percolation on undirected spatial networks, with the probability density function of long-range links’ lengths being a power law with tunable exponent. Setting the size of the giant active component as the order parameter, we find a parameter-dependent critical value for the power-law exponent, above which there is a double phase transition, mixed of a second-order phase transition and a hybrid phase transition with two varying critical points, otherwise there is only a second-order phase transition. We further find a parameter-independent critical value around -1, about which the two critical points for the double phase transition are almost constant. To our surprise, this critical value -1 is just equal or very close to the values of many real online social networks, including LiveJournal, HP Labs email network, Belgian mobile phone network, etc. This work helps us in better understanding the self-organization of spatial structure of online social networks, in terms of the effective function for information spreading.

Rotationally symmetric viscous gas flows

NASA Astrophysics Data System (ADS)

Weigant, W.; Plotnikov, P. I.

2017-03-01

The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.

Critical behavior of the van der Waals bonded ferromagnet Fe3 -xGeTe2

NASA Astrophysics Data System (ADS)

Liu, Yu; Ivanovski, V. N.; Petrovic, C.

2017-10-01

The critical properties of the single-crystalline van der Waals bonded ferromagnet Fe3 -xGeTe2 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic (FM) phase transition. The Fe3 -xGeTe2 single crystals grown by self-flux method with Fe deficiency x ≈0.36 exhibit bulk FM ordering below Tc=152 K. The Mössbauer spectroscopy was used to provide information on defects and local atomic environment in such crystals. Critical exponents β =0.372 (4 ) with a critical temperature Tc=151.25 (5 ) K and γ =1.265 (15 ) with Tc=151.17 (12 ) K are obtained by the Kouvel-Fisher method, whereas δ =4.50 (1 ) is obtained by a critical isotherm analysis at Tc=151 K. These critical exponents obey the Widom scaling relation δ =1 +γ /β , indicating self-consistency of the obtained values. With these critical exponents the isotherm M (H ) curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation m =f±(h ) , where m and h are renormalized magnetization and field, respectively. The exponents determined in this study are close to those calculated from the results of the renormalization group approach for a heuristic model of three-dimensional Heisenberg (d =3 ,n =3 ) spins coupled with the attractive long-range interactions between spins that decay as J (r ) ≈r-(3 +σ ) with σ =1.89 .

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

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

Dynamic behavior of the interface of striplike structures in driven lattice gases

NASA Astrophysics Data System (ADS)

Saracco, Gustavo P.; Albano, Ezequiel V.

2008-09-01

In this work, the dynamic behavior of the interfaces in both the standard and random driven lattice gas models (DLG and RDLG, respectively) is investigated via numerical Monte Carlo simulations in two dimensions. These models consider a lattice gas of density ρ=1/2 with nearest-neighbor attractive interactions between particles under the influence of an external driven field applied along one fixed direction in the case of the DLG model, and a randomly varying direction in the case of the RDLG model. The systems are also in contact with a reservoir at temperature T . Those systems undergo a second-order nonequilibrium phase transition between an ordered state characterized by high-density strips crossing the sample along the driving field, and a quasilattice gas disordered state. For T≲Tc , the average interface width of the strips (W) was measured as a function of the lattice size and the anisotropic shape factor. It was found that the saturation value Wsat2 only depends on the lattice size parallel to the external field axis Ly and exhibits two distinct regimes: Wsat2∝lnLy for low temperatures, that crosses over to Wsat2∝Ly2αI near the critical zone, αI=1/2 being the roughness exponent of the interface. By using the relationship αI=1/(1+ΔI) , the anisotropic exponent for the interface of the DLG model was estimated, giving ΔI≃1 , in agreement with the computed value for anisotropic bulk exponent ΔB in a recently proposed theoretical approach. At the crossover region between both regimes, we observed indications of bulk criticality. The time evolution of W at Tc was also monitored and shows two growing stages: first one observes that W∝lnt for several decades, and in the following times one has W∝tβI , where βI is the dynamic exponent of the interface width. By using this value we estimated the dynamic critical exponent of the correlation length in the perpendicular direction to the external field, giving z⊥I≈4 , which is consistent with the dynamic exponent of the bulk critical transition z⊥B in both theoretical approaches developed for the standard model. A similar scenario was also observed in the RDLG model, suggesting that both models may belong to the same universality class.

Criticality and phase diagram of quantum long-range O(N ) models

NASA Astrophysics Data System (ADS)

Defenu, Nicolò; Trombettoni, Andrea; Ruffo, Stefano

2017-09-01

Several recent experiments in atomic, molecular, and optical systems motivated a huge interest in the study of quantum long-range systems. Our goal in this paper is to present a general description of their critical behavior and phases, devising a treatment valid in d dimensions, with an exponent d +σ for the power-law decay of the couplings in the presence of an O(N ) symmetry. By introducing a convenient ansatz for the effective action, we determine the phase diagram for the N -component quantum rotor model with long-range interactions, with N =1 corresponding to the Ising model. The phase diagram in the σ -d plane shows a nontrivial dependence on σ . As a consequence of the fact that the model is quantum, the correlation functions are anisotropic in the spatial and time coordinates for σ smaller than a critical value, and in this region the isotropy is not restored even at criticality. Results for the correlation length exponent ν , the dynamical critical exponent z , and a comparison with numerical findings for them are presented.

Critical spreading dynamics of parity conserving annihilating random walks with power-law branching

NASA Astrophysics Data System (ADS)

Laise, T.; dos Anjos, F. C.; Argolo, C.; Lyra, M. L.

2018-09-01

We investigate the critical spreading of the parity conserving annihilating random walks model with Lévy-like branching. The random walks are considered to perform normal diffusion with probability p on the sites of a one-dimensional lattice, annihilating in pairs by contact. With probability 1 - p, each particle can also produce two offspring which are placed at a distance r from the original site following a power-law Lévy-like distribution P(r) ∝ 1 /rα. We perform numerical simulations starting from a single particle. A finite-time scaling analysis is employed to locate the critical diffusion probability pc below which a finite density of particles is developed in the long-time limit. Further, we estimate the spreading dynamical exponents related to the increase of the average number of particles at the critical point and its respective fluctuations. The critical exponents deviate from those of the counterpart model with short-range branching for small values of α. The numerical data suggest that continuously varying spreading exponents sets up while the branching process still results in a diffusive-like spreading.

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

PubMed

Watanabe, Hiroshi; Ito, Nobuyasu; Hu, Chin-Kun

2012-05-28

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

Universality class of the two-dimensional polymer collapse transition

NASA Astrophysics Data System (ADS)

Nahum, Adam

2016-05-01

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

Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Sanders, Sören; Holthaus, Martin

2017-10-01

We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose-Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.

Superconductor-insulator quantum phase transition in disordered FeSe thin films.

PubMed

Schneider, R; Zaitsev, A G; Fuchs, D; V Löhneysen, H

2012-06-22

The evolution of two-dimensional electronic transport with increasing disorder in epitaxial FeSe thin films is studied. Disorder is generated by reducing the film thickness. The extreme sensitivity of the films to disorder results in a superconductor-insulator transition. The finite-size scaling analysis in the critical regime based on the Bose-glass model strongly supports the idea of a continuous quantum phase transition. The obtained value for the critical-exponent product of approximately 7/3 suggests that the transition is governed by quantum percolation. Finite-size scaling with the same critical-exponent product is also substantiated when the superconductor-insulator transition is tuned with an applied magnetic field.

Light-induced metal-insulator transition in a switchable mirror.

PubMed

Hoekstra, A F; Roy, A S; Rosenbaum, T F; Griessen, R; Wijngaarden, R J; Koeman, N J

2001-06-04

Rare earth hydride films can be converted reversibly from metallic mirrors to insulating windows simply by changing the surrounding hydrogen gas pressure at room temperature. At low temperatures, in situ doping is not possible in this way as hydrogen cannot diffuse. However, our finding of persistent photoconductivity under ultraviolet illumination offers an attractive possibility to tune yttrium hydride through the T = 0 metal-insulator transition. Conductivity and Hall measurements are used to determine critical exponents. The unusually large value for the product of the static and dynamical critical exponents appears to signify the important role played by electron-electron interactions.

Holographic Lifshitz superconductors: Analytic solution

NASA Astrophysics Data System (ADS)

Natsuume, Makoto; Okamura, Takashi

2018-03-01

We construct an analytic solution for a one-parameter family of holographic superconductors in asymptotically Lifshitz spacetimes. We utilize this solution to explore various properties of the systems such as (1) the superfluid phase background and the grand canonical potential, (2) the order parameter response function or the susceptibility, (3) the London equation, and (4) the background with a superfluid flow or a magnetic field. From these results, we identify the dual Ginzburg-Landau theory including numerical coefficients. Also, the dynamic critical exponent zD associated with the critical point is given by zD=2 irrespective of the value of the Lifshitz exponent z .

Critical behavior of the van der Waals bonded ferromagnet Fe 3 - x GeTe 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yu; Ivanovski, V. N.; Petrovic, C.

The critical properties of the single-crystalline van der Waals bonded ferromagnet Fe 3-xGeTe 2 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic (FM) phase transition. The Fe 3-xGeTe 2 single crystals grown by self-flux method with Fe deficiency x ≈ 0.36 exhibit bulk FM ordering below T c = 152 K. The Mössbauer spectroscopy was used to provide information on defects and local atomic environment in such crystals. Critical exponents β = 0.372(4) with a critical temperature T c= 151.25(5) K and γ = 1.265(15) with T c = 151.17(12) K are obtained by the Kouvel-Fisher method,more » whereas δ = 4.50 ( 1 ) is obtained by a critical isotherm analysis at T c = 151 K. These critical exponents obey the Widom scaling relation δ = 1 + γ / β , indicating self-consistency of the obtained values. With these critical exponents the isotherm M(H) curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation m = f±(h), where m and h are renormalized magnetization and field, respectively. The exponents determined in this study are close to those calculated from the results of the renormalization group approach for a heuristic model of three-dimensional Heisenberg (d = 3,n = 3) spins coupled with the attractive long-range interactions between spins that decay as J(r) ≈ r -(3+σ) with σ = 1.89.« less

Critical behavior of the van der Waals bonded ferromagnet Fe 3 - x GeTe 2

DOE PAGES

Liu, Yu; Ivanovski, V. N.; Petrovic, C.

2017-10-29

The critical properties of the single-crystalline van der Waals bonded ferromagnet Fe 3-xGeTe 2 were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic (FM) phase transition. The Fe 3-xGeTe 2 single crystals grown by self-flux method with Fe deficiency x ≈ 0.36 exhibit bulk FM ordering below T c = 152 K. The Mössbauer spectroscopy was used to provide information on defects and local atomic environment in such crystals. Critical exponents β = 0.372(4) with a critical temperature T c= 151.25(5) K and γ = 1.265(15) with T c = 151.17(12) K are obtained by the Kouvel-Fisher method,more » whereas δ = 4.50 ( 1 ) is obtained by a critical isotherm analysis at T c = 151 K. These critical exponents obey the Widom scaling relation δ = 1 + γ / β , indicating self-consistency of the obtained values. With these critical exponents the isotherm M(H) curves below and above the critical temperatures collapse into two independent universal branches, obeying the single scaling equation m = f±(h), where m and h are renormalized magnetization and field, respectively. The exponents determined in this study are close to those calculated from the results of the renormalization group approach for a heuristic model of three-dimensional Heisenberg (d = 3,n = 3) spins coupled with the attractive long-range interactions between spins that decay as J(r) ≈ r -(3+σ) with σ = 1.89.« less

On the universal behavior of some thermodynamic properties along the whole liquid-vapor coexistence curve

NASA Astrophysics Data System (ADS)

Román, F. L.; White, J. A.; Velasco, S.; Mulero, A.

2005-09-01

When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.

Polarized neutron scattering studies of chiral criticality, and new universality classes of phase transitions

NASA Astrophysics Data System (ADS)

Plakhty, V. P.; Wosnitza, J.; Kulda, J.; Brückel, Th.; Schweika, W.; Visser, D.; Gavrilov, S. V.; Moskvin, E. V.; Kremer, R. K.; Banks, M. G.

2006-11-01

Using a novel polarised neutron scattering technique, the critical exponents for the spin chirality and chiral susceptibility are determined for the triangular lattice antiferromagnet (TLA) CsMnBr 3 in the ranges of reduced temperature τ>10 -3 and τ>7×10 -3, respectively. Their values, βC=0.44(2) and γC=0.85(3), together with the scaling relation α+2β+γ=2.13(9), including the critical exponent where α for the specific heat, prove that the spin-ordering transition belongs to the XY chiral universality class. In the case of helimagnet Ho, it is found that β-2β=0.14(4), where β is the staggered magnetisation exponent. The scaling relation α+2β+γ=2 could be fulfilled with a reasonable α=0.23(4), although for the chiral critical exponents βC=0.90(2) and γC=0.69(5) one needs α=-0.49(5) in contradiction with any experimental data. As the scaling relation always holds, we assume that the spin-ordering transition in Ho is of the first order. In the quantum antiferromagnet CsCuCl 3, a triangular spin order coexists with a long-period Dzyaloshinskii helix. The Dzyaloshinskii axial vector should remove the helix chiral degeneracy, which has not been observed in reality. The critical exponent β=0.22(2) is found to be in agreement with the XY chiral scenario for a TLA. Chiral scattering above TN is very weak, probably being masked by zero-point quantum fluctuations. A modulation of the crystal structure with the periodicity of the helix is observed, indicating strong coupling of the Dzyaloshinskii-Moriya interaction with the lattice.

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

NASA Astrophysics Data System (ADS)

Chen, Sheng; Täuber, Uwe C.

2016-04-01

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

Critical behaviour and filed dependence of magnetic entropy change in K-doped manganites Pr0.8Na0.2-xKxMnO3 (x = 0.10 and 0.15)

NASA Astrophysics Data System (ADS)

Ben Khlifa, H.; M'nassri, R.; Tarhouni, S.; Regaieg, Y.; Cheikhrouhou-Koubaa, W.; Chniba-Boudjada, N.; Cheikhrouhou, A.

2018-01-01

The orthorhombic Pr0.8Na0.2-xKxMnO3 (x = 0.10 and 0.15) manganites are prepared by using the solid state reaction at high temperatures. The critical exponents (β, γ, δ) are investigated through various techniques such as modified Arrott plot, Kouvel-Fisher method and critical isotherm analysis based on the data of the magnetic measurements recorded around the Curie temperature. The critical exponents are derived from the magnetization data using the Kouvel-Fisher method, are found to be β = 0.32(4) and γ = 1.29(2) at TC 123 K for x = 0.10 and β = 0.31(1) and γ = 1.25(2) at TC 133 K for x = 0.15. The critical exponent values obtained for both samples are comparable to the values predicted by the 3D-Ising model, and have also been verified by the scaling equation of state. Such results demonstrate the existence of ferromagnetic short-range order in our materials. The magnetic entropy changes of polycrystalline samples with a second-order phase transition are investigated. A large magnetic entropy change deduced from isothermal magnetization curves, is observed in our samples with a peak centered on their respective Curie temperatures (TC). The field dependence of the magnetic entropy changes are analyzed, which show power law dependence ΔSmax ≈ a(μ0 H) n at transition temperature. The values of n obey to the Curie Weiss law above the transition temperature. It is shown that for the investigated materials, the magnetic entropy change follow a master curve behaviour. The rescaled magnetic entropy change curves for different applied fields collapse onto a single curve for both samples.

On the temperature derivative of the surface tension at a critical end point

NASA Astrophysics Data System (ADS)

Robert, M.; Tavan, P.

1983-03-01

It is shown that, according to the van der Waals theory of fluid interfaces, the surface tension of the interface between a This result holds for any number of phases and independently varying densities and is not restricted to classical values of the critical exponents.

Superconductor-Metal-Insulator transition in two dimensional Ta thin Films

NASA Astrophysics Data System (ADS)

Park, Sun-Gyu; Kim, Eunseong

2013-03-01

Superconductor-insulator transition has been induced by tuning film thickness or magnetic field. Recent electrical transport measurements of MoGe, Bi, Ta thin films revealed an interesting intermediate metallic phase which intervened superconducting and insulating phases at certain range of magnetic field. Especially, Ta thin films show the characteristic IV behavior at each phase and the disorder tuned intermediate metallic phase [Y. Li, C. L. Vicente, and J. Yoon, Physical Review B 81, 020505 (2010)]. This unexpected metallic phase can be interpreted as a consequence of vortex motion or contribution of fermionic quasiparticles. In this presentation, we report the scaling behavior during the transitions in Ta thin film as well as the transport measurements in various phases. Critical exponents v and z are obtained in samples with wide ranges of disorder. These results reveal new universality class appears when disorder exceeds a critical value. Dynamical exponent z of Superconducting sample is found to be 1, which is consistent with theoretical prediction of unity. z in a metallic sample is suddenly increased to be approximately 2.5. This critical exponent is much larger than the value found in other system and theoretical prediction. We gratefully acknowledge the financial support by the National Research Foundation of Korea through the Creative Research Initiatives.

Insulating phase in Sr2IrO4: An investigation using critical analysis and magnetocaloric effect

NASA Astrophysics Data System (ADS)

Bhatti, Imtiaz Noor; Pramanik, A. K.

2017-01-01

The nature of insulating phase in 5d based Sr2IrO4 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 Sr2IrO4 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 Tc. We infer that though the insulating phase in Sr2IrO4 is more close to be Slater-type but the simultaneous presence of both Slater- and Mott-type is the likely scenario for this material.

Scaling properties of a rice-pile model: inertia and friction effects.

PubMed

Khfifi, M; Loulidi, M

2008-11-01

We present a rice-pile cellular automaton model that includes inertial and friction effects. This model is studied in one dimension, where the updating of metastable sites is done according to a stochastic dynamics governed by a probabilistic toppling parameter p that depends on the accumulated energy of moving grains. We investigate the scaling properties of the model using finite-size scaling analysis. The avalanche size, the lifetime, and the residence time distributions exhibit a power-law behavior. Their corresponding critical exponents, respectively, tau, y, and yr, are not universal. They present continuous variation versus the parameters of the system. The maximal value of the critical exponent tau that our model gives is very close to the experimental one, tau=2.02 [Frette, Nature (London) 379, 49 (1996)], and the probability distribution of the residence time is in good agreement with the experimental results. We note that the critical behavior is observed only in a certain range of parameter values of the system which correspond to low inertia and high friction.

Hybrid phase transition into an absorbing state: Percolation and avalanches

NASA Astrophysics Data System (ADS)

Lee, Deokjae; Choi, S.; Stippinger, M.; Kertész, J.; Kahng, B.

2016-04-01

Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the transition point the order parameter has a jump but there are also critical phenomena related to it. Here we study these phenomena on the Erdős-Rényi and the two-dimensional interdependent networks and show that the hybrid percolation transition exhibits two kinds of critical behaviors: divergence of the fluctuations of the order parameter and power-law size distribution of finite avalanches at a transition point. At the transition point global or "infinite" avalanches occur, while the finite ones have a power law size distribution; thus the avalanche statistics also has the nature of a HPT. The exponent βm of the order parameter is 1 /2 under general conditions, while the value of the exponent γm characterizing the fluctuations of the order parameter depends on the system. The critical behavior of the finite avalanches can be described by another set of exponents, βa and γa. These two critical behaviors are coupled by a scaling law: 1 -βm=γa .

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D -2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D =5 . We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤D <6 to their values in the pure Ising model at D -2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

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

PubMed

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

2017-04-01

The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D-2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D=5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3≤D<6 to their values in the pure Ising model at D-2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions.

FAST TRACK COMMUNICATION Critical exponents of domain walls in the two-dimensional Potts model

NASA Astrophysics Data System (ADS)

Dubail, Jérôme; Lykke Jacobsen, Jesper; Saleur, Hubert

2010-12-01

We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e. connected domains where the spin takes a constant value). These clusters are different from the usual Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross and branch. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. This leads to an infinite series of fundamental critical exponents h_{\\ell _1-\\ell _2,2\\ell _1}, valid for 0 <= Q <= 4, that describe the insertion of ell1 thin and ell2 thick domain walls.

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

PubMed

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.

Crossover phenomena in the critical range near magnetic ordering transition

NASA Astrophysics Data System (ADS)

Köbler, U.

2018-05-01

Among the most important issues of Renormalization Group (RG) theory are crossover events and relevant (or non-relevant) interactions. These terms are unknown to atomistic theories but they will be decisive for future field theories of magnetism. In this experimental study the importance of these terms for the critical dynamics above and below magnetic ordering transition is demonstrated on account of new analyses of published data. When crossover events are overlooked and critical data are fitted by a single power function of temperature over a temperature range including a crossover event, imprecise critical exponents result. The rather unsystematic and floating critical exponents reported in literature seem largely to be due to this problem. It is shown that for appropriate data analyses critical exponents are obtained that are to a good approximation rational numbers. In fact, rational critical exponents can be expected when spin dynamics is controlled by the bosons of the continuous magnetic medium (Goldstone bosons). The bosons are essentially magnetic dipole radiation generated by the precessing spins. As a result of the here performed data analyses, critical exponents for the magnetic order parameter of β = 1/2, 1/3, 1/4 and 1/6 are obtained. For the critical paramagnetic susceptibility the exponents are γ = 1 and γ = 4/3.

Critical desertification transition in semi-arid ecosystems: The role of local facilitation and colonization rate

NASA Astrophysics Data System (ADS)

Corrado, Raffaele; Cherubini, Anna Maria; Pennetta, Cecilia

2015-05-01

In this work we study the effect of two different ecological mechanisms on the desertification transition in arid or semi-arid ecosystems, modeled by a stochastic cellular automaton. Namely we consider the role of the facilitation mechanism, i.e. the local positive effects of plants on their neighborhood and of colonization factors, such as seed production, survival and germination probabilities. Within the model, the strength of these two mechanisms is determined by the parameters f and b, respectively controlling the rates of the recovery and colonization processes. In particular we focus on the full desertification transition occurring at increasing value of the mortality rate m and we discuss how the values of f and b affect the critical mortality mc , the critical exponents β and γσ‧, determining the power-law scaling of the average vegetation density and of the root-mean-square deviation of the density fluctuations, and the character of the transition: continuous or abrupt. We show that mc strongly depends on both f and b, a dependence which accounts for the higher resilience of the ecosystems to external stresses as a consequence of an increased effectiveness of positive feedback effects. On the other hand, concerning the value of the exponents and the character of the transition, our results point out that both these features are unaffected by changes in the strength of the local facilitation. Viceversa, we show that an increase of the colonization factor b significantly modifies the values of the exponents and the order of the transition, changing a continuous transition into an abrupt one. We explain these results in terms of the different range of the interactions characterizing facilitation and colonization mechanisms.

Condensation and critical exponents of an ideal non-Abelian gas

NASA Astrophysics Data System (ADS)

Talaei, Zahra; Mirza, Behrouz; Mohammadzadeh, Hosein

2017-11-01

We investigate an ideal gas obeying non-Abelian statistics and derive the expressions for some thermodynamic quantities. It is found that thermodynamic quantities are finite at the condensation point where their derivatives diverge and, near this point, they behave as \\vert T-Tc\\vert^{-ρ} in which Tc denotes the condensation temperature and ρ is a critical exponent. The critical exponents related to the heat capacity and compressibility are obtained by fitting numerical results and others are obtained using the scaling law hypothesis for a three-dimensional non-Abelian ideal gas. This set of critical exponents introduces a new universality class.

Application of the coherent anomaly method to percolation

NASA Astrophysics Data System (ADS)

Takayasu, Misako; Takayasu, Hideki

1988-03-01

Applying the coherent anomaly method (CAM) to site percolation problems, we estimate the percolation threshold pc and critical exponents. We obtain pc=0.589, β=0.140, γ=2.426 on the two-dimensional square lattice. These values are in good agreement with the values already known. We also investigate higher-dimensional cases by this method.

Application of the Coherent Anomaly Method to Percolation

NASA Astrophysics Data System (ADS)

Takayasu, Misako; Takayasu, Hideki

Applying the coherent anomaly method (CAM) to site percolation problems, we estimate the percolation threshold ϱc and critical exponents. We obtain pc = 0.589, Β=0.140, Γ = 2.426 on the two-dimensional square lattice. These values are in good agreement with the values already known. We also investigate higher-dimensional cases by this method.

Temperature, concentration, and frequency dependence of the dielectric constant near the critical point of the binary liquid mixture nitrobenzene-tetradecane

NASA Astrophysics Data System (ADS)

Leys, Jan; Losada-Pérez, Patricia; Cordoyiannis, George; Cerdeiriña, Claudio A.; Glorieux, Christ; Thoen, Jan

2010-03-01

Detailed results are reported for the dielectric constant ɛ as a function of temperature, concentration, and frequency near the upper critical point of the binary liquid mixture nitrobenzene-tetradecane. The data have been analyzed in the context of the recently developed concept of complete scaling. It is shown that the amplitude of the low frequency critical Maxwell-Wagner relaxation (with a relaxation frequency around 10 kHz) along the critical isopleth is consistent with the predictions of a droplet model for the critical fluctuations. The temperature dependence of ɛ in the homogeneous phase can be well described with a combination of a (1-α) power law term (with α the heat capacity critical exponent) and a linear term in reduced temperature with the Ising value for α. For the proper description of the temperature dependence of the difference Δɛ between the two coexisting phases below the critical temperature, it turned out that good fits with the Ising value for the order parameter exponent β required the addition of a corrections-to-scaling contribution or a linear term in reduced temperature. Good fits to the dielectric diameter ɛd require a (1-α) power law term, a 2β power law term (in the past considered as spurious), and a linear term in reduced temperature, consistent with complete scaling.

Statistical Systems with Z

NASA Astrophysics Data System (ADS)

William, Peter

In this dissertation several two dimensional statistical systems exhibiting discrete Z(n) symmetries are studied. For this purpose a newly developed algorithm to compute the partition function of these models exactly is utilized. The zeros of the partition function are examined in order to obtain information about the observable quantities at the critical point. This occurs in the form of critical exponents of the order parameters which characterize phenomena at the critical point. The correlation length exponent is found to agree very well with those computed from strong coupling expansions for the mass gap and with Monte Carlo results. In Feynman's path integral formalism the partition function of a statistical system can be related to the vacuum expectation value of the time ordered product of the observable quantities of the corresponding field theoretic model. Hence a generalization of ordinary scale invariance in the form of conformal invariance is focussed upon. This principle is very suitably applicable, in the case of two dimensional statistical models undergoing second order phase transitions at criticality. The conformal anomaly specifies the universality class to which these models belong. From an evaluation of the partition function, the free energy at criticality is computed, to determine the conformal anomaly of these models. The conformal anomaly for all the models considered here are in good agreement with the predicted values.

Nonequilibrium critical dynamics of the two-dimensional Ashkin-Teller model at the Baxter line

NASA Astrophysics Data System (ADS)

Fernandes, H. A.; da Silva, R.; Caparica, A. A.; de Felício, J. R. Drugowich

2017-04-01

We investigate the short-time universal behavior of the two-dimensional Ashkin-Teller model at the Baxter line by performing time-dependent Monte Carlo simulations. First, as preparatory results, we obtain the critical parameters by searching the optimal power-law decay of the magnetization. Thus, the dynamic critical exponents θm and θp, related to the magnetic and electric order parameters, as well as the persistence exponent θg, are estimated using heat-bath Monte Carlo simulations. In addition, we estimate the dynamic exponent z and the static critical exponents β and ν for both order parameters. We propose a refined method to estimate the static exponents that considers two different averages: one that combines an internal average using several seeds with another, which is taken over temporal variations in the power laws. Moreover, we also performed the bootstrapping method for a complementary analysis. Our results show that the ratio β /ν exhibits universal behavior along the critical line corroborating the conjecture for both magnetization and polarization.

Percolation behavior of polymer/metal composites on modification of filler

NASA Astrophysics Data System (ADS)

Panda, M.; Srinivas, V.; Thakur, A. K.

2014-02-01

Polymer-metal composites with different fillers, such as nanocrystalline nickel (n-Ni), core shell n-Ni and nickel oxide (NiO)[n-Ni@NiO] were prepared under the same processing conditions with polyvinyledene fluoride matrix. The larger value of critical exponents (s and s') and percolation threshold (fc 0.30) for n-Ni@NiO composites as compared to n-Ni composites (fc 0.07) and a comparable effective dielectric constant (ɛeff 300) with low loss tangent (tan δ 0.1) at 100 Hz in case of percolative n-Ni@NiO composite was observed. The core shell structure [n-Ni@NiO] also shows a very high value of ɛeff 6000 with tan δ 8 at 40 Hz. The results have been explained by using boundary layer capacitor effect and the percolation theory. The difference in fc and critical exponents is attributed to NiO insulating layer that gives rise to different extent of continuumness at fc and have been explained with the help of Swiss cheese model.

Fractal dimension, walk dimension and conductivity exponent of karst networks around Tulum.

NASA Astrophysics Data System (ADS)

Hendrick, Martin; Renard, Philippe

2016-06-01

Understanding the complex structure of karst networks is a challenge. In this work, we characterize the fractal properties of some of the largest coastal karst network systems in the world. They are located near the town of Tulum (Quintana Roo, Mexico). Their fractal dimension d_f, conductivity exponent ˜{μ} and walk dimension d_w are estimated using real space renormalization and numerical simulations. We obtain the following values for these exponents: d_f≈ 1.5, d_w≈ 2.4, ˜{μ}≈ 0.9. We observe that the Einstein relation holds for these structures ˜{μ} ≈ -d_f + d_w. These results indicate that coastal karst networks can be considered as critical systems and this provides some foundations to model them within this framework.

Conductivity fluctuations in polymer's networks

NASA Astrophysics Data System (ADS)

Samukhin, A. N.; Prigodin, V. N.; Jastrabík, L.

1998-01-01

A Polymer network is treated as an anisotropic fractal with fractional dimensionality D = 1 + ε close to one. Percolation model on such a fractal is studied. Using real space renormalization group approach of Migdal and Kadanoff, we find the threshold value and all the critical exponents in the percolation model to be strongly nonanalytic functions of ε, e.g. the critical exponent of the conductivity was obtained to be ε-2 exp (-1 - 1/ε). The main part of the finite-size conductivities distribution function at the threshold was found to be universal if expressed in terms of the fluctuating variable which is proportional to a large power of the conductivity, but with ε-dependent low-conductivity cut-off. Its reduced central momenta are of the order of e -1/ε up to a very high order.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II.

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

The critical exponents of the bond percolation model are calculated in the D(= 2,3,…)-dimensional simple cubic lattice on the basis of Suzuki's coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

Fragmentation scaling of percolation clusters in two and three dimensions: Large-cell Monte Carlo RG approach

NASA Astrophysics Data System (ADS)

Cheon, M.; Chang, I.

1999-04-01

The scaling behavior for a binary fragmentation of critical percolation clusters is investigated by a large-cell Monte Carlo real-space renormalization group method in two and three dimensions. We obtain accurate values of critical exponents λ and phi describing the scaling of fragmentation rate and the distribution of fragments' masses produced by a binary fragmentation. Our results for λ and phi show that the fragmentation rate is proportional to the size of mother cluster, and the scaling relation σ = 1 + λ - phi conjectured by Edwards et al. to be valid for all dimensions is satisfied in two and three dimensions, where σ is the crossover exponent of the average cluster number in percolation theory, which excludes the other scaling relations.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

Gracey, J. A.

2018-05-01

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

Magnetocaloric effect and critical field analysis in Eu substituted La0.7-xEuxSr0.3MnO3 (x = 0.0, 0.1, 0.2, 0.3) manganites

NASA Astrophysics Data System (ADS)

Vadnala, Sudharshan; Asthana, Saket

2018-01-01

In this study, we have investigated magnetic behavior, magnetocaloric effect and critical exponent analysis of La0.7-xEuxSr0.3MnO3 (x = 0.0, 0.1, 0.2, 0.3) manganites synthesized through solid state reaction route. The crystallographic data obtained from refinement of X-ray diffraction patterns reveal that crystal structure changes from rhombohedral (for x = 0.0) to orthorhombic (for x ≥ 0.1). The average ionic radius of A-site is decreased from 1.384 Å (for x = 0.0) to 1.360 Å (for x = 0.3) with Eu3+ substitution which in turn decreases the Mn-O-Mn bond angles. Magnetization measurements are performed in the vicinity of TC to determine magnetocaloric effect (MCE) and critical field behavior. The maximum magnetic entropy change (Δ SMmax) (for μ0ΔH = 6T) increases with the Eu3+ substitution from 3.88 J/kg K (for x = 0.0) to 5.03 J/kg K (for x = 0.3) at the transition temperature. The critical field behaviour of compounds was analysed using various methods such as modified Arrott plots, Kouvel-Fisher method and critical isotherm to determine critical temperature and critical exponents (β, γ and δ). The obtained critical exponents are in good accordance with scaling relation. The temperature dependence of the order parameter n, for different magnetic fields, is studied using the relation ΔSMαHn. The values of n are found to obey the Curie-Weiss law for temperatures above the transition temperature. The rescaled change in entropy data for all compounds collapses into the same universal curve, revealing a second order phase transition.

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

NASA Astrophysics Data System (ADS)

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.

Intrinsic pinning and the critical current scaling of clean epitaxial Fe(Se,Te) thin films

NASA Astrophysics Data System (ADS)

Iida, Kazumasa; Hänisch, Jens; Reich, Elke; Kurth, Fritz; Hühne, Ruben; Schultz, Ludwig; Holzapfel, Bernhard; Ichinose, Ataru; Hanawa, Masafumi; Tsukada, Ichiro; Schulze, Michael; Aswartham, Saicharan; Wurmehl, Sabine; Büchner, Bernd

2013-03-01

We report on the transport properties of clean, epitaxial Fe(Se,Te) thin films prepared on Fe-buffered MgO (001) single crystalline substrates by pulsed laser deposition. Near Tc a steep slope of the upper critical field for H||ab was observed (74.1 T/K), leading to a very short out-of-plane coherence length, ξc(0), of 0.2 nm, yielding 2ξc(0)≈0.4nm. This value is shorter than the interlayer distance (0.605 nm) between the Fe-Se(Te) planes, indicative of modulation of the superconducting order parameter along the c axis. An inverse correlation between the power law exponent N of the electric field-current density(E-J) curve and the critical current density Jc has been observed at 4 K, when the orientation of H was close to the ab plane. These results prove the presence of intrinsic pinning in Fe(Se,Te). A successful scaling of the angular dependent Jc and the corresponding exponent N can be realized by the anisotropic Ginzburg Landau approach with appropriate Γ values 2˜3.5. The temperature dependence of Γ behaves almost identically to that of the penetration depth anisotropy.

Many-body localization in Ising models with random long-range interactions

NASA Astrophysics Data System (ADS)

Li, Haoyuan; Wang, Jia; Liu, Xia-Ji; Hu, Hui

2016-12-01

We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, Vi j∝|i-j |-α , where the exponent of the interaction range α can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing α , the critical exponent experiences a sharp increase at about αc≃1.2 and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For α <αc , we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for α >αc , the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.

Accurate estimates of 3D Ising critical exponents using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

An analysis of the critical behavior of the three-dimensional Ising model using the coherent-anomaly method (CAM) is presented. Various sources of errors in CAM estimates of critical exponents are discussed, and an improved scheme for the CAM data analysis is tested. Using a set of mean-field type approximations based on the variational series expansion approach, accuracy comparable to the most precise conventional methods has been achieved. Our results for the critical exponents are given by α = 0.108(5), β = 0.327(4), γ = 1.237(4) and δ = 4.77(5).

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

NASA Astrophysics Data System (ADS)

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.

Percolation of the site random-cluster model by Monte Carlo method

NASA Astrophysics Data System (ADS)

Wang, Songsong; Zhang, Wanzhou; Ding, Chengxiang

2015-08-01

We propose a site random-cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the Swendsen-Wang methods to design a highly efficient cluster algorithm with a small critical slowing-down phenomenon. To verify whether or not it is consistent with the bond random-cluster model, we measure several quantities, such as the wrapping probability Re, the percolating cluster density P∞, and the magnetic susceptibility per site χp, as well as two exponents, such as the thermal exponent yt and the fractal dimension yh of the percolating cluster. We find that for different exponents of cluster weight q =1.5 , 2, 2.5 , 3, 3.5 , and 4, the numerical estimation of the exponents yt and yh are consistent with the theoretical values. The universalities of the site random-cluster model and the bond random-cluster model are completely identical. For larger values of q , we find obvious signatures of the first-order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site. Our results are helpful for the understanding of the percolation of traditional statistical models.

Hyperscaling breakdown and Ising spin glasses: The Binder cumulant

NASA Astrophysics Data System (ADS)

Lundow, P. H.; Campbell, I. A.

2018-02-01

Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by Schwartz (1991) that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region.

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

NASA Astrophysics Data System (ADS)

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 .

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

PubMed

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 D_{u}=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 d_{f}, which is found to be 1.50±0.02≈3/2=d_{f}^{GFF}.

Maximum Rate of Growth of Enstrophy in Solutions of the Fractional Burgers Equation

NASA Astrophysics Data System (ADS)

Yun, Dongfang; Protas, Bartosz

2018-02-01

This investigation is a part of a research program aiming to characterize the extreme behavior possible in hydrodynamic models by analyzing the maximum growth of certain fundamental quantities. We consider here the rate of growth of the classical and fractional enstrophy in the fractional Burgers equation in the subcritical and supercritical regimes. Since solutions to this equation exhibit, respectively, globally well-posed behavior and finite-time blowup in these two regimes, this makes it a useful model to study the maximum instantaneous growth of enstrophy possible in these two distinct situations. First, we obtain estimates on the rates of growth and then show that these estimates are sharp up to numerical prefactors. This is done by numerically solving suitably defined constrained maximization problems and then demonstrating that for different values of the fractional dissipation exponent the obtained maximizers saturate the upper bounds in the estimates as the enstrophy increases. We conclude that the power-law dependence of the enstrophy rate of growth on the fractional dissipation exponent has the same global form in the subcritical, critical and parts of the supercritical regime. This indicates that the maximum enstrophy rate of growth changes smoothly as global well-posedness is lost when the fractional dissipation exponent attains supercritical values. In addition, nontrivial behavior is revealed for the maximum rate of growth of the fractional enstrophy obtained for small values of the fractional dissipation exponents. We also characterize the structure of the maximizers in different cases.

Critical exponents of the explosive percolation transition

NASA Astrophysics Data System (ADS)

da Costa, R. A.; Dorogovtsev, S. N.; Goltsev, A. V.; Mendes, J. F. F.

2014-04-01

In a new type of percolation phase transition, which was observed in a set of nonequilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential merging of small components and delays the emergence of the percolation cluster. First simulations led to a conclusion that a percolation cluster in this irreversible process is born discontinuously, by a discontinuous phase transition, which results in the term "explosive percolation transition." We have shown that this transition is actually continuous (second order) though with an anomalously small critical exponent of the percolation cluster. Here we propose an efficient numerical method enabling us to find the critical exponents and other characteristics of this second-order transition for a representative set of explosive percolation models with different number of choices. The method is based on gluing together the numerical solutions of evolution equations for the cluster size distribution and power-law asymptotics. For each of the models, with high precision, we obtain critical exponents and the critical point.

Anisotropic Weyl symmetry and cosmology

NASA Astrophysics Data System (ADS)

Moon, Taeyoon; Oh, Phillial; Sohn, Jongsu

2010-11-01

We construct an anisotropic Weyl invariant theory in the ADM formalism and discuss its cosmological consequences. It extends the original anisotropic Weyl invariance of Hořava-Lifshitz gravity using an extra scalar field. The action is invariant under the anisotropic transformations of the space and time metric components with an arbitrary value of the critical exponent z. One of the interesting features is that the cosmological constant term maintains the anisotropic symmetry for z = -3. We also include the cosmological fluid and show that it can preserve the anisotropic Weyl invariance if the equation of state satisfies P = zρ/3. Then, we study cosmology of the Einstein-Hilbert-anisotropic Weyl (EHaW) action including the cosmological fluid, both with or without anisotropic Weyl invariance. The correlation of the critical exponent z and the equation of state parameter bar omega provides a new perspective of the cosmology. It is also shown that the EHaW action admits a late time accelerating universe for an arbitrary value of z when the anisotropic conformal invariance is broken, and the anisotropic conformal scalar field is interpreted as a possible source of dark energy.

Observations in Fracture Toughness Testing of Glasses and Optical Ceramics

NASA Technical Reports Server (NTRS)

Salem, Jon

2017-01-01

Fracture toughness is a critical structural design parameter and an excellent metrics to rank materials. Itdetermines fracture strength by way of the flaws, both inherent and induced, and defines the endpoint of the slow crackgrowth curve. The fracture toughness of structural and optical ceramics, and glasses as measured by several techniques is compared. When good metrology is employed, the results are very comparable with two exceptions: materials exhibiting crack growth resistance and those with a low SCG exponents. For materials with R-curves, the result is a function of extension and can be minimized with short cracks. For materials with low SCG exponents, such as glasses, elimination of the corrosive media andor increasing the stress intensity rate minimizes effects. A summary of values is given, and it appears that highly modified glasses exhibit lower fracture toughness and slow crack growth exponent than high purity glasses such as fused silica.

Effective theory and breakdown of conformal symmetry in a long-range quantum chain

NASA Astrophysics Data System (ADS)

Lepori, L.; Vodola, D.; Pupillo, G.; Gori, G.; Trombettoni, A.

2016-11-01

We deal with the problem of studying the symmetries and the effective theories of long-range models around their critical points. A prominent issue is to determine whether they possess (or not) conformal symmetry (CS) at criticality and how the presence of CS depends on the range of the interactions. To have a model, both simple to treat and interesting, where to investigate these questions, we focus on the Kitaev chain with long-range pairings decaying with distance as power-law with exponent α. This is a quadratic solvable model, yet displaying non-trivial quantum phase transitions. Two critical lines are found, occurring respectively at a positive and a negative chemical potential. Focusing first on the critical line at positive chemical potential, by means of a renormalization group approach we derive its effective theory close to criticality. Our main result is that the effective action is the sum of two terms: a Dirac action SD, found in the short-range Ising universality class, and an "anomalous" CS breaking term SAN. While SD originates from low-energy excitations in the spectrum, SAN originates from the higher energy modes where singularities develop, due to the long-range nature of the model. At criticality SAN flows to zero for α > 2, while for α < 2 it dominates and determines the breakdown of the CS. Out of criticality SAN breaks, in the considered approximation, the effective Lorentz invariance (ELI) for every finite α. As α increases such ELI breakdown becomes less and less pronounced and in the short-range limit α → ∞ the ELI is restored. In order to test the validity of the determined effective theory, we compared the two-fermion static correlation functions and the von Neumann entropy obtained from them with the ones calculated on the lattice, finding agreement. These results explain two observed features characteristic of long-range models, the hybrid decay of static correlation functions within gapped phases and the area-law violation for the von Neumann entropy. The proposed scenario is expected to hold in other long-range models displaying quasiparticle excitations in ballistic regime. From the effective theory one can also see that new phases emerge for α < 1. Finally we show that at every finite α the critical exponents, defined as for the short-range (α → ∞) model, are not altered. This also shows that the long-range paired Kitaev chain provides an example of a long-range model in which the value of α where the CS is broken does not coincide with the value at which the critical exponents start to differ from the ones of the corresponding short-range model. At variance, for the second critical line, having negative chemical potential, only SAN (SD) is present for 1 < α < 2 (for α > 2). Close to this line, where the minimum of the spectrum coincides with the momentum where singularities develop, the critical exponents change where CS is broken.

Critical short-time dynamics in a system with interacting static and diffusive populations

NASA Astrophysics Data System (ADS)

Argolo, C.; Quintino, Yan; Gleria, Iram; Lyra, M. L.

2012-01-01

We study the critical short-time dynamical behavior of a one-dimensional model where diffusive individuals can infect a static population upon contact. The model presents an absorbing phase transition from an active to an inactive state. Previous calculations of the critical exponents based on quasistationary quantities have indicated an unusual crossover from the directed percolation to the diffusive contact process universality classes. Here we show that the critical exponents governing the slow short-time dynamic evolution of several relevant quantities, including the order parameter, its relative fluctuations, and correlation function, reinforce the lack of universality in this model. Accurate estimates show that the critical exponents are distinct in the regimes of low and high recovery rates.

Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks.

PubMed

Lombardi, F; Herrmann, H J; de Arcangelis, L

2017-04-01

The 1/f-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitutes evidence of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here, we study the relationship between network inhibition and the scaling exponent β of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality. We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value β = 1 for a percentage of about 30%. More specifically, β is close to 2, namely, Brownian noise, for purely excitatory networks and decreases towards values in the interval [1, 1.4] as the percentage of inhibitory synapses ranges between 20% and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.

Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks

NASA Astrophysics Data System (ADS)

Lombardi, F.; Herrmann, H. J.; de Arcangelis, L.

2017-04-01

The 1/f-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitutes evidence of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here, we study the relationship between network inhibition and the scaling exponent β of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality. We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value β = 1 for a percentage of about 30%. More specifically, β is close to 2, namely, Brownian noise, for purely excitatory networks and decreases towards values in the interval [1, 1.4] as the percentage of inhibitory synapses ranges between 20% and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.

Adsorption of a single polymer chain on a surface: Effects of the potential range

NASA Astrophysics Data System (ADS)

Klushin, Leonid I.; Polotsky, Alexey A.; Hsu, Hsiao-Ping; Markelov, Denis A.; Binder, Kurt; Skvortsov, Alexander M.

2013-02-01

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value Uc corresponding to the adsorption transition scales as W-1/ν, where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory Uc≈((π2)/(24))(W+1/2)-2 and in the best-fit equation for the MC simulation data Uc=0.585(W+1/2)-5/3. Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NUc,U/Uc). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value /=0.320±0.003 only at N˜5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent ϕeff(N). Strong corrections to scaling of order N-0.5 are observed, and the extrapolated value ϕ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of ϕeff(N) were identified as the asymptotic value for the crossover exponent.

Majority-Vote Model with Heterogeneous Agents on Square Lattice

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2013-11-01

We study a nonequilibrium model with up-down symmetry and a noise parameter q known as majority-vote model (MVM) of [M. J. Oliveira, J. Stat. Phys.66, 273 (1992)] with heterogeneous agents on square lattice (SL). By Monte Carlo (MC) simulations and finite-size scaling relations, the critical exponents β/ν, γ/ν and 1/ν and points qc and U* are obtained. After extensive simulations, we obtain β/ν = 0.35(1), γ/ν = 1.23(8) and 1/ν = 1.05(5). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.1589(4) and U* = 0.604(7). Within the error bars, the exponents obey the relation 2β/ν + γ/ν = 2 and the results presented here demonstrate that the MVM heterogeneous agents belongs to a different universality class than the nonequilibrium MVM with homogeneous agents on SL.

Majority-Vote Model on Opinion-Dependent Network

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2013-09-01

We study a nonequilibrium model with up-down symmetry and a noise parameter q known as majority-vote model (MVM) of Oliveira 1992 on opinion-dependent network or Stauffer-Hohnisch-Pittnauer (SHP) networks. By Monte Carlo (MC) simulations and finite-size scaling relations the critical exponents β/ν, γ/ν and 1/ν and points qc and U* are obtained. After extensive simulations, we obtain β/ν = 0.230(3), γ/ν = 0.535(2) and 1/ν = 0.475(8). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.166(3) and U* = 0.288(3). Within the error bars, the exponents obey the relation 2β/ν + γ/ν = 1 and the results presented here demonstrate that the MVM belongs to a different universality class than the equilibrium Ising model on SHP networks, but to the same class as majority-vote models on some other networks.

One-dimensional long-range percolation: A numerical study

NASA Astrophysics Data System (ADS)

Gori, G.; Michelangeli, M.; Defenu, N.; Trombettoni, A.

2017-07-01

In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C /rd +σ , where r is the distance length between distinct sites and d =1 . We introduce and test an order-N Monte Carlo algorithm and we determine as a function of σ the critical value Cc at which percolation occurs. The critical exponents in the range 0 <σ <1 are reported. Our analysis is in agreement, up to a numerical precision ≈10-3 , with the mean-field result for the anomalous dimension η =2 -σ , showing that there is no correction to η due to correlation effects. The obtained values for Cc are compared with a known exact bound, while the critical exponent ν is compared with results from mean-field theory, from an expansion around the point σ =1 and from the ɛ -expansion used with the introduction of a suitably defined effective dimension deff relating the long-range model with a short-range one in dimension deff. We finally present a formulation of our algorithm for bond percolation on general graphs, with order N efficiency on a large class of graphs including short-range percolation and translationally invariant long-range models in any spatial dimension d with σ >0 .

Influence of enteric-coated lactose on the release profile of 4-aminopyridine from HPMC matrix tablets.

PubMed

Martínez-González, Ilona; Villafuerte-Robles, Leopoldo

2004-01-01

A weakly basic experimental drug, 4-aminopyridine, was taken as a model to study the influence of enteric-coated lactose (EL) on the release profile from hydroxypropyl methylcellulose matrices. Powder mixtures were wet-granulated with water. The dried granulation was compressed with a hydraulic press at 85 MPa. Dissolution studies were made using HCl 0.1 N and then phosphate buffer pH 7.4. Dissolution curves were described by M(t)/M(inf) = k*t(N). A trend toward increasing exponent (n) and decreasing release constant (k) values is observed with increasing EL concentrations up to 9%; this is attributed to an increasing obstruction of the diffusion path by isolated EL particles that are insoluble in HCl and are surrounded by a water-filled space. After a critical EL concentration, the water-filled spaces surrounding EL particles percolate, producing the opposite effect, increasing the release constant and decreasing the exponent (n) values as the EL proportion increases from 10% to 50%. EL particles (2% to 9%) decrease the drug and water transport in matrices dissolving in HCl. Thereafter, at pH 7.4, the pores formed by dissolution of EL particles produce the opposite. Both processes contribute to flattening the release profile. Release profiles with decreasing release constant values show a logarithmic trend toward increasing values of the exponent (n), changing from diffusion toward relaxation-erosion-controlled processes.

Strong-coupling analysis of two-dimensional O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campostrini, M.; Pelissetto, A.; Rossi, P.

1996-09-01

The critical behavior of two-dimensional (2D) O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices is investigated by an analysis of the strong-coupling expansion of the two-point fundamental Green{close_quote}s function {ital G}({ital x}), calculated up to 21st order on the square lattice, 15th order on the triangular lattice, and 30th order on the honeycomb lattice. For {ital N}{lt}2 the critical behavior is of power-law type, and the exponents {gamma} and {nu} extracted from our strong-coupling analysis confirm exact results derived assuming universality with solvable solid-on-solid models. At {ital N}=2, i.e., for the 2D {ital XY} model,more » the results from all lattices considered are consistent with the Kosterlitz-Thouless exponential approach to criticality, characterized by an exponent {sigma}=1/2, and with universality. The value {sigma}=1/2 is confirmed within an uncertainty of few percent. The prediction {eta}=1/4 is also roughly verified. For various values of {ital N}{le}2, we determine some ratios of amplitudes concerning the two-point function {ital G}({ital x}) in the critical limit of the symmetric phase. This analysis shows that the low-momentum behavior of {ital G}({ital x}) in the critical region is essentially Gaussian at all values of {ital N}{le}2. Exact results for the long-distance behavior of {ital G}({ital x}) when {ital N}=1 (Ising model in the strong-coupling phase) confirm this statement. {copyright} {ital 1996 The American Physical Society.}« less

Critical dynamic approach to stationary states in complex systems

NASA Astrophysics Data System (ADS)

Rozenfeld, A. F.; Laneri, K.; Albano, E. V.

2007-04-01

A dynamic scaling Ansatz for the approach to stationary states in complex systems is proposed and tested by means of extensive simulations applied to both the Bak-Sneppen (BS) model, which exhibits robust Self-Organised Critical (SOC) behaviour, and the Game of Life (GOL) of J. Conway, whose critical behaviour is under debate. Considering the dynamic scaling behaviour of the density of sites (ρ(t)), it is shown that i) by starting the dynamic measurements with configurations such that ρ(t=0) →0, one observes an initial increase of the density with exponents θ= 0.12(2) and θ= 0.11(2) for the BS and GOL models, respectively; ii) by using initial configurations with ρ(t=0) →1, the density decays with exponents δ= 0.47(2) and δ= 0.28(2) for the BS and GOL models, respectively. It is also shown that the temporal autocorrelation decays with exponents Ca = 0.35(2) (Ca = 0.35(5)) for the BS (GOL) model. By using these dynamically determined critical exponents and suitable scaling relationships, we also obtain the dynamic exponents z = 2.10(5) (z = 2.10(5)) for the BS (GOL) model. Based on this evidence we conclude that the dynamic approach to stationary states of the investigated models can be described by suitable power-law functions of time with well-defined exponents.

Critical behavior of the quasi-two-dimensional weak itinerant ferromagnet trigonal chromium telluride Cr 0.62 Te

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yu; Petrovic, C.

The critical properties of flux-grown single-crystalline quasi-two-dimensional weak itinerant ferromagnet Cr 0.62 Te were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents β = 0.315 ( 7 ) with a critical temperature T c = 230.6 ( 3 ) K and γ = 1.81 ( 2 ) with T c = 229.1 ( 1 ) K are obtained by the Kouvel-Fisher method whereas δ = 6.35 ( 4 ) is obtained by a critical isotherm analysis at T c = 230 K. With these obtained exponents, the magnetization-field-temperature curves collapse into two independentmore » curves following a single scaling equation M | T-T c/T c| -β = f ± ( H |T-T c/T c| -β δ ) around T c , suggesting the reliability of the obtained exponents. Additionally, the determined exponents of Cr 0.62 Te exhibit an Ising-like behavior with a change from short-range order to long-range order in the nature of magnetic interaction and with an extension from two to three dimensions on cooling through T c.« less

Critical behavior of the quasi-two-dimensional weak itinerant ferromagnet trigonal chromium telluride Cr 0.62 Te

DOE PAGES

Liu, Yu; Petrovic, C.

2017-10-09

The critical properties of flux-grown single-crystalline quasi-two-dimensional weak itinerant ferromagnet Cr 0.62 Te were investigated by bulk dc magnetization around the paramagnetic to ferromagnetic phase transition. Critical exponents β = 0.315 ( 7 ) with a critical temperature T c = 230.6 ( 3 ) K and γ = 1.81 ( 2 ) with T c = 229.1 ( 1 ) K are obtained by the Kouvel-Fisher method whereas δ = 6.35 ( 4 ) is obtained by a critical isotherm analysis at T c = 230 K. With these obtained exponents, the magnetization-field-temperature curves collapse into two independentmore » curves following a single scaling equation M | T-T c/T c| -β = f ± ( H |T-T c/T c| -β δ ) around T c , suggesting the reliability of the obtained exponents. Additionally, the determined exponents of Cr 0.62 Te exhibit an Ising-like behavior with a change from short-range order to long-range order in the nature of magnetic interaction and with an extension from two to three dimensions on cooling through T c.« less

Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces

NASA Astrophysics Data System (ADS)

Odavić, Jovan; Mali, Petar; Tekić, Jasmina; Pantić, Milan; Pavkov-Hrvojević, Milica

2017-06-01

Dynamics of driven dissipative Frenkel-Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces is studied by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to examine system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is the standard sinusoidal one, calculation of the largest Lyapunov exponent offers a more sensitive way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and the critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points out an advantage of this technique since by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the dynamics of the system when driving forces are applied. Additionally, the system is shown to be not chaotic even in the case of incommensurate structures and large amplitudes of external force, which is a consequence of overdampness of the model and the Middleton's no passing rule.

Superfluid-insulator transition in a disordered two-dimensional quantum rotor model with random on-site interactions

NASA Astrophysics Data System (ADS)

An, Taeyang; Cha, Min-Chul

2013-03-01

We study the superfluid-insulator quantum phase transition in a disordered two-dimensional quantum rotor model with random on-site interactions in the presence of particle-hole symmetry. Via worm-algorithm Monte Carlo calculations of superfluid density and compressibility, we find the dynamical critical exponent z ~ 1 . 13 (2) and the correlation length critical exponent 1 / ν ~ 1 . 1 (1) . These exponents suggest that the insulating phase is a incompressible Mott glass rather than a Bose glass.

Self-organized dynamics in local load-sharing fiber bundle models.

PubMed

Biswas, Soumyajyoti; Chakrabarti, Bikas K

2013-10-01

We study the dynamics of a local load-sharing fiber bundle model in two dimensions under an external load (which increases with time at a fixed slow rate) applied at a single point. Due to the local load-sharing nature, the redistributed load remains localized along the boundary of the broken patch. The system then goes to a self-organized state with a stationary average value of load per fiber along the (increasing) boundary of the broken patch (damaged region) and a scale-free distribution of avalanche sizes and other related quantities are observed. In particular, when the load redistribution is only among nearest surviving fiber(s), the numerical estimates of the exponent values are comparable with those of the Manna model. When the load redistribution is uniform along the patch boundary, the model shows a simple mean-field limit of this self-organizing critical behavior, for which we give analytical estimates of the saturation load per fiber values and avalanche size distribution exponent. These are in good agreement with numerical simulation results.

Self-organized criticality in a cold plasma

NASA Astrophysics Data System (ADS)

Alex, Prince; Carreras, Benjamin Andres; Arumugam, Saravanan; Sinha, Suraj Kumar

2017-12-01

We present direct evidence for the existence of self-organized critical behavior in cold plasma. A multiple anodic double layer structure generated in a double discharge plasma setup shows critical behavior for the anode bias above a threshold value. Analysis of the floating potential fluctuations reveals the existence of long-range time correlations and power law behavior in the tail of the probability distribution function of the fluctuations. The measured Hurst exponent and the power law tail in the rank function are strong indication of the self-organized critical behavior of the system and hence provide a condition under which complexities arise in cold plasma.

Scientific Objectives of the Critical Viscosity Experiment

NASA Technical Reports Server (NTRS)

Berg, R. F.; Moldover, M. R.

1993-01-01

In microgravity, the Critical Viscosity Experiment will measure the viscosity of xenon 15 times closer to the critical point than is possible on earth. The results are expected to include the first direct observation of the predicted power-law divergence of viscosity in a pure fluid and they will test calculations of the value of the exponent associated with the divergence. The results, when combined with Zeno's decay-rate data, will strengthen the test of mode coupling theory. Without microgravity viscosity data, the Zeno test will require an extrapolation of existing 1-g viscosity data by as much as factor of 100 in reduced temperature. By necessity, the extrapolation would use an incompletely verified theory of viscosity crossover. With the microgravity viscosity data, the reliance on crossover models will be negligible allowing a more reliable extrapolation. During the past year, new theoretical calculations for the viscosity exponent finally achieved consistency with the best experimental data for pure fluids. This report gives the justification for the proposed microgravity Critical Viscosity Experiment in this new context. This report also combines for the first time the best available light scattering data with our recent viscosity data to demonstrate the current status of tests of mode coupling theory.

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

NASA Astrophysics Data System (ADS)

Minati, Ludovico; de Candia, Antonio; Scarpetta, Silvia

2016-07-01

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.

Static critical behavior of the q-states Potts model: High-resolution entropic study

NASA Astrophysics Data System (ADS)

Caparica, A. A.; Leão, Salviano A.; DaSilva, Claudio J.

2015-11-01

Here we report a precise computer simulation study of the static critical properties of the two-dimensional q-states Potts model using very accurate data obtained from a modified Wang-Landau (WL) scheme proposed by Caparica and Cunha-Netto (2012). This algorithm is an extension of the conventional WL sampling, but the authors changed the criterion to update the density of states during the random walk and established a new procedure to windup the simulation run. These few changes have allowed a more precise microcanonical averaging which is essential to a reliable finite-size scaling analysis. In this work we used this new technique to determine the static critical exponents β, γ, and ν, in an unambiguous fashion. The static critical exponents were determined as β = 0.10811(77) , γ = 1.4459(31) , and ν = 0.8197(17) , for the q = 3 case, and β = 0.0877(37) , γ = 1.3161(69) , and ν = 0.7076(10) , for the q = 4 Potts model. A comparison of the present results with conjectured values and with those obtained from other well established approaches strengthens this new way of performing WL simulations.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: ludovico.minati@ifj.edu; Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Kraków; Candia, Antonio de

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-ordermore » 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.« less

Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully nonuniversal

NASA Astrophysics Data System (ADS)

Krčmár, Roman; Šamaj, Ladislav

2018-01-01

The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents η and δ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents ηe and δe which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.

Indications for a critical point in the phase diagram for hot and dense nuclear matter

NASA Astrophysics Data System (ADS)

Lacey, Roy A.

2016-12-01

Two-pion interferometry measurements are studied for a broad range of collision centralities in Au+Au (√{sNN} = 7.7- 200 GeV) and Pb+Pb (√{sNN} = 2.76 TeV) collisions. They indicate non-monotonic excitation functions for the Gaussian emission source radii difference (Rout -Rside), suggestive of reaction trajectories which spend a fair amount of time near a soft point in the equation of state (EOS) that coincides with the critical end point (CEP). A Finite-Size Scaling (FSS) analysis of these excitation functions, provides further validation tests for the CEP. It also indicates a second order phase transition at the CEP, and the values Tcep ∼ 165 MeV and μBcep ∼ 95 MeV for its location in the (T ,μB)-plane of the phase diagram. The static critical exponents (ν ≈ 0.66 and γ ≈ 1.2) extracted via the same FSS analysis, place this CEP in the 3D Ising model (static) universality class. A Dynamic Finite-Size Scaling analysis of the excitation functions, gives the estimate z ∼ 0.87 for the dynamic critical exponent, suggesting that the associated critical expansion dynamics is dominated by the hydrodynamic sound mode.

Critical behavior of modulus of gel

NASA Astrophysics Data System (ADS)

Tokita, Masayuki; Niki, Ryoya; Hikichi, Kunio

1985-09-01

The critical behavior of the shear modulus of casein gel is studied. The shear modulus of casein gel scales with the conductivity exponent in the immediate vicinity of the sol-gel transition point. The asymptotic behavior of the modulus in the region far above the transition point is governed by a different exponent which is much larger than the conductivity exponent. These results are explainable by the crossover behavior of the percolation process. This study shows that the gelation of the casein micelle solution is a realization of the percolation process.

Reversible island nucleation and growth with anomalous diffusion

NASA Astrophysics Data System (ADS)

Sabbar, Ehsan H.; Amar, Jacques G.

2017-10-01

Motivated by recent experiments on submonolayer organic film growth with anomalous diffusion, a general rate-equation (RE) theory of submonolayer island nucleation and growth was developed (Amar and Semaan, 2016) [23], which takes into account the critical island-size i, island fractal dimension df, substrate dimension d, and diffusion exponent μ, and good agreement with simulations was found for the case of irreversible growth corresponding to a critical island-size i = 1 with d = 2 . However, since many experiments correspond to a critical island-size larger than 1, it is of interest to determine if the RE predictions also hold in the case of reversible island nucleation with anomalous diffusion. Here we present the results of simulations of submonolayer growth with i = 2 (d = 2) which were carried out for both the case of superdiffusion (μ > 1) and subdiffusion (μ < 1) as well as for both ramified islands (df ≃ 2) and point-islands (df = ∞) . In the case of superdiffusion, corresponding to 'hot' freshly deposited monomers, excellent agreement is obtained with the predictions of the generalized RE theory for the exponents χ(μ) and χ1(μ) which describe the dependence of the island and monomer densities at fixed coverage on deposition rate F. In addition, the exponents do not depend on whether or not monomers remain superdiffusive or are thermalized (e.g. undergo regular diffusion) after detaching from a dimer. However, we also find that, as was previously found in the case of irreversible growth, the exponent χ only approaches its asymptotic value logarithmically with increasing 1/F. This result has important implications for the interpretation of experiments. Good agreement with the RE theory is also found in the case of subdiffusion for point-islands. However, in the case of ramified islands with subdiffusion and i = 2 , the exponents are significantly higher than predicted due to the fact that monomer capture dominates in the nucleation regime. A modified RE theory which takes this into account is presented, and excellent agreement is found with our simulations.

Coexistence of short- and long-range ferromagnetic order in nanocrystalline Fe2Mn1-xCuxAl (x=0.0, 0.1 and 0.3) synthesized by high-energy ball milling

NASA Astrophysics Data System (ADS)

Thanh, Tran Dang; Nanto, Dwi; Tuyen, Ngo Thi Uyen; Nan, Wen-Zhe; Yu, YiKyung; Tartakovsky, Daniel M.; Yu, S. C.

2015-11-01

In this work, we prepared nanocrystalline Fe2Mn1-xCuxAl (x=0.0, 0.1 and 0.3) powders by the high energy ball milling technique, and then studied their critical properties. Our analysis reveals that the increase of Cu-doping concentration (up to x=0.3) in these powders leads to a gradual increase of the ferromagnetic-paramagnetic transition temperature from 406 to 452 K. The Banerjee criterion suggests that all the samples considered undergo a second-order phase transition. A modified Arrott plot and scaling analysis indicate that the critical exponents (β=0.419 and 0.442, γ=1.082 and 1.116 for x=0.0 and 0.1, respectively) are located in between those expected for the 3D-Heisenberg and the mean-field models; the values of β=0.495 and γ=1.046 for x=0.3 sample are very close to those of the mean-field model. These features reveal the coexistence of the short- and long-range ferromagnetic order in the nanocrystalline Fe2Mn1-xCuxAl powders. Particularly, as the concentration of Cu increases, values of the critical exponent shift towards those of the mean-field model. Such results prove the Cu doping favors establishing a long-range ferromagnetic order.

Scaling behavior of an airplane-boarding model.

PubMed

Brics, Martins; Kaupužs, Jevgenijs; Mahnke, Reinhard

2013-04-01

An airplane-boarding model, introduced earlier by Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)], is studied with the aim of determining precisely its asymptotic power-law scaling behavior for a large number of passengers N. Based on Monte Carlo simulation data for very large system sizes up to N=2(16)=65536, we have analyzed numerically the scaling behavior of the mean boarding time and other related quantities. In analogy with critical phenomena, we have used appropriate scaling Ansätze, which include the leading term as some power of N (e.g., [proportionality]N(α) for ), as well as power-law corrections to scaling. Our results clearly show that α=1/2 holds with a very high numerical accuracy (α=0.5001±0.0001). This value deviates essentially from α=/~0.69, obtained earlier by Frette and Hemmer from data within the range 2≤N≤16. Our results confirm the convergence of the effective exponent α(eff)(N) to 1/2 at large N as observed by Bernstein. Our analysis explains this effect. Namely, the effective exponent α(eff)(N) varies from values about 0.7 for small system sizes to the true asymptotic value 1/2 at N→∞ almost linearly in N(-1/3) for large N. This means that the variation is caused by corrections to scaling, the leading correction-to-scaling exponent being θ≈1/3. We have estimated also other exponents: ν=1/2 for the mean number of passengers taking seats simultaneously in one time step, β=1 for the second moment of t(b), and γ≈1/3 for its variance.

Adsorption of a single polymer chain on a surface: effects of the potential range.

PubMed

Klushin, Leonid I; Polotsky, Alexey A; Hsu, Hsiao-Ping; Markelov, Denis A; Binder, Kurt; Skvortsov, Alexander M

2013-02-01

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth U and width W is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value U(c) corresponding to the adsorption transition scales as W(-1/ν), where the exponent ν=1/2 for ideal chains and ν≈3/5 for self-avoiding walks. Lattice corrections for finite W are incorporated in the analytical prediction of the ideal chain theory U(c)≈(π(2)/24)(W+1/2)(-2) and in the best-fit equation for the MC simulation data U(c)=0.585(W+1/2)(-5/3). Tail, loop, and train distributions at the critical point are evaluated by MC simulations for 1≤W≤10 and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction θ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: θ(N,U,W)=θ(NU(c),U/U(c)). By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value /=0.320±0.003 only at N~5000. Finite-N corrections for this ratio turn out to be of the opposite sign for W=1 and for W≥2. We also study the N dependence of the apparent crossover exponent φ(eff)(N). Strong corrections to scaling of order N(-0.5) are observed, and the extrapolated value φ=0.483±0.003 is found for all values of W. The strong correction to scaling effects found here explain why for smaller values of N, as used in most previous work, misleadingly large values of φ(eff)(N) were identified as the asymptotic value for the crossover exponent.

Complex Critical Exponents for Percolation Transitions in Josephson-Junction Arrays, Antiferromagnets, and Interacting Bosons

NASA Astrophysics Data System (ADS)

Fernandes, Rafael M.; Schmalian, Jörg

2011-02-01

We show that the critical behavior of the XY quantum-rotor model undergoing a percolation transition is dramatically affected by its topological Berry phase 2πρ. In particular, for irrational ρ, its low-energy excitations emerge as spinless fermions with fractal spectrum. As a result, critical properties not captured by the usual Ginzburg-Landau-Wilson description of phase transitions arise, such as complex critical exponents, log-periodic oscillations and dynamically broken scale invariance.

Coherent forward scattering as a signature of Anderson metal-insulator transitions

NASA Astrophysics Data System (ADS)

Ghosh, Sanjib; Miniatura, Christian; Cherroret, Nicolas; Delande, Dominique

2017-04-01

We show that the coherent forward scattering (CFS) interference peak amplitude sharply jumps from zero to a finite value upon crossing a metal-insulator transition. Extensive numerical simulations reveal that the CFS peak contrast obeys the one-parameter scaling hypothesis and gives access to the critical exponents of the transition. We also discover that the critical CFS peak directly controls the spectral compressibility at the transition where eigenfunctions are multifractal, and we demonstrate the universality of this property with respect to various types of disorder.

Critical behavior in graphene with Coulomb interactions.

PubMed

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.

Inhibitory neurons promote robust critical firing dynamics in networks of integrate-and-fire neurons.

PubMed

Lu, Zhixin; Squires, Shane; Ott, Edward; Girvan, Michelle

2016-12-01

We study the firing dynamics of a discrete-state and discrete-time version of an integrate-and-fire neuronal network model with both excitatory and inhibitory neurons. When the integer-valued state of a neuron exceeds a threshold value, the neuron fires, sends out state-changing signals to its connected neurons, and returns to the resting state. In this model, a continuous phase transition from non-ceaseless firing to ceaseless firing is observed. At criticality, power-law distributions of avalanche size and duration with the previously derived exponents, -3/2 and -2, respectively, are observed. Using a mean-field approach, we show analytically how the critical point depends on model parameters. Our main result is that the combined presence of both inhibitory neurons and integrate-and-fire dynamics greatly enhances the robustness of critical power-law behavior (i.e., there is an increased range of parameters, including both sub- and supercritical values, for which several decades of power-law behavior occurs).

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

NASA Astrophysics Data System (ADS)

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.

Stock markets and criticality in the current economic crisis

NASA Astrophysics Data System (ADS)

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.

Roughness exponent in two-dimensional percolation, Potts model, and clock model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Redinz, Jose Arnaldo; Martins, Marcelo Lobato

We present a numerical study of the self-affine profiles obtained from configurations of the q-state Potts (with q=2,3, and 7) and p=10 clock models as well as from the occupation states for site percolation on the square lattice. The first and second order static phase transitions of the Potts model are located by a sharp change in the value of the roughness exponent {alpha} characterizing those profiles. The low temperature phase of the Potts model corresponds to flat ({alpha}{approx_equal}1) profiles, whereas its high temperature phase is associated with rough ({alpha}{approx_equal}0.5) ones. For the p=10 clock model, in addition to themore » flat (ferromagnetic) and rough (paramagnetic) profiles, an intermediate rough (0.5{lt}{alpha}{lt}1) phase{emdash}associated with a soft spin-wave one{emdash}is observed. Our results for the transition temperatures in the Potts and clock models are in agreement with the static values, showing that this approach is able to detect the phase transitions in these models directly from the spin configurations, without any reference to thermodynamical potentials, order parameters, or response functions. Finally, we show that the roughness exponent {alpha} is insensitive to geometric critical phenomena.« less

Finite-size scaling in the system of coupled oscillators with heterogeneity in coupling strength

NASA Astrophysics Data System (ADS)

Hong, Hyunsuk

2017-07-01

We consider a mean-field model of coupled phase oscillators with random heterogeneity in the coupling strength. The system that we investigate here is a minimal model that contains randomness in diverse values of the coupling strength, and it is found to return to the original Kuramoto model [Y. Kuramoto, Prog. Theor. Phys. Suppl. 79, 223 (1984), 10.1143/PTPS.79.223] when the coupling heterogeneity disappears. According to one recent paper [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122], when the natural frequency of the oscillator in the system is "deterministically" chosen, with no randomness in it, the system is found to exhibit the finite-size scaling exponent ν ¯=5 /4 . Also, the critical exponent for the dynamic fluctuation of the order parameter is found to be given by γ =1 /4 , which is different from the critical exponents for the Kuramoto model with the natural frequencies randomly chosen. Originally, the unusual finite-size scaling behavior of the Kuramoto model was reported by Hong et al. [H. Hong, H. Chaté, H. Park, and L.-H. Tang, Phys. Rev. Lett. 99, 184101 (2007), 10.1103/PhysRevLett.99.184101], where the scaling behavior is found to be characterized by the unusual exponent ν ¯=5 /2 . On the other hand, if the randomness in the natural frequency is removed, it is found that the finite-size scaling behavior is characterized by a different exponent, ν ¯=5 /4 [H. Hong, H. Chaté, L.-H. Tang, and H. Park, Phys. Rev. E 92, 022122 (2015), 10.1103/PhysRevE.92.022122]. Those findings brought about our curiosity and led us to explore the effects of the randomness on the finite-size scaling behavior. In this paper, we pay particular attention to investigating the finite-size scaling and dynamic fluctuation when the randomness in the coupling strength is considered.

Diagram reduction in problem of critical dynamics of ferromagnets: 4-loop approximation

NASA Astrophysics Data System (ADS)

Adzhemyan, L. Ts; Ivanova, E. V.; Kompaniets, M. V.; Vorobyeva, S. Ye

2018-04-01

Within the framework of the renormalization group approach to the models of critical dynamics, we propose a method for a considerable reduction of the number of integrals needed to calculate the critical exponents. With this method we perform a calculation of the critical exponent z of model A at 4-loop level, where our method allows one to reduce the number of integrals from 66 to 17. The way of constructing the integrand in a Feynman representation of such diagrams is discussed. Integrals were estimated numerically with a sector decomposition technique.

Criticality of the mean-field spin-boson model: boson state truncation and its scaling analysis

NASA Astrophysics Data System (ADS)

Hou, Y.-H.; Tong, N.-H.

2010-11-01

The spin-boson model has nontrivial quantum phase transitions at zero temperature induced by the spin-boson coupling. The bosonic numerical renormalization group (BNRG) study of the critical exponents β and δ of this model is hampered by the effects of boson Hilbert space truncation. Here we analyze the mean-field spin boson model to figure out the scaling behavior of magnetization under the cutoff of boson states N b . We find that the truncation is a strong relevant operator with respect to the Gaussian fixed point in 0 < s < 1/2 and incurs the deviation of the exponents from the classical values. The magnetization at zero bias near the critical point is described by a generalized homogeneous function (GHF) of two variables τ = α - α c and x = 1/ N b . The universal function has a double-power form and the powers are obtained analytically as well as numerically. Similarly, m( α = α c ) is found to be a GHF of γ and x. In the regime s > 1/2, the truncation produces no effect. Implications of these findings to the BNRG study are discussed.

Complex Analysis of Combat in Afghanistan

DTIC Science & Technology

2014-12-01

analysis we have β−ffE ~)( where β= 2H - 1 = 1 - γ, with H being the Hurst exponent , related to the correlation exponent γ. Usually, real-world data are...statistical nature. In every instance we found strong power law correlations in the data, and were able to extract accurate scaling exponents . On the... exponents , α. The case αɘ.5 corresponds to long-term anti-correlations, meaning that large values are most likely to be followed by small values and

Self-interacting polymer chains terminally anchored to adsorbing surfaces of three-dimensional fractal lattices

NASA Astrophysics Data System (ADS)

Živić, I.; Elezović-Hadžić, S.; Milošević, S.

2018-01-01

We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b ≥ 2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1 ,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b = 2 , 3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.

Zero-temperature directed polymer in random potential in 4+1 dimensions.

PubMed

Kim, Jin Min

2016-12-01

Zero-temperature directed polymer in random potential in 4+1 dimensions is described. The fluctuation ΔE(t) of the lowest energy of the polymer varies as t^{β} with β=0.159±0.007 for polymer length t and ΔE follows ΔE(L)∼L^{α} at saturation with α=0.275±0.009, where L is the system size. The dynamic exponent z≈1.73 is obtained from z=α/β. The estimated values of the exponents satisfy the scaling relation α+z=2 very well. We also monitor the end to end distance of the polymer and obtain z independently. Our results show that the upper critical dimension of the Kardar-Parisi-Zhang equation is higher than d=4+1 dimensions.

Silicon dioxide space coatings studied ellipsometrically

NASA Technical Reports Server (NTRS)

De, Bhola N.; Zhao, Yong; Hruska, Jane; Peterkin, Jane; Woollam, John A.

1990-01-01

Mechanisms of initial oxidation of silicon for the formation of silicon dioxide have been investigated. The oxidation of silicon in an atomic oxigen plasma environment is found to exhibit two distinct and linear oxide growth curves for each of the plasma powers used in ashing (25, 50, and 100 watts). Data obtained indicate that the exponent to the pressure in the oxide growth rate formula changes from 1.4 + or - 0.1 to 0.7 + or - 0.1 as one crosses the critical thickness. These data contradict the theory predicting that this exponent should be 1 for both regimes. The activation energy for oxidation in the zone reaction regime is found to be 0.17 eV, in contrast to the published value of 1-2 eV for thermally grown oxides.

Critical exponents of extremal Kerr perturbations

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.; Zimmerman, Peter

2018-05-01

We show that scalar, electromagnetic, and gravitational perturbations of extremal Kerr black holes are asymptotically self-similar under the near-horizon, late-time scaling symmetry of the background metric. This accounts for the Aretakis instability (growth of transverse derivatives) as a critical phenomenon associated with the emergent symmetry. We compute the critical exponent of each mode, which is equivalent to its decay rate. It follows from symmetry arguments that, despite the growth of transverse derivatives, all generally covariant scalar quantities decay to zero.

Beyond Critical Exponents in Neuronal Avalanches

NASA Astrophysics Data System (ADS)

Friedman, Nir; Butler, Tom; Deville, Robert; Beggs, John; Dahmen, Karin

2011-03-01

Neurons form a complex network in the brain, where they interact with one another by firing electrical signals. Neurons firing can trigger other neurons to fire, potentially causing avalanches of activity in the network. In many cases these avalanches have been found to be scale independent, similar to critical phenomena in diverse systems such as magnets and earthquakes. We discuss models for neuronal activity that allow for the extraction of testable, statistical predictions. We compare these models to experimental results, and go beyond critical exponents.

Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition

NASA Astrophysics Data System (ADS)

Roy, Bappaditya; Santra, S. B.

2018-05-01

A random growth lattice filling model of percolation with a touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty lattice sites and clusters are grown from these nucleation centers with a growth probability g. For a given g (), the system passes through a critical point during the growth process where the transition from a disconnected to a connected phase occurs. The model is found to exhibit second order continuous percolation transitions as ordinary percolation for whereas for it exhibits weak first order discontinuous percolation transitions. The continuous transitions are characterized by estimating the values of the critical exponents associated with the order parameter fluctuation and the fractal dimension of the spanning cluster over the whole range of g. The discontinuous transitions, however, are characterized by a compact spanning cluster, lattice size independent fluctuation of the order parameter per lattice, departure from power law scaling in the cluster size distribution and weak bimodal distribution of the order parameter. The nature of transitions are further confirmed by studying the Binder cumulant. Instead of a sharp tricritical point, a tricritical region is found to occur for 0.5  <  g  <  0.8 within which the values of the critical exponents change continuously until the crossover from continuous to discontinuous transition is completed.

Photon orbits and thermodynamic phase transition of d -dimensional charged AdS black holes

NASA Astrophysics Data System (ADS)

Wei, Shao-Wen; Liu, Yu-Xiao

2018-05-01

We study the relationship between the null geodesics and thermodynamic phase transition for the charged AdS black hole. In the reduced parameter space, we find that there exist nonmonotonic behaviors of the photon sphere radius and the minimum impact parameter for the pressure below its critical value. The study also shows that the changes of the photon sphere radius and the minimum impact parameter can serve as order parameters for the small-large black hole phase transition. In particular, these changes have an universal exponent of 1/2 near the critical point for any dimension d of spacetime. These results imply that there may exist universal critical behavior of gravity near the thermodynamic critical point of the black hole system.

Tree Morphologic Plasticity Explains Deviation from Metabolic Scaling Theory in Semi-Arid Conifer Forests, Southwestern USA

PubMed Central

O’Connor, Christopher D.; Lynch, Ann M.

2016-01-01

A significant concern about Metabolic Scaling Theory (MST) in real forests relates to consistent differences between the values of power law scaling exponents of tree primary size measures used to estimate mass and those predicted by MST. Here we consider why observed scaling exponents for diameter and height relationships deviate from MST predictions across three semi-arid conifer forests in relation to: (1) tree condition and physical form, (2) the level of inter-tree competition (e.g. open vs closed stand structure), (3) increasing tree age, and (4) differences in site productivity. Scaling exponent values derived from non-linear least-squares regression for trees in excellent condition (n = 381) were above the MST prediction at the 95% confidence level, while the exponent for trees in good condition were no different than MST (n = 926). Trees that were in fair or poor condition, characterized as diseased, leaning, or sparsely crowned had exponent values below MST predictions (n = 2,058), as did recently dead standing trees (n = 375). Exponent value of the mean-tree model that disregarded tree condition (n = 3,740) was consistent with other studies that reject MST scaling. Ostensibly, as stand density and competition increase trees exhibited greater morphological plasticity whereby the majority had characteristically fair or poor growth forms. Fitting by least-squares regression biases the mean-tree model scaling exponent toward values that are below MST idealized predictions. For 368 trees from Arizona with known establishment dates, increasing age had no significant impact on expected scaling. We further suggest height to diameter ratios below MST relate to vertical truncation caused by limitation in plant water availability. Even with environmentally imposed height limitation, proportionality between height and diameter scaling exponents were consistent with the predictions of MST. PMID:27391084

Tree Morphologic Plasticity Explains Deviation from Metabolic Scaling Theory in Semi-Arid Conifer Forests, Southwestern USA.

PubMed

Swetnam, Tyson L; O'Connor, Christopher D; Lynch, Ann M

2016-01-01

A significant concern about Metabolic Scaling Theory (MST) in real forests relates to consistent differences between the values of power law scaling exponents of tree primary size measures used to estimate mass and those predicted by MST. Here we consider why observed scaling exponents for diameter and height relationships deviate from MST predictions across three semi-arid conifer forests in relation to: (1) tree condition and physical form, (2) the level of inter-tree competition (e.g. open vs closed stand structure), (3) increasing tree age, and (4) differences in site productivity. Scaling exponent values derived from non-linear least-squares regression for trees in excellent condition (n = 381) were above the MST prediction at the 95% confidence level, while the exponent for trees in good condition were no different than MST (n = 926). Trees that were in fair or poor condition, characterized as diseased, leaning, or sparsely crowned had exponent values below MST predictions (n = 2,058), as did recently dead standing trees (n = 375). Exponent value of the mean-tree model that disregarded tree condition (n = 3,740) was consistent with other studies that reject MST scaling. Ostensibly, as stand density and competition increase trees exhibited greater morphological plasticity whereby the majority had characteristically fair or poor growth forms. Fitting by least-squares regression biases the mean-tree model scaling exponent toward values that are below MST idealized predictions. For 368 trees from Arizona with known establishment dates, increasing age had no significant impact on expected scaling. We further suggest height to diameter ratios below MST relate to vertical truncation caused by limitation in plant water availability. Even with environmentally imposed height limitation, proportionality between height and diameter scaling exponents were consistent with the predictions of MST.

Choosing the Allometric Exponent in Covariate Model Building.

PubMed

Sinha, Jaydeep; Al-Sallami, Hesham S; Duffull, Stephen B

2018-04-27

Allometric scaling is often used to describe the covariate model linking total body weight (WT) to clearance (CL); however, there is no consensus on how to select its value. The aims of this study were to assess the influence of between-subject variability (BSV) and study design on (1) the power to correctly select the exponent from a priori choices, and (2) the power to obtain unbiased exponent estimates. The influence of WT distribution range (randomly sampled from the Third National Health and Nutrition Examination Survey, 1988-1994 [NHANES III] database), sample size (N = 10, 20, 50, 100, 200, 500, 1000 subjects), and BSV on CL (low 20%, normal 40%, high 60%) were assessed using stochastic simulation estimation. A priori exponent values used for the simulations were 0.67, 0.75, and 1, respectively. For normal to high BSV drugs, it is almost impossible to correctly select the exponent from an a priori set of exponents, i.e. 1 vs. 0.75, 1 vs. 0.67, or 0.75 vs. 0.67 in regular studies involving < 200 adult participants. On the other hand, such regular study designs are sufficient to appropriately estimate the exponent. However, regular studies with < 100 patients risk potential bias in estimating the exponent. Those study designs with limited sample size and narrow range of WT (e.g. < 100 adult participants) potentially risk either selection of a false value or yielding a biased estimate of the allometric exponent; however, such bias is only relevant in cases of extrapolating the value of CL outside the studied population, e.g. analysis of a study of adults that is used to extrapolate to children.

Freezing transition of the random bond RNA model: Statistical properties of the pairing weights

NASA Astrophysics Data System (ADS)

Monthus, Cécile; Garel, Thomas

2007-03-01

To characterize the pairing specificity of RNA secondary structures as a function of temperature, we analyze the statistics of the pairing weights as follows: for each base (i) of the sequence of length N , we consider the (N-1) pairing weights wi(j) with the other bases (j≠i) of the sequence. We numerically compute the probability distributions P1(w) of the maximal weight wimax=maxj[wi(j)] , the probability distribution Π(Y2) of the parameter Y2(i)=∑jwi2(j) , as well as the average values of the moments Yk(i)=∑jwik(j) . We find that there are two important temperatures TcTgap , the distribution P1(w) vanishes at some value w0(T)<1 , and accordingly the moments Yk(i)¯ decay exponentially as [w0(T)]k in k . For T

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

DOE PAGES

Anticic, T.; Baatar, B.; Bartke, J.; ...

2015-12-12

Here, we look for fluctuations expected for the QCD critical point using an 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 158A GeV. We find evidence of power-law fluctuations for the Si+Si data. The fitted power-law exponent Φ 2=0.96 +0.38 –0.25 (stat.) ± 0.16 (syst.) is consistent with the value expected for critical fluctuations. Power-law fluctuations had previously also been observed in low-mass π +π – pairs in the same Si+Si collisions.

Critical field-exponents for secure message-passing in modular networks

NASA Astrophysics Data System (ADS)

Shekhtman, Louis M.; Danziger, Michael M.; Bonamassa, Ivan; Buldyrev, Sergey V.; Caldarelli, Guido; Zlatić, Vinko; Havlin, Shlomo

2018-05-01

We study secure message-passing in the presence of multiple adversaries in modular networks. We assume a dominant fraction of nodes in each module have the same vulnerability, i.e., the same entity spying on them. We find both analytically and via simulations that the links between the modules (interlinks) have effects analogous to a magnetic field in a spin-system in that for any amount of interlinks the system no longer undergoes a phase transition. We then define the exponents δ, which relates the order parameter (the size of the giant secure component) at the critical point to the field strength (average number of interlinks per node), and γ, which describes the susceptibility near criticality. These are found to be δ = 2 and γ = 1 (with the scaling of the order parameter near the critical point given by β = 1). When two or more vulnerabilities are equally present in a module we find δ = 1 and γ = 0 (with β ≥ 2). Apart from defining a previously unidentified universality class, these exponents show that increasing connections between modules is more beneficial for security than increasing connections within modules. We also measure the correlation critical exponent ν, and the upper critical dimension d c , finding that ν {d}c=3 as for ordinary percolation, suggesting that for secure message-passing d c = 6. These results provide an interesting analogy between secure message-passing in modular networks and the physics of magnetic spin-systems.

A comment on measuring the Hurst exponent of financial time series

NASA Astrophysics Data System (ADS)

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.

The Angstrom Exponent and Bimodal Aerosol Size Distributions

NASA Technical Reports Server (NTRS)

Schuster, Gregory L.; Dubovik, Oleg; Holben, Brent H.

2005-01-01

Powerlaws have long been used to describe the spectral dependence of aerosol extinction, and the wavelength exponent of the aerosol extinction powerlaw is commonly referred to as the Angstrom exponent. The Angstrom exponent is often used as a qualitative indicator of aerosol particle size, with values greater than two indicating small particles associated with combustion byproducts, and values less than one indicating large particles like sea salt and dust. In this study, we investigate the relationship between the Angstrom exponent and the mode parameters of bimodal aerosol size distributions using Mie theory calculations and Aerosol Robotic Network (AERONET) retrievals. We find that Angstrom exponents based upon seven wavelengths (0.34, 0.38, 0.44, 0.5, 0.67, 0.87, and 1.02 micrometers) are sensitive to the volume fraction of aerosols with radii less then 0.6 micrometers, but not to the fine mode effective radius. The Angstrom exponent is also known to vary with wavelength, which is commonly referred to as curvature; we show how the spectral curvature can provide additional information about aerosol size distributions for intermediate values of the Angstrom exponent. Curvature also has a significant effect on the conclusions that can be drawn about two-wavelength Angstrom exponents; long wavelengths (0.67, 0.87 micrometers) are sensitive to fine mode volume fraction of aerosols but not fine mode effective radius, while short wavelengths (0.38, 0.44 micrometers) are sensitive to the fine mode effective radius but not the fine mode volume fraction.

Critical weight statistics of the random energy model and of the directed polymer on the Cayley tree

NASA Astrophysics Data System (ADS)

Monthus, Cécile; Garel, Thomas

2007-05-01

We consider the critical point of two mean-field disordered models: (i) the random energy model (REM), introduced by Derrida as a mean-field spin-glass model of N spins and (ii) the directed polymer of length N on a Cayley Tree (DPCT) with random bond energies. Both models are known to exhibit a freezing transition between a high-temperature phase where the entropy is extensive and a low-temperature phase of finite entropy, where the weight statistics coincides with the weight statistics of Lévy sums with index μ=T/Tc<1 . In this paper, we study the weight statistics at criticality via the entropy S=-∑wilnwi and the generalized moments Yk=∑wik , where the wi are the Boltzmann weights of the 2N configurations. In the REM, we find that the critical weight statistics is governed by the finite-size exponent ν=2 : the entropy scales as Smacr N(Tc)˜N1/2 , the typical values elnYk¯ decay as N-k/2 , and the disorder-averaged values Yk¯ are governed by rare events and decay as N-1/2 for any k>1 . For the DPCT, we find that the entropy scales similarly as Smacr N(Tc)˜N1/2 , whereas another exponent ν'=1 governs the Yk statistics: the typical values elnYk¯ decay as N-k , and the disorder-averaged values Yk¯ decay as N-1 for any k>1 . As a consequence, the asymptotic probability distribution π¯N=∞(q) of the overlap q , in addition to the delta function δ(q) , which bears the whole normalization, contains an isolated point at q=1 , as a memory of the delta peak (1-T/Tc)δ(q-1) of the low-temperature phase T

Applicability of mode-coupling theory to polyisobutylene: a molecular dynamics simulation study.

PubMed

Khairy, Y; Alvarez, F; Arbe, A; Colmenero, J

2013-10-01

The applicability of Mode Coupling Theory (MCT) to the glass-forming polymer polyisobutylene (PIB) has been explored by using fully atomistic molecular dynamics simulations. MCT predictions for the so-called asymptotic regime have been successfully tested on the dynamic structure factor and the self-correlation function of PIB main-chain carbons calculated from the simulated cell. The factorization theorem and the time-temperature superposition principle are satisfied. A consistent fitting procedure of the simulation data to the MCT asymptotic power-laws predicted for the α-relaxation regime has delivered the dynamic exponents of the theory-in particular, the exponent parameter λ-the critical non-ergodicity parameters, and the critical temperature T(c). The obtained values of λ and T(c) agree, within the uncertainties involved in both studies, with those deduced from depolarized light scattering experiments [A. Kisliuk et al., J. Polym. Sci. Part B: Polym. Phys. 38, 2785 (2000)]. Both, λ and T(c)/T(g) values found for PIB are unusually large with respect to those commonly obtained in low molecular weight systems. Moreover, the high T(c)/T(g) value is compatible with a certain correlation of this parameter with the fragility in Angell's classification. Conversely, the value of λ is close to that reported for real polymers, simulated "realistic" polymers and simple polymer models with intramolecular barriers. In the framework of the MCT, such finding should be the signature of two different mechanisms for the glass-transition in real polymers: intermolecular packing and intramolecular barriers combined with chain connectivity.

Lyapunov exponent and criticality in the Hamiltonian mean field model

NASA Astrophysics Data System (ADS)

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.

Dynamic scaling in natural swarms

NASA Astrophysics Data System (ADS)

Cavagna, Andrea; Conti, Daniele; Creato, Chiara; Del Castello, Lorenzo; Giardina, Irene; Grigera, Tomas S.; Melillo, Stefania; Parisi, Leonardo; Viale, Massimiliano

2017-09-01

Collective behaviour in biological systems presents theoretical challenges beyond the borders of classical statistical physics. The lack of concepts such as scaling and renormalization is particularly problematic, as it forces us to negotiate details whose relevance is often hard to assess. In an attempt to improve this situation, we present here experimental evidence of the emergence of dynamic scaling laws in natural swarms of midges. We find that spatio-temporal correlation functions in different swarms can be rescaled by using a single characteristic time, which grows with the correlation length with a dynamical critical exponent z ~ 1, a value not found in any other standard statistical model. To check whether out-of-equilibrium effects may be responsible for this anomalous exponent, we run simulations of the simplest model of self-propelled particles and find z ~ 2, suggesting that natural swarms belong to a novel dynamic universality class. This conclusion is strengthened by experimental evidence of the presence of non-dissipative modes in the relaxation, indicating that previously overlooked inertial effects are needed to describe swarm dynamics. The absence of a purely dissipative regime suggests that natural swarms undergo a near-critical censorship of hydrodynamics.

Geometrical model for martensitic phase transitions: Understanding criticality and weak universality during microstructure growth.

PubMed

Torrents, Genís; Illa, Xavier; Vives, Eduard; Planes, Antoni

2017-01-01

A simple model for the growth of elongated domains (needle-like) during a martensitic phase transition is presented. The model is purely geometric and the only interactions are due to the sequentiality of the kinetic problem and to the excluded volume, since domains cannot retransform back to the original phase. Despite this very simple interaction, numerical simulations show that the final observed microstructure can be described as being a consequence of dipolar-like interactions. The model is analytically solved in 2D for the case in which two symmetry related domains can grow in the horizontal and vertical directions. It is remarkable that the solution is analytic both for a finite system of size L×L and in the thermodynamic limit L→∞, where the elongated domains become lines. Results prove the existence of criticality, i.e., that the domain sizes observed in the final microstructure show a power-law distribution characterized by a critical exponent. The exponent, nevertheless, depends on the relative probabilities of the different equivalent variants. The results provide a plausible explanation of the weak universality of the critical exponents measured during martensitic transformations in metallic alloys. Experimental exponents show a monotonous dependence with the number of equivalent variants that grow during the transition.

Disordered two-dimensional electron systems with chiral symmetry

NASA Astrophysics Data System (ADS)

Markoš, P.; Schweitzer, L.

2012-10-01

We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior of the density of states and the logarithmic scaling of the smallest Lyapunov exponents in the vicinity of the chiral quantum critical point in the band center at E=0. The observed peaks or depressions in the density of states, the distribution of the critical conductances, and the possible non-universality of the critical exponents for certain chiral unitary models are discussed.

Scaling identity connects human mobility and social interactions.

PubMed

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

2016-06-28

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

Relation between self-organized criticality and grain aspect ratio in granular piles

NASA Astrophysics Data System (ADS)

Denisov, D. V.; Villanueva, Y. Y.; Lőrincz, K. A.; May, S.; Wijngaarden, R. J.

2012-05-01

We investigate experimentally whether self-organized criticality (SOC) occurs in granular piles composed of different grains, namely, rice, lentils, quinoa, and mung beans. These four grains were selected to have different aspect ratios, from oblong to oblate. As a function of aspect ratio, we determined the growth (β) and roughness (α) exponents, the avalanche fractal dimension (D), the avalanche size distribution exponent (τ), the critical angle (γ), and its fluctuation. At superficial inspection, three types of grains seem to have power-law-distributed avalanches with a well-defined τ. However, only rice is truly SOC if we take three criteria into account: a power-law-shaped avalanche size distribution, finite size scaling, and a universal scaling relation relating characteristic exponents. We study SOC as a spatiotemporal fractal; in particular, we study the spatial structure of criticality from local observation of the slope angle. From the fluctuation of the slope angle we conclude that greater fluctuation (and thus bigger avalanches) happen in piles consisting of grains with larger aspect ratio.

Scaling identity connects human mobility and social interactions

PubMed Central

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

2016-01-01

Massive datasets that capture human movements and social interactions have catalyzed rapid advances in our quantitative understanding of human behavior during the past years. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws, each characterized by its specific critical exponents. Although human mobility and social networks develop concomitantly as two prolific yet largely separated fields, we lack any known relationships between the critical exponents explored by them, despite the fact that they often study the same datasets. Here, by exploiting three different mobile phone datasets that capture simultaneously these two aspects, we discovered a new scaling relationship, mediated by a universal flux distribution, which links the critical exponents characterizing the spatial dependencies in human mobility and social networks. Therefore, the widely studied scaling laws uncovered in these two areas are not independent but connected through a deeper underlying reality. PMID:27274050

FAST TRACK COMMUNICATION: Ground-state fidelity and entanglement entropy for the quantum three-state Potts model in one spatial dimension

NASA Astrophysics Data System (ADS)

Dai, Yan-Wei; Hu, Bing-Quan; Zhao, Jian-Hui; Zhou, Huan-Qiang

2010-09-01

The ground-state fidelity per lattice site is computed for the quantum three-state Potts model in a transverse magnetic field on an infinite-size lattice in one spatial dimension in terms of the infinite matrix product state algorithm. It is found that, on the one hand, a pinch point is identified on the fidelity surface around the critical point, and on the other hand, the ground-state fidelity per lattice site exhibits bifurcations at pseudo critical points for different values of the truncation dimension, which in turn approach the critical point as the truncation dimension becomes large. This implies that the ground-state fidelity per lattice site enables us to capture spontaneous symmetry breaking when the control parameter crosses the critical value. In addition, a finite-entanglement scaling of the von Neumann entropy is performed with respect to the truncation dimension, resulting in a precise determination of the central charge at the critical point. Finally, we compute the transverse magnetization, from which the critical exponent β is extracted from the numerical data.

Quench in the 1D Bose-Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynamics

PubMed Central

Dziarmaga, Jacek; Zurek, Wojciech H.

2014-01-01

Kibble-Zurek mechanism (KZM) uses critical scaling to predict density of topological defects and other excitations created in second order phase transitions. We point out that simply inserting asymptotic critical exponents deduced from the immediate vicinity of the critical point to obtain predictions can lead to results that are inconsistent with a more careful KZM analysis based on causality – on the comparison of the relaxation time of the order parameter with the “time distance” from the critical point. As a result, scaling of quench-generated excitations with quench rates can exhibit behavior that is locally (i.e., in the neighborhood of any given quench rate) well approximated by the power law, but with exponents that depend on that rate, and that are quite different from the naive prediction based on the critical exponents relevant for asymptotically long quench times. Kosterlitz-Thouless scaling (that governs e.g. Mott insulator to superfluid transition in the Bose-Hubbard model in one dimension) is investigated as an example of this phenomenon. PMID:25091996

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

NASA Astrophysics Data System (ADS)

Peres, Lucas R.; Fontanari, José F.

2015-09-01

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

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

Hunt, Allen G.

2016-04-01

Percolation theory can be used to find water flow paths of least resistance. Application of percolation theory to drainage networks allows identification of the range of exponent values that describe the tortuosity of rivers in real river networks, which is then used to generate the observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on an assessment of the heterogeneity of the substrate.

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

NASA Astrophysics Data System (ADS)

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.

On universality of scaling law describing roughness of triple line.

PubMed

Bormashenko, Edward; Musin, Albina; Whyman, Gene; Barkay, Zahava; Zinigrad, Michael

2015-01-01

The fine structure of the three-phase (triple) line was studied for different liquids, various topographies of micro-rough substrates and various wetting regimes. Wetting of porous and pillar-based micro-scaled polymer surfaces was investigated. The triple line was visualized with the environmental scanning electron microscope and scanning electron microscope for the "frozen" triple lines. The value of the roughness exponent ζ for water (ice)/rough polymer systems was located within 0.55-0.63. For epoxy glue/rough polymer systems somewhat lower values of the exponent, 0.42 < ζ < 0.54, were established. The obtained values of ζ were close for the Cassie and Wenzel wetting regimes, different liquids, and different substrates' topographies. Thus, the above values of the exponent are to a great extent universal. The switch of the exponent, when the roughness size approaches to the correlation length of the defects, is also universal.

Synchronization on Erdös-Rényi networks.

PubMed

Gong, Baihua; Yang, Lei; Yang, Kongqing

2005-09-01

In this Brief Report, by analyzing the spectral properties of the Laplacian matrix of Erdös-Rényi networks, we obtained the critical coupling strength of the complete synchronization analytically. In particular, for any size of the networks, when the average degree is greater than a threshold and the coupling strength is large enough, the networks can synchronize. Here, the threshold is determined by the value of the maximal Lyapunov exponent of each dynamical unit.

Application of an Entropic Approach to Assessing Systems Integration

DTIC Science & Technology

2012-03-01

two econometrical measures of information efficiency – Shannon entropy and Hurst exponent . Shannon entropy (which is explained in Chapter III) can be...applied to evaluate long-term correlation of time series, while Hurst exponent can be applied to classify the time series in accordance to existence...of trend. Hurst exponent is the statistical measure of time series long-range dependence, and its value falls in the interval [0, 1] – a value in

Precise calculation of a bond percolation transition and survival rates of nodes in a complex network.

PubMed

Kawamoto, Hirokazu; Takayasu, Hideki; Jensen, Henrik Jeldtoft; Takayasu, Misako

2015-01-01

Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition.

X-ray scattering study of the spin-Peierls phase transition

NASA Astrophysics Data System (ADS)

Lumsden, Mark Douglas

1999-11-01

Scattering techniques are an essential tool in the experimental study of properties in the vicinity of a critical phase transition. Such techniques have been applied to the study of the spin-Peierls transition in pure and doped samples of CuGeO3 and in the organic compound MEM(TCNQ) 2. The spin-Peierls phase transition occurs in one-dimensional S = 1/2 Heisenberg spin chains with short-range, antiferromagnetic interactions. Such a system is unstable against a dimerization of the chains with the subsequent appearance of a gap in the magnetic excitation spectrum. Such a gap acts to lower the magnetic energy in the system and, in the presence of coupling with the lattice, causes a phase transition to a dimerized, spin-Peierls, state. High temperature stability measurements of the order parameter associated with this transition in the inorganic compound CuGeO3 indicate a continuous phase transition at a temperature of 14.05 K with a corresponding critical exponent beta of 0.345 +/- 0.03. This value is in agreement with conventional 3D universality and in closest agreement with 3D XY behaviour. We also observe a narrow asymptotic critical region which is largely responsible for the inconsistency in previously reported results. High resolution measurements of relative lattice constant changes, performed using a novel approach, indicate spontaneous strains which scale with the square of the order parameter expect near the transition temperature where differences are observed. Similar order parameter measurements were performed on samples of CuGeO 3 doped with Zn, Si, and Cd. For the case of Zn and Si doping, we obtain and exponent beta consistent with that for the pure material. Measurements on two Cd doped samples indicate results which clearly deviate from that observed in pure CuGeO3 with an exponent beta of about 0.5 consistent with mean field behaviour. We explain this change in behaviour as resulting from local strains induced by the presence of the much larger Cd2+ dopant ion. Relative lattice constant measurements indicate spontaneous strains which scale with the square of the order parameter for the doped samples as was the case for pure CuGeO3. X-ray scattering measurements of both the order parameter and critical scattering in the vicinity of the transition temperature have been performed for the organic spin-Peierls compound MEM(TCNQ)2. Order parameter measurements indicate a value of the exponent beta of 0.35 +/- 0.06 consistent with 3D universality, as was observed in the inorganic spin-Peierls material CuGeO3, and inconsistent with previous measurements which suggested mean-field behaviour. Critical scattering measurements suggest a lineshape not described by a traditional Ornstein-Zernike, Lorentzian, form but well described by a Lorentzian with a varying power or a Lorentzian+Lorentzian 2. The latter form is reminiscent of recent x-ray scattering measurements of critical phenomena associated with structural phase transitions in perovskites or with magnetic x-ray scattering measurements on Ho, Tb, and some U-based compounds. Differences between this and previous measurements are discussed.

Critical exponents of the 3D antiferromagnetic three-state Potts model using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using the coherent-anomaly method (CAM). The CAM analysis provides the estimates for the critical exponents which indicate the XY universality class, namely α = -0.011, β = 0.351, γ = 1.309 and δ = 4.73. This observation corroborates the results of the recent Monte Carlo simulations, and disagrees with the proposal of a new universality class.

Influence of Ti Doping on the Critical Behavior and Magnetocaloric Effect in Disordered Ferromagnets La0.7Ba0.3Mn1- x Ti x O3

NASA Astrophysics Data System (ADS)

Ho, T. A.; Phan, M. H.; Phuc, N. X.; Lam, V. D.; Phan, T. L.; Yu, S. C.

2016-05-01

The Ti-substitution influence on the magnetic and magnetocaloric properties of La0.7Ba0.3Mn1- x Ti x O3 ( x = 0.05 and 0.1) was investigated. Based on Banerjee's criteria and Franco's universal curves, we proved the existence of a second-order magnetic phase transition in the samples. Using the modified Arrott plot method, we determined the critical parameters T C ≈ 245 K, β = 0.374 ± 0.013, γ = 1.228 ± 0.045, and δ = 4.26 ± 0.03 for x = 0.05, and T C ≈ 169 K, β = 0.339 ± 0.001, γ = 1.307 ± 0.003, and δ = 4.78 ± 0.02 for x = 0.1. With these critical values, the predictable scaling behavior of the M( H) data above and below T C proves that the calculated exponents are unambiguous and intrinsic. The values β = 0.374 for x = 0.05 and β = 0.339 for x = 0.1 suggest that the magnetic phase transition of the samples falls into the three-dimensional (3D) Heisenberg and 3D Ising universality classes, respectively, corresponding to short-range ferromagnetic (FM) order due to FM clusters in a wide temperature range even above T C, as confirmed by electron spin resonance studies. In reference to the magnetocaloric effect around T C, the magnetic entropy change reaches maximum values (|ΔSmax|) of about 4 and 3 J kg-1 K-1 for x = 0.05 and 0.1, respectively, for a magnetic field change 50 kOe. Magnetic field dependencies of |ΔSmax| obey a power function |ΔSmax( H)| ∝ H n , where exponent values n = 0.59 and 0.61 for x = 0.05 and 0.1, respectively, were determined from the relation n = 1 + ( β-1)/( β + γ). The difference between the experimental n values and the theoretical value n = 2/3 of the mean field model is due to the presence of short-range FM order in the samples.

Phase and vortex correlations in superconducting Josephson-junction arrays at irrational magnetic frustration.

PubMed

Granato, Enzo

2008-07-11

Phase coherence and vortex order in a Josephson-junction array at irrational frustration are studied by extensive Monte Carlo simulations using the parallel-tempering method. A scaling analysis of the correlation length of phase variables in the full equilibrated system shows that the critical temperature vanishes with a power-law divergent correlation length and critical exponent nuph, in agreement with recent results from resistivity scaling analysis. A similar scaling analysis for vortex variables reveals a different critical exponent nuv, suggesting that there are two distinct correlation lengths associated with a decoupled zero-temperature phase transition.

Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in O(N) models

NASA Astrophysics Data System (ADS)

Péli, Zoltán; Nagy, Sándor; Sailer, Kornel

2018-02-01

The effect of the O(partial4) terms of the gradient expansion on the anomalous dimension η and the correlation length's critical exponent ν of the Wilson-Fisher fixed point has been determined for the Euclidean 3-dimensional O( N) models with N≥ 2 . Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory is well approximated by the effective average action preserving O( N) symmetry with an accuracy of O(η).

Equilibrium and nonequilibrium models on Solomon networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2016-05-01

We investigate the critical properties of the equilibrium and nonequilibrium systems on Solomon networks. The equilibrium and nonequilibrium systems studied here are the Ising and Majority-vote models, respectively. These systems are simulated by applying the Monte Carlo method. We calculate the critical points, as well as the critical exponents ratio γ/ν, β/ν and 1/ν. We find that both systems present identical exponents on Solomon networks and are of different universality class as the regular two-dimensional ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Coherent-Anomaly Method in Critical Phenomena. III.

NASA Astrophysics Data System (ADS)

Hu, Xiao; Katori, Makoto; Suzuki, Masuo

Two kinds of systematic mean-field transfer-matrix methods are formulated in the 2-dimensional Ising spin system, by introducing Weiss-like and Bethe-like approximations. All the critical exponents as well as the true critical point can be estimated in these methods following the CAM procedure. The numerical results of the above system are Tc* = 2.271 (J/kB), γ=γ' ≃ 1.749, β≃0.131 and δ ≃ 15.1. The specific heat is confirmed to be continuous and to have a logarithmic divergence at the true critical point, i.e., α=α'=0. Thus, the finite-degree-of-approximation scaling ansatz is shown to be correct and very powerful in practical estimations of the critical exponents as well as the true critical point.

Theoretical Insight Into the Empirical Tortuosity-Connectivity Factor in the Burdine-Brooks-Corey Water Relative Permeability Model

NASA Astrophysics Data System (ADS)

Ghanbarian, Behzad; Ioannidis, Marios A.; Hunt, Allen G.

2017-12-01

A model commonly applied to the estimation of water relative permeability krw in porous media is the Burdine-Brooks-Corey model, which relies on a simplified picture of pores as a bundle of noninterconnected capillary tubes. In this model, the empirical tortuosity-connectivity factor is assumed to be a power law function of effective saturation with an exponent (μ) commonly set equal to 2 in the literature. Invoking critical path analysis and using percolation theory, we relate the tortuosity-connectivity exponent μ to the critical scaling exponent t of percolation that characterizes the power law behavior of the saturation-dependent electrical conductivity of porous media. We also discuss the cause of the nonuniversality of μ in terms of the nonuniversality of t and compare model estimations with water relative permeability from experiments. The comparison supports determining μ from the electrical conductivity scaling exponent t, but also highlights limitations of the model.

Weyl holographic superconductor in the Lifshitz black hole background

NASA Astrophysics Data System (ADS)

Mansoori, S. A. Hosseini; Mirza, B.; Mokhtari, A.; Dezaki, F. Lalehgani; Sherkatghanad, Z.

2016-07-01

We investigate analytically the properties of the Weyl holographic superconductor in the Lifshitz black hole background. We find that the critical temperature of the Weyl superconductor decreases with increasing Lifshitz dynamical exponent, z, indicating that condensation becomes difficult. In addition, it is found that the critical temperature and condensation operator could be affected by applying the Weyl coupling, γ. Moreover, we compute the critical magnetic field and investigate its dependence on the parameters γ and z. Finally, we show numerically that the Weyl coupling parameter γ and the Lifshitz dynamical exponent z together control the size and strength of the conductivity peak and the ratio of gap frequency over critical temperature ω g /T c .

Non-Abelian Bosonization and Fractional Quantum Hall Transitions

NASA Astrophysics Data System (ADS)

Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah

A fully satisfying theoretical description for the quantum phase transition between fractional quantum Hall plateaus remains an outstanding problem. Experiments indicate scaling exponents that are not readily obtained in conventional theories. Using insights from duality, we describe a class of quantum critical effective theories that produce qualitatively realistic scaling exponents for the transition. We discuss the implications of our results for the physically-relevant interactions controlling this broad class of quantum critical behavior. Supported by National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1650441.

Role of initial state and final quench temperature on aging properties in phase-ordering kinetics.

PubMed

Corberi, Federico; Villavicencio-Sanchez, Rodrigo

2016-05-01

We study numerically the two-dimensional Ising model with nonconserved dynamics quenched from an initial equilibrium state at the temperature T_{i}≥T_{c} to a final temperature T_{f} below the critical one. By considering processes initiating both from a disordered state at infinite temperature T_{i}=∞ and from the critical configurations at T_{i}=T_{c} and spanning the range of final temperatures T_{f}∈[0,T_{c}[ we elucidate the role played by T_{i} and T_{f} on the aging properties and, in particular, on the behavior of the autocorrelation C and of the integrated response function χ. Our results show that for any choice of T_{f}, while the autocorrelation function exponent λ_{C} takes a markedly different value for T_{i}=∞ [λ_{C}(T_{i}=∞)≃5/4] or T_{i}=T_{c} [λ_{C}(T_{i}=T_{c})≃1/8] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing T_{f} is considered, although this is expected to play no role in the large-scale and long-time properties of the system, we show important effects on the quantitative behavior of χ. In particular, data for quenches to T_{f}=0 are consistent with a value of the response function exponent λ_{χ}=1/2λ_{C}(T_{i}=∞)=5/8 different from the one [λ_{χ}∈(0.5-0.56)] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important preasymptotic corrections associated to T_{f}>0.

Critical dynamics on a large human Open Connectome network

NASA Astrophysics Data System (ADS)

Ódor, Géza

2016-12-01

Extended numerical simulations of threshold models have been performed on a human brain network with N =836 733 connected nodes available from the Open Connectome Project. While in the case of simple threshold models a sharp discontinuous phase transition without any critical dynamics arises, variable threshold models exhibit extended power-law scaling regions. This is attributed to fact that Griffiths effects, stemming from the topological or interaction heterogeneity of the network, can become relevant if the input sensitivity of nodes is equalized. I have studied the effects of link directness, as well as the consequence of inhibitory connections. Nonuniversal power-law avalanche size and time distributions have been found with exponents agreeing with the values obtained in electrode experiments of the human brain. The dynamical critical region occurs in an extended control parameter space without the assumption of self-organized criticality.

Superconductor to weak-insulator transitions in disordered tantalum nitride films

NASA Astrophysics Data System (ADS)

Breznay, Nicholas P.; Tendulkar, Mihir; Zhang, Li; Lee, Sang-Chul; Kapitulnik, Aharon

2017-10-01

We study the two-dimensional superconductor-insulator transition (SIT) in thin films of tantalum nitride. At zero magnetic field, films can be disorder-tuned across the SIT by adjusting thickness and film stoichiometry; insulating films exhibit classical hopping transport. Superconducting films exhibit a magnetic-field-tuned SIT, whose insulating ground state at high field appears to be a quantum-corrected metal. Scaling behavior at the field-tuned SIT shows classical percolation critical exponents z ν ≈1.3 , with a corresponding critical field Hc≪Hc 2 , the upper critical field. The Hall effect exhibits a crossing point near Hc, but with a nonuniversal critical value ρxy c comparable to the normal-state Hall resistivity. We propose that high-carrier-density metals will always exhibit this pattern of behavior at the boundary between superconducting and (trivially) insulating ground states.

Shock wave structure in a strongly nonlinear lattice with viscous dissipation.

PubMed

Herbold, E B; Nesterenko, V F

2007-02-01

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (F proportional to delta(n)) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient p(c), defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3/2) . The expression for p(c) in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

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

PubMed

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

2015-10-01

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

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

NASA Astrophysics Data System (ADS)

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.

Revisiting Kawasaki dynamics in one dimension

NASA Astrophysics Data System (ADS)

Grynberg, M. D.

2010-11-01

Critical exponents of the Kawasaki dynamics in the Ising chain are re-examined numerically through the spectrum gap of evolution operators constructed both in spin and domain-wall representations. At low-temperature regimes the latter provides a rapid finite-size convergence to these exponents, which tend to z≃3.11 for instant quenches under ferromagnetic couplings, while approaching to z≃2 in the antiferro case. The spin representation complements the evaluation of dynamic exponents at higher temperature scales, where the kinetics still remains slow.

Renormalization-group study of the Nagel-Schreckenberg model

NASA Astrophysics Data System (ADS)

Teoh, Han Kheng; Yong, Ee Hou

2018-03-01

We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) model by using the dynamically driven renormalization group (DDRG). The breaking probability p that governs the driving strategy is investigated. For the deterministic case p =0 , the dynamics remain invariant in each renormalization-group (RG) transformation. Two fully attractive fixed points, ρc*=0 and 1, and one unstable fixed point, ρc*=1 /(vmax+1 ) , are obtained. The critical exponent ν which is related to the correlation length is calculated for various vmax. The critical exponent appears to decrease weakly with vmax from ν =1.62 to the asymptotical value of 1.00. For the random case p >0 , the transition rules in the coarse-grained scale are found to be different from the NS specification. To have a qualitative understanding of the effect of stochasticity, the case p →0 is studied with simulation, and the RG flow in the ρ -p plane is obtained. The fixed points p =0 and 1 that govern the driving strategy of the NS model are found. A short discussion on the extension of the DDRG method to the NS model with the open-boundary condition is outlined.

Outbreak statistics and scaling laws for externally driven epidemics.

PubMed

Singh, Sarabjeet; Myers, Christopher R

2014-04-01

Power-law scalings are ubiquitous to physical phenomena undergoing a continuous phase transition. The classic susceptible-infectious-recovered (SIR) model of epidemics is one such example where the scaling behavior near a critical point has been studied extensively. In this system the distribution of outbreak sizes scales as P(n)∼n-3/2 at the critical point as the system size N becomes infinite. The finite-size scaling laws for the outbreak size and duration are also well understood and characterized. In this work, we report scaling laws for a model with SIR structure coupled with a constant force of infection per susceptible, akin to a "reservoir forcing". We find that the statistics of outbreaks in this system fundamentally differ from those in a simple SIR model. Instead of fixed exponents, all scaling laws exhibit tunable exponents parameterized by the dimensionless rate of external forcing. As the external driving rate approaches a critical value, the scale of the average outbreak size converges to that of the maximal size, and above the critical point, the scaling laws bifurcate into two regimes. Whereas a simple SIR process can only exhibit outbreaks of size O(N1/3) and O(N) depending on whether the system is at or above the epidemic threshold, a driven SIR process can exhibit a richer spectrum of outbreak sizes that scale as O(Nξ), where ξ∈(0,1]∖{2/3} and O((N/lnN)2/3) at the multicritical point.

Coherent-Anomaly Method in Critical Phenomena. III. Mean-Field Transfer-Matrix Method in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Katori, Makoto; Suzuki, Masuo

1987-11-01

Two kinds of systematic mean-field transfer-matrix methods are formulated in the 2-dimensional Ising spin system, by introducing Weiss-like and Bethe-like approximations. All the critical exponents as well as the true critical point can be estimated in these methods following the CAM procedure. The numerical results of the above system are Tc*≃2.271 (J/kB), γ{=}γ'≃1.749, β≃0.131 and δ≃15.1. The specific heat is confirmd to be continuous and to have a logarithmic divergence at the true critical point, i.e., α{=}α'{=}0. Thus, the finite-degree-of-approximation scaling ansatz is shown to be correct and very powerful in practical estimations of the critical exponents as well as the true critical point.

Three-dimensional magnetic critical behavior in CrI 3

DOE PAGES

Liu, Yu; Petrovic, C.

2018-01-18

CrI 3 is a promising candidate for the van der Waals bonded ferromagnetic devices since its ferromagnetism can be maintained upon exfoliating of bulk crystals down to single layer. In this work we studied critical properties of bulk CrI 3 single crystals around the paramagnetic to ferromagnetic phase transition. Critical exponents β= 0.260(4) with a critical temperature T c= 60.05(13) K and γ= 1.136(6) with T c= 60.43(4) K are obtained by the Kouvel-Fisher method, whereas δ= 5.32(2) is obtained by a critical isotherm analysis at T c= 60 K. In conclusion, the critical exponents determined in bulk CrI 3more » single crystals suggest a three-dimensional long-range magnetic coupling with the exchange distance decaying as J(r)≈r -4:69« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yu; Petrovic, C.

CrI 3 is a promising candidate for the van der Waals bonded ferromagnetic devices since its ferromagnetism can be maintained upon exfoliating of bulk crystals down to single layer. In this work we studied critical properties of bulk CrI 3 single crystals around the paramagnetic to ferromagnetic phase transition. Critical exponents β= 0.260(4) with a critical temperature T c= 60.05(13) K and γ= 1.136(6) with T c= 60.43(4) K are obtained by the Kouvel-Fisher method, whereas δ= 5.32(2) is obtained by a critical isotherm analysis at T c= 60 K. In conclusion, the critical exponents determined in bulk CrI 3more » single crystals suggest a three-dimensional long-range magnetic coupling with the exchange distance decaying as J(r)≈r -4:69« less

The temperature dependence of the conductivity peak values in the single and the double quantum well nanostructures n-InGaAs/GaAs after IR-illumination

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arapov, Yu. G.; Gudina, S. V.; Klepikova, A. S., E-mail: klepikova@imp.uran.ru

2017-02-15

The dependences of the longitudinal and Hall resistances on a magnetic field in n-InGaAs/GaAs heterostructures with a single and double quantum wells after infrared illumination are measured in the range of magnetic fields Ð’ = 0–16 T and temperatures T = 0.05–4.2 K. Analysis of the experimental results was carried out on a base of two-parameter scaling hypothesis for the integer quantum Hall effect. The value of the second (irrelevant) critical exponent of the theory of two-parameter scaling was estimated.

Coherent-Anomaly Method in Critical Phenomena. IV.

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

The systematic Weiss-like and Bethe-like approximations based on the mean-field transfer-matrix method are used to investigate the asymptotic behavior of the induced magnetization on a semi-infinite square lattice, and to investigate the wave-number dependence of the susceptibility in a nonuniform external field. The critical exponents ν, ν', ηi and η are estimated following the general CAM prescription. A new scaling relation ν·ηi=β is obtained in the framework of the finite-degree-of-approximation scaling. Together with previous papers, all the static critical exponents have been estimated by the CAM, and are shown to satisfy the well-known scaling relations.

Critical exponents of the disorder-driven superfluid-insulator transition in one-dimensional Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cestari, J. C. C.; Foerster, A.; Gusmao, M. A.

2011-11-15

We investigate the nature of the superfluid-insulator quantum phase transition driven by disorder for noninteracting ultracold atoms on one-dimensional lattices. We consider two different cases: Anderson-type disorder, with local energies randomly distributed, and pseudodisorder due to a potential incommensurate with the lattice, which is usually called the Aubry-Andre model. A scaling analysis of numerical data for the superfluid fraction for different lattice sizes allows us to determine quantum critical exponents characterizing the disorder-driven superfluid-insulator transition. We also briefly discuss the effect of interactions close to the noninteracting quantum critical point of the Aubry-Andre model.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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 with some general findings concerning HR coupling topologies. As a perspective, besides the synchronization overview from different standpoints, we hope that the proposed numerical approach for conditional Lyapunov exponent evaluation could outline a valuable strategy for studying neuronal stability, especially when realistic models are considered, in which analytical or even Jacobian evaluation could define a laborious or impracticable task.

Probabilistic Multi-Factor Interaction Model for Complex Material Behavior

NASA Technical Reports Server (NTRS)

Abumeri, Galib H.; Chamis, Christos C.

2010-01-01

Complex material behavior is represented by a single equation of product form to account for interaction among the various factors. The factors are selected by the physics of the problem and the environment that the model is to represent. For example, different factors will be required for each to represent temperature, moisture, erosion, corrosion, etc. It is important that the equation represent the physics of the behavior in its entirety accurately. The Multi-Factor Interaction Model (MFIM) is used to evaluate the divot weight (foam weight ejected) from the external launch tanks. The multi-factor has sufficient degrees of freedom to evaluate a large number of factors that may contribute to the divot ejection. It also accommodates all interactions by its product form. Each factor has an exponent that satisfies only two points - the initial and final points. The exponent describes a monotonic path from the initial condition to the final. The exponent values are selected so that the described path makes sense in the absence of experimental data. In the present investigation, the data used were obtained by testing simulated specimens in launching conditions. Results show that the MFIM is an effective method of describing the divot weight ejected under the conditions investigated. The problem lies in how to represent the divot weight with a single equation. A unique solution to this problem is a multi-factor equation of product form. Each factor is of the following form (1 xi/xf)ei, where xi is the initial value, usually at ambient conditions, xf the final value, and ei the exponent that makes the curve represented unimodal that meets the initial and final values. The exponents are either evaluated by test data or by technical judgment. A minor disadvantage may be the selection of exponents in the absence of any empirical data. This form has been used successfully in describing the foam ejected in simulated space environmental conditions. Seven factors were required to represent the ejected foam. The exponents were evaluated by least squares method from experimental data. The equation is used and it can represent multiple factors in other problems as well; for example, evaluation of fatigue life, creep life, fracture toughness, and structural fracture, as well as optimization functions. The software is rather simplistic. Required inputs are initial value, final value, and an exponent for each factor. The number of factors is open-ended. The value is updated as each factor is evaluated. If a factor goes to zero, the previous value is used in the evaluation.

Weak- versus strong-disorder superfluid—Bose glass transition in one dimension

NASA Astrophysics Data System (ADS)

Doggen, Elmer V. H.; Lemarié, Gabriel; Capponi, Sylvain; Laflorencie, Nicolas

2017-11-01

Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter Kc takes its universal Giamarchi-Schulz value Kc=3 /2 . Conversely, a nonuniversal Kc>3 /2 emerges for stronger attraction where weak-link physics is relevant. In this strong-disorder regime, the transition is characterized by self-similar power-law-distributed weak links with a continuously varying characteristic exponent α .

Probing the role of long-range interactions in the dynamics of a long-range Kitaev chain

NASA Astrophysics Data System (ADS)

Dutta, Anirban; Dutta, Amit

2017-09-01

We study the role of long-range interactions (more precisely, the long-range superconducting gap term) on the nonequilibrium dynamics considering a long-range p -wave superconducting chain in which the superconducting term decays with distance between two sites in a power-law fashion characterized by an exponent α . We show that the Kibble-Zurek scaling exponent, dictating the power-law decay of the defect density in the final state reached following a slow (in comparison to the time scale associated with the minimum gap in the spectrum of the Hamiltonian) quenching of the chemical potential μ across a quantum critical point, depends nontrivially on the exponent α as long as α <2 ; on the other hand, for α >2 , we find that the exponent saturates to the corresponding well-known value of 1 /2 expected for the short-range model. Furthermore, studying the dynamical quantum phase transitions manifested in the nonanalyticities in the rate function of the return possibility I (t ) in subsequent temporal evolution following a sudden change in μ , we show the existence of a new region; in this region, we find three instants of cusp singularities in I (t ) associated with a single sector of Fisher zeros. Notably, the width of this region shrinks as α increases and vanishes in the limit α →2 , indicating that this special region is an artifact of the long-range nature of the Hamiltonian.

Memory-induced resonancelike suppression of spike generation in a resonate-and-fire neuron model

NASA Astrophysics Data System (ADS)

Mankin, Romi; Paekivi, Sander

2018-01-01

The behavior of a stochastic resonate-and-fire neuron model based on a reduction of a fractional noise-driven generalized Langevin equation (GLE) with a power-law memory kernel is considered. The effect of temporally correlated random activity of synaptic inputs, which arise from other neurons forming local and distant networks, is modeled as an additive fractional Gaussian noise in the GLE. Using a first-passage-time formulation, in certain system parameter domains exact expressions for the output interspike interval (ISI) density and for the survival probability (the probability that a spike is not generated) are derived and their dependence on input parameters, especially on the memory exponent, is analyzed. In the case of external white noise, it is shown that at intermediate values of the memory exponent the survival probability is significantly enhanced in comparison with the cases of strong and weak memory, which causes a resonancelike suppression of the probability of spike generation as a function of the memory exponent. Moreover, an examination of the dependence of multimodality in the ISI distribution on input parameters shows that there exists a critical memory exponent αc≈0.402 , which marks a dynamical transition in the behavior of the system. That phenomenon is illustrated by a phase diagram describing the emergence of three qualitatively different structures of the ISI distribution. Similarities and differences between the behavior of the model at internal and external noises are also discussed.

Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory

NASA Astrophysics Data System (ADS)

Evans, Robert; Stewart, Maria C.; Wilding, Nigel B.

2017-07-01

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν∥, which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects.

Drying and wetting transitions of a Lennard-Jones fluid: Simulations and density functional theory.

PubMed

Evans, Robert; Stewart, Maria C; Wilding, Nigel B

2017-07-28

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hard wall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finite-size scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν ∥ , which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects.

Relaxation phenomena in AOT-water-decane critical and dense microemulsions

NASA Astrophysics Data System (ADS)

Letamendia, L.; Pru-Lestret, E.; Panizza, P.; Rouch, J.; Sciortino, F.; Tartaglia, P.; Hashimoto, C.; Ushiki, H.; Risso, D.

2001-11-01

We report on extensive measurements of the low and high frequencies sound velocity and sound absorption in AOT-water-decane microemulsions deduced from ultrasonic and, for the first time as far as the absorption is concerned, from Brillouin scattering experiments. New experimental results on dielectric relaxation are also reported. Our results, which include data taken for critical as well as dense microemulsions, show new interesting relaxation phenomena. The relaxation frequencies deduced from very high frequency acoustical measurements are in good agreement with new high frequency dielectric relaxation measurements. We show that along the critical isochore, sound dispersion, relaxation frequency, and static dielectric permittivity can be accurately fitted to power laws. The absolute values of the new exponents we derived from experimental data are nearly equal, and they are very close to β=0.33 characterising the shape of the coexistence curve. The exponent characterising the infinite frequency permittivity is very close to 0.04 relevant to the diverging shear viscosity. For dense microemulsions, two well defined relaxation domains have been identified and the temperature variations of the sound absorption and the zero frequency dielectric permittivity bear striking similarities. We also show that the relaxation frequency of the slow relaxation process is almost independent of temperature and volume fraction and so cannot be attributed to percolation phenomena, whereas it can more likely be attributed to an intrinsic relaxation process probably connected to membrane fluctuations.

Phase diagram and criticality of the two-dimensional prisoner's dilemma model

NASA Astrophysics Data System (ADS)

Santos, M.; Ferreira, A. L.; Figueiredo, W.

2017-07-01

The stationary states of the prisoner's dilemma model are studied on a square lattice taking into account the role of a noise parameter in the decision-making process. Only first neighboring players—defectors and cooperators—are considered in each step of the game. Through Monte Carlo simulations we determined the phase diagrams of the model in the plane noise versus the temptation to defect for a large range of values of the noise parameter. We observed three phases: cooperators and defectors absorbing phases, and a coexistence phase between them. The phase transitions as well as the critical exponents associated with them were determined using both static and dynamical scaling laws.

Applications of the CAM Based on a New Decoupling Procedure of Correlation Functions in the One-Dimensional Contact Process

NASA Astrophysics Data System (ADS)

Konno, Norio; Katori, Makoto

The one-dimensional contact process (CP) is studied by a systematic series of approximations. A new decoupling procedure of correlation functions is proposed by combining the idea of Suzuki's correlation-identity-decoupling (CID) with a concept of window. Liggett's approximations are also considered. Applying Suzuki's coherent-anomaly method (CAM) to the mean-field-type solutions, the values of the critical point and the critical exponents are estimated as λc = 1.6490(±0.0008), β=0.280(±0.013), Δ(= Δ/δ)= 1.734(±O.OO1), β=0.627(±0.005). Finally a comparison with other estimates is shown.

Applications of the CAM Based on a New Decoupling Procedure of Correlation Functions in the One-Dimensional Contact Process

NASA Astrophysics Data System (ADS)

Konno, Norio; Katori, Makoto

1990-05-01

The one-dimensional contact process (CP) is studied by a systematic series of approximations. A new decoupling procedure of correlation functions is proposed by combining the idea of Suzuki’s correlation-identity-decoupling (CID) with a concept of window. Liggett’s approximations are also considered. Applying Suzuki’s coherent-anomaly method (CAM) to the mean-field-type solutions, the values of the critical point and the critical exponents are estimated as λc{=}1.6490(± 0.0008), β{=}0.280(± 0.013), \\varDelta({=}β/δ){=}1.734(± 0.001), \\hatβ{=}0.627(± 0.005). Finally a comparison with other estimates is shown.

Precise Calculation of a Bond Percolation Transition and Survival Rates of Nodes in a Complex Network

PubMed Central

Kawamoto, Hirokazu; Takayasu, Hideki; Jensen, Henrik Jeldtoft; Takayasu, Misako

2015-01-01

Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relation network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point, and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition. PMID:25885791

Moessbauer effect: Study of disordered magnetic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Xiao Sha.

1989-01-01

This dissertation describes Moessbauer spectroscopy studies of two chemically disordered binary, crystalline alloys having the composition A{sub 1-x}B{sub x}. Both systems are random 3d Heisenberg ferromagnets. In each case both A and B atoms carry a magnetic moment. The first study concerns a Moessbauer absorber experiment on Fe{sub 1-x} V{sub x}, in which the disorder in the critical region is of the annealed random exchange type. To eliminate the effect of concentration inhomogeneity, the measurement of the critical exponent {beta} was done on the alloy with x = 0.125, where dT{sub C}/dx = 0, yielding {beta} = 0.362(8) over themore » reduced temperature range 1.4 {times} 10{sup {minus}3} < t < 4.88 {times} 10{sup {minus}1}. This result confirms the theoretical prediction that the annealed disorder is irrelevant to critical behavior in this case. As expected the critical exponent {beta} is consistent with the expectation for the 3d Heisenberg model as well as the measured exponent of pure Fe. The second study involves a Moessbauer source experiment on {sup 57} CoPd{sub 0.80}Co{sub 0.20}, in which disorder is of the quenched random exchange type perturbed by a very weak random anisotropy interaction. The critical exponent {beta} deduced over the range 1 {times} 10{sup {minus}2} < t < 2 {times} 10{sup {minus}1} is 0.385(20), and is consistent with the theoretical prediction for quenched disordered 3d Heisenberg systems: the disorder is irrelevant to the critical behavior. However, because of the restricted range of reduced temperature, the result is insufficiently asymptotic to serve as a conclusive test of the theory. Outside the critical region the distribution of Fe{sup 57} hyperfine field in Pd{sub 0.80}Co{sub 0.20} is observed to have an anomalous temperature dependence characterized by a linear increase in the width of the field distribution for T/T{sub C} {ge} 0.6.« less

Gravity-darkening exponents in semi-detached binary systems from their photometric observations. II.

NASA Astrophysics Data System (ADS)

Djurašević, G.; Rovithis-Livaniou, H.; Rovithis, P.; Georgiades, N.; Erkapić, S.; Pavlović, R.

2006-01-01

This second part of our study concerning gravity-darkening presents the results for 8 semi-detached close binary systems. From the light-curve analysis of these systems the exponent of the gravity-darkening (GDE) for the Roche lobe filling components has been empirically derived. The method used for the light-curve analysis is based on Roche geometry, and enables simultaneous estimation of the systems' parameters and the gravity-darkening exponents. Our analysis is restricted to the black-body approximation which can influence in some degree the parameter estimation. The results of our analysis are: 1) For four of the systems, namely: TX UMa, β Per, AW Cam and TW Cas, there is a very good agreement between empirically estimated and theoretically predicted values for purely convective envelopes. 2) For the AI Dra system, the estimated value of gravity-darkening exponent is greater, and for UX Her, TW And and XZ Pup lesser than corresponding theoretical predictions, but for all mentioned systems the obtained values of the gravity-darkening exponent are quite close to the theoretically expected values. 3) Our analysis has proved generally that with the correction of the previously estimated mass ratios of the components within some of the analysed systems, the theoretical predictions of the gravity-darkening exponents for stars with convective envelopes are highly reliable. The anomalous values of the GDE found in some earlier studies of these systems can be considered as the consequence of the inappropriate method used to estimate the GDE. 4) The empirical estimations of GDE given in Paper I and in the present study indicate that in the light-curve analysis one can apply the recent theoretical predictions of GDE with high confidence for stars with both convective and radiative envelopes.

The isentropic exponent in plasmas

NASA Astrophysics Data System (ADS)

Burm, K. T. A. L.; Goedheer, W. J.; Schram, D. C.

1999-06-01

The isentropic exponent for gases is a physical quantity that can ease significantly the hydrodynamic modeling effort. In gas dynamics the isentropic exponent depends only on the number of degrees of freedom of the considered gas. The isentropic exponent for a plasma is lower due to an extra degree of freedom caused by ionization. In this paper it will be shown that, like for gases, the isentropic exponent for atomic plasmas is also constant, as long as the ionization degree is between 5%-80%. Only a very weak dependence on the electron temperature and the two nonequilibrium parameters remain. An argon plasma is used to demonstrate the behavior of the isentropic exponent on the plasma conditions, and to make an estimation of the value of the isentropic exponent of a customary plasma. For atmospheric plasmas, which usually have an electron temperature of about 1 eV, a sufficiently accurate estimate for the isentropic exponent of plasmas is 1.16.

Quantum criticality of one-dimensional multicomponent Fermi gas with strongly attractive interaction

NASA Astrophysics Data System (ADS)

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 H1, H2 (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.

Coexistence Curve of Perfluoromethylcyclohexane-Isopropyl Alcohol

NASA Technical Reports Server (NTRS)

Jacobs, D. T.; Kuhl, D. E.; Selby, C. E.

1996-01-01

The coexistence curve of the binary fluid mixture perfluoromethylcyclohexane-isopropyl alcohol was determined by precisely measuring the refractive index both above and below its upper critical consolute point. Sixty-seven two-phase data points were obtained over a wide range of reduced temperatures, 10(exp -5) less than t less than 2.5 x 10(exp -1), to determine the location of the critical point: critical temperature=89.901 C, and critical composition = 62.2% by volume perfluoromethylcyclohexane. These data were analyzed to determine the critical exponent 8 close to the critical point, the amplitude B, and the anomaly in the diameter. The volume-fraction coexistence curve is found to be as symmetric as any composition like variable. Correction to scaling is investigated as well as the need for a crossover theory. A model is proposed that describes the asymptotic approach to zero of the effective exponent Beta, which allows an estimation of the temperature regime free of crossover effects.

Exact Critical Exponents for the Antiferromagnetic Quantum Critical Metal in Two Dimensions

NASA Astrophysics Data System (ADS)

Schlief, Andres; Lunts, Peter; Lee, Sung-Sik

2017-04-01

Unconventional metallic states which do not support well-defined single-particle excitations can arise near quantum phase transitions as strong quantum fluctuations of incipient order parameters prevent electrons from forming coherent quasiparticles. Although antiferromagnetic phase transitions occur commonly in correlated metals, understanding the nature of the strange metal realized at the critical point in layered systems has been hampered by a lack of reliable theoretical methods that take into account strong quantum fluctuations. We present a nonperturbative solution to the low-energy theory for the antiferromagnetic quantum critical metal in two spatial dimensions. Being a strongly coupled theory, it can still be solved reliably in the low-energy limit as quantum fluctuations are organized by a new control parameter that emerges dynamically. We predict the exact critical exponents that govern the universal scaling of physical observables at low temperatures.

A tensor product state approach to spin-1/2 square J1-J2 antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality

NASA Astrophysics Data System (ADS)

Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank; Wen, Xiang-Gang

We study this model using the cluster update algorithm for tensor product states (TPSs). We find that the ground state energies at finite sizes and in the thermodynamic limit are in good agreement with the exact diagonalization study. At the largest bond dimension available D = 9 and through finite size scaling of the magnetization order near the transition point, we accurately determine the critical point J2c1 = 0 . 53 (1) J1 and the critical exponents β = 0 . 50 (4) . In the intermediate region we find a paramagnetic ground state without any static valence bond solid (VBS) order, supported by an exponentially decaying spin-spin correlation while a power law decaying dimer-dimer correlation. By fitting a universal scaling function for the spin-spin correlation we find the critical exponents ν = 0 . 68 (3) and ηs = 0 . 34 (6) , which is very close to the observed critical exponents for deconfined quantum critical point (DQCP) in other systems. Thus our numerical results strongly suggest a Landau forbidden phase transition from Neel order to VBS order at J2c1 = 0 . 53 (1) J1 . This project is supported by the EU Strep project QUEVADIS, the ERC Grant QUERG, and the FWF SFB Grants FoQuS and ViCoM; and the Institute for Quantum Information and Matter.

Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging Different Concepts of Nonequilibrium Criticality

NASA Astrophysics Data System (ADS)

Žunkovič, Bojan; Heyl, Markus; Knap, Michael; Silva, Alessandro

2018-03-01

We theoretically study the dynamics of a transverse-field Ising chain with power-law decaying interactions characterized by an exponent α , which can be experimentally realized in ion traps. We focus on two classes of emergent dynamical critical phenomena following a quantum quench from a ferromagnetic initial state: The first one manifests in the time-averaged order parameter, which vanishes at a critical transverse field. We argue that such a transition occurs only for long-range interactions α ≤2 . The second class corresponds to the emergence of time-periodic singularities in the return probability to the ground-state manifold which is obtained for all values of α and agrees with the order parameter transition for α ≤2 . We characterize how the two classes of nonequilibrium criticality correspond to each other and give a physical interpretation based on the symmetry of the time-evolved quantum states.

Quantum phase transition from mixed atom-molecule phase to pure molecule phase: Characteristic scaling laws and Berry-curvature signature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Shengchang; Graduate School, China Academy of Engineering Physics, Beijing 100088; Fu Libin

2011-08-15

We investigate the quantum phase transition in an ultracold atom-molecule conversion system. It is found that the system undergoes a phase transition from a mixed atom-molecule phase to a pure molecule phase when the energy bias exceeds a critical value. By constructing a coherent state as variational state, we get a good approximation of the quantum ground state of the system. Using this variational state, we deduce the critical point analytically. We then discuss the scaling laws characterizing the transition and obtain the corresponding critical exponents. Furthermore, the Berry curvature signature of the transition is studied. In particular, we findmore » that the derivatives of the Berry curvature with respect to total particle number intersect at the critical point. The underlying mechanism of this finding is discussed as well.« less

A quasi-crisis

NASA Astrophysics Data System (ADS)

Wang, Ying-Mei; Wang, Wen-Xiu; Chen, He-Sheng; Zhang, Kai; Jiang, Yu-Mei; Wang, Xu-Ming; He, Da-Ren

2002-03-01

A system concatenated by two area-preserving maps may be addressed as "quasi- dissipative," since such a system can display dissipative behaviors^1. This is due to noninvertibility induced by discontinuity in the system function. In such a system, the image set of the discontinuous border forms a chaotic quasi-attractor. At a critical control parameter value the quasi-attractor suddenly vanishes. The chaotic iterations escape, via a leaking hole, to an emergent period-8 elliptic island. The hole is the intersection of the chaotic quasi-attractor and the period-8 island. The chaotic quasi-attractor thus changes to chaotic quasi-transients. The scaling behavior that drives the quasi-crisis has been investigated numerically. It reads: ∝ (p-p_c)^-ν , where is defined as the averaged length of quasi-transients. The scaling exponent ν=1.66 ± 0.04. The critical parameter value equals p_c=-1.0069799. ^1 J. Wang et al., Phys.Rev.E, 64(2001)026202.

Mixed-order phase transition of the contact process near multiple junctions.

PubMed

Juhász, Róbert; Iglói, Ferenc

2017-02-01

We have studied the phase transition of the contact process near a multiple junction of M semi-infinite chains by Monte Carlo simulations. As opposed to the continuous transitions of the translationally invariant (M=2) and semi-infinite (M=1) system, the local order parameter is found to be discontinuous for M>2. Furthermore, the temporal correlation length diverges algebraically as the critical point is approached, but with different exponents on the two sides of the transition. In the active phase, the estimate is compatible with the bulk value, while in the inactive phase it exceeds the bulk value and increases with M. The unusual local critical behavior is explained by a scaling theory with an irrelevant variable, which becomes dangerous in the inactive phase. Quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results.

Time-dependent fiber bundles with local load sharing. II. General Weibull fibers.

PubMed

Phoenix, S Leigh; Newman, William I

2009-12-01

Fiber bundle models (FBMs) are useful tools in understanding failure processes in a variety of material systems. While the fibers and load sharing assumptions are easily described, FBM analysis is typically difficult. Monte Carlo methods are also hampered by the severe computational demands of large bundle sizes, which overwhelm just as behavior relevant to real materials starts to emerge. For large size scales, interest continues in idealized FBMs that assume either equal load sharing (ELS) or local load sharing (LLS) among fibers, rules that reflect features of real load redistribution in elastic lattices. The present work focuses on a one-dimensional bundle of N fibers under LLS where life consumption in a fiber follows a power law in its load, with exponent rho , and integrated over time. This life consumption function is further embodied in a functional form resulting in a Weibull distribution for lifetime under constant fiber stress and with Weibull exponent, beta. Thus the failure rate of a fiber depends on its past load history, except for beta=1 . We develop asymptotic results validated by Monte Carlo simulation using a computational algorithm developed in our previous work [Phys. Rev. E 63, 021507 (2001)] that greatly increases the size, N , of treatable bundles (e.g., 10(6) fibers in 10(3) realizations). In particular, our algorithm is O(N ln N) in contrast with former algorithms which were O(N2) making this investigation possible. Regimes are found for (beta,rho) pairs that yield contrasting behavior for large N. For rho>1 and large N, brittle weakest volume behavior emerges in terms of characteristic elements (groupings of fibers) derived from critical cluster formation, and the lifetime eventually goes to zero as N-->infinity , unlike ELS, which yields a finite limiting mean. For 1/21 but with 0

Time-dependent fiber bundles with local load sharing. II. General Weibull fibers

NASA Astrophysics Data System (ADS)

Phoenix, S. Leigh; Newman, William I.

2009-12-01

Fiber bundle models (FBMs) are useful tools in understanding failure processes in a variety of material systems. While the fibers and load sharing assumptions are easily described, FBM analysis is typically difficult. Monte Carlo methods are also hampered by the severe computational demands of large bundle sizes, which overwhelm just as behavior relevant to real materials starts to emerge. For large size scales, interest continues in idealized FBMs that assume either equal load sharing (ELS) or local load sharing (LLS) among fibers, rules that reflect features of real load redistribution in elastic lattices. The present work focuses on a one-dimensional bundle of N fibers under LLS where life consumption in a fiber follows a power law in its load, with exponent ρ , and integrated over time. This life consumption function is further embodied in a functional form resulting in a Weibull distribution for lifetime under constant fiber stress and with Weibull exponent, β . Thus the failure rate of a fiber depends on its past load history, except for β=1 . We develop asymptotic results validated by Monte Carlo simulation using a computational algorithm developed in our previous work [Phys. Rev. EPLEEE81063-651X 63, 021507 (2001)] that greatly increases the size, N , of treatable bundles (e.g., 106 fibers in 103 realizations). In particular, our algorithm is O(NlnN) in contrast with former algorithms which were O(N2) making this investigation possible. Regimes are found for (β,ρ) pairs that yield contrasting behavior for large N . For ρ>1 and large N , brittle weakest volume behavior emerges in terms of characteristic elements (groupings of fibers) derived from critical cluster formation, and the lifetime eventually goes to zero as N→∞ , unlike ELS, which yields a finite limiting mean. For 1/2≤ρ≤1 , however, LLS has remarkably similar behavior to ELS (appearing to be virtually identical for ρ=1 ) with an asymptotic Gaussian lifetime distribution and a finite limiting mean for large N . The coefficient of variation follows a power law in increasing N but, except for ρ=1 , the value of the negative exponent is clearly less than 1/2 unlike in ELS bundles where the exponent remains 1/2 for 1/2<ρ≤1 . For sufficiently small values 0<ρ≪1 , a transition occurs, depending on β , whereby LLS bundle lifetimes become dominated by a few long-lived fibers. Thus the bundle lifetime appears to approximately follow an extreme-value distribution for the longest lived of a parallel group of independent elements, which applies exactly to ρ=0 . The lower the value of β , the higher the transition value of ρ , below which such extreme-value behavior occurs. No evidence was found for limiting Gaussian behavior for ρ>1 but with 0<β(ρ+1)<1 , as might be conjectured from quasistatic bundle models where β(ρ+1) mimics the Weibull exponent for fiber strength.

Equilibrium and nonequilibrium models on solomon networks with two square lattices

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios γ/ν, β/ν, and 1/ν. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Quantum Griffiths singularity of superconductor-metal transition in Ga thin films.

PubMed

Xing, Ying; Zhang, Hui-Min; Fu, Hai-Long; Liu, Haiwen; Sun, Yi; Peng, Jun-Ping; Wang, Fa; Lin, Xi; Ma, Xu-Cun; Xue, Qi-Kun; Wang, Jian; Xie, X C

2015-10-30

The Griffiths singularity in a phase transition, caused by disorder effects, was predicted more than 40 years ago. Its signature, the divergence of the dynamical critical exponent, is challenging to observe experimentally. We report the experimental observation of the quantum Griffiths singularity in a two-dimensional superconducting system. We measured the transport properties of atomically thin gallium films and found that the films undergo superconductor-metal transitions with increasing magnetic field. Approaching the zero-temperature quantum critical point, we observed divergence of the dynamical critical exponent, which is consistent with the Griffiths singularity behavior. We interpret the observed superconductor-metal quantum phase transition as the infinite-randomness critical point, where the properties of the system are controlled by rare large superconducting regions. Copyright © 2015, American Association for the Advancement of Science.

Ising Critical Behavior of Inhomogeneous Curie-Weiss Models and Annealed Random Graphs

NASA Astrophysics Data System (ADS)

Dommers, Sander; Giardinà, Cristian; Giberti, Claudio; van der Hofstad, Remco; Prioriello, Maria Luisa

2016-11-01

We study the critical behavior for inhomogeneous versions of the Curie-Weiss model, where the coupling constant {J_{ij}(β)} for the edge {ij} on the complete graph is given by {J_{ij}(β)=β w_iw_j/( {sum_{kin[N]}w_k})}. We call the product form of these couplings the rank-1 inhomogeneous Curie-Weiss model. This model also arises [with inverse temperature {β} replaced by {sinh(β)} ] from the annealed Ising model on the generalized random graph. We assume that the vertex weights {(w_i)_{iin[N]}} are regular, in the sense that their empirical distribution converges and the second moment converges as well. We identify the critical temperatures and exponents for these models, as well as a non-classical limit theorem for the total spin at the critical point. These depend sensitively on the number of finite moments of the weight distribution. When the fourth moment of the weight distribution converges, then the critical behavior is the same as on the (homogeneous) Curie-Weiss model, so that the inhomogeneity is weak. When the fourth moment of the weights converges to infinity, and the weights satisfy an asymptotic power law with exponent {τ} with {τin(3,5)}, then the critical exponents depend sensitively on {τ}. In addition, at criticality, the total spin {S_N} satisfies that {S_N/N^{(τ-2)/(τ-1)}} converges in law to some limiting random variable whose distribution we explicitly characterize.

Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: effects of strong compressibility and large-scale anisotropy.

PubMed

Antonov, N V; Kostenko, M M

2014-12-01

The field theoretic renormalization group and the operator product expansion are applied to two models of passive scalar quantities (the density and the tracer fields) advected by a random turbulent velocity field. The latter is governed by the Navier-Stokes equation for compressible fluid, subject to external random force with the covariance ∝δ(t-t')k(4-d-y), where d is the dimension of space and y is an arbitrary exponent. The original stochastic problems are reformulated as multiplicatively renormalizable field theoretic models; the corresponding renormalization group equations possess infrared attractive fixed points. It is shown that various correlation functions of the scalar field, its powers and gradients, demonstrate anomalous scaling behavior in the inertial-convective range already for small values of y. The corresponding anomalous exponents, identified with scaling (critical) dimensions of certain composite fields ("operators" in the quantum-field terminology), can be systematically calculated as series in y. The practical calculation is performed in the leading one-loop approximation, including exponents in anisotropic contributions. It should be emphasized that, in contrast to Gaussian ensembles with finite correlation time, the model and the perturbation theory presented here are manifestly Galilean covariant. The validity of the one-loop approximation and comparison with Gaussian models are briefly discussed.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Macías-Díaz, Jorge E.; Kofané, Timoléon Crépin

2018-03-01

We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α ∈ [1,2]. We perform a linear stability analysis and derive the conditions for diffusion-driven wave instabilities. Emphasis is placed on the effect of the superdiffusion exponent α , the diffusion ratio d , and the inertial time τ . As the superdiffusive exponent increases, so does the wave number of the Turing instability. Opposite to the requirement for Turing instability, the activator needs to diffuse sufficiently faster than the inhibitor in order for the wave instability to occur. The critical wave number for wave instability decreases with the superdiffusive exponent and increases with the inertial time. The maximum value of the inertial time for a wave instability to occur in the system is τmax=3.6 . As one of the main results of this work, we conclude that both anomalous diffusion and inertial time influence strongly the conditions for wave instabilities in hyperbolic fractional reaction-diffusion systems. Some numerical simulations are conducted as evidence of the analytical predictions derived in this work.

Influence of Inertial, Visous and Capillary Effects on the Apical Behavior of Taylor Cone Formation in Liquid Metals

NASA Astrophysics Data System (ADS)

Albertson, Theodore; Troian, Sandra

Above a critical applied field strength, the surface of a liquid metal can deform into a conical shape whose apex can emit ions. The precursor shape and dynamics to that event have been debated for decades. In a landmark paper, Zubarev (2001) invoked potential flow theory to predict the existence of self-similar apical sharpening for the case of an ideal perfectly conducting liquid. He found that the Maxwell and capillary pressures at the cone tip scale in time as -2/3 upon approach to the singularity. In this talk, we examine the behavior of thin electrified microscale films placed in close proximity to a grounded planar counter electrode to probe how inertial and viscous forces, diminished or neglected in the original analysis, modify the power law exponents governing the apical self-similar regime. We employ finite element, moving mesh simulations to investigate these effects for low, intermediate and high electric Reynolds and capillary numbers. We confirm the robustness of the self-similar regime characterized by power law exponents despite the lack of potential flow - however, the power law exponents, no longer -2/3, assume values which depend on the choice of dimensionless numbers. TGA gratefully acknowledges support from a NASA Space Technology Research Fellowship.

Sample and population exponents of generalized Taylor's law.

PubMed

Giometto, Andrea; Formentin, Marco; Rinaldo, Andrea; Cohen, Joel E; Maritan, Amos

2015-06-23

Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. Its ubiquitous empirical verification suggests a context-independent mechanism. Sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b = 2. Some theoretical models of population growth, however, predict a broad range of values for the population exponent b pertaining to the mean and variance of population density, depending on details of the growth process. Is the widely reported sample exponent b ≃ 2 the result of ecological processes or could it be a statistical artifact? Here, we apply large deviations theory and finite-sample arguments to show exactly that in a broad class of growth models the sample exponent is b ≃ 2 regardless of the underlying population exponent. We derive a generalized TL in terms of sample and population exponents b(jk) for the scaling of the kth vs. the jth cumulants. The sample exponent b(jk) depends predictably on the number of samples and for finite samples we obtain b(jk) ≃ k = j asymptotically in time, a prediction that we verify in two empirical examples. Thus, the sample exponent b ≃ 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly. Given the broad class of models investigated, our results apply to many fields where TL is used although inadequately understood.

Second Sound Measurements Very Near the Lambda Point

NASA Technical Reports Server (NTRS)

Adriaans, M.; Lipa, J.

1999-01-01

The sound was generated by wire-wound heaters embedded in the end opposite the sensor in each cavity. The superfluid density was determined from second sound measurements and the critical exponent v was obtained from fits to the data. The results from the exponent were found to be very sensitive to the treatment of systematic effects in the data.

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

NASA Astrophysics Data System (ADS)

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.

Correlation between the Hurst exponent and the maximal Lyapunov exponent: Examining some low-dimensional conservative maps

NASA Astrophysics Data System (ADS)

Tarnopolski, Mariusz

2018-01-01

The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this space. A tight correlation between the HEs and mLEs is found, with the Spearman rank ρ = 0 . 83 and ρ = 0 . 75 for the Chirikov and 2D Froeschlé maps, respectively. Based on this relation, a machine learning (ML) procedure, using the nearest neighbor algorithm, is performed to reproduce the HE distribution based on the mLE distribution alone. A few thousand HE and mLE values from the mixed spaces were used for training, and then using 2 - 2 . 4 × 105 mLEs, the HEs were retrieved. The ML procedure allowed to reproduce the structure of the mixed spaces in great detail.

Extracting sensitive spectrum bands of rapeseed using multiscale multifractal detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Jiang, Shan; Wang, Fang; Shen, Luming; Liao, Guiping; Wang, Lin

2017-03-01

Spectrum technology has been widely used in crop non-destructive testing diagnosis for crop information acquisition. Since spectrum covers a wide range of bands, it is of critical importance to extract the sensitive bands. In this paper, we propose a methodology to extract the sensitive spectrum bands of rapeseed using multiscale multifractal detrended fluctuation analysis. Our obtained sensitive bands are relatively robust in the range of 534 nm-574 nm. Further, by using the multifractal parameter (Hurst exponent) of the extracted sensitive bands, we propose a prediction model to forecast the Soil and plant analyzer development values ((SPAD), often used as a parameter to indicate the chlorophyll content) and an identification model to distinguish the different planting patterns. Three vegetation indices (VIs) based on previous work are used for comparison. Three evaluation indicators, namely, the root mean square error, the correlation coefficient, and the relative error employed in the SPAD values prediction model all demonstrate that our Hurst exponent has the best performance. Four rapeseed compound planting factors, namely, seeding method, planting density, fertilizer type, and weed control method are considered in the identification model. The Youden indices calculated by the random decision forest method and the K-nearest neighbor method show that our Hurst exponent is superior to other three Vis, and their combination for the factor of seeding method. In addition, there is no significant difference among the five features for other three planting factors. This interesting finding suggests that the transplanting and the direct seeding would make a big difference in the growth of rapeseed.

The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance

PubMed Central

Liu, Kun; Wang, Hongrui; Xiao, Jinzhuang

2015-01-01

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. PMID:26064182

Variation of alluvial-channel width with discharge and character of sediment

USGS Publications Warehouse

Osterkamp, W.R.

1979-01-01

Use of channel measurements to estimate discharge characteristics of alluvial streams has shown that little agreement exists for the exponent of the width-discharge relation. For the equation Q = aWAb, where Q is mean discharge and WA is active-channel width, it is proposed that the exponent, b, should be of fixed value for most natural, perennial, alluvial stream channels and that the coefficient, a, varies with the characteristics of the bed and bank material.Three groups of perennial stream channels with differing characteristics were selected for study using consistent procedures of data collection. A common feature of the groups was general channel stability, that is, absence of excessive widening by erosive discharges. Group 1 consisted of 32 channels of gradient exceeding 0.0080, low suspended-sediment discharge, high channel roughness, and low discharge variability. Group 2 consisted of 13 streams in Kansas having at least 70 percent silt and clay in the bed material and having similar discharge variability, climate, gradient, and riparian vegetation. Group 3, in southern Missouri, consisted of discharge channels of 18 springs having similar conditions of very low discharge variability, climate and vegetation, but variable bed and bank material. Values for the exponent for the three groups of data are 1.98, 1.97, and 1.97, respectively, whereas values of the coefficients are 0.017, 0.042, and 0.011 when discharge is expressed in cubic meters per second and width is in meters. The relation for high-gradient channels (group 1) is supported by published data from laboratory flumes.The similarity of the three values of the exponent demonstrates that a standard exponent of 2.0, significant to two figures, is reasonable for the width-mean discharge relation of perennial, alluvial stream channels, and that the exponent is independent of other variables. Using a fixed exponent of 2.0, a family of simple power-function equations was developed expressing the manner in which channel sediment affects the width-discharge relation.

Defect production in nonlinear quench across a quantum critical point.

PubMed

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.

Stochastic bifurcation in a model of love with colored noise

NASA Astrophysics Data System (ADS)

Yue, Xiaokui; Dai, Honghua; Yuan, Jianping

2015-07-01

In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.

Phase transition in the spin- 3 / 2 Blume-Emery-Griffiths model with antiferromagnetic second neighbor interactions

NASA Astrophysics Data System (ADS)

Yezli, M.; Bekhechi, S.; Hontinfinde, F.; EZ-Zahraouy, H.

2016-04-01

Two nonperturbative methods such as Monte-Carlo simulation (MC) and Transfer-Matrix Finite-Size-Scaling calculations (TMFSS) have been used to study the phase transition of the spin- 3 / 2 ​Blume-Emery-Griffiths model (BEG) with quadrupolar and antiferromagnetic next-nearest-neighbor exchange interactions. Ground state and finite temperature phase diagrams are obtained by means of these two methods. New degenerate phases are found and only second order phase transitions occur for all values of the parameter interactions. No sign of the intermediate phase is found from both methods. Critical exponents are also obtained from TMFSS calculations. Ising criticality and nonuniversal behaviors are observed depending on the strength of the second neighbor interaction.

Magnetism of epitaxial Tb films on W(110) studied by spin-polarized low-energy electron microscopy

NASA Astrophysics Data System (ADS)

Prieto, J. E.; Chen, Gong; Schmid, A. K.; de la Figuera, J.

2016-11-01

Thin epitaxial films of Tb metal were grown on a clean W(110) substrate in ultrahigh vacuum and studied in situ by low-energy electron microscopy. Annealed films present magnetic contrast in spin-polarized low-energy electron microscopy. The energy dependence of the electron reflectivity was determined and a maximum value of its spin asymmetry of about 1% was measured. The magnetization direction of the Tb films is in-plane. Upon raising the temperature, no change in the domain distribution is observed, while the asymmetry in the electron reflectivity decreases when approaching the critical temperature, following a power law ˜(1-T /TC) β with a critical exponent β of 0.39.

Scaling behaviors of precipitation over China

NASA Astrophysics Data System (ADS)

Jiang, Lei; Li, Nana; Zhao, Xia

2017-04-01

Scaling behaviors in the precipitation time series derived from 1951 to 2009 over China are investigated by detrended fluctuation analysis (DFA) method. The results show that there exists long-term memory for the precipitation time series in some stations, where the values of the scaling exponent α are less than 0.62, implying weak persistence characteristics. The values of scaling exponent in other stations indicate random behaviors. In addition, the scaling exponent α in precipitation records varies from station to station over China. A numerical test is made to verify the significance in DFA exponents by shuffling the data records many times. We think it is significant when the values of scaling exponent before shuffled precipitation records are larger than the interval threshold for 95 % confidence level after shuffling precipitation records many times. By comparison, the daily precipitation records exhibit weak positively long-range correlation in a power law fashion mainly at the stations taking on zonal distributions in south China, upper and middle reaches of the Yellow River, northern part of northeast China. This may be related to the subtropical high. Furthermore, the values of scaling exponent which cannot pass the significance test do not show a clear distribution pattern. It seems that the stations are mainly distributed in coastal areas, southwest China, and southern part of north China. In fact, many complicated factors may affect the scaling behaviors of precipitation such as the system of the east and south Asian monsoon, the interaction between sea and land, and the big landform of the Tibetan Plateau. These results may provide a better prerequisite to long-term predictor of precipitation time series for different regions over China.

Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Um, Jaegon; Yi, Su Do; Kim, Beom Jun

2011-11-01

In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional lattices, however, one can also consider infinite-dimensional structures, and the question is whether this mean-field character extends to quantum-mechanical cases as well. We therefore investigate the transverse-field quantum Ising model on the globally coupled network and on the Watts-Strogatz small-world network by means of quantum Monte Carlo simulations and the finite-size scaling analysis. We confirm that both of the structures exhibit critical behavior consistent with the mean-field description. In particular, we show that the existing cumulant method has difficulty in estimating the correct dynamic critical exponent and suggest that an order parameter based on the quantum-mechanical expectation value can be a practically useful numerical observable to determine critical behavior when there is no well-defined dimensionality.

A discrete model on Sierpinski gasket substrate for a conserved current equation with a conservative noise

NASA Astrophysics Data System (ADS)

Kim, Dae Ho; Kim, Jin Min

2012-09-01

A conserved discrete model on the Sierpinski gasket substrate is studied. The interface width W in the model follows the Family-Vicsek dynamic scaling form with growth exponent β ≈ 0.0542, roughness exponent α ≈ 0.240 and dynamic exponent z ≈ 4.42. They satisfy a scaling relation α + z = 2zrw, where zrw is the random walk exponent of the fractal substrate. Also, they are in a good agreement with the predicted values of a fractional Langevin equation \\frac{\\partial h}{\\partial t}={\

Dynamics of social contagions with limited contact capacity.

PubMed

Wang, Wei; Shu, Panpan; Zhu, Yu-Xiao; Tang, Ming; Zhang, Yi-Cheng

2015-10-01

Individuals are always limited by some inelastic resources, such as time and energy, which restrict them to dedicate to social interaction and limit their contact capacities. Contact capacity plays an important role in dynamics of social contagions, which so far has eluded theoretical analysis. In this paper, we first propose a non-Markovian model to understand the effects of contact capacity on social contagions, in which each adopted individual can only contact and transmit the information to a finite number of neighbors. We then develop a heterogeneous edge-based compartmental theory for this model, and a remarkable agreement with simulations is obtained. Through theory and simulations, we find that enlarging the contact capacity makes the network more fragile to behavior spreading. Interestingly, we find that both the continuous and discontinuous dependence of the final adoption size on the information transmission probability can arise. There is a crossover phenomenon between the two types of dependence. More specifically, the crossover phenomenon can be induced by enlarging the contact capacity only when the degree exponent is above a critical degree exponent, while the final behavior adoption size always grows continuously for any contact capacity when degree exponent is below the critical degree exponent.

Coherent-Anomaly Method in Critical Phenomena. IV. Study of the Wave-Number-Dependent Susceptibility in the 2D Ising Model

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

1988-03-01

The systematic Weiss-like and Bethe-like approximations based on the mean-field transfer-matrix method are used to investigate the asymptotic behavior of the induced magnetization on a semi-infinite square lattice, and to investigate the wave-number dependence of the susceptibility in a nonuniform external field. The critical exponents ν, ν', ηi and η are estimated following the general CAM prescription. A new scaling relation ν{\\cdot}ηi{=}β is obtained in the framework of the finite-degree-of-approximation scaling. Together with previous papers, all the static critical exponents have been estimated by the CAM, and are shown to satisfy the well-known scaling relations.

Slow Relaxation in Anderson Critical Systems

NASA Astrophysics Data System (ADS)

Choi, Soonwon; Yao, Norman; Choi, Joonhee; Kucsko, Georg; Lukin, Mikhail

2016-05-01

We study the single particle dynamics in disordered systems with long range hopping, focusing on the critical cases, i.e., the hopping amplitude decays as 1 /rd in d-dimension. We show that with strong on-site potential disorder, the return probability of the particle decays as power-law in time. As on-site potential disorder decreases, the temporal profile smoothly changes from a simple power-law to the sum of multiple power-laws with exponents ranged from 0 to νmax. We analytically compute the decay exponents using a simple resonance counting argument, which quantitatively agrees with exact numerical results. Our result implies that the dynamics in Anderson Critical systems are dominated by resonances. Harvard-MIT CUA, Kwanjeong Educational Fellowship, AFOSR MURI, Samsung Scholarship.

Critical exponents and universal magnetic behavior of noncentrosymmetric Fe0.6Co0.4Si

NASA Astrophysics Data System (ADS)

Shanmukharao Samatham, S.; Suresh, K. G.

2018-05-01

The critical magnetic properties of a non-centrosymmetric B20 cubic helimagnet Fe0.6Co0.4Si are investigated using magnetization isotherms. It belongs to the 3D-Heisenberg universality class with short range magnetic coupling as inferred from the self-consistent critical exponents , , and in combination with exchange interaction . Itinerant magnetic nature of the compound is realized by the Rhodes–Wholfarth analysis. Field-induced weak first (parahelical) to second (parafield-polarized) order transition is reported to occur at low critical field due to the weak spin–orbit coupling arising from the weak Dzyaloshinksii–Moriya interactions. Our study suggests the distinct phenomenological magnetic structures for Fe-based cubic magnets (Fe1‑x Co x Si and FeGe) and MnSi which cause contrasting physical properties.

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

NASA Astrophysics Data System (ADS)

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.

Crystallization kinetics of orthorhombic paracetamol from supercooled melts studied by non-isothermal DSC.

PubMed

Nikolakakis, Ioannis; Kachrimanis, Kyriakos

2017-02-01

A simple and highly reproducible procedure was established for the study of orthorhombic paracetamol crystallization kinetics, comprising melting, quench-cooling of the melt and scanning the formed glass by DSC at different heating rates. Results were analyzed on the basis of the mean as well as local values of the Avrami exponent, n, the energy of activation, as well as the Šesták-Berggren two-parameter autocatalytic kinetic model. The mean value of the Avrami kinetic exponent, n, ranged between 3 and 5, indicating deviation from the nucleation and growth mechanism underlying the Johnson-Mehl, Avrami-Kolmogorov (JMAK) model. To verify the extent of the deviation, local values of the Avrami exponent as a function of the volume fraction transformed were calculated. Inspection of the local exponent values indicates that the crystallization mechanism changes over time, possibly reflecting the uncertainty of crystallization onset, instability of nucleation due to an autocatalytic effect of the crystalline phase, and growth anisotropy due to impingement of spherulites in the last stages of crystallization. The apparent energy of activation, E a , has a rather low mean value, close to 81 kJ/mol, which is in agreement with the observed instability of glassy-state paracetamol. Isoconversional methods revealed that E a tends to decrease with the volume fraction transformed, possibly because of the different energy demands of nucleation and growth. The exponents of the Šesták-Berggren two-parameter model showed that the crystallized fraction influences the process, confirming the complexity of the crystallization mechanism.

Lyapunov exponents of stochastic systems—from micro to macro

NASA Astrophysics Data System (ADS)

Laffargue, Tanguy; Tailleur, Julien; van Wijland, Frédéric

2016-03-01

Lyapunov exponents of dynamical systems are defined from the rates of divergence of nearby trajectories. For stochastic systems, one typically assumes that these trajectories are generated under the ‘same noise realization’. The purpose of this work is to critically examine what this expression means. For Brownian particles, we consider two natural interpretations of the noise: intrinsic to the particles or stemming from the fluctuations of the environment. We show how they lead to different distributions of the largest Lyapunov exponent as well as different fluctuating hydrodynamics for the collective density field. We discuss, both at microscopic and macroscopic levels, the limits in which these noise prescriptions become equivalent. We close this paper by providing an estimate of the largest Lyapunov exponent and of its fluctuations for interacting particles evolving with Dean-Kawasaki dynamics.

Multivalued classical mechanics arising from singularity loops in complex time

NASA Astrophysics Data System (ADS)

Koch, Werner; Tannor, David J.

2018-02-01

Complex-valued classical trajectories in complex time encounter singular times at which the momentum diverges. A closed time contour around such a singular time may result in final values for q and p that differ from their initial values. In this work, we develop a calculus for determining the exponent and prefactor of the asymptotic time dependence of p from the singularities of the potential as the singularity time is approached. We identify this exponent with the number of singularity loops giving distinct solutions to Hamilton's equations of motion. The theory is illustrated for the Eckart, Coulomb, Morse, and quartic potentials. Collectively, these potentials illustrate a wide variety of situations: poles and essential singularities at finite and infinite coordinate values. We demonstrate quantitative agreement between analytical and numerical exponents and prefactors, as well as the connection between the exponent and the time circuit count. This work provides the theoretical underpinnings for the choice of time contours described in the studies of Doll et al. [J. Chem. Phys. 58(4), 1343-1351 (1973)] and Petersen and Kay [J. Chem. Phys. 141(5), 054114 (2014)]. It also has implications for wavepacket reconstruction from complex classical trajectories when multiple branches of trajectories are involved.

Analysis of the heat capacity for pure CH4 and CH4/CCl4 on graphite near the melting point and calculation of the T-X phase diagram for (CH3)CCl3 + CCl4

NASA Astrophysics Data System (ADS)

Yurtseven, Hamit; Yılmaz, Aygül

2016-06-01

We study the temperature dependence of the heat capacity Cp for the pure CH4 and the coadsorbed CH4/CCl4 on graphite near the melting point. The heat capacity peaks are analyzed using the experimental data from the literature by means of the power-law formula. The critical exponents for the heat capacity are deduced below and above the melting point for CH4 (Tm = 104.8 K) and CH4/CCl4 (Tm = 99.2 K). Our exponent values are larger as compared with the predicted values of some theoretical models exhibiting second order transition. Our analyses indicate that the pure methane shows a nearly second order (weak discontinuity in the heat capacity peak), whereas the transition in coadsorbed CH4/CCl4 is of first order (apparent discontinuity in Cp). We also study the T - X phase diagram of a two-component system of CH3CCl3+CCl4 using the Landau phenomenological model. Phase lines of the R+L (rhombohedral+liquid) and FCC+L (face-centred cubic + liquid) are calculated using the observed T - X phase diagram of this binary mixture. Our results show that the Landau mean field theory describes the observed behavior of CH3CCl3+CCl4 adequately. From the calculated T - X phase diagram, critical behavior of some thermodynamic quantities can be predicted at various temperatures and concentrations (CCl4) for a binary mixture of CH3CCl3+CCl4.

Critical scaling analysis for displacive-type organic ferroelectrics around ferroelectric transition

NASA Astrophysics Data System (ADS)

Ding, L. J.

2017-04-01

The critical scaling properties of displacive-type organic ferroelectrics, in which the ferroelectric-paraelectric transition is induced by spin-Peierls instability, are investigated by Green's function theory through the modified Arrott plot, critical isothermal and electrocaloric effect (ECE) analysis around the transition temperature TC. It is shown that the electric entropy change - ΔS follows a power-law dependence of electric field E : - ΔS ∼En with n satisfying the Franco equation n(TC) = 1 +(β - 1) /(β + γ) = 0.618, wherein the obtained critical exponents β = 0.440 and γ = 1.030 are not only corroborated by Kouvel-Fisher method, but also confirm the Widom critical relation δ = 1 + γ / β. The self-consistency and reliability of the obtained critical exponents are further verified by the scaling equations. Additionally, a universal curve of - ΔS is constructed with rescaling temperature and electric field, so that one can extrapolate the ECE in a certain temperature and electric field range, which would be helpful in designing controlled electric refrigeration devices.

Potts-model formulation of the random resistor network

NASA Astrophysics Data System (ADS)

Harris, A. B.; Lubensky, T. C.

1987-05-01

The randomly diluted resistor network is formulated in terms of an n-replicated s-state Potts model with a spin-spin coupling constant J in the limit when first n, then s, and finally 1/J go to zero. This limit is discussed and to leading order in 1/J the generalized susceptibility is shown to reproduce the results of the accompanying paper where the resistor network is treated using the xy model. This Potts Hamiltonian is converted into a field theory by the usual Hubbard-Stratonovich transformation and thereby a renormalization-group treatment is developed to obtain the corrections to the critical exponents to first order in ɛ=6-d, where d is the spatial dimensionality. The recursion relations are shown to be the same as for the xy model. Their detailed analysis (given in the accompanying paper) gives the resistance crossover exponent as φ1=1+ɛ/42, and determines the critical exponent, t for the conductivity of the randomly diluted resistor network at concentrations, p, just above the percolation threshold: t=(d-2)ν+φ1, where ν is the critical exponent for the correlation length at the percolation threshold. These results correct previously accepted results giving φ=1 to all orders in ɛ. The new result for φ1 removes the paradox associated with the numerical result that t>1 for d=2, and also shows that the Alexander-Orbach conjecture, while numerically quite accurate, is not exact, since it disagrees with the ɛ expansion.

Endogenous and exogenous dynamics in the fluctuations of capital fluxes. An empirical analysis of the Chinese stock market

NASA Astrophysics Data System (ADS)

Jiang, Z.-Q.; Guo, L.; Zhou, W.-X.

2007-06-01

A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is carried out on the Chinese stock market using mean-variance analysis, fluctuation analysis, and their generalizations to higher orders. Non-universal dynamics have been found not only in the scaling exponent α, which is different from the universal values 1/2 and 1, but also in the distributions of the ratio η= σexo / σendo of individual stocks. Both the scaling exponent α of fluctuations and the Hurst exponent Hi increase in logarithmic form with the time scale Δt and the mean traded value per minute , respectively. We find that the scaling exponent αendo of the endogenous fluctuations is independent of the time scale. Multiscaling and multifractal features are observed in the data as well. However, the inhomogeneous impact model is not verified.

Hydropathic self-organized criticality: a magic wand for protein physics.

PubMed

Phillips, J C

2012-10-01

Self-organized criticality (SOC) is a popular concept that has been the subject of more than 3000 articles in the last 25 years. The characteristic signature of SOC is the appearance of self-similarity (power-law scaling) in observable properties. A characteristic observable protein property that describes protein-water interactions is the water-accessible (hydropathic) interfacial area of compacted globular protein networks. Here we show that hydropathic power-law (size- or length-scale-dependent) exponents derived from SOC enable theory to connect standard Web-based (BLAST) short-range amino acid (aa) sequence similarities to long-range aa sequence hydropathic roughening form factors that hierarchically describe evolutionary trends in water - membrane protein interactions. Our method utilizes hydropathic aa exponents that define a non-Euclidean metric realistically rooted in the atomic coordinates of 5526 protein segments. These hydropathic aa exponents thereby encapsulate universal (but previously only implicit) non-Euclidean long-range differential geometrical features of the Protein Data Bank. These hydropathic aa exponents easily organize small mutated aa sequence differences between human and proximate species proteins. For rhodopsin, the most studied transmembrane signaling protein associated with night vision, analysis shows that this approach separates Euclidean short- and non-Euclidean long-range aa sequence properties, and shows that they correlate with 96% success for humans, monkeys, cats, mice and rabbits. Proper application of SOC using hydropathic aa exponents promises unprecedented simplifications of exponentially complex protein sequence-structure-function problems, both conceptual and practical.

Three-state Potts model on non-local directed small-world lattices

NASA Astrophysics Data System (ADS)

Ferraz, Carlos Handrey Araujo; Lima, José Luiz Sousa

2017-10-01

In this paper, we study the non-local directed Small-World (NLDSW) disorder effects in the three-state Potts model as a form to capture the essential features shared by real complex systems where non-locality effects play a important role in the behavior of these systems. Using Monte Carlo techniques and finite-size scaling analysis, we estimate the infinite lattice critical temperatures and the leading critical exponents in this model. In particular, we investigate the first- to second-order phase transition crossover when NLDSW links are inserted. A cluster-flip algorithm was used to reduce the critical slowing down effect in our simulations. We find that for a NLDSW disorder densities p

The mass distribution of coarse particulate organic matter exported from an Alpine headwater stream

NASA Astrophysics Data System (ADS)

Turowski, J. M.; Badoux, A.; Bunte, K.; Rickli, C.; Federspiel, N.; Jochner, M.

2013-09-01

Coarse particulate organic matter (CPOM) particles span sizes from 1 mm, with a dry mass less than 1 mg, to large logs and entire trees, which can have a dry mass of several hundred kilograms. Pieces of different size and mass play different roles in stream environments, from being the prime source of energy in stream ecosystems to macroscopically determining channel morphology and local hydraulics. We show that a single scaling exponent can describe the mass distribution of CPOM heavier than 0.1 g transported in the Erlenbach, a steep mountain stream in the Swiss pre-Alps. This exponent takes an average value of -1.8, is independent of discharge and valid for particle masses spanning almost seven orders of magnitude. Similarly, the mass distribution of in-stream large woody debris (LWD) in several Swiss streams can be described by power law scaling distributions, with exponents varying between -1.8 and -2.0, if all in-stream LWD is considered, and between -1.3 and -1.8 for material locked in log jams. We found similar values for in-stream and transported material in the literature. We had expected that scaling exponents are determined by stream type, vegetation, climate, substrate properties, and the connectivity between channels and hillslopes. However, none of the descriptor variables tested here, including drainage area, channel bed slope and the percentage of forested area, show a strong control on exponent value. Together with a rating curve of CPOM transport rates with discharge, the scaling exponents can be used in the design of measuring strategies and in natural hazard mitigation.

Genetic Algorithms and Nucleation in VIH-AIDS transition.

NASA Astrophysics Data System (ADS)

Barranon, Armando

2003-03-01

VIH to AIDS transition has been modeled via a genetic algorithm that uses boom-boom principle and where population evolution is simulated with a cellular automaton based on SIR model. VIH to AIDS transition is signed by nucleation of infected cells and low probability of infection are obtained for different mutation rates in agreement with clinical results. A power law is obtained with a critical exponent close to the critical exponent of cubic, spherical percolation, colossal magnetic resonance, Ising Model and liquid-gas phase transition in heavy ion collisions. Computations were carried out at UAM-A Supercomputing Lab and author acknowledges financial support from Division of CBI at UAM-A.

Field-Tuned Superconductor-Insulator Transition with and without Current Bias.

PubMed

Bielejec, E; Wu, Wenhao

2002-05-20

The magnetic-field-tuned superconductor-insulator transition has been studied in ultrathin beryllium films quench condensed near 20 K. In the zero-current limit, a finite-size scaling analysis yields the scaling exponent product nuz = 1.35+/-0.10 and a critical sheet resistance, R(c), of about 1.2R(Q), with R(Q) = h/4e(2). However, in the presence of dc bias currents that are smaller than the zero-field critical currents, nuz becomes 0.75+/-0.10. This new set of exponents suggests that the field-tuned transitions with and without a dc bias current belong to different universality classes.

Impact of network topology on self-organized criticality

NASA Astrophysics Data System (ADS)

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.

Confirming Time-reversal Symmetry of a Directed Percolation Phase Transition in a Model of Neutral Evolutionary Dynamics

NASA Astrophysics Data System (ADS)

Ordway, Stephen; King, Dawn; Bahar, Sonya

Reaction-diffusion processes, such as branching-coalescing random walks, can be used to describe the underlying dynamics of nonequilibrium phase transitions. In an agent-based, neutral model of evolutionary dynamics, we have previously shown that our system undergoes a continuous, nonequilibrium phase transition, from extinction to survival, as various system parameters were tuned. This model was shown to belong to the directed percolation (DP) universality class, by measuring the critical exponents corresponding to correlation length ξ⊥, correlation time ξ| |, and particle density β. The fourth critical exponent that defines the DP universality class is β', which measures the survival probability of growth from a single seed organism. Since DP universality is theorized to have time-reversal symmetry, it is assumed that β = β '. In order to confirm the existence of time-reversal symmetry in our model, we evaluate the system growth from a single asexually reproducing organism. Importantly, the critical exponent β' could be useful for comparison to experimental studies of phase transitions in biological systems, since observing growth of microbial populations is significantly easier than observing death. This research was supported by funding from the James S. McDonnell Foundation.

Critical exponents and universal magnetic behavior of noncentrosymmetric Fe0.6Co0.4Si.

PubMed

Samatham, S Shanmukharao; Suresh, K G

2018-05-31

The critical magnetic properties of a non-centrosymmetric B20 cubic helimagnet Fe 0.6 Co 0.4 Si are investigated using magnetization isotherms. It belongs to the 3D-Heisenberg universality class with short range magnetic coupling as inferred from the self-consistent critical exponents [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in combination with exchange interaction [Formula: see text]. Itinerant magnetic nature of the compound is realized by the Rhodes-Wholfarth analysis. Field-induced weak first (para[Formula: see text]helical) to second (para[Formula: see text]field-polarized) order transition is reported to occur at low critical field due to the weak spin-orbit coupling arising from the weak Dzyaloshinksii-Moriya interactions. Our study suggests the distinct phenomenological magnetic structures for Fe-based cubic magnets (Fe 1-x Co x Si and FeGe) and MnSi which cause contrasting physical properties.

Dynamical critical exponent of the Jaynes-Cummings-Hubbard model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hohenadler, M.; Aichhorn, M.; Schmidt, S.

2011-10-15

An array of high-Q electromagnetic resonators coupled to qubits gives rise to the Jaynes-Cummings-Hubbard model describing a superfluid to Mott-insulator transition of lattice polaritons. From mean-field and strong-coupling expansions, the critical properties of the model are expected to be identical to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid density on the square lattice suggested that this does not hold for the fixed-density transition through the Mott lobe tip. Instead, mean-field behavior with a dynamical critical exponent z=2 was found. We perform large-scale quantum Monte Carlo simulations to investigate the critical behavior of the superfluid densitymore » and the compressibility. We find z=1 at the tip of the insulating lobe. Hence the transition falls in the three-dimensional XY universality class, analogous to the Bose-Hubbard model.« less

Probing the critical exponent of the superfluid fraction in a strongly interacting Fermi gas

NASA Astrophysics Data System (ADS)

Hu, Hui; Liu, Xia-Ji

2013-11-01

We theoretically investigate the critical behavior of a second-sound mode in a harmonically trapped ultracold atomic Fermi gas with resonant interactions. Near the superfluid phase transition with critical temperature Tc, the frequency or the sound velocity of the second-sound mode crucially depends on the critical exponent β of the superfluid fraction. In an isotropic harmonic trap, we predict that the mode frequency diverges like (1-T/Tc)β-1/2 when β<1/2. In a highly elongated trap, the speed of the second sound reduces by a factor of 1/2β+1 from that in a homogeneous three-dimensional superfluid. Our prediction could readily be tested by measurements of second-sound wave propagation in a setup, such as that exploited by Sidorenkov [Nature (London)NATUAS0028-083610.1038/nature12136 498, 78 (2013)] for resonantly interacting lithium-6 atoms, once the experimental precision is improved.

p-exponent and p-leaders, Part II: Multifractal analysis. Relations to detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Leonarduzzi, R.; Wendt, H.; Abry, P.; Jaffard, S.; Melot, C.; Roux, S. G.; Torres, M. E.

2016-04-01

Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and image processing tool and is commonly used in numerous applications of different natures. In its common formulation, it relies on the Hölder exponent as a measure of local regularity, which is by nature restricted to positive values and can hence be used for locally bounded functions only. In this contribution, it is proposed to replace the Hölder exponent with a collection of novel exponents for measuring local regularity, the p-exponents. One of the major virtues of p-exponents is that they can potentially take negative values. The corresponding wavelet-based multiscale quantities, the p-leaders, are constructed and shown to permit the definition of a new multifractal formalism, yielding an accurate practical estimation of the multifractal properties of real-world data. Moreover, theoretical and practical connections to and comparisons against another multifractal formalism, referred to as multifractal detrended fluctuation analysis, are achieved. The performance of the proposed p-leader multifractal formalism is studied and compared to previous formalisms using synthetic multifractal signals and images, illustrating its theoretical and practical benefits. The present contribution is complemented by a companion article studying in depth the theoretical properties of p-exponents and the rich classification of local singularities it permits.

Multiscale Auroral Emission Statistics as Evidence of Turbulent Reconnection in Earth's Midtail Plasma Sheet

NASA Technical Reports Server (NTRS)

Klimas, Alex; Uritsky, Vadim; Donovan, Eric

2010-01-01

We provide indirect evidence for turbulent reconnection in Earth's midtail plasma sheet by reexamining the statistical properties of bright, nightside auroral emission events as observed by the UVI experiment on the Polar spacecraft and discussed previously by Uritsky et al. The events are divided into two groups: (1) those that map to absolute value of (X(sub GSM)) < 12 R(sub E) in the magnetotail and do not show scale-free statistics and (2) those that map to absolute value of (X(sub GSM)) > 12 R(sub E) and do show scale-free statistics. The absolute value of (X(sub GSM)) dependence is shown to most effectively organize the events into these two groups. Power law exponents obtained for group 2 are shown to validate the conclusions of Uritsky et al. concerning the existence of critical dynamics in the auroral emissions. It is suggested that the auroral dynamics is a reflection of a critical state in the magnetotail that is based on the dynamics of turbulent reconnection in the midtail plasma sheet.

The Hack's law applied to young volcanic basin: the Tahiti case

NASA Astrophysics Data System (ADS)

Ye, F.; Sichoix, L.; Barriot, J.; Serafini, J.

2010-12-01

We study the channel morphology over the Tahiti island from the Hack’s law perspective. The Hack’s law is an empirical power relationship between basin drainage area and the length of its main channel. It had also been shown that drainage area becomes more elongate with increasing basin size. For typical continental basins, the exponent value lies between 0.47 for basins larger than 260,000 km2 and 0.7 for those spanning less than 20,720 km2 (Muller, 1973). In Tahiti, we extracted 27 principal basins ranging from 7 km2 to 90 km2 from a Digital Terrain Model of the island with a 5 m-resolution. We demonstrate that the Hack’s law still apply for such small basins (correlation coefficient R2=0.7) with an exponent value being approximately 0.5. It appears that the exponent value is influenced by the local geomorphic condition, and does not follow the previous study results (the exponent value decreases with increasing drainage area.) Our exponent value matches the result found w.r.t. debris-flow basins of China for drainage areas less than 100 km2 (Li et al., 2008). Otherwise, the young volcanic basins of Tahiti do not become longer and narrower with increasing basin size (R2=0.1). Besides, there is no correlation between the basin area and the basin convexity (R2=0). This means that there is no statistical change in basin shape with basin size. We present also the drainage area-slope relationship with respect to sediment or transport-limited processes. Key words: Hack’s law, channel morphology, DTM

Critical Two-Point Function for Long-Range O( n) Models Below the Upper Critical Dimension

NASA Astrophysics Data System (ADS)

Lohmann, Martin; Slade, Gordon; Wallace, Benjamin C.

2017-12-01

We consider the n-component |φ|^4 lattice spin model (n ≥ 1) and the weakly self-avoiding walk (n=0) on Z^d, in dimensions d=1,2,3. We study long-range models based on the fractional Laplacian, with spin-spin interactions or walk step probabilities decaying with distance r as r^{-(d+α )} with α \\in (0,2). The upper critical dimension is d_c=2α . For ɛ >0, and α = 1/2 (d+ɛ ), the dimension d=d_c-ɛ is below the upper critical dimension. For small ɛ , weak coupling, and all integers n ≥ 0, we prove that the two-point function at the critical point decays with distance as r^{-(d-α )}. This "sticking" of the critical exponent at its mean-field value was first predicted in the physics literature in 1972. Our proof is based on a rigorous renormalisation group method. The treatment of observables differs from that used in recent work on the nearest-neighbour 4-dimensional case, via our use of a cluster expansion.

Coalescence preference and droplet size inequality during fluid phase segregation

NASA Astrophysics Data System (ADS)

Roy, Sutapa

2018-02-01

Using molecular dynamics simulations and scaling arguments, we investigate the coalescence preference dynamics of liquid droplets in a phase-segregating off-critical, single-component fluid. It is observed that the preferential distance of the product drop from its larger parent, during a coalescence event, gets smaller for large parent size inequality. The relative coalescence position exhibits a power-law dependence on the parent size ratio with an exponent q ≃ 3.1 . This value of q is in strong contrast with earlier reports 2.1 and 5.1 in the literature. The dissimilarity is explained by considering the underlying coalescence mechanisms.

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

PubMed

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.

Ameba-like diffusion in two-dimensional polymer melts: how critical exponents determine the structural relaxation

NASA Astrophysics Data System (ADS)

Kreer, Torsten; Meyer, Hendrik; Baschnagel, Joerg

2008-03-01

By means of numerical investigations we demonstrate that the structural relaxation of linear polymers in two dimensional (space-filling) melts is characterized by ameba-like diffusion, where the chains relax via frictional dissipation at their interfacial contact lines. The perimeter length of the contact line determines a new length scale, which does not exist in three dimensions. We show how this length scale follows from the critical exponents, which hence characterize not only the static but also the dynamic properties of the melt. Our data is in agreement with recent theoretical predictions, concerning the time-dependence of single-monomer mean-square displacements and the scaling of concomitant relaxation times with the degree of polymerization. For the latter we demonstrate a density crossover-scaling as an additional test for ameba-like relaxation. We compare our results to the conceptually different Rouse model, which predicts numerically close exponents. Our data can clearly rule out the classical picture as the relevant relaxation mechanism in two-dimensional polymer melts.

Spin-glass freezing in a Ni-vermiculite intercalation compound.

PubMed

Marcos, C; Argüelles, A; Khainakov, S A; Rodríguez Fernández, J; Blanco, J A

2012-08-29

We report on the magnetic properties of a Ni(2+)-vermiculite intercalation compound from Santa Olalla, Huelva (Spain). This modified vermiculite was studied by means of DC and AC magnetic measurements. The existence of two maxima in magnetic susceptibility below 10 K was interpreted in terms of the Cole-Cole formalism as being due to spin-glass freezing in this material. The temperature, frequency and external magnetic field dependences of these anomalies located at temperatures around 2-3 K and 8-10 K in the imaginary part of the magnetic susceptibility, χ″, seem to suggest the existence of spin-relaxation phenomena between the magnetic moments of the Ni(2+) ions. A dynamic study of the relaxation processes associated with these phenomena considering the Cole-Cole formalism allows us to interpret the anomaly found at 2-3 K according to a law of activated dynamics, obtaining values for the critical exponent, ψν < 1, characteristic of a d = 2 spin-glass-like system, while the maximum observed in χ″ at 8-10 K can be described by means of a law of standard dynamics with a value of the exponent z of around 5, representative of a d = 3 spin-glass-like system.

Long-run growth rate in a random multiplicative model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pirjol, Dan

2014-08-01

We consider the long-run growth rate of the average value of a random multiplicative process x{sub i+1} = a{sub i}x{sub i} where the multipliers a{sub i}=1+ρexp(σW{sub i}₋1/2 σ²t{sub i}) have Markovian dependence given by the exponential of a standard Brownian motion W{sub i}. The average value (x{sub n}) is given by the grand partition function of a one-dimensional lattice gas with two-body linear attractive interactions placed in a uniform field. We study the Lyapunov exponent λ=lim{sub n→∞}1/n log(x{sub n}), at fixed β=1/2 σ²t{sub n}n, and show that it is given by the equation of state of the lattice gas inmore » thermodynamical equilibrium. The Lyapunov exponent has discontinuous partial derivatives along a curve in the (ρ, β) plane ending at a critical point (ρ{sub C}, β{sub C}) which is related to a phase transition in the equivalent lattice gas. Using the equivalence of the lattice gas with a bosonic system, we obtain the exact solution for the equation of state in the thermodynamical limit n → ∞.« less

2D scaling behavior of nanotextured GaN surfaces: A case study of hillocked and terraced surfaces

NASA Astrophysics Data System (ADS)

Mutta, Geeta Rani; Carapezzi, Stefania

2018-07-01

The 2D scaling properties of GaN surfaces have been studied by means of the 2D height-height correlation function (HHCF). The GaN layers under investigation presented exemplar morphologies, generated by distinct growth methods: a molecular beam epitaxy (MBE) grown surface decorated by hillocks and a metal organic vapor phase epitaxy (MOVPE) grown surface with terraced structure. The 2D statistical analysis of these surfaces has allowed assessing quantitatively the degree of morphological variability along all the different directions across each surface, their corresponding roughness exponents and correlation lengths. A scaling anisotropy as well as correlation length anisotropy has been detected for both hillocked and terraced surfaces. Especially, a marked dependence of correlation length from the direction across the terraced surface has been observed. Additionally, the terraced surfaces showed the lower root mean square (RMS) roughness value and at the same time, the lower roughness exponent value. This could appear as a contradiction, given that a low RMS value is associated to a smooth surface, and usually the roughness exponent is interpreted as a "measure" of the smoothness of the surface, the smoother the surface, the higher (approaching the unity) is the roughness exponent. Our case study is an experimental demonstration in which the roughness exponent should be, more appropriately, interpreted as a quantification of how the roughness changes with length scale.

First Passage Time Analysis on Climate Indices

DTIC Science & Technology

2008-01-01

13) 12 with 0 1H< < . Here H is the Hurst exponent . For H = 1/2, the random process is the ordinary...14) with 0α ~1/2. Since the Hurst exponent of an ordinary Brownian motion is H = 1/2, the empirically observed...ρ = 10, 20, and 30 for SOI. From this figure it is seen that the tail exponent , ρα , is rather insensitive to the value of ρ . In particular one

Electric Field Induced Interfacial Instabilities

NASA Technical Reports Server (NTRS)

Kusner, Robert E.; Min, Kyung Yang; Wu, Xiao-lun; Onuki, Akira

1999-01-01

The study of the interface in a charge-free, critical and near-critical binary fluid in the presence of an externally applied electric field is presented. At sufficiently large fields, the interface between the two phases of the binary fluid should become unstable and exhibit an undulation with a predefined wavelength on the order of the capillary length. As the critical point is approached, this wavelength is reduced, potentially approaching length-scales such as the correlation length or critical nucleation radius. At this point the critical properties of the system may be affected. In this paper, the flat interface of a marginally polar binary fluid mixture is stressed by a perpendicular alternating electric field and the resulting instability is characterized by the critical electric field E(sub c) and the pattern observed. The character of the surface dynamics at the onset of instability is found to be strongly dependent on the frequency f of the field applied. The plot of E(sub c) vs. f for a fixed temperature shows a sigmoidal shape, whose low and high frequency limits are well described by a power-law relationship, E(sub c) = epsilon(exp zeta) with zeta = 0.35 and zeta = 0.08, respectively. The low-limit exponent compares well with the value zeta = 4 for a system of conducting and non-conducting fluids. On the other hand, the high-limit exponent coincides with what was first predicted by Onuki. The instability manifests itself as the conducting phase penetrates the non-conducting phase. As the frequency increases, the shape of the pattern changes from an array of bifurcating strings to an array of column-like (or rod-like) protrusions, each of which spans the space between the plane interface and one of the electrodes. For an extremely high frequency, the disturbance quickly grows into a parabolic cone pointing toward the upper plate. As a result, the interface itself changes its shape from that of a plane to that of a high sloping pyramid.

Influence of grain size and sintering temperature grain size on the critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.67Sr0.33MnO3 nanoparticles

NASA Astrophysics Data System (ADS)

Baaziz, H.; Tozri, A.; Dhahri, E.; Hlil, E. K.

2018-03-01

We have undertaken a systematic study of critical behavior in La0.67Sr0.33MnO3 nanoparticles, sintered at different temperatures (L6, L8, L10 and L12 sintered at 600 °C, 800 °C, 1000 °C, 1200 °C respectively), by magnetization measurements. The critical exponents are estimated by various techniques such as the Modified Arrott plot, Kouvel-Fisher plot and critical isotherm technique. Compared to standard models, the critical exponents are close to those expected by the Mean-field model (with β = 0.5 γ = 1, and δ = 3) for (L6, L8, and L10) samples and by the (3D) Heisenberg model (β = 0.365, γ = 1.336 and δ = 4.80) for L12 sample. We conclude that the reduction of grain size strongly influences the universality class.

A Brief Survey of the Equilibrium and Transport Properties of Critical Fluids and the Degree to Which Microgravity is Required for Their Experimental Investigation

NASA Technical Reports Server (NTRS)

Ferrell, Richard A.

1996-01-01

The modern theory of second order phase transitions is very successful in calculating the critical exponents as an asymptotic expansion in powers of epsilon = 4 - D, the deviation of D = 3, the spatial dimension of the actual physical system from that of the abstract four-dimensional reference model. This remarkable mathematical 'tour de force' leaves unanswered, however, many fundamental questions concerning the exact nature of how the fluctuations interact. I discuss here some experiments which would help to further our understanding of the equilibrium critical properties. Especially promising would be a measurement of the temperature dependence of the turbidity very close to the critical point. This has the promise of determining the small and elusive but fundamentally important anomalous dimension exponent eta. I also review various ways of measuring the critical transport coefficients and point out some cases where ground based experiments may usefully supplement flight experiments.

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badiev, M. K., E-mail: m-zagir@mail.ru; Murtazaev, A. K.; Ramazanov, M. K.

2016-10-15

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scalingmore » theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.« less

On the formation and expansion of H II regions

NASA Technical Reports Server (NTRS)

Franco, Jose; Tenorio-Tagle, Guillermo; Bodenheimer, Peter

1990-01-01

The evolution of H II regions in spherical clouds with small, constant-density cores and power-law density distributions r exp -w outside the core is described analytically. It is found that there is a critical exponent above which the cloud becomes completely ionized. Its value in the formation phase depends on the initial conditions, but it has a well-defined value w(crit) = 3/2 during the expansion phase. For w less than w(crit), the radius of the H II region grows at a given rate, while neutral mass accumulates in the interphase between the ionization and shock fronts. For w = w(crit), the fronts move together without mass accumulation. Cases with w greater than w(crit) lead to the champagne phase: once the cloud is fully ionized, the expansion becomes supersonic. For self-gravitating disks without magnetic fields, the main features include a new 'variable-size' stage. The initial shape of the H II region has a critical point beyond which the disk becomes completely ionized.

Critical phases in the raise and peel model

NASA Astrophysics Data System (ADS)

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 the model is known to be noncritical, while for 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.

Relative permeability of hydrate-bearing sediments from percolation theory and critical path analysis: theoretical and experimental results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Daigle, Hugh; Rice, Mary Anna; Daigle, Hugh

Relative permeabilities to water and gas are important parameters for accurate modeling of the formation of methane hydrate deposits and production of methane from hydrate reservoirs. Experimental measurements of gas and water permeability in the presence of hydrate are difficult to obtain. The few datasets that do exist suggest that relative permeability obeys a power law relationship with water or gas saturation with exponents ranging from around 2 to greater than 10. Critical path analysis and percolation theory provide a framework for interpreting the saturation-dependence of relative permeability based on percolation thresholds and the breadth of pore size distributions, whichmore » may be determined easily from 3-D images or gas adsorption-desorption hysteresis. We show that the exponent of the permeability-saturation relationship for relative permeability to water is related to the breadth of the pore size distribution, with broader pore size distributions corresponding to larger exponents. Relative permeability to water in well-sorted sediments with narrow pore size distributions, such as Berea sandstone or Toyoura sand, follows percolation scaling with an exponent of 2. On the other hand, pore-size distributions determined from argon adsorption measurements we performed on clays from the Nankai Trough suggest that relative permeability to water in fine-grained intervals may be characterized by exponents as large as 10 as determined from critical path analysis. We also show that relative permeability to the gas phase follows percolation scaling with a quadratic dependence on gas saturation, but the threshold gas saturation for percolation changes with hydrate saturation, which is an important consideration in systems in which both hydrate and gas are present, such as during production from a hydrate reservoir. Our work shows how measurements of pore size distributions from 3-D imaging or gas adsorption may be used to determine relative permeabilities.« less

Effect of Roller Geometry on Roller Bearing Load-Life Relation

NASA Technical Reports Server (NTRS)

Oswald, Fred B.; Zaretsky, Erwin V.; Poplawski, Joseph V.

2015-01-01

Cylindrical roller bearings typically employ roller profile modification to equalize load distribution, minimize stress concentration at roller ends and allow for a small amount of misalignment. The 1947 Lundberg-Palmgren analysis reported an inverse fourth power relation between load and life for roller bearings with line contact. In 1952, Lundberg and Palmgren changed their load-life exponent to 10/3 for roller bearings, assuming mixed line and point contact. The effect of roller-crown profile was reanalyzed in this paper to determine the actual load-life relation for modified roller profiles. For uncrowned rollers (line contact), the load-life exponent is p = 4, in agreement with the 1947 Lundberg-Palmgren value but crowning reduces the value of the exponent, p. The lives of modern roller bearings made from vacuum-processed steels significantly exceed those predicted by the Lundberg-Palmgren theory. The Zaretsky rolling-element bearing life model of 1996 produces a load-life exponent of p = 5 for flat rollers, which is more consistent with test data. For the Zaretsky model with fully crowned rollers p = 4.3. For an aerospace profile and chamfered rollers, p = 4.6. Using the 1952 Lundberg-Palmgren value p = 10/3, the value incorporated in ANSI/ABMA and ISO bearing standards, can create significant life calculation errors for roller bearings.

Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy.

PubMed

Zhang, Wenqing; Qiu, Lu; Xiao, Qin; Yang, Huijie; Zhang, Qingjun; Wang, Jianyong

2012-11-01

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (∼0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (∼0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (∼10^{2}), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

Evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy

NASA Astrophysics Data System (ADS)

Zhang, Wenqing; Qiu, Lu; Xiao, Qin; Yang, Huijie; Zhang, Qingjun; Wang, Jianyong

2012-11-01

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments (˜0.8). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages (˜0.7). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series (˜102), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

Strain-driven criticality underlies nonlinear mechanics of fibrous networks

NASA Astrophysics Data System (ADS)

Sharma, A.; Licup, A. J.; Rens, R.; Vahabi, M.; Jansen, K. A.; Koenderink, G. H.; MacKintosh, F. C.

2016-10-01

Networks with only central force interactions are floppy when their average connectivity is below an isostatic threshold. Although such networks are mechanically unstable, they can become rigid when strained. It was recently shown that the transition from floppy to rigid states as a function of simple shear strain is continuous, with hallmark signatures of criticality [Sharma et al., Nature Phys. 12, 584 (2016), 10.1038/nphys3628]. The nonlinear mechanical response of collagen networks was shown to be quantitatively described within the framework of such mechanical critical phenomenon. Here, we provide a more quantitative characterization of critical behavior in subisostatic networks. Using finite-size scaling we demonstrate the divergence of strain fluctuations in the network at well-defined critical strain. We show that the characteristic strain corresponding to the onset of strain stiffening is distinct from but related to this critical strain in a way that depends on critical exponents. We confirm this prediction experimentally for collagen networks. Moreover, we find that the apparent critical exponents are largely independent of the spatial dimensionality. With subisostaticity as the only required condition, strain-driven criticality is expected to be a general feature of biologically relevant fibrous networks.

Heat Capacity Anomaly Near the Lower Critical Consolute Point of Triethylamine-Water

NASA Technical Reports Server (NTRS)

Flewelling, Anne C.; DeFonseka, Rohan J.; Khaleeli, Nikfar; Partee, J.; Jacobs, D. T.

1996-01-01

The heat capacity of the binary liquid mixture triethylamine-water has been measured near its lower critical consolute point using a scanning, adiabatic calorimeter. Two data runs are analyzed to provide heat capacity and enthalpy data that are fitted by equations with background terms and a critical term that includes correction to scaling. The critical exponent a was determined to be 0.107 +/- 0.006, consistent with theoretical predictions. When alpha was fixed at 0.11 to determine various amplitudes consistently, our values of A(+) and A(-) agreed with a previous heat capacity measurement, but the value of A(-) was inconsistent with values determined by density or refractive index measurements. While our value for the amplitude ratio A(+)/ A(-) = 0.56 +/- 0.02 was consistent with other recent experimental determinations in binary liquid mixtures, it was slightly larger than either theoretical predictions or recent experimental values in liquid-vapor systems. The correction to scaling amplitude ratio D(+)/D(-) = 0.5 +/- 0.1 was half of that predicted. As a result of several more precise theoretical calculations and experimental determinations, the two-scale-factor universality ratio X, which we found to be 0.019 +/- 0.003, now is consistent among experiments and theories. A new 'universal' amplitude ratio R(sup +/-)(sub Bcr) involving the amplitudes for the specific heat was tested. Our determination of R(sup +/-)(sub Bcr) = -0.5 +/- 0.1 and R(sup -)(sub Bcr) = 1.1 +/- 0.1 is smaller in magnitude than predicted and is the first such determination in a binary fluid mixture.

Bayesian estimation of self-similarity exponent

NASA Astrophysics Data System (ADS)

Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias

2011-08-01

In this study we propose a Bayesian approach to the estimation of the Hurst exponent in terms of linear mixed models. Even for unevenly sampled signals and signals with gaps, our method is applicable. We test our method by using artificial fractional Brownian motion of different length and compare it with the detrended fluctuation analysis technique. The estimation of the Hurst exponent of a Rosenblatt process is shown as an example of an H-self-similar process with non-Gaussian dimensional distribution. Additionally, we perform an analysis with real data, the Dow-Jones Industrial Average closing values, and analyze its temporal variation of the Hurst exponent.

Optimal Combining Data for Improving Ocean Modeling

DTIC Science & Technology

2008-09-30

hyperbolic or elliptic) and on the Hurst exponent characterizing the dynamics type (local or non-local). 3. Fusion data for estimating RD. Theoretical...1) RD vs time and different values of Hurst exponent h = 0.1 (black), h = 1 (red), h = 2 (blue) γ = 0.1,Ω = 0, 2) Same for γ = 0.1,Ω = 2 ). 3...accurate estimating the upper ocean velocity field and mixing characteristics such as relative dispersion and finite size Lyapunov exponent , (2

Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Sheykhi, Ahmad; Hashemi Asl, Doa; Dehyadegari, Amin

2018-06-01

We investigate analytically as well as numerically the properties of s-wave holographic superconductors in d-dimensional spacetime and in the presence of Logarithmic nonlinear electrodynamics. We study three aspects of this kind of superconductors. First, we obtain, by employing analytical Sturm-Liouville method as well as numerical shooting method, the relation between critical temperature and charge density, ρ, and disclose the effects of both nonlinear parameter b and the dimensions of spacetime, d, on the critical temperature Tc. We find that in each dimension, Tc /ρ 1 / (d - 2) decreases with increasing the nonlinear parameter b while it increases with increasing the dimension of spacetime for a fixed value of b. Then, we calculate the condensation value and critical exponent of the system analytically and numerically and observe that in each dimension, the dimensionless condensation get larger with increasing the nonlinear parameter b. Besides, for a fixed value of b, it increases with increasing the spacetime dimension. We confirm that the results obtained from our analytical method are in agreement with the results obtained from numerical shooting method. This fact further supports the correctness of our analytical method. Finally, we explore the holographic conductivity of this system and find out that the superconducting gap increases with increasing either the nonlinear parameter or the spacetime dimension.

Finite-size scaling with respect to interaction and disorder strength at the many-body localization transition

NASA Astrophysics Data System (ADS)

Kudo, Kazue; Deguchi, Tetsuo

2018-06-01

We present a finite-size scaling for both interaction and disorder strengths in the critical regime of the many-body localization (MBL) transition for a spin-1/2 X X Z spin chain with a random field by studying level statistics. We show how the dynamical transition from the thermal to MBL phase depends on interaction together with disorder by evaluating the ratio of adjacent level spacings, and thus, extend previous studies in which interaction coupling is fixed. We introduce an extra critical exponent in order to describe the nontrivial interaction dependence of the MBL transition. It is characterized by the ratio of the disorder strength to the power of the interaction coupling with respect to the extra critical exponent and not by the simple ratio between them.

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

PubMed

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

NASA Astrophysics Data System (ADS)

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 .

Estimation of critical behavior from the density of states in classical statistical models

NASA Astrophysics Data System (ADS)

Malakis, A.; Peratzakis, A.; Fytas, N. G.

2004-12-01

We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling.

Observation of the Anderson metal-insulator transition with atomic matter waves: Theory and experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lemarie, Gabriel; Delande, Dominique; Chabe, Julien

Using a cold atomic gas exposed to laser pulses - a realization of the chaotic quasiperiodic kicked rotor with three incommensurate frequencies - we study experimentally and theoretically the Anderson metal-insulator transition in three dimensions. Sensitive measurements of the atomic wave function and the use of finite-size scaling techniques make it possible to unambiguously demonstrate the existence of a quantum phase transition and to measure its critical exponents. By taking proper account of systematic corrections to one-parameter scaling, we show the universality of the critical exponent {nu}=1.59{+-}0.01, which is found to be equal to the one previously computed for themore » Anderson model.« less

On the use of relative velocity exponents for jet engine exhaust noise

NASA Technical Reports Server (NTRS)

Stone, J. R.

1978-01-01

The effect of flight on jet engine exhaust noise has often been presented in terms of a relative velocity exponent, n, as a function of radiation angle. The value of n is given by the OASPL reduction due to relative velocity divided by 10 times the logarithm of the ratio of relative jet velocity to absolute jet velocity. In such terms, classical subsonic jet noise theory would result in a value of n being approximately 7 at 90 degree angle to the jet axis with n decreasing, but remaining positive, as the inlet axis is approached and increasing as the jet axis is approached. However, flight tests have shown a wide range of results, including negative values of n in some cases. In this paper it is shown that the exponent n is positive for pure subsonic jet mixing noise and varies, in a systematic manner, as a function of flight conditions and jet velocity.

The effect of respiratory oscillations in heart rate on detrended fluctuation analysis

NASA Astrophysics Data System (ADS)

Govindan, Rathinaswamy B.; Kota, Srinivas; Al-Shargabi, Tareq; Swisher, Christopher B.; du Plessis, Adre

2017-10-01

Characterization of heart rate using detrended fluctuation analysis (DFA) is impeded by respiratory oscillations. In particular, the short-term exponent measured from 15 to 30 beats is compromised in the DFA. We reconstruct respiratory signal from electrocardiograms and attenuate the respiratory oscillation in the heart rate using a frequency-dependent subtraction approach. We validate this method by applying it to an electrocardiogram signal simulated using a coupled differential equation with the respiratory oscillation modelled using a sine function. The exponent estimated using the proposed approach agreed with the exponent incorporated in the model within a narrow range. In contrast, the exponent obtained from the raw data deviated from the expected value. Furthermore, the exponents obtained for the raw heart rate are smaller than the exponents obtained for the respiration oscillation attenuated heart rate. We apply this approach to heart rate measured from 12 preterm infants that were being treated for prematurity related complications. As observed in the simulated data, we show that compared to the raw heart rate, the respiratory oscillation attenuated heart rate shows higher short-term exponent (p < 0.001).

Neutron diffraction and μ SR studies of two polymorphs of nickel niobate NiNb 2 O 6

DOE PAGES

Munsie, T. J. S.; Wilson, M. N.; Millington, A.; ...

2017-10-13

Neutron diffraction and muon spin relaxation (μSR) studies are presented in this paper for the newly characterized polymorph of NiNb 2O 6 (β-NiNb 2O 6) with space group P4 2/n and μSR data only for the previously known columbite structure polymorph with space group Pbcn. The magnetic structure of the P4 2/n form was determined from neutron diffraction using both powder and single-crystal data. Powder neutron diffraction determined an ordering wave vector →k=( 1/ 2, 1/ 2, 1/ 2). Single-crystal data confirmed the same →k vector and showed that the correct magnetic structure consists of antiferromagnetically coupled chains running alongmore » the a or b axis in adjacent Ni 2+ layers perpendicular to the c axis, which is consistent with the expected exchange interaction hierarchy in this system. The refined magnetic structure is compared with the known magnetic structures of the closely related trirutile phases, NiSb 2O 6 and NiTa 2O 6. μSR data finds a transition temperature of T N~15K for this system, while the columbite polymorph exhibits a lower T N=5.7(3) K. Our μSR measurements also allowed us to estimate the critical exponent of the order parameter β for each polymorph. We found β =0.25(3) and 0.16(2) for the β and columbite polymorphs, respectively. The single-crystal neutron scattering data give a value for the critical exponent β =0.28(3) for β-NiNb 2O 6, in agreement with the μSR value. While both systems have β values less than 0.3, which is indicative of reduced dimensionality, this effect appears to be much stronger for the columbite system. Finally, in other words, although both systems appear to be well described by S=1 spin chains, the interchain interactions in the β polymorph are likely much larger.« less

Neutron diffraction and μ SR studies of two polymorphs of nickel niobate NiNb2O6

NASA Astrophysics Data System (ADS)

Munsie, T. J. S.; Wilson, M. N.; Millington, A.; Thompson, C. M.; Flacau, R.; Ding, C.; Guo, S.; Gong, Z.; Aczel, A. A.; Cao, H. B.; Williams, T. J.; Dabkowska, H. A.; Ning, F.; Greedan, J. E.; Luke, G. M.

2017-10-01

Neutron diffraction and muon spin relaxation (μ SR ) studies are presented for the newly characterized polymorph of NiNb2O6 (β -NiNb2O6) with space group P4 2/n and μ SR data only for the previously known columbite structure polymorph with space group P b c n . The magnetic structure of the P4 2/n form was determined from neutron diffraction using both powder and single-crystal data. Powder neutron diffraction determined an ordering wave vector k ⃗=(1/2 ,1/2 ,1/2 ) . Single-crystal data confirmed the same k ⃗ vector and showed that the correct magnetic structure consists of antiferromagnetically coupled chains running along the a or b axis in adjacent Ni2 + layers perpendicular to the c axis, which is consistent with the expected exchange interaction hierarchy in this system. The refined magnetic structure is compared with the known magnetic structures of the closely related trirutile phases, NiSb2O6 and NiTa2O6 . μ SR data finds a transition temperature of TN˜15 K for this system, while the columbite polymorph exhibits a lower TN=5.7 (3 ) K. Our μ SR measurements also allowed us to estimate the critical exponent of the order parameter β for each polymorph. We found β =0.25 (3 ) and 0.16(2) for the β and columbite polymorphs, respectively. The single-crystal neutron scattering data give a value for the critical exponent β =0.28 (3 ) for β -NiNb2O6 , in agreement with the μ SR value. While both systems have β values less than 0.3, which is indicative of reduced dimensionality, this effect appears to be much stronger for the columbite system. In other words, although both systems appear to be well described by S =1 spin chains, the interchain interactions in the β polymorph are likely much larger.

Frequency-Dependent Viscosity of Xenon Near the Critical Point

NASA Technical Reports Server (NTRS)

Berg, Robert F.; Moldover, Michael R.; Zimmerli, Gregory A.

1999-01-01

We used a novel, overdamped oscillator aboard the Space Shuttle to measure the viscosity eta of xenon near its critical density rho(sub c), and temperature T(sub c). In microgravity, useful data were obtained within 0.1 mK of T(sub c), corresponding to a reduced temperature t = (T -T(sub c))/T(sub c) = 3 x 10(exp -7). The data extend two decades closer to T(sub c) than the best ground measurements, and they directly reveal the expected power-law behavior eta proportional to t(sup -(nu)z(sub eta)). Here nu is the correlation length exponent, and our result for the small viscosity exponent is z(sub eta) = 0.0690 +/- 0.0006. (All uncertainties are one standard uncertainty.) Our value for z(sub eta) depends only weakly on the form of the viscosity crossover function, and it agrees with the value 0.067 +/- 0.002 obtained from a recent two-loop perturbation expansion. The measurements spanned the frequency range 2 Hz less than or equal to f less than or equal to 12 Hz and revealed viscoelasticity when t less than or equal to 10(exp -1), further from T(sub c) than predicted. The viscoelasticity scales as Af(tau), where tau is the fluctuation-decay time. The fitted value of the viscoelastic time-scale parameter A is 2.0 +/- 0.3 times the result of a one-loop perturbation calculation. Near T(sub c), the xenon's calculated time constant for thermal diffusion exceeded days. Nevertheless, the viscosity results were independent of the xenon's temperature history, indicating that the density was kept near rho(sub c), by judicious choices of the temperature vs. time program. Deliberately bad choices led to large density inhomogeneities. At t greater than 10(exp -5), the xenon approached equilibrium much faster than expected, suggesting that convection driven by microgravity and by electric fields slowly stirred the sample.

Neutron diffraction and μ SR studies of two polymorphs of nickel niobate NiNb 2 O 6

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munsie, T. J. S.; Wilson, M. N.; Millington, A.

Neutron diffraction and muon spin relaxation (μSR) studies are presented in this paper for the newly characterized polymorph of NiNb 2O 6 (β-NiNb 2O 6) with space group P4 2/n and μSR data only for the previously known columbite structure polymorph with space group Pbcn. The magnetic structure of the P4 2/n form was determined from neutron diffraction using both powder and single-crystal data. Powder neutron diffraction determined an ordering wave vector →k=( 1/ 2, 1/ 2, 1/ 2). Single-crystal data confirmed the same →k vector and showed that the correct magnetic structure consists of antiferromagnetically coupled chains running alongmore » the a or b axis in adjacent Ni 2+ layers perpendicular to the c axis, which is consistent with the expected exchange interaction hierarchy in this system. The refined magnetic structure is compared with the known magnetic structures of the closely related trirutile phases, NiSb 2O 6 and NiTa 2O 6. μSR data finds a transition temperature of T N~15K for this system, while the columbite polymorph exhibits a lower T N=5.7(3) K. Our μSR measurements also allowed us to estimate the critical exponent of the order parameter β for each polymorph. We found β =0.25(3) and 0.16(2) for the β and columbite polymorphs, respectively. The single-crystal neutron scattering data give a value for the critical exponent β =0.28(3) for β-NiNb 2O 6, in agreement with the μSR value. While both systems have β values less than 0.3, which is indicative of reduced dimensionality, this effect appears to be much stronger for the columbite system. Finally, in other words, although both systems appear to be well described by S=1 spin chains, the interchain interactions in the β polymorph are likely much larger.« less

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

NASA Astrophysics Data System (ADS)

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.

Study of polytropic exponent based on high pressure switching expansion reduction

NASA Astrophysics Data System (ADS)

Wang, Xuanyin; Luo, Yuxi; Xu, Zhipeng

2011-10-01

Switching expansion reduction (SER) uses a switch valve to substitute the throttle valve to reduce pressure for high pressure pneumatics. The experiments indicate that the simulation model well predicts the actual characteristics. The heat transfers and polytropic exponents of the air in expansion tank and supply tanks of SER have been studied on the basis of the experiments and the simulation model. Through the mathematical reasoning in this paper, the polytropic exponent can be calculated by the air mass, heat, and work exchanges of the pneumatic container. For the air in a constant volume tank, when the heat-absorption is large enough to raise air temperature in discharging process, the polytropic exponent is less than 1; when the air is experiencing a discharging and heat-releasing process, the polytropic exponent exceeds the specific heat ratio (the value of 1.4).

Critical behaviour in DOPC/DPPC/cholesterol mixtures: static (2)H NMR line shapes near the critical point.

PubMed

Davis, James H; Schmidt, Miranda L

2014-05-06

Static (2)H NMR spectroscopy is used to study the critical behavior of mixtures of 1,2-dioleoyl-phosphatidylcholine/1,2-dipalmitoyl-phosphatidylcholine (DPPC)/cholesterol in molar proportion 37.5:37.5:25 using either chain perdeuterated DPPC-d62 or chain methyl deuterated DPPC-d6. The temperature dependence of the first moment of the (2)H spectrum of the sample made with DPPC-d62 and of the quadrupolar splittings of the chain-methyl-labeled DPPC-d6 sample are directly related to the temperature dependence of the critical order parameter η, which scales as [Formula: see text] near the critical temperature. Analysis of the data reveals that for the chain perdeuterated sample, the value of Tc is 301.51 ± 0.1 K, and that of the critical exponent, βc = 0.391 ± 0.02. The line shape analysis of the methyl labeled (d6) sample gives Tc = 303.74 ± 0.07 K and βc = 0.338 ± 0.009. These values obtained for βc are in good agreement with the predictions of a three-dimensional Ising model. The difference in critical temperature between the two samples having nominally the same molar composition arises because of the lowering of the phase transition temperature that occurs due to the perdeuteration of the DPPC. Copyright © 2014 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Skew information in the XY model with staggered Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Qiu, Liang; Quan, Dongxiao; Pan, Fei; Liu, Zhi

2017-06-01

We study the performance of the lower bound of skew information in the vicinity of transition point for the anisotropic spin-1/2 XY chain with staggered Dzyaloshinskii-Moriya interaction by use of quantum renormalization-group method. For a fixed value of the Dzyaloshinskii-Moriya interaction, there are two saturated values for the lower bound of skew information corresponding to the spin-fluid and Néel phases, respectively. The scaling exponent of the lower bound of skew information closely relates to the correlation length of the model and the Dzyaloshinskii-Moriya interaction shifts the factorization point. Our results show that the lower bound of skew information can be a good candidate to detect the critical point of XY spin chain with staggered Dzyaloshinskii-Moriya interaction.

Magnetism of internal surfaces in a fractal structure

NASA Astrophysics Data System (ADS)

Branco, N. S.; Chame, Anna

1993-09-01

We study the inhomogeneous magnetization behavior of an Ising ferromagnet in Sierpiński pastry shells, using a real-space renormalization group approach. Two qualitatively different regions on the fractal are distinguished: the bulk and the set of internal surfaces which border the eliminated portions. We obtain the spontaneous mean magnetizations for these regions as a function of the temperature for different values of α = JS/ JB (J S and J B are the internal surface and bulk coupling constants respectively) and different geometrical parameters b and l. The critical β exponents are obtained for the several transitions. We obtain different universality classes for the bulk transitions, depending on what occurs at the surfaces, and a step-like behavior of the magnetization as a function of the temperature of some values of b and l.

Many-body delocalization with random vector potentials

NASA Astrophysics Data System (ADS)

Cheng, Chen; Mondaini, Rubem

2016-11-01

We study the ergodic properties of excited states in a model of interacting fermions in quasi-one-dimensional chains subjected to a random vector potential. In the noninteracting limit, we show that arbitrarily small values of this complex off-diagonal disorder trigger localization for the whole spectrum; the divergence of the localization length in the single-particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. When short-range interactions are included, the localization is lost, and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields.

Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

NASA Astrophysics Data System (ADS)

Batac, Rene C.; Paguirigan, Antonino A., Jr.; Tarun, Anjali B.; Longjas, Anthony G.

2017-04-01

We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy distributions closely follow power-law probability density functions (PDFs) with a scaling exponent of around -1. 6, consistent with the expectations of the Gutenberg-Richter (GR) law, for a wide range of the targeted triggering probability values. Additionally, for targeted triggering probabilities within the range 0.004-0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, the foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, while introducing minimal parameters in the simple rules of the sandpile. We believe that the critical targeting probability parameterizes the memory that is inherently present in earthquake-generating regions.

The asymptotic behaviour of parton distributions at small and large x.

PubMed

Ball, Richard D; Nocera, Emanuele R; Rojo, Juan

2016-01-01

It has been argued from the earliest days of quantum chromodynamics that at asymptotically small values of x the parton distribution functions (PDFs) of the proton behave as [Formula: see text], where the values of [Formula: see text] can be deduced from Regge theory, while at asymptotically large values of x the PDFs behave as [Formula: see text], where the values of [Formula: see text] can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents [Formula: see text] and [Formula: see text] from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio [Formula: see text] at large x , and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.

Fractal rigidity in migraine

NASA Astrophysics Data System (ADS)

Latka, Miroslaw; Glaubic-Latka, Marta; Latka, Dariusz; West, Bruce J.

2004-04-01

We study the middle cerebral artery blood flow velocity (MCAfv) in humans using transcranial Doppler ultrasonography (TCD). Scaling properties of time series of the axial flow velocity averaged over a cardiac beat interval may be characterized by two exponents. The short time scaling exponent (STSE) determines the statistical properties of fluctuations of blood flow velocities in short-time intervals while the Hurst exponent describes the long-term fractal properties. In many migraineurs the value of the STSE is significantly reduced and may approach that of the Hurst exponent. This change in dynamical properties reflects the significant loss of short-term adaptability and the overall hyperexcitability of the underlying cerebral blood flow control system. We call this effect fractal rigidity.

Representation of Renormalization Group Functions By Nonsingular Integrals in a Model of the Critical Dynamics of Ferromagnets: The Fourth Order of The ɛ-Expansion

NASA Astrophysics Data System (ADS)

Adzhemyan, L. Ts.; Vorob'eva, S. E.; Ivanova, E. V.; Kompaniets, M. V.

2018-04-01

Using the representation for renormalization group functions in terms of nonsingular integrals, we calculate the dynamical critical exponents in the model of critical dynamics of ferromagnets in the fourth order of the ɛ-expansion. We calculate the Feynman diagrams using the sector decomposition technique generalized to critical dynamics problems.

Revisiting the phase transition of AdS-Maxwell-power-Yang-Mills black holes via AdS/CFT tools

NASA Astrophysics Data System (ADS)

El Moumni, H.

2018-01-01

In the present work we investigate the Van der Waals-like phase transition of AdS black hole solution in the Einstein-Maxwell-power-Yang-Mills gravity (EMPYM) via different approaches. After reconsidering this phase structure in the entropy-thermal plane, we recall the nonlocal observables such as holographic entanglement entropy and two point correlation function to show that the both observables exhibit a Van der Waals-like behavior as the case of the thermal entropy. By checking the Maxwell's equal area law and calculating the critical exponent for different values of charge C and nonlinearity parameter q we confirm that the first and the second order phases persist in the holographic framework. Also the validity of the Maxwell law is governed by the proximity to the critical point.

Measurements of the magnetic-field-tuned conductivity of disordered two-dimensional Mo43Ge57 and InOx superconducting films: evidence for a universal minimum superfluid response.

PubMed

Misra, S; Urban, L; Kim, M; Sambandamurthy, G; Yazdani, A

2013-01-18

Our measurements of the low frequency ac conductivity in strongly disordered two-dimensional films near the magnetic-field-tuned superconductor-to-insulator transition show a sudden drop in the phase stiffness of superconducting order with either increased temperature or magnetic field. Surprisingly, for two different material systems, the abrupt drop in the superfluid density in a magnetic field has the same universal value as that expected for a Berezinskii-Kosterlitz-Thouless transition in a zero magnetic field. The characteristic temperature at which phase stiffness is suddenly lost can be tuned to zero at a critical magnetic field, following a power-law behavior with a critical exponent consistent with that obtained in previous dc transport studies on the dissipative side of the transition.

Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution

NASA Astrophysics Data System (ADS)

Tamarit, F. A.; Cannas, S. A.; Tsallis, C.

1998-03-01

We consider biological evolution as described within the Bak and Sneppen 1993 model. We exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions, calculate the associated exponent, and relate it to the recently introduced nonextensive thermostatistics. The scenario which here emerges without tuning strongly reminds of that of the tuned onset of chaos in say logistic-like one-dimensional maps. We also calculate the dynamical exponent z.

The mass distribution of coarse particulate organic matter exported from an alpine headwater stream

NASA Astrophysics Data System (ADS)

Turowski, J. M.; Badoux, A.; Bunte, K.; Rickli, C.; Federspiel, N.; Jochner, M.

2013-05-01

Coarse particulate organic matter (CPOM) particles span sizes from 1 mm, with masses less than 1 mg, to large logs and whole trees, which may have masses of several hundred kilograms. Different size and mass classes play different roles in stream environments, from being the prime source of energy in stream ecosystems to macroscopically determining channel morphology and local hydraulics. We show that a single scaling exponent can describe the mass distribution of CPOM transported in the Erlenbach, a steep mountain stream in the Swiss Prealps. This exponent takes an average value of -1.8, is independent of discharge and valid for particle masses spanning almost seven orders of magnitude. Together with a rating curve of CPOM transport rates with discharge, we discuss the importance of the scaling exponent for measuring strategies and natural hazard mitigation. Similar to CPOM, the mass distribution of in-stream large woody debris can likewise be described by power law scaling distributions, with exponents varying between -1.8 and -2.0, if all in-stream material is considered, and between -1.4 and -1.8 for material locked in log jams. We expect that scaling exponents are determined by stream type, vegetation, climate, substrate properties, and the connectivity between channels and hillslopes. However, none of the descriptor variables tested here, including drainage area, channel bed slope and forested area, show a strong control on exponent value. The number of streams studied in this paper is too small to make final conclusions.

Determination of the magnetization scaling exponent for single-crystal La0.8Sr0.2MnO3 by broadband microwave surface impedance measurements

NASA Astrophysics Data System (ADS)

Schwartz, Andrew; Scheffler, Marc; Anlage, Steven M.

2000-01-01

Employing a broadband microwave reflection configuration, we have measured the complex surface impedance, ZS(ω,T), of single-crystal La0.8Sr0.2MnO3, as a function of frequency (0.045-45 GHz) and temperature (250-325 K). Through the dependence of the microwave surface impedance on the magnetic permeability, μ⁁(ω,T), we have studied the local magnetic behavior of this material, and have extracted the spontaneous magnetization, M0(T), in zero applied field. The broadband nature of these measurements and the fact that no external field is applied to the material provide a unique opportunity to analyze the critical behavior of the spontaneous magnetization at temperatures very close to the ferromagnetic phase transition. We find a Curie temperature TC=305.5+/-0.5 K and scaling exponent β=0.45+/-0.05, in agreement with the prediction of mean-field theory. We also discuss other recent determinations of the magnetization critical exponent in this and similar materials and show why our results are more definitive.

Scaling laws for impact fragmentation of spherical solids.

PubMed

Timár, G; Kun, F; Carmona, H A; Herrmann, H J

2012-07-01

We investigate the impact fragmentation of spherical solid bodies made of heterogeneous brittle materials by means of a discrete element model. Computer simulations are carried out for four different system sizes varying the impact velocity in a broad range. We perform a finite size scaling analysis to determine the critical exponents of the damage-fragmentation phase transition and deduce scaling relations in terms of radius R and impact velocity v(0). The scaling analysis demonstrates that the exponent of the power law distributed fragment mass does not depend on the impact velocity; the apparent change of the exponent predicted by recent simulations can be attributed to the shifting cutoff and to the existence of unbreakable discrete units. Our calculations reveal that the characteristic time scale of the breakup process has a power law dependence on the impact speed and on the distance from the critical speed in the damaged and fragmented states, respectively. The total amount of damage is found to have a similar behavior, which is substantially different from the logarithmic dependence on the impact velocity observed in two dimensions.

Testing critical point universality along the λ-line

NASA Astrophysics Data System (ADS)

Nissen, J. A.; Swanson, D. R.; Geng, Z. K.; Dohm, V.; Israelsson, U. E.; DiPirro, M. J.; Lipa, J. A.

1998-02-01

We are currently building a prototype for a new test of critical-point universality at the lambda transition in 4He, which is to be performed in microgravity conditions. The flight experiment will measure the second-sound velocity as a function of temperature at pressures from 1 to 30 bars in the region close to the lambda line. The critical exponents and other parameters characterizing the behavior of the superfluid density will be determined from the measurements. The microgravity measurements will be quite extensive, probably taking 30 days to complete. In addition to the superfluid density, some measurements of the specific heat will be made using the low-g simulator at the Jet Propulsion Laboratory. The results of the superfluid density and specific heat measurements will be used to compare the asymptotic exponents and other universal aspects of the superfluid density with the theoretical predictions currently established by renormalization group techniques.

Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.; Simms, R. M.

2018-04-01

We introduce a more general set of kinematic renormalization schemes than the original momentum subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter ω , which tags the external momentum of one of the legs of the three-point vertex functions in QCD. In each of the three new schemes, we renormalize QCD in the Landau and maximal Abelian gauges and establish the three-loop renormalization group functions in each gauge. For an application, we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases

NASA Astrophysics Data System (ADS)

Yu, Yi-Cong; Guan, Xi-Wen

2017-06-01

We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with SU(w) symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent ν = 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU(w) and non-SU(w) symmetries in one dimension. Supported by the National Natural Science Foundation of China under Grant No 11374331 and the key NSFC under Grant No 11534014. XWG has been partially supported by the Australian Research Council.

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

NASA Astrophysics Data System (ADS)

Gontijo, Guilherme L.; Souza, Flávia B.; Braga, Rafael M. L.; Silva, Pedro H. E.; Correia, Maury D.; Atman, A. P. F.

2017-06-01

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.

Gaussian free field in the background of correlated random clusters, formed by metallic nanoparticles

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, Jafar; Najafi, Morteza N.; Mohammadzadeh, Hossein

2018-05-01

The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T - T c . The fractal dimension of iso-potential lines ( D f ), the exponent of the distribution function of the gyration radius ( τ r ), and the loop lengths ( τ l ), and also the exponent of the loop Green function x l change in terms of T - T c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D f ( T) - D f ( T c ) 1/√ ξ( T), in which ξ( T) is the spin correlation length in the Ising model.

Two-dimensional Ising model on random lattices with constant coordination number

NASA Astrophysics Data System (ADS)

Schrauth, Manuel; Richter, Julian A. J.; Portela, Jefferson S. E.

2018-02-01

We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014), 10.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.

Self-Similar Taylor Cone Formation in Conducting Viscous Films: Computational Study of the Influence of Reynolds Number

NASA Astrophysics Data System (ADS)

Albertson, Theodore; Troian, Sandra

2017-11-01

Previous studies by Zubarev (2001) and Suvorov and Zubarev (2004) have shown that above a critical field strength, an ideal (inviscid) conducting fluid film will deform into a singular profile characterized by a conic cusp. The governing equations for the electrohydrodynamic response beneath the cusp admit self-similar solutions leading to so-called blow-up behavior in the Maxwell pressure, capillary pressure and kinetic energy density. The runaway behavior in these variables reflects divergence in time characterized by an exponent of -2/3. Here we extend the physical system to include viscous effects and conduct a computational study of the cusp region as a function of increasing electrical Reynolds number ReE . We employ a finite element, moving mesh algorithm to examine the behavior of the film shape, Maxwell pressure and capillary pressure upon approach to the blow-up event. Our study indicates that self-similarity establishes at relatively low ReE despite the presence of vorticity, which is localized to the cusp surface region. With increasing ReE , the period of self-similiarity extends further in time as the exponent changes from about -4/5 to the ideal value of -2/3, with slightly different values distinguishing the Maxwell and capillary stresses. T. Albertson gratefully acknowledges support from a NASA Space Technology Research Fellowship.

CAN A NANOFLARE MODEL OF EXTREME-ULTRAVIOLET IRRADIANCES DESCRIBE THE HEATING OF THE SOLAR CORONA?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tajfirouze, E.; Safari, H.

2012-01-10

Nanoflares, the basic units of impulsive energy release, may produce much of the solar background emission. Extrapolation of the energy frequency distribution of observed microflares, which follows a power law to lower energies, can give an estimation of the importance of nanoflares for heating the solar corona. If the power-law index is greater than 2, then the nanoflare contribution is dominant. We model a time series of extreme-ultraviolet emission radiance as random flares with a power-law exponent of the flare event distribution. The model is based on three key parameters: the flare rate, the flare duration, and the power-law exponentmore » of the flare intensity frequency distribution. We use this model to simulate emission line radiance detected in 171 A, observed by Solar Terrestrial Relation Observatory/Extreme-Ultraviolet Imager and Solar Dynamics Observatory/Atmospheric Imaging Assembly. The observed light curves are matched with simulated light curves using an Artificial Neural Network, and the parameter values are determined across the active region, quiet Sun, and coronal hole. The damping rate of nanoflares is compared with the radiative losses cooling time. The effect of background emission, data cadence, and network sensitivity on the key parameters of the model is studied. Most of the observed light curves have a power-law exponent, {alpha}, greater than the critical value 2. At these sites, nanoflare heating could be significant.« less

Application of wavelet based MFDFA on Mueller matrix images for cervical pre-cancer detection

NASA Astrophysics Data System (ADS)

Zaffar, Mohammad; Pradhan, Asima

2018-02-01

A systematic study has been conducted on application of wavelet based multifractal de-trended fluctuation analysis (MFDFA) on Mueller matrix (MM) images of cervical tissue sections for early cancer detection. Changes in multiple scattering and orientation of fibers are observed by utilizing a discrete wavelet transform (Daubechies) which identifies fluctuations over polynomial trends. Fluctuation profiles, after 9th level decomposition, for all elements of MM qualitatively establish a demarcation of different grades of cancer from normal tissue. Moreover, applying MFDFA on MM images, Hurst exponent profiles for images of MM qualitatively are seen to display differences. In addition, the values of Hurst exponent increase for the diagonal elements of MM with increasing grades of the cervical cancer, while the value for the elements which correspond to linear polarizance decrease. However, for circular polarizance the value increases with increasing grades. These fluctuation profiles reveal the trend of local variation of refractive -indices and along with Hurst exponent profile, may serve as a useful biological metric in the early detection of cervical cancer. The quantitative measurements of Hurst exponent for diagonal and first column (polarizance governing elements) elements which reflect changes in multiple scattering and structural anisotropy in stroma, may be sensitive indicators of pre-cancer.

Rare regions and Griffiths singularities at a clean critical point: the five-dimensional disordered contact process.

PubMed

Vojta, Thomas; Igo, John; Hoyos, José A

2014-07-01

We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent z' saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion, which implies that weak disorder is renormalization-group irrelevant, and the rare-region classification, which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte Carlo simulations of systems with up to 70(5) sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)], and we discuss implications for other phase transitions.

Static and dynamic dielectric properties of strongly polar liquids in the vicinity of first order and weakly first order phase transitions

NASA Astrophysics Data System (ADS)

Jadżyn, Jan; Czechowski, Grzegorz; Legrand, Christian; Douali, Redouane

2003-04-01

The paper presents the results of measurements of the linear dielectric properties of the compounds from the homologous series of alkylcyanobiphenyls (CnH2n+1PhPhCN, nCB) in the vicinity of the first order transition (from the isotropic liquid to the crystalline phase) of nonmesogenic nCB’s (n=2 4) and the weakly first order transition (from the isotropic liquid to the nematic phase) of 5CB. The experimental method for the separation of the critical part of the static permittivity derivative and the activation energy for rotation of the mesogenic molecules, in the vicinity of weakly first order phase transition, is proposed. It is shown that the critical temperature dependence of the permittivity and the activation energy can be described with a function of (T-T*)-α type, with the same values of the temperature of virtual transition of the second order (T*) and the critical exponent (α).

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

NASA Astrophysics Data System (ADS)

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.

Dust Cloud Modeling and Propagation Effects for Radar and Communications Codes

DTIC Science & Technology

1978-11-01

particles can be described by a power law probabi 1it Y d i st r i ut i on with a power exponent of 4. Four is a typical value for dust particlIs from...loose unconsolidated soils such as desert alluviun, blust ,eera ted from a nuclear cratering explosion in rock and cohes ive soil s haN pO,,e r exponent ...da p = power law exponent amin = minimum particle diameter in the distribution (cm) a = maximum particle diameter in the distribution (cm).max The log

Stochastic Processes and their Applications Conference, (32nd), held in Champaign, Illinois, August 6, 7, 8, 9, 10, 2007

DTIC Science & Technology

2007-08-01

by a jump to do it continuouslyn exponent ) of the polymer when the time parameter goes to infinity: the polymer is proved to be superdiffusive, with a...wandering exponent exceeding any value less 2 Modelin Financial Bubbles than 3/5. This result is obtained by assuming that the5 2 PhZli Fina n ell... exponent greater than 1/2, but we cannot entire economics. The modern theory of the absence of get arbitrarily close to 3/5. This is joint work with Dr

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

PubMed

Chan, H B; Stambaugh, C

2007-08-10

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

Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control.

PubMed

Hou, Huazhou; Zhang, Qingling

2016-11-01

In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Spatial variation of deterministic chaos in mean daily temperature and rainfall over Nigeria

NASA Astrophysics Data System (ADS)

Fuwape, I. A.; Ogunjo, S. T.; Oluyamo, S. S.; Rabiu, A. B.

2017-10-01

Daily rainfall and temperature data from 47 locations across Nigeria for the 36-year period 1979-2014 were treated to time series analysis technique to investigate some nonlinear trends in rainfall and temperature data. Some quantifiers such as Lyapunov exponents, correlation dimension, and entropy were obtained for the various locations. Positive Lyapunov exponents were obtained for the time series of mean daily rainfall for all locations in the southern part of Nigeria while negative Lyapunov exponents were obtained for all locations in the Northern part of Nigeria. The mean daily temperature had positive Lyapunov exponent values (0.35-1.6) for all the locations. Attempts were made in reconstructing the phase space of time series of rainfall and temperature.

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

PubMed Central

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

Spin chirality and polarised neutron scattering

NASA Astrophysics Data System (ADS)

Plakhty, V. P.; Maleyev, S. V.; Kulda, J.; Visser, E. D.; Wosnitza, J.; Moskvin, E. V.; Brückel, Th.; Kremer, R. K.

2001-03-01

Possibilities of polarised neutrons in studies of chiral criticality are discussed. The critical exponents β C of the average chirality below TN, as well as φ C=β C+γ C and, therefore, γ C of the chiral susceptibility above TN are determined for a XY triangular lattice antiferromagnet (TLA) CsMnBr3: β C=0.44(2) , γ C=0.84(7) . The critical behaviour of the chirality that orders at TN with a relative precision of 5×10 -4 proves that the phase transition belongs to a new chiral universality class. For the TLA CsNiCl 3 ( S=1) we found in the XY region ( B=3 T) φ C=1.24(7) in agreement with the Monte-Carlo value φ C=1.22(6) for the chiral universality class. In the easy-axis region at B=1 T, φ C=0.54(4) , and the Haldane excitations are observed in the polarisation-dependent inelastic cross section above TN. The helimagnet holmium exhibits a different chiral criticality with φ C=1.56(5) , essentially higher than for TLAs.

Fermion-induced quantum critical points in two-dimensional Dirac semimetals

NASA Astrophysics Data System (ADS)

Jian, Shao-Kai; Yao, Hong

2017-11-01

In this paper we investigate the nature of quantum phase transitions between two-dimensional Dirac semimetals and Z3-ordered phases (e.g., Kekule valence-bond solid), where cubic terms of the order parameter are allowed in the quantum Landau-Ginzberg theory and the transitions are putatively first order. From large-N renormalization-group (RG) analysis, we find that fermion-induced quantum critical points (FIQCPs) [Z.-X. Li et al., Nat. Commun. 8, 314 (2017), 10.1038/s41467-017-00167-6] occur when N (the number of flavors of four-component Dirac fermions) is larger than a critical value Nc. Remarkably, from the knowledge of space-time supersymmetry, we obtain an exact lower bound for Nc, i.e., Nc>1 /2 . (Here the "1/2" flavor of four-component Dirac fermions is equivalent to one flavor of four-component Majorana fermions). Moreover, we show that the emergence of two length scales is a typical phenomenon of FIQCPs and obtain two different critical exponents, i.e., ν ≠ν' , by large-N RG calculations. We further give a brief discussion of possible experimental realizations of FIQCPs.

Scaling and percolation in the small-world network model

NASA Astrophysics Data System (ADS)

Newman, M. E. J.; Watts, D. J.

1999-12-01

In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one nontrivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the crossover from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Padé approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model.

Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system

NASA Astrophysics Data System (ADS)

Maliborski, Maciej; Rinne, Oliver

2018-02-01

We study critical behavior in gravitational collapse of a general spherically symmetric Yang-Mills field coupled to the Einstein equations. Unlike the magnetic ansatz used in previous numerical work, the general Yang-Mills connection has two degrees of freedom in spherical symmetry. This fact changes the phenomenology of critical collapse dramatically. The magnetic sector features both type I and type II critical collapse, with universal critical solutions. In contrast, in the general system type I disappears and the critical behavior at the threshold between dispersal and black hole formation is always type II. We obtain values of the mass scaling and echoing exponents close to those observed in the magnetic sector, however we find some indications that the critical solution differs from the purely magnetic discretely self-similar attractor and exact self-similarity and universality might be lost. The additional "type III" critical phenomenon in the magnetic sector, where black holes form on both sides of the threshold but the Yang-Mills potential is in different vacuum states and there is a mass gap, also disappears in the general system. We support our dynamical numerical simulations with calculations in linear perturbation theory; for instance, we compute quasi-normal modes of the unstable attractor (the Bartnik-McKinnon soliton) in type I collapse in the magnetic sector.

Collapsing lattice animals and lattice trees in two dimensions

NASA Astrophysics Data System (ADS)

Hsu, Hsiao-Ping; Grassberger, Peter

2005-06-01

We present high statistics simulations of weighted lattice bond animals and lattice trees on the square lattice, with fugacities for each non-bonded contact and for each bond between two neighbouring monomers. The simulations are performed using a newly developed sequential sampling method with resampling, very similar to the pruned-enriched Rosenbluth method (PERM) used for linear chain polymers. We determine with high precision the line of second-order transitions from an extended to a collapsed phase in the resulting two-dimensional phase diagram. This line includes critical bond percolation as a multicritical point, and we verify that this point divides the line into different universality classes. One of them corresponds to the collapse driven by contacts and includes the collapse of (weakly embeddable) trees. There is some evidence that the other is subdivided again into two parts with different universality classes. One of these (at the far side from collapsing trees) is bond driven and is represented by the Derrida-Herrmann model of animals having bonds only (no contacts). Between the critical percolation point and this bond-driven collapse seems to be an intermediate regime, whose other end point is a multicritical point P* where a transition line between two collapsed phases (one bond driven and the other contact driven) sparks off. This point P* seems to be attractive (in the renormalization group sense) from the side of the intermediate regime, so there are four universality classes on the transition line (collapsing trees, critical percolation, intermediate regime, and Derrida-Herrmann). We obtain very precise estimates for all critical exponents for collapsing trees. It is already harder to estimate the critical exponents for the intermediate regime. Finally, it is very difficult to obtain with our method good estimates of the critical parameters of the Derrida-Herrmann universality class. As regards the bond-driven to contact-driven transition in the collapsed phase, we have some evidence for its existence and rough location, but no precise estimates of critical exponents.

Simulating statistics of lightning-induced and man made fires

NASA Astrophysics Data System (ADS)

Krenn, R.; Hergarten, S.

2009-04-01

The frequency-area distributions of forest fires show power-law behavior with scaling exponents α in a quite narrow range, relating wildfire research to the theoretical framework of self-organized criticality. Examples of self-organized critical behavior can be found in computer simulations of simple cellular automata. The established self-organized critical Drossel-Schwabl forest fire model (DS-FFM) is one of the most widespread models in this context. Despite its qualitative agreement with event-size statistics from nature, its applicability is still questioned. Apart from general concerns that the DS-FFM apparently oversimplifies the complex nature of forest dynamics, it significantly overestimates the frequency of large fires. We present a straightforward modification of the model rules that increases the scaling exponent α by approximately 1•3 and brings the simulated event-size statistics close to those observed in nature. In addition, combined simulations of both the original and the modified model predict a dependence of the overall distribution on the ratio of lightning induced and man made fires as well as a difference between their respective event-size statistics. The increase of the scaling exponent with decreasing lightning probability as well as the splitting of the partial distributions are confirmed by the analysis of the Canadian Large Fire Database. As a consequence, lightning induced and man made forest fires cannot be treated separately in wildfire modeling, hazard assessment and forest management.

Field-tuned superconductor-insulator transitions and Hall resistance in thin polycrystalline MoN films

NASA Astrophysics Data System (ADS)

Makise, Kazumasa; Ichikawa, Fusao; Asano, Takayuki; Shinozaki, Bunju

2018-02-01

We report on the superconductor-insulator transitions (SITs) of disordered molybdenum nitride (MoN) thin films on (1 0 0) MgO substrates as a function of the film thickness and magnetic fields. The T c of the superconducting MoN films, which exhibit a sharp superconducting transition, monotonically decreases as the normal state R sq increases with a decreasing film thickness. For several films with different thicknesses, we estimate the critical field H c and the product zν  ≃  0.6 of the dynamical exponent z and the correlation length exponent ν using a finite scaling analysis. The value of this product can be explained by the (2  +  1) XY model. We found that the Hall resistance ΔR xy (H) is maximized when the magnetic field satisfies H HP(T) \\propto |1  -  T/T C0| in the superconducting state and also in the normal states owning to the superconducting fluctuation corresponding to the ghost critical magnetic field. We measured the Hall conductivity δσ xy (H)  =  σ xy (H)  -  σ xyn and fit the Gaussian approximation theory for δσ xy (H) to the experimental data. Agreement between the data and the theory beyond H c suggests the survival of the Cooper pair in the insulating region of the SIT.

Field-tuned superconductor-insulator transitions and Hall resistance in thin polycrystalline MoN films.

PubMed

Makise, Kazumasa; Ichikawa, Fusao; Asano, Takayuki; Shinozaki, Bunju

2018-02-14

We report on the superconductor-insulator transitions (SITs) of disordered molybdenum nitride (MoN) thin films on (1 0 0) MgO substrates as a function of the film thickness and magnetic fields. The T c of the superconducting MoN films, which exhibit a sharp superconducting transition, monotonically decreases as the normal state R sq increases with a decreasing film thickness. For several films with different thicknesses, we estimate the critical field H c and the product zν  ≃  0.6 of the dynamical exponent z and the correlation length exponent ν using a finite scaling analysis. The value of this product can be explained by the (2  +  1) XY model. We found that the Hall resistance ΔR xy (H) is maximized when the magnetic field satisfies H HP (T) [Formula: see text] |1  -  T/T C0 | in the superconducting state and also in the normal states owning to the superconducting fluctuation corresponding to the ghost critical magnetic field. We measured the Hall conductivity δσ xy (H)  =  σ xy (H)  -  [Formula: see text] and fit the Gaussian approximation theory for δσ xy (H) to the experimental data. Agreement between the data and the theory beyond H c suggests the survival of the Cooper pair in the insulating region of the SIT.

Intrinsic anomalous surface roughening of TiN films deposited by reactive sputtering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Auger, M. A.; Centro Nacional de Investigaciones Metalurgicas; Vazquez, L.

2006-01-15

We study surface kinetic roughening of TiN films grown on Si(100) substrates by dc reactive sputtering. The surface morphology of films deposited for different growth times under the same experimental conditions were analyzed by atomic force microscopy. The TiN films exhibit intrinsic anomalous scaling and multiscaling. The film kinetic roughening is characterized by a set of local exponent values {alpha}{sub loc}=1.0 and {beta}{sub loc}=0.39, and global exponent values {alpha}=1.7 and {beta}=0.67, with a coarsening exponent of 1/z=0.39. These properties are correlated to the local height-difference distribution function obeying power-law statistics. We associate this intrinsic anomalous scaling with the instability duemore » to nonlocal shadowing effects that take place during thin-film growth by sputtering.« less

On the Prony series representation of stretched exponential relaxation

NASA Astrophysics Data System (ADS)

Mauro, John C.; Mauro, Yihong Z.

2018-09-01

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β. The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its "fat tail" at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grebogi, C.; Yorke, J.A.

This report discusses the following topics: controlling chaotic dynamical systems; embedding of experimental data; effect of noise on critical exponents of crises; transition to chaotic scattering; and distribution of floaters on a fluid surface. (LSP)

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

PubMed

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

PubMed Central

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

2016-01-01

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. PMID:27009399

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

NASA Astrophysics Data System (ADS)

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.

Unconventional minimal subtraction and Bogoliubov-Parasyuk-Hepp-Zimmermann method: Massive scalar theory and critical exponents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carvalho, Paulo R. S.; Leite, Marcelo M.

2013-09-15

We introduce a simpler although unconventional minimal subtraction renormalization procedure in the case of a massive scalar λφ{sup 4} theory in Euclidean space using dimensional regularization. We show that this method is very similar to its counterpart in massless field theory. In particular, the choice of using the bare mass at higher perturbative order instead of employing its tree-level counterpart eliminates all tadpole insertions at that order. As an application, we compute diagrammatically the critical exponents η and ν at least up to two loops. We perform an explicit comparison with the Bogoliubov-Parasyuk-Hepp-Zimmermann (BPHZ) method at the same loop order,more » show that the proposed method requires fewer diagrams and establish a connection between the two approaches.« less

Critical exponents for diluted resistor networks

NASA Astrophysics Data System (ADS)

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 φ up to second order in ɛ=6-d, where d is the spatial dimension. Our result φ=1+ɛ/42+4ɛ2/3087 verifies a previous calculation by Lubensky and Wang, which itself was based on the Potts-model formulation of the random resistor network.

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

NASA Astrophysics Data System (ADS)

Benhaiem, David; Joyce, Michael; Sicard, François

2013-03-01

One-dimensional versions of dissipationless cosmological N-body simulations have been shown to share many qualitative behaviours of the three-dimensional problem. Their interest lies in the fact that they can resolve a much greater range of time and length scales, and admit exact numerical integration. We use such models here to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the three-dimensional Einstein-de Sitter (EdS) model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two-point correlation function. We study how the corresponding exponent γ depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κ controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γ depends strongly on both n and κ and where it agrees very well with a simple generalization of the so-called stable clustering hypothesis in three dimensions; and (2) a region in which γ is more or less independent of both the spectrum and the expansion of the universe. The boundary in (n, κ) space dividing the `stable clustering' region from the `universal' region is very well approximated by a `critical' value of the predicted stable clustering exponent itself. We explain how this division of the (n, κ) space can be understood as a simple physical criterion which might indeed be expected to control the validity of the stable clustering hypothesis. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of `universality' of non-linear clustering in this context.

How sensitivity to ongoing interaural temporal disparities is affected by manipulations of temporal features of the envelopes of high-frequency stimuli

PubMed Central

Bernstein, Leslie R.; Trahiotis, Constantine

2009-01-01

This study addressed how manipulating certain aspects of the envelopes of high-frequency stimuli affects sensitivity to envelope-based interaural temporal disparities (ITDs). Listener’s threshold ITDs were measured using an adaptive two-alternative paradigm employing “raised-sine” stimuli [John, M. S., et al. (2002). Ear Hear. 23, 106–117] which permit independent variation in their modulation frequency, modulation depth, and modulation exponent. Threshold ITDs were measured while manipulating modulation exponent for stimuli having modulation frequencies between 32 and 256 Hz. The results indicated that graded increases in the exponent led to graded decreases in envelope-based threshold ITDs. Threshold ITDs were also measured while parametrically varying modulation exponent and modulation depth. Overall, threshold ITDs decreased with increases in the modulation depth. Unexpectedly, increases in the exponent of the raised-sine led to especially large decreases in threshold ITD when the modulation depth was low. An interaural correlation-based model was generally able to capture changes in threshold ITD stemming from changes in the exponent, depth of modulation, and frequency of modulation of the raised-sine stimuli. The model (and several variations of it), however, could not account for the unexpected interaction between the value of raised-sine exponent and its modulation depth. PMID:19425666

Extreme event distribution in Space Weather: Characterization of heavy tail distribution using Hurst exponents

NASA Astrophysics Data System (ADS)

Setty, V.; Sharma, A.

2013-12-01

Characterization of extreme conditions of space weather is essential for potential mitigation strategies. The non-equilibrium nature of magnetosphere makes such efforts complicated and new techniques to understand its extreme event distribution are required. The heavy tail distribution in such systems can be a modeled using Stable distribution whose stability parameter is a measure of scaling in the cumulative distribution and is related to the Hurst exponent. This exponent can be readily measured in stationary time series using several techniques and detrended fluctuation analysis (DFA) is widely used in the presence of non-stationarities. However DFA has severe limitations in cases with non-linear and atypical trends. We propose a new technique that utilizes nonlinear dynamical predictions as a measure of trends and estimates the Hurst exponents. Furthermore, such a measure provides us with a new way to characterize predictability, as perfectly detrended data have no long term memory akin to Gaussian noise Ab initio calculation of weekly Hurst exponents using the auroral electrojet index AL over a span of few decades shows that these exponents are time varying and so is its fractal structure. Such time series data with time varying Hurst exponents are modeled well using multifractional Brownian motion and it is shown that DFA estimates a single time averaged value for Hurst exponent in such data. Our results show that using time varying Hurst exponent structure, we can (a) Estimate stability parameter, -a measure of scaling in heavy tails, (b) Define and identify epochs when the magnetosphere switches between regimes with and without extreme events, and, (c) Study the dependence of the Hurst exponents on the solar activity.

The use of the Hurst exponent to investigate the global maximum of the Warsaw Stock Exchange WIG20 index

NASA Astrophysics Data System (ADS)

Domino, Krzysztof

2012-01-01

The WIG20 index-the index of the 20 biggest companies traded on the Warsaw Stock Exchange-reached the global maximum on 29th October 2007. I have used the local DFA (Detrended Functional Analysis) to obtain the Hurst exponent (diffusion exponent) and investigate the signature of anti-correlation of share price evolution around the maximum. The analysis was applied to the share price evolution for variable DFA parameters. For many values of parameters, the evidence of anti-correlation near the WIG20 maximum was pointed out.

The Effects of Sand Sediment Volume Heterogeneities on Sound Propagation and Scattering

DTIC Science & Technology

2013-08-19

power law exponent is larger then the value found for the exponential correlation function. With the correlation function given by Eq. (76) or the...summation approximation given by Eq. (84), it is possible to model the frequency dependence of the attenuation for a broad range of exponents , beyond...2 −1 0 1 0 0.5 1 1.5 2 2.5 3 m Ex po ne nt fo r s ca tte rin g co nt rib ut io n to a tte nu at io n FIG. 5. Exponent for the scattering

Relationship between efficiency and predictability in stock price change

NASA Astrophysics Data System (ADS)

Eom, Cheoljun; Oh, Gabjin; Jung, Woo-Sung

2008-09-01

In this study, we evaluate the relationship between efficiency and predictability in the stock market. The efficiency, which is the issue addressed by the weak-form efficient market hypothesis, is calculated using the Hurst exponent and the approximate entropy (ApEn). The predictability corresponds to the hit-rate; this is the rate of consistency between the direction of the actual price change and that of the predicted price change, as calculated via the nearest neighbor prediction method. We determine that the Hurst exponent and the ApEn value are negatively correlated. However, predictability is positively correlated with the Hurst exponent.

Variational Approach to Monte Carlo Renormalization Group

NASA Astrophysics Data System (ADS)

Wu, Yantao; Car, Roberto

2017-12-01

We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The two-dimensional Ising model is used to illustrate the method.

Quantum spin chains with multiple dynamics

NASA Astrophysics Data System (ADS)

Chen, Xiao; Fradkin, Eduardo; Witczak-Krempa, William

2017-11-01

Many-body systems with multiple emergent time scales arise in various contexts, including classical critical systems, correlated quantum materials, and ultracold atoms. We investigate such nontrivial quantum dynamics in a different setting: a spin-1 bilinear-biquadratic chain. It has a solvable entangled ground state, but a gapless excitation spectrum that is poorly understood. By using large-scale density matrix renormalization group simulations, we find that the lowest excitations have a dynamical exponent z that varies from 2 to 3.2 as we vary a coupling in the Hamiltonian. We find an additional gapless mode with a continuously varying exponent 2 ≤z <2.7 , which establishes the presence of multiple dynamics. In order to explain these striking properties, we construct a continuum wave function for the ground state, which correctly describes the correlations and entanglement properties. We also give a continuum parent Hamiltonian, but show that additional ingredients are needed to capture the excitations of the chain. By using an exact mapping to the nonequilibrium dynamics of a classical spin chain, we find that the large dynamical exponent is due to subdiffusive spin motion. Finally, we discuss the connections to other spin chains and to a family of quantum critical models in two dimensions.

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

NASA Astrophysics Data System (ADS)

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.

Chiral symmetry restoration at finite temperature and chemical potential in the improved ladder approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Taniguchi, Y.; Yoshida, Y.

1997-02-01

The chiral symmetry of QCD is studied at finite temperature and chemical potential using the Schwinger-Dyson equation in the improved ladder approximation. We calculate three order parameters: the vacuum expectation value of the quark bilinear operator, the pion decay constant, and the quark mass gap. We have a second order phase transition at the temperature T{sub c}=169 MeV along the zero chemical potential line, and a first order phase transition at the chemical potential {mu}{sub c}=598 MeV along the zero temperature line. We also calculate the critical exponents of the three order parameters. {copyright} {ital 1997} {ital The American Physicalmore » Society}« less

The Josephson plasma resonance in Bi2Sr2CaCu2O8 in a tilted field

NASA Astrophysics Data System (ADS)

Bayrakci, S.; Tsui, Ophelia K. C.; Ong, N. P.; Kishio, K.; Watauchi, S.

1999-04-01

The dependence of the Josephson plasma frequency ωp in Bi2Sr2CaCu2O8 on a tilted field H is reported. Measurements over a large range of B and tilt angle θ allow a detailed comparison with a recent calculation by Koshelev. With a slight modification of the model, close agreement is obtained. From the fits, we find values for the in-plane correlation length and the zero-field critical current density Jc0 (4600 A/cm2 at 30 K). An analogy to Bragg diffraction is described, as well as a picture for the fractional-exponent behavior of ωp vs. H

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

NASA Astrophysics Data System (ADS)

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 multifractality singular spectrum can be classified into two categories, confirming the appearance of two types of mobility edges.

Extracting Lyapunov exponents from the echo dynamics of Bose-Einstein condensates on a lattice

NASA Astrophysics Data System (ADS)

Tarkhov, Andrei E.; Wimberger, Sandro; Fine, Boris V.

2017-08-01

We propose theoretically an experimentally realizable method to demonstrate the Lyapunov instability and to extract the value of the largest Lyapunov exponent for a chaotic many-particle interacting system. The proposal focuses specifically on a lattice of coupled Bose-Einstein condensates in the classical regime describable by the discrete Gross-Pitaevskii equation. We suggest to use imperfect time reversal of the system's dynamics known as the Loschmidt echo, which can be realized experimentally by reversing the sign of the Hamiltonian of the system. The routine involves tracking and then subtracting the noise of virtually any observable quantity before and after the time reversal. We support the theoretical analysis by direct numerical simulations demonstrating that the largest Lyapunov exponent can indeed be extracted from the Loschmidt echo routine. We also discuss possible values of experimental parameters required for implementing this proposal.

Fractal characterization and wettability of ion treated silicon surfaces

NASA Astrophysics Data System (ADS)

Yadav, R. P.; Kumar, Tanuj; Baranwal, V.; Vandana, Kumar, Manvendra; Priya, P. K.; Pandey, S. N.; Mittal, A. K.

2017-02-01

Fractal characterization of surface morphology can be useful as a tool for tailoring the wetting properties of solid surfaces. In this work, rippled surfaces of Si (100) are grown using 200 keV Ar+ ion beam irradiation at different ion doses. Relationship between fractal and wetting properties of these surfaces are explored. The height-height correlation function extracted from atomic force microscopic images, demonstrates an increase in roughness exponent with an increase in ion doses. A steep variation in contact angle values is found for low fractal dimensions. Roughness exponent and fractal dimensions are found correlated with the static water contact angle measurement. It is observed that after a crossover of the roughness exponent, the surface morphology has a rippled structure. Larger values of interface width indicate the larger ripples on the surface. The contact angle of water drops on such surfaces is observed to be lowest. Autocorrelation function is used for the measurement of ripple wavelength.

Scaling behavior of the surface roughness of platinum films grown by oblique angle deposition

NASA Astrophysics Data System (ADS)

Dolatshahi-Pirouz, A.; Hovgaard, M. B.; Rechendorff, K.; Chevallier, J.; Foss, M.; Besenbacher, F.

2008-03-01

Thin platinum films with well-controlled rough surface morphologies are grown by e-gun evaporation at an oblique angle of incidence between the deposition flux and the substrate normal. Atomic force microscopy is used to determine the root-mean-square value w of the surface roughness on the respective surfaces. From the scaling behavior of w , we find that while the roughness exponent α remains nearly unchanged at about 0.90, the growth exponent β changes from 0.49±0.04 to 0.26±0.01 as the deposition angle approaches grazing incidence. The values of the growth exponent β indicate that the film growth is influenced by both surface diffusion and shadowing effects, while the observed change from 0.49 to 0.26 can be attributed to differences in the relative importance of diffusion and shadowing with the deposition angle.

Fractality of eroded coastlines of correlated landscapes.

PubMed

Morais, P A; Oliveira, E A; Araújo, N A M; Herrmann, H J; Andrade, J S

2011-07-01

Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines.

Optical Study of the Critical Behaviour of Pure Fluids and Binary Mixtures.

NASA Astrophysics Data System (ADS)

Narger, Ulrike

1990-01-01

Optical techniques were used to study the critical behaviour of the pure fluids CHF_3, CClF_3 and Xe, and binary mixtures He-Xe and nicotine + water. We find that for all these substances, the order parameter is described by a power law in the reduced temperature t = (T _{c} - T)/T_{c} with a leading exponent beta = 0.327 +/- 0.002. Also, we determine the first correction to scaling exponent to be Delta = 0.43 +/- 0.02 for the pure fluids and Delta = 0.50 +/- 0.02 for the He-Xe system. The coexistence curve diameter in CHF _3 and CClF_3 exhibits a deviation from recti-linear diameter, in agreement with a modern theory which interprets this behaviour as resulting from three-body effects. In contrast, no such deviation is observed in Xe where, according to that theory, it should be more pronounced than in other substances. In the polar fluid CHF_3, the order parameter, isothermal compressibility and the chemical potential along the critical isotherm were simultaneously measured in the same experiment in an effort to ensure self-consistency of the results. From the data, two amplitude ratios which are predicted to be universal are determined: Gamma_sp{0}{+} /Gamma_sp{0}{ -} = 4.8 +/- 0.6 and D_0 Gamma_sp{0}{+ } B_sp{0}{delta-1} = 1.66 +/- 0.14. In the binary liquid system nicotine + water, the diffusivity was measured both by light scattering and by interferometry. The results agree qualitatively, but differ by a factor of ~2. From the light scattering data, the critical exponent of the viscosity is found to be z_{eta } = 0.044 +/- 0.008. The interferometric experiments on Xe and He-Xe furnish a direct way to measure the effects of wetting: From the data, the exponent of the surface tension is found to be n = 1.24 +/- 0.06. The similarity of the order parameter and compressibility in Xe and a He-Xe mixture containing 5% He indicate that the phase transition in this He-Xe mixture is of the liquid -gas type rather than the binary liquid type.

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

NASA Astrophysics Data System (ADS)

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.

Scaling universality at the dynamic vortex Mott transition

DOE PAGES

Lankhorst, M.; Poccia, N.; Stehno, M. P.; ...

2018-01-17

The cleanest way to observe a dynamic Mott insulator-to-metal transition (DMT) without the interference from disorder and other effects inherent to electronic and atomic systems, is to employ the vortex Mott states formed by superconducting vortices in a regular array of pinning sites. Here, we report the critical behavior of the vortex system as it crosses the DMT line, driven by either current or temperature. We find universal scaling with respect to both, expressed by the same scaling function and characterized by a single critical exponent coinciding with the exponent for the thermodynamic Mott transition. We develop a theory formore » the DMT based on the parity reflection-time reversal (PT) symmetry breaking formalism and find that the nonequilibrium-induced Mott transition has the same critical behavior as the thermal Mott transition. Our findings demonstrate the existence of physical systems in which the effect of a nonequilibrium drive is to generate an effective temperature and hence the transition belonging in the thermal universality class.« less

Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2003-09-01

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.

Scaling universality at the dynamic vortex Mott transition

NASA Astrophysics Data System (ADS)

Lankhorst, M.; Poccia, N.; Stehno, M. P.; Galda, A.; Barman, H.; Coneri, F.; Hilgenkamp, H.; Brinkman, A.; Golubov, A. A.; Tripathi, V.; Baturina, T. I.; Vinokur, V. M.

2018-01-01

The cleanest way to observe a dynamic Mott insulator-to-metal transition (DMT) without the interference from disorder and other effects inherent to electronic and atomic systems, is to employ the vortex Mott states formed by superconducting vortices in a regular array of pinning sites. Here, we report the critical behavior of the vortex system as it crosses the DMT line, driven by either current or temperature. We find universal scaling with respect to both, expressed by the same scaling function and characterized by a single critical exponent coinciding with the exponent for the thermodynamic Mott transition. We develop a theory for the DMT based on the parity reflection-time reversal (P T ) symmetry breaking formalism and find that the nonequilibrium-induced Mott transition has the same critical behavior as the thermal Mott transition. Our findings demonstrate the existence of physical systems in which the effect of a nonequilibrium drive is to generate an effective temperature and hence the transition belonging in the thermal universality class.

Tree morphologic plasticity explains deviation from metabolic scaling theory in semi-arid conifer forests, southwestern USA

Treesearch

Tyson L. Swetnam; Christopher D. O' Connor; Ann M. Lynch

2016-01-01

A significant concern about Metabolic Scaling Theory (MST) in real forests relates to consistent differences between the values of power law scaling exponents of tree primary size measures used to estimate mass and those predicted by MST. Here we consider why observed scaling exponents for diameter and height relationships deviate from MST predictions across...

Modeling Fractal Structure of City-Size Distributions Using Correlation Functions

PubMed Central

Chen, Yanguang

2011-01-01

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences. PMID:21949753

Power Law Distributions of Patents as Indicators of Innovation

NASA Astrophysics Data System (ADS)

O'Neale, Dion; Hendy, Shaun

2013-03-01

The total number of patents produced by a country (or the number of patents produced per capita) is often used as an indicator for innovation. Such figures however give an overly simplistic measure of innovation within a country. Here we present evidence that the distribution of patents amongst applicants within many countries is well-fitted to a power law distribution with exponents that vary between 1.66 (Japan) and 2.37 (Poland). We suggest that this exponent is a useful new metric for studying innovation. Using simulations based on simple preferential attachment-type rules that generate power laws, we find we can explain some of the variation in exponents between countries, with countries that have larger numbers of patents per applicant generally exhibiting smaller exponents in both the simulated and actual data. Similarly we find that the exponents for most countries are inversely correlated with other indicators of innovation, such as research and development intensity or the ubiquity of export baskets. This suggests that in more advanced economies, which tend to have smaller values of the exponent, a greater proportion of the total number of patents are filed by large companies than in less advanced countries.

Anomalous charge storage exponents of organic bulk heterojunction solar cells.

NASA Astrophysics Data System (ADS)

Nair, Pradeep; Dwivedi, Raaz; Kumar, Goutam; Dept of Electrical Engineering, IIT Bombay Team

2013-03-01

Organic bulk heterojunction (BHJ) devices are increasingly being researched for low cost solar energy conversion. The efficiency of such solar cells is dictated by various recombination processes involved. While it is well known that the ideality factor and hence the charge storage exponents of conventional PN junction diodes are influenced by the recombination processes, the same aspects are not so well understood for organic solar cells. While dark currents of such devices typically show an ideality factor of 1 (after correcting for shunt resistance effects, if any), surprisingly, a wide range of charge storage exponents for such devices are reported in literature alluding to apparent concentration dependence for bi-molecular recombination rates. In this manuscript we critically analyze the role of bi-molecular recombination processes on charge storage exponents of organic solar cells. Our results indicate that the charge storage exponents are fundamentally influenced by the electrostatics and recombination processes and can be correlated to the dark current ideality factors. We believe that our findings are novel, and advance the state-of the art understanding on various recombination processes that dictate the performance limits of organic solar cells. The authors would like to thank the Centre of Excellence in Nanoelectronics (CEN) and the National Centre for Photovoltaic Research and Education (NCPRE), IIT Bombay for computational and financial support

Universality classes for unstable crystal growth

NASA Astrophysics Data System (ADS)

Biagi, Sofia; Misbah, Chaouqi; Politi, Paolo

2014-06-01

Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with nonequilibrium problems, however, the distinction in universality classes is not as clear and few are the examples, such as phase separation and kinetic roughening, for which universality has allowed to classify results in a general spirit. Here we focus on an out-of-equilibrium case, unstable crystal growth, lying in between phase ordering and pattern formation. We consider a well-established 2+1-dimensional family of continuum nonlinear equations for the local height h(x,t) of a crystal surface having the general form ∂th(x,t)=-∇.[j(∇h)+∇(∇2h)]: j (∇h) is an arbitrary function, which is linear for small ∇h, and whose structure expresses instabilities which lead to the formation of pyramidlike structures of planar size L and height H. Our task is the choice and calculation of the quantities that can operate as critical exponents, together with the discussion of what is relevant or not to the definition of our universality class. These aims are achieved by means of a perturbative, multiscale analysis of our model, leading to phase diffusion equations whose diffusion coefficients encapsulate all relevant information on dynamics. We identify two critical exponents: (i) the coarsening exponent, n, controlling the increase in time of the typical size of the pattern, L ˜tn; (ii) the exponent β, controlling the increase in time of the typical slope of the pattern, M ˜tβ, where M ≈H/L. Our study reveals that there are only two different universality classes, according to the presence (n =1/3, β =0) or the absence (n =1/4, β >0) of faceting. The symmetry of the pattern, as well as the symmetry of the surface mass current j (∇h) and its precise functional form, is irrelevant. Our analysis seems to support the idea that also space dimensionality is irrelevant.

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

NASA Astrophysics Data System (ADS)

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.

Entanglement entropy for the long-range Ising chain in a transverse field.

PubMed

Koffel, Thomas; Lewenstein, M; Tagliacozzo, Luca

2012-12-28

We consider the Ising model in a transverse field with long-range antiferromagnetic interactions that decay as a power law with their distance. We study both the phase diagram and the entanglement properties as a function of the exponent of the interaction. The phase diagram can be used as a guide for future experiments with trapped ions. We find two gapped phases, one dominated by the transverse field, exhibiting quasi-long-range order, and one dominated by the long-range interaction, with long-range Néel ordered ground states. We determine the location of the quantum critical points separating those two phases. We determine their critical exponents and central charges. In the phase with quasi-long-range order the ground states exhibit exotic corrections to the area law for the entanglement entropy coexisting with gapped entanglement spectra.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model.

PubMed

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.

Universal Scaling and Critical Exponents of the Anisotropic Quantum Rabi Model

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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.

Superlinear scaling of offspring at criticality in branching processes

NASA Astrophysics Data System (ADS)

Saichev, A.; Sornette, D.

2014-01-01

For any branching process, we demonstrate that the typical total number rmp(ντ) of events triggered over all generations within any sufficiently large time window τ exhibits, at criticality, a superlinear dependence rmp(ντ)˜(ντ)γ (with γ >1) on the total number ντ of the immigrants arriving at the Poisson rate ν. In branching processes in which immigrants (or sources) are characterized by fertilities distributed according to an asymptotic power-law tail with tail exponent 1<γ ⩽2, the exponent of the superlinear law for rmp(ντ) is identical to the exponent γ of the distribution of fertilities. For γ >2 and for standard branching processes without power-law distribution of fertilities, rmp(ντ)˜(ντ)2. This scaling law replaces and tames the divergence ντ /(1-n) of the mean total number R¯t(τ) of events, as the branching ratio (defined as the average number of triggered events of first generation per source) tends to 1. The derivation uses the formalism of generating probability functions. The corresponding prediction is confirmed by numerical calculations, and an heuristic derivation enlightens its underlying mechanism. We also show that R¯t(τ) is always linear in ντ even at criticality (n =1). Our results thus illustrate the fundamental difference between the mean total number, which is controlled by a few extremely rare realizations, and the typical behavior represented by rmp(ντ).

Lyapunov exponent for aging process in induction motor

NASA Astrophysics Data System (ADS)

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 focused on the controlling the mechanical parameters of the electrical machines. Brushless DC motor (BLDCM) and the other general purpose permanent magnet (PM) motors are the most widely examined motors [1, 8, 9]. But the researches, about Lyapunov Exponent, subjected to the induction motors are mostly focused on the control theory of the motors. Flux estimation of rotor, external load disturbances and speed tracking and vector control position system are the main research areas for induction motors [10, 11, 12-14]. For all the data sets which can be collected from an induction motor, vibration data have the key role for understanding the mechanical behaviours like aging, bearing damage and stator insulation damage [15-18]. In this paper aging of an induction motor is investigated by using the vibration signals. The signals consist of new and aged motor data. These data are examined by their 2 dimensional phase portraits and the geometric interpretation is applied for detecting the Lyapunov Exponents. These values are compared in order to define the character and state estimation of the aging processes.

QSPR modeling: graph connectivity indices versus line graph connectivity indices

PubMed

Basak; Nikolic; Trinajstic; Amic; Beslo

2000-07-01

Five QSPR models of alkanes were reinvestigated. Properties considered were molecular surface-dependent properties (boiling points and gas chromatographic retention indices) and molecular volume-dependent properties (molar volumes and molar refractions). The vertex- and edge-connectivity indices were used as structural parameters. In each studied case we computed connectivity indices of alkane trees and alkane line graphs and searched for the optimum exponent. Models based on indices with an optimum exponent and on the standard value of the exponent were compared. Thus, for each property we generated six QSPR models (four for alkane trees and two for the corresponding line graphs). In all studied cases QSPR models based on connectivity indices with optimum exponents have better statistical characteristics than the models based on connectivity indices with the standard value of the exponent. The comparison between models based on vertex- and edge-connectivity indices gave in two cases (molar volumes and molar refractions) better models based on edge-connectivity indices and in three cases (boiling points for octanes and nonanes and gas chromatographic retention indices) better models based on vertex-connectivity indices. Thus, it appears that the edge-connectivity index is more appropriate to be used in the structure-molecular volume properties modeling and the vertex-connectivity index in the structure-molecular surface properties modeling. The use of line graphs did not improve the predictive power of the connectivity indices. Only in one case (boiling points of nonanes) a better model was obtained with the use of line graphs.

Colossal dielectric response in all-ceramic percolative composite 0.65Pb(Mg1/3Nb2/3)O3-0.35PbTiO3-Pb2Ru2O6.5

NASA Astrophysics Data System (ADS)

Bobnar, V.; Hrovat, M.; Holc, J.; Filipič, C.; Levstik, A.; Kosec, M.

2009-02-01

An exceptionally high dielectric constant was obtained by making use of the conductive percolative phenomenon in all-ceramic composite, comprising of Pb2Ru2O6.5 with high electrical conductivity denoted as the conductive phase and ferroelectric 0.65Pb(Mg1/3Nb2/3)O3-0.35PbTiO3 (PMN-PT) perovskite systems. Structural analysis revealed a uniform distribution of conductive ceramic grains within the PMN-PT matrix. Consequently, the dielectric response in the PMN-PT-Pb2Ru2O6.5 composite follows the predictions of the percolation theory. Thus, close to the percolation point exceptionally high values of the dielectric constant were obtained—values higher than 105 were detected at room temperature at 1 kHz. Fit of the data, obtained for samples of different compositions, revealed critical exponent and percolation point, which reasonably agree with the theoretically predicted values.

Ground-state entropy of the potts antiferromagnet with next-nearest-neighbor spin-spin couplings on strips of the square lattice

PubMed

Chang; Shrock

2000-10-01

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and W(q), the exponent of the ground-state entropy, for the q-state Potts antiferromagnet with next-nearest-neighbor spin-spin couplings on square lattice strips, of width L(y)=3 and L(y)=4 vertices and arbitrarily great length Lx vertices, with both free and periodic boundary conditions. The resultant values of W for a range of physical q values are compared with each other and with the values for the full two-dimensional lattice. These results give insight into the effect of such nonnearest-neighbor couplings on the ground-state entropy. We show that the q=2 (Ising) and q=4 Potts antiferromagnets have zero-temperature critical points on the Lx-->infinity limits of the strips that we study. With the generalization of q from Z+ to C, we determine the analytic structure of W(q) in the q plane for the various cases.

Inferring wavelength dependence of AOD and Ångström exponent over a sub-tropical station in South Africa using AERONET data: influence of meteorology, long-range transport and curvature effect.

PubMed

Kumar, K Raghavendra; Sivakumar, V; Reddy, R R; Gopal, K Rama; Adesina, A Joseph

2013-09-01

Aerosol optical properties over a southern sub-tropical site Skukuza, South Africa were studied to determine the variability of the aerosol characteristics using CIMEL Sunphotometer data as part of the AErosol RObotic NETwork (AERONET) from December 2005 to November 2006. Aerosol optical depth (AOD), Ångström exponent (α), and columnar water vapor (CWV) data were collected, analyzed, and compiled. Participating in this network provided a unique opportunity for understanding the sources of aerosols affecting the atmosphere of South Africa (SA) and the regional radiation budget. The meteorological patterns significantly (p<0.05) influenced the amount and size distribution of the aerosols. Results showed that seasonal variation of AOD at 500 nm (AOD500) over the observation site were characterized by low values (0.10-0.13) in autumn, moderate values (0.14-0.16) in summer and winter seasons, and high to very high values (0.18-0.40) during the spring, with an overall mean value of 0.18±0.12. Ångström exponent α(440-870), varied from 0.5 to 2.89, with significant (p<0.0001) seasonal variability. CWV showed a strong annual cycle with maximum values in the summer and autumn seasons. The relationship between AOD, Ångström exponent (α), and CWV showed a strong dependence (p<0.0001) of α on AOD and CWV, while there was no significant correlation between AOD and CWV. Investigation of the adequacy of the simple use of the spectral AOD and Ångström exponent data was used in deriving the curvature (a2) showed to obtain information for determining the aerosol-particle size. The negative a2 values are characterized by aerosol-size dominated by fine-mode (0.1-1 μm), while the positive curvatures indicate abundance of coarse particles (>1 μm). Trajectory cluster analyses revealed that the air masses during the autumn and winter seasons have longer advection pathways, passing over the ocean and continent. This is reflected in the aerosol properties that are derived from the ocean, desert, and anthropogenic activities that include biomass burning and industrial pollution. Copyright © 2013 Elsevier B.V. All rights reserved.

Electrical and optical percolations in PMMA/GNP composite films

NASA Astrophysics Data System (ADS)

Arda, Ertan; Mergen, Ömer Bahadır; Pekcan, Önder

2018-05-01

Effects of graphene nanoplatelet (GNP) addition on the electrical conductivity and optical absorbance of poly(methyl methacrylate)/graphene nanoplatelet (PMMA/GNP) composite films were studied. Optical absorbance and two point probe resistivity techniques were used to determine the variations of the optical and electrical properties of the composites, respectively. Absorbance intensity, A, and surface resistivity, Rs, of the composite films were monitored as a function of GNP mass fraction (M) at room temperature. Absorbance intensity values of the composites were increased and surface resistivity values were decreased by increasing the content of GNP in the composite. Electrical and optical percolation thresholds of composite films were determined as Mσ = 27.5 wt.% and Mop = 26.6 wt.%, respectively. The conductivity and the optical results were attributed to the classical and site percolation theories, respectively. Optical (βop) and electrical (βσ) critical exponents were calculated as 0.40 and 1.71, respectively.

Expansion of a quantum wave packet in a one-dimensional disordered potential in the presence of a uniform bias force

NASA Astrophysics Data System (ADS)

Crosnier de Bellaistre, C.; Trefzger, C.; Aspect, A.; Georges, A.; Sanchez-Palencia, L.

2018-01-01

We study numerically the expansion dynamics of an initially confined quantum wave packet in the presence of a disordered potential and a uniform bias force. For white-noise disorder, we find that the wave packet develops asymmetric algebraic tails for any ratio of the force to the disorder strength. The exponent of the algebraic tails decays smoothly with that ratio and no evidence of a critical behavior on the wave density profile is found. Algebraic localization features a series of critical values of the force-to-disorder strength where the m th position moment of the wave packet diverges. Below the critical value for the m th moment, we find fair agreement between the asymptotic long-time value of the m th moment and the predictions of diagrammatic calculations. Above it, we find that the m th moment grows algebraically in time. For correlated disorder, we find evidence of systematic delocalization, irrespective to the model of disorder. More precisely, we find a two-step dynamics, where both the center-of-mass position and the width of the wave packet show transient localization, similar to the white-noise case, at short time and delocalization at sufficiently long time. This correlation-induced delocalization is interpreted as due to the decrease of the effective de Broglie wavelength, which lowers the effective strength of the disorder in the presence of finite-range correlations.

Holographic conductivity of holographic superconductors with higher-order corrections

NASA Astrophysics Data System (ADS)

Sheykhi, Ahmad; Ghazanfari, Afsoon; Dehyadegari, Amin

2018-02-01

We analytically and numerically disclose the effects of the higher-order correction terms in the gravity and in the gauge field on the properties of s-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss-Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that, for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss-Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics makes the condensation harder. We also study the holographic conductivity of the system and disclose the effects of the Gauss-Bonnet and nonlinear parameters α and b on the superconducting gap. We observe that, for various values of α and b, the real part of the conductivity is proportional to the frequency per temperature, ω /T, as the frequency is large enough. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing temperature.

Effect of nanowire curviness on the percolation resistivity of transparent, conductive metal nanowire networks

NASA Astrophysics Data System (ADS)

Hicks, Jeremy; Li, Junying; Ying, Chen; Ural, Ant

2018-05-01

We study the effect of nanowire curviness on the percolation resistivity of transparent, conductive metal nanowire networks by Monte Carlo simulations. We generate curvy nanowires as one-dimensional sticks using 3rd-order Bézier curves. The degree of curviness in the network is quantified by the concept of curviness angle and curl ratio. We systematically study the interaction between the effect of curviness and five other nanowire/device parameters on the network resistivity, namely nanowire density, nanowire length, device length, device width, and nanowire alignment. We find that the resistivity exhibits a power law dependence on the curl ratio, which is a signature of percolation transport. In each case, we extract the power-law scaling critical exponents and explain the results using geometrical and physical arguments. The value of the curl ratio critical exponent is not universal, but increases as the other nanowire/device parameters drive the network toward the percolation threshold. We find that, for randomly oriented networks, curviness is undesirable since it increases the resistivity. For well-aligned networks, on the other hand, some curviness is highly desirable, since the resistivity minimum occurs for partially curvy nanowires. We explain these results by considering the two competing effects of curviness on the percolation resistivity. The results presented in this work can be extended to any network, film, or nanocomposite consisting of one-dimensional nanoelements. Our results show that Monte Carlo simulations are an essential predictive tool for both studying the percolation transport and optimizing the electronic properties of transparent, conductive nanowire networks for a wide range of applications.

Magnetic and critical properties of Pr0.6Sr0.4MnO3 nanocrystals prepared by a combination of the solid state reaction and the mechanical ball milling methods

NASA Astrophysics Data System (ADS)

Dung, Nguyen Thi; Linh, Dinh Chi; Huyen Yen, Pham Duc; Yu, Seong Cho; Van Dang, Nguyen; Dang Thanh, Tran

2018-06-01

Influence of the crystallite size on the magnetic and critical properties of nanocrystals has been investigated. The results show that Curie temperature and magnetization slightly decrease with decreasing average crystallite size . Based on the mean-field theory and the magnetic-field dependences of magnetization at different temperatures , we pointed out that the ferromagnetic-paramagnetic phase transition in the samples undergoes the second-order phase transition with the critical exponents (, , and ) close to those of the mean-field theory. However, there is a small deviation from those expected for the mean-field theory of the values of , and obtained for the samples. It means that short-range ferromagnetic interactions appear in the smaller particles. In other words, nanocrystals become more magnetically inhomogeneous with smaller crystallite sizes that could be explained by the presence of surface-related effects, lattice strain and distortions, which lead the strength of ferromagnetic interaction is decreased in the small crystallite sizes.

Scale invariance and universality in economic phenomena

NASA Astrophysics Data System (ADS)

Stanley, H. E.; Amaral, L. A. N.; Gopikrishnan, P.; Plerou, V.; Salinger, M. A.

2002-03-01

This paper discusses some of the similarities between work being done by economists and by computational physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two such new results. Specifically, we discuss the two newly discovered scaling results that appear to be `universal', in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent -4 extending over 102 standard deviations (a factor of 108 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behaviour of the response function at the critical point (zero magnetic field) leads to large fluctuations. We discuss a curious `symmetry breaking' for values of Σ above a certain threshold value Σc here Σ is defined to be the local first moment of the probability distribution of demand Ω - the difference between the number of shares traded in buyer-initiated and seller-initiated trades. This feature is qualitatively identical to the behaviour of the probability density of the magnetization for fixed values of the inverse temperature.

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

NASA Astrophysics Data System (ADS)

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).

Complex conductivity of oil-contaminated clayey soils

NASA Astrophysics Data System (ADS)

Deng, Y.; Revil, A.; Shi, X.

2017-12-01

Non-intrusive hydrogeophysical techniques have been wildly applied to detect organic contaminants because of the difference of electrical properties for contaminated soil. Among them, spectral induced polarization (SIP) has emerged as a promising tool for the identification of contamination due to its sensitivity to the chemistry of pore water, solid-fluid interfaces and fluid content. Previous works have investigated the influences of oil on the electrical signatures of porous media, which demonstrated the potentials of SIP in the detection of hydrocarbon contamination. However, few works have done on the SIP response of oil in clayey soils. In this study, we perform a set of SIP measurements on the clayey samples under different water saturations. These clayey soils are characterized by relatively high cation exchange capacity. The objective in this work is to test the empirical relationships between the three exponents, including the cementation exponent (m), the saturation exponent (n) and the quadrature conductivity exponent (p), which is expected to reduce the model parameters needed in geophysical and hydraulic properties predictions. Our results show that the complex conductivity are saturation dependent. The magnitude of both in-phase and quadrature conductivities generally decrease with decreasing water saturation. The shape of quadrature conductivity spectra slightly changes when water saturation decreases in some cases. The saturation exponent slightly increases with cation exchange capacity, specific surface area and clay content, with an average value around 2.05. Compared to saturation exponent, the quadrature conductivity exponent apparently increases with cation exchange capacity and specific surface area while has little to do with the clay content. Further, the results indicate that the quadrature conductivity exponent p does not strictly obey to p=n-1 as proposed by Vinegar and Waxman (1984). Instead, it mostly ranges between p=n-1.5 and p=n-0.5. The relationship between the saturation exponent n and the cementation exponent m is comprised between m=n and m=n-0.5.

Quenching and anisotropy of hydromagnetic turbulent transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karak, Bidya Binay; Brandenburg, Axel; Rheinhardt, Matthias

2014-11-01

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for themore » quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the Ω×J effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.« less

Regulator dependence of fixed points in quantum Einstein gravity with R 2 truncation

NASA Astrophysics Data System (ADS)

Nagy, S.; Fazekas, B.; Peli, Z.; Sailer, K.; Steib, I.

2018-03-01

We performed a functional renormalization group analysis for the quantum Einstein gravity including a quadratic term in the curvature. The ultraviolet non-gaussian fixed point and its critical exponent for the correlation length are identified for different forms of regulators in case of dimension 3. We searched for that optimized regulator where the physical quantities show the least regulator parameter dependence. It is shown that the Litim regulator satisfies this condition. The infrared fixed point has also been investigated, it is found that the exponent is insensitive to the third coupling introduced by the R 2 term.

Critical percolation clusters in seven dimensions and on a complete graph

NASA Astrophysics Data System (ADS)

Huang, Wei; Hou, Pengcheng; Wang, Junfeng; Ziff, Robert M.; Deng, Youjin

2018-02-01

We study critical bond percolation on a seven-dimensional hypercubic lattice with periodic boundary conditions (7D) and on the complete graph (CG) of finite volume (number of vertices) V . We numerically confirm that for both cases, the critical number density n (s ,V ) of clusters of size s obeys a scaling form n (s ,V ) ˜s-τn ˜(s /Vdf*) with identical volume fractal dimension df*=2 /3 and exponent τ =1 +1 /df*=5 /2 . We then classify occupied bonds into bridge bonds, which includes branch and junction bonds, and nonbridge bonds; a bridge bond is a branch bond if and only if its deletion produces at least one tree. Deleting branch bonds from percolation configurations produces leaf-free configurations, whereas deleting all bridge bonds leads to bridge-free configurations composed of blobs. It is shown that the fraction of nonbridge (biconnected) bonds vanishes, ρn ,CG→0 , for large CGs, but converges to a finite value, ρn ,7 D=0.006 193 1 (7 ) , for the 7D hypercube. Further, we observe that while the bridge-free dimension dbf*=1 /3 holds for both the CG and 7D cases, the volume fractal dimensions of the leaf-free clusters are different: dlf,7 D *=0.669 (9 ) ≈2 /3 and dlf,CG *=0.3337 (17 ) ≈1 /3 . On the CG and in 7D, the whole, leaf-free, and bridge-free clusters all have the shortest-path volume fractal dimension dmin*≈1 /3 , characterizing their graph diameters. We also study the behavior of the number and the size distribution of leaf-free and bridge-free clusters. For the number of clusters, we numerically find the number of leaf-free and bridge-free clusters on the CG scale as ˜lnV , while for 7D they scale as ˜V . For the size distribution, we find the behavior on the CG is governed by a modified Fisher exponent τ'=1 , while for leaf-free clusters in 7D, it is governed by Fisher exponent τ =5 /2 . The size distribution of bridge-free clusters in 7D displays two-scaling behavior with exponents τ =4 and τ'=1 . The probability distribution P (C1,V ) d C1 of the largest cluster of size C1 for whole percolation configurations is observed to follow a single-variable function P ¯(x ) d x , with x ≡C1/Vdf* for both CG and 7D. Up to a rescaling factor for the variable x , the probability functions for CG and 7D collapse on top of each other within the entire range of x . The analytical expressions in the x →0 and x →∞ limits are further confirmed. Our work demonstrates that the geometric structure of high-dimensional percolation clusters cannot be fully accounted for by their complete-graph counterparts.

Avalanche statistics from data with low time resolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

LeBlanc, Michael; Nawano, Aya; Wright, Wendelin J.

Extracting avalanche distributions from experimental microplasticity data can be hampered by limited time resolution. We compute the effects of low time resolution on avalanche size distributions and give quantitative criteria for diagnosing and circumventing problems associated with low time resolution. We show that traditional analysis of data obtained at low acquisition rates can lead to avalanche size distributions with incorrect power-law exponents or no power-law scaling at all. Furthermore, we demonstrate that it can lead to apparent data collapses with incorrect power-law and cutoff exponents. We propose new methods to analyze low-resolution stress-time series that can recover the size distributionmore » of the underlying avalanches even when the resolution is so low that naive analysis methods give incorrect results. We test these methods on both downsampled simulation data from a simple model and downsampled bulk metallic glass compression data and find that the methods recover the correct critical exponents.« less

Avalanche statistics from data with low time resolution

DOE PAGES

LeBlanc, Michael; Nawano, Aya; Wright, Wendelin J.; ...

2016-11-22

Extracting avalanche distributions from experimental microplasticity data can be hampered by limited time resolution. We compute the effects of low time resolution on avalanche size distributions and give quantitative criteria for diagnosing and circumventing problems associated with low time resolution. We show that traditional analysis of data obtained at low acquisition rates can lead to avalanche size distributions with incorrect power-law exponents or no power-law scaling at all. Furthermore, we demonstrate that it can lead to apparent data collapses with incorrect power-law and cutoff exponents. We propose new methods to analyze low-resolution stress-time series that can recover the size distributionmore » of the underlying avalanches even when the resolution is so low that naive analysis methods give incorrect results. We test these methods on both downsampled simulation data from a simple model and downsampled bulk metallic glass compression data and find that the methods recover the correct critical exponents.« less

Finite-size scaling of clique percolation on two-dimensional Moore lattices

NASA Astrophysics Data System (ADS)

Dong, Jia-Qi; Shen, Zhou; Zhang, Yongwen; Huang, Zi-Gang; Huang, Liang; Chen, Xiaosong

2018-05-01

Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdős-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.

Effect of long-range interactions on the phase transition of Axelrod's model

NASA Astrophysics Data System (ADS)

Reia, Sandro M.; Fontanari, José F.

2016-11-01

Axelrod's model with F =2 cultural features, where each feature can assume k states drawn from a Poisson distribution of parameter q , exhibits a continuous nonequilibrium phase transition in the square lattice. Here we use extensive Monte Carlo simulations and finite-size scaling to study the critical behavior of the order parameter ρ , which is the fraction of sites that belong to the largest domain of an absorbing configuration averaged over many runs. We find that it vanishes as ρ ˜(qc0-q )β with β ≈0.25 at the critical point qc0≈3.10 and that the exponent that measures the width of the critical region is ν0≈2.1 . In addition, we find that introduction of long-range links by rewiring the nearest-neighbors links of the square lattice with probability p turns the transition discontinuous, with the critical point qcp increasing from 3.1 to 27.17, approximately, as p increases from 0 to 1. The sharpness of the threshold, as measured by the exponent νp≈1 for p >0 , increases with the square root of the number of nodes of the resulting small-world network.

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

PubMed

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.

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

DOE PAGES

Fu, Bo; Zhu, Wei; Shi, Qinwei; ...

2017-04-03

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 behaviormore » 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. Furthermore, we show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.« less

On projectile fragmentation at high-velocity perforation of a thin bumper

NASA Astrophysics Data System (ADS)

Myagkov, N. N.; Stepanov, V. V.

2014-09-01

By means of 3D numerical simulations, we study the statistical properties of the fragments cloud formed during high-velocity impact of a spherical projectile on a mesh bumper. We present a quantitative description of the projectile fragmentation, and study the nature of the transition from the damage to the fragmentation of the projectile when the impact velocity varies. A distinctive feature of the present work is that the calculations are carried out by smoothed particle hydrodynamics (SPH) method applied to the equations of mechanics of deformable solids (MDS). We describe the materials behavior by the Mie-Grüneisen equation of state and the Johnson-Cook model for the yield strength. The maximum principal stress spall model is used as the fracture model. It is shown that the simulation results of fragmentation based on the MDS equations by the SPH method are qualitatively consistent with the results obtained earlier on the basis of the molecular dynamics and discrete element models. It is found that the power-law distribution exponent does not depend on energy imparted to the projectile during the high-velocity impact. At the same time, our calculations show that the critical impact velocity, the power-law exponent and other critical exponents depend on the fracture criterion.

Superconductor-insulator transition on annealed complex networks.

PubMed

Bianconi, Ginestra

2012-06-01

Cuprates show multiphase and multiscale complexity that has hindered physicists search for the mechanism of high T{c} for many years. Recently the interest has been addressed to a possible optimum inhomogeneity of dopants, defects, and interstitials, and the structural scale invariance of dopants detected by scanning micro-x-ray diffraction has been reported to promote the critical temperature. In order to shed light on critical phenomena on granular materials, here we propose a stylized model capturing the essential characteristics of the superconducting-insulator transition of a highly dynamical, heterogeneous granular material: the random transverse Ising model (RTIM) on annealed complex network. We show that when the networks encode for high heterogeneity of the expected degrees described by a power-law distribution, the critical temperature for the onset of the superconducting phase diverges to infinity as the power-law exponent γ of the expected degree distribution is less than 3, i.e., γ<3. Moreover we investigate the case in which the critical state of the electronic background is triggered by an external parameter g that determines an exponential cutoff in the power-law expected degree distribution characterized by an exponent γ. We find that for g=g{c} the critical temperature for the superconducting-insulator transition has a maximum if γ>3 and diverges if γ<3.

Complex networks: Effect of subtle changes in nature of randomness

NASA Astrophysics Data System (ADS)

Goswami, Sanchari; Biswas, Soham; Sen, Parongama

2011-03-01

In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and although the qualitative results remain the same, finite differences in the exponents are observed. In the Euclidean type networks, where at least one finite phase transition occurs, two models differing in a similar way have been considered. The results show a possible shift in one of the phase transition points but no change in the values of the exponents. The WS and Euclidean type models are equivalent for extreme values of the parameters; we compare their behaviour for intermediate values.

Different universality classes at the yielding transition of amorphous systems

NASA Astrophysics Data System (ADS)

Jagla, E. A.

2017-08-01

We study the yielding transition of a two-dimensional amorphous system under shear by using a mesoscopic elasto-plastic model. The model combines a full (tensorial) description of the elastic interactions in the system and the possibility of structural reaccommodations that are responsible for the plastic behavior. The possible structural reaccommodations are encoded in the form of a "plastic disorder" potential, which is chosen independently at each position of the sample to account for local heterogeneities. We observe that the stress must exceed a critical value σc in order for the system to yield. In addition, when the system yields a flow curve (relating stress σ and strain rate γ ˙) of the form γ ˙˜(σ-σc) β is obtained. Remarkably, we observe the value of β to depend on some details of the plastic disorder potential. For smooth potentials a value of β ≃2.0 is obtained, whereas for potentials obtained as a concatenation of smooth pieces a value β ≃1.5 is observed in the simulations. This indicates a dependence of critical behavior on details of the plastic behavior. In addition, by integrating out nonessential, harmonic degrees of freedom, we derive a simplified scalar version of the model that represents a collection of interacting Prandtl-Tomlinson particles. A mean-field treatment of this interaction reproduces the difference of β exponents for the two classes of plastic disorder potentials and provides values of β that compare favorably with those found in the full simulations.

A Direct Method for Viewing Ferromagnetic Phase Transition.

ERIC Educational Resources Information Center

Lue, Chin-Shan

1994-01-01

Provides a method, using the Rowland ring as a specimen, to observe the phase transition process directly on the oscilloscope and even extract the critical exponent of ferromagnetic transition. Includes theory, experimental setup, and results. (MVL)

A holographic c-theorem for Schrödinger spacetimes

DOE PAGES

Liu, James T.; Zhong, Weishun

2015-12-29

We prove a c-theorem for holographic renormalization group flows in a Schrodinger spacetime that demonstrates that the effective radius L(r) monotonically decreases from the UV to the IR, where r is the bulk radial coordinate. This result assumes that the bulk matter satisfies the null energy condition, but holds regardless of the value of the critical exponent z. We also construct several numerical examples in a model where the Schrodinger background is realized by a massive vector coupled to a real scalar. Finally, the full Schrodinger group is realized when z = 2, and in this case it is possiblemore » to construct solutions with constant effective z(r) = 2 along the entire flow.« less

On the wing behaviour of the overtones of self-localized modes

NASA Astrophysics Data System (ADS)

Dusi, R.; Wagner, M.

1998-08-01

In this paper the solutions for self-localized modes in a nonlinear chain are investigated. We present a converging iteration procedure, which is based on analytical information of the wings and which takes into account higher overtones of the solitonic oscillations. The accuracy is controlled in a step by step manner by means of a Gaussian error analysis. Our numerical procedure allows for highly accurate solutions, in all anharmonicity regimes, and beyond the rotating-wave approximation (RWA). It is found that the overtone wings change their analytical behaviour at certain critical values of the energy of the self-localized mode: there is a turnover in the exponent of descent. The results are shown for a Fermi-Pasta-Ulam (FPU) chain with quartic anharmonicity.

F4 symmetric ϕ3 theory at four loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.

2017-03-01

The renormalization group functions for six dimensional scalar ϕ3 theory with an F4 symmetry are provided at four loops in the modified minimal subtraction (MS ¯ ) scheme. Aside from the anomalous dimension of ϕ and the β -function this includes the mass operator and a ϕ2-type operator. The anomalous dimension of the latter is computed explicitly at four loops for the 26 and 324 representations of F4. The ɛ expansion of all the related critical exponents are determined to O (ɛ4). For instance the value for Δϕ agrees with recent conformal bootstrap estimates in 5 and 5.95 dimensions. The renormalization group functions are also provided at four loops for the group E6.

Critical reflexivity in financial markets: a Hawkes process analysis

NASA Astrophysics Data System (ADS)

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.

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

PubMed

Schnyder, Simon K; Horbach, Jürgen

2018-02-16

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

Self-consistent expansion for the molecular beam epitaxy equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2002-03-01

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the nonlinear molecular beam epitaxy (MBE) equation, a self-consistent expansion for the nonlinear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form D(r-->-r',t-t')=2D0\\|r-->- r'\\|2ρ-dδ(t-t'). I find a lower critical dimension dc(ρ)=4+2ρ, above which the linear MBE solution appears. Below the lower critical dimension a ρ-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe nonlinear MBE, using a reliable method that proved itself in the past by giving reasonable results for the strong-coupling regime of the Kardar-Parisi-Zhang system (for d>1), where DRG failed to do so.

Self-consistent expansion for the molecular beam epitaxy equation.

PubMed

Katzav, Eytan

2002-03-01

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the nonlinear molecular beam epitaxy (MBE) equation, a self-consistent expansion for the nonlinear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form D(r-r('),t-t('))=2D(0)[r-->-r(')](2rho-d)delta(t-t(')). I find a lower critical dimension d(c)(rho)=4+2rho, above which the linear MBE solution appears. Below the lower critical dimension a rho-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe nonlinear MBE, using a reliable method that proved itself in the past by giving reasonable results for the strong-coupling regime of the Kardar-Parisi-Zhang system (for d>1), where DRG failed to do so.

Nonlinear Midinfrared Photothermal Spectroscopy Using Zharov Splitting and Quantum Cascade Lasers.

PubMed

Mertiri, Alket; Altug, Hatice; Hong, Mi K; Mehta, Pankaj; Mertz, Jerome; Ziegler, Lawrence D; Erramilli, Shyamsunder

2014-08-20

We report on the mid-infrared nonlinear photothermal spectrum of the neat liquid crystal 4-octyl-4'-cyanobiphenyl (8CB) using a tunable Quantum Cascade Laser (QCL). The nonequilibrium steady state characterized by the nonlinear photothermal infrared response undergoes a supercritical bifurcation. The bifurcation, observed in heterodyne two-color pump-probe detection, leads to ultrasharp nonlinear infrared spectra similar to those reported in the visible region. A systematic study of the peak splitting as a function of absorbed infrared power shows the bifurcation has a critical exponent of 0.5. The observation of an apparently universal critical exponent in a nonequilibrium state is explained using an analytical model analogous of mean field theory. Apart from the intrinsic interest for nonequilibrium studies, nonlinear photothermal methods lead to a dramatic narrowing of spectral lines, giving rise to a potential new contrast mechanism for the rapidly emerging new field of mid-infrared microspectroscopy using QCLs.

Nonlinear Midinfrared Photothermal Spectroscopy Using Zharov Splitting and Quantum Cascade Lasers

PubMed Central

2015-01-01

We report on the mid-infrared nonlinear photothermal spectrum of the neat liquid crystal 4-octyl-4′-cyanobiphenyl (8CB) using a tunable Quantum Cascade Laser (QCL). The nonequilibrium steady state characterized by the nonlinear photothermal infrared response undergoes a supercritical bifurcation. The bifurcation, observed in heterodyne two-color pump–probe detection, leads to ultrasharp nonlinear infrared spectra similar to those reported in the visible region. A systematic study of the peak splitting as a function of absorbed infrared power shows the bifurcation has a critical exponent of 0.5. The observation of an apparently universal critical exponent in a nonequilibrium state is explained using an analytical model analogous of mean field theory. Apart from the intrinsic interest for nonequilibrium studies, nonlinear photothermal methods lead to a dramatic narrowing of spectral lines, giving rise to a potential new contrast mechanism for the rapidly emerging new field of mid-infrared microspectroscopy using QCLs. PMID:25541620

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

NASA Astrophysics Data System (ADS)

Schnyder, Simon K.; Horbach, Jürgen

2018-02-01

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

Dynamic renormalization-group analysis of the d+1 dimensional Kuramoto-Sivashinsky equation with both conservative and nonconservative noises

NASA Astrophysics Data System (ADS)

Zhang, L.; Tang, G.; Xun, Z.; Han, K.; Chen, H.; Hu, B.

2008-05-01

The long-wavelength properties of the (d + 1)-dimensional Kuramoto-Sivashinsky (KS) equation with both conservative and nonconservative noises are investigated by use of the dynamic renormalization-group (DRG) theory. The dynamic exponent z and roughness exponent α are calculated for substrate dimensions d = 1 and d = 2, respectively. In the case of d = 1, we arrive at the critical exponents z = 1.5 and α = 0.5 , which are consistent with the results obtained by Ueno et al. in the discussion of the same noisy KS equation in 1+1 dimensions [Phys. Rev. E 71, 046138 (2005)] and are believed to be identical with the dynamic scaling of the Kardar-Parisi-Zhang (KPZ) in 1+1 dimensions. In the case of d = 2, we find a fixed point with the dynamic exponents z = 2.866 and α = -0.866 , which show that, as in the 1 + 1 dimensions situation, the existence of the conservative noise in 2 + 1 or higher dimensional KS equation can also lead to new fixed points with different dynamic scaling exponents. In addition, since a higher order approximation is adopted, our calculations in this paper have improved the results obtained previously by Cuerno and Lauritsen [Phys. Rev. E 52, 4853 (1995)] in the DRG analysis of the noisy KS equation, where the conservative noise is not taken into account.

Autonomous strange nonchaotic oscillations in a system of mechanical rotators

NASA Astrophysics Data System (ADS)

Jalnine, Alexey Yu.; Kuznetsov, Sergey P.

2017-05-01

We investigate strange nonchaotic self-oscillations in a dissipative system consisting of three mechanical rotators driven by a constant torque applied to one of them. The external driving is nonoscillatory; the incommensurable frequency ratio in vibrational-rotational dynamics arises due to an irrational ratio of diameters of the rotating elements involved. It is shown that, when losing stable equilibrium, the system can demonstrate two- or three-frequency quasi-periodic, chaotic and strange nonchaotic self-oscillations. The conclusions of the work are confirmed by numerical calculations of Lyapunov exponents, fractal dimensions, spectral analysis, and by special methods of detection of a strange nonchaotic attractor (SNA): phase sensitivity and analysis using rational approximation for the frequency ratio. In particular, SNA possesses a zero value of the largest Lyapunov exponent (and negative values of the other exponents), a capacitive dimension close to 2 and a singular continuous power spectrum. In general, the results of this work shed a new light on the occurrence of strange nonchaotic dynamics.

Statistics of Lyapunov exponents of quasi-one-dimensional disordered systems

NASA Astrophysics Data System (ADS)

Zhang, Yan-Yang; Xiong, Shi-Jie

2005-10-01

Statistical properties of Lyapunov exponents (LE) are numerically calculated in a quasi-one-dimensional (1D) Anderson model, which is in a 2D or 3D lattice with a finite cross section. The single-parameter scaling (SPS) variable τ relating the Lyapunov exponents γ and their variances σ by τ≡σ2L/⟨γ⟩ is calculated for different lateral coupling t and disorder strength W . In a wide range of t , τ is approximately independent of W , but it has different values for LEs in different channels. For small t , the distribution of the smallest LE is non-Gaussian and τ strongly depends on W , remarkably different from the 1D SPS hypothesis.

Automatic detection of sleep apnea based on EEG detrended fluctuation analysis and support vector machine.

PubMed

Zhou, Jing; Wu, Xiao-ming; Zeng, Wei-jie

2015-12-01

Sleep apnea syndrome (SAS) is prevalent in individuals and recently, there are many studies focus on using simple and efficient methods for SAS detection instead of polysomnography. However, not much work has been done on using nonlinear behavior of the electroencephalogram (EEG) signals. The purpose of this study is to find a novel and simpler method for detecting apnea patients and to quantify nonlinear characteristics of the sleep apnea. 30 min EEG scaling exponents that quantify power-law correlations were computed using detrended fluctuation analysis (DFA) and compared between six SAS and six healthy subjects during sleep. The mean scaling exponents were calculated every 30 s and 360 control values and 360 apnea values were obtained. These values were compared between the two groups and support vector machine (SVM) was used to classify apnea patients. Significant difference was found between EEG scaling exponents of the two groups (p < 0.001). SVM was used and obtained high and consistent recognition rate: average classification accuracy reached 95.1% corresponding to the sensitivity 93.2% and specificity 98.6%. DFA of EEG is an efficient and practicable method and is helpful clinically in diagnosis of sleep apnea.

Universality in the Self Organized Critical behavior of a cellular model of superconducting vortex dynamics

NASA Astrophysics Data System (ADS)

Sun, Yudong; Vadakkan, Tegy; Bassler, Kevin

2007-03-01

We study the universality and robustness of variants of the simple model of superconducting vortex dynamics first introduced by Bassler and Paczuski in Phys. Rev. Lett. 81, 3761 (1998). The model is a coarse-grained model that captures the essential features of the plastic vortex motion. It accounts for the repulsive interaction between vortices, the pining of vortices at quenched disordered locations in the material, and the over-damped dynamics of the vortices that leads to tearing of the flux line lattice. We report the results of extensive simulations of the critical ``Bean state" dynamics of the model. We find a phase diagram containing four distinct phases of dynamical behavior, including two phases with distinct Self Organized Critical (SOC) behavior. Exponents describing the avalanche scaling behavior in the two SOC phases are determined using finite-size scaling. The exponents are found to be robust within each phase and for different variants of the model. The difference of the scaling behavior in the two phases is also observed in the morphology of the avalanches.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Bo; Zhu, Wei; Shi, Qinwei

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 behaviormore » 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. Furthermore, we show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.« less

The allometric exponent for scaling clearance varies with age: a study on seven propofol datasets ranging from preterm neonates to adults.

PubMed

Wang, Chenguang; Allegaert, Karel; Peeters, Mariska Y M; Tibboel, Dick; Danhof, Meindert; Knibbe, Catherijne A J

2014-01-01

For scaling clearance between adults and children, allometric scaling with a fixed exponent of 0.75 is often applied. In this analysis, we performed a systematic study on the allometric exponent for scaling propofol clearance between two subpopulations selected from neonates, infants, toddlers, children, adolescents and adults. Seven propofol studies were included in the analysis (neonates, infants, toddlers, children, adolescents, adults1 and adults2). In a systematic manner, two out of the six study populations were selected resulting in 15 combined datasets. In addition, the data of the seven studies were regrouped into five age groups (FDA Guidance 1998), from which four combined datasets were prepared consisting of one paediatric age group and the adult group. In each of these 19 combined datasets, the allometric scaling exponent for clearance was estimated using population pharmacokinetic modelling (nonmem 7.2). The allometric exponent for propofol clearance varied between 1.11 and 2.01 in cases where the neonate dataset was included. When two paediatric datasets were analyzed, the exponent varied between 0.2 and 2.01, while it varied between 0.56 and 0.81 when the adult population and a paediatric dataset except for neonates were selected. Scaling from adults to adolescents, children, infants and neonates resulted in exponents of 0.74, 0.70, 0.60 and 1.11 respectively. For scaling clearance, ¾ allometric scaling may be of value for scaling between adults and adolescents or children, while it can neither be used for neonates nor for two paediatric populations. For scaling to neonates an exponent between 1 and 2 was identified. © 2013 The British Pharmacological Society.

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

NASA Astrophysics Data System (ADS)

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.

Towards a unifying basis of auditory thresholds: binaural summation.

PubMed

Heil, Peter

2014-04-01

Absolute auditory threshold decreases with increasing sound duration, a phenomenon explainable by the assumptions that the sound evokes neural events whose probabilities of occurrence are proportional to the sound's amplitude raised to an exponent of about 3 and that a constant number of events are required for threshold (Heil and Neubauer, Proc Natl Acad Sci USA 100:6151-6156, 2003). Based on this probabilistic model and on the assumption of perfect binaural summation, an equation is derived here that provides an explicit expression of the binaural threshold as a function of the two monaural thresholds, irrespective of whether they are equal or unequal, and of the exponent in the model. For exponents >0, the predicted binaural advantage is largest when the two monaural thresholds are equal and decreases towards zero as the monaural threshold difference increases. This equation is tested and the exponent derived by comparing binaural thresholds with those predicted on the basis of the two monaural thresholds for different values of the exponent. The thresholds, measured in a large sample of human subjects with equal and unequal monaural thresholds and for stimuli with different temporal envelopes, are compatible only with an exponent close to 3. An exponent of 3 predicts a binaural advantage of 2 dB when the two ears are equally sensitive. Thus, listening with two (equally sensitive) ears rather than one has the same effect on absolute threshold as doubling duration. The data suggest that perfect binaural summation occurs at threshold and that peripheral neural signals are governed by an exponent close to 3. They might also shed new light on mechanisms underlying binaural summation of loudness.

Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs

NASA Astrophysics Data System (ADS)

van der Hofstad, Remco; Kliem, Sandra; van Leeuwaarden, Johan S. H.

2018-04-01

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 \\in (3,4), the sequence of clusters ordered in decreasing size and multiplied through by n^{-(τ -2)/(τ -1)} converges as n→ ∞ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237-269, 2001) for the Erdős-Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.

"A Body Shape Index" in middle-age and older Indonesian population: scaling exponents and association with incident hypertension.

PubMed

Cheung, Yin Bun

2014-01-01

"A Body Shape Index" (ABSI) is a recently proposed index that standardizes waist circumference for body mass index (BMI) and height. This study aims to: (a) examine if the ABSI scaling exponents for standardizing waist circumference for BMI and height are valid in middle-aged and older Indonesian population, and (b) compare the association between incident hypertension and ABSI and other anthropometric measures. The Indonesian Family Life Survey Wave 3 measured anthropometric variables and blood pressure of 8255 adults aged between 40 to 85 years in 2000. The relationship between two anthropometric quantities, e.g. weight (w) and height (h), can be expressed as the power law-equivalent [Formula: see text], where p = 2 is the scaling exponent in the derivation of the BMI and can be estimated by linear regression analysis. This was extended to the regression analysis of the log-transformed waist circumference, weight and height to establish the scaling exponents in the ABSI. The values for men were similar to those developed by the previous American study, which were 2/3 (BMI) and 1/2 (height). Those for women were somewhat smaller, at 3/5 (BMI) and 1/5 (height). The original (American) ABSI leads to mild negative correlation with BMI (-0.14) and height (-0.12) in the female population. Analysis of the development of hypertension between Waves 3 and 4 (average interval 7.5 years) in relation to ABSI measured at Wave 3 showed stronger association if the locally derived (Indonesian) scaling exponents were used. However, both versions of the ABSI were less associated with incident hypertension than waist circumference and BMI. The values for the scaling exponents for ABSI are roughly similar between the American population and the middle-aged and older Indonesian population, although larger discrepancy was found in women. The ABSI is less associated with incident hypertension than waist circumference and BMI.

Multiplicity of solutions of the bi-harmonic Schrödinger equation with critical growth

NASA Astrophysics Data System (ADS)

Zhang, Jian; Lou, Zhenluo; Ji, Yanju; Shao, Wei

2018-04-01

In this paper, we study multiplicity of solutions of the critical bi-harmonic equation ɛ ^4 Δ ^2 u +V(x) u =h(x) f(u)+g(x) u^{2_*-1} in R^N, where 2_*=2N/N-4 is the critical exponent. When ɛ >0 is small, we establish the relationship between the number of solutions and the profile of V, h, g. Also, without the restriction on ɛ , we obtain a multiplicity result.

Competition-Induced Criticality in a Model of Meme Popularity

NASA Astrophysics Data System (ADS)

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.

Competition-induced criticality in a model of meme popularity.

PubMed

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.

Detrended fluctuation analysis of short datasets: An application to fetal cardiac data

NASA Astrophysics Data System (ADS)

Govindan, R. B.; Wilson, J. D.; Preißl, H.; Eswaran, H.; Campbell, J. Q.; Lowery, C. L.

2007-02-01

Using detrended fluctuation analysis (DFA) we perform scaling analysis of short datasets of length 500-1500 data points. We quantify the long range correlation (exponent α) by computing the mean value of the local exponents αL (in the asymptotic regime). The local exponents are obtained as the (numerical) derivative of the logarithm of the fluctuation function F(s) with respect to the logarithm of the scale factor s:αL=dlog10F(s)/dlog10s. These local exponents display huge variations and complicate the correct quantification of the underlying correlations. We propose the use of the phase randomized surrogate (PRS), which preserves the long range correlations of the original data, to minimize the variations in the local exponents. Using the numerically generated uncorrelated and long range correlated data, we show that performing DFA on several realizations of PRS and estimating αL from the averaged fluctuation functions (of all realizations) can minimize the variations in αL. The application of this approach to the fetal cardiac data (RR intervals) is discussed and we show that there is a statistically significant correlation between α and the gestation age.

DNA bubble dynamics as a quantum Coulomb problem.

PubMed

Fogedby, Hans C; Metzler, Ralf

2007-02-16

We study the dynamics of denaturation bubbles in double-stranded DNA. Demonstrating that the associated Fokker-Planck equation is equivalent to a Coulomb problem, we derive expressions for the bubble survival distribution W(t). Below Tm, W(t) is associated with the continuum of scattering states of the repulsive Coulomb potential. At Tm, the Coulomb potential vanishes and W(t) assumes a power-law tail with nontrivial dynamic exponents: the critical exponent of the entropy loss factor may cause a finite mean lifetime. Above Tm (attractive potential), the long-time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

Spectrum of Lyapunov exponents of non-smooth dynamical systems of integrate-and-fire type.

PubMed

Zhou, Douglas; Sun, Yi; Rangan, Aaditya V; Cai, David

2010-04-01

We discuss how to characterize long-time dynamics of non-smooth dynamical systems, such as integrate-and-fire (I&F) like neuronal network, using Lyapunov exponents and present a stable numerical method for the accurate evaluation of the spectrum of Lyapunov exponents for this large class of dynamics. These dynamics contain (i) jump conditions as in the firing-reset dynamics and (ii) degeneracy such as in the refractory period in which voltage-like variables of the network collapse to a single constant value. Using the networks of linear I&F neurons, exponential I&F neurons, and I&F neurons with adaptive threshold, we illustrate our method and discuss the rich dynamics of these networks.

Visibility graph approach to exchange rate series

NASA Astrophysics Data System (ADS)

Yang, Yue; Wang, Jianbo; Yang, Huijie; Mang, Jingshi

2009-10-01

By means of a visibility graph, we investigate six important exchange rate series. It is found that the series convert into scale-free and hierarchically structured networks. The relationship between the scaling exponents of the degree distributions and the Hurst exponents obeys the analytical prediction for fractal Brownian motions. The visibility graph can be used to obtain reliable values of Hurst exponents of the series. The characteristics are explained by using the multifractal structures of the series. The exchange rate of EURO to Japanese Yen is widely used to evaluate risk and to estimate trends in speculative investments. Interestingly, the hierarchies of the visibility graphs for the exchange rate series of these two currencies are significantly weak compared with that of the other series.

Complexity of Continuous Glucose Monitoring Data in Critically Ill Patients: Continuous Glucose Monitoring Devices, Sensor Locations, and Detrended Fluctuation Analysis Methods

PubMed Central

Signal, Matthew; Thomas, Felicity; Shaw, Geoffrey M.; Chase, J. Geoffrey

2013-01-01

Background Critically ill patients often experience high levels of insulin resistance and stress-induced hyperglycemia, which may negatively impact outcomes. However, evidence surrounding the causes of negative outcomes remains inconclusive. Continuous glucose monitoring (CGM) devices allow researchers to investigate glucose complexity, using detrended fluctuation analysis (DFA), to determine whether it is associated with negative outcomes. The aim of this study was to investigate the effects of CGM device type/calibration and CGM sensor location on results from DFA. Methods This study uses CGM data from critically ill patients who were each monitored concurrently using Medtronic iPro2s on the thigh and abdomen and a Medtronic Guardian REAL-Time on the abdomen. This allowed interdevice/calibration type and intersensor site variation to be assessed. Detrended fluctuation analysis is a technique that has previously been used to determine the complexity of CGM data in critically ill patients. Two variants of DFA, monofractal and multifractal, were used to assess the complexity of sensor glucose data as well as the precalibration raw sensor current. Monofractal DFA produces a scaling exponent (H), where H is inversely related to complexity. The results of multifractal DFA are presented graphically by the multifractal spectrum. Results From the 10 patients recruited, 26 CGM devices produced data suitable for analysis. The values of H from abdominal iPro2 data were 0.10 (0.03–0.20) higher than those from Guardian REAL-Time data, indicating consistently lower complexities in iPro2 data. However, repeating the analysis on the raw sensor current showed little or no difference in complexity. Sensor site had little effect on the scaling exponents in this data set. Finally, multifractal DFA revealed no significant associations between the multifractal spectrums and CGM device type/calibration or sensor location. Conclusions Monofractal DFA results are dependent on the device/calibration used to obtain CGM data, but sensor location has little impact. Future studies of glucose complexity should consider the findings presented here when designing their investigations. PMID:24351175

Intraspecific variation in the metabolic scaling exponent in ectotherms: testing the effect of latitudinal cline, ontogeny and transgenerational change in the land snail Cornu aspersum.

PubMed

Gaitán-Espitia, Juan Diego; Bruning, Andrea; Mondaca, Fredy; Nespolo, Roberto F

2013-06-01

The strong dependence of metabolic rates on body mass has attracted the interest of ecological physiologists, as it has important implications to many aspects of biology including species variations in body size, the evolution of life history, and the structure and function of biological communities. The great diversity of observed scaling exponents has led some authors to conclude that there is no single universal scaling exponent, but instead it ranges from 2/3 to 1. Most of the telling evidence against the universality of power scaling exponents comes from ontogenetic changes. Nevertheless, there could be other sources of phenotypic variation that influence this allometric relationship at least at the intraspecific level. In order to explore the general concept of the metabolic scaling in terrestrial molluscs we tested the role of several biological and methodological sources of variation on the empirically estimated scaling exponent. Specifically, we measured a proxy of metabolic rate (CO(2) production) in 421 individuals, during three generations, in three different populations. Additionally, we measured this scaling relationship in 208 individuals at five developmental stages. Our results suggest that the metabolic scaling exponent at the intraspecific level does not have a single stationary value, but instead it shows some degree of variation across geographic distribution, transgenerational change and ontogenetic stages. The major differences in the metabolic scaling exponent that we found were at different developmental stages of snails, because ontogeny involves increases in size at different rates, which in turn, generate differential energy demands. Copyright © 2013 Elsevier Inc. All rights reserved.

Meteoroid stream flux densities and the zenith exponent

NASA Astrophysics Data System (ADS)

Molau, Sirko; Barentsen, Geert

2013-01-01

The MetRec software was recently extended to measure the limiting magnitude in real-time, and to determine meteoroid stream flux densities. This paper gives a short overview of the applied algorithms. We introduce the MetRec Flux Viewer, a web tool to visualize activity profiles on- line. Starting from the Lyrids 2011, high-quality flux density profiles were derived from IMO Video Network observations for every major meteor shower. They are often in good agreement with visual data. Analyzing the 2011 Perseids, we found systematic daily variations in the flux density profile, which can be attributed to a zenith exponent gamma > 1.0. We analyzed a number of meteor showers in detail and found zenith exponent variations from shower to shower in the range between 1.55 and 2.0. The average value over all analyzed showers is gamma = 1.75. In order to determine the zenith exponent precisely, the observations must cover a large altitude range (at least 45 degrees).

Anomalous transport in Charney-Hasegawa-Mima flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leoncini, Xavier; Agullo, Olivier; Benkadda, Sadruddin

2005-08-01

The transport properties of particles evolving in a system governed by the Charney-Hasegawa-Mima equation are investigated. Transport is found to be anomalous with a nonlinear evolution of the second moments with time. The origin of this anomaly is traced back to the presence of chaotic jets within the flow. All characteristic transport exponents have a similar value around {mu}=1.75, which is also the one found for simple point vortex flows in the literature, indicating some kind of universality. Moreover, the law {gamma}={mu}+1 linking the trapping-time exponent within jets to the transport exponent is confirmed, and an accumulation toward zero ofmore » the spectrum of the finite-time Lyapunov exponent is observed. The localization of a jet is performed, and its structure is analyzed. It is clearly shown that despite a regular coarse-grained picture of the jet, the motion within the jet appears as chaotic, but that chaos is bounded on successive small scales.« less

Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series

NASA Astrophysics Data System (ADS)

Pal, Mayukha; Madhusudana Rao, P.; Manimaran, P.

2014-12-01

We apply the recently developed multifractal detrended cross-correlation analysis method to investigate the cross-correlation behavior and fractal nature between two non-stationary time series. We analyze the daily return price of gold, West Texas Intermediate and Brent crude oil, foreign exchange rate data, over a period of 18 years. The cross correlation has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, the existence of multifractal cross-correlation between all of these time series is found. We also found that the cross correlation between gold and oil prices possess uncorrelated behavior and the remaining bivariate time series possess persistent behavior. It was observed for five bivariate series that the cross-correlation exponents are less than the calculated average generalized Hurst exponents (GHE) for q<0 and greater than GHE when q>0 and for one bivariate series the cross-correlation exponent is greater than GHE for all q values.

Cost Benefit Assessment of Candidate Decision Aids for Naval Air ASW.

DTIC Science & Technology

1981-09-01

and I respectively), the value of the term where they appear has an increasingly pronounced effect. The exponents were included simply to limit the...effect of these terms to the cases when the limits are very nearly reached. The difference in exponents reflects giving more weight to T than to S. The...MD 20670 Dr. G. Hurst University of Pennsylvania Dr. Amos Freedy Wharton School Perceptronics, Inc. Philadelphia, PA 19174 6271 Variel Avenue

How big, and how long-lasting, will an extreme burst above threshold be ? Lessons from self-organised criticality

NASA Astrophysics Data System (ADS)

Watkins, N. W.; Chapman, S. C.; Hnat, B.

2011-12-01

The idea that there might not be a typical scale for energy release in some space physics systems is a relatively new one [see e.g. mini-review of early work in Freeman and Watkins, Science, 2002; & Aschwanden, Self Organized Criticality (SOC) in Astrophysics, Springer, 2011]. In part it resulted from the widespread approximate fractality seen elsewhere in nature. SOC was introduced by Bak et al [PRL, 1987] as a physical explanation of such widespread space-time fractality. SOC inspired the introduction into magnetospheric physics of "burst" diagnostics by Takalo [1993] & Consolini [1996]. These quantified events in a time series by "size" (integrated area above a fixed threshold) and "duration", and revealed a long tailed population of events across a broad range of sizes, subsequently also seen in solar wind drivers like Akasofu's epsilon function [Freeman et al, PRE & GRL, 2000]. Spatiotemporal bursts have an interest beyond SOC, however. Estimating the probability of a burst of a given size and duration bears directly on the problem of correlated extreme events, or "bunched black swans" [e.g. Watkins et al, EGU, 2011 presentation at the URL below]. With a view both to space physics and this wider context we here consider an interesting development of the burst idea made by Uritsky et al [GRL, 2001]. These authors adapted the spatiotemporal spreading exponent [e.g. Marro & Dickman, Nonequilibrium phase transitions in lattice models, 1999], calculating a superposed epoch average of surviving activity in bursts after their first excursion above a threshold. In a 1D time series, the 1-minute AL auroral index (averaged over 5 minutes), they found scaling behaviour up to ~ 2 hours. We investigate the relationships between exponents found by this method and other, more widely known exponents governing a fractal (or multifractal) time series such as the self-similarity exponent H and long-range dependence exponent d. We conclude by discussing the applications of these techniques to problems such as the forecasting the probability of a single short-lived large burst versus that of a long correlated sequence of more moderate exceedences above a threshold.

Dynamical implications of sample shape for avalanches in 2-dimensional random-field Ising model with saw-tooth domain wall

NASA Astrophysics Data System (ADS)

Tadić, Bosiljka

2018-03-01

We study dynamics of a built-in domain wall (DW) in 2-dimensional disordered ferromagnets with different sample shapes using random-field Ising model on a square lattice rotated by 45 degrees. The saw-tooth DW of the length Lx is created along one side and swept through the sample by slow ramping of the external field until the complete magnetisation reversal and the wall annihilation at the open top boundary at a distance Ly. By fixing the number of spins N =Lx ×Ly = 106 and the random-field distribution at a value above the critical disorder, we vary the ratio of the DW length to the annihilation distance in the range Lx /Ly ∈ [ 1 / 16 , 16 ] . The periodic boundary conditions are applied in the y-direction so that these ratios comprise different samples, i.e., surfaces of cylinders with the changing perimeter Lx and height Ly. We analyse the avalanches of the DW slips between following field updates, and the multifractal structure of the magnetisation fluctuation time series. Our main findings are that the domain-wall lengths materialised in different sample shapes have an impact on the dynamics at all scales. Moreover, the domain-wall motion at the beginning of the hysteresis loop (HLB) probes the disorder effects resulting in the fluctuations that are significantly different from the large avalanches in the central part of the loop (HLC), where the strong fields dominate. Specifically, the fluctuations in HLB exhibit a wide multi-fractal spectrum, which shifts towards higher values of the exponents when the DW length is reduced. The distributions of the avalanches in this segments of the loops obey power-law decay and the exponential cutoffs with the exponents firmly in the mean-field universality class for long DW. In contrast, the avalanches in the HLC obey Tsallis density distribution with the power-law tails which indicate the new categories of the scale invariant behaviour for different ratios Lx /Ly. The large fluctuations in the HLC, on the other hand, have a rather narrow spectrum which is less sensitive to the length of the wall. These findings shed light to the dynamical criticality of the random-field Ising model at its lower critical dimension; they can be relevant to applications of the dynamics of injected domain walls in two-dimensional nanowires and ferromagnetic films.

Forecasting of magnitude and duration of currency crises based on the analysis of distortions of fractal scaling in exchange rate fluctuations

NASA Astrophysics Data System (ADS)

Uritskaya, Olga Y.

2005-05-01

Results of fractal stability analysis of daily exchange rate fluctuations of more than 30 floating currencies for a 10-year period are presented. It is shown for the first time that small- and large-scale dynamical instabilities of national monetary systems correlate with deviations of the detrended fluctuation analysis (DFA) exponent from the value 1.5 predicted by the efficient market hypothesis. The observed dependence is used for classification of long-term stability of floating exchange rates as well as for revealing various forms of distortion of stable currency dynamics prior to large-scale crises. A normal range of DFA exponents consistent with crisis-free long-term exchange rate fluctuations is determined, and several typical scenarios of unstable currency dynamics with DFA exponents fluctuating beyond the normal range are identified. It is shown that monetary crashes are usually preceded by prolonged periods of abnormal (decreased or increased) DFA exponent, with the after-crash exponent tending to the value 1.5 indicating a more reliable exchange rate dynamics. Statistically significant regression relations (R=0.99, p<0.01) between duration and magnitude of currency crises and the degree of distortion of monofractal patterns of exchange rate dynamics are found. It is demonstrated that the parameters of these relations characterizing small- and large-scale crises are nearly equal, which implies a common instability mechanism underlying these events. The obtained dependences have been used as a basic ingredient of a forecasting technique which provided correct in-sample predictions of monetary crisis magnitude and duration over various time scales. The developed technique can be recommended for real-time monitoring of dynamical stability of floating exchange rate systems and creating advanced early-warning-system models for currency crisis prevention.

Effect of hockey-stick-shaped molecules on the critical behavior at the nematic to isotropic and smectic-A to nematic phase transitions in octylcyanobiphenyl

NASA Astrophysics Data System (ADS)

Chakraborty, Anish; Chakraborty, Susanta; Das, Malay Kumar

2015-03-01

In the field of soft matter research, the characteristic behavior of both nematic-isotropic (N -I ) and smectic-A nematic (Sm -A N ) phase transitions has gained considerable attention due to their several attractive features. In this work, a high-resolution measurement of optical birefringence (Δ n ) has been performed to probe the critical behavior at the N -I and Sm -A N phase transitions in a binary system comprising the rodlike octylcyanobiphenyl and a laterally methyl substituted hockey-stick-shaped mesogen, 4-(3-n -decyloxy-2-methyl-phenyliminomethyl)phenyl 4-n -dodecyloxycinnamate. For the investigated mixtures, the critical exponent β related to the limiting behavior of the nematic order parameter close to the N -I phase transition has come out to be in good conformity with the tricritical hypothesis. Moreover, the yielded effective critical exponents (α', β', γ') characterizing the critical fluctuation near the Sm -A N phase transition have appeared to be nonuniversal in nature. With increasing hockey-stick-shaped dopant concentration, the Sm -A N phase transition demonstrates a strong tendency to be driven towards a first-order nature. Such a behavior has been accounted for by considering a modification of the effective intermolecular interactions and hence the related coupling between the nematic and smectic order parameters, caused by the introduction of the angular mesogenic molecules.

Universal thermodynamics of the one-dimensional attractive Hubbard model

NASA Astrophysics Data System (ADS)

Cheng, Song; Yu, Yi-Cong; Batchelor, M. T.; Guan, Xi-Wen

2018-03-01

The one-dimensional (1D) Hubbard model, describing electrons on a lattice with an on-site repulsive interaction, provides a paradigm for the physics of quantum many-body phenomena. Here, by solving the thermodynamic Bethe ansatz equations, we study the universal thermodynamics, quantum criticality, and magnetism of the 1D attractive Hubbard model. We show that the compressibility and the susceptibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state obey simple additivity rules at low temperatures, indicating an existence of two free quantum fluids. The magnetic properties, such as magnetization and susceptibility, reveal three physical regions: quantum fluids at low temperatures, a non-Fermi liquid at high temperatures, and the quantum fluid to non-Fermi liquid crossover in between. The lattice interaction is seen to significantly influence the nature of the FFLO-like state in 1D. Furthermore, we show that the dimensionless Wilson ratio provides an ideal parameter to map out the various phase boundaries and to characterize the two free fluids of the FLLO-like state. The quantum scaling functions for the thermal and magnetic properties yield the same dynamic critical exponent z =2 and correlation critical exponent ν =1 /2 in the quantum critical region whenever a phase transition occurs. Our results provide a rigorous understanding of quantum criticality and free fluids of many-body systems on a 1D lattice.

A Conserved Current Solid-on-Solid Model on a Sierpinski Tetrahedron Substrate

NASA Astrophysics Data System (ADS)

Kim, Jin Min; Kang, Daeseung

2018-03-01

A conserved current solid-on-solid model with conservative noise on a 3D Sierpinski tetrahedron substrate is studied. The interface width W grows as t β , with β = 0.0396 ± 0.0009, and becomes saturated as L α, with α = 0.195±0.005, where L is the system size. The dynamic exponent z ≈ 4.92 is estimated from the relation z = α/β. These values satisfy a scaling relation α+z = 2z rw , where z rw is the random walk exponent of the fractal substrate. Our results are consistent with the values estimated from a fractional Langevin equation with a conservative noise.

Modeling transport across the running-sandpile cellular automaton by means of fractional transport equations

NASA Astrophysics Data System (ADS)

Sánchez, R.; Newman, D. E.; Mier, J. A.

2018-05-01

Fractional transport equations are used to build an effective model for transport across the running sandpile cellular automaton [Hwa et al., Phys. Rev. A 45, 7002 (1992), 10.1103/PhysRevA.45.7002]. It is shown that both temporal and spatial fractional derivatives must be considered to properly reproduce the sandpile transport features, which are governed by self-organized criticality, at least over sufficiently long or large scales. In contrast to previous applications of fractional transport equations to other systems, the specifics of sand motion require in this case that the spatial fractional derivatives used for the running sandpile must be of the completely asymmetrical Riesz-Feller type. Appropriate values for the fractional exponents that define these derivatives in the case of the running sandpile are obtained numerically.

A critical blow-up exponent in a chemotaxis system with nonlinear signal production

NASA Astrophysics Data System (ADS)

Winkler, Michael

2018-05-01

This paper is concerned with radially symmetric solutions of the Keller–Segel system with nonlinear signal production, as given by in the ball for and R  >  0, where f is a suitably regular function generalizing the prototype determined by the choice , , with . The main results assert that if in this setting the number κ satisfies then for any prescribed mass level m  >  0, there exist initial data u 0 with , for which the solution of the corresponding Neumann initial-boundary value problem blows up in finite time. The condition in () is essentially optimal and is indicated by a complementary result according to which in the case , for widely arbitrary initial data, a global bounded classical solution can always be found.

Static friction boost in edge-driven incommensurate contacts

NASA Astrophysics Data System (ADS)

Mandelli, Davide; Guerra, Roberto; Ouyang, Wengen; Urbakh, Michael; Vanossi, Andrea

2018-04-01

We present a numerical investigation of the size scaling of static friction in incommensurate two-dimensional contacts performed for different lateral loading configurations. Results of model simulations show that both the absolute value of the force Fs and the scaling exponent γ strongly depend on the loading configuration adopted to drive the slider along the substrate. Under edge loading, a sharp increase of static friction is observed above a critical size corresponding to the appearance of a localized commensurate dislocation. Noticeably, the existence of sublinear scaling, which is a fingerprint of superlubricity, does not conflict with the possibility to observe shear-induced localized commensurate regions at the contact interface. Atomistic simulations of gold islands sliding over graphite corroborate these findings, suggesting that similar elasticity effects should be at play in real frictional contacts.

Mapping of the Bak, Tang, and Wiesenfeld sandpile model on a two-dimensional Ising-correlated percolation lattice to the two-dimensional self-avoiding random walk

NASA Astrophysics Data System (ADS)

Cheraghalizadeh, J.; Najafi, M. N.; Dashti-Naserabadi, H.; Mohammadzadeh, H.

2017-11-01

The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling. Based on our numerical results, we propose that at the Ising critical temperature Tc the model is compatible with the universality class of two-dimensional (2D) self-avoiding walk (SAW). Especially the fractal dimension of the loops, which are defined as the external frontier of the avalanches, is very close to DfSAW=4/3 . Also, the corresponding open curves has conformal invariance with the root-mean-square distance Rrms˜t3 /4 (t being the parametrization of the curve) in accordance with the 2D SAW. In the finite-size study, we observe that at T =Tc the model has some aspects compatible with the 2D BTW model (e.g., the 1 /log(L ) -dependence of the exponents of the distribution functions) and some in accordance with the Ising model (e.g., the 1 /L -dependence of the fractal dimensions). The finite-size scaling theory is tested and shown to be fulfilled for all statistical observables in T =Tc . In the off-critical temperatures in the close vicinity of Tc the exponents show some additional power-law behaviors in terms of T -Tc with some exponents that are reported in the text. The spanning cluster probability at the critical temperature also scales with L1/2, which is different from the regular 2D BTW model.

Effect of Coulomb stress on the Gutenberg-Richter law

NASA Astrophysics Data System (ADS)

Navas-Portella, V.; Corral, A.; Jimenez, A.

2017-12-01

Coulomb stress theory has been used for years in seismology to understand how earthquakes trigger each other. Whenever an earthquake occurs, the stress field changes in its neighbourhood, with places with positive values brought closer to failure, whereas negative values distance away that location from failure. Earthquake models that relate rate changes and Coulomb stress after a main event, such as the rate-and-state model, assume negative and positive stress values affect rate changes according to the same functional form. As a first order approximation, under uniform background seismicity before the main event, different values of the b-exponent in the Gutenberg-Richter law would indicate different behaviour for positive and negative stress. In this work, we study the Gutenberg-Richter law in the aftershock sequence of the Landers earthquake (California, 1992, MW=7.3). By using a statistically based fitting method, we discuss whether the sign of Coulomb stresses and the distance to the fault have a significant effect on the value of the b-exponent.

Centrifuge impact cratering experiments: Scaling laws for non-porous targets

NASA Technical Reports Server (NTRS)

Schmidt, Robert M.

1987-01-01

A geotechnical centrifuge was used to investigate large body impacts onto planetary surfaces. At elevated gravity, it is possible to match various dimensionless similarity parameters which were shown to govern large scale impacts. Observations of crater growth and target flow fields have provided detailed and critical tests of a complete and unified scaling theory for impact cratering. Scaling estimates were determined for nonporous targets. Scaling estimates for large scale cratering in rock proposed previously by others have assumed that the crater radius is proportional to powers of the impactor energy and gravity, with no additional dependence on impact velocity. The size scaling laws determined from ongoing centrifuge experiments differ from earlier ones in three respects. First, a distinct dependence of impact velocity is recognized, even for constant impactor energy. Second, the present energy exponent for low porosity targets, like competent rock, is lower than earlier estimates. Third, the gravity exponent is recognized here as being related to both the energy and the velocity exponents.

Influence of Turbulent Flow and Fractal Scaling on Effective Permeability of Fracture Network

NASA Astrophysics Data System (ADS)

Zhu, J.

2017-12-01

A new approach is developed to calculate hydraulic gradient dependent effective permeability of a fractal fracture network where both laminar and turbulent flows may occur in individual fractures. A critical fracture length is used to distinguish flow characteristics in individual fractures. The developed new solutions can be used for the case of a general scaling relationship, an extension to the linear scaling. We examine the impact on the effective permeability of the network of fractal fracture network characteristics, which include the fractal scaling coefficient and exponent, fractal dimension, ratio of minimum over maximum fracture lengths. Results demonstrate that the developed solution can explain more variations of the effective permeability in relation to the fractal dimensions estimated from the field observations. At high hydraulic gradient the effective permeability decreases with the fractal scaling exponent, but increases with the fractal scaling exponent at low gradient. The effective permeability increases with the scaling coefficient, fractal dimension, fracture length ratio and maximum fracture length.

Bipartite fidelity and Loschmidt echo of the bosonic conformal interface

NASA Astrophysics Data System (ADS)

Zhou, Tianci; Lin, Mao

2017-12-01

We study the quantum quench problem for a class of bosonic conformal interfaces by computing the Loschmidt echo and the bipartite fidelity. The quench can be viewed as a sudden change of boundary conditions parametrized by θ when connecting two one-dimensional critical systems. They are classified by S (θ ) matrices associated with the current scattering processes on the interface. The resulting Loschmidt echo of the quench has long time algebraic decay t-α, whose exponent also appears in the finite size bipartite fidelity as L-α/2. We perform analytic and numerical calculations of the exponent α , and find that it has a quadratic dependence on the change of θ if the prior and post-quench boundary conditions are of the same type of S , while remaining 1/4 otherwise. Possible physical realizations of these interfaces include, for instance, connecting different quantum wires (Luttinger liquids), quench of the topological phase edge states, etc., and the exponent can be detected in an x-ray edge singularity-type experiment.

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; Fittipaldi, I. P.

1994-05-01

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

Spatio-temporal correlations in the Manna model in one, three and five dimensions

NASA Astrophysics Data System (ADS)

Willis, Gary; Pruessner, Gunnar

2018-02-01

Although the paradigm of criticality is centered around spatial correlations and their anomalous scaling, not many studies of self-organized criticality (SOC) focus on spatial correlations. Often, integrated observables, such as avalanche size and duration, are used, not least as to avoid complications due to the unavoidable lack of translational invariance. The present work is a survey of spatio-temporal correlation functions in the Manna Model of SOC, measured numerically in detail in d = 1,3 and 5 dimensions and compared to theoretical results, in particular relating them to “integrated” observables such as avalanche size and duration scaling, that measure them indirectly. Contrary to the notion held by some of SOC models organizing into a critical state by re-arranging their spatial structure avalanche by avalanche, which may be expected to result in large, nontrivial, system-spanning spatial correlations in the quiescent state (between avalanches), correlations of inactive particles in the quiescent state have a small amplitude that does not and cannot increase with the system size, although they display (noisy) power law scaling over a range linear in the system size. Self-organization, however, does take place as the (one-point) density of inactive particles organizes into a particular profile that is asymptotically independent of the driving location, also demonstrated analytically in one dimension. Activity and its correlations, on the other hand, display nontrivial long-ranged spatio-temporal scaling with exponents that can be related to established results, in particular avalanche size and duration exponents. The correlation length and amplitude are set by the system size (confirmed analytically for some observables), as expected in systems displaying finite size scaling. In one dimension, we find some surprising inconsistencies of the dynamical exponent. A (spatially extended) mean field theory (MFT) is recovered, with some corrections, in five dimensions.

Evaluation of nonlinear properties of epileptic activity using largest Lyapunov exponent

NASA Astrophysics Data System (ADS)

Medvedeva, Tatiana M.; Lüttjohann, Annika; van Luijtelaar, Gilles; Sysoev, Ilya V.

2016-04-01

Absence seizures are known to be highly non-linear large amplitude oscillations with a well pronounced main time scale. Whilst the appearance of the main frequency is usually considered as a transition from noisy complex dynamics of baseline EEG to more regular absence activity, the dynamical properties of this type of epileptiformic activity in genetic absence models was not studied precisely. Here, the estimation of the largest Lyapunov exponent from intracranial EEGs of 10 WAG/Rij rats (genetic model of absence epilepsy) was performed. Fragments of 10 seizures and 10 episodes of on-going EEG each of 4 s length were used for each animal, 3 cortical and 2 thalamic channels were analysed. The method adapted for short noisy data was implemented. The positive values of the largest Lyapunov exponent were found as for baseline as for spike wave discharges (SWDs), with values for SWDs being significantly less than for on-going activity. Current findings may indicate that SWD is a chaotic process with a well pronounced main timescale rather than a periodic regime. Also, the absence activity was shown to be less chaotic than the baseline one.

Numerical simulation of a lattice polymer model at its integrable point

NASA Astrophysics Data System (ADS)

Bedini, A.; Owczarek, A. L.; Prellberg, T.

2013-07-01

We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Blöte and Nienhuis (1989 J. Phys. A: Math. Gen. 22 1415) and it describes polymers with some attraction, providing thus a model for the polymer collapse transition. At a particular set of Boltzmann weights the model is integrable and the exponents ν = 12/23 ≈ 0.522 and γ = 53/46 ≈ 1.152 have been computed via identification of the scaling dimensions xt = 1/12 and xh = -5/48. We directly investigate the polymer scaling exponents via Monte Carlo simulations using the pruned-enriched Rosenbluth method algorithm. By simulating this polymer model for walks up to length 4096 we find ν = 0.576(6) and γ = 1.045(5), which are clearly different from the predicted values. Our estimate for the exponent ν is compatible with the known θ-point value of 4/7 and in agreement with very recent numerical evaluation by Foster and Pinettes (2012 J. Phys. A: Math. Theor. 45 505003).

Quantum criticality of a spin-1 XY model with easy-plane single-ion anisotropy via a two-time Green function approach avoiding the Anderson-Callen decoupling

NASA Astrophysics Data System (ADS)

Mercaldo, M. T.; Rabuffo, I.; De Cesare, L.; Caramico D'Auria, A.

2016-04-01

In this work we study the quantum phase transition, the phase diagram and the quantum criticality induced by the easy-plane single-ion anisotropy in a d-dimensional quantum spin-1 XY model in absence of an external longitudinal magnetic field. We employ the two-time Green function method by avoiding the Anderson-Callen decoupling of spin operators at the same sites which is of doubtful accuracy. Following the original Devlin procedure we treat exactly the higher order single-site anisotropy Green functions and use Tyablikov-like decouplings for the exchange higher order ones. The related self-consistent equations appear suitable for an analysis of the thermodynamic properties at and around second order phase transition points. Remarkably, the equivalence between the microscopic spin model and the continuous O(2) -vector model with transverse-Ising model (TIM)-like dynamics, characterized by a dynamic critical exponent z=1, emerges at low temperatures close to the quantum critical point with the single-ion anisotropy parameter D as the non-thermal control parameter. The zero-temperature critic anisotropy parameter Dc is obtained for dimensionalities d > 1 as a function of the microscopic exchange coupling parameter and the related numerical data for different lattices are found to be in reasonable agreement with those obtained by means of alternative analytical and numerical methods. For d > 2, and in particular for d=3, we determine the finite-temperature critical line ending in the quantum critical point and the related TIM-like shift exponent, consistently with recent renormalization group predictions. The main crossover lines between different asymptotic regimes around the quantum critical point are also estimated providing a global phase diagram and a quantum criticality very similar to the conventional ones.

Surface critical behavior of thin Ising films at the ‘special point’

NASA Astrophysics Data System (ADS)

Moussa, Najem; Bekhechi, Smaine

2003-03-01

The critical surface phenomena of a magnetic thin Ising film is studied using numerical Monte-Carlo method based on Wolff cluster algorithm. With varying the surface coupling, js= Js/ J, the phase diagram exhibits a special surface coupling jsp at which all the films have a unique critical temperature Tc for an arbitrary thickness n. In spite of this, the critical exponent of the surface magnetization at the special point is found to increase with n. Moreover, non-universal features as well as dimensionality crossover from two- to three-dimensional behavior are found at this point.

Rogue waves driven by polarization instabilities in a long ring fiber oscillator

NASA Astrophysics Data System (ADS)

Kolpakov, S. A.; Kbashi, Hani; Sergeyev, Sergey

2017-05-01

We present an experimental and theoretical results of a study of a complex nonlinear polarization dynamics in a passively self-mode-locked erbium-doped fiber oscillator implemented in a ring configuration and operating near lasing threshold. The theoretical model consists of seven coupled non-linear equations and takes into account both orthogonal states of polarizations in the fiber. The experiment confirmed the existence of seven eigenfrequencies, predicted by the model due to polarization instability near lasing threshold. By adjusting the state of polarization of the pump and in-cavity birefringence we changed some eigenfrequencies from being different (non-degenerate state) to matching (degenerate state). The non-degenerate states of oscillator lead to the L-shaped probability distribution function and true rogue wave regime with a positive dominant Lyapunov exponent value between 1.4 and 2.6. Small detuning from partially degenerate case also leads to L-shaped probability distribution function with the tail trespassing eight standard deviations threshold, giving periodic patterns of pulses along with positive dominant Lyapunov exponent of a filtered signal between 0.6 and 3.2. The partial degeneration, in turn, guides to quasi-symmetric distribution and the value of dominant Lyapunov exponent of 42 which is a typical value for systems with a source of the strongly nonhomogeneous external noise.

Scaling law governing the roughness of the swash edge line

NASA Astrophysics Data System (ADS)

Bormashenko, E.; Musin, A.; Grynyov, R.

2014-09-01

The paper is devoted to the analysis of the shape of the swash edge line. Formation of the swash boundary is treated as an interfacial phenomenon. The simplest quantitative characteristic of the roughness of interface is its width w, defined as the root-mean-square fluctuation around the average position. For rough interfaces, the scaling with size of the system L is observed in the form w(L)~Lζ. The concept of scaling supplies a simple framework for classifying interfaces. It is suggested that the fine structure of the swash boundary results from the combined action of the pinning force applied by random defects of the beach and elasticity of distorted swash boundary. The roughness of the swash front was studied at the Mediterranean Sea coast for uprush and backwash flows. Value of exponent ζ for receding swash front line was 0.64 +/- 0.02, when in the case of advancing swash the value 0.73 +/- 0.03 was calculated. The scaling exponent established for the receding phase of the swash is very close to the values of the exponent established for the roughness of the triple line for water droplets deposited on rough surfaces, crack propagation front in Plexiglas, and for the motion of a magnetic domain walls.

Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons

NASA Astrophysics Data System (ADS)

Koop, Cornelie; Wessel, Stefan

2017-10-01

We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic interedge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intraedge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the interedge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intraedge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intrachain couplings. The results for the critical exponents are compared also to several recent renormalization-group calculations for related long-ranged interacting quantum systems.

On universal procrastination

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2017-09-01

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

Collisional evolution - an analytical study for the non steady-state mass distribution.

NASA Astrophysics Data System (ADS)

Vieira Martins, R.

1999-05-01

To study the collisional evolution of asteroidal groups one can use an analytical solution for the self-similar collision cascades. This solution is suitable to study the steady-state mass distribution of the collisional fragmentation. However, out of the steady-state conditions, this solution is not satisfactory for some values of the collisional parameters. In fact, for some values for the exponent of the mass distribution power law of an asteroidal group and its relation to the exponent of the function which describes "how rocks break" the author arrives at singular points for the equation which describes the collisional evolution. These singularities appear since some approximations are usually made in the laborious evaluation of many integrals that appear in the analytical calculations. They concern the cutoff for the smallest and the largest bodies. These singularities set some restrictions to the study of the analytical solution for the collisional equation. To overcome these singularities the author performed an algebraic computation considering the smallest and the largest bodies and he obtained the analytical expressions for the integrals that describe the collisional evolution without restriction on the parameters. However, the new distribution is more sensitive to the values of the collisional parameters. In particular the steady-state solution for the differential mass distribution has exponents slightly different from 11/6 for the usual parameters in the asteroid belt. The sensitivity of this distribution with respect to the parameters is analyzed for the usual values in the asteroidal groups. With an expression for the mass distribution without singularities, one can evaluate also its time evolution. The author arrives at an analytical expression given by a power series of terms constituted by a small parameter multiplied by the mass to an exponent, which depends on the initial power law distribution. This expression is a formal solution for the equation which describes the collisional evolution.

Universality of modulation length and time exponents.

PubMed

Chakrabarty, Saurish; Dobrosavljević, Vladimir; Seidel, Alexander; Nussinov, Zohar

2012-10-01

We study systems with a crossover parameter λ, such as the temperature T, which has a threshold value λ(*) across which the correlation function changes from exhibiting fixed wavelength (or time period) modulations to continuously varying modulation lengths (or times). We introduce a hitherto unknown exponent ν(L) characterizing the universal nature of this crossover and compute its value in general instances. This exponent, similar to standard correlation length exponents, is obtained from motion of the poles of the momentum (or frequency) space correlation functions in the complex k-plane (or ω-plane) as the parameter λ is varied. Near the crossover (i.e., for λ→λ(*)), the characteristic modulation wave vector K(R) in the variable modulation length "phase" is related to that in the fixed modulation length "phase" q via |K(R)-q|[proportionality]|T-T(*)|(νL). We find, in general, that ν(L)=1/2. In some special instances, ν(L) may attain other rational values. We extend this result to general problems in which the eigenvalue of an operator or a pole characterizing general response functions may attain a constant real (or imaginary) part beyond a particular threshold value λ(*). We discuss extensions of this result to multiple other arenas. These include the axial next-nearest-neighbor Ising (ANNNI) model. By extending our considerations, we comment on relations pertaining not only to the modulation lengths (or times), but also to the standard correlation lengths (or times). We introduce the notion of a Josephson time scale. We comment on the presence of aperiodic "chaotic" modulations in "soft-spin" and other systems. These relate to glass-type features. We discuss applications to Fermi systems, with particular application to metal to band insulator transitions, change of Fermi surface topology, divergent effective masses, Dirac systems, and topological insulators. Both regular periodic and glassy (and spatially chaotic behavior) may be found in strongly correlated electronic systems.

Scaling of peak flows with constant flow velocity in random self-similar networks

USGS Publications Warehouse

Troutman, Brent M.; Mantilla, Ricardo; Gupta, Vijay K.

2011-01-01

A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters pi and pe, respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ > β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β(E) and φ(E) that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β(E) and φ(E) and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ(E) and φ with respect to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs.

Many-body delocalization with random vector potentials

NASA Astrophysics Data System (ADS)

Cheng, Chen; Mondaini, Rubem

In this talk we present the ergodic properties of excited states in a model of interacting fermions in quasi-one dimensional chains subjected to a random vector potential. In the non-interacting limit, we show that arbitrarily small values of this complex off-diagonal disorder triggers localization for the whole spectrum; the divergence of the localization length in the single particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. However, when short-ranged interactions are included, the localization is lost and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields. This research is financially supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. U1530401 and 11674021). RM also acknowledges support from NSFC (Grant No. 11650110441).

On the Plasticity of Amorphous Solids

NASA Astrophysics Data System (ADS)

Lin, Jie

Mechanical behaviors of amorphous materials under external stress are central to various phenomena including earthquakes and landslides. Most amorphous materials possess a well defined yield stress when thermal fluctuations are negligible. Only when the shear stress is above the yield stress, the material can flow as a fluid, otherwise it deforms as a solid. There are accumulating evidences that the yielding transition between the flowing and solid phase is a critical phenomenon, and one evidence is the long ranged correlations of plastic strain during adiabatic shear. In spite of this, we still have not fully understood the associated critical exponents and their scaling relations. In the last decade, it has been widely accepted that the elementary rearrangements in amorphous solids are not well-defined topological defects as crystals, instead they are local irreversible rearrangements of a few particles, denoted as shear transformations. Because a single shear transformation changes the local arrangement of particles, it therefore generates an elastic stress field propagating over the whole system. The resulting changes in the local stresses in other regions of the system may in turn trigger more shear transformations. A central feature that complicates the yielding transition is the long range and anisotropic stress field generated by shear transformations. This peculiar interaction between shear transformations leads to two important characteristics: 1.the mechanical noises generated by plastic deformation are broadly distributed 2.those regions that are undergoing plastic deformation has equal probability to make other parts of the material to be more stable or more unstable, depending on the direction between them. In this thesis, we show that these two important factors leads to a singular density of shear transformations, P( x) xtheta at small x, where x is a local measure of stability, namely, the extra stress one needs to add locally to reach the elastic instabilities. We denote such a singular distribution as a pseudo gap, and the theta exponent as the pseudo gap exponent. The fact that the plastic avalanche rates, i.e., number of avalanches per unit strain, during quasi-static shear is not proportional to system size implies the existence of a finite pseudo gap exponent. Arguments based on stability against local perturbations lead to a lower bound of the pseudo gap exponents. In the flowing phase, we construct the scaling description of the yielding transition of soft amorphous solids at zero temperature. The yielding transition shares similarities with another well studied dynamic phase transition, the depinning transition where an elastic interface is driven in a disordered medium, however, there are also striking differences between them. Avalanches are fractal in the yielding transition, characterized by a fractal dimension smaller than the spatial dimension, while avalanches are compact with a fractal dimension, not smaller than the spatial dimension in the depinning transition. We make connections between the Herschel-Bulkley exponent characterizing the singularity of the flow curve near the yield stress, the extension and duration of the avalanches of plasticity, and the pseudo gap exponent. On the other hand, in the solid phase, the pseudo gap also plays a significant role as one increases the shear stress adiabatically. We point out the connection between the local slope of stress-strain curve in the transient state and mean avalanche sizes as the system approaches failure. We argue that the entire solid phase below the yield stress is critical as long as there is finite amount of plastic strain, and plasticity always involves system-spanning events because of the finite pseudo gap exponent. We use the elasto-plastic model, a mesoscopic approach, to verify our theoretical predictions and obtain satisfying results. Finally, a mean field description of plastic flow in amorphous solids are proposed and solved analytically. The mean field models captures the broad distribution of mechanical noise generated by plasticity, leading to a biased Levy flight behavior of local stresses, with the elastic instabilities as the absorbing boundary. The mean field model implies an upper critical dimension as dc = 4.

Moving line model and avalanche statistics of Bingham fluid flow in porous media.

PubMed

Chevalier, Thibaud; Talon, Laurent

2015-07-01

In this article, we propose a simple model to understand the critical behavior of path opening during flow of a yield stress fluid in porous media as numerically observed by Chevalier and Talon (2015). This model can be mapped to the problem of a contact line moving in an heterogeneous field. Close to the critical point, this line presents an avalanche dynamic where the front advances by a succession of waiting time and large burst events. These burst events are then related to the non-flowing (i.e. unyielded) areas. Remarkably, the statistics of these areas reproduce the same properties as in the direct numerical simulations. Furthermore, even if our exponents seem to be close to the mean field universal exponents, we report an unusual bump in the distribution which depends on the disorder. Finally, we identify a scaling invariance of the cluster spatial shape that is well fit, to first order, by a self-affine parabola.

Percolation of spatially constraint networks

NASA Astrophysics Data System (ADS)

Li, Daqing; Li, Guanliang; Kosmidis, Kosmas; Stanley, H. E.; Bunde, Armin; Havlin, Shlomo

2011-03-01

We study how spatial constraints are reflected in the percolation properties of networks embedded in one-dimensional chains and two-dimensional lattices. We assume long-range connections between sites on the lattice where two sites at distance r are chosen to be linked with probability p(r)~r-δ. Similar distributions have been found in spatially embedded real networks such as social and airline networks. We find that for networks embedded in two dimensions, with 2<δ<4, the percolation properties show new intermediate behavior different from mean field, with critical exponents that depend on δ. For δ<2, the percolation transition belongs to the universality class of percolation in Erdös-Rényi networks (mean field), while for δ>4 it belongs to the universality class of percolation in regular lattices. For networks embedded in one dimension, we find that, for δ<1, the percolation transition is mean field. For 1<δ<2, the critical exponents depend on δ, while for δ>2 there is no percolation transition as in regular linear chains.

Criticality and Chaos in Systems of Communities

NASA Astrophysics Data System (ADS)

Ostilli, Massimo; Figueiredo, Wagner

2016-01-01

We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a Glauber-like dynamics. We analyze and compare four different versions of the dynamics: flow (differential equations), map (discretetime dynamics), local-time update flow, and local-time update map. The presence of only bilinear interactions prevent the flow cases to develop any dynamical instability, the system converging always to the thermal equilibrium. The situation is different for the map when unfriendly couplings are involved, where period-two oscillations arise. In the case of the map with local-time updates, oscillations of any period and chaos can arise as a consequence of the reciprocal “tension” accumulated among the communities during their sleeping time interval. The resulting chaos can be of two kinds: true chaos characterized by positive Lyapunov exponent and bifurcation cascades, or marginal chaos characterized by zero Lyapunov exponent and critical continuous regions.

Probabilistic Multi-Factor Interaction Model for Complex Material Behavior

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Abumeri, Galib H.

2008-01-01

The Multi-Factor Interaction Model (MFIM) is used to evaluate the divot weight (foam weight ejected) from the launch external tanks. The multi-factor has sufficient degrees of freedom to evaluate a large number of factors that may contribute to the divot ejection. It also accommodates all interactions by its product form. Each factor has an exponent that satisfies only two points, the initial and final points. The exponent describes a monotonic path from the initial condition to the final. The exponent values are selected so that the described path makes sense in the absence of experimental data. In the present investigation the data used was obtained by testing simulated specimens in launching conditions. Results show that the MFIM is an effective method of describing the divot weight ejected under the conditions investigated.

Probabilistic Multi-Factor Interaction Model for Complex Material Behavior

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Abumeri, Galib H.

2008-01-01

The Multi-Factor Interaction Model (MFIM) is used to evaluate the divot weight (foam weight ejected) from the launch external tanks. The multi-factor has sufficient degrees of freedom to evaluate a large number of factors that may contribute to the divot ejection. It also accommodates all interactions by its product form. Each factor has an exponent that satisfies only two points the initial and final points. The exponent describes a monotonic path from the initial condition to the final. The exponent values are selected so that the described path makes sense in the absence of experimental data. In the present investigation, the data used was obtained by testing simulated specimens in launching conditions. Results show that the MFIM is an effective method of describing the divot weight ejected under the conditions investigated.

Columnar Aerosol Properties from Sun-and-star Photometry: Statistical Comparisons and Day-to-night Dynamic

NASA Technical Reports Server (NTRS)

Ramirez, Daniel Perez; Lyamani, H.; Olmo, F. J.; Whiteman, D. N.; Alados-Arboledas, L.

2012-01-01

This work presents the first analysis of longterm correlative day-to-night columnar aerosol optical properties. The aim is to better understand columnar aerosol dynamic from ground-based observations, which are poorly studied until now. To this end we have used a combination of sun-and-star photometry measurements acquired in the city of Granada (37.16 N, 3.60 W, 680 ma.s.l.; South-East of Spain) from 2007 to 2010. For the whole study period, mean aerosol optical depth (AOD) around 440 nm (+/-standard deviation) is 0.18 +/- 0.10 and 0.19 +/- 0.11 for daytime and nighttime, respectively, while the mean Angstr¨om exponent (alpha ) is 1.0 +/- 0.4 and 0.9 +/- 0.4 for daytime and nighttime. The ANOVA statistical tests reveal that there are no significant differences between AOD and obtained at daytime and those at nighttime. Additionally, the mean daytime values of AOD and obtained during this study period are coherent with the values obtained in the surrounding AERONET stations. On the other hand, AOD around 440 nm present evident seasonal patterns characterised by large values in summer (mean value of 0.20 +/- 0.10 both at daytime and nighttime) and low values in winter (mean value of 0.15 +/- 0.09 at daytime and 0.17 +/- 0.10 at nighttime). The Angstr¨om exponents also present seasonal patterns, but with low values in summer (mean values of 0.8 +/- 0.4 and 0.9 +/- 0.4 at dayand night-time) and relatively large values in winter (mean values of 1.2 +/- 0.4 and 1.0 +/- 0.3 at daytime and nighttime). These seasonal patterns are explained by the differences in the meteorological conditions and by the differences in the strength of the aerosol sources. To take more insight about the changes in aerosol particles between day and night, the spectral differences of the Angstrom exponent as function of the Angstr¨om exponent are also studied. These analyses reveal increases of the fine mode radius and of the fine mode contribution to AOD during nighttime, being more remarkable in the summer seasons. These variations are explained by the changes of the local aerosol sources and by the meteorological conditions between daytime and nighttime, as well as aerosol aging processes. Case studies during summer and winter for different aerosol loads and types are also presented to clearly illustrate these findings.

Critical behavior study around the ferromagnetic phase transition in Pr2Pt2In

NASA Astrophysics Data System (ADS)

Tchokonté, M. B. Tchoula; Mboukam, J. J.; Sondezi, B. M.; Bashir, A. K. H.; Britz, D.; Strydom, A. M.; Kaczorowski, D.

2018-05-01

The magnetic ordering in Pr2Pt2In was investigated by means of magnetization and magnetic susceptibility measurements. The compound was found to order ferromagnetically at TC = 8.8(2) K with a second-order phase transition. The derived critical exponents β = 0.325(2), γ = 1.058(2) and δ = 4.26(4) are close to those expected for a 3D Ising ferromagnet.

Diffraction-controlled backscattering threshold and application to Raman gap

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rose, Harvey A.; Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544; Mounaix, Philippe

2011-04-15

In most classic analytical models of linear stimulated scatter, light diffraction is omitted, a priori. However, modern laser optic typically includes a variant of the random phase plate [Y. Kato et al., Phys. Rev. Lett. 53, 1057 (1984)], resulting in diffraction limited laser intensity fluctuations - or localized speckles - which may result in explosive reflectivity growth as the average laser intensity approaches a critical value [H. A. Rose and D. F. DuBois, Phys. Rev. Lett. 72, 2883 (1994)]. Among the differences between stimulated Raman scatter (SRS) and stimulated Brillouin scatter is that the SRS scattered light diffracts more stronglymore » than the laser light with increase of electron density. This weakens the tendency of the SRS light to closely follow the most amplified paths, diminishing gain. Let G{sub 0} be the one-dimensional power gain exponent of the stimulated scatter. In this paper we show that differential diffraction gives rise to an increase of G{sub 0} at the SRS physical threshold with increase of electron density up to a drastic disruption of SRS as electron density approaches one fourth of its critical value from below. For three wave interaction lengths not small compared to a speckle length, this is a physically robust Raman gap mechanism.« less

Exact renormalization group equation for the Lifshitz critical point

NASA Astrophysics Data System (ADS)

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.

The language of gene ontology: a Zipf's law analysis.

PubMed

Kalankesh, Leila Ranandeh; Stevens, Robert; Brass, Andy

2012-06-07

Most major genome projects and sequence databases provide a GO annotation of their data, either automatically or through human annotators, creating a large corpus of data written in the language of GO. Texts written in natural language show a statistical power law behaviour, Zipf's law, the exponent of which can provide useful information on the nature of the language being used. We have therefore explored the hypothesis that collections of GO annotations will show similar statistical behaviours to natural language. Annotations from the Gene Ontology Annotation project were found to follow Zipf's law. Surprisingly, the measured power law exponents were consistently different between annotation captured using the three GO sub-ontologies in the corpora (function, process and component). On filtering the corpora using GO evidence codes we found that the value of the measured power law exponent responded in a predictable way as a function of the evidence codes used to support the annotation. Techniques from computational linguistics can provide new insights into the annotation process. GO annotations show similar statistical behaviours to those seen in natural language with measured exponents that provide a signal which correlates with the nature of the evidence codes used to support the annotations, suggesting that the measured exponent might provide a signal regarding the information content of the annotation.

Localization in a quantum spin Hall system.

PubMed

Onoda, Masaru; Avishai, Yshai; Nagaosa, Naoto

2007-02-16

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.

An Analytical Approach to the Evolution and Death of AGB Stars

NASA Astrophysics Data System (ADS)

Prager, Henry Alexander; Willson, Lee Anne M.; Marengo, Massimo; Creech-Eakman, Michelle J.

2017-01-01

Pop. I and II stars have a significant amount of metals throughout their structure, In the final stages of their evolution, intermediate mass stars (between 0.7 and 2 solar masses) ascend the Asymptotic Giant Branch (AGB). During their last few hundred thousand years on the AGB, these stars quickly lose their envelopes, recycling their metals as dust into the interstellar medium. The rate at which this happens consequently impacts the formation rate of stars, stellar systems, and the wider distribution of s-process isotopes.At the end of their life cycles, AGB stars experience a steep increase in mass loss rate. We can define the death line in two steps. First we define the critical mass loss rate to be where the mass loss rate equals the initial mass divided by the evolution time. Then the death line is where the rate of change of logMdot equals the rate of change of logL. Most of the stars we observe to be rapidly losing mass appear in the death zone between 0.1 and 10 times the critical mass loss rate.Assuming the mass loss rate increases exponentially with time, or, equivalently, the luminosity increases as a power of a characteristic exponent b, then the width of the death zone is the change in logL. This directly implies time is inversely proportional to b. This can be found for any mass-loss rate formula near the death line. By combining this with what we know about the initial-final mass relation and the core mass-luminosity relation, we can test for b with three observables — duration (width) of the death zone, the amplitude of mass loss variations (when L varies on an observable time scale such as a shell flash), and distributions of luminosity and pulsation period.By applying the initial mass function (IMF) and star formation rate (SFR) of an observed region, we can relate these observables to the characteristic exponent. We will need to look at nearby regions where we can see large numbers of AGB stars, such as the Magellanic clouds. We will show that by fixing the death line and the characteristic exponent that intermediate changes in the mass loss rate better fit observations than extreme values. This is consistent with dust-driven as opposed to pulsation-driven processes.

Fourth Annual Conference on Public and Non-Public Schools: Value Education. December 1, 1977. Proceedings.

ERIC Educational Resources Information Center

Lachman, Seymour P., Ed.

Convened to offer a forum for discussion of values education to over 100 representatives of public and private schools, the conference explored moral dilemmas, educational trends, cognitive moral development, and educational objectives. The keynote address by values education exponent Dr. Edwin Fenton (Director, Carnegie-Mellon Education Center,…

Hurst exponent used as a tool to differentiate between magmatic and fluid-induced processes as reflected in crystal geochemistry

NASA Astrophysics Data System (ADS)

Domonik, A.; Słaby, E.; Śmigielski, M.

2012-04-01

A self-similarity parameter, the Hurst exponent (H) (called also roughness exponent) has been used to show the long-range dependence of element behaviour during the processes. The H value ranges between 0 and 1; a value of 0.5 indicates a random distribution indistinguishable from noise. For values greater or less than 0.5, the system shows non-linear dynamics. H < 0.5 represents anti-persistent (more chaotic) behaviour, whereas H > 0.5 corresponds to increasing persistence (less chaotic). Such persistence is characterized as an effect of a long-term memory, and thus by a large degree of positive correlation. In theory, the preceding data constantly affect the next in the whole temporal series. Applied to chaotic dynamics, the system shows a subtle sensitivity to initial conditions. The process can show some degree of chaos, due to local variations, but generally, the trend preserves its persistent character through time. If the exponent value is low, the process shows frequent and sudden reversals e.g. the trends of such a process show mutual negative correlation of the succeding values in the data series. Thus, the system can be described as having a high degree of deterministic chaos. Alkali feldspar megacrysts grown from mixed magmas and recrystallized due to interaction with fluids have been selected for the study (Słaby et al., 2011). Hurst exponent variability has been calculated within some primary-magmatic and secondary-recrystallized crystal domains for some elements redistributed by crystal fluid interaction. Based on the Hurst exponent value two different processes can easily be recognized. In the core of the megacrysts the element distribution can be ascribed to magmatic growth. By contrast, the marginal zones can relate to inferred late crystal-fluid interactions. Both processes are deterministic, not random. The spatial distribution of elements in the crystal margins is irregular, with high-H values identifying the process as persistent. The trace element distributions in feldspar cores are almost homogeneous and only relatively small and irregular variations in trace element contents makes their growth morphology slightly patchy. Despite homogenization the fractal statistics reveal that trace elements were incorporated chaotically into the growing crystal. The anti-persistent chaotic behaviour of elements during magmatic growth of the feldspars progressively changes into persistent behaviour within domains, where re-crystallization reaction took place. Elements demonstrate variable dynamics of this exchange corresponding to increasing persistency. This dynamics is different for individual elements compared to analogical, observed for crystallization process proceeding from mixed magmas. Consequently, it appears that fractal statistics clearly discriminate between two different processes, with contrasted element behaviour during these processes. One process is magma crystallization and it is recorded in the core of the megacrysts; the second is recorded in the crystal rims and along cleavages and cracks, such that it can be related to a post-crystallization process linked to fluid percolation. Słaby, E., Martin, H., Hamada, M., Śmigielski, M., Domonik, A., Götze, J., Hoefs, J., Hałas, S., Simon, K., Devidal, J-L., Moyen, J-F., Jayananda, M. (2011) Evidence in Archaean alkali-feldspar megacrysts for high-temperature interaction with mantle fluids. Journal of Petrology (on line). doi:10.1093/petrology/egr056

Flux flow and flux dynamics in high-Tc superconductors

NASA Technical Reports Server (NTRS)

Bennett, L. H.; Turchinskaya, M.; Swartzendruber, L. J.; Roitburd, A.; Lundy, D.; Ritter, J.; Kaiser, D. L.

1991-01-01

Because high temperature superconductors, including BYCO and BSSCO, are type 2 superconductors with relatively low H(sub c 1) values and high H(sub c 2) values, they will be in a critical state for many of their applications. In the critical state, with the applied field between H(sub c 1) and H(sub c 2), flux lines have penetrated the material and can form a flux lattice and can be pinned by structural defects, chemical inhomogeneities, and impurities. A detailed knowledge of how flux penetrates the material and its behavior under the influence of applied fields and current flow, and the effect of material processing on these properties, is required in order to apply, and to improve the properties of these superconductors. When the applied field is changed rapidly, the time dependence of flux change can be divided into three regions, an initial region which occurs very rapidly, a second region in which the magnetization has a 1n(t) behavior, and a saturation region at very long times. A critical field is defined for depinning, H(sub c,p) as that field at which the hysteresis loop changes from irreversible to reversible. As a function of temperature, it is found that H(sub c,p) is well described by a power law with an exponent between 1.5 and 2.5. The behavior of H(sub c,p) for various materials and its relationship to flux flow and flux dynamics are discussed.

Local Stability of the Trunk in Patients with Degenerative Cerebellar Ataxia During Walking.

PubMed

Chini, Giorgia; Ranavolo, Alberto; Draicchio, Francesco; Casali, Carlo; Conte, Carmela; Martino, Giovanni; Leonardi, Luca; Padua, Luca; Coppola, Gianluca; Pierelli, Francesco; Serrao, Mariano

2017-02-01

This study aims to evaluate trunk local stability in a group of patients with degenerative primary cerebellar ataxia and to correlate it with spatio-temporal parameters, clinical variables, and history of falls. Sixteen patients affected by degenerative cerebellar ataxia and 16 gender- and age-matched healthy adults were studied by means of an inertial sensor to measure trunk kinematics and spatio-temporal parameters during over-ground walking. Trunk local dynamic stability was quantified by the maximum Lyapunov exponent with short data series of the acceleration data. According to this index, low values indicate more stable trunk dynamics, while high values denote less stable trunk dynamics. Disease severity was assessed by means of International Cooperative Ataxia Rating Scale (ICARS) according to which higher values correspond to more severe disease, while lower values correspond to less severe disease.Patients displayed a higher short-term maximum Lyapunov exponent than controls in all three spatial planes, which was correlated with the age, onset of the disease, and history of falls. Furthermore, the maximum Lyapunov exponent was negatively correlated with ICARS balance, ICARS posture, and ICARS total scores.These findings indicate that trunk local stability during gait is lower in patients with cerebellar degenerative ataxia than that in healthy controls and that this may increase the risk of falls. Local dynamic stability of the trunk seems to be an important aspect in patients with ataxia and could be a useful tool in the evaluation of rehabilitative and pharmacological treatment outcomes.

Effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

NASA Astrophysics Data System (ADS)

Salerno, K. Michael; Robbins, Mark O.

2013-12-01

Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with 103-106 particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes. For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions. The spatial extent of plastic deformation is proportional to the energy dissipated in an avalanche. Both rise much more rapidly with system size in the underdamped limit where inertia is important. Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults. The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems. For overdamped and crossover systems the stress variation scales inversely with the square root of the system size. For underdamped systems the variation is determined by the size of the largest events.

Non-Abelian fermionization and fractional quantum Hall transitions

NASA Astrophysics Data System (ADS)

Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah

2018-02-01

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent ν ≈2.3 and that ν is observed to be superuniversal, i.e., the same in the vicinity of distinct critical points [Sondhi et al., Rev. Mod. Phys. 69, 315 (1997), 10.1103/RevModPhys.69.315]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with U (Nc) gauge group coupled to Nf=1 fermion. We study one class of theories in a controlled limit where Nf≫Nc and calculate ν to leading nontrivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent ν within the large Nf≫Nc expansion, they do offer a new parameter space of theories that is apparently different from prior works involving Abelian Chern-Simons gauge fields [Wen and Wu, Phys. Rev. Lett. 70, 1501 (1993), 10.1103/PhysRevLett.70.1501; Chen et al., Phys. Rev. B 48, 13749 (1993), 10.1103/PhysRevB.48.13749].

Long-term persistence of solar activity

NASA Technical Reports Server (NTRS)

Ruzmaikin, Alexander; Feynman, Joan; Robinson, Paul

1994-01-01

We examine the question of whether or not the non-periodic variations in solar activity are caused by a white-noise, random process. The Hurst exponent, which characterizes the persistence of a time series, is evaluated for the series of C-14 data for the time interval from about 6000 BC to 1950 AD. We find a constant Hurst exponent, suggesting that solar activity in the frequency range from 100 to 3000 years includes an important continuum component in addition to the well-known periodic variations. The value we calculate, H approximately 0.8, is significantly larger than the value of 0.5 that would correspond to variations produced by a white-noise process. This value is in good agreement with the results for the monthly sunspot data reported elsewhere, indicating that the physics that produces the continuum is a correlated random process and that it is the same type of process over a wide range of time interval lengths.

The effect of 1/f fluctuation in inter-stimulus intervals on auditory evoked mismatch field.

PubMed

Harada, Nobuyoshi; Masuda, Tadashi; Endo, Hiroshi; Nakamura, Yukihiro; Takeda, Tsunehiro; Tonoike, Mitsuo

2005-05-13

This study focused on the effect of regularity of environmental stimuli on the informational order extracting function of human brain. The regularity of environmental stimuli can be described with the exponent n of the fluctuation 1/f(n). We studied the effect of the exponent of the fluctuation in the inter-stimulus interval (ISI) on the elicitation of auditory evoked mismatch fields (MMF) with two sounds with alternating frequency. ISI times were given by three types of fluctuation, 1/f(0), 1/f(1), 1/f(2), and with a fixed interval (1/f(infinity)). The root mean square (RMS) value of the MMF increased significantly (F(3/9)=4.95, p=0.027) with increases in the exponent of the fluctuation. Increments in the regularity of the fluctuation provoked enhancement of the MMF, which reflected the production of a memory trace, based on the anticipation of the stimulus timing. The gradient of the curve, indicating the ratio of increments between the MMF and the exponent of fluctuation, can express a subject's capability to extract regularity from fluctuating stimuli.

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

PubMed

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.

[Spatial heterogeneity in body condition of small yellow croaker in Yellow Sea and East China Sea based on mixed-effects model and quantile regression analysis].

PubMed

Liu, Zun-Lei; Yuan, Xing-Wei; Yan, Li-Ping; Yang, Lin-Lin; Cheng, Jia-Hua

2013-09-01

By using the 2008-2010 investigation data about the body condition of small yellow croaker in the offshore waters of southern Yellow Sea (SYS), open waters of northern East China Sea (NECS), and offshore waters of middle East China Sea (MECS), this paper analyzed the spatial heterogeneity of body length-body mass of juvenile and adult small yellow croakers by the statistical approaches of mean regression model and quantile regression model. The results showed that the residual standard errors from the analysis of covariance (ANCOVA) and the linear mixed-effects model were similar, and those from the simple linear regression were the highest. For the juvenile small yellow croakers, their mean body mass in SYS and NECS estimated by the mixed-effects mean regression model was higher than the overall average mass across the three regions, while the mean body mass in MECS was below the overall average. For the adult small yellow croakers, their mean body mass in NECS was higher than the overall average, while the mean body mass in SYS and MECS was below the overall average. The results from quantile regression indicated the substantial differences in the allometric relationships of juvenile small yellow croakers between SYS, NECS, and MECS, with the estimated mean exponent of the allometric relationship in SYS being 2.85, and the interquartile range being from 2.63 to 2.96, which indicated the heterogeneity of body form. The results from ANCOVA showed that the allometric body length-body mass relationships were significantly different between the 25th and 75th percentile exponent values (F=6.38, df=1737, P<0.01) and the 25th percentile and median exponent values (F=2.35, df=1737, P=0.039). The relationship was marginally different between the median and 75th percentile exponent values (F=2.21, df=1737, P=0.051). The estimated body length-body mass exponent of adult small yellow croakers in SYS was 3.01 (10th and 95th percentiles = 2.77 and 3.1, respectively). The estimated body length-body mass relationships were significantly different from the lower and upper quantiles of the exponent (F=3.31, df=2793, P=0.01) and the median and upper quantiles (F=3.56, df=2793, P<0.01), while no significant difference was observed between the lower and median quantiles (F=0.98, df=2793, P=0.43).

Entanglement entropies and fermion signs of critical metals

NASA Astrophysics Data System (ADS)

Kaplis, N.; Krüger, F.; Zaanen, J.

2017-04-01

The fermion sign problem is often viewed as a sheer inconvenience that plagues numerical studies of strongly interacting electron systems. Only recently has it been suggested that fermion signs are fundamental for the universal behavior of critical metallic systems and crucially enhance their degree of quantum entanglement. In this work we explore potential connections between emergent scale invariance of fermion sign structures and scaling properties of bipartite entanglement entropies. Our analysis is based on a wave-function Ansatz that incorporates collective, long-range backflow correlations into fermionic Slater determinants. Such wave functions mimic the collapse of a Fermi liquid at a quantum critical point. Their nodal surfaces, a representation of the fermion sign structure in many-particle configurations space, show fractal behavior up to a length scale ξ that diverges at a critical backflow strength. We show that the Hausdorff dimension of the fractal nodal surface depends on ξ , the number of fermions and the exponent of the backflow. For the same wave functions we numerically calculate the second Rényi entanglement entropy S2. Our results show a crossover from volume scaling, S2˜ℓθ (θ =2 in d =2 dimensions), to the characteristic Fermi-liquid behavior S2˜ℓ lnℓ on scales larger than ξ . We find that volume scaling of the entanglement entropy is a robust feature of critical backflow fermions, independent of the backflow exponent and hence the fractal dimension of the scale invariant sign structure.

Scaling tunable network model to reproduce the density-driven superlinear relation

NASA Astrophysics Data System (ADS)

Gao, Liang; Shan, Xiaoya; Qin, Yuhao; Yu, Senbin; Xu, Lida; Gao, Zi-You

2018-03-01

Previous works have shown the universality of allometric scaling under total and density values at the city level, but our understanding of the size effects of regions on the universality of allometric scaling remains inadequate. Here, we revisit the scaling relations between the gross domestic production (GDP) and the population based on the total and density values and first reveal that the allometric scaling under density values for different regions is universal. The scaling exponent β under the density value is in the range of (1.0, 2.0], which unexpectedly exceeds the range observed by Pan et al. [Nat. Commun. 4, 1961 (2013)]. For the wider range, we propose a network model based on a 2D lattice space with the spatial correlation factor α as a parameter. Numerical experiments prove that the generated scaling exponent β in our model is fully tunable by the spatial correlation factor α. Our model will furnish a general platform for extensive urban and regional studies.

Patterns and Correlations in Economic Phenomena Uncovered Using Concepts of Statistical Physics

NASA Astrophysics Data System (ADS)

Stanley, H.E.; Gopikrishnan, P.; Plerou, H.V.; Salinger, M.A.

This paper discusses some of the similarities between work being done by economists and by physicists seeking to find "patterns" in economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two such new results. Specifically, we discuss the two newly-discovered scaling results that appear to be "universal", in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function (PDF), which is a simple power law with exponent alpha + 1 = 4 extending over 102 standard deviations (a factor of 108 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent approx 0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations. We discuss a curious "symmetry breaking" for values of Sigma above a certain threshold value Σ_c; here Σ is defined to be the local first moment of the probability distribution of demand Ω - the difference between the number of shares traded in buyer-initiated and seller-initiated trades. This feature is qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature.

Application of computational statistical physics to scale invariance and universality in economic phenomena

NASA Astrophysics Data System (ADS)

Stanley, H. E.; Amaral, L. A. N.; Gopikrishnan, P.; Plerou, V.; Salinger, M. A.

2002-06-01

This paper discusses some of the similarities between work being done by economists and by computational physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two such new results. Specifically, we discuss the two newly-discovered scaling results that appear to be "universal", in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function (PDF), which is a simple power law with exponent -4 extending over 10 2 standard deviations (a factor of 10 8 on the y-axis); this result is analogous to the Gutenberg-Richter power law describing the histogram of earthquakes of a given strength; (ii) for a wide range of economic organizations, the histogram that shows how size of organization is inversely correlated to fluctuations in size with an exponent ≈0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations. We discuss a curious "symmetry breaking" for values of Σ above a certain threshold value Σc; here Σ is defined to be the local first moment of the probability distribution of demand Ω—the difference between the number of shares traded in buyer-initiated and seller-initiated trades. This feature is qualitatively identical to the behavior of the probability density of the magnetization for fixed values of the inverse temperature.

Critical behavior of dissipative two-dimensional spin lattices

NASA Astrophysics Data System (ADS)

Rota, R.; Storme, F.; Bartolo, N.; Fazio, R.; Ciuti, C.

2017-04-01

We explore critical properties of two-dimensional lattices of spins interacting via an anisotropic Heisenberg Hamiltonian that are subject to incoherent spin flips. We determine the steady-state solution of the master equation for the density matrix via the corner-space renormalization method. We investigate the finite-size scaling and critical exponent of the magnetic linear susceptibility associated with a dissipative ferromagnetic transition. We show that the von Neumann entropy increases across the critical point, revealing a strongly mixed character of the ferromagnetic phase. Entanglement is witnessed by the quantum Fisher information, which exhibits a critical behavior at the transition point, showing that quantum correlations play a crucial role in the transition.

Criticality and turbulence in a resistive magnetohydrodynamic current sheet

NASA Astrophysics Data System (ADS)

Klimas, Alexander J.; Uritsky, Vadim M.

2017-02-01

Scaling properties of a two-dimensional (2d) plasma physical current-sheet simulation model involving a full set of magnetohydrodynamic (MHD) equations with current-dependent resistivity are investigated. The current sheet supports a spatial magnetic field reversal that is forced through loading of magnetic flux containing plasma at boundaries of the simulation domain. A balance is reached between loading and annihilation of the magnetic flux through reconnection at the current sheet; the transport of magnetic flux from boundaries to current sheet is realized in the form of spatiotemporal avalanches exhibiting power-law statistics of lifetimes and sizes. We identify this dynamics as self-organized criticality (SOC) by verifying an extended set of scaling laws related to both global and local properties of the current sheet (critical susceptibility, finite-size scaling of probability distributions, geometric exponents). The critical exponents obtained from this analysis suggest that the model operates in a slowly driven SOC state similar to the mean-field state of the directed stochastic sandpile model. We also investigate multiscale correlations in the velocity field and find them numerically indistinguishable from certain intermittent turbulence (IT) theories. The results provide clues on physical conditions for SOC behavior in a broad class of plasma systems with propagating instabilities, and suggest that SOC and IT may coexist in driven current sheets which occur ubiquitously in astrophysical and space plasmas.

Criticality and turbulence in a resistive magnetohydrodynamic current sheet.

PubMed

Klimas, Alexander J; Uritsky, Vadim M

2017-02-01

Scaling properties of a two-dimensional (2d) plasma physical current-sheet simulation model involving a full set of magnetohydrodynamic (MHD) equations with current-dependent resistivity are investigated. The current sheet supports a spatial magnetic field reversal that is forced through loading of magnetic flux containing plasma at boundaries of the simulation domain. A balance is reached between loading and annihilation of the magnetic flux through reconnection at the current sheet; the transport of magnetic flux from boundaries to current sheet is realized in the form of spatiotemporal avalanches exhibiting power-law statistics of lifetimes and sizes. We identify this dynamics as self-organized criticality (SOC) by verifying an extended set of scaling laws related to both global and local properties of the current sheet (critical susceptibility, finite-size scaling of probability distributions, geometric exponents). The critical exponents obtained from this analysis suggest that the model operates in a slowly driven SOC state similar to the mean-field state of the directed stochastic sandpile model. We also investigate multiscale correlations in the velocity field and find them numerically indistinguishable from certain intermittent turbulence (IT) theories. The results provide clues on physical conditions for SOC behavior in a broad class of plasma systems with propagating instabilities, and suggest that SOC and IT may coexist in driven current sheets which occur ubiquitously in astrophysical and space plasmas.

A Unique Computational Algorithm to Simulate Probabilistic Multi-Factor Interaction Model Complex Material Point Behavior

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Abumeri, Galib H.

2010-01-01

The Multi-Factor Interaction Model (MFIM) is used to evaluate the divot weight (foam weight ejected) from the launch external tanks. The multi-factor has sufficient degrees of freedom to evaluate a large number of factors that may contribute to the divot ejection. It also accommodates all interactions by its product form. Each factor has an exponent that satisfies only two points--the initial and final points. The exponent describes a monotonic path from the initial condition to the final. The exponent values are selected so that the described path makes sense in the absence of experimental data. In the present investigation, the data used was obtained by testing simulated specimens in launching conditions. Results show that the MFIM is an effective method of describing the divot weight ejected under the conditions investigated.

Decomposing intraday dependence in currency markets: evidence from the AUD/USD spot market

NASA Astrophysics Data System (ADS)

Batten, Jonathan A.; Ellis, Craig A.; Hogan, Warren P.

2005-07-01

The local Hurst exponent, a measure employed to detect the presence of dependence in a time series, may also be used to investigate the source of intraday variation observed in the returns in foreign exchange markets. Given that changes in the local Hurst exponent may be due to either a time-varying range, or standard deviation, or both of these simultaneously, values for the range, standard deviation and local Hurst exponent are recorded and analyzed separately. To illustrate this approach, a high-frequency data set of the spot Australian dollar/US dollar provides evidence of the returns distribution across the 24-hour trading ‘day’, with time-varying dependence and volatility clearly aligning with the opening and closing of markets. This variation is attributed to the effects of liquidity and the price-discovery actions of dealers.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oliveira, Gilson F. de, E-mail: gilson@otica.ufpb.br; Lorenzo, Orlando di; Chevrollier, Martine

We study the statistics of the amplitude of the synchronization error in chaotic electronic circuits coupled through linear feedback. Depending on the coupling strength, our system exhibits three qualitatively different regimes of synchronization: weak coupling yields independent oscillations; moderate to strong coupling produces a regime of intermittent synchronization known as attractor bubbling; and stronger coupling produces complete synchronization. In the regime of moderate coupling, the probability distribution for the sizes of desynchronization events follows a power law, with an exponent that can be adjusted by changing the coupling strength. Such power-law distributions are interesting, as they appear in many complexmore » systems. However, most of the systems with such a behavior have a fixed value for the exponent of the power law, while here we present an example of a system where the exponent of the power law is easily tuned in real time.« less

Ising kinetics with hundred Giga-sites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stauffer, D.; Knecht, R.

1996-12-01

From presumed world-record simulations up to 4800{sup 3} and 112{sup 5} and from the Ito algorithm applied to smaller 3D lattices we obtain the dynamical critical exponent z near 2.05 in three dimensions and J/{kappa}{sub B}T{sub c} = 0.11391 in five.

Near Critical Preferential Attachment Networks have Small Giant Components

NASA Astrophysics Data System (ADS)

Eckhoff, Maren; Mörters, Peter; Ortgiese, Marcel

2018-05-01

Preferential attachment networks with power law exponent τ >3 are known to exhibit a phase transition. There is a value ρ c>0 such that, for small edge densities ρ ≤ ρ c every component of the graph comprises an asymptotically vanishing proportion of vertices, while for large edge densities ρ >ρ c there is a unique giant component comprising an asymptotically positive proportion of vertices. In this paper we study the decay in the size of the giant component as the critical edge density is approached from above. We show that the size decays very rapidly, like \\exp (-c/ √{ρ -ρ c}) for an explicit constant c>0 depending on the model implementation. This result is in contrast to the behaviour of the class of rank-one models of scale-free networks, including the configuration model, where the decay is polynomial. Our proofs rely on the local neighbourhood approximations of Dereich and Mörters (Ann Probab 41(1):329-384, 2013) and recent progress in the theory of branching random walks (Gantert et al. in Ann Inst Henri Poincaré Probab Stat 47(1):111-129, 2011).

Random gauge models of the superconductor-insulator transition in two-dimensional disordered superconductors

NASA Astrophysics Data System (ADS)

Granato, Enzo

2017-11-01

We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass, and a Gaussian phase glass. The first two models describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field, while the last two describe the effects of random negative Josephson-junction couplings or π junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge- and flux-glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin-film superconductors in a magnetic field, in the large disorder limit.