Punctuation effects in english and esperanto texts

A statistical physics study of punctuation effects on sentence lengths is presented for written texts: Alice in wonderland and Through a looking glass. The translation of the first text into esperanto is also considered as a test for the role of punctuation in defining a style, and for contrasting natural and artificial, but written, languages. Several log-log plots of the sentence-length-rank relationship are presented for the major punctuation marks. Different power laws are observed with characteristic exponents. The exponent can take a value much less than unity (ca. 0.50 or 0.30) depending on how a sentence is defined. The texts are also mapped into time series based on the word frequencies. The quantitative differences between the original and translated texts are very minutes, at the exponent level. It is argued that sentences seem to be more reliable than word distributions in discussing an author style.     

Finite size correction for fixed word length Zipf analysis

Zipf’s original law deals with the statistics of ranked words in natural languages. It has recently been generalized to “words” defined as n-tuples of symbols derived by translation of real-valued univariate timeseries into a literal sequence. We verify that the rank-frequency plot of these words shows, for fractional Brownian motion, the previously found power laws, but with large finite length corrections. We verify a finite size scaling ansatz for these corrections and, as aresult, demonstrate greatly improved estimates of the (generalized) Zipf exponents. This allows us to find the correct relation between the Zipf exponent and the Hurst exponent characterizing the fractional Brownian motion.     

Statistical linguistic characterization of variability in observed and synthetic daily precipitation series

This paper deals with an application of Zipf law in climatology. This analysis allows the extraction of information not available by standard methods. In particular, rainfall temporal aggregation patterns associated with different climates are characterized by means of exponents derived from the resulting scaling laws. The analogy with linguistic analysis is obtained using a particular coding of precipitation as a discrete variable with four states (corresponding to four standard precipitation thresholds); each weekly symbolic sequence of observed precipitation is considered as a “word”, and each local station defines a “language” characterized by the observed words in a period representative of the climatology. To characterize these precipitation languages, we obtained characteristic exponents derived from the Zipf law for a set of representative stations of the main Köppen's climates and subclimates. We found different scaling behaviors for different subclimates, given by a single exponent in the range 0.6$0.6$ (humid tropical climates) to 1.4$1.4$ (polar climates); some humid middle-latitude subclimates exhibit a crossover with two different characteristic exponents corresponding to high and low frequency aggregation patterns (no explanation for this behavior is provided).     

On computing the entropy of the Henon attractor

In a recent article D. Ruelle [inLecture Notes in Physics, No. 80 (Springer, Berlin, 1978)] has conjectured that for the Hénon attractor its measure theoretic entropy should be equal to its characteristic exponent. This result is known to be true for systems which satisfy Smale's Axiom A. In this article we report the results of our computations which suggest that Ruelle's conjecture may be true for the Hénon attractor. Further, in our study we are confronted with fundamental questions which suggest that certain existence theorems from ergodic theory are not sufficient from a computational point of view.     

Lyapunov Exponents for Particles Advected in Compressible Random Velocity Fields at Small and Large Kubo Numbers

We calculate the Lyapunov exponents describing spatial clustering of particles advected in one- and two-dimensional random velocity fields at finite Kubo numbers $\operatorname {Ku}$ (a dimensionless parameter characterising the correlation time of the velocity field). In one dimension we obtain accurate results up to $\operatorname {Ku}\sim 1$ by resummation of a perturbation expansion in $\operatorname {Ku}$ . At large Kubo numbers we compute the Lyapunov exponent by taking into account the fact that the particles follow the minima of the potential function corresponding to the velocity field. The Lyapunov exponent is always negative. In two spatial dimensions the sign of the maximal Lyapunov exponent λ ₁ may change, depending upon the degree of compressibility of the flow and the Kubo number. For small Kubo numbers we compute the first four non-vanishing terms in the small- $\operatorname {Ku}$ expansion of the Lyapunov exponents. By resumming these expansions we obtain a precise estimate of the location of the path-coalescence transition (where λ ₁ changes sign) for Kubo numbers up to approximately $\operatorname{Ku} = 0.5$ . For large Kubo numbers we estimate the Lyapunov exponents for a partially compressible velocity field by assuming that the particles sample those stagnation points of the velocity field that have a negative real part of the maximal eigenvalue of the matrix of flow-velocity gradients.     

Estimating ultimate bound and finding topological horseshoe for a new chaotic system

This paper presents a new three-dimensional autonomous chaotic system with only one positive term. Basic dynamical properties of the new attractor are demonstrated in terms of phase portraits, equilibria, Lyapunov exponents, Poincare mapping, bifurcation diagram. Furthermore, we derive a three-dimensional spheriform ultimate bound and positively invariant set for all the positive values of its parameters a, b, c. At last, the horseshoe chaos in this system is investigated based on the topological theory.     

Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The Multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of the mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, , is λ=1.17±0.04 which is almost similar for all underlying rivers at 1σ confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long-range cross-correlation between the sunspot numbers and the underlying streamflow records. The magnitude of the scaling exponent and the corresponding cross-correlation exponent are λ∈(0.76,0.85) and γ_×∈(0.30,0.48), respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), is confirmed.     

Critical behavior of the 3D Ising model on a poissonian random lattice

The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D ferromagnetic Ising model on 3D Voronoi-Delauney lattices. It is assumed that the coupling factor J varies with the distance r between the first neighbors as J(r)∝e^−ar, with a≥0. The critical exponents γ/ν, β/ν, and ν are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure 3D ferromagnetic Ising model.     

Critical exponents for the Reggeon quantum spin model

The Reggeon quantum spin (RQS) model on the transverse lattice in D dimensional impact parameter space has been conjectured to have the same critical behaviour as the Reggeon field theory (RFT). Thus from a high “temperature” series of ten (D = 2) and twenty (D = 1) terms for the RQS model we extrapolate to the critical temperature T = T_c by Padé approximants to obtain the exponents η=0.238±0.008, z=1.16±0.01, v=1.271±0.007 for D=2 and η=0.317±0.002, z=1.272±0.007, v=1.736±0.001, λ=0.57±0.03 for D=1. These exponents naturally interpolate between the D=0 and D=4?ε results for RFT as expected on the basis of the universality conjecture.     

Coevolutionary extremal dynamics on gasket fractal

We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2.     

Response function of superfluid nuclei and low-lying quadrupole vibrations

The response of superfluid spherical nuclei to an external quadrupole field is considered. The mixed (r,λ) representation technique is developed, being the generalization of the coordinate (r) representation for magic nuclei. The transition densities p^tr(r) are shown to possess sharp surface bumps of hydrodynamical nature and pronounced volume quantum components. The shapes of transition densities of 2⁺₂ states in some typical nonmagic nuclei are predicted.     

Magnetic phase transition in Heisenberg antiferromagnetic films with easy-axis single-ion anisotropy

The staggered susceptibility of spin-1 and spin-3/2 Heisenberg antiferromagnet with easy-axis single-ion anisotropy on the cubic lattice films consisting of n=2, 3, 4, 5 and 6 interacting square lattice layers is studied by high-temperature series expansions. Sixth order series in J/k_BT have been obtained for free-surface boundary conditions. The dependence of the Néel temperature on film thickness n and easy-axis anisotropy D has been investigated. The shifts of the Néel temperature from the bulk value can be described by a power law n^−λ with a shift exponent λ, where λ is the inverse of the bulk correlation length exponent. The effect of easy-axis single-ion anisotropy on shift exponent of antiferromagnetic films has been studied. A comparison is made with related works. The results obtained are qualitatively consistent with the predictions of finite-size scaling theory.     

Critical behavior of a stochastic anisotropic Bak–Sneppen model

In this paper we present our study on the critical behavior of a stochastic anisotropic Bak–Sneppen (saBS) model, in which a parameter α is introduced to describe the interaction strength among nearest species. We estimate the threshold fitness f _c and the critical exponent τ _r by numerically integrating a master equation for the distribution of avalanche spatial sizes. Other critical exponents are then evaluated from previously known scaling relations. The numerical results are in good agreement with the counterparts yielded by the Monte Carlo simulations. Our results indicate that all saBS models with nonzero interaction strength exhibit self-organized criticality, and fall into the same universality class, by sharing the universal critical exponents.     

Can analysis of word frequency distinguish between writings of different authors?

Various literature writings are compared by the “rank distance”, d, between two word frequency Zipf plots introduced by S. Havlin (Physica A 216 (1995) 148). We studied 22 books written by six authors. For this ensemble of books we find that the mean distance between books written by the same authors (〈d〉 = 15.2 ± 2.6) is considerably smaller than that between books written by different authors (〈d〉 = 21.8 ± 3.2), in good agreement with earlier results on a smaller sample of books. Our results suggest that the distribution of the rank difference of the same words in different books decays exponentially.     

On spectral invariance of single scattering albedo for water droplets and ice crystals at weakly absorbing wavelengths

The single scattering albedo ω_0λ in atmospheric radiative transfer is the ratio of the scattering coefficient to the extinction coefficient. For cloud water droplets both the scattering and absorption coefficients, thus the single scattering albedo, are functions of wavelength λ and droplet size r. This note shows that for water droplets at weakly absorbing wavelengths, the ratio ω_0λ(r)/ω_0λ(r₀) of two single scattering albedo spectra is a linear function of ω_0λ(r). The slope and intercept of the linear function are wavelength independent and sum to unity. This relationship allows for a representation of any single scattering albedo spectrum ω_0λ(r) via one known spectrum ω_0λ(r₀). We provide a simple physical explanation of the discovered relationship. Similar linear relationships were found for the single scattering albedo spectra of non-spherical ice crystals.     

Multicritical behaviour at surfaces

The critical behaviour of a semi-infiniten-vector model with a surface term (c/2) ∫d Sφ² is studied in 4-ε dimensions near the special transition. It is shown that all critical surface exponents derive from bulk exponents and η_∥, the anomalous dimension of the order parameter at the surface. The surface exponents and the crossover exponent Φ for the variablec are calculated to second order in ε. It is found that Φ does not satisfy the relation Φ=1-ν predicted by Bray and Moore. The order-parameter profilem(z)=<ø> is calculated to first order in ε. In contrast to mean-field theory,m(z) is not flat nor does it satisfy a Neumann boundary condition. General aspects of the field-theoretic renormalization program for systems with surfaces are discussed with particular attention paid to the explanation of the unfamiliar new features caused by the presence of surfaces.     

Spherically compressed helium atom described by perturbative and variational methods

We analyze the energy spectrum of the three lowest-lying S symmetry states for the spherically confined helium atom as a function of the box radius by using an approach based on a time independent perturbation theory and two variational methods. The first treatment depends on exact solutions for confined one-electron atoms, whereas in the latter two methods exponents and linear coefficients are variationally optimized via {s,t,u}-Hylleraas functions and Generalized {r₁,r₂,r₁₂}-Hylleraas basis sets that fulfill appropriate boundary conditions. Although it is found that throughout most of the box radii here analyzed the variational energies for the three states lie below those perturbatively obtained, an opposite trend occurs toward the weak and strong confinement regions for the singlet excited and triplet states, respectively.     

Statefinder Diagnostic for Variable Generalized Chaplygin Gas with the Sign-Changeable Interaction

In this paper, we apply the statefinder diagnostic to variable generalized Chaplygin gas (VGCG) with the sign-changeable interaction in which the interaction term Q can change its sign from Q<0 to Q>0 as the universe expands. The evolution trajectories of the statefinder pairs {r,s} and {r,q} are obtained under the circumstance where different values of model parameters are chosen. It is found that the coupling term does not affect the location of the late time attractor, but has an influence on the evolution of the statefinder parameters. Furthermore, it is shown that the evolution trajectories of our model in the r(s) diagram are different from those of other dark energy models.     

A special type of attractor and transitions in a delayed system

We discuss strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors in a quasiperiodically driven system with time delays. A route and the associated mechanism are described for a special type of attractor called strange-nonchaotic-attractor-like (SNA-like) through T² torus bifurcation. The type of attractor can be observed in large parameter domains and it is easily mistaken for a true SNA judging merely from the phase portrait, power spectrum and the largest Lyapunov exponent. SNA-like attractor is not strange and has no phase sensitivity. Conditions for Neimark-Sacker bifurcation are obtained by theoretical analysis for the unforced system. Complicated and interesting dynamical transitions are investigated among the different tongues.     

Estimation of Saturation Exponent from Nuclear Magnetic Resonance (NMR) Logs in Low Permeability Reservoirs

The resistivity experimental measurements of 36 core samples, which were drilled from low permeability reservoirs of southwest China, illustrate that the saturation exponents are not agminate, but vary from 1.627 to 3.48; this leads to a challenge for water saturation estimation in low permeability formations. Based on the analysis of resistivity experiments, laboratory nuclear magnetic resonance (NMR) measurements for all 36 core samples, and mercury injection measurements for 20 of them, it was observed that the saturation exponent is proportional to the proportion of small pore components and inversely proportional to the logarithmic mean of NMR T ₂ spectrum (T _2lm). For rocks with high proportion of small pore components and low T _2lm, there will be high saturation exponents, and vice versa. The proportion of small pore components is characterized by three different kinds of irreducible water saturations, which are estimated by defining 30, 40 and 50 ms as T ₂ cutoffs separately. By integrating these three different kinds of irreducible water saturations and using T _2lm, a technique of calculating the saturation exponent from NMR logs is proposed and the corresponding model is established. The credibility of this technique is confirmed by comparing the predicted saturation exponents with the results from the core analysis. For more than 85 % of core samples, the absolute errors between the predicted saturation exponents from NMR logs and the experimental results are lower than 0.25. Once this technique is extended to field application, the accuracy of water saturation estimation in low permeability reservoirs will be improved significantly.