Watts-Strogatz Model Research Articles

Latent heat flux over Cabernet Sauvignon vineyard using the Shuttleworth and Wallace model

The Shuttleworth and Wallace model (SW) was evaluated to estimate latent heat flux above a drip-irrigated Cabernet Sauvignon vineyard, located in the Pencahue Valley, Region del Maule, Chile (35°22′ LS; 71°47′ LW; 150 m above sea level). The performance of the WS model (LEws) was evaluated against the eddy-covariance method (LEed) on a 30 min time interval. Results indicate that the root mean square error (RMSE) and mean absolute error (MAE) were 29 W m−2 and 22 W m−2, respectively. For the vine evapotranspiration (ETv), RMSE was 0.42 mm day−1 and MAE was 0.36 mm day−1. The largest disagreements between LEed and LEws were observed under dry atmospheric conditions. Also, the sensitivity analysis indicates that predicted ETv by the SW model was sensitive to errors of ±30% in leaf area index and mean stomatal resistance, but it was not affected by errors in the estimation of aerodynamic resistances.

Small World Properties Generated by a New AlgorithmUnder Same Degree of All Nodes

Based on the model of the same degree of all nodes we proposedbefore, a new algorithm, the so-called ``spread all over vertices" (SAV) algorithm, isproposed for generating small-world properties from a regular ring lattices.During randomly rewiring connections the SAV is used to keep the unchangednumber of links. Comparing the SAV algorithm with the Watts–Strogatzmodel and the ``spread all over boundaries" algorithm, three methodscan have the same topological properties of the small world networks. Theseresults offer diverse formation of small world networks. It is helpful tothe research of some applications for dynamics of mutual oscillator insidenodes and interacting automata associated with networks.

Thin Watts-Strogatz networks

A modified version of the Watts-Strogatz (WS) network model is proposed, in which the number of shortcuts scales with the network size N as Nalpha, with alpha < 1. In these networks, the ratio of the number of shortcuts to the network size approaches zero as N --> infinity, whereas in the original WS model, this ratio is constant. We call such networks "thin Watts-Strogatz networks." We show that even though the fraction of shortcuts becomes vanishingly small for large networks, they still cause a kind of small-world effect, in the sense that the length L of the network increases sublinearly with the size. We develop a mean-field theory for these networks, which predicts that the length scales as N1-alpha ln N for large N. We also study how a search using only local information works in thin WS networks. We find that the search performance is enhanced compared to the regular network, and we predict that the search time tau scales as N1-alpha/2. These theoretical results are tested using numerical simulations. We comment on the possible relevance of thin WS networks for the design of high-performance low-cost communication networks.

Instability of defensive alliances in the predator-prey model on complex networks

A model of six-species food web is studied in the viewpoint of spatial interaction structures. Each species has two predators and two preys, and it was previously known that the defensive alliances of three cyclically predating species self-organize in two dimensions. The alliance-breaking transition occurs as either the mutation rate is increased or interaction topology is randomized in the scheme of the Watts-Strogatz model. In the former case of temporal disorder, via the finite-size scaling analysis, the transition is clearly shown to belong to the two-dimensional Ising universality class. In contrast, the geometric or spatial randomness for the latter case yields a discontinuous phase transition. The mean-field limit of the model is analytically solved and then compared with numerical results. The dynamic universality and the temporally periodic behaviors are also discussed.

Frequency clustering of coupled phase oscillators on small-world networks

We analyze the phenomenon of frequency clustering in a system of coupled phase oscillators. The oscillators, which in the absence of coupling have uniformly distributed natural frequencies, are coupled through a small-world network, built according to the Watts-Strogatz model. We study the time evolution and determine variations in the transient times depending on the disorder of the network and on the coupling strength. We investigate the effects of fluctuations in the average frequencies, and discuss the definition of the threshold for synchronization. We characterize the structure of clusters and the distribution of cluster sizes in the synchronization transition, and define suitable order parameters to describe the aggregation of the oscillators as the network disorder and the coupling strength change. The non-monotonic behavior observed in some order parameters is related to fluctuations in the mean frequencies.

A Small-world Network Where All Nodes Have the Same Connectivity, with Application to the Dynamics of Boolean Interacting Automata

This paper introduces the equal number of links (ENL) algorithm to generate small-world networks starting from a regular lattice, by randomly rewiring some connections. The approach is similar to the well-known Watts-Strogatz (WS) model, but the present method is different as it leaves the number of connections k of each node unchanged, while the WS algorithm gives rise to a Poisson distribution of connectivities. Motivation for the ENL algorithm stems from interest in studying the dynamics of interacting oscillators or automata (associated to the nodes of the network). Indeed, leaving k unaltered allows one to study how the dynamics of these networks are affected by rewiring only (which gives rise to small-world properties) disentangling its effects from those related to modifying the connectivity of some nodes. The ENL algorithm is compared with that of Watts and Strogatz, by studying the topological properties of the network as a function of the number of rewirings. The effects on the dynamics are tested in the case of the majority rule, and it is shown that key dynamical properties (i.e., number of attractors, size of basins of attraction, transient duration) are modified by rewiring. The quantitative differences between the dynamics of an ENL network and a WS network are discussed in detail. Comparisons with scale-free networks of the Barabasi-Albert type and with completely random networks are also given.

Temporal series analysis approach to spectra of complex networks.

The spacing of nearest levels of the spectrum of a complex network can be regarded as a time series. Joint use of the multifractal detrended fluctuation approach (MF-DFA) and diffusion entropy (DE) is employed to extract characteristics from this time series. For the Watts-Strogatz small-world model, there exists a critical point at rewiring probability P(r) =0.32. For a network generated in the range 0< P(r) <0.32, the correlation exponent is in the range of 1.0-1.64. Above this critical point, all the networks behave similar to that at p(r) =1. For the Erdos-Renyi model, the time series behaves like fractional Brownian motion noise at p(ER) =1/N. For the growing random network (GRN) model, the values of the long-range correlation exponent are in the range of 0.74-0.83. For most of the GRN networks the probability distribution function of a constructed time series obeys a Gaussian form. In the joint use of MF-DFA and DE, the shuffling procedure in DE is essential to obtain a reliable result.

Aggregation process on complex networks.

We study the dynamics of the aggregation of particles and the evolution of the mass distribution, on a complex network which is built following the Watts-Strogatz model. The particles perform random walks following the links on the network, and aggregate when they meet other particles. On disordered networks the density of particles decays as t(-1), while on regular networks it decays as t(-1/2). For intermediate levels of network disorder the dynamics follows that of regular networks at intermediate density, and for low density the disorder of the network becomes relevant and the density decays as t(-1). The crossover time between these two regimes scales with network disorder as t approximately p(-2). We study also an annealed model for the aggregation process, in which the quenched disorder of the network is replaced by stochastic long range jumps in the particle dynamics. The annealed model is found to obey a different scaling with network disorder, with a crossover time t approximately p(-1).

Evaluation of Solar Radiation Prediction Models in North America

Solar radiation data at the earth's surface (Rs, MJ m−2 d−1) are not typically recorded at weather stations, but they may be predicted from other meteorological measurements. For one location, Keiser, AR, we developed an empirical equation for predicting Rs. The mechanistic models of Hargreaves–Samani (HS) and two forms of the Bristow–Campbell model, described by Thornton and Running (TR) and Weiss et al. (WS), were also evaluated for predicting Rs at 13 sites, covering a 23° range in latitude and a 42° range in longitude. For the HS, TR, and WS models, we used coefficients as they were originally published, and for the HS model, a site‐specific coefficient (HS‐SS) was derived and evaluated for each site. Regression of predicted vs. observed Rs values using the empirical equation for Keiser gave r2 values (0.77) similar to the best of the mechanistic models. The HS‐SS model had the lowest root mean square error of 3.50 MJ m−2 d−1, followed by the TR (3.56), the HS (3.86), and the WS (4.33) models. Predicted vs. observed values gave r2 values ranging from 0.72 (TR model) to 0.56 (WS model). There was a slight superiority of the TR model over the HS‐SS and HS models. Similar fits (r2 &gt; 0.87) and errors were found among the TR, HS‐SS, and HS models when Rs values were averaged over a 7‐d period, and it was concluded that these three models provided accurate and precise Rs estimations for our sites without further model modification.

Optimal paths in disordered complex networks.

We study the optimal distance in networks, l(opt), defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution P(k) approximately k(-lambda), we find that l(opt) scales as N((lambda-3)/(lambda-1)) for 3<lambda<4 and as N(1/3) for lambda> or =4. Thus, for these networks, the small-world nature is destroyed. For 2<lambda<3, our numerical results suggest that l(opt) scales as ln(lambda-1N. We also find numerically that for weak disorder l(opt) approximately ln(N for both the ER and WS models as well as for SF networks.

Extension of the Wong-Sandler mixing rule to the three-parameter Patel-Teja equation of state: Application up to the near-critical region

The Wong-Sandler mixing rule was extended to the Patel-Teja three-parameter cubic equation of state by introducing suitable corresponding parameters. The new model, PT–WS model, has been extensively tested on various classes of binary/ternary mixtures, special attention was paid to the effects on the representation of mixture phase behavior in the near-critical region. The test results indicate that the new model is capable of improving both the vapor–liquid equilibrium and volumetric properties significantly, especially for highly asymmetric systems. The proposed method of implementing the Wong-Sandler mixing rule can be applied to other multi-parameter cubic equations of state.

Approximate resonating-group calculations with Woods-Saxon target-nucleus wave functions

Differential cross sections and analyzing powers in n + 16O and n + 40Ca scattering are calculated with a simplified version of the reasonating-group method in the cases where the wave functions of the target nuclei are constructed with single-nucleon functions generated from Woods-Saxon and harmonic-oscillator potential wells (WS and HO models). A comparison of the calculated results shows that the angular distributions for these quantities obtained in the two models are characteristically similar in all respects. This suggests that scattering properties are mainly sensitive to the gross structure of the target-nucleus density distribution and computationally-simpler harmonic-oscillator wave functions may be reliably adopted in future resonating-group calculations when the scattering energy is not too low.

About the isoscalar piece of the weak neutral current

The available neutral current induced one-pion production data at intermediate energy are analyzed in a model-independent way in the framework of a recent approach to the corresponding production mechanism. Clear indications about the structure of the isoscalar piece of the weak neutral current are obtained and more stringent evidence of agreement with the standard WS model is seen to emerge. For the first time the relative influence of the different amplitudes contributing to the production mechanism is analyzed, by adopting the neutral current parametrization provided by the WS model.

Superweak CP violation mediated by neutral Higgs bosons

I t is known that the weak and electromagnetic interactions can be unified in the framework of gauge theories (~). Actually, the bulk of the experimental data, in various domains, included atomic physics (~) and neutrino physics are in very good agreement with the minimal model of W]~I~BERG and SALAM (3). Nevertheless some controversies still remain in the hadronic sector with regard to the AI ~ 89 rule (4) and to the CP violation (~). The main point is that CP violation has been only detected in the (K0, Ko) system, and that the upper experimental linlit of the electric-dipole moment of the neutron (EDM), becomes smaller and smaller so tha~ it appears that a gauge theory of weak interactions must describe CP violation in a superweak way (e), preserving at the same t ime the features of the WS model. We show in this note tha t this can be accomplished using a two-Higgs-doublet boson model (7). The key is that only one of the two doublets entering in the composition of the invariant scalar energy term and in the Yukawa flavour interaction, has a complex mixing. Then CP violation can be restricted to the Higgs potential , and can occur in Lhe theory if o~e chooses the set of parameters of the Higgs potential in such a way that spontaneous symmetry breaking (1) generates a tr iplet and a singlet of Higgs bosons of different masses. According to this scheme let

The cosmological constant, broken gauge theories and 3 K black-body radiation

It is suggested that the cosmological constant today be identified with the one provided by gauge theories at T = 3 K and not T = 0 K or T = 10 15 K as done so far. We then calculate Λ(3 K) in the σ-model, Weinberg-Salam model and Mohapatra and Sidhu model. While an acceptable value is obtained with the rather ideal σ-model, a very small Λ is obtained with the WS model. For the MS model, Λ can be fitted only if at least one of the Higgs mesons has a very light mass (≈3 K).

Weak and Electromagnetic Interactions in Superconductivity Model

Starting with a Lagrangian of self-interacting lepton fields only, we construct an effective Lagrangian of the W einberg-Salam type. This shows that the photon, the Higgs boson and the weak-vector bosons are all composites of lepton and antilepton. Arbitrary parameters involved in the original WS model are largely removed. W einberg 11 and Salam 21 (WS) have proposed a unified model of weak and electromagnetic interactions through the use of the Higgs mechanism. In their model there are many elementary fields, i.e., the Riggs-scalar boson, the weak­ vector bosons, the electromagnetic field, and the leptons. We propose here a composite model of those particles except for leptons. We start with a Nambu­ J ona-Lasinio type Lagrangian 31 which describes a system of self-interacting lepton fields only, and obtain an effective Lagrangian of the WS type. This shows that the created Higgs boson, electromagnetic field, and weak-vector bosons can be considered composites of lepton and antilepton. At this point our program resembles works of Bjorken 41 and others 5> in spinor electrodynamics where they claim that a photon is a Nambu-Goldstone composite boson associated with a spontaneous breakdown of Lorentz invariance. Our pro­ gram is also analogous to the work of Eguchi and Sugawara 6> and its non-Abelian generalizationn where the authors have derived effective Lagrangians for expecta­ tion values of fermion fields which describe interactions among fermion-antifermion bound states in superconductivity models of hadrons. In these works there are certain difficulties associated with the Poincare invariance of the theory. Recently, however, we showed 8l that these difficulties can be avoided if operator equations for fermion fields are adopted, rather than the use of expectation values of fermion fields. Subsequently, Kikkawa 9 l and Kugo 101 proposed a simple derivation of the above effective Lagrangian by making use of the path-integral technique with a trick clue to Gross and Neveu.w In the present paper ~we consider how to realize the WS model in the frame­ work of superconductivity model by using the path-integral technique, and find that arbitrary parameters involved in the original WS model are largely removed. We begin with the following Lagrangian of the WS massless leptons only: