Aging of the field-induced asymmetry in a disordered ferroelectric

The isothermal aging of the asymmetry induced in the disordered dielectric crystal (x=0.027) submitted to the biasing electric field E, is investigated. To this end, the response of the complex dielectric constant to infinitesimal field changes , applied to the sample after a variable aging delay, has been measured for different magnitudes of E and after different aging delays. Two different experimental procedures have been used: in both cases the response strongly depends on the time spent under field. For short aging delays, the response has a strong contribution proportional to δE and a weak quadratic contribution proportional to . As time elapses, the linear and the quadratic contributions age in opposite ways: the former decreases whereas the latter increases. This paradoxical behaviour is analyzed in the framework of a model which attributes aging and the related effects (rejuvenation, memory) to the evolution of polarization domain walls: the decrease of the linear contribution is related to the decrease of the total wall area, while the increase of the quadratic term is attributed to wall reconformations.     

Stretched exponential relaxation on the hypercube and the glass transition

We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution p the form of the relaxation of the memory function q(t) can be accurately parametrized by a stretched exponential over several orders of magnitude in q(t). As the critical dilution for percolation is approached, the time constant tends to diverge and the stretching exponent drops towards 1/3. As the same pattern of relaxation is observed in a wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube appears to be a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition may be pictured as a percolation transition in phase space. Received 16 June 2000 and Received in final form 13 October 2000     

Random networks of fibres display maximal heterogeneity in the distribution of elastic energy

Above a small length scale, the distribution of local elastic energies in a material under an external load is typically Gaussian, and the dependence of the average elastic energy on strain defines the stiffness of the material. Some particular materials, such as granular packings, suspensions at the jamming transition, crumpled sheets and dense cellular aggregates, display under compression an exponential distribution of elastic energies, but also in this case the elastic properties are well defined. We demonstrate here that networks of fibres, which form uncorrelated non-fractal structures, have under external load a scale invariant distribution of elastic energy (epsilon) at the fibre-fibre contacts proportional to 1/epsilon. This distribution is much broader than any other distribution observed before for elastic energies in a material. We show that for small compressions it holds over 10 orders of magnitude in epsilon. In such a material a few 'hot spots' carry most of the elastic load. Consequently, these materials are highly susceptible to local irreversible deformations, and are thereby extremely efficient for damping vibrations.     

Statistical verification of crystallization in hard sphere packings under densification

The performance of various structure characteristics in the task of indicating structural peculiarities in packings of hard spheres is investigated. Various characteristics based on Voronoi polyhedra, spherical harmonics, and Delaunay simplices are considered together with the pair correlation function and the mean number of r-close triples. They are applied to a set of hard sphere packings of density φ from 0.62 to 0.72. It turns out that all used structure characteristics are able to indicate changes of order from non-crystalline to crystalline packings. However, not all of them are sensitive enough to indicate different stages of structure transformation under densification. The characteristics based on Delaunay simplices turn out to be the most sensitive for this purpose. For the models considered three principal structure classes are found: packings of densities lower than the known critical value 0.64 showing a non-crystalline behavior; packings with considerable crystalline regions for φ up to 0.66–0.67; rather complete crystals although with numerous defects for φ above 0.67.     

Dynamic domain networks

A model for a dynamic network consisting of changing local interactions is presented in this work. While the network maintains solely local connections, certain properties known only to Small World Networks may be extracted due to the dynamic nature of the model. At each time step the individuals are grouped into clusters creating neighborhoods or domains of fully connected agents. The boundaries of these domains change in time, corresponding to a situation where the links between individuals are dynamic only throughout the history of the network. A question that we pose is whether our model, which maintains a local structure such that diffusion calculations are possible, might lead to analytic or conceptual advances for the much more complicated case of diffusion on a static disordered network that exhibits the same macroscopic properties as our dynamic ordered network. To answer this, we compare certain properties which characterize the dynamic domain network to those of a Small World Network, and then analyze the diffusion coefficients for three possible domain mutations. We close with a comparison and confirmation of previous epidemiological work carried out on networks.     

Statistical analysis of shear cracks on rock surfaces

A set of 3873 cracks on exposed granite rock surfaces are analyzed in order to investigate possible fracture mechanisms. The fracture patterns are compared with the Mohr-Coulomb and the Roscoe fracture models, which can be combined into a single fracture scheme. A third model for comparison is based on interacting `penny-shaped' micro cracks introduced by Healy et al. [Nature 439, 64 (2006)]. The former models predict a bimodal fracture angle distribution, with two narrow peaks separated by 60^○-90^○ symmetrically on both sides of the direction of the largest principal stress, while the latter predicts a single broader peak in the same direction with standard deviation in the range 15^○-20^○. The crack length distributions seem consistent with numerical simulation, whereas the fracture patterns are Euclidean rather than fractal. The statistical analyses indicate that none of the models fully describe the fracture patterns. It seems that natural shear fractures easily become a complex combination of different fracture mechanisms.     

Density-correlator signatures of the vulcanization transition

Certain density correlators, measurable via various experimental techniques, are studied in the context of the vulcanization transition. It is shown that these correlators contain essential information about both the vulcanization transition and the emergent amorphous solid state. Contact is made with various physical ingredients that have featured in experimental studies of amorphous colloidal and gel systems and in theoretical studies of the glassy state. Received 30 September 2000     

Evidence for a compressed fluid phase of Xe clusters

We report on the formation and detection of a compressed fluid phase of Xe clusters in as- implanted Si, at room temperature. The simultaneous structural characterization of the Xe clusters and of the Si matrix was performed by X-ray diffraction at grazing incidence coupled with two-dimensional detection; in both cases, the nearest-neighbor distance and the coordination were obtained. In order to investigate the early stage of the atomic inclusion and the cluster segregation, the average compression and size of Xe fluid clusters within the amorphous Si matrix were explained within the simple Hard Sphere model. Received 4 September 2000 and Received in final form 13 December 2000     

Limited resolution in complex network community detection with Potts model approach

According to Fortunato and Barthélemy, modularity-based community detection algorithms have a resolution threshold such that small communities in a large network are invisible. Here we generalize their work and show that the q-state Potts community detection method introduced by Reichardt and Bornholdt also has a resolution threshold. The model contains a parameter by which this threshold can be tuned, but no a priori principle is known to select the proper value. Single global optimization criteria do not seem capable for detecting all communities if their size distribution is broad.     

High-temperature behaviour of average structure and vibrational density of states in the ternary superionic compound AgCuSe

Results of simultaneous thermal analysis (STA), synchrotron powder diffraction (in the range 300–973 K) and inelastic neutron scattering (at 285 and 505 K) on non-superionic β- and superionic α-AgCuSe are reported. The sample is stable in argon on heating. The volume change at the superionic phase transition is about 5%. A model for the average structure of α-AgCuSe is proposed. No anomalies in the temperature dependence of the parameters of the average structure were revealed. Ionic conductivity in α-AgCuSe can originate from cation jumps in “skewed” 〈100 〉 directions between nearest-neighbour tetrahedral sites via the peripheries of the octahedral cavities. A correlation between the temperature dependence of the cation redistribution in α-AgCuSe and the temperature dependence of the ionic conductivity is supposed. Various contributions (anharmonic effects, time-average static disorder and phonon-phonon scattering) to the widths of individual phonons upon temperature increase lead to pronounced changes in the neutron-weighted densities of states of β- and α-AgCuSe and accompany the superionic phase transition as well.     

Decline of minorities in stubborn societies

Opinion compromise models can give insight into how groups of individuals may either come to form consensus or clusters of opinion groups, corresponding to parties. We consider models where randomly selected individuals interact pairwise. If the opinions of the interacting agents are not within a certain confidence threshold, the agents retain their own point of view. Otherwise, they constructively dialogue and smooth their opinions. Persuasible agents are inclined to compromise with interacting individuals. Stubborn individuals slightly modify their opinion during the interaction. Collective states for persuasible societies include extremist minorities, which instead decline in stubborn societies. We derive a mean field approximation for the compromise model in stubborn populations. Bifurcation and clustering analysis of this model compares favorably with Monte Carlo analysis found in the literature.     

Correlation and volatility in an Indian stock market: A random matrix approach

We examine the volatility of an Indian stock market in terms of correlation of stocks and quantify the volatility using the random matrix approach. First we discuss trends observed in the pattern of stock prices in the Bombay Stock Exchange for the three-year period 2000–2002. Random matrix analysis is then applied to study the relationship between the coupling of stocks and volatility. The study uses daily returns of 70 stocks for successive time windows of length 85 days for the year 2001. We compare the properties of matrix C of correlations between price fluctuations in time regimes characterized by different volatilities. Our analyses reveal that (i) the largest (deviating) eigenvalue of C correlates highly with the volatility of the index, (ii) there is a shift in the distribution of the components of the eigenvector corresponding to the largest eigenvalue across regimes of different volatilities, (iii) the inverse participation ratio for this eigenvector anti-correlates significantly with the market fluctuations and finally, (iv) this eigenvector of C can be used to set up a Correlation Index, CI whose temporal evolution is significantly correlated with the volatility of the overall market index.     

Roughness and finite size effect in the NYSE stock-price fluctuations

We consider the roughness properties of NYSE (New York Stock Exchange) stock-price fluctuations. The statistical properties of the data are relatively homogeneous within the same day but the large jumps between different days prevent the extension of the analysis to large times. This leads to intrinsic finite size effects which alter the apparent Hurst (H) exponent. We show, by analytical methods, that finite size effects always lead to an enhancement of H. We then consider the effect of fat tails on the analysis of the roughness and show that the finite size effects are strongly enhanced by the fat tails. The non stationarity of the stock price dynamics also enhances the finite size effects which, in principle, can become important even in the asymptotic regime. We then compute the Hurst exponent for a set of stocks of the NYSE and argue that the interpretation of the value of H is highly ambiguous in view of the above results. Finally we propose an alternative determination of the roughness in terms of the fluctuations from moving averages with variable characteristic times. This permits to eliminate most of the previous problems and to characterize the roughness in useful way. In particular this approach corresponds to the automatic elimination of trends at any scale.     

Graph kernels,hierarchical clustering,and network community structure: experiments and comparative analysis

There has been a quickly growing interest in properties of complex networks, such as the small world property, power-law degree distribution, network transitivity, and community structure, which seem to be common to many real world networks. In this study, we consider the community property which is also found in many real networks. Based on the diffusion kernels of networks, a hierarchical clustering approach is proposed to uncover the community structure of different extent of complex networks. We test the method on some networks with known community structures and find that it can detect significant community structure in these networks. Comparison with related methods shows the effectiveness of the method.     

Effect of topological thresholds on thermal behaviour of germanium telluride glasses containing metallic additive

Differential Scanning Calorimetric (DSC) studies on Ag_xGe₁₅Te_85-x glasses have been undertaken over a wide range of compositions, to understand the effect of topological thresholds on thermal properties. It is found that the compositional dependence of glass transition temperature (T _g ), crystallization temperature (T _c ), activation energy for crystallization and thermal stability show anomalies at the rigidity percolation threshold. Unusual variations also observed in different thermal properties at the composition x = 20, clearly establishes the occurrence of chemical threshold in these glasses. Received: 27 January 1998 / Revised: 12 June 1998 / Accepted: 3 July 1998     

Polymer adsorption on heterogeneous surfaces

The adsorption of a single ideal polymer chain on energetically heterogeneous and rough surfaces is investigated using a variational procedure introduced by Garel and Orland (Phys. Rev. B 55, 226 (1997)). The mean polymer size is calculated perpendicular and parallel to the surface and is compared to the Gaussian conformation and to the results for polymers at flat and energetically homogeneous surfaces. The disorder-induced enhancement of adsorption is confirmed and is shown to be much more significant for a heterogeneous interaction strength than for spatial roughness. This difference also applies to the localization transition, where the polymer size becomes independent of the chain length. The localization criterion can be quantified, depending on an effective interaction strength and the length of the polymer chain. Received: 29 October 1997 / Revised: 19 December 1997 / Accepted: 6 March 1998     

Compromise and synchronization in opinion dynamics

We discuss two models of opinion dynamics. We first present a brief review of the Hegselmann and Krause (HK) compromise model in two dimensions, showing that it is possible to simulate the dynamics in the limit of an infinite number of agents by solving numerically a rate equation for a continuum distribution of opinions. Then, we discuss the Opinion Changing Rate (OCR) model, which allows to study under which conditions a group of agents with a different natural tendency (rate) to change opinion can find the agreement. In the context of the this model, consensus is viewed as a synchronization process.     

Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase frustration to study the effect of dilution in a spin liquid state. This provides a “minimal” ordering by disorder from an Ising paramagnet to an Ising spin glass. Received 9 April 1999 and Received in final form 27 September 1999     

Thermoelectric transport properties in disordered systems near the Anderson transition

We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition (MIT). In particular, we investigate the dependence of the thermoelectric power S, the thermal conductivity K, and the Lorenz number L₀ on temperature T. We first calculate the T dependence of the chemical potential μ from the number density n of electrons at the MIT using an averaged density of states obtained by diagonalization. Without any additional approximation, we determine from the behavior of S, K and L₀ at low T as the MIT is approached. We find that and K decrease to zero at the MIT as and show that S does not diverge. Both S and L₀ become temperature independent at the MIT and depend only on the critical behavior of the conductivity. Received 5 February 1999     

Empirical analysis of dependence between stations in Chinese railway network

A railway transportation system can be represented by a bipartite network consisting of trains and stations, where a train is connected to all stations where it stops. In this paper, motivated by the resource-allocation process taking place on networks, we design a method to project a Chinese train-station bipartite network into a weighted station network. A new metric is proposed to quantify the dependence between pairs of stations, which is shown to follow a shifted power-law distribution. In addition, we compare the resource-allocation method and the well-known multiple-edge method, and the results indicate that our proposed method is more reasonable.