Showing papers in "European Physical Journal B in 1998"

How popular is your paper? An empirical study of the citation distribution

Abstract: Numerical data for the distribution of citations are examined for: (i) papers published in 1981 in journals which are catalogued by the Institute for Scientific Information (783,339 papers) and (ii) 20 years of publications in Physical Review D, vols. 11-50 (24,296 papers). A Zipf plot of the number of citations to a given paper versus its citation rank appears to be consistent with a power-law dependence for leading rank papers, with exponent close to -1/2. This, in turn, suggests that the number of papers with x citations, N(x), has a large-x power law decay $$N(x) \sim {x^{ - a}}$$ , with $$a \approx 3$$ .

Stretched exponential distributions in nature and economy: ``fat tails'' with characteristic scales

Abstract: To account quantitatively for many reported “natural” fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power law distributions. It has many advantages, among which to be economical with only two adjustable parameters with clear physical interpretation. Furthermore, it derives from a simple and generic mechanism in terms of multiplicative processes. We show that stretched exponentials describe very well the distributions of radio and light emissions from galaxies, of US GOM OCS oilfield reserve sizes, of World, US and French agglomeration sizes, of country population sizes, of daily Forex US-Mark and Franc-Mark price variations, of Vostok (near the south pole) temperature variations over the last 400 000 years, of the Raup-Sepkoski's kill curve and of citations of the most cited physicists in the world. We also discuss its potential for the distribution of earthquake sizes and fault displacements. We suggest physical interpretations of the parameters and provide a short toolkit of the statistical properties of the stretched exponentials. We also provide a comparison with other distributions, such as the shifted linear fractal, the log-normal and the recently introduced parabolic fractal distributions.

Metastable states in cellular automata for traffic flow

Abstract: Measurements on real traffic have revealed the existence of metastable states with very high flow. Such states have not been observed in the Nagel-Schreckenberg (NaSch) model which is the basic cellular automaton for the description of traffic. Here we propose a simple generalization of the NaSch model by introducing a velocity-dependent randomization. We investigate a special case which belongs to the so-called slow-to-start rules. It is shown that this model exhibits metastable states, thus sheding some light on the prerequisites for the occurance of hysteresis effects in the flow-density relation.

Inverse cubic law for the distribution of stock price variations

Abstract: The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period January 1994 - December 1995. A sample of 40 million data points is extracted, which is substantially larger than studied hitherto. We find an asymptotic power-law behavior for the cumulative distribution with an exponent $$a \approx 3$$ , well outside the Levy regime $$(0 < \alpha < 2)$$ .

A Langevin approach to stock market fluctuations and crashes

Abstract: We propose a non linear Langevin equation as a model for stock market fluctuations and crashes. This equation is based on an identification of the different processes influencing the demand and supply, and their mathematical transcription. We emphasize the importance of feedback effects of price variations onto themselves. Risk aversion, in particular, leads to an “up-down” symmetry breaking term which is responsible for crashes, where “panic” is self reinforcing. It is also responsible for the sudden collapse of speculative bubbles. Interestingly, these crashes appear as rare, “activated” events, and have an exponentially small probability of occurence. The model leads to a specific “shape” of the falldown of the price during a crash, which we compare with the October 1987 data. The normal regime, where the stock price exhibits behavior similar to that of a random walk, however reveals non trivial correlations on different time scales, in particular on the time scale over which operators perceive a change of trend.

Evaluation of the capacitive force between an atomic force microscopy tip and a metallic surface

Abstract: We propose a very simple method to determine the electrical tip-surface force in Atomic Force Microscopes used to study the electrical properties of metallic or insulating materials; the analysis of the measurements as well as determination of the appropriate experimental procedures requiring an analytical model of the tip-surface capacitance. The comparison of force expressions obtained by this method with those obtained by exact derivation in the case of the sphere-infinite plane system shows very good agreement. This method is then applied to determine the tip-surface force, the real shape of the tip being introduced in the derivation. The obtained expression is compared to experimental and numerical data. We emphasize that this method is very general and can be applied to any axially symmetric capacitor.

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

Abstract: We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagome lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Neel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic ( $$(\Delta S = 1)$$ ) excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic ( $$(\Delta S = 0)$$ ) excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagome lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets.

Wealth distributions in asset exchange models

Abstract: A model for the evolution of the wealth distribution in an economically interacting population is introduced, in which a specified amount of assets are exchanged between two individuals when they interact. The resulting wealth distributions are determined for a variety of exchange rules. For “random” exchange, either individual is equally likely to gain in a trade, while “greedy” exchange, the richer individual gains. When the amount of asset traded is fixed, random exchange leads to a Gaussian wealth distribution, while greedy exchange gives a Fermi-like scaled wealth distribution in the long-time limit. Multiplicative processes are also investigated, where the amount of asset exchanged is a finite fraction of the wealth of one of the traders. For random multiplicative exchange, a steady state occurs, while in greedy multiplicative exchange a continuously evolving power law wealth distribution arises.

”Direct” causal cascade in the stock market

Abstract: We use wavelets to decompose the volatility (standard deviation) of intraday (S&P500) return data across scales. We show that when investigating two-point correlation functions of the volatility logarithms across different time scales, one reveals the existence of a causal information cascade from large scales (i.e. small frequencies) to fine scales. We quantify and visualize the information flux across scales. We provide a possible interpretation of our findings in terms of market dynamics.

Modeling film flows down inclined planes

Abstract: A new model of film flow down an inclined plane is derived by a method combining results of the classical long wavelength expansion to a weighted-residuals technique. It can be expressed as a set of three coupled evolution equations for three slowly varying fields, the thickness h, the flow-rate q, and a new variable Ƭ that measures the departure of the wall shear from the shear predicted by a parabolic velocity profile. Results of a preliminary study are in good agreement with theoretical asymptotic properties close to the instability threshold, laboratory experiments beyond threshold and numerical simulations of the full Navier-Stokes equations.

Behavior of one inelastic ball bouncing repeatedly off the ground

Abstract: An experimental study of the behavior of one bead bouncing repeatedly off a static flat horizontal surface is presented. We observe that the number of bounces made by the bead is finite. When the duration between two successive bounces becomes of the order of the impact duration, the bead no longer bounces but oscillates on the elastically deformed surface before coming to rest. This transition is explained with a modified Hertz interaction law in which gravity is taken into account during the interaction. For each bounce, measurement of both the duration of collision and the restitution coefficient have been done. The effective restitution coefficient is essentially constant and close to 1 during almost all bounces before decreasing to zero when the impact velocity vanishes. This is due to an interplay between gravity and viscoelastic dissipation.

Stock market crashes are outliers

Abstract: We call attention against what seems to be a widely held misconception according to which large crashes are the largest events of distributions of price variations with fat tails. We demonstrate on the Dow Jones Industrial Average that with high probability the three largest crashes in this century are outliers. This result supports the suggestion that large crashes result from specific amplification processes that might lead to observable pre-cursory signatures.

An experimental test of the critical behaviour of fracture precursors

Abstract: The statistical properties and the localization of fracture precursors on heteregeneous materials is studied by recording their acoustic emission as a function of the applied load. It's found that the microcrack cluster together as the load increases and the instantaneous acoustic energy has an invariant power law distribution. The integrated acoustic energy presents a critical divergency close to the failure load for the sample. These result support the idea that fracture can be viewed as a critical phenomenon. Finally a measure of the concentration of microcraks, which allows us to predict the failure load, is introduced. These properties are studied also when a periodic load is applied to the sample. It's found that the Kaiser effect is not strictly satisfied in heteregeneous materials.

Light-induced bistability in spin transition solids leading to thermal and optical hysteresis

Abstract: We investigate the behaviour of photo-excitable, bistable systems, under permanent light irradiation, in presence of relaxation towards the non-excited state. Cooperativity causes bistability of the steady state, leading to light-induced thermal and optical hysteresis (LITH and LIOH). The light-induced instability is expected to induce demixtion, i.e. the coexistence of domains of the two stable steady states. Such effects are evidenced by magnetic and reflectivity measurements on the spin-crossover solid solution: [Fex , with x= 0.3, 0.5, 0.85. Experimental data are in quantitative agreement with a simple macroscopic model which includes a non-linear relaxation term in the master equation.

Statistical analysis of the transition to turbulence in plane Couette flow

Abstract: We argue on general grounds that the transition to turbulence in plane Couette flow is best studied experimentally at a statistical level. We present such a statistical analysis of experimental data guided by a parallel investigation of a simple coupled map lattice model for spatiotemporal intermittency. We confirm that this generic type of spatiotemporal chaos is relevant in the context of plane Couette flow, where the linear stability of the laminar regime at all Reynolds numbers insures the necessary local subcriticality. Using large ensembles of similar experiments, we show the existence of a well-defined threshold Reynolds number above which a unique, turbulent, intermittent attractor coexists with the laminar flow. Furthermore, our data reveals that this transition to spatiotemporal intermittency is discontinuous, i.e. akin to a first-order phase transition.

Evolution from BCS superconductivity to Bose condensation : analytic results for the crossover in three dimensions

Abstract: We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution.

Electrostatics of DNA-cationic lipid complexes : isoelectric instability

Abstract: We propose a Poisson-Boltzmann electrostatic theory for DNA/cationic lipid complexes modeled as a stack of aligned DNA chains intercalated with lipid bilayers, a structure suggested by the recent X-ray synchrotron studies of Radler et al. Poisson-Boltzmann theory is shown to predict that the isoelectric point - where the DNA and cationic lipid charges are in balance - is unstable against absorption of extra DNA or lipid material. The instability is caused by the entropy gain obtained following the release of small ions inside the complex and is manifested by singular behavior of the rod-rod spacing near the isoelectric point. We apply the theory to a discussion of the results of Radler et al.

Correlated transport and non-Fermi-liquid behavior in single-wall carbon nanotubes

Abstract: We derive the effective low-energy theory for single-wall carbon nanotubes including the Coulomb interactions among electrons. The generic model found here consists of two spin- $${1 \over 2}$$ fermion chains which are coupled by the interaction. We analyze the theory using bosonization, renormalization-group techniques, and Majorana refermionization. Several experimentally relevant consequences of the breakdown of Fermi liquid theory observed here are discussed in detail, e.g., magnetic instabilities, anomalous conductance laws, and impurity screening profiles.

Tilt model of inverted amphiphilic mesophases

Abstract: We present an alternative model of structure and energetics of the inverted amphiphilic mesophases. The previous studies of the inverted hexagonal, HII, and inverted micellar cubic, QII, phases considered the amphiphilic monolayers to be homogeneously bent. In contrast, we assume a unit cell of an inverted mesophase to consist of flat fragments of monolayer. Hence, the unit cells of the HII and QII phases are represented by a hexagonal rod and a polyhedron, respectively. Our model is motivated by Turner and Gruner's X-ray diffraction reconstruction of structure of the HII phase. The only deformation of the amphiphilic monolayers we consider is tilt of the hydrocarbon chains with respect to the monolayer surface, determined by the packing constraints imposed in the mesophases. Applying our recent model for the elastic energy of tilt in liquid membranes [#!ref23!#], we show that: i) tilt accounts in a natural way for the frustration energy of mesophases resulting from filling by the hydrocarbon chains the corners of the unit cells, ii) the energy of tilt variation along the membrane surface is analogous to the bending energy. We compute the energetics of the HII, QIIsc and QIIfcc phases and obtain a hypothetical phase diagram in terms of the elastic constants of monolayers. Moreover, we calculate the structural dimensions of the mesophases. We verify the model showing that the obtained phase diagram describes the recent data for the glycolipids/water systems; the predicted dimensions of the QII phase are in accord with the measured values; the model treats quantitatively the structural features observed for the HII phase.

Multi-affine analysis of typical currency exchange rates

Abstract: For foreign currency exchange rates, multi-affine analysis can put quantitatively into evidence the differences between correlated (daily closing market) values and random walks in time dependent data. The H(q) spectrum is presented and discussed here for the USD/DEM and JPY/USD exchange rates. The time-evolution of these ratios is found to be multi-affine. The \(h(\gamma )\)-curve describing the hierarchy of exponents is numerically obtained. Our findings suggest that the modelling of exchange rate time-evolution from day to day is possible within the framework of modern statistical physics and related to models of turbulence in the physics of fluids. Finally, we argue that there is a multiplicity of information levels in the foreign exchange market such that the “efficient market theory” is a crude oversimplification indeed.

Interplay between chains of S=5/2 localised spins and two-dimensional sheets of organic donors in the synthetically built magnetic multilayer λ-(BETS)2FeCl4

Abstract: In order to understand the magnetic field-induced restoration of a highly conductive state in λ ‒ (BETS)2FeCl4, static (SQUID) and dynamic (ESR and AFR) magnetization measurements were performed on polycrystalline samples and single crystals, respectively. In addition, cantilever and resistivity measurements under steady fields were performed. While the metal-insulator transition curve of the (T, B) phase diagram exhibits a first order character, a “spin-flop” transition line divides the insulating state when the magnetic field is applied along the easy axis of magnetization. The effects of a RKKY-type indirect exchange and of applied magnetic field are described within the framework of a generalized Kondo lattice, namely two chains of S = 5/2 Fe3+ localised spins coupled through the itinerant spins of the 2D sheets of BETS. The calculations, which can incorporate intramolecular electron correlations within a mean field theory, are in qualitative agreement with the field induced transition from the antiferromagnetic insulating ground state to a canted one, i.e. a not fully oriented paramagnetic, but metallic state.

Fragmentation of grains in a two-dimensional packing

Abstract: A numerical model of fragmentation of a two-dimensional granular medium under pressure is investigated. The fragmentation process is found to be strongly dependent on the type of force used as the criterion for breaking the grains. The fragmentation mode affects the process less dramatically. There is a power-law divergence in the pressure when the medium approaches the full packing limit, . Both log-normal and power-law fragment-size distributions are found. Gravity is demonstrated to be an important factor.

How the financial crash of October 1997 could have been predicted

Abstract: From the analysis of (closing value) stock market index like the Dow Jones Industrial average and the S&P500 it is possible to observe the precursor of a so-called crash. This is shown on the Oct. 1987 and Oct. 1997 cases. The data analysis indicates that the index divergence has followed twice a “universal” behavior, i.e. a logarithmic dependence, superposed on a well defined oscillation pattern. The prediction of the crash date is remarkable and can be done two months in advance. In the spirit of phase transition phenomena, the economic index is said to be analogous to a signal signature found in a two dimensional fluid of vortices.

Macroscopic Properties of Smectic CG Liquid Crystals

Abstract: We discuss the macroscopic behavior of smectic CG liquid crystals. Smectic CG is the most general tilted smectic phase that is fluid in the layers. It is characterized by global C1 symmetry. Consequently, it is ferroelectric, pyroelectric and piezoelectric, opening up a number of possible applications for such a phase. As smectic CG-phase has a macroscopic hand due to its structure, it is a natural candidate to explain the recent experimental observations of left and right-handed helices in a system composed of achiral molecules. We also discuss critically to what extent smectic CG could be important for liquid crystalline phases formed by banana-shaped molecules. Phase transitions involving a smectic CG phase and defects of its in-plane director are briefly discussed.

Transverse transport in (TM)2X organic conductors: possible evidence for a Luttinger liquid

Abstract: We present c-axis resistivity measurements performed on the organic conductors and under pressure. The aim is to probe the density of states of quasi-one dimensional compounds the high temperature properties of which are those of a Luttinger liquid. It is found that the 1-D Luttinger description breaks down below a specific pressure-dependent temperature, giving rise to a transient regime. The Fermi liquid behaviour is however restored at low temperature i.e. around 10 K, as evidenced by NMR measurements. Accordingly, two different energy scales 100 K and 10 K are required to get a fair understanding of all observed physical phenomena. Our interpretation supports the picture of a power law exponent for the correlation functions of the order of 0.25–0.30.

Filling carbon nanotubes with metals by the arc-discharge method: the key role of sulfur

Abstract: Various filled carbon nanotubes have recently been successfully produced by the arc-discharge method by doping a 99.4% graphite anode with a transition metal like Cr, Ni, a rare earth like Yb, Dy, or a covalent element like S, Ge. In this work, the structural characteristics of these encapsulated nanowires were studied by High Resolution Transmission Electron Microscopy and their chemical composition was investigated using Electron Energy-Loss Spectroscopy with high spatial resolution: this analysis mode provides elemental concentration profiles across or along the filled nanotubes. Except in the case of Ge for which only pure Ge fillings were identified, surprising amounts of sulfur, which was present as an impurity ( $$( \approx 0.25\% )$$ 0.25%) in the graphite rods, were found within numerous filling materials. When using high purity carbon rods, no filled nanotube was obtained. We chose the case of Cr to clearly evidence that the addition of sulfur in catalytic quantity is responsible for the formation of filled nanotubes, including sulfur free encapsulated nanowires. A growth mechanism based on a catalytic process involving three elements, i.e. carbon, a metal and sulfur, and taking into account the experimental results is proposed.

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

Abstract: We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T/J=10-24) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given.

Response of bubbles to diagnostic ultrasound: a unifying theoretical approach

Abstract: The scattering of ultrasound from bubbles of $\sim 1~\mu$m radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and ``active'' emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scattering and absorption cross-sections. We show that several well-known formulas are recovered in the linear limit of this ansatz. In the case of strongly nonlinear oscillations, however, the cross-sections can be larger than those for linear response by several orders of magnitude. The major part of the incident sound energy is then converted into emitted sound, unlike what happens in the linear case, where the absorption cross-sections exceed the scattering cross-sections.

Ladders in a magnetic field: a strong coupling approach

Abstract: We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (Hc1, Hc2, the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration.

Microscopic conditions favoring itinerant ferromagnetism: Hund's rule coupling and orbital degeneracy

Abstract: The importance of Hund's rule coupling for the stabilization of itinerant ferromagnetism is investigated within a two-band Hubbard model. The magnetic phase diagram is calculated by finite-temperature quantum Monte-Carlo simulations within the dynamical mean-field theory. Ferromagnetism is found in a broad range of electron fillings whereas antiferromagnetism exists only near half filling. The possibility of orbital ordering at quarter filling is also analyzed.