arXiv subjects

J. -P. Bouchaud

Publications and source records attributed to J. -P. Bouchaud.

43 records · Page 3Linked to original sources

arXiv1998

Aging in K$_{1-x}$Li$_x$Ta0$_3$: a domain growth interpretation

The aging behaviour of the a.c. susceptibility of randomly substituted K$_{1-x}$Li$_x$Ta0$_3$ crystals reveals marked differences with spin-glasses in that cooling rate effects are very important. The response to temperature steps (including temperature cycles) was carefully studied. A model based on thermally activated domain growth accounts for all the experimental results, provided one allows for a large distribution of pinning energies, in such a way that `slow' and `fast' domains coexist. Interesting similarities with deeply supercooled liquids are underlined.

cond-mat↗

arXiv1997

Phenomenology of the Interest Rate Curve

This paper contains a phenomenological description of the whole U.S. forward rate curve (FRC), based on an data in the period 1990-1996. We find that the average FRC (measured from the spot rate) grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate volatility. This suggests that forward rate market prices include a risk premium, comparable to the probable changes of the spot rate between now and maturity, which can be understood as a `Value-at-Risk' type of pricing. The instantaneous FRC however departs form a simple square-root law. The distortion is maximum around one year, and reflects the market anticipation of a local trend on the spot rate. This anticipated trend is shown to be calibrated on the past behaviour of the spot itself. We show that this is consistent with the volatility `hump' around one year found by several authors (and which we confirm). Finally, the number of independent components needed to interpret most of the FRC fluctuations is found to be small. We rationalize this by showing that the dynamical evolution of the FRC contains a stabilizing second derivative (line tension) term, which tends to suppress short scale distortions of the FRC. This shape dependent term could lead, in principle, to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. We suggest that the presence of transaction costs (or other market `imperfections') is crucial for model building, for a much wider class of models becomes eligible to represent reality.

cond-mat.stat-mech↗

arXiv1997

A Scalar Arching Model

In this paper we propose an extension of the model of Liu, Coppersmith et al., in order to allow for arch formation. This extended model qualitatively captures interesting properties of granular materials due to fluctuations of stress paths, such as stress fluctuations and stick-slip motion.

cond-mat↗

arXiv1997

Models of stress propagation in granular media

Stress patterns in static granular media exhibit unusual features when compared to either liquids or elastic solids. Qualitatively, we attribute these features to the presence of `stress paths', whose geometry depends on the construction history and controls the propagation of stresses. Stress paths can cause random focussing of stresses (large fluctuations) as well as systematic deflections (arching). We describe simple physical models that capture some of these effects. In these models, the `stress paths' become identified with the characteristic `light rays' of wavelike (hyperbolic) equations for force propagation. Such models account for the `pressure dip' below conical sandpiles built by pouring from a point source, and explain qualitatively the large stress fluctuations observed experimentally in granular matter. The differences between this approach and more conventional modelling strategies (based on elastoplastic or rigid-plastic models) are highlighted, focusing on the role of boundary conditions. Our models provide a continuum picture in which granular materials are viewed as fragile matter, able to support without rearranging only a subset of the static external loadings admissible for a normal elastic solid.

cond-mat↗

arXiv1997

Models of stress fluctuations in granular media

We investigate in detail two models describing how stresses propagate and fluctuate in granular media. The first one is a scalar model where only the vertical component of the stress tensor is considered. In the continuum limit, this model is equivalent to a diffusion equation (where the rôle of time is played by the vertical coordinate) plus a randomly varying convection term. We calculate the response and correlation function of this model, and discuss several properties, in particular related to the stress distribution function. We then turn to the tensorial model, where the basic starting point is a wave equation which, in the absence of disorder, leads to a ray-like propagation of stress. In the presence of disorder, the rays acquire a diffusive width and the angle of propagation is shifted. A striking feature is that the response function becomes negative, which suggests that the contact network is mechanically unstable to very weak perturbations. The stress correlation function reveals characteristic features related to the ray-like propagation, which are absent in the scalar description. Our analytical calculations are confirmed and extended by a numerical analysis of the stochastic wave equation.

cond-mat↗

arXiv1996

Static avalanches and Giant stress fluctuations in Silos

We propose a simple model for arch formation in silos. We show that small pertubations (such as the thermal expansion of the beads) may lead to giant stress fluctuations on the bottom plate of the silo. The relative amplitude $Δ$ of these fluctuations are found to be power-law distributed, as $Δ^{-τ}$, $τ\simeq 1.0$. These fluctuations are related to large scale `static avalanches', which correspond to long-range redistributions of stress paths within the silo.

cond-mat↗

arXiv1996

Velocity fluctuations in forced Burgers turbulence

We propose a simple method to compute the velocity difference statistics in forced Burgers turbulence in any dimension. Within a reasonnable assumption concerning the nucleation and coalescence of shocks, we find in particular that the `left' tail of the distribution decays as an inverse square power, which is compatible with numerical data. Our results are compared to those of various recent approaches: instantons, operator product expansion, replicas.

cond-mat↗