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J. V. Andersen

Publications and source records attributed to J. V. Andersen.

17 recordsLinked to original sources
arXiv2005

Optimal Prediction of Time-to-Failure from Information Revealed by Damage

We present a general prediction scheme of failure times based on updating continuously with time the probability for failure of the global system, conditioned on the information revealed on the pre-existing idiosyncratic realization of the system by the damage that has occurred until the present time. Its implementation on a simple prototype system of interacting elements with unknown random lifetimes undergoing irreversible damage until a global rupture occurs shows that the most probable predicted failure time (mode) may evolve non-monotonically with time as information is incorporated in the prediction scheme. In addition, both the mode, its standard deviation and, in fact, the full distribution of predicted failure times exhibit sensitive dependence on the realization of the system, similarly to ``chaos'' in spinglasses, providing a multi-dimensional dynamical explanation for the broad distribution of failure times observed in many empirical situations.

cond-mat.mtrl-sci↗
arXiv2004

Response Functions to Critical Shocks in Social Sciences: An Empirical and Numerical Study

We show that, provided one focuses on properly selected episodes, one can apply to the social sciences the same observational strategy that has proved successful in natural sciences such as astrophysics or geodynamics. For instance, in order to probe the cohesion of a policy, one can, in different countries, study the reactions to some huge and sudden exogenous shocks, which we call Dirac shocks. This approach naturally leads to the notion of structural (as opposed or complementary to temporal) forecast. Although structural predictions are by far the most common way to test theories in the natural sciences, they have been much less used in the social sciences. The Dirac shock approach opens the way to testing structural predictions in the social sciences. The examples reported here suggest that critical events are able to reveal pre-existing ``cracks'' because they probe the social cohesion which is an indicator and predictor of future evolution of the system, and in some cases foreshadows a bifurcation. We complement our empirical work with numerical simulations of the response function (``damage spreading'') to Dirac shocks in the Sznajd model of consensus build-up. We quantify the slow relaxation of the difference between perturbed and unperturbed systems, the conditions under which the consensus is modified by the shock and the large variability from one realization to another.

cond-mat.stat-mech↗
arXiv2003

Fearless versus Fearful Speculative Financial Bubbles

Using a recently introduced rational expectation model of bubbles, based on the interplay between stochasticity and positive feedbacks of prices on returns and volatility, we develop a new methodology to test how this model classifies 9 time series that have been previously considered as bubbles ending in crashes. The model predicts the existence of two anomalous behaviors occurring simultaneously: (i) super-exponential price growth and (ii) volatility growth, that we refer to as the ``fearful singular bubble'' regime. Out of the 9 time series, we find that 5 pass our tests and can be characterized as ``fearful singular bubbles.'' The 4 other cases are the information technology Nasdaq bubble and three bubbles of the Hang Seng index ending in crashes in 1987, 1994 and 1997. According to our analysis, these four bubbles have developed with essentially no significant increase of their volatility. This paper thus proposes that speculative bubbles ending in crashes form two groups hitherto unrecognized, namely those accompanied by increasing volatility (reflecting increasing risk perception) and those without change of volatility (reflecting an absence of risk perception).

cond-mat.stat-mech↗
arXiv2003

Slider-Block Friction Model for Landslides: Application to Vaiont and La Clapiere Landslides

Accelerating displacements preceding some catastrophic landslides have been found empirically to follow a time-to-failure power law, corresponding to a finite-time singularity of the velocity $v \sim 1/(t_c-t)$ [{\it Voight}, 1988]. Here, we provide a physical basis for this phenomenological law based on a slider-block model using a state and velocity dependent friction law established in the laboratory and used to model earthquake friction. This physical model accounts for and generalizes Voight's observation: depending on the ratio $B/A$ of two parameters of the rate and state friction law and on the initial frictional state of the sliding surfaces characterized by a reduced parameter $x_i$, four possible regimes are found. Two regimes can account for an acceleration of the displacement. We use the slider-block friction model to analyze quantitatively the displacement and velocity data preceding two landslides, Vaiont and La Clapière. The Vaiont landslide was the catastrophic culmination of an accelerated slope velocity. La Clapière landslide was characterized by a peak of slope acceleration that followed decades of ongoing accelerating displacements, succeeded by a restabilizing phase. Our inversion of the slider-block model on these data sets shows good fits and suggest to classify the Vaiont (respectively La Clapière) landslide as belonging to the velocity weakening unstable (respectively strengthening stable) sliding regime.

cond-mat.stat-mech↗
arXiv2003

Towards Landslide Predictions: Two Case Studies

In a previous work [Helmstetter, 2003], we have proposed a simple physical model to explain the accelerating displacements preceding some catastrophic landslides, based on a slider-block model with a state and velocity dependent friction law. This model predicts two regimes of sliding, stable and unstable leading to a critical finite-time singularity. This model was calibrated quantitatively to the displacement and velocity data preceding two landslides, Vaiont (Italian Alps) and La Clapière (French Alps), showing that the former (resp. later) landslide is in the unstable (resp. stable) sliding regime. Here, we test the predictive skills of the state-and-velocity-dependent model on these two landslides, using a variety of techniques. For the Vaiont landslide, our model provides good predictions of the critical time of failure up to 20 days before the collapse. Tests are also presented on the predictability of the time of the change of regime for la Clapière landslide.

physics.geo-ph↗
arXiv2002

A Nonlinear Super-Exponential Rational Model of Speculative Financial Bubbles

Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finite-time singularity formula transforms a Gaussian white noise into a rich time series possessing all the stylized facts of empirical prices, as well as accelerated speculative bubbles preceding crashes. We use the formula to invert the two years of price history prior to the recent crash on the Nasdaq (april 2000) and prior to the crash in the Hong Kong market associated with the Asian crisis in early 1994. These complex price dynamics are captured using only one exponent controlling the explosion, the variance and mean of the underlying random walk. This offers a new and powerful detection tool of speculative bubbles and herding behavior.

cond-mat.stat-mech↗
arXiv2000

Functional Renormalization Prediction of Rupture

We develop theoretical formulas for the prediction of the rupture of systems which are known to exhibit a critical behavior, based solely on the knowledge of the early time evolution of an observable, such as the acoustic emission rate as a function of time or of stress. From the parameterization of such early time evolution in terms of a low-order polynomial, we use the functional renormalization approach introduced by Yukalov and Gluzman to transform this polynomial into a function which is asymptotically a power law. The value of the critical time tc,conditioned on the assumption that tc exists, is thus determined from the knowledge of the coefficients of the polynomials. We test with success this prediction scheme with respect to the order of the polynomials and as a function of noise.

cond-mat.stat-mech↗
arXiv1999

Fundamental Framework for Technical Analysis

Starting from the characterization of the past time evolution of market prices in terms of two fundamental indicators, price velocity and price acceleration, we construct a general classification of the possible patterns characterizing the deviation or defects from the random walk market state and its time-translational invariant properties. The classification relies on two dimensionless parameters, the Froude number characterizing the relative strength of the acceleration with respect to the velocity and the time horizon forecast dimensionalized to the training period. Trend-following and contrarian patterns are found to coexist and depend on the dimensionless time horizon. The classification is based on the symmetry requirements of invariance with respect to change of price units and of functional scale-invariance in the space of scenarii. This ``renormalized scenario'' approach is fundamentally probabilistic in nature and exemplifies the view that multiple competing scenarii have to be taken into account for the same past history. Empirical tests are performed on on about nine to thirty years of daily returns of twelve data sets comprising some major indices (Dow Jones, SP500, Nasdaq, DAX, FTSE, Nikkei), some major bonds (JGB, TYX) and some major currencies against the US dollar (GBP, CHF, DEM, JPY). Our ``renormalized scenario'' exhibits statistically significant predictive power in essentially all market phases. In constrast, a trend following strategy and trend + acceleration following strategy perform well only on different and specific market phases. The value of the ``renormalized scenario'' approach lies in the fact that it always finds the best of the two, based on a calculation of the stability of their predicted market trajectories.

cond-mat.stat-mech↗
arXiv1999

Have your cake and eat it too: increasing returns while lowering large risks!

Based on a faithful representation of the heavy tail multivariate distribution of asset returns introduced previously (Sornette et al., 1998, 1999) that we extend to the case of asymmetric return distributions, we generalize the return-risk efficient frontier concept to incorporate the dimensions of large risks embedded in the tail of the asset distributions. We demonstrate that it is often possible to increase the portfolio return while decreasing the large risks as quantified by the fourth and higher order cumulants. Exact theoretical formulas are validated by empirical tests.

cond-mat.stat-mech↗
arXiv1999

"Nonlinear" covariance matrix and portfolio theory for non-Gaussian multivariate distributions

This paper offers a precise analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a non-linear fractional covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good-conditionning. The portfolio distribution is obtained as the solution of a mapping to a so-called phi-q field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The main result of our theory is that minimizing the portfolio variance (i.e. the relatively ``small'' risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive empirical tests are presented on the foreign exchange market that validate satisfactorily the theory. For ``fat tail'' distributions, we show that an adequete prediction of the risks of a portfolio relies much more on the correct description of the tail structure rather than on their correlations.

cond-mat.stat-mech↗
arXiv1998

Minimizing volatility increases large risks

We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonous as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixture of assets. The portfolio which minimizes the variance, i.e. the relatively small risks, often increases larger risks as measured by higher normalized cumulants and by the Value-at-risk.

cond-mat.stat-mech↗
arXiv1997

Conditions for abrupt failure in the democratic fiber bundle model

We argue that the existence of abrupt failure in the democratic fiber bundle model is more general than concluded by da Silveira in his comment (cond-mat/9709327). We refute his claim that the nature of the rupture process in the DFBM depends on the ``disorder distribution only via its large failure strength behavior''.

cond-mat.stat-mech↗
arXiv1997

Scaling with respect to disorder in time-to-failure

We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of time-to-rupture and of the amplitude of the disorder, which allows us to collapse neatly the numerical simulations over more than five decades in time and more than one decade in disorder amplitude onto a single master curve. We thus conclude that, at least in this model, dynamical rupture in systems with long-range elasticity is a genuine critical phenomenon occurring as soon as the disorder is non-vanishing.

cond-mat.stat-mech↗
arXiv1997

New model for surface fracture induced by dynamical stress

We introduce a model where an isotropic, dynamically-imposed stress induces fracture in a thin film. Using molecular dynamics simulations, we study how the integrated fragment distribution function depends on the rate of change and magnitude of the imposed stress, as well as on temperature. A mean-field argument shows that the system becomes unstable for a critical value of the stress. We find a striking invariance of the distribution of fragments for fixed ratio of temperature and rate of change of the stress; the interval over which this invariance holds is determined by the force fluctuations at the critical value of the stress.

cond-mat.mtrl-sci↗
arXiv1996

Tri-critical behavior in rupture induced by disorder

We discover a qualitatively new behavior for systems where the load transfer has limiting stress amplification as in real fiber composites. We find that the disorder is a relevant field leading to tri--criticality, separating a first-order regime where rupture occurs without significant precursors from a second-order regime where the macroscopic elastic coefficient exhibit power law behavior. Our results are based on analytical analysis of fiber bundle models and numerical simulations of a two-dimensional tensorial spring-block system in which stick-slip motion and fracture compete.

cond-mat↗
arXiv1995

Pinning of a solid--liquid--vapour interface by stripes of obstacles

We use a macroscopic Hamiltonian approach to study the pinning of a solid--liquid--vapour contact line on an array of equidistant stripes of obstacles perpendicular to the liquid. We propose an estimate of the density of pinning stripes for which collective pinning of the contact line happens. This estimate is shown to be in good agreement with Langevin equation simulation of the macroscopic Hamiltonian. Finally we introduce a 2--dimensional mean field theory which for small strength of the pinning stripes and for small capillary length gives an excellent description of the averaged height of the contact line.

cond-mat↗