Jørgen Vitting Andersen

Tricritical 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 tricriticality, separating a first-order regime where rupture occurs without significant precursors from a second-order regime where the macroscopic elastic coefficient exhibits 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. {copyright} {ital 1997} {ital The American Physical Society}

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.

Towards landslide predictions: two case studies

In a previous work (J. Geophys. Res. (2004)), 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 Clapiere (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 with a variety of techniques using (i) a finite-time singularity power law, (ii) the state- and velocity-dependent friction law and (iii) resummation methods extrapolating from early times. 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 Clapiere landslide.

Scaling with respect to disorder in time-to-failure

Abstract: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.

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 nine 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 nine time series, we find that five pass our tests and can be characterized as “fearful singular bubbles”. The four 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).

Fundamental Framework for Technical Analysis

Abstract: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 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 contrast, a trend following strategy and + 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 selects the best of the two, based on a calculation of the stability of their predicted market trajectories.

Dynamical scaling of oxygen ordering in YBa2Cu3O7- delta.

Comptuer simulation on a two-dimensional anisotropic lattice-gas model of oxygen ordering in high-{ital T}{sub {ital c}} supeconductors of the YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} -type shows that the ordering dynamics obey algebraic growth laws which are different in the ortho-I and ortho-II phases. It is possible to relate this dynamical scaling behavior to a similar scaling in the experimentally observed temporal variation of the superconductivity transition temperature, hence suggesting a specific coupling between the coherence of oxygen order in the basal Cu-O planes and the superconducting state.

Detecting Anchoring in Financial Markets

Anchoring is a term used in psychology to describe the common human tendency to rely too heavily (anchor) on one piece of information when making decisions. A trading algorithm inspired by biological motors, introduced by L. Gil, is suggested as a testing ground for anchoring in financial markets. An exact solution of the algorithm is presented for arbitrary price distributions. Furthermore the algorithm is extended to cover the case of a market neutral portfolio, revealing additional evidence that anchoring is involved in the decision making of market participants. The exposure of arbitrage possibilities created by anchoring gives yet another illustration on the difficulty proving market efficiency by only considering lower order correlations in past price time series.

Increments of Uncorrelated Time Series Can Be Predicted With a Universal 75% Probability of Success

We present a simple and general result that the sign of the variations or increments of uncorrelated times series are predictable with a remarkably high success probability of 75% for symmetric sign distributions. The origin of this paradoxical result is explained in details. We also present some tests on synthetic, financial and global temperature time series.

Fracturing Described by a Spring-Block Model

A spring-block model containing only one parameter, the ratio between the threshold for block slips and the threshold for springs to break, is introduced to study general features of the statics and dynamics of fracturing. We find that a domain growth of positive and negative components of the stress field before cracking sets in is crucial for the pattern formations of the cracks. The domain growth obeys an algebraic growth law. The total number of cracks and the size distribution for crack events have been calculated as a function of the ratio between the threshold for spring breaking and the threshold for block slips, and as a function of time.