Stripe-hexagon competition in forced pattern forming systems with broken up-down symmetry

We investigate the response of two-dimensional pattern forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a $1:2$ and $1:1$ ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system. Both sets of coupled amplitude equations are derived by a perturbative method from the Lengyel-Epstein model describing a chemical reaction showing Turing patterns, which gives us the opportunity to relate the generic response scenarios to a specific pattern forming system. The nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence, stability and coexistence is determined. Whereas without modulations hexagonal patterns are always preferred near onset of pattern formation, single mode solutions (stripes) are favored close to threshold for modulation amplitudes beyond some critical value. Hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude. Furthermore depending on the modulation amplitude the transition between stripes and distorted hexagons is either sub- or supercritical.Comment: 10 pages, 12 figures, submitted to Physical Review

Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime

An improved generator for continuous unitary transformations is introduced to describe systems with unstable quasiparticles. Its general properties are derived and discussed. To illustrate this approach we investigate the asymmetric antiferromagnetic spin-1/2 Heisenberg ladder which allows for spontaneous triplon decay. We present results for the low energy spectrum and the momentum resolved spectral density of this system. In particular, we show the resonance behavior of the decaying triplon explicitly.Comment: 40 pages, 12 figure

Validation of Agent-Based Models in Economics and Finance

Since the survey by Windrum et al. (Journal of Artificial Societies and Social Simulation 10:8, 2007), research on empirical validation of agent-based models in economics has made substantial advances, thanks to a constant flow of high-quality contributions. This Chapter attempts to take stock of such recent literature to offer an updated critical review of the existing validation techniques. We sketch a simple theoretical framework that conceptualizes existing validation approaches, which we examine along three different dimensions: (i) comparison between artificial and real-world data; (ii) calibration and estimation of model parameters; and (iii) parameter space exploration. Finally, we discuss open issues in the field of ABM validation and estimation. In particular, we argue that more research efforts should be devoted toward advancing hypothesis testing in ABM, with specific emphasis on model stationarity and ergodicity

Giant boulders and Last Interglacial storm intensity in the North Atlantic

As global climate warms and sea level rises, coastal areas will be subject to more frequent extreme flooding and hurricanes. Geologic evidence for extreme coastal storms during past warm periods has the potential to provide fundamental insights into their future intensity. Recent studies argue that during the Last Interglacial (MIS 5e, ∼128–116 ka) tropical and extratropical North Atlantic cyclones may have been more intense than at present, and may have produced waves larger than those observed historically. Such strong swells are inferred to have created a number of geologic features that can be observed today along the coastlines of Bermuda and the Bahamas. In this paper, we investigate the most iconic among these features: massive boulders atop a cliff in North Eleuthera, Bahamas. We combine geologic field surveys, wave models, and boulder transport equations to test the hypothesis that such boulders must have been emplaced by storms of greater-than-historical intensity. By contrast, our results suggest that with the higher relative sea level (RSL) estimated for the Bahamas during MIS 5e, boulders of this size could have been transported by waves generated by storms of historical intensity. Thus, while the megaboulders of Eleuthera cannot be used as geologic proof for past “superstorms,” they do show that with rising sea levels, cliffs and coastal barriers will be subject to significantly greater erosional energy, even without changes in storm intensity