23 research outputs found
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
and 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, âŒ128â116 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 âsuperstorms,â 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