Transitions across Melancholia States in a climate model: reconciling the deterministic and stochastic points of view

The Earth is well known to be, in the current astronomical configuration, in a regime where two asymptotic states can be realized. The warm state we live in is in competition with the ice-covered snowball state. The bistability exists as a result of the positive ice-albedo feedback. In a previous investigation performed on a intermediate complexity climate model we identified the unstable climate states (melancholia states) separating the coexisting climates, and studied their dynamical and geometrical properties. The melancholia states are ice covered up to the midlatitudes and attract trajectories initialized on the basin boundary. In this Letter, we study how stochastically perturbing the parameter controlling the intensity of the incoming solar radiation impacts the stability of the climate. We detect transitions between the warm and the snowball state and analyze in detail the properties of the noise-induced escapes from the corresponding basins of attraction. We determine the most probable paths for the transitions and find evidence that the melancholia states act as gateways, similarly to saddle points in an energy landscape

Lorenz-like systems and classical dynamical equations with memory forcing: a new point of view for singling out the origin of chaos

A novel view for the emergence of chaos in Lorenz-like systems is presented. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one dimensional motion of a particle in a two-well potential, with a forcing term depending on the ``memory'' of the particle past motion. The dynamics of the original Lorenz system in the new particle phase space can then be rewritten in terms of an one-dimensional first-exit-time problem. The emergence of chaos turns out to be due to the discontinuous solutions of the transcendental equation ruling the time for the particle to cross the intermediate potential wall. The whole problem is tackled analytically deriving a piecewise linearized Lorenz-like system which preserves all the essential properties of the original model.Comment: 48 pages, 25 figure

Exact solutions to chaotic and stochastic systems

We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check, analytically, some recent results about the complexity of random dynamical systems. We confirm the result that a negative Lyapunov exponent does not imply predictability in random systems. We test the effectiveness of forecasting methods in distinguishing between chaotic and random time-series. Using the explicit random functions, we can give explicit analytical formulas for the output signal in some systems with stochastic resonance. We study the influence of chaos on the stochastic resonance. We show, theoretically, the existence of a new type of solitonic stochastic resonance, where the shape of the kink is crucial. Using our models we can predict specific patterns in the output signal of stochastic resonance systems.Comment: 31 pages, 18 figures (.eps). To appear in Chaos, March 200

Spatial and temporal variability of the dimethylsulfide to chlorophyll ratio in the surface ocean: an assessment based on phytoplankton group dominance determined from space

Dimethylsulfoniopropionate (DMSP) is produced in surface seawater by phytoplankton. Phytoplankton culture experiments have shown that nanoeucaryotes (NANO) display much higher mean DMSP-to-Carbon or DMSP-to-Chlorophyll (Chl) ratios than Prochlorococcus (PRO), Synechococcus (SYN) or diatoms (DIAT). Moreover, the DMSP-lyase activity of algae which cleaves DMSP into dimethylsulfide (DMS) is even more group specific than DMSP itself. Ship-based observations have shown at limited spatial scales, that sea surface DMS-to-Chl ratios (DMS:Chl) are dependent on the composition of phytoplankton groups. Here we use satellite remote sensing of Chl (from SeaWiFS) and of Phytoplankton Group Dominance (PGD from PHYSAT) with ship-based sea surface DMS concentrations (8 cruises in total) to assess this dependence on an unprecedented spatial scale. PHYSAT provides PGD (either NANO, PRO, SYN, DIAT, Phaeocystis (PHAEO) or coccolithophores (COC)) in each satellite pixel (1/4° horizontal resolution). While there are identification errors in the PHYSAT method, it is important to note that these errors are lowest for NANO PGD which we typify by high DMSP:Chl. In summer, in the Indian sector of the Southern Ocean, we find that mean DMS:Chl associated with NANO + PHAEO and PRO + SYN + DIAT are 13.6±8.4 mmol g−1 (n=34) and 7.3±4.8 mmol g−1 (n=24), respectively. That is a statistically significant difference (P<0.001) that is consistent with NANO and PHAEO being relatively high DMSP producers. However, in the western North Atlantic between 40° N and 60° N, we find no significant difference between the same PGD. This is most likely because coccolithophores account for the non-dominant part of the summer phytoplankton assemblages. Meridional distributions at 22° W in the Atlantic, and 95° W and 110° W in the Pacific, both show a marked drop in DMS:Chl near the equator, down to few mmol g−1, yet the basins exhibit different PGD (NANO in the Atlantic, PRO and SYN in the Pacific). In tropical and subtropical Atlantic and Pacific waters away from the equatorial and coastal upwelling, mean DMS:Chl associated with high and low DMSP producers are statistically significantly different, but the difference is opposite of that expected from culture experiments. Hence, in a majority of cases PGD is not of primary importance in controlling DMS:Chl variations. We therefore conclude that water-leaving radiance spectra obtained simultaneously from ocean color sensor measurements of Chl concentrations and dominant phytoplankton groups can not be used to predict global fields of DMS

Three-dimensional jamming and flows of soft glassy materials

Various disordered dense systems such as foams, gels, emulsions and colloidal suspensions, exhibit a jamming transition from a liquid state (they flow) to a solid state below a yield stress. Their structure, thoroughly studied with powerful means of 3D characterization, exhibits some analogy with that of glasses which led to call them soft glassy materials. However, despite its importance for geophysical and industrial applications, their rheological behavior, and its microscopic origin, is still poorly known, in particular because of its nonlinear nature. Here we show from two original experiments that a simple 3D continuum description of the behaviour of soft glassy materials can be built. We first show that when a flow is imposed in some direction there is no yield resistance to a secondary flow: these systems are always unjammed simultaneously in all directions of space. The 3D jamming criterion appears to be the plasticity criterion encountered in most solids. We also find that they behave as simple liquids in the direction orthogonal to that of the main flow; their viscosity is inversely proportional to the main flow shear rate, as a signature of shear-induced structural relaxation, in close similarity with the structural relaxations driven by temperature and density in other glassy systems.Comment: http://www.nature.com/nmat/journal/v9/n2/abs/nmat2615.htm

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

Prenatal Programming of Metabolic Syndrome in the Common Marmoset Is Associated With Increased Expression of 11β-Hydroxysteroid Dehydrogenase Type 1

OBJECTIVE: Recent studies in humans and animal models of obesity have shown increased adipose tissue activity of 11beta-hydroxysteroid dehydrogenase type 1 (11beta-HSD1), which amplifies local tissue glucocorticoid concentrations. The reasons for this 11beta-HSD1 dysregulation are unknown. Here, we tested whether 11beta-HSD1 expression, like the metabolic syndrome, is "programmed" by prenatal environmental events in a nonhuman primate model, the common marmoset monkey. RESEARCH DESIGN AND METHODS: We used a "fetal programming" paradigm where brief antenatal exposure to glucocorticoids leads to the metabolic syndrome in the offspring. Pregnant marmosets were given the synthetic glucocorticoid dexamethasone orally for 1 week in either early or late gestation, or they were given vehicle. Tissue 11beta-HSD1 and glucocorticoid receptor mRNA expression were examined in the offspring at 4 and 24 months of age. RESULTS: Prenatal dexamethasone administration, selectively during late gestation, resulted in early and persistent elevations in 11beta-HSD1 mRNA expression and activity in the liver, pancreas, and subcutaneous-but not visceral-fat. The increase in 11beta-HSD1 occurred before animals developed obesity or overt features of the metabolic syndrome. In contrast to rodents, in utero dexamethasone exposure did not alter glucocorticoid receptor expression in metabolic tissues in marmosets. CONCLUSIONS: These data suggest that long-term upregulation of 11beta-HSD1 in metabolically active tissues may follow prenatal "stress" hormone exposure and indicates a novel mechanism for fetal origins of adult obesity and the metabolic syndrome

Driven diffusion in a periodically compartmentalized tube: homogeneity versus intermittency of particle motion

We study the effect of a driving force F on drift and diffusion of a point Brownian particle in a tube formed by identical ylindrical compartments, which create periodic entropy barriers for the particle motion along the tube axis. The particle transport exhibits striking features: the effective mobility monotonically decreases with increasing F, and the effective diffusivity diverges as F → ∞, which indicates that the entropic effects in diffusive transport are enhanced by the driving force. Our consideration is based on two different scenarios of the particle motion at small and large F, homogeneous and intermittent, respectively. The scenarios are deduced from the careful analysis of statistics of the particle transition times between neighboring openings. From this qualitative picture, the limiting small-F and large-F behaviors of the effective mobility and diffusivity are derived analytically. Brownian dynamics simulations are used to find these quantities at intermediate values of the driving force for various compartment lengths and opening radii. This work shows that the driving force may lead to qualitatively different anomalous transport features, depending on the geometry design