Avalanches, breathers, and flow reversal in a continuous Lorenz-96 model

For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model

Stochastic resonance for nonequilibrium systems

Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy systems, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values. We propose here a general mathematical framework based on large deviation theory and, specifically, on the theory of quasipotentials, for describing SR in noisy N -dimensional nonequilibrium systems possessing two metastable states and undergoing a periodically modulated forcing. The drift and the volatility fields of the equations of motion can be fairly general, and the competing attractors of the deterministic dynamics and the edge state living on the basin boundary can, in principle, feature chaotic dynamics. Similarly, the perturbation field of the forcing can be fairly general. Our approach is able to recover as special cases the classical results previously presented in the literature for systems obeying detailed balance and allows for expressing the parameters describing SR and the statistics of residence times in the two-state approximation in terms of the unperturbed drift field, the volatility field, and the perturbation field. We clarify which specific properties of the forcing are relevant for amplifying or suppressing SR in a system and classify forcings according to classes of equivalence. Our results indicate a route for a detailed understanding of SR in rather general systems

Universal Properties of Nonlinear Response Functions of Nonequilibrium Steady States

We derive universal properties of nonlinear response functions of nonequilibrium steady states. In particular, sum rules and asymptotic behaviors are derived. Their consequences are illustrated for nonlinear optical materials and nonlinear electrical conductors.Comment: 10 pages, 1 figure; added a few sentences and references to explain detail

Dimension reduction of noisy interacting systems

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally, nonequilibrium setting. We provide a systematic dimension reduction methodology for constructing low-dimensional, reduced-order dynamics based on the cumulants of the probability distribution of the infinite system. We show that the low-dimensional dynamics returns the correct diagnostic properties since it produces a quantitatively accurate representation of the stationary phase diagram of the system that we compare with exact analytical results and numerical simulations. Moreover, we prove that the reduced order dynamics yields also the prognostic, i.e., time-dependent properties, as it provides the correct response of the system to external perturbations. On the one hand, this validates the use of our complexity reduction methodology since it retains information not only of the invariant measure of the system but also of the transition probabilities and time-dependent correlation properties of the stochastic dynamics. On the other hand, the breakdown of linear response properties is a key signature of the occurence of a phase transition. We show that the reduced response operators capture the correct diverging resonant behavior by quantitatively assessing the singular nature of the susceptibility of the system and the appearance of a pole for real values of frequencies. Hence, this methodology can be interpreted as a low-dimensional, reduced order approach to the investigation and detection of critical phenomena in high-dimensional interacting systems in settings where order parameters are not known

Coronary Artery Disease: A Study on the Joint Role of Birth Weight, Adenosine Deaminase, and Gender

An inverse relationship between birth weight and coronary artery diseases is well documented but it remains unclear which exposure in early life might underlie such association. Recently it has been reported an association between adenosine deaminase genetic polymorphism and coronary artery diseases. Gender differences in the degree of this association have been also observed. These observations prompted us to study the possible joint effects of BW, ADA, and gender on the susceptibility to coronary artery diseases. 222 subjects admitted to hospital for nonfatal coronary artery diseases, and 762 healthy consecutive newborns were studied. ADA genotypes were determined by DNA analysis. A highly significant complex relationship has emerged among ADA, birth weight, and gender concerning their role on susceptibility to coronary artery diseases in adult life. Odds ratio analysis suggests that low birth weight is more important in females than in males. ADA∗2 allele appears protective in males, while in females such effect is obscured by birth weight

Phosphotyrosine-protein-phosphatases and human reproduction: an association between low molecular weight acid phosphatase (ACP1) and spontaneous abortion.

ACP1 (low molecular weight acid phosphatase) genetic polymorphism has been studied in 173 women with a history of two or more consecutive spontaneous abortions and in 1508 control subjects, including 482 normal pregnant women. The proportion of carriers of ACP1 *C allele (* A/ *C, *B/*C) in women with a history of repeated spontaneous abortion is lower than in normal pregnant women and other control groups, Women with repeated spontaneous abortion show a specific decrease of ACPI S isoform concentration as compared to normal pregnant women, The other component of ACP I activity, the F isoform, does not show a significant difference between the two groups. The data suggest that women with ACP1 genotypes showing a high concentration of S isoform are relatively 'protected' against spontaneous abortion, Preliminary analysis of a sample of 352 normal puerperae along with their newborn babies supports this hypothesis

How to be causal: time, spacetime, and spectra

I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers Kronig relations. The specification of causality in terms of temporal differential eqations then shows us the way to write down dynamical models so that their causal nature /in the sense used here/ should be obvious to all. To extend existing treatments of causality that work only in the frequency domain, I derive a reformulation of the long-standing Kramers Kronig relations applicable not only to just temporal causality, but also to spacetime "light-cone" causality based on signals carried by waves. I also apply this causal reasoning to Maxwell's equations, which is an instructive example since their casual properties are sometimes debated.Comment: v4 - add Appdx A, "discrete" picture (not in EJP); v5 - add Appdx B, cause classification/frames (not in EJP); v7 - unusual model case; v8 add reference

Habitability and multistability in earth-like planets

We explore the potential multistability of the climate for a planet around the habitable zone. We focus on conditions reminiscent to those of the Earth system, but our investigation aims at presenting a general methodology for dealing with exoplanets. We provide a thorough analysis of the non-equilibrium thermodynamical properties of the climate system and explore, using a a flexible climate model, how such properties depend on the energy input of the parent star, on the infrared atmospheric opacity, and on the rotation rate. It is possible to reproduce the multi-stability properties reminiscent of the paleoclimatologically relevant snowball (SB) - warm (W) conditions. We then study the thermodynamics of the W and SB states, clarifying the role of the hydrological cycle in shaping the irreversibility and the efficiency of the W states, and emphasizing the extreme diversity of the SB states, where dry conditions are realized. Thermodynamics provides the clue for studying the tipping points of the system and leads us to constructing parametrizations where the main thermodynamic properties are expressed as functions of the emission temperature of the planet only. Such functions are rather robust with respect to changing the rotation rate of the planet from the current terrestrial one to half of it. We then explore the dynamical range of slowy rotating and phase locked planets. There is a critical rotation rate below which the multi-stability properties are lost. Such critical rotation rate corresponds roughly to the phase lock 2:1 condition. Therefore, if an Earth-like planet is 1:1 phase locked with respect to the parent star, only one climatic state would be compatible with a given set of astronomical and astrophysical parameters. These results have relevance for the general theory of planetary circulation and for the definition of necessary and sufficient conditions for habitability

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

Response formulae for n-point correlations in statistical mechanical systems and application to a problem of coarse graining

Predicting the response of a system to perturbations is a key challenge in mathematical and natural sciences. Under suitable conditions on the nature of the system, of the perturbation, and of the observables of interest, response theories allow to construct operators describing the smooth change of the invariant measure of the system of interest as a function of the small parameter controlling the intensity of the perturbation. In particular, response theories can be developed both for stochastic and chaotic deterministic dynamical systems, where in the latter case stricter conditions imposing some degree of structural stability are required. In this paper we extend previous findings and derive general response formulae describing how n-point correlations are affected by perturbations to the vector flow. We also show how to compute the response of the spectral properties of the system to perturbations. We then apply our results to the seemingly unrelated problem of coarse graining in multiscale systems: we find explicit formulae describing the change in the terms describing parameterisation of the neglected degrees of freedom resulting from applying perturbations to the full system. All the terms envisioned by the Mori-Zwanzig theory - the deterministic, stochastic, and non-Markovian terms - are affected at 1st order in the perturbation. The obtained results provide a more comprehesive understanding of the response of statistical mechanical systems to perturbations and contribute to the goal of constructing accurate and robust parameterisations and are of potential relevance for fields like molecular dynamics, condensed matter, and geophysical fluid dynamics. We envision possible applications of our general results to the study of the response of climate variability to anthropogenic and natural forcing and to the study of the equivalence of thermostatted statistical mechanical systems