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The early stages of self-assembly of the elementary building blocks of nanophase materials are studied. The relative roles of entropic and energetic factors in determining the relative abundance of the final products present is analyzed using both a kinetic mean field model and a mesoscopic approach in which self-assembly is viewed as an encounter-controlled process on a discrete lattice. The relevance of the results in zeolite synthesis in connection with the ordered liquid phases recently discovered in these materials is discussed. [ABSTRACT FROM AUTHOR]

Evaluates thermodynamic entropy production in different parts of the attractor of two representative reactive models giving rise to periodic and chaotic behavior. Variability patterns observed as the system runs over the attractor; Comparison with the variability of indicators of the intrinsic complexity of the dynamics such as the local Lyapunov exponents.

General expressions for the dynamical behaviour of prediction errors of time-averaged observables involved in extended-range forecasts are derived and applied to systems giving rise to chaotic dynamics, systems close to criticalities and stochastically forced systems. The role of the initial conditions, of the parameters present and of the averaging period, in the properties of the error, and in particular in the predictability gain with respect to the error associated with the instantaneous observables, are revealed, providing insights on optimal choices of this period depending on the intrinsic properties of the system of interest. [ABSTRACT FROM AUTHOR]

A linear response theory of systems of interest in atmospheric and climate dynamics taking fully into account the nonlinearities of the underlying processes is developed. Under the assumption that the source of intrinsic variability can be modeled as a white-noise process, a Fokker-Planck equation approach leads to fluctuation-dissipation-type expressions in the form of time cross-correlation functions, linking the perturbation-induced shift of an observable to the statistical and dynamical properties of the reference system. These expressions feature a generalized potential function and enable one to go systematically beyond the Gaussian approximation usually adopted in the literature. Full solutions and explicit expressions are derived for different subclasses of systems, including a global climate model giving rise to oscillatory behavior. [ABSTRACT FROM AUTHOR]

We present a comparative analysis of sequential versus hierarchical mechanisms of self-assembly in supramolecular architectures. The analysis is multifaceted, drawing on and inter-relating insights from a kinetic mean-field analysis and one based on the theory of finite Markov processes, complemented by Monte Carlo calculations. We give explicit results for two reaction pathways that are likely to dominate in early stages of self-assembly, and draw attention to experimental studies to which our results pertain: crystallization of zeolites from the bulk phase and aggregation of surface-supported supramolecular structures. Among the several conclusions that can be drawn from the theory and the simulations is a crossover from one mechanism to another, depending on the values of system parameters. [ABSTRACT FROM AUTHOR]

We review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deterministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction. Two important results refer to (i) the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum; and (ii) the need for coupled modeling of natural and socio-economic systems. Both these results have implications for the study and prediction of natural hazards and their human impacts. [ABSTRACT FROM AUTHOR]

The transient evolution of prediction errors in the short to intermediate time regime is considered under the combined effect of initial condition and model errors. Some generic features are brought out and connected with intrinsic properties. Under the assumption of small uncorrelated initial errors and of small parameter errors, the conditions of existence of a time at which the mean quadratic error reaches a minimum and of a crossover time at which the contribution of initial condition errors matches that of model errors are determined. The results are illustrated and tested on representative low-order models of atmospheric dynamics exhibiting bistability, saddle-point behavior, and chaotic behavior. [ABSTRACT FROM AUTHOR]

We consider the distribution of the maximum for finite, deterministic, periodic and quasiperiodic sequences, and contrast the extreme value distributions in these cases with the classical results for iidrv's. A significant feature in the case of deterministic sequences is a multi-step structure for the distribution function. The extreme value distribution for the circle map with an irrational parameter is obtained in closed form with the help of the three-gap theorem for the map Xj+1 = (Xj + a) mod 1 where a ∈ (0,1) is an irrational number. [ABSTRACT FROM AUTHOR]

The dynamical properties of forecasts corrected using model output statistics (MOS) schemes are explored, with emphasis on the respective role of model and initial condition uncertainties. Analytical and numerical investigations of low-order systems displaying chaos indicate that MOS schemes are able to partly correct the impact of both initial and model errors on model forecasting. Nevertheless the amplitude of the correction is much more sensitive to the presence of (state dependent) model errors, and if initial condition errors are much larger than model uncertainties then MOS schemes become less effective. Furthermore, the amplitude of the MOS correction depends strongly on the statistical properties of the phase space velocity difference between the model and reference systems, such as its mean and its covariance with the model predictors in the MOS scheme. Large corrections are expected when the predictors are closely related to the sources of model errors. The practical implications of these results are briefly discussed. [ABSTRACT FROM AUTHOR]

The different modes of the early stages of the response of a forecasting model to a small error in the boundary conditions are analyzed. A general formulation of the problem based on the use of Green’s functions is developed and implemented on systems in which the operators acting on the spatial coordinates of the fields involved are diffusion-like and advection-like. It is shown that the generic behavior displays a nonanalytic structure not reducible to a power of time for short times. [ABSTRACT FROM AUTHOR]

A connection between dynamical systems and network theory is outlined based on a mapping of the dynamics into a discrete probabilistic process, whereby the phase space is partitioned into finite size cells. It is found that the connectivity patterns of networks generated by deterministic systems can be related to the indicators of the dynamics such as local Lyapunov exponents. The procedure is extended to networks generated by stochastic processes. [ABSTRACT FROM AUTHOR]

A systematic formulation of model error is developed accounting for both its dynamical and probabilistic aspects. Some generic features, largely independent of the particular model under consideration, are brought out in connection with power-law behavior in the short time regime. The lifetime of this regime is shown to be related to the spectrum of the Lyapunov exponents and the decay characteristics of the time correlation functions involved. The results are illustrated and tested on representative low-order models of atmospheric dynamics exhibiting oscillations, bistability, and chaotic behavior. [ABSTRACT FROM AUTHOR]

The coexistence of different regimes in a class of atmospheric flow models is analyzed from the standpoint of irreversible thermodynamics. The entropy production, measuring the degree of dissipation within the system is evaluated across the bifurcation point. Some interesting trends are brought out, regarding the relative importance of dissipation in two qualitatively different circulation regimes referred to as zonal and blocked flows. It is shown that in the presence of stochastic disturbances entropy production exhibits critical behavior both in the vicinity of the bifurcation point and in parameter values where the two flow regimes are equally probable. [ABSTRACT FROM AUTHOR]

Rainfall is a highly intermittent field over a wide range of time and space scales. We study a high resolution rainfall time series exhibiting large intensity fluctuations and localized events. We consider the return times of a given intensity, and show that the time series composed of these return times is itself also very intermittent, obeying to a hyperbolic probability density, entailing that the mean return time diverges. This is an unexpected property since mean return times are often introduced in meteorology, especially for the study of risk associated to extreme events. It suggests that the intermittency of first return times of extreme events should be taken into account when making statistical predictions. [ABSTRACT FROM AUTHOR]

An exact expression is derived for the distribution of successive recurrences in a finitecell partition of a general family of one-dimensional maps exhibiting intermittent chaos due to a tangency at a marginally stable fixed point, characterized by an index α. It is shown that multiple recurrences are not statistically independent events in the strict sense of the term. The asymptotic factorization of the joint distribution into a product of first recurrence time distributions is also analyzed. [ABSTRACT FROM AUTHOR]

Provides information on a study which applied thermodynamics to the shallow water model. Details on Lorenz's shallow water model; Formulation of energy dissipation and entropy balance in the shallow water model; Conclusions.

Different strategies for building high-resolution models providing a more detailed description of a limited area of interest as for example, in regional weather forecasts are developed. They are subsequently compared, on the basis of the dynamical behavior generated by the corresponding models. The statistical properties of the relevant fields are analyzed, and predictability experiments are performed on statistical ensembles of close lying trajectories whose mean distance represents the uncertainty in the initial state of the system. The results show that a global, variable-mesh model performs much better than a limited area fine mesh one embedded into a coarser global model. [ABSTRACT FROM AUTHOR]

Presents information on a dynamical approach to atmospheric analogs extending the statistical formulation. Who developed the formulation; Details on explicit analytical formulas; Indication of an analysis of this formula; Identification of the findings of the analysis.

Presents a systematic study on the short and intermediate time predictability properties of a quasigeostrophic T21L3 model in which emphasis is placed on the role of the Lyapunov vectors in the growth patterns of generic initial error fields. The atmospheric model; Error dynamics; Damping timescales and norms.

Investigates the properties of the time-averaged observables of a red noise atmosphere and of a simplified model of thermal convection. Lorenz model and its `climate;' Averaging, error growth and predictability.

The effect of fluctuations on a simple energy balance model is examined. A new, long characteristic time scale referring to the passage between different stable climatic states is identified. It is shown that a weak external forcing whose period is comparable to this scale enables the system to switch between different states with a high probability. The connection with glaciation cycles is pointed out. [ABSTRACT FROM AUTHOR]

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We investigate the probabilistic properties of recurrence times for the simplest form of aperiodic deterministic dynamics, quasi-periodic motion. Previous results using number theory techniques predict two fundamental recurrence times for uniform quasi-periodic motion on a two-dimensional torus, while no analogous analytic result seems to exist for higher dimensional tori. The two-dimensional uniform case is reanalyzed from a more geometric point of view and new, workable expressions are derived that enable us fully to understand and predict the recurrence phenomenon and to analyze its parameter dependence. Emphasis is placed on the statistical properties and, in particular, on the variability of recurrence times around their mean, in relation to local Farey tree structure. Higher-dimensional tori are considered, and seen to also display a high variability in their finite-time recurrence behavior. The results are finally extended to the non-uniform quasi-periodic case. [ABSTRACT FROM AUTHOR]

The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markow maps the recurrence problem is cast into a-renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values. [ABSTRACT FROM AUTHOR]

Climatic variability arising from the coupling between ocean temperature and sea-ice extent is studied in a spatially distributed system. A spatial degree of freedom is crudely introduced by the coupling, through energy transfer, of two 'box models' each of which describes a different space region. The evolution equations are cast into a normal form and some qualitative features of this general class of models are predicted. It is shown, both analytically and numerically, that internally generated complexity in the form of aperiodic behaviour can be a natural consequence of spatially distributed systems. [ABSTRACT FROM AUTHOR]