Nonlinear symmetric stability of planetary atmospheres

The energy–Casimir method is applied to the problem of symmetric stability in the context of a compressible, hydrostatic planetary atmosphere with a general equation of state. Formal stability criteria for symmetric disturbances to a zonally symmetric baroclinic flow are obtained. In the special case of a perfect gas the results of Stevens (1983) are recovered. Finite-amplitude stability conditions are also obtained that provide an upper bound on a certain positive-definite measure of disturbance amplitude.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Time development of small disturbances to plane Couette Flow

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.

Seasonal to interannual Arctic sea-ice predictability in current GCMs

We establish the first inter-model comparison of seasonal to interannual predictability of present-day Arctic climate by performing coordinated sets of idealized ensemble predictions with four state-of-the-art global climate models. For Arctic sea-ice extent and volume, there is potential predictive skill for lead times of up to three years, and potential prediction errors have similar growth rates and magnitudes across the models. Spatial patterns of potential prediction errors differ substantially between the models, but some features are robust. Sea-ice concentration errors are largest in the marginal ice zone, and in winter they are almost zero away from the ice edge. Sea-ice thickness errors are amplified along the coasts of the Arctic Ocean, an effect that is dominated by sea-ice advection. These results give an upper bound on the ability of current global climate models to predict important aspects of Arctic climate.

Climate responses to anthropogenic emissions of short-lived climate pollutants

Policies to control air quality focus on mitigating emissions of aerosols and their precursors, and other short-lived climate pollutants (SLCPs). On a local scale, these policies will have beneficial impacts on health and crop yields, by reducing particulate matter (PM) and surface ozone concentrations; however, the climate impacts of reducing emissions of SLCPs are less straightforward to predict. In this paper we consider a set of idealised, extreme mitigation strategies, in which the total anthropogenic emissions of individual SLCP emissions species are removed. This provides an upper bound on the potential climate impacts of such air quality strategies. We focus on evaluating the climate responses to changes in anthropogenic emissions of aerosol precursor species: black carbon (BC), organic carbon (OC) and sulphur dioxide (SO2). We perform climate integrations with four fully coupled atmosphere-ocean global climate models (AOGCMs), and examine the effects on global and regional climate of removing the total land-based anthropogenic emissions of each of the three aerosol precursor species. We find that the SO2 emissions reductions lead to the strongest response, with all three models showing an increase in surface temperature focussed in the northern hemisphere high latitudes, and a corresponding increase in global mean precipitation and run-off. Changes in precipitation and run-off patterns are driven mostly by a northward shift in the ITCZ, consistent with the hemispherically asymmetric warming pattern driven by the emissions changes. The BC and OC emissions reductions give a much weaker forcing signal, and there is some disagreement between models in the sign of the climate responses to these perturbations. These differences between models are due largely to natural variability in sea-ice extent, circulation patterns and cloud changes. This large natural variability component to the signal when the ocean circulation and sea-ice are free-running means that the BC and OC mitigation measures do not necessarily lead to a discernible climate response.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen: (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes. (C) 2011 Elsevier B.V. All rights reserved.

EFFECTIVE NETWORKS FOR REAL-TIME DISTRIBUTED PROCESSING

This paper applies the concepts and methods of complex networks to the development of models and simulations of master-slave distributed real-time systems by introducing an upper bound in the allowable delivery time of the packets with computation results. Two representative interconnection models are taken into account: Uniformly random and scale free (Barabasi-Albert), including the presence of background traffic of packets. The obtained results include the identification of the uniformly random interconnectivity scheme as being largely more efficient than the scale-free counterpart. Also, increased latency tolerance of the application provides no help under congestion.

An information-theoretic approach to statistical dependence: Copula information

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum-entropy distribution. The idea of marginal invariant dependence measures is also discussed and used to show that empirical linear correlation underestimates the amplitude of the actual correlation in the case of non-Gaussian marginals. The mutual information is shown to provide an upper bound for the asymptotic empirical log-likelihood of a copula. An analytical expression for the information excess of T-copulas is provided, allowing for simple model identification within this family. We illustrate the framework in a financial data set. Copyright (C) EPLA, 2009

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

Bounds for the probability distribution function of the linear ACD process

This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p, q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.

From commitment to non-commitment: allowing type dynamic in Laffont and Tirole's regulation model

This paper investigates the introduction of type dynamic in the La ont and Tirole's regulation model. The regulator and the rm are engaged in a two period relationship governed by short-term contracts, where, the regulator observes cost but cannot distinguish how much of the cost is due to e ort on cost reduction or e ciency of rm's technology, named type. There is asymmetric information about the rm's type. Our model is developed in a framework in which the regulator learns with rm's choice in the rst period and uses that information to design the best second period incentive scheme. The regulator is aware of the possibility of changes in types and takes that into account. We show how type dynamic builds a bridge between com- mitment and non-commitment situations. In particular, the possibility of changing types mitigates the \ratchet e ect". We show that for small degree of type dynamic the equilibrium shows separation and the welfare achived is close to his upper bound (given by the commitment allocation).

General equilibrium model with restricted participation in financial markets

The paper analyses a general equilibrium model with financiaI markets in which households may face restrictions in trading financiaI assets such as borrowing constraints and collateral (restricted participation model). However, markets are not assumed to be incomplete. We consider a standard general equilibrium model with H > 1 households, 2 periods and S states of nature in the second period. We show that generically the set of equilibrium allocations ia indeterminate, provided the existence of at least one nominal asset and one household for who some restriction is binding. Suppose there are C > 1 commodities in each state of nature and assets pays in units of some commodity. In this case for each household with binding restrictions it is possible to reduce the set of feasible assets trading and obtain a new equilibrium that utility improve alI those households. There is however an upper bound on the number of households to be improved related to the number of states of nature and the number of commodities. In particular, if the number of households ia smaller than the number of states of nature it is possible to Pareto improve any equilibrium by reducing the feasible choice set for each household.

LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)