Critical ruptures in a bundle of slowly relaxing fibers

We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime ʧ of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life tʄ and the characteristic time tm of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of ʧ from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements

Noise and dynamics of self-organized critical phenomena

Different microscopic models exhibiting self-organized criticality are studied numerically and analytically. Numerical simulations are performed to compute critical exponents, mainly the dynamical exponent, and to check universality classes. We find that various models lead to the same exponent, but this universality class is sensitive to disorder. From the dynamic microscopic rules we obtain continuum equations with different sources of noise, which we call internal and external. Different correlations of the noise give rise to different critical behavior. A model for external noise is proposed that makes the upper critical dimensionality equal to 4 and leads to the possible existence of a phase transition above d=4. Limitations of the approach of these models by a simple nonlinear equation are discussed.

Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

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Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

On the critical periods of perturbed isochronous centers

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The Ideas Debate in International and European Studies: Towards a Cartography and Critical Assessment

The appeal to ideas as causal variables and/or constitutive features of political processes increasingly characterises political analysis. Yet, perhaps because of the pace of this ideational intrusion, too often ideas have simply been grafted onto pre-existing explanatory theories at precisely the point at which they seem to get into difficulties, with little or no consideration either of the status of such ideational variables or of the character or consistency of the resulting theoretical hybrid. This is particularly problematic for ideas are far from innocent variables – and can rarely, if ever, be incorporated seamlessly within existing explanatory and/or constitutive theories without ontological and epistemological consequence. We contend that this tendency along with the limitations of the prevailing Humean conception of causality, and associated epistemological polemic between causal and constitutive logics, continue to plague almost all of the literature that strives to accord an explanatory role to ideas. In trying to move beyond the current vogue for epistemological polemic, we argue that the incommensurability thesis between causal and constitutive logics is only credible in the context of a narrow, Humean, conception of causation. If we reject this in favour of a more inclusive (and ontologically realist) understanding then it is perfectly possible to chart the causal significance of constitutive processes and reconstrue the explanatory role of ideas as causally constitutive.

Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

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Environmental Kuznets Curves for Carbon Emissions: A Critical Survey

The empirical finding of an inverse U-shaped relationship between per capita income and pollution, the so-called Environmental Kuznets Curve (EKC), suggests that as countries experience economic growth, environmental deterioration decelerates and thus becomes less of an issue. Focusing on the prime example of carbon emissions, the present article provides a critical review of the new econometric techniques that have questioned the baseline polynomial specification in the EKC literature. We discuss issues related to the functional form, heterogeneity, “spurious” regressions and spatial dependence to address whether and to what extent the EKC can be observed. Despite these new approaches, there is still no clear-cut evidence supporting the existence of the EKC for carbon emissions. JEL classifications: C20; Q32; Q50; O13 Keywords: Environmental Kuznets Curve; Carbon emissions; Functional form; Heterogeneity; “Spurious” regressions; Spatial dependence.Residential satisfaction is often used as a barometer to assess the performance of public policy and programmes designed to raise individuals' well-being. However, the fact that responses elicited from residents might be biased by subjective, non-observable factors casts doubt on whether these responses can be taken as trustable indicators of the individuals' housing situation. Emotional factors such as aspirations or expectations might affect individuals' cognitions of their true residential situation. To disentangle this puzzle, we investigated whether identical residential attributes can be perceived differently depending on tenure status. Our results indicate that tenure status is crucial not only in determining the level of housing satisfaction, but also regarding how dwellers perceive their housing characteristics. Keywords: Housing satisfaction, subjective well-being, homeownership. JEL classification: D1, R2.

A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

A critical application of securitization theory: overcoming the normative dilemma of writing security

This article addresses the normative dilemma located within the application of `securitization,’ as a method of understanding the social construction of threats and security policies. Securitization as a theoretical and practical undertaking is being increasingly used by scholars and practitioners. This scholarly endeavour wishes to provide those wishing to engage with securitization with an alternative application of this theory; one which is sensitive to and self-reflective of the possible normative consequences of its employment. This article argues that discussing and analyzing securitization processes have normative implications, which is understood here to be the negative securitization of a referent. The negative securitization of a referent is asserted to be carried out through the unchallenged analysis of securitization processes which have emerged through relations of exclusion and power. It then offers a critical understanding and application of securitization studies as a way of overcoming the identified normative dilemma. First, it examines how the Copenhagen School’s formation of securitization theory gives rise to a normative dilemma, which is situated in the performative and symbolic power of security as a political invocation and theoretical concept. Second, it evaluates previous attempts to overcome the normative dilemma of securitization studies, outlining the obstacles that each individual proposal faces. Third, this article argues that the normative dilemma of applying securitization can be avoided by firstly, deconstructing the institutional power of security actors and dominant security subjectivities and secondly, by addressing countering or alternative approaches to security and incorporating different security subjectivities. Examples of the securitization of international terrorism and immigration are prominent throughout.

Power laws and scaling of rain events and dry spells in the Catalonia region

We analyze the statistics of rain-event sizes, rain-event durations, and dry-spell durations in a network of 20 rain gauges scattered in an area situated close to the NW Mediterranean coast. Power-law distributions emerge clearly for the dryspell durations, with an exponent around 1.50 ± 0.05, although for event sizes and durations the power-law ranges are rather limited, in some cases. Deviations from power-law behavior are attributed to finite-size effects. A scaling analysis helps to elucidate the situation, providing support for the existence of scale invariance in these distributions. It is remarkable that rain data of not very high resolution yield findings in agreement with self-organized critical phenomena.