DM - Artículos de Revistashttp://hdl.handle.net/10016/58552016-09-30T22:01:26Z2016-09-30T22:01:26ZUnbounded solutions of the nonlocal heat equationBrandle, C.Chasseigne, E.Ferreira, Raúlhttp://hdl.handle.net/10016/221862016-02-08T12:28:30Z2011-11-01T00:00:00ZUnbounded solutions of the nonlocal heat equation
Brandle, C.; Chasseigne, E.; Ferreira, Raúl
We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: where is a symmetric continuous probability density. Depending on the tail of , we give a rather complete picture of the problem in optimal classes of data by: estimating the initial trace of (possibly unbounded) solutions; showing existence and uniqueness results in a suitable class; proving blow-up in finite time in the case of some critical growths; giving explicit unbounded polynomial solutions.
2011-11-01T00:00:00ZTowards a proper assignment of systemic risk: the combined roles of network topology and shock characteristicsLoepfe, LasseCabrales, AntonioSánchez, Angelhttp://hdl.handle.net/10016/213972015-07-27T08:58:21Z2013-10-17T00:00:00ZTowards a proper assignment of systemic risk: the combined roles of network topology and shock characteristics
Loepfe, Lasse; Cabrales, Antonio; Sánchez, Angel
The 2007-2008 financial crisis solidified the consensus among policymakers that a macro-prudential approach to regulation and supervision should be adopted. The currently preferred policy option is the regulation of capital requirements, with the main focus on combating procyclicality and on identifying the banks that have a high systemic importance, those that are "too big to fail". Here we argue that the concept of systemic risk should include the analysis of the system as a whole and we explore systematically the most important properties for policy purposes of networks topology on resistance to shocks. In a thorough study going from analytical models to empirical data, we show two sharp transitions from safe to risky regimes: 1) diversification becomes harmful with just a small fraction (~2%) of the shocks sampled from a fat tailed shock distributions and 2) when large shocks are present a critical link density exists where an effective giant cluster forms and most firms become vulnerable. This threshold depends on the network topology, especially on modularity. Firm size heterogeneity has important but diverse effects that are heavily dependent on shock characteristics. Similarly, degree heterogeneity increases vulnerability only when shocks are directed at the most connected firms. Furthermore, by studying the structure of the core of the transnational corporation network from real data, we show that its stability could be clearly increased by removing some of the links with highest centrality betweeness. Our results provide a novel insight and arguments for policy makers to focus surveillance on the connections between firms, in addition to capital requirements directed at the nodes.
This proceeding at: European Conference on Complex Systems, took place 2013, setember, 16-20, in Barcelona (Spain).
2013-10-17T00:00:00ZOn the nature of radial transport across sheared zonal flows in electrostatic ion-temperature-gradient gyrokinetic tokamak plasma turbulenceSánchez, RaúlNewman, David E.Leboeuf, J.-N.Carreras, Benjamín A.Decyk, V. K.http://hdl.handle.net/10016/91092013-09-30T16:58:59Z2009-05-01T00:00:00ZOn the nature of radial transport across sheared zonal flows in electrostatic ion-temperature-gradient gyrokinetic tokamak plasma turbulence
Sánchez, Raúl; Newman, David E.; Leboeuf, J.-N.; Carreras, Benjamín A.; Decyk, V. K.
It is argued that the usual understanding of the suppression of radial turbulent transport across a sheared zonal flow based on a reduction in effective transport coefficients is, by itself, incomplete. By means of toroidal gyrokinetic simulations of electrostatic, ion-temperature-gradient turbulence, it is found instead that the character of the radial transport is altered fundamentally by the presence of a sheared zonal flow, changing from diffusive to anticorrelated and subdiffusive. Furthermore, if the flows are self-consistently driven by the turbulence via the Reynolds stresses (in contrast to being induced externally), radial transport becomes non-Gaussian as well. These results warrant a reevaluation of the traditional description of radial transport across sheared flows in tokamaks via effective transport coefficients, suggesting that such description is oversimplified and poorly captures the underlying dynamics, which may in turn compromise its predictive capabilities.
11 pages, 12 figures.-- PACS nrs.: 52.35.Ra, 52.55.Fa, 05.40.Fb.
2009-05-01T00:00:00ZFinite temperature field theory on the Moyal planeAkofor, EarnestBalachandran, Aiyalan P.http://hdl.handle.net/10016/69362013-09-30T17:03:54Z2009-08-01T00:00:00ZFinite temperature field theory on the Moyal plane
Akofor, Earnest; Balachandran, Aiyalan P.
In this paper, we initiate the study of finite temperature quantum field theories on the Moyal plane. Such theories violate causality which influences the properties of these theories. In particular, causality influences the fluctuation-dissipation theorem: as we show, a disturbance in a space-time region M1 creates a response in a space-time region M2 spacelike with respect to M1 (M1×M2). The relativistic Kubo formula with and without noncommutativity is discussed in detail, and the modified properties of relaxation time and the dependence of mean square fluctuations on time are derived. In particular, the Sinha-Sorkin result [Phys. Rev. B 45, 8123 (1992)] on the logarithmic time dependence of the mean square fluctuations is discussed in our context. We derive an exact formula for the noncommutative susceptibility in terms of the susceptibility for the corresponding commutative case. It shows that noncommutative corrections in the four-momentum space have remarkable periodicity properties as a function of the four-momentum k. They have direction dependence as well and vanish for certain directions of the spatial momentum. These are striking observable signals for noncommutativity. The Lehmann representation is also generalized to any value of the noncommutativity parameter θ(μν) and finite temperatures.
10 pages, no figures.-- PACS nr.: 11.10.Wx.-- ArXiv pre-print available at: http://arxiv.org/abs/0907.0905v1.pdf
2009-08-01T00:00:00Z