On the geometrization of matter by exotic smoothness

In this paper we discuss the question how matter may emerge from space. For that purpose we consider the smoothness structure of spacetime as underlying structure for a geometrical model of matter. For a large class of compact 4-manifolds, the elliptic surfaces, one is able to apply the knot surgery of Fintushel and Stern to change the smoothness structure. The influence of this surgery to the Einstein-Hilbert action is discussed. Using the Weierstrass representation, we are able to show that the knotted torus used in knot surgery is represented by a spinor fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. For sufficient complicated links and knots, there are "connecting tubes" (graph manifolds, torus bundles) which introduce an action term of a gauge field. Both terms are genuinely geometrical and characterized by the mean curvature of the components. We also discuss the gauge group of the theory to be U(1)xSU(2)xSU(3).Comment: 30 pages, 3 figures, svjour style, complete reworking now using Fintushel-Stern knot surgery of elliptic surfaces, discussion of Lorentz metric and global hyperbolicity for exotic 4-manifolds added, final version for publication in Gen. Rel. Grav, small typos errors fixe

From dynamical scaling to local scale-invariance: a tutorial

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schr\"odinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for

Integrated assessment of social and environmental sustainability dynamics in the Ganges-Brahmaputra-Meghna delta, Bangladesh

Deltas provide diverse ecosystem services and benefits for their populations. At the same time, deltas are also recognised as one of the most vulnerable coastal environments, with a range of drivers operating at multiple scales, from global climate change and sea-level rise to deltaic-scale subsidence and land cover change. These drivers threaten these ecosystem services, which often provide livelihoods for the poorest communities in these regions. The imperative to maintain ecosystem services presents a development challenge: how to develop deltaic areas in ways that are sustainable and benefit all residents including the most vulnerable. Here we present an integrated framework to analyse changing ecosystem services in deltas and the implications for human well-being, focussing in particular on the provisioning ecosystem services of agriculture, inland and offshore capture fisheries, aquaculture and mangroves that directly support livelihoods. The framework is applied to the world’s most populated delta, the Ganges-Brahmaputra-Meghna Delta within Bangladesh. The framework adopts a systemic perspective to represent the principal biophysical and socio-ecological components and their interaction. A range of methods are integrated within a quantitative framework, including biophysical and socio-economic modelling and analyses of governance through scenario development. The approach is iterative, with learning both within the project team and with national policy-making stakeholders. The analysis is used to explore physical and social outcomes for the delta under different scenarios and policy choices. We consider how the approach is transferable to other deltas and potentially other coastal areas

Role of chaos for the validity of statistical mechanics laws: diffusion and conduction

Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the problem of diffusion and heat conduction in deterministic systems. Is microscopic chaos a necessary ingredient to observe such macroscopic phenomena?Comment: Latex, 27 pages, 10 eps-figures. Proceedings of the Conference "FPU 50 years since" Rome 7-8 May 200