Mean Curvature Flow on Ricci Solitons

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat type equation integrated over embedded submanifolds evolving by mean curvature flow and we study their monotonicity properties. This is part of an ongoing project with Magni and Mantegazzawhich will treat the case of non-solitonic backgrounds \cite{a_14}.Comment: 19 page

The Simplicial Ricci Tensor

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area -- an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimension.Comment: 19 pages, 2 figure

Exploring the synergy between promoting active participation in work and in society and social, health and long-term care strategies

The purpose of this study is to provide information that can help the Commission and EU Member States engage in policy discussion on how social, health and long-term care systems can help enhance participation in work and family, social and community activities and how, in turn, participation in paid employment, family, social and community activities can contribute to healthy and autonomous living at present and in the future. Part I presents a review of the literature on the synergy between health and activity/work. Health affects work and social participation but on the other side work and activity affect health. We focus on people aged 55 and over as this interrelation (double causality) seems to be significant for important life events (retirement decision, social participation, etc.) of this age group. Part II presents a quantitative analysis and tries to identify national specificities. It presents the lessons which we can draw from European surveys. It presents a quantitative analysis based on the LFS, the EU-SILC, the ECHP UDB and SHARE surveys. The fourth step summarises national policies and gives a comparative analysis, while the fifth step presents the best practices. Finally, the last part summarises the main conclusions and the policy implications

Investigating Off-shell Stability of Anti-de Sitter Space in String Theory

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow, and then show this implies its geometric stability with respect to Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.Comment: 29 pages, references added in this version to appear in Classical and Quantum Gravit

Against the Tide. A Critical Review by Scientists of How Physics and Astronomy Get Done

Nobody should have a monopoly of the truth in this universe. The censorship and suppression of challenging ideas against the tide of mainstream research, the blacklisting of scientists, for instance, is neither the best way to do and filter science, nor to promote progress in the human knowledge. The removal of good and novel ideas from the scientific stage is very detrimental to the pursuit of the truth. There are instances in which a mere unqualified belief can occasionally be converted into a generally accepted scientific theory through the screening action of refereed literature and meetings planned by the scientific organizing committees and through the distribution of funds controlled by "club opinions". It leads to unitary paradigms and unitary thinking not necessarily associated to the unique truth. This is the topic of this book: to critically analyze the problems of the official (and sometimes illicit) mechanisms under which current science (physics and astronomy in particular) is being administered and filtered today, along with the onerous consequences these mechanisms have on all of us.\ud \ud The authors, all of them professional researchers, reveal a pessimistic view of the miseries of the actual system, while a glimmer of hope remains in the "leitmotiv" claim towards the freedom in doing research and attaining an acceptable level of ethics in science

Topological mirror symmetry with fluxes

Motivated by SU(3) structure compactifications, we show explicitly how to construct half--flat topological mirrors to Calabi--Yau manifolds with NS fluxes. Units of flux are exchanged with torsion factors in the cohomology of the mirror; this is the topological complement of previous differential--geometric mirror rules. The construction modifies explicit SYZ fibrations for compact Calabi--Yaus. The results are of independent interest for SU(3) compactifications. For example one can exhibit explicitly which massive forms should be used for Kaluza--Klein reduction, proving previous conjectures. Formality shows that these forms carry no topological information; this is also confirmed by infrared limits and old classification theorems.Comment: 35 pages, 5 figure

On the nonlinear stability of mKdV breathers

A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.Comment: 7 p

Functional Responses of South African Rangelands in Contrasting Tenure Systems

Land degradation in South African rangelands has frequently been studied in the context of tenure systems, because both governmental policy and range management practices were historically implemented in contrasting forms. We compared the functional response of vegetation along grazing gradients between a communal (CU) and commercial (CO) farming areas. One transect was established per farm from the waterpoint to a mid-field position. Six equally spaced plots (5 m × 5 m) were set up along each transect. Using a taxon-free sampling procedure, we recorded the response of 15 community-aggregated plant functional traits (CPFT) in: (1) mature standing biomass; and (2) after four weeks’ regrowth following clipping. Additionally, species identity was recorded. Grazing on CU was continuous and stocking rate not controlled, while CO applied rotational grazing with recommended stocking rates. From the results, CPFT differences were not significant (Student’s t-test, P \u3c 0.01) between tenure systems. A principal component analysis of CPFT showed largely overlapping functional responses in the two tenure systems in the case of mature standing biomass, while the functional response of regrowing vegetation was clearly separated in the ordination space. Communal rangelands had twice the species richness of commercial farms.We concluded that, from a functional perspective, communities under different tenure systems were similar. However, the functional response of vegetation regrowth might be different as well as the ecological services provided (biodiversity)

Dirichlet sigma models and mean curvature flow

The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renormalization group equation of Dirichlet sigma models away from conformality, to lowest order in perturbation theory. D-branes appear as fixed points of this flow having conformally invariant boundary conditions. Simple running solutions include the paper-clip and the hair-pin (or grim-reaper) models on the plane, as well as scaling solutions associated to rational (p, q) closed curves and the decay of two intersecting lines. Stability analysis is performed in several cases while searching for transitions among different brane configurations. The combination of Ricci with the mean curvature flow is examined in detail together with several explicit examples of deforming curves on curved backgrounds. Some general aspects of the mean curvature flow in higher dimensional ambient spaces are also discussed and obtain consistent truncations to lower dimensional systems. Selected physical applications are mentioned in the text, including tachyon condensation in open string theory and the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure