Duality Rotations in Nonlinear Electrodynamics and in Extended Supergravity

We review the general theory of duality rotations which, in four dimensions, exchange electric with magnetic fields. Necessary and sufficient conditions in order for a theory to have duality symmetry are established. A nontrivial example is Born-Infeld theory with n abelian gauge fields and with Sp(2n,R) self-duality. We then review duality symmetry in supergravity theories. In the case of N=2 supergravity duality rotations are in general not a symmetry of the theory but a key ingredient in order to formulate the theory itself. This is due to the beautiful relation between the geometry of special Kaehler manifolds and duality rotations.Comment: Invited contribution to Rivista del Nuovo Cimento in occasion of the 2005 Enrico Fermi Prize of the Italian Physical Society. 96 pages, corrected typo

Risk-seeking behavior of preschool children in a gambling task

A recent neurobiology study showed that monkeys systematically prefer risky targets in a visual gambling task. We set a similar experiment with preschool children to assess their attitudes toward risk and found the children, like the monkeys, to be risk seeking. This suggests that adult humans are not born risk averse, but become risk averse. Our experiment also suggests that this behavioral change may be due to learning from negative experiences in their risky choices. We also showed that though emotional states and predetermined prenatal testosterone can influence children’s preferences toward risk, these factors could not override learning experiences.Risk; Children

Nonlinear normal modes of a two degree of freedom oscillator with a bilateral elastic stop

A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to obtain the Nonlinear Normal Mode (NNM), the harmonic balance method with a large number of harmonics, combined with the asymptotic numerical method, is used to solve the regularized problem. These methods are present in the software "package" MANLAB. The results are validated from periodic orbits obtained analytically in the time domain by direct integration of the non regular problem. The two NNMs starting respectively from the two linear normal modes of the associated underlying linear system are discussed. The energy-frequency plot is used to present a global vision of the behavior of the modes. The dynamics of the modes are also analyzed comparing each periodic orbits and modal lines. The first NNM shows an elaborate dynamics with the occurrence of multiple impacts per period. On the other hand, the second NNM presents a more simple dynamics with a localization of the displacement on the first mass

Duality, Entropy and ADM Mass in Supergravity

We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both "large" and "small" extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.Comment: 45 pages, typos corrected, references adde

La crisi e le responsabilità della teoria economica: la paura della complessità

The debate on the financial crisis risks to hide the black holes which are nested in accepted theories and policy guidelines. Among such black holes there are important issues: how money is created in a growing economy, which is the role of wealth assets not linked with current production, which are the relations between such phenomena and monetary savings, how chronological time affects production and in its changes, how the emergence of sophisticated contracts and the explosion of discretionary behaviours have complicated the problem of coordination. The paper, which aims at reaching an audience of social scientists wider than the economists’ community, shows that the endogenous creation of money for financing the productive activities (Wicksell) is unlikely to be sufficient to feed a moving economy. Additional money is likely to be needed. It can be provided by public deficit or by credit going to finance speculative investments. In the meanwhile monetary savings have a high probability to result, in developed economies, in excess with respect to productive investments. These interrelated elements may imply an inflation concerning the prices of unproductive assets and a possible displacement of real activities. However, while the inflation concerning productive flows is considered as an evil, everybody seems to be happy when the values of assets not directly connected with current production increase, and the central banks end up admitting that they support such tendencies. The paper discusses how we ought to revise policy strategies, favouring a non-Keynesian policy of deficit spending linked to long lasting programs and adopting banking policies for the financing of industrial projects.

Versatilità, produzione e tempo: i fondamenti dei cambiamenti economici

Despite Böhm Bawerk early hints, few contributions deal with the fact that production takes time –so that in each period a share of workers is allocated to build the capacity that will feed the future production of consumption goods- and its consequences, which are relevant, in terms of cost structures and of coordination, out of steady dynamics, when changes occur. There are two different perspectives, a sectoral one (Hicks 1965; Löwe 1976), and the Neo Austrian one (Hicks 1970, 1973), further developed by Amendola and Gaffard. In the first approach both capital and consumption goods require previously produced specific capital capacities; in the second one the only factor is labour. Löwe has been correctly criticised because his model, by assuming malleability of capital when innovations occur, fails to capture the problems raised by the construction of a different capacity. This brought Amendola to conclude that any sectoral approach forestalls to consider the problems connected to changes. My paper provides a sectoral model that escapes such criticisms and allows to perform the same out-of-equilibrium analyses which are allowed by the Neo Austrian one. It shows that the core of the problem is connected with the, always limited, versatility not only of labour but also of technologies. A new way of regarding the problem of innovation, based on the concept of “transition technology”, is set up. The evolution of technologies and of productions is thus regarded as a long chain of efforts which began when human beings first discovered that utensils could be used not only for better producing consumption goods, but also to produce better utensils. The conclusion is that what we are today depends on this chain rooted in our past history, a debt that cannot be acknowledged in terms of value, but only because it exists; the only way we have to pay it back is through efforts for building today the conditions for a better future.

SMC west halo: a slice of the galaxy that is being tidally stripped? Star clusters trace age and metallicity gradients

(ABRIDGED) The evolution and structure of the Magellanic Clouds is presently under debate. The classical scenario where both the Large and Small Magellanic Clouds (LMC, SMC) are orbiting the Milky Way has been challenged by an alternative where the LMC and SMC are in their first close passage to our Galaxy. Detailed studies of stellar populations in the galaxies should constrain the proposed scenarios. In particular, the west halo of the SMC was recently characterized with radial trends in age and metallicity which indicates tidal disruption. We increase the sample of star clusters in the west halo of the SMC with homogeneous age, metallicity, and distance derivations, to determine better age and metallicity gradients. Comparisons of observed and synthetic V,(B-V) colour-magnitude diagrams are used to derive parameters for west halo star clusters. We derived age and metallicity for the reference cluster NGC 152 compatible with literature parameters. Age and metallicity gradients are confirmed in the west halo: 2.6 +/- 0.6 Gyr/deg and -0.19 +/- 0.09 dex/deg, respectively. Age-metallicity relation for the west halo has low dispersion in metallicity and it is compatible with a burst model of chemical enrichment. All WH clusters seem to follow the same predicted stellar distribution, with exception of AM-3 that should belong to the counter-bridge. Bruck 6 is only 130 +/- 40 Myr old and it could have been formed during a recent tidal interaction of the SMC-LMC. We suggest that it is crucial to split the SMC cluster population in groups: main body, wing/bridge, counter-bridge and west halo. This is the way to analyse the complex star formation and dynamical history of our neighbour. In particular we show that west halo has clear age and metallicity gradients and age-metallicity relation, also compatible with the dynamical model of tidal influence of the LMC over the SMC.Comment: 17 pages, 16 figures, 6 tables, in press in A&

FORS2/VLT survey of Milky Way globular clusters I. Description of the method for derivation of metal abundances in the optical and application to NGC 6528, NGC 6553, M 71, NGC 6558, NGC 6426 and Terzan 8

(abridged) We have observed almost 1/3 of the globular clusters in the Milky Way, targeting distant and/or highly reddened objects, besides a few reference clusters. A large sample of red giant stars was observed with FORS2@VLT/ESO at R ~ 2,000. The method for derivation of stellar parameters is presented with application to six reference clusters. We aim at deriving the stellar parameters effective temperature, gravity, metallicity and alpha-element enhancement, as well as radial velocity, for membership confirmation of individual stars in each cluster. We analyse the spectra collected for the reference globular clusters NGC 6528, NGC 6553, M 71, NGC 6558, NGC 6426 and Terzan 8. They cover the full range of globular cluster metallicities, and are located in the bulge, disc and halo. Full spectrum fitting techniques are applied, by comparing each target spectrum with a stellar library in the optical region at 4560-5860 A. We employed the library of observed spectra MILES, and the synthetic library by Coelho et al. (2005). Validation of the method is achieved through recovery of the known atmospheric parameters for 49 well-studied stars that cover a wide range in the parameter space. We adopted as final stellar parameters (effective temperatures, gravities, metallicities) the average of results using MILES and Coelho et al. libraries. We identified 4 member stars in NGC 6528, 13 in NGC 6553, 10 in M 71, 5 in NGC 6558, 5 in NGC 6426 and 12 in Terzan 8. Radial velocities, Teff, log(g), [Fe/H] and alpha-element enhancements were derived. We derived abundances for NGC 6426 from spectroscopy for the first time. The method proved to be reliable for red giant stars observed with resolution R ~ 2,000, yielding results compatible with high-resolution spectroscopy. The derived alpha-element abundances show [A/Fe] vs. [Fe/H] consistent with that of field stars at the same metallicities.Comment: 22 pages, 21 figures, accepted for publication in A&