Metriplectic framework for dissipative magneto-hydrodynamics

The metriplectic framework, which allows for the formulation of an algebraic structure for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics (MHD), adapting what had already been done for non-ideal Hydrodynamics (HD). The result is obtained by extending the HD symmetric bracket and free energy to include magnetic field dynamics and resistive dissipation. The correct equations of motion are obtained once one of the Casimirs of the Poisson bracket for ideal MHD is identified with the total thermodynamic entropy of the plasma. The metriplectic framework of MHD is shown to be invariant under the Galileo Group. The metriplectic structure also permits us to obtain the asymptotic equilibria toward which the dynamics of the system evolves. This scheme is finally adapted to the two-dimensional incompressible resistive MHD, that is of major use in many applications.     

Classical geometry to quantum behavior correspondence in a virtual extra dimension

In the Lorentz invariant formalism of compact space–time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In Dolce (2011) [18] we have shown, for instance, that the ordinary Feynman path integral is obtained from the interference between the classical paths with different winding numbers associated with the cyclic dynamics of the field solutions. By means of the boundary conditions, the kinematical information of interactions can be encoded on the relativistic geometrodynamics of the boundary, see Dolce (2012) [8]. Furthermore, such a purely four-dimensional theory is manifestly dual to an extra-dimensional field theory. The resulting correspondence between extra-dimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple Quark–Gluon–Plasma freeze-out model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology.     

Unveiling the connectivity structure of financial networks via high-frequency analysis

The paper deals with the problem of reconstructing the internal link structure of a network of agents subject to mutual dependencies. We show that standard multivariate approaches based on a correlation analysis are not well suited to detect mutual influences and dependencies, especially in the presence of delayed or propagative relations and when the sampling rate is sufficiently high to capture them. In particular, we develop and apply a metric based on the coherence function to take into account these dynamical phenomena. The effectiveness of the proposed approach is illustrated through numerical examples and through the analysis of a real complex networked system, i.e. a set of 100 high volume stocks of the New York Stock Exchange, observed during March 2008 and sampled at high frequency.     

Hysteresis models of dynamic mode atomic force microscopes: analysis and identification via harmonic balance

A new class of models based on hysteresis functions is developed to describe the operation of dynamic mode atomic force microscopy. Such models can account for dissipative phenomena affecting the interaction between the probe and the sample. The model analysis, which is developed using frequency domain techniques, provides a insights into experimentally observed behavior. Experimental data corroborates the models developed.     

Compact Time and Determinism for Bosons: Foundations

Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this compactification naturally leads to a quantized energy spectrum. As a consequence of the relation between periodicity and energy arising from the de Broglie relation, the compactification must be regarded as dynamical and local. The theory, whose foundamental set-up is presented in this paper, turns out to be consistent with special relativity and in particular respects causality. The non trivial classical dynamics of these periodic fields show remarkable overlaps with ordinary quantum field theory. This can be interpreted as a generalization of the AdS/CFT correspondence.     

Gauge interaction as periodicity modulation

The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space–time dimensions (Dolce, 2011) [8]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space–time coordinates. Therefore gauge interactions are described as invariance of the theory under local deformations of the boundary. The resulting local variations of the field solution are interpreted as internal transformations. The internal symmetries of the gauge theory turn out to be related to corresponding space–time local symmetries. In the approximation of local infinitesimal isometric transformations, Maxwell’s kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED.