Thermodynamic Limit for Mean-Field Spin Models

If the Boltzmann-Gibbs state $\omega_N$ of a mean-field $N$-particle system with Hamiltonian $H_N$ verifies the condition $$\omega_N(H_N) \ge \omega_N(H_{N_1}+H_{N_2})$$ for every decomposition $N_1+N_2=N$, then its free energy density increases with $N$. We prove such a condition for a wide class of spin models which includes the Curie-Weiss model, its p-spin generalizations (for both even and odd p), its random field version and also the finite pattern Hopfield model. For all these cases the existence of the thermodynamic limit by subadditivity and boundedness follows.Comment: 15 pages, few improvements. To appear in MPE

Design Of An Induction Probe For Simultaneous Measurements Of Permittivity And Resistivity

In this paper, we propose a discussion of the theoretical design and move towards the development and engineering of an induction probe for electrical spectroscopy which performs simultaneous and non invasive measurements on the electrical RESistivity \rho and dielectric PERmittivity \epsilon r of non-saturated terrestrial ground and concretes (RESPER probe). In order to design a RESPER which measures \rho and \epsilon r with inaccuracies below a prefixed limit (10%) in a band of low frequencies (LF) (B=100kHz), the probe should be connected to an appropriate analogical digital converter (ADC), which samples in uniform or in phase and quadrature (IQ) mode, otherwise to a lock-in amplifier. The paper develops only a suitable number of numerical simulations, using Mathcad, which provide the working frequencies, the electrode-electrode distance and the optimization of the height above ground minimizing the inaccuracies of the RESPER, in galvanic or capacitive contact with terrestrial soils or concretes, of low or high resistivity. As findings of simulations, we underline that the performances of a lock-in amplifier are preferable even when compared to an IQ sampling ADC with high resolution, under the same operating conditions. As consequences in the practical applications: if the probe is connected to a data acquisition system (DAS) as an uniform or an IQ sampler, then it could be commercialized for companies of building and road paving, being employable for analyzing "in situ" only concretes; otherwise, if the DAS is a lock-in amplifier, the marketing would be for companies of geophysical prospecting, involved to analyze "in situ" even terrestrial soils.Comment: 37 pages, 7 figures, 3 table

Pansharpening techniques to detect mass monument damaging in Iraq

The recent mass destructions of monuments in Iraq cannot be monitored with the terrestrial survey methodologies, for obvious reasons of safety. For the same reasons, it’s not advisable the use of classical aerial photogrammetry, so it was obvious to think to the use of multispectral Very High Resolution (VHR) satellite imagery. Nowadays VHR satellite images resolutions are very near airborne photogrammetrical images and usually they are acquired in multispectral mode. The combination of the various bands of the images is called pan-sharpening and it can be carried on using different algorithms and strategies. The correct pansharpening methodology, for a specific image, must be chosen considering the specific multispectral characteristics of the satellite used and the particular application. In this paper a first definition of guidelines for the use of VHR multispectral imagery to detect monument destruction in unsafe area, is reported. The proposed methodology, agreed with UNESCO and soon to be used in Libya for the coastal area, has produced a first report delivered to the Iraqi authorities. Some of the most evident examples are reported to show the possible capabilities of identification of damages using VHR images

Asymptotics of LQG fusion coefficients

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into $SU(2)_L\times SU(2)_R$ semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.Comment: 14 pages, minor change

On the reconstruction of planar lattice-convex sets from the covariogram

A finite subset $K$ of $\mathbb{Z}^d$ is said to be lattice-convex if $K$ is the intersection of $\mathbb{Z}^d$ with a convex set. The covariogram $g_K$ of $K\subseteq \mathbb{Z}^d$ is the function associating to each u \in \integer^d the cardinality of $K\cap (K+u)$. Daurat, G\'erard, and Nivat and independently Gardner, Gronchi, and Zong raised the problem on the reconstruction of lattice-convex sets $K$ from $g_K$. We provide a partial positive answer to this problem by showing that for $d=2$ and under mild extra assumptions, $g_K$ determines $K$ up to translations and reflections. As a complement to the theorem on reconstruction we also extend the known counterexamples (i.e., planar lattice-convex sets which are not reconstructible, up to translations and reflections) to an infinite family of counterexamples.Comment: accepted in Discrete and Computational Geometr

Variable sequence of events during the past seven terminations in two deep-sea cores from the Southern Ocean

The relationships among internally consistent records of summer sea-surface temperature (SSST), winter sea ice (WSI), and diatomaceous stable isotopes were studied across seven terminations over the last 660 ka in sedimentary cores from ODP sites 1093 and 1094. The sequence of events at both sites indicates that SSST and WSI changes led the carbon and nitrogen isotopic changes in three Terminations (TI, TII and TVI) and followed them in the other four Terminations (TIII, TIV, TV and TVII). In both TIII and TIV, the leads and lags between the proxies were related to weak glacial mode, while in TV and TVII they were due to the influence of the mid-Pleistocene transition. We show that the sequence of events is not unique and does not follow the same pattern across terminations, implying that the processes that initiated climate change in the Southern Ocean has varied through time

Real Time 3D Ionospheric Modelling with Ray Tracing Application over Mediterranean Area

This poster deals with some practical examples of instantaneous 3D modelling of regional ionosphere, based on ionosondes data from the Istituto Nazionale di Geofisica e Vulcanologia, INGV. Characteristic anchor points have been chosen for each ionospheric region. These points are joint by an adaptive ionospheric profiler derived from the one used in Autoscala. For the F2 region the anchor point is given by the real height hmF2 of the layer and its critical frequency foF2. These values are obtained basing on the observed heights (hmF2ROME[OBS] and hmF2GIBILMANNA[OBS]) and critical frequencies (foF2ROME[OBS] and foF2GIBILMANNA[OBS]) of the F2 layer, which are compared with the corresponding monthly median given by CCIR maps using Shimazaki’s formulation. The differences dhmF2ROME = hmF2ROME[OBS] - hmF2ROME[CCIR] dhmF2GIBILMANNA = hmF2 GIBILMANNA [OBS] - hmF2 GIBILMANNA [CCIR] are thus computed and used in Kriging method to update the values given by CCIR maps. For the F1 region the critical frequency is derived form a solar zenith angle dependent model adjusted to match the values of foF1 measured in Rome and Gibilmanna. For the E region the height is set to 110 km, while the critical frequency is estimated by a standard solar zenith angle and solar activity dependent model. The model produces as an output a 3D matrix which can be profitably used as an input for a Matlab/Fortran based ray tracing program recently developed at INGV

Simple model for quantum general relativity from loop quantum gravity

New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation as a generalized topological quantum field theory with an infinite number of degrees of freedom, and its relation to lattice theory. I list the indications supporting the conjecture that the model is related to general relativity and UV finite.Comment: 8 pages, 3 figure

The EPRL intertwiners and corrected partition function

Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective for n-valent vertex in case when it is a map from SO(3) into SO(3)xSO(3) representations. We find, however, that the EPRL map is not isometric. In the consequence, in order to be written in a SU(2) amplitude form, the formula for the partition function has to be rederived. We do it and obtain a new, complete formula for the partition function. The result goes beyond the SU(2) spin-foam models framework.Comment: RevTex4, 15 pages, 5 figures; theorem of injectivity of EPRL map correcte