A renormalization group computation of the critical exponents of hierarchical spin glasses

The infrared behaviour of a non-mean field spin-glass system is analysed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the epsilon-expansion technique with two independent methods. Both methods yield the same result confirming that the infrared behaviour of the theory if well-defined and the underlying ideas of the Renormalization Group hold also in such non-mean field disordered model. By pushing such calculation to high orders in epsilon, a consistent and predictive non-mean field theory for such disordered system could be established

Non-perturbative effects in spin glasses

We present a numerical study of an Ising spin glass with hierarchical interactions - the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to $d\geq4$ and $d<4$ for the $d$-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the $\epsilon$-expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent $\nu$ in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only $\sim 2\%$ from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects

Focusing on soil-foundation heterogeneity through high-resolution electrical and seismic tomography

The reconstruction of the current status of a historic building is essential for seismic safety assessment and for designing the retrofitting interventions since different safety and confidence factors have to be assumed, depending on the level of information about the subsoil structure. In this work, we present an investigation of the shallow subsurface below and around a historic building affected by differential settlements in order to define its geometry and to characterise its stiffness at low strain. To this end, we employed high-resolution electrical resistivity and seismic (both P-wave and S-wave) tomographies. A three-dimensional electrical resistivity tomography survey was performed to obtain more information about the type and the maximum depth of the building foundation. Electrical resistivity and seismic tomographies were carried out alongside the building, aimed at imaging the top soils and the near-surface geometry. The corresponding inverted models pointed out a remarkable heterogeneity of the shallow subsoil below the building, which is partly founded on a weathered layer and partly on a more rigid lithotype. This heterogeneity is probably a concurrent cause of the building's instability under both static and seismic loading. Our results demonstrate that the man-made fillings and the top soils have to be thoroughly investigated to fully understand the soil-structure behaviour. In this light, the integration of non-invasive high-resolution geophysical techniques, especially tomographic methods, has been proved to properly address the problem of imaging the shallow subsoil

Focusing on Soil Foundation Heterogeneity through High-resolution Tomography

An historical building affected by differential settlements, which were triggered by an earthquake, is investigated by means of high-resolution tomography, both electrical and seismic. The objective is to image the geometric structure of the shallow soil below the building and to characterize its stiffness at low strain. A preliminary reconstruction of the geological units has been recovered through the combined use of electrical and seismic data, where the depth of the travertine bedrock varies significantly within the study site. The range of variation of the main geophysical parameters (resistivity, P- and S-wave velocities) inferred from these models has been set as reference point for tuning the results obtained from the geophysical survey performed near the building. The inverted tomographic models obtained from data acquired alongside the building exhibit heterogeneity of the shallow subsoil, which is partly founded on a weathered layer and partly on a more rigid lithotype, probably a fractured travertine or a gravel layer. Therefore the fill anthropic soils can play a relevant role for the structural stability in case of shallow foundations built on a heterogeneous subsoil

Model Checking Paxos in Spin

We present a formal model of a distributed consensus algorithm in the executable specification language Promela extended with a new type of guards, called counting guards, needed to implement transitions that depend on majority voting. Our formalization exploits abstractions that follow from reduction theorems applied to the specific case-study. We apply the model checker Spin to automatically validate finite instances of the model and to extract preconditions on the size of quorums used in the election phases of the protocol.Comment: In Proceedings GandALF 2014, arXiv:1408.556