A network model of conviction-driven social segregation

In order to measure, predict, and prevent social segregation, it is necessary to understand the factors that cause it. While in most available descriptions space plays an essential role, one outstanding question is whether and how this phenomenon is possible in a well-mixed social network. We define and solve a simple model of segregation on networks based on discrete convictions. In our model, space does not play a role, and individuals never change their conviction, but they may choose to connect socially to other individuals based on two criteria: sharing the same conviction, and individual popularity (regardless of conviction). The trade-off between these two moves defines a parameter, analogous to the "tolerance" parameter in classical models of spatial segregation. We show numerically and analytically that this parameter determines a true phase transition (somewhat reminiscent of phase separation in a binary mixture) between a well-mixed and a segregated state. Additionally, minority convictions segregate faster and inter-specific aversion alone may lead to a segregation threshold with similar properties. Together, our results highlight the general principle that a segregation transition is possible in absence of spatial degrees of freedom, provided that conviction-based rewiring occurs on the same time scale of popularity rewirings.Comment: 11 pages, 8 figure

Rate dependence of current and fluctuations in jump models with negative differential mobility

Negative differential mobility is the phenomenon in which the velocity of a particle decreases when the force driving it increases. We study this phenomenon in Markov jump models where a particle moves in the presence of walls that act as traps. We consider transition rates that obey local detailed balance but differ in normalisation, the inclusion of a rate to cross a wall and a load factor. We illustrate the full counting statistics for different choices of the jumping rates. We also show examples of thermodynamic uncertainty relations. The variety of behaviours we encounter highlights that negative differential mobility depends crucially on the chosen rates and points out the necessity that such choices should be based on proper coarse-graining studies of a more microscopic description

Eigenvalue crossing as a phase transition in relaxation dynamics

When a system's parameter is abruptly changed, a relaxation towards the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation matrix results in a relaxation trajectory singularity, which is analogous to a first-order equilibrium phase transition. We demonstrate this in a minimal 4-state system and in the thermodynamic limit of the 1D Ising model

Universal singularities of anomalous diffusion in the Richardson class

Inhomogeneous environments are rather ubiquitous in nature, often implying anomalies resulting in deviation from Gaussianity of diffusion processes. While sub- and superdiffusion are usually due to conversing environmental features (hindering or favoring the motion, respectively), they are both observed in systems ranging from the micro- to the cosmological scale. Here we show how a model encompassing sub- and superdiffusion in an inhomogeneous environment exhibits a critical singularity in the normalized generator of the cumulants. The singularity originates directly from the asymptotics of the non-Gaussian scaling function of displacement, which we prove to be independent of other details and hence to retain a universal character. Our analysis, based on the method first applied in [A. L. Stella et al., arXiv:2209.02042 (2022)], further allows to establish a relation between the asympototics and diffusion exponents characteristic of processes in the Richardson class. Extensive numerical tests fully confirm the results

Methodological approach for evaluating the geo-exchange potential: VIGOR Project

In the framework of VIGOR Project, a national project coordinated by the Institute of Geosciences and Earth Resources (CNR-IGG) and sponsored by the Ministry of Economic Development (MiSE), dedicated to the evaluation of geothermal potential in the regions of the Convergence Objective in Italy (Puglia, Calabria, Campania and Sicily), is expected to evaluate the ability of the territory to heat exchange with the ground for air conditioning of buildings. To identify the conditions for the development of low enthalpy geothermal systems collected and organized on a regional scale geological and stratigraphic data useful for the preparation of a specific thematic mapping, able to represent in a synergistic and simplified way the physical parameters (geological, lithostratigraphic, hydrogeological, thermodynamic) that most influence the subsoil behavior for thermal exchange. The litho-stratigraphic and hydrogeological database created for every region led to the production of different cartographic thematic maps, such as the thermal conductivity (lithological and stratigraphical), the surface geothermal flux, the average annual temperature of air, the climate zoning, the areas of hydrogeological restrictions. To obtain a single representation of the geo-exchange potential of the region, the different thematic maps described must be combined together by means of an algorithm, defined on the basis of the SINTACS methodology. The purpose is to weigh the contributions of the involved parameters and to produce a preliminary synthesis map able to identify the territorial use of geothermal heat pump systems, based on the geological characteristics and in agreement with the existing regulatory constraints

Out of equilibrium dynamics: from an entropy of the growth to the growth of entropy production

Entropy and growth are recurrent keywords in the most recent developments of statistical mechanics and Physics of complex systems. In this thesis we show how these concepts reveal fundamental both in the analysis of trades among macro-economies and in the coarse-graining of systems out of equilibrium. In the first part of the thesis we address the topic of Economic Complexity, a new frontier of Econophysics. Here we exploit tools and methods of the Physics of complex systems to understand, replicate and predict the dynamics that drives the trade of commodities among Countries. Novel ranking schemes inspired by Shannon’s entropy function establish measures for the development of countries and the complexity of products, allowing us to accomplish the main goal of the whole field of Economic Complexity. Our results are supported by the insights provided by the original parameters that characterize the dynamical model. Making full use of these quantities we are able to distinct, from multiple perspectives, among developed, emerging, underdeveloped and risky economies. The dynamical model produced consistent results over two unrelated datasets, redacted following different product codifications and covering different time windows (1962-2000 and 1995-2015). The knowledge gathered from the study of growth in the macroeconomic context revealed to be useful in obtaining the results on non-equilibrium systems, presented in the second half of this thesis. Here we address the general issue of formalizing coarse-graining procedures of Markov jump processes to understand how fluctuation relations apply to the dynamics of coarse-grained systems. Our approach allows to preserve the entropy production in the resulting decimated system. The Cramer's function remains identical to microscopic one satisfying fluctuation relations, also when net current carrying loops are erased. We are also able to identify the terms responsible for the memory effects introduced by the procedure. Eliminating this terms allows to restore Markovianity while preserving the average rates of entropy production. An analysis of Markov models exhibiting the phenomenon of negative differential mobility shows the need to make fully consistent stochastic descriptions working at different levels of space resolution. Comparisons with experimental works support the need to pursue this line of research, whose ambitious aim is to understand how to generally perform coarse-graining procedures of non-equilibrium systems with the preservation of entropy production acting as guiding principle.Entropia e crescita sono parole chiave ricorrenti negli ultimi sviluppi della meccanica statistica e nella fisica dei sistemi complessi. In questa tesi mostriamo come questi due concetti si rivelino fondamentali sia nell’analisi di di scambi di merci tra macro-economie che nelle procedure di coarse-graining di sistemi fuori equilibrio. Nella prima parte della tesi affrontiamo il tema della Economic Complexity, una nuova frontiera nell’ambito della ricerca dell’Econofisica. Grazie a metodi e strumenti ereditati dalla Fisica dei sistemi complessi, illustriamo come sia possibile riprodurre e predire la dinamica che guida gli scambi di merci tra i paesi. Un innovativo algoritmo di ranking ispirato all’entropia di Shannon ci consente di misurare il livello di sviluppo dei paesi e la complessità delle merci, permettendoci così di raggiungere l’obbiettivo principale che definisce il campo dell’Economic Complexity. I risultati che abbiamo ottenuto sono in accordo e vengono allo stesso tempo supportati dai parametri liberi che costituiscono il modello dinamico, fornendo un’originale chiave di lettura dei dati. Utilizzando queste informazioni siamo in grado di distinguere, sotto molteplici prospettive, economie di paesi sviluppati, emergenti, sottosviluppati ed a rischio. Questo modello dinamico è stato applicato con risultati consistenti su due diversi database, che copriono diversi periodi temporali (1962-2000 e 1915-2015), ed in cui i prodotti sono classificati attraverso differenti codifiche. Le conoscenze ottenute dallo studio del fenomeno della crescita nel contesto macroeconomico si sono rivelate estremamente utili nell'ottenere i risultati sui sistemi fuori equilibrio presentati nella seconda parte della tesi. Qui ci occupiamo del problema di carattere generale di formalizzare procedure di decimazione di sistemi Markoviani a salti per testare la validità dei teoremi di fluttuazione nell’ambito della dinamica dei sistemi coarse-grained. Il metodo che presentiamo permette di preservare la produzione di entropia nel sistema decimato. La funzione di Cramer resta identica a quella microscopica soddisfacente ai teoremi di fluttuazione, anche nel caso di eliminazione di loop percorsi da corrente netta. Questa procedura ci permette inoltre di identificare i termini responsabili degli effetti di memoria che sono stati introdotti nel coarse-graining, la cui eliminazione ci permette di ristabilire un sistema Markoviano con lo stesso valor medio di entropia prodotta originaria. Un’analisi di sistemi Markoviani caratterizzati dal fenomeno della mobilità differenziale negativa mostra chiaramente come sia necessario rendere consistenti descrizioni di sistemi stocastici a diversi livelli di risoluzione spaziale. Un confronto con lavori sperimentali caratterizzati da tale fenomeno mostra la necessità di approfondire questa linea di ricerca, il cui obbiettivo ambizioso è quello di capire come effettuare, in generale, procedure di coarse-graining di sistemi fuori equilibrio, seguendo come principio guida la preservazione della produzione di entropia

Out of equilibrium dynamics: from an entropy of the growth to the growth of entropy production

Entropy and growth are recurrent keywords in the most recent developments of statistical mechanics and Physics of complex systems. In this thesis we show how these concepts reveal fundamental both in the analysis of trades among macro-economies and in the coarse-graining of systems out of equilibrium. In the first part of the thesis we address the topic of Economic Complexity, a new frontier of Econophysics. Here we exploit tools and methods of the Physics of complex systems to understand, replicate and predict the dynamics that drives the trade of commodities among Countries. Novel ranking schemes inspired by Shannon’s entropy function establish measures for the development of countries and the complexity of products, allowing us to accomplish the main goal of the whole field of Economic Complexity. Our results are supported by the insights provided by the original parameters that characterize the dynamical model. Making full use of these quantities we are able to distinct, from multiple perspectives, among developed, emerging, underdeveloped and risky economies. The dynamical model produced consistent results over two unrelated datasets, redacted following different product codifications and covering different time windows (1962-2000 and 1995-2015). The knowledge gathered from the study of growth in the macroeconomic context revealed to be useful in obtaining the results on non-equilibrium systems, presented in the second half of this thesis. Here we address the general issue of formalizing coarse-graining procedures of Markov jump processes to understand how fluctuation relations apply to the dynamics of coarse-grained systems. Our approach allows to preserve the entropy production in the resulting decimated system. The Cramer's function remains identical to microscopic one satisfying fluctuation relations, also when net current carrying loops are erased. We are also able to identify the terms responsible for the memory effects introduced by the procedure. Eliminating this terms allows to restore Markovianity while preserving the average rates of entropy production. An analysis of Markov models exhibiting the phenomenon of negative differential mobility shows the need to make fully consistent stochastic descriptions working at different levels of space resolution. Comparisons with experimental works support the need to pursue this line of research, whose ambitious aim is to understand how to generally perform coarse-graining procedures of non-equilibrium systems with the preservation of entropy production acting as guiding principle

Data Driven Approach to the Dynamics of Import and Export of G7 Countries

The dynamics of imports plus exports of 226 product classes by the G7 countries between 1962 and 2000 is described in terms of stochastic differential equations. The model allows interesting comparisons among the different economies related to the compositions of the national baskets. Synthetic solutions can also be used to estimate hidden and unexploited growth potentials. These prerogatives are strictly connected with the fact that a network structure is at the basis of the model. Such a network expresses the mutual influences of different products through resource transfers, and is a key ingredient producing cooperative growth effects which can be quantified and distinguished from those generated by deterministic drifts and representing direct resource inputs. An analysis of this network, which differs substantially from those previously considered within the economic complexity approach, allows to estimate the centrality of different products in each national basket, highlighting the most essential commodities for each economy. Solutions of the model give the possibility of performing counterfactual analyses aimed at estimating how much the growth of each country could have profited from a general strengthening, or weakening, of the links in the same products network

Integration of laser scanning and thermal imaging in monitoring optimization and assessment of rockfall hazard: a case history in the Carnic Alps (Northeastern Italy)

Rock cliff monitoring to evaluate related rockfall hazard requires a deep knowledge of the geometry and kinematics of the rock mass and a real-time survey of some key features. If a sedimentary rock system has sloping discontinuity planes, an open joint could become a potential sliding surface and its conditions must be monitored. It is the case of the Passo della Morte landslide (Carnic Alps, Northeastern Italy), where sub-vertical joints exist. Remote sensing techniques such as terrestrial laser scanning (TLS) and infrared thermography (IRT) allow a fast and efficient contactless geometrical and geomechanical examination of a rock mass. Therefore, they can be used to recognize those joints that require monitoring with on-site instrumentation such as extensometers and/or inclinometers, or also acoustic emission sensors, aiding the arrangement of monitoring systems which are generally quite expensive to install. Repeated IRT surveys would provide useful information about the evolution of unstable slopes, thus suggesting how the on-site monitoring system could be improved. Moreover, data gathered by TLS and IRT can be directly used in landslide hazard assessment. In the test site, an open joint was recognized together with a fair joint that could change in the next future. The results were validated by means of extensometer data