Time Fractional Cable Equation And Applications in Neurophysiology

We propose an extension of the cable equation by introducing a Caputo time fractional derivative. The fundamental solutions of the most common boundary problems are derived analitically via Laplace Transform, and result be written in terms of known special functions. This generalization could be useful to describe anomalous diffusion phenomena with leakage as signal conduction in spiny dendrites. The presented solutions are computed in Matlab and plotted.Comment: 10 figures. arXiv admin note: substantial text overlap with arXiv:1702.0532

Firms in International Trade: Importers and Exporters Heterogeneity in the Italian Manufacturing Industry

This paper offers a portrait of Italian firms that trade goods. Combining data on firms' structural characteristics and economic performance with data on their exporting and importing activity, we uncover evidence supporting recent theories on firm heterogeneity and international trade, together with some new facts. In particular, we find that importing can be as important as exporting as a source of firm heterogeneity. First, we document that trade is more concentrated than employment and sales, and we show that import is even more concentrated than export both within sectors and along the sector and country extensive margins. Second, while supporting the fact that firms involved in both importing and exporting (two-way traders) are the best performers, we also find that firms involved only in importing activities perform better than those involved only in exporting. We submit that this may have to do with being mainly importers of high-tech capital goods. Third, the performance premia of internationalized firms correlate relatively more with the degree of geographical and sectoral diversification of imports.Heterogeneous firms; Exports; Imports

Resonance contributions to nucleon spin structure in Holographic QCD

We study polarized inelastic electron-nucleon scattering at low momentum transfer, in the Witten-Sakai-Sugimoto model of holographic QCD. We focus in particular on resonance production contributions to the nucleon spin structure functions. Our analysis includes both spin $3/2$ and spin $1/2$ low-lying nucleon resonances with positive and negative parity. We determine, in turn, the helicity amplitudes for nucleon-resonance transitions and the resonance contributions to the neutron and proton generalized spin polarizabilities. Extrapolating the model parameters to realistic QCD data, our analysis, triggered by recent experimental results from Jefferson Lab, agrees with the observation that the $\Delta(1232)$ resonance gives the dominant contribution to the forward spin polarizabilities at low momentum transfer. The contribution is negative and increases towards zero as the momentum transfer increases. As expected, the contribution of the $\Delta(1232)$ to the longitudinal-transverse polarizabilities is instead negligible. Our analysis shows that different spin $1/2$ resonances give different contributions, in sign and magnitude, to the generalized longitudinal-transverse spin polarizabilities. In the proton case they globally give rise to a positive function which decreases towards zero as the momentum transfer increases. In the neutron case, the net effect produces a negative increasing function. These features are in qualitative agreement with experimental data.Comment: 43 pages, 17 figures, 2 table

mechanical behaviour of wind turbines operating above design conditions

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Multi-Scale Wind Turbine Bearings Supervision Techniques Using Industrial SCADA and Vibration Data

Timely damage diagnosis of wind turbine rolling elements is a keystone for improving availability and eventually diminishing the cost of wind energy: from this point of view, it is a priority to integrate high-level practices into the real-world operation and maintenance of wind farms. On this basis, the present study is devoted to the formulation of reliable methodologies for the supervision of wind turbine bearings, which possibly can be integrated in the industrial practice. For this reason, this study is a collaboration between a company (ENGIE Italia), the University of Perugia and the Politecnico di Torino. The analysis is based on the exploitation of the data types which are available to wind farm managers from industrial control systems: SCADA (Supervisory Control And Data Acquisition) and TCM (Turbine Condition Monitoring). Due to the intrinsic sampling time difference between SCADA and TCM data (a few minutes the former, up to the millisecond for the latter), the proposed methodology is designed as multi-scale. At first, historical SCADA data are processed and the behavior of the oil filter pressure is analyzed for all the wind turbines in the farm: this provides preliminary advice for identifying presumably healthy wind turbines from those suspected of damage. A second step for the SCADA analysis is then represented by the study of the temperature trends of the bearings through a Support Vector Regression: the incoming damage is individuated from the analysis of the mismatch between measurements and estimates provided by the normal behavior model. Finally, the healthy units are selected as the reference and the faulty as the target for the analysis of TCM vibration data in the time domain: statistical features are computed on independent chunks of the signals and, using a Novelty Index, it was possible to distinguish the damaged wind turbines with respect to the reference ones. In light of the interest in application of the proposed methodology, good practice criteria in selecting and managing the data are discussed as well

Overconfidence in the art market: a bargaining pricing model with asymmetric disinformation

This paper develops a Nash bargaining model of price formation in the art market. Agents can be naïve, if they are overconfident and either overestimate artistic quality or underestimate their uncertainty of artistic quality, or sophisticated, if they correctly use all the available information. Overconfidence turns out to have a positive impact on both the price and the average quality of the artworks traded in the market. The impact of overconfidence on expected quality is weaker than the corresponding price increase, so sellers overcharge buyers. In addition, the buyer’s (seller’s) overconfidence has a positive (negative) impact on the likelihood of trade. If many pairs of agents may bargain simultaneously, we find that seller’s market power is negatively affected by the number of sellers and positively affected by the number of buyers. If sophisticated and naïve buyers coexist, naïve buyers exert a negative externality on the sophisticated ones, increasing the price the latter pay

Emergence of Fractional Kinetics in Spiny Dendrites

Fractional extensions of the cable equation have been proposed in the literature to describe transmembrane potential in spiny dendrites. The anomalous behavior has been related in the literature to the geometrical properties of the system, in particular, the density of spines, by experiments, computer simulations, and in comb-like models.~The same PDE can be related to more than one stochastic process leading to anomalous diffusion behavior. The time-fractional diffusion equation can be associated to a continuous time random walk (CTRW) with power-law waiting time probability or to a special case of the Erd\'ely-Kober fractional diffusion, described by the ggBm. In this work, we show that time fractional generalization of the cable equation arises naturally in the CTRW by considering a superposition of Markovian processes and in a {\it ggBm-like} construction of the random variable.Comment: 8 page

A systems approach to analyze the robustness of infrastructure networks to complex spatial hazards

Ph. D. ThesisInfrastructure networks such as water supply systems, power networks, railway networks, and road networks provide essential services that underpin modern society’s health, wealth, security, and wellbeing. However, infrastructures are susceptible to damage and disruption caused by extreme weather events such as floods and windstorms. For instance, in 2007, extensive disruption was caused by floods affecting a number of electricity substations in the United Kingdom, resulting in an estimated damage of GBP£3.18bn (US$4bn). In 2017, Hurricane Harvey hit the Southern United States, causing an approximated US$125bn (GBP£99.35bn) in damage due to the resulting floods and high winds. The magnitude of these impacts is at risk of being compounded by the effects of Climate Change, which is projected to increase the frequency of extreme weather events. As a result, it is anticipated that an estimated US$3.7tn (GBP£2.9tn) in investment will be required, per year, to meet the expected need between 2019 and 2035. A key reason for the susceptibility of infrastructure networks to extreme weather events is the wide area that needs to be covered to provide essential services. For example, in the United Kingdom alone there are over 800,000 km of overhead electricity cables, suggesting that the footprint of infrastructure networks can be as extended as that of an entire Country. These networks possess different spatial structures and attributes, as a result of their evolution over long timeframes, and respond to damage and disruption in different and complex ways. Existing approaches to understanding the impact of hazards on infrastructure networks typically either (i) use computationally expensive models, which are unable to support the investigation of enough events and scenarios to draw general insights, or (ii) use low complexity representations of hazards, with little or no consideration of their spatial properties. Consequently, this has limited the understanding of the relationship between spatial hazards, the spatial form and connectivity of infrastructure networks, and infrastructure reliability. This thesis investigates these aspects through a systemic modelling approach, applied to a synthetic and a real case study, to evaluate the response of infrastructure networks to spatially complex hazards against a series of robustness metrics. In the first case study, non-deterministic spatial hazards are generated by a fractal method which allows to control their spatial variability, resulting in spatial configurations that very closely resemble natural phenomena such as floods or windstorms. These hazards are then superimposed on a range of synthetic network layouts, which have spatial structures consistent with real infrastructure networks reported in the literature. Failure of network components is initially determined as a function of hazard intensity, and cascading failure of further components is also investigated. The performance of different infrastructure configurations is captured by an array of metrics which cover different aspects of robustness, ranging from the proneness to partitioning to the ability to process flows in the face of disruptions. Whereas analyses to date have largely adopted low complexity representations of hazards, this thesis shows that consideration of a high complexity representation which includes hazard spatial variability can reduce the robustness of the infrastructure network by nearly 40%. A “small-world” network, in which each node is within a limited number of steps from any other node, is shown to be the most robust of all the modelled networks to the different structures of spatial hazard. The second case study uses real data to assess the robustness of a power supply network operating in the Hull region in the United Kingdom, which is split in high and low voltage lines. The spatial hazard is represented by a high-resolution wind gust model and tested under current and future climate scenarios. The analysis reveals how the high and low voltage lines interact with each other in the event of faults, which lines would benefit the most from increased robustness, and which are most exposed to cascading failures. The second case study also reveals the importance of the spatial footprint of the hazard relative to the location of the infrastructure, and how particular hazard patterns can affect low voltage lines that are more often located in exposed areas at the edge of the network. The impact of Climate Change on windstorms is highly uncertain, although it could further reduce network robustness due to more severe events. Overall the two case studies provide important insights for infrastructure designers, asset managers, the academic sector, and practitioners in general. In fact, in the first case study, this thesis defines important design principles, such as the adoption of a small-world network layout, that can integrate the traditional design drivers of demand, efficiency, and cost. In the second case study, this thesis lays out a methodology that can help identify assets requiring increased robustness and protection against cascading failures, resulting in more effective prioritized infrastructure investments and adaptation plans

condition monitoring techniques for machine bearings in non stationary operation

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