GPR applications for geotechnical stability of transportation infrastructures

Nowadays, severe meteorological events are always more frequent all over the world. This causes a strong impact on the environment such as numerous landslides, especially in rural areas. Rural roads are exposed to an increased risk for geotechnical instability. In the meantime, financial resources for maintenance are certainly decreased due to the international crisis and other different domestic factors. In this context, the best allocation of funds becomes a priority: efficiency and effectiveness of plans and actions are crucially requested. For this purpose, the correct localisation of geotechnically instable domains is strategic. In this paper, the use of Ground-Penetrating Radar (GPR) for geotechnical inspection of pavement and sub-pavement layers is proposed. A three-step protocol has been calibrated and validated to allocate efficiently and effectively the maintenance funds. In the first step, the instability is localised through an inspection at traffic speed using a 1-GHz GPR horn launched antenna. The productivity is generally about or over 300 Km/day. Data are processed offline by automatic procedures. In the second step, a GPR inspection restricted to the critical road sections is carried out using two coupled antennas. One antenna is used for top pavement inspection (1.6 GHz central frequency) and a second antenna (600 MHz central frequency) is used for sub-pavement structure diagnosis. Finally, GPR data are post-processed in the time and frequency domains to identify accurately the geometry of the instability. The case study shows the potentiality of this protocol applied to the rural roads exposed to a landslide

Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein space. In particular, we consider the Cauchy problem for a transport equation, where the velocity field depends on the measure itself. We deal with numerical schemes for this problem and prove convergence of a Lagrangian scheme to the solution, when the discretization parameters approach zero. We also prove convergence of an Eulerian scheme, under more strict hypotheses. Both schemes are discretizations of the push-forward formula defined by the transport equation. As a by-product, we obtain existence and uniqueness of the solution. All the results of convergence are proved with respect to the Wasserstein distance. We also show that $L^1$ spaces are not natural for such equations, since we lose uniqueness of the solution

Advertising, Labor Supply and the Aggregate Economy. A long run Analysis

This paper studies the influence of persuasive advertising in a neoclassical growth model with monopolistically competitive firms. Our findings show that advertising can significantly affect the stationary equilibrium of a model economy in which the labor supply is endogenous. In this case, for empirically plausible calibrations, we find that the equilibrium level of hours worked, GDP, and consumption increase with the amount of resources invested in advertising. These findings are consistent with a new stylized fact provided in this paper: over the past decade, per-capita advertising expenditures have been positively correlated with per-capita output, consumption and hours worked across OECD countries. Because of the connection between advertising and labor supply, we show that our model improves on its neoclassical counterpart in explaining both within-country and cross-country variability of hours worked per capita.Advertising, Labor Wedge, Labor supply, Economic Growth, Hours Worked.

Advertising and Business Cycle Fluctuations

This paper provides new empirical evidence for quarterly U.S. aggregate advertisingexpenditures, showing that advertising has a well defined pattern over the BusinessCycle. To understand this pattern we develop a general equilibrium model wheretargeted advertising increases the marginal utility of the advertised good. Advertisingintensity is endogenously determined by profit maximizing firms. We embed thisassumption into an otherwise standard model of the business cycle withmonopolistic competition. We find that advertising affects the aggregate dynamics ina relevant way, and it exacerbates the welfare costs of fluctuations for the consumer.Finally, we provide estimates of our setup using Bayesian techniques.Advertising, DSGE model, Business Cycle fluctuations, Bayesian

Mean-Field Sparse Optimal Control

We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modeling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dynamics of the probability distribution of the followers. In the classical mean-field theory one studies the behavior of a large number of small individuals freely interacting with each other, by simplifying the effect of all the other individuals on any given individual by a single averaged effect. In this paper we address instead the situation where the leaders are actually influenced also by an external policy maker, and we propagate its effect for the number $N$ of followers going to infinity. The technical derivation of the sparse mean-field optimal control is realized by the simultaneous development of the mean-field limit of the equations governing the followers dynamics together with the $\Gamma$-limit of the finite dimensional sparse optimal control problems.Comment: arXiv admin note: text overlap with arXiv:1306.591

Control to flocking of the kinetic Cucker-Smale model

The well-known Cucker-Smale model is a macroscopic system reflecting flocking, i.e. the alignment of velocities in a group of autonomous agents having mutual interactions. In the present paper, we consider the mean-field limit of that model, called the kinetic Cucker-Smale model, which is a transport partial differential equation involving nonlocal terms. It is known that flocking is reached asymptotically whenever the initial conditions of the group of agents are in a favorable configuration. For other initial configurations, it is natural to investigate whether flocking can be enforced by means of an appropriate external force, applied to an adequate time-varying subdomain. In this paper we prove that we can drive to flocking any group of agents governed by the kinetic Cucker-Smale model, by means of a sparse centralized control strategy, and this, for any initial configuration of the crowd. Here, "sparse control" means that the action at each time is limited over an arbitrary proportion of the crowd, or, as a variant, of the space of configurations; "centralized" means that the strategy is computed by an external agent knowing the configuration of all agents. We stress that we do not only design a control function (in a sampled feedback form), but also a time-varying control domain on which the action is applied. The sparsity constraint reflects the fact that one cannot act on the whole crowd at every instant of time. Our approach is based on geometric considerations on the velocity field of the kinetic Cucker-Smale PDE, and in particular on the analysis of the particle flow generated by this vector field. The control domain and the control functions are designed to satisfy appropriate constraints, and such that, for any initial configuration, the velocity part of the support of the measure solution asymptotically shrinks to a singleton, which means flocking

Control of reaction-diffusion equations on time-evolving manifolds

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon

Mean-field sparse Jurdjevic-Quinn control

International audienceWe consider nonlinear transport equations with non-local velocity, describing the time-evolution of a measure, which in practice may represent the density of a crowd. Such equations often appear by taking the mean-field limit of finite-dimensional systems modelling collective dynamics. We first give a sense to dissipativity of these mean-field equations in terms of Lie derivatives of a Lyapunov function depending on the measure. Then, we address the problem of controlling such equations by means of a time-varying bounded control action localized on a time-varying control subset with bounded Lebesgue measure (sparsity space constraint). Finite-dimensional versions are given by control-affine systems, which can be stabilized by the well known Jurdjevic–Quinn procedure. In this paper, assuming that the uncontrolled dynamics are dissipative, we develop an approach in the spirit of the classical Jurdjevic–Quinn theorem, showing how to steer the system to an invariant sublevel of the Lyapunov function. The control function and the control domain are designed in terms of the Lie derivatives of the Lyapunov function, and enjoy sparsity properties in the sense that the control support is small. Finally, we show that our result applies to a large class of kinetic equations modelling multi-agent dynamics

A signal processing methodology for assessing the performance of ASTM standard test methods for GPR systems

Ground penetrating radar (GPR) is one of the most promising and effective non-destructive testing techniques (NDTs), particularly for the interpretation of the soil properties. Within the framework of international Agencies dealing with the standardization of NDTs, the American Society for Testing and Materials (ASTM) has published several standard test methods related to GPR, none of which is focused on a detailed analysis of the system performance, particularly in terms of precision and bias of the testing variable under consideration. This work proposes a GPR signal processing methodology, calibrated and validated on the basis of a consistent amount of data collected by means of laboratory-scale tests, to assess the performance of the above standard test methods for GPR systems. The (theoretical) expressions of the bias and variance of the estimation error are here investigated by a reduced Taylor's expansion up to the second order. Therefore, a closed form expression for theoretically tuning the optimal threshold according to a fixed target value of the GPR signal stability is proposed. Finally, the study is extended to GPR systems with different antenna frequencies to analyze the specific relationship between the frequency of investigation, the optimal thresholds, and the signal stability