Base e Vertice: conflitto e complementarità. Elementi essenziali per una ricomposizione concettuale.

Analisi del rapporto tra base e vertice nella storia delle teorie organizzative nell'ambito della lavorazione. Cercando di motivare la particolare attenzione delle teorie manageriali contemporanee per il coinvolgimento e la partecipazione del lavoratore, si definisce un percorso teorico che attraversa il pensiero di alcuni dei più importanti critici dell'organizzazione del lavoro degli ultimi due Secoli. Si chiude con alcune considerazioni relative alla situazione attuale delle dinamiche presentate

Recent Trends on Nonlinear Filtering for Inverse Problems

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in view of the limit for infinitely particles and extensions towards stability analysis and multi--objective optimization. We illustrate the performance of the method by using test inverse problems from the literature

Properties of the LWR model with time delay

In this article, we investigate theoretical and numerical properties of the first-order Lighthill-Whitham-Richards (LWR) traffic flow model with time delay. Since standard results from the literature are not directly applicable to the delayed model, we mainly focus on the numerical analysis of the proposed finite difference discretization. The simulation results also show that the delay model is able to capture Stop & Go waves

Mathematical models and methods for traffic flow and stop & go waves

In this thesis we are concerned with mathematical methods and models for traffic flow, with special emphasis to second-order effects like Stop & Go waves. To begin with, we investigate the sensitivity of the celebrated Lighthill-Whitham-Richards model on network to its parameters and to the network itself. The quantification of sensitivity is obtained by measuring the Wasserstein distance between two LWR solutions corresponding to different inputs. To this end, we propose a numerical method to approximate the Wasserstein distance between two density distributions defined on a network. After that, we present a new multi-scale method for reproducing traffic flow, which couples a first order macroscopic model with a second-order microscopic model, avoiding any interface or boundary conditions between them. The new multi-scale model is characterized by the fact that microscopic and macroscopic descriptions are not spatially or temporally separated. Furthermore, a delayed LWR model on networks is proposed in order to allow simple first-order models to describe complex second-order effects caused by bounded accelerations. A time delay term is introduced in the flux term and its impact is studied from the numerical point of view. Lastly, we focus on Stop & Go waves, a typical phenomenon of congested traffic flow. Real data are used to point out the main features of this phenomenon, then we investigate the possibility to reproduce it using new traffic models specifically conceived for this purpos

Uncertainty quantification in hierarchical vehicular flow models

We consider kinetic vehicular traffic flow models of BGK type [24]. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic BGK–model is extended by introducing a parametric stochastic variable to describe possible uncertainty in traffic. The interplay of uncertainty with the given model hierarchy is studied in detail. Theoretical results on consistent formulations of the stochastic differential equations on the hydrodynamic level are given. The effect of the possibly negative diffusion in the stochastic hydrodynamic model is studied and numerical simulations of uncertain traffic situations are presented

Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation

We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in terms of wavelet-based series expansions. Then, they are projected to obtain a deterministic system for the coefficients in the truncated series. Stochastic Galerkin formulations are presented in conservative form and for smooth solutions also in the corresponding non-conservative form. This allows to obtain stabilization results, when the system is relaxed to a first-order model. Computational tests illustrate the theoretical results

Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID-19

In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic and of disease models generally. Most works follow the susceptible-infected-removed (SIR) compartmental framework, modeling the epidemic with a system of ordinary differential equations. Alternative formulations using a partial differential equation (PDE) to incorporate both spatial and temporal resolution have also been introduced, with their numerical results showing potentially powerful descriptive and predictive capacity. In the present work, we introduce a new variation to such models by using delay differential equations (DDEs). The dynamics of many infectious diseases, including COVID-19, exhibit delays due to incubation periods and related phenomena. Accordingly, DDE models allow for a natural representation of the problem dynamics, in addition to offering advantages in terms of computational time and modeling, as they eliminate the need for additional, difficult-to-estimate, compartments (such as exposed individuals) to incorporate time delays. In the present work, we introduce a DDE epidemic model in both an ordinary and partial differential equation framework. We present a series of mathematical results assessing the stability of the formulation. We then perform several numerical experiments, validating both the mathematical results and establishing model's ability to reproduce measured data on realistic problems

A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time-fractional derivative

We prove a representation formula of Hopf-Lax type for solutions to Hamilton-Jacobi equation involving a Caputo time-fractional derivative. Equations of this type are associated with optimal control problems where the controlled dynamics is given by a time-changed stochastic process describing the trajectory of a particle subject to random trapping effects