Structure preserving stochastic Galerkin methods for Fokker-Planck equations with background interactions

This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external distribution, that we refer to as a background distribution. The proposed methods are capable to preserve physical properties in the approximation of statistical moments of the problem like nonnegativity, entropy dissipation and asymptotic behaviour of the expected solution. The introduced methods are second order accurate in the transient regimes and high order for large times. We present applications of the developed schemes to the case of fixed and dynamic background distribution for models of collective behaviour

Boltzmann-type models with uncertain binary interactions

In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics. We consider deterministic (i.e., a priori averaged) and stochastic kinetic models, corresponding to different ways of understanding the role of uncertainty in the system dynamics, and compare some thermodynamic quantities of interest, such as the mean and the energy, which characterise the asymptotic trends. Furthermore, via suitable scaling techniques we derive the corresponding deterministic and stochastic Fokker-Planck equations in order to gain more detailed insights into the respective asymptotic distributions. We also provide numerical evidences of the trends estimated theoretically by resorting to recently introduced structure preserving uncertainty quantification methods

Hybrid stochastic kinetic description of two-dimensional traffic dynamics

In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. Assuming that lane changes are less frequent than interactions along the same lane and considering that their mathematical description can be done up to some uncertainty in the model parameters, we derive a hybrid stochastic Fokker-Planck-Boltzmann equation in the quasi-invariant interaction limit. By means of suitable numerical methods, precisely structure preserving and direct Monte Carlo schemes, we use this equation to compute theoretical speed-density diagrams of traffic both along and across the lanes, including estimates of the data dispersion, and validate them against real data

Eco-management and sustainability aspects of innovative development strategies

During the post-industrial revolutions, until the 20th century. By the last third of the 20th century, two basic directions of industrial development could be defined. One preferred to invest in local resources, with the help of state-owned companies, while the other favored industrial innovation in the export of capital by national companies. The two directions of industrial development were in some ways similar. Ecological sustainability aspects have not been taken into account during the development and operation of the technology. From this, we can see that ecomanagement as the management of eco-conscious companies in terms of environmental management was not a preferred aspect at that time. In the last third of the 20th century, environmental problems and the social and economic effects of pollution had also become globalize and were becoming increasingly important aspects of corporate governance. This is also due to the fact that the environmental spread of contaminants did not stop within the boundaries of a particular company, but because of the environmental conditions, they showed increasing risks to human health and the environment. As a result, companies have increasingly focused on environmental and human aspects, avoiding negative externalities and risks

Recent Advances in Industrial and Applied Mathematics

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress

Micro-macro stochastic Galerkin methods for nonlinear Fokker-Plank equations with random inputs

Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and biological dynamics. Their mathematical formulation has often to face with physical forces having a significant random component or with particles living in a random environment which characterization may be deduced through experimental data and leading consequently to uncertainty-dependent equilibrium states. In this work, to address the problem of effectively solving stochastic Fokker-Planck systems, we will construct a new equilibrium preserving scheme through a micro-macro approach based on stochastic Galerkin methods. The resulting numerical method, contrarily to the direct application of a stochastic Galerkin projection in the parameter space of the unknowns of the underlying Fokker-Planck model, leads to highly accurate description of the uncertainty dependent large time behavior. Several numerical tests in the context of collective behavior for social and life sciences are presented to assess the validity of the present methodology against standard ones

Recent Advances in Industrial and Applied Mathematics

This open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress

World Order Transformation and Security Policy Challenges

This study has a twofold aim. It focuses on the complex challenges that emerge as a result of the redistribution and coordination of economic power, adding the aspects related to the functional transformation of human society ‒ the so-called connectography ‒ to the horizon of interpretation. Taking into account the possible scenarios of power shifts, it examines the new security aspects which arise primarily as a result of players’ inability to adapt to the complexity of the political challenge. The authors pay special attention to the global and regional contexts of the possibilities for the creation of the strategic security environment. They discuss the potential consequences of the simultaneous application of hard and soft power, i.e. “flexible geometry”. The authors also analyse the changes envisaged for the period until 2050, which tie the importance of the shift in the geopolitical competition to the appreciation of water resources, which will render the efforts made to acquire energy carriers less fierce