78 research outputs found
Structure preserving schemes for mean-field equations of collective behavior
In this paper we consider the development of numerical schemes for mean-field
equations describing the collective behavior of a large group of interacting
agents. The schemes are based on a generalization of the classical Chang-Cooper
approach and are capable to preserve the main structural properties of the
systems, namely nonnegativity of the solution, physical conservation laws,
entropy dissipation and stationary solutions. In particular, the methods here
derived are second order accurate in transient regimes whereas they can reach
arbitrary accuracy asymptotically for large times. Several examples are
reported to show the generality of the approach.Comment: Proceedings of the XVI International Conference on Hyperbolic
Problem
Uncertainty quantification for kinetic models in socio-economic and life sciences
Kinetic equations play a major rule in modeling large systems of interacting
particles. Recently the legacy of classical kinetic theory found novel
applications in socio-economic and life sciences, where processes characterized
by large groups of agents exhibit spontaneous emergence of social structures.
Well-known examples are the formation of clusters in opinion dynamics, the
appearance of inequalities in wealth distributions, flocking and milling
behaviors in swarming models, synchronization phenomena in biological systems
and lane formation in pedestrian traffic. The construction of kinetic models
describing the above processes, however, has to face the difficulty of the lack
of fundamental principles since physical forces are replaced by empirical
social forces. These empirical forces are typically constructed with the aim to
reproduce qualitatively the observed system behaviors, like the emergence of
social structures, and are at best known in terms of statistical information of
the modeling parameters. For this reason the presence of random inputs
characterizing the parameters uncertainty should be considered as an essential
feature in the modeling process. In this survey we introduce several examples
of such kinetic models, that are mathematically described by nonlinear Vlasov
and Fokker--Planck equations, and present different numerical approaches for
uncertainty quantification which preserve the main features of the kinetic
solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic
Equations
A Multilevel Monte Carlo Asymptotic-Preserving Particle Method for Kinetic Equations in the Diffusion Limit
We propose a multilevel Monte Carlo method for a particle-based
asymptotic-preserving scheme for kinetic equations. Kinetic equations model
transport and collision of particles in a position-velocity phase-space. With a
diffusive scaling, the kinetic equation converges to an advection-diffusion
equation in the limit of zero mean free path. Classical particle-based
techniques suffer from a strict time-step restriction to maintain stability in
this limit. Asymptotic-preserving schemes provide a solution to this time step
restriction, but introduce a first-order error in the time step size. We
demonstrate how the multilevel Monte Carlo method can be used as a bias
reduction technique to perform accurate simulations in the diffusive regime,
while leveraging the reduced simulation cost given by the asymptotic-preserving
scheme. We describe how to achieve the necessary correlation between simulation
paths at different levels and demonstrate the potential of the approach via
numerical experiments.Comment: 20 pages, 7 figures, published in Monte Carlo and Quasi-Monte Carlo
Methods 2018, correction of minor typographical error
Women and citizenship post-trafficking : the case of Nepal
The research for this paper was funded by the Economic and Social Research Council – ESRC Res-062-23-1490: ‘Post Trafficking in Nepal: Sexuality and Citizenship in Livelihood Strategies’. Diane Richardson would like to acknowledge the support provided by the award of a Leverhulme TrustMajor Research Fellowship, ‘Transforming Citizenship: Sexuality, Gender and Citizenship Struggles’ [award MRF-2012-106].This article analyses the relationship between gender, sexuality and citizenship embedded in models of citizenship in the Global South, specifically in South Asia, and the meanings associated with having - or not having - citizenship. It does this through an examination of women's access to citizenship in Nepal in the context of the construction of the emergent nation state in the 'new' Nepal 'post-conflict'. Our analysis explores gendered and sexualized constructions of citizenship in this context through a specific focus on women who have experienced trafficking, and are beginning to organize around rights to sustainable livelihoods and actively lobby for changes in citizenship rules which discriminate against women. Building from this, in the final section we consider important implications of this analysis of post-trafficking experiences for debates about gender, sexuality and citizenship more broadly.Publisher PDFPeer reviewe
Modelling opinion formation by means of kinetic equations
In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophysical literature or no, can enter in this framework. While describing some contributions appeared in the literature, we enlighten some mathematical tools of kinetic theory that can be useful in the context of sociophysics
Weak and strong solutions of equations of compressible magnetohydrodynamics
International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques
Spatial Learning and Action Planning in a Prefrontal Cortical Network Model
The interplay between hippocampus and prefrontal cortex (PFC) is fundamental to
spatial cognition. Complementing hippocampal place coding, prefrontal
representations provide more abstract and hierarchically organized memories
suitable for decision making. We model a prefrontal network mediating
distributed information processing for spatial learning and action planning.
Specific connectivity and synaptic adaptation principles shape the recurrent
dynamics of the network arranged in cortical minicolumns. We show how the PFC
columnar organization is suitable for learning sparse topological-metrical
representations from redundant hippocampal inputs. The recurrent nature of the
network supports multilevel spatial processing, allowing structural features of
the environment to be encoded. An activation diffusion mechanism spreads the
neural activity through the column population leading to trajectory planning.
The model provides a functional framework for interpreting the activity of PFC
neurons recorded during navigation tasks. We illustrate the link from single
unit activity to behavioral responses. The results suggest plausible neural
mechanisms subserving the cognitive “insight” capability originally
attributed to rodents by Tolman & Honzik. Our time course analysis of neural
responses shows how the interaction between hippocampus and PFC can yield the
encoding of manifold information pertinent to spatial planning, including
prospective coding and distance-to-goal correlates
Linear stability of thick sprays equations
The coupling through both drag force and volume fraction (of gas) of a kinetic equation of Vlasov type and a system of Euler or Navier-Stokes type (in which the volume fraction explicity appears) leads to the socalled thick sprays equations. Those equations are used to describe sprays (droplets or dust specks in a surrounding gas) in which the volume fraction of the disperse phase is non negligible. As for other multiphase flows systems, the issues related to the linear stability around homogeneous solutions is important for the applications. We show in this paper that this stability indeed holds for thick sprays equations, under physically reasonable assumptions. The analysis which is performed makes use of Lyapunov functionals for the linearized equations
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