1,605 research outputs found
Memory effects in measure transport equations
Transport equations with a nonlocal velocity field have been introduced as a
continuum model for interacting particle systems arising in physics, chemistry
and biology. Fractional time derivatives, given by convolution integrals of the
time-derivative with power-law kernels, are typical for memory effects in
complex systems. In this paper we consider a nonlinear transport equation with
a fractional time-derivative. We provide a well-posedness theory for weak
measure solutions of the problem and an integral formula which generalizes the
classical push-forward representation formula to this setting
A time-fractional mean field game
We consider a Mean Field Games model where the dynamics of the agents is
subdiffusive. According to the optimal control interpretation of the problem,
we get a system involving fractional time-derivatives for the
Hamilton-Jacobi-Bellman and the Fokker-Planck equations. We discuss separately
the well-posedness for each of the two equations and then we prove existence
and uniqueness of the solution to the Mean Field Games syste
A measure theoretic approach to traffic flow optimization on networks
We consider a class of optimal control problems for measure-valued nonlinear
transport equations describing traffic flow problems on networks. The objective
isto minimise/maximise macroscopic quantities, such as traffic volume or
average speed,controlling few agents, for example smart traffic lights and
automated cars. The measuretheoretic approach allows to study in a same setting
local and nonlocal drivers interactionsand to consider the control variables as
additional measures interacting with the driversdistribution. We also propose a
gradient descent adjoint-based optimization method, ob-tained by deriving
first-order optimality conditions for the control problem, and we providesome
numerical experiments in the case of smart traffic lights for a 2-1 junction.Comment: 20 pages, 6 figure
The BAR Domain Superfamily: Membrane-Molding Macromolecules
Membrane-shaping proteins of the BAR domain superfamily are determinants of organelle biogenesis, membrane trafficking, cell division, and cell migration. An upsurge of research now reveals new principles of BAR domain-mediated membrane remodeling, enhancing our understanding of membrane curvature-mediated information processing
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