42 research outputs found
Fokker-Planck Asymptotics for Traffic Flow Models
Starting from microscopic interaction rules we derive kinetic models of
Fokker--Planck type for vehicular traffic flow. The derivation is based on
taking a suitable asymptotic limit of the corresponding Boltzmann model. As
particular cases, the derived models comprise existing models.
New Fokker--Planck models are also given and their differences to existing
models are highlighted. Finally, we report on numerical experiments
Kinetic-controlled hydrodynamics for multilane traffic models
We study the application of a recently introduced hierarchical description of
traffic flow control by driver-assist vehicles to include lane changing
dynamics. Lane-dependent feedback control strategies are implemented at the
level of vehicles and the aggregate trends are studied by means of
Boltzmann-type equations determining three different hydrodynamics based on the
lane switching frequency. System of first order macroscopic equations
describing the evolution of densities along the lanes are then consistently
determined through a suitable closured strategy. Numerical examples are then
presented to illustrate the features of the proposed hierarchical approach
Control of a lane-drop bottleneck through variable speed limits
In this study, we formulate the VSL control problem for the traffic system in
a zone upstream to a lane-drop bottleneck based on two traffic flow models: the
Lighthill-Whitham-Richards (LWR) model, which is an infinite-dimensional
partial differential equation, and the link queue model, which is a
finite-dimensional ordinary differential equation. In both models, the
discharging flow-rate is determined by a recently developed model of capacity
drop, and the upstream in-flux is regulated by the speed limit in the VSL zone.
Since the link queue model approximates the LWR model and is much simpler, we
first analyze the control problem and develop effective VSL strategies based on
the former. First for an open-loop control system with a constant speed limit,
we prove that a constant speed limit can introduce an uncongested equilibrium
state, in addition to a congested one with capacity drop, but the congested
equilibrium state is always exponentially stable. Then we apply a feedback
proportional-integral (PI) controller to form a closed-loop control system, in
which the congested equilibrium state and, therefore, capacity drop can be
removed by the I-controller. Both analytical and numerical results show that,
with appropriately chosen controller parameters, the closed-loop control system
is stable, effect, and robust. Finally, we show that the VSL strategies based
on I- and PI-controllers are also stable, effective, and robust for the LWR
model. Since the properties of the control system are transferable between the
two models, we establish a dual approach for studying the control problems of
nonlinear traffic flow systems. We also confirm that the VSL strategy is
effective only if capacity drop occurs. The obtained method and insights can be
useful for future studies on other traffic control methods and implementations
of VSL strategies.Comment: 31 pages, 14 figure
Using the Sharp Operator for edge detection and nonlinear diffusion
In this paper we investigate the use of the sharp function known from functional analysis in image processing. The sharp function gives a measure of the variations of a function and can be used as an edge detector. We extend the classical notion of the sharp function for measuring anisotropic behaviour and give a fast anisotropic edge detection variant inspired by the sharp function. We show that these edge detection results are useful to steer isotropic and anisotropic nonlinear diffusion filters for image enhancement
Intracellular transport driven by cytoskeletal motors: General mechanisms and defects
Cells are strongly out-of-equilibrium systems driven by continuous energy
supply. They carry out many vital functions requiring active transport of
various ingredients and organelles, some being small, others being large. The
cytoskeleton, composed of three types of filaments, determines the shape of the
cell and plays a role in cell motion. It also serves as a road network for the
so-called cytoskeletal motors. These molecules can attach to a cytoskeletal
filament, perform directed motion, possibly carrying along some cargo, and then
detach. It is a central issue to understand how intracellular transport driven
by molecular motors is regulated, in particular because its breakdown is one of
the signatures of some neuronal diseases like the Alzheimer.
We give a survey of the current knowledge on microtubule based intracellular
transport. We first review some biological facts obtained from experiments, and
present some modeling attempts based on cellular automata. We start with
background knowledge on the original and variants of the TASEP (Totally
Asymmetric Simple Exclusion Process), before turning to more application
oriented models. After addressing microtubule based transport in general, with
a focus on in vitro experiments, and on cooperative effects in the
transportation of large cargos by multiple motors, we concentrate on axonal
transport, because of its relevance for neuronal diseases. It is a challenge to
understand how this transport is organized, given that it takes place in a
confined environment and that several types of motors moving in opposite
directions are involved. We review several features that could contribute to
the efficiency of this transport, including the role of motor-motor
interactions and of the dynamics of the underlying microtubule network.
Finally, we discuss some still open questions.Comment: 74 pages, 43 figure
A proof of convergence of a finite volume scheme for modified steady Richards’ equation describing transport processes in the pressing section of a paper machine
A number of water flow problems in porous media are modelled by Richards’ equation [1]. There exist a lot of different applications of this model. We are concerned with the simulation of the pressing section of a paper machine. This part of the industrial process provides the dewatering of the paper layer by the use of clothings, i.e. press felts, which absorb the water during pressing [2]. A system of nips are formed in the simplest case by rolls, which increase sheet dryness by pressing against each other (see Figure 1). A lot of theoretical studies were done for Richards’ equation (see [3], [4] and references therein). Most articles consider the case of x-independent coefficients. This simplifies the system considerably since, after Kirchhoff’s transformation of the problem, the elliptic operator becomes linear. In our case this condition is not satisfied and we have to consider nonlinear operator of second order. Moreover, all these articles are concerned with the nonstationary problem, while we are interested in the stationary case. Due to complexity of the physical process our problem has a specific feature. An additional convective term appears in our model because the porous media moves with the constant velocity through the pressing rolls. This term is zero in immobile porous media. We are not aware of papers, which deal with such kind of modified steady Richards’ problem. The goal of this paper is to obtain the stability results, to show the existence of a solution to the discrete problem, to prove the convergence of the approximate solution to the weak solution of the modified steady Richards’ equation, which describes the transport processes in the pressing section. In Section 2 we present the model which we consider. In Section 3 a numerical scheme obtained by the finite volume method is given. The main part of this paper is theoretical studies, which are given in Section 4. Section 5 presents a numerical experiment. The conclusion of this work is given in Section 6
Statistical Physics of Vehicular Traffic and Some Related Systems
In the so-called "microscopic" models of vehicular traffic, attention is paid
explicitly to each individual vehicle each of which is represented by a
"particle"; the nature of the "interactions" among these particles is
determined by the way the vehicles influence each others' movement. Therefore,
vehicular traffic, modeled as a system of interacting "particles" driven far
from equilibrium, offers the possibility to study various fundamental aspects
of truly nonequilibrium systems which are of current interest in statistical
physics. Analytical as well as numerical techniques of statistical physics are
being used to study these models to understand rich variety of physical
phenomena exhibited by vehicular traffic. Some of these phenomena, observed in
vehicular traffic under different circumstances, include transitions from one
dynamical phase to another, criticality and self-organized criticality,
metastability and hysteresis, phase-segregation, etc. In this critical review,
written from the perspective of statistical physics, we explain the guiding
principles behind all the main theoretical approaches. But we present detailed
discussions on the results obtained mainly from the so-called
"particle-hopping" models, particularly emphasizing those which have been
formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include
Single- and multi-population kinetic models for vehicular traffic reproducing fundamental diagrams and with low computational complexity.
In this work, we focus on kinetic theory of vehicular traffic. We introduce (Boltzmann and Fokker-Planck) models having the following properties: they are amenable for computations and analytical investigations, but at the same time they are able to characterize and to explain the features of experimental diagrams.
The scattering observed in experimental data is reproduced by a multi-population model. We propose a new interpretation of the dispersion of data since it can be attributed to the heterogeneous composition of the flow. In fact, the scattering is obtained by treating traffic as a mixture of vehicles with different physical and kinematic characteristics.
The multi-population model is built as generalization of a new single-population model for which the analytical expression of the steady state can be computed explicitly. This is possible thanks to the particular choice of the microscopic interactions. These models are able to catch the macroscopic properties of the flow at equilibrium, as the phase transition, the capacity drop and the scattering of data.
The proposed models are endowed with a robust mathematical structure. We study the mathematical properties which induce the structure of diagrams, the well posedness with the existence and uniqueness proof of the solution of the kinetic equations.
A further result of this thesis is the analysis of the effects of the microscopic interactions on the macroscopic dynamics. This purely multiscale issue which is tackled by an asymptotic study of the model in the Fokker-Planck limit