1,721,006 research outputs found
A hyperbolic model of multi-phase flow
No full textWe consider a hyperbolic model for the flow of an inviscid fluid admitting liquid and vapor phases.
We consider and prove here, as a preliminary study for a forthcoming paper, the basic features of the system: wave curves, Riemann problem, wave interactions
A system of ionized gas dynamics
No full textThe aim of this paper is to study a system of three equations for ionized gas dynamics at high temperature in one spatial dimension. In addition to the mass density, pressure, and particle velocity, a further quantity is needed, namely, the degree of ionization. The system is supplemented by the first and second law of thermodynamics and by an equation of state; all of them involve the degree of ionization. Finally, under the assumption of local thermodynamic equilibrium, the system is closed by requiring Saha's ionization equation. The geometric properties of the system are rather complicated: in particular, we prove the loss of convexity (genuine nonlinearity) for both forward and backward characteristic fields and hence the loss of concavity of the physical entropy. This takes place in a small bounded region, which we are able to characterize by numerical estimates on the state functions. The structure of shock waves is also studied by a detailed analysis of the Hugoniot locus
A hyperbolic model of multiphase flow
No full textWe consider a model for the flow of an inviscid fluid admitting liquid and vapor phases. We consider and prove here, as a preliminary study for a
forthcoming paper, the basic features of such a system:
wave curves, Riemann problem, wave interactions
Hysteresis and stop-and-go waves in traffic flows
No full textStop-and-go waves, also called phantom jams, are often observed in real traffic flows but can be produced neither by the classical Lighthill-Whitham-Richards (LWR) model nor by its known variants. To capture stop-and-go waves, we add hysteresis to the LWR model. For the model we propose, all possible viscous waves are found, and necessary and sufficient conditions for their existence are provided. In particular, deceleration and acceleration shocks appear; the latter were never rigorously defined before, in spite of the fact that they were observed in real traffic flows. Stop-and-go waves can be constructed by a pair of deceleration and acceleration shocks that completes a hysteresis cycle, illustrating how hysteresis loops lead to stop-and-go waves. In contrast, in the phase region where anticipation (i.e. negative hysteresis) loops exist, stop-and-go waves are not present, and speed variations decay. Riemann solutions are then found for all possible Riemann data. We explicitly show that, in the phase region where hysteresis loops exist, a sufficient deviation in speed of a few vehicles in an otherwise uniform car platoon can generate stop-and-go waves, confirming observations of real traffic experiments
Glimm estimates for a model of multiphase flow
No full textWe prove Glimm interaction estimates for a 3x3 hyperbolic system of conservation laws
arising in the modeling of multi-phase flows. No smallness of the interacting waves is
assumed. Our proof simplies and improves a previous result by Y.-J. Peng [9]
The hysteretic Aw–Rascle–Zhang model
No full textA novel hyperbolic system of partial differential equations is introduced to model traffic flows. This system comprises three equations, with two being linearly degenerate; its main feature is the inclusion of a hysteretic term in a generalized Aw-Rascle-Zhang (ARZ) model. First, a maximum principle for the diffusive version of the model is proven. Then, it is demonstrated that a solution to the Riemann problem exists, which is unique among solutions that are monotone in velocity; all waves exploited in the construction have suitable viscous profiles. Through several examples it is shown how, as a consequence of different driving habits, the system can model the decay, emergence, or persistence of stop-and-go waves (a feature that is missing in the ARZ model), and such behavior is characterized by a simple geometric condition. Furthermore, the model allows the study of traffic flows with a mixture of drivers whose hysteresis loops are either clockwise or counterclockwise. In particular, the presence of sufficiently many of the former dampens speed oscillations
String stability in traffic flows
No full textString stability or instability is a fundamental issue in traffic flow about whether the speed oscillations of the leading vehicle are damped or amplified as such oscillations pass through the platoon. If they are amplified, then traffic jams will occur. In this paper, we propose a suitable notion of string stability for continuum models of traffic flows, and study what kinds of driving behaviors lead to string stability or instability. We find that the well-known Lighthill-Whitham-Richards model and Aw-Rascle-Zhang model are string stable for wide classes of perturbations. As a consequence, the driving behaviors described by these models suppress speed oscillations and hence do not cause traffic jams. Once the hysteresis behavior is added to the Lighthill-Whitham-Richards model, an example is given to show that string instability can occur for large perturbations, leading to phan- tom jams. Under small perturbations, however, examples as well as approximate solution analysis suggest that the hysteretic traffic flow is string stable. The approximation solution analysis is developed to replace linear stability analysis, as hysteretic flow model cannot be linearized
Coherence and flow-maximization of a one-way valve
No full textWe consider a mathematical model for the gas flow through a one-way valve and focus on two issues. First, we propose a way to eliminate the chattering (the fast switch on and off of the valve) by slightly modifying the design of the valve. This mathematically amounts to the construction of a coupling Riemann solver with a suitable stability property, namely, coherence. We provide a numerical comparison of the behavior of the two valves. Second, we analyze, both analytically and numerically, for several significative situations, the maximization of the flow through the modified valve according to a control parameter of the valve and time
Wavefronts for Generalized Perona-Malik Equations
No full textWe consider a generalization of Perona-Malik equation with reaction and convective terms. By assuming that the reaction is monostable, we prove the existence of regular wavefronts as well as some of their qualitative properties. It turns out that the admissible speeds for subcritical or critical wavefronts form a closed half-line; the threshold cannot be computed explicitly but an estimate is provided. Moreover, the wavefronts are strictly monotone and their slope is bounded by the critical values of the diffusion
Wavefronts for degenerate diffusion-convection reaction equations with sign-changing diffusivity
No full textWe consider in this paper a diffusion-convection reaction equation in one space dimension. The main assumptions are about the reaction term, which is monostable, and the diffusivity, which changes sign once or even more than once; then, we deal with a forward-backward parabolic equation. Our main results concern the existence of globally defined traveling waves, which connect two equilibria and cross both regions where the diffusivity is positive and regions where it is negative. We also investigate the monotony of the profiles and show the appearance of sharp behaviors at the points where the diffusivity degenerates. In particular, if such points are interior points, then the sharp behaviors are new and unusual
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