1,721,231 research outputs found
On the singular limit problem in nonlocal balance laws: Applications to nonlocal lane-changing traffic flow models
No full textWe present a convergence result from nonlocal to local behavior for a system of nonlocal balance laws. The velocity field of the underlying conservation laws is diagonal. In contrast, the coupling to the remaining balance laws involves a nonlinear right-hand side that depends on the solution, nonlocal term, and other factors. The nonlocal operator integrates the density around a specific spatial point, which introduces nonlocality into the problem. Inspired by multi-lane traffic flow modeling and lane-changing, the nonlocal kernel is discontinuous and only looks downstream. In this paper, we prove the convergence of the system to the local entropy solutions when the nonlocal operator (chosen to be of an exponential type for simplicity) converges to a Dirac distribution. Numerical illustrations that support the main results are also presented. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/)
Perfect wedding: hadiah terindah untuk cinta
No full textNovel ini mempunyai konsep yang unik. Kisah tentang sebuah pernikahan yang dipandang dari tiga sisi yang berbeda oleh tiga wanita. Siapa bilang pernikahan adalah impian semua wanita, kadang ada beberapa wanita yang punya prinsip berbeda tentang pernikahan dan ada yang terbelenggu sebuah masa lalu sehingga gamang untuk melangkah ke dalam pernikahan. Dengan kover yang cantik minta ampun ini, tiga penulis: Putu Felisia, Catz Link Tristan dan Achi Narahashi merangkai tiga buah kisah.
Novel ini dawali dengan kisah tentang J atau Julia karya Catz Link Tristan. Dengan sudut pandang orang pertama yaitu dari sisi Julia, saya dijejali dengan keluh kesah si calon penganti wanita ini. Julia digambarkan sebagai karakter yang menyepelekan pernikahan. Bagi dia yang penting ada pria sempurna yang melamar, urusan cinta bisa dipupuk belakangan.
Kisah yang kedua adalah kisah Mei karya Achi Narahashi.
Yang terakhir adalah kisah Octa karya Putu Felisia
Macroscopic limits of non-local kinetic descriptions of vehicular traffic
Get PDFWe study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of
non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle dynamics produce a first order macroscopic model with non-local flux. Next, we show that non-local follow-the-leader vehicle dynamics have a universal macroscopic counterpart in the second order Aw-Rascle-Zhang traffic model, at least when the non-locality of the interactions is sufficiently small. Finally, we show that the same qualitative result holds also for a general class of follow-the-leader dynamics based on the headway of the vehicles rather than
on their speed. We also investigate the correspondence between the solutions to particle models and their macroscopic limits by means of numerical simulations
A statistical mechanics approach to macroscopic limits of car-following traffic dynamics
Get PDFWe study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towards a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic processes. If FTL interactions dominate then one gets an inhomogeneous Aw-Rascle-Zhang model, whose (pseudo) pressure and stability of the uniform flow are precisely defined by some features of the microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is comparable to that of FTL interactions then one gets a Lighthill-Whitham-Richards model ruled only by the OV function. We further confirm these findings by means of numerical simulations of the particle system and the macroscopic models. Unlike other formally analogous results, our approach builds the macroscopic models as physical limits of particle dynamics rather than assessing the convergence of microscopic to macroscopic solutions under suitable numerical discretisations
A NONLOCAL AW-RASCLE-ZHANG SYSTEM WITH LINEAR PRESSURE TERM
No full textIn this paper, we study a nonlocal extension of the Aw-Rascle-Zhang traffic model, where the pressure-like term is modeled as a convolution between vehicle density and a kernel function. This formulation captures nonlocal driver interactions and aligns structurally with the Euler-alignment system studied in Leslie-Tan, Comm. PDE (2023). Using a sticky particle approximation, we construct entropy solutions to the equation for the cumulative density and prove convergence of approximate solutions to weak solutions of the nonlocal system. The analysis includes well-posedness, stability estimates, and an entropic selection principle
Euler-flocking system with nonlocal dissipation in 1D: periodic entropy solutions
No full textWe consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in a periodic domain in one-space dimension with linear pressure term. The main result is the global existence of periodic entropy weak solutions, for periodic initial data having finite total variation and initial density bounded away from zero
Blow up for nonlinear wave-type equations with perturbed derivatives
No full textWe investigate semilinear wave-type equations that can be recast as wave equations with derivatives perturbed by zero-order terms. This framework covers several well-studied cases, including the scale-invariant wave equation. In this setting, we refine existing blow-up results for radial initial data with suitable decay, and identify conditions on the zero-order terms that govern the interplay between derivative perturbations, initial data size, and nonlinearity exponent
Hydrodynamic traffic flow models including random accidents: A kinetic derivation
No full textWe present a formal kinetic derivation of a second order macroscopic traffic model from a stochastic particle model. The macroscopic model is given by a system of hyperbolic partial differential equations (PDEs) with a discontinuous flux function, in which the traffic density and the headway are the averaged quantities. A numerical study illustrates the performance of the second order model compared to the particle approach. We also analyse numerically uncertain traffic accidents by considering statistical measures of the solution to the PDEs
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