Entropy solutions for a traffic model with phase transitions

In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front tracking method to prove existence and a priori bounds for weak solutions. Then, in the case the characteristic field corresponding to the free phase is linearly degenerate, we prove that the obtained weak solutions are in fact entropy solutions \`a la Kruzhkov. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions

Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit

We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. More precisely, we prove that the empirical measure (respectively the discretised density) obtained from the follow-the-leader system converges in the 1-Wasserstein topology (respectively in $L^1_{loc}$) to the unique Kruzkov entropy solution of the conservation law. The initial data are taken in $L^1\cap L^\infty$, nonnegative, and with compact support, hence we are able to handle densities with vacuum. Our result holds for a reasonably general class of velocity maps (including all the relevant examples in the applications, e.g. in the Lighthill-Whitham-Richards model for traffic flow) with possible degenerate slope near the vacuum state. The proof of the result is based on discrete BV estimates and on a discrete version of the one-sided Oleinik-type condition. In particular, we prove that the regularizing effect $L^1\cap L^\infty \mapsto BV$ for nonlinear scalar conservation laws is intrinsic of the discrete model

Noise and diffusion of particles obeying asymmetric exclusion processes

The relation between noise and Fick's diffusion coefficient in barrier limited transport associated with hopping or tunneling mechanisms of particles obeying the asymmetric simple exclusion processes (ASEP) is physically assessed by Monte Carlo simulations. For a closed ring consisting of a large number of barriers the diffusion coefficient is related explicitly to the current noise thus revealing the existence of a generalized Nyquist-Einstein relation. Both diffusion and noise are confirmed to decrease as the square root of the number of barriers as a consequence of the correlation induced by ASEP. By contrast, for an open linear chain of barriers the diffusion coefficient is found to be no longer related to current noise. Here diffusion depends on particle concentration but is independent of the number of barriers

Labour market and social policy in Italy. Challenges and changes

Eight years after the outbreak of the financial crisis, Italy has still to cope with and overcome a plethora of economic and social challenges. On top of this, it faces an unfavourable demographic structure and severe disparities between its northern and southern regions. Some promising reforms have recently been enacted, specifically targeting poverty and social exclusion. However, much more remains to be done on the way towards greater economic stability and widely shared prosperity

Library Class: Model Pembelajaran Literasi Informasi Tingkat Sekolah Dasar (Studi Kasus SD Madania)

Literasi Informasi merupakan komponen keterampilan yang sangat penting dalam pembelajaran seumur hidup bagi siswa. Sekolah Dasar Madania Parung Bogor merupakan salah satu sekolah di Indonesia yang menerapkan pembelajaran literasi informasi sejak tingkat sekolah dasar. Pengkajian bertujuan untuk merancang desain pembelajaran literasi informasi sejak sekolah dasar. Pengkajian ini merupakan studi kasus tentang karakteristik model pembelajaran literasi informasi di Sekolah Dasar Madania. Hasil kajian memperlihatkan bahwa keterampilan literasi informasi perlu diberikan bagi siswa sejak tingkat sekolah dasar agar menjadi bekal keterampilan pembelajar mandiri. Pembelajaran literasi informasi di SD Madania berbentuk kelas klasikal yang disebut dengan Library Class. Library Class memiliki peranan dalam meningkatkan kemampuan literasi informasi siswa. Hasil lainnya adalah tersusunnya ruang lingkup utama yang menjadi dasar pengembangan topik lain yang mendukung pencapaian tujuan pembelajaran. Keenam ruang lingkup utama tersebut adalah (1) Orientasi dan nilai-nilai kepustakaan atau library values;(2) Sumbersumber informasi atau resource literacy; (3) Penelusuran informasi atau research literacy; (4) Pengolahan dan pemanfaatan informasi atau organization of information; (5) Evaluasi informasi atau critical literacy; dan (6) Penyajian informasi atau publishing literacy. Keenam ruang lingkup utama tersebut dituangkan dalam bentuk silabus yang dapat menjadi rekomendasi bagi para pengelola perpustakaan sekolah, guru, dan kepala sekolah untuk mengintegrasikan literasi informasi dalam proses pengajaran dan pembelajaran di kelas sehingga tercapai keterpaduan dan kolaborasi antar berbagai pihak di sekolah dalam meningkatkan kualitas pembelajaran

Coupling conditions for isothermal gas flow and applications to valves

We consider an isothermal gas flowing through a straight pipe and study the effects of a two-way electronic valve on the flow. The valve is either open or closed according to the pressure gradient and is assumed to act without any time or reaction delay. We first give a notion of coupling solution for the corresponding Riemann problem; then, we highlight and investigate several important properties for the solver, such as coherence, consistence, continuity on initial data and invariant domains. In particular, the notion of coherence introduced here is new and related to commuting behaviors of valves. We provide explicit conditions on the initial data in order that each of these properties is satisfied. The modeling we propose can be easily extended to a very wide class of valves

Riemann problems with non--local point constraints and capacity drop

In the present note we discuss in details the Riemann problem for a one--dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the problem, namely in the case, relevant for numerical applications, of a discretized exit capacity. We devote particular attention to the case in which the constraint is given by a non--local operator depending on the solution itself. We provide several explicit examples. We also give the detailed proof of some results announced in the paper [Andreainov, Donadello, Rosini, "Crowd dynamics and conservation laws with non--local point constraints and capacity drop", which is devoted to existence and stability for a more general class of Cauchy problems subject to Lipschitz continuous non--local point constraints.Comment: 19 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1304.628