A variational approach for continuous supply chain networks

We consider a continuous supply chain network consisting of buffering queues and processors first proposed by [D. Armbruster, P. Degond, and C. Ringhofer, SIAM J. Appl. Math., 66 (2006), pp. 896–920] and subsequently analyzed by [D. Armbruster, P. Degond, and C. Ringhofer, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), pp. 433–460] and [D. Armbruster, C. De Beer, M. Fre- itag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104–114]. A model was proposed for such a network by [S. G ̈ottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559] using a system of coupling ordinary differential equations and partial differential equations. In this article, we propose an alternative approach based on a variational method to formulate the network dynamics. We also derive, based on the variational method, a computational algorithm that guarantees numerical stability, allows for rigorous error estimates, and facilitates efficient computations. A class of network flow optimization problems are formulated as mixed integer programs (MIPs). The proposed numerical algorithm and the corresponding MIP are compared theoretically and numerically with existing ones [A. Fu ̈genschuh, S. Go ̈ttlich, M. Herty, A. Klar, and A. Martin, SIAM J. Sci. Comput., 30 (2008), pp. 1490–1507; S. Go ̈ttlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559], which demonstrates the modeling and computational advantages of the variational approach

A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure

Data-driven linear decision rule approach for distributionally robust optimization of on-line signal control

We propose a two-stage, on-line signal control strategy for dynamic networks using a linear decision rule (LDR) approach and a distributionally robust optimization (DRO) technique. The first (off-line) stage formulates a LDR that maps real-time traffic data to optimal signal control policies. A DRO problem is solved to optimize the on-line performance of the LDR in the presence of uncertainties associated with the observed traffic states and ambiguity in their underlying distribution functions. We employ a data-driven calibration of the uncertainty set, which takes into account historical traffic data. The second (on-line) stage implements a very efficient linear decision rule whose performance is guaranteed by the off-line computation. We test the proposed signal control procedure in a simulation environment that is informed by actual traffic data obtained in Glasgow, and demonstrate its full potential in on-line operation and deployability on realistic networks, as well as its effectiveness in improving traffic

On the continuum approximation of the on-and-off signal control on dynamic traffic networks

In the modeling of traffic networks, a signalized junction is typically treated using a binary variable to model the on-and-off nature of signal operation. While accurate, the use of binary variables can cause problems when studying large networks with many intersections. Instead, the signal control can be approximated through a continuum approach where the on-and-off control variable is replaced by a continuous priority parameter. Advantages of such approximation include elimination of the need for binary variables, lower time resolution requirements, and more flexibility and robustness in a decision environment. It also resolves the issue of discontinuous travel time functions arising from the context of dynamic traffic assignment. Despite these advantages in application, it is not clear from a theoretical point of view how accurate is such continuum approach; i.e., to what extent is this a valid approximation for the on-and-off case. The goal of this paper is to answer these basic research questions and provide further guidance for the application of such continuum signal model. In particular, by employing the Lighthill-Whitham-Richards model (Lighthill and Whitham, 1955; Richards, 1956) on a traffic network, we investigate the convergence of the on-and-off signal model to the continuum model in regimes of diminishing signal cycles. We also provide numerical analyses on the continuum approximation error when the signal cycles are not infinitesimal. As we explain, such convergence results and error estimates depend on the type of fundamental diagram assumed and whether or not vehicle spillback occurs to the signalized intersection in question. Finally, a traffic signal optimization problem is presented and solved which illustrates the unique advantages of applying the continuum signal model instead of the on-and-off model

Induced Magnetic Ordering by Proton Irradiation in Graphite

We provide evidence that proton irradiation of energy 2.25 MeV on highly-oriented pyrolytic graphite samples triggers ferro- or ferrimagnetism. Measurements performed with a superconducting quantum interferometer device (SQUID) and magnetic force microscopy (MFM) reveal that the magnetic ordering is stable at room temperature.Comment: 3 Figure

Magnetoresistance in the superconducting state at the (111) LaAlO3_3/SrTiO3_3 interface

Condensed matter systems that simultaneously exhibit superconductivity and ferromagnetism are rare due the antagonistic relationship between conventional spin-singlet superconductivity and ferromagnetic order. In materials in which superconductivity and magnetic order is known to coexist (such as some heavy-fermion materials), the superconductivity is thought to be of an unconventional nature. Recently, the conducting gas that lives at the interface between the perovskite band insulators LaAlO$_3$ (LAO) and SrTiO$_3$ (STO) has also been shown to host both superconductivity and magnetism. Most previous research has focused on LAO/STO samples in which the interface is in the (001) crystal plane. Relatively little work has focused on the (111) crystal orientation, which has hexagonal symmetry at the interface, and has been predicted to have potentially interesting topological properties, including unconventional superconducting pairing states. Here we report measurements of the magnetoresistance of (111) LAO/STO heterostructures at temperatures at which they are also superconducting. As with the (001) structures, the magnetoresistance is hysteretic, indicating the coexistence of magnetism and superconductivity, but in addition, we find that this magnetoresistance is anisotropic. Such an anisotropic response is completely unexpected in the superconducting state, and suggests that (111) LAO/STO heterostructures may support unconventional superconductivity.Comment: 6 Pages 4 figure