Queue replacement principle for corridor problems with heterogeneous commuters

This study investigates the theoretical properties of a departure time choice problem considering commuters' heterogeneity with respect to the value of schedule delay in corridor networks. Specifically, we develop an analytical method to solve the dynamic system optimal (DSO) and dynamic user equilibrium (DUE) problems. To derive the DSO solution, we first demonstrate the bottleneck-based decomposition property, i.e., the DSO problem can be decomposed into multiple single bottleneck problems. Subsequently, we obtain the analytical solution by applying the theory of optimal transport to each decomposed problem and derive optimal congestion prices to achieve the DSO state. To derive the DUE solution, we prove the queue replacement principle (QRP) that the time-varying optimal congestion prices are equal to the queueing delay in the DUE state at every bottleneck. This principle enables us to derive a closed-form DUE solution based on the DSO solution. Moreover, as an application of the QRP, we prove that the equilibrium solution under various policies (e.g., on-ramp metering, on-ramp pricing, and its partial implementation) can be obtained analytically. Finally, we compare these equilibria with the DSO state.Comment: 36 pages, 15 figure

Global stability of day-to-day dynamics for schedule-based Markovian transit assignment with boarding queues

Schedule-based transit assignment describes congestion in public transport services by modeling the interactions of passenger behavior in a time-space network built directly on a transit schedule. This study investigates the theoretical properties of scheduled-based Markovian transit assignment with boarding queues. When queues exist at a station, passenger boarding flows are loaded according to the residual vehicle capacity, which depends on the flows of passengers already on board with priority. An equilibrium problem is formulated under this nonseparable link cost structure as well as explicit capacity constraints. The network generalized extreme value (NGEV) model, a general class of additive random utility models with closed-form expression, is used to describe the path choice behavior of passengers. A set of formulations for the equilibrium problem is presented, including variational inequality and fixed-point problems, from which the day-to-day dynamics of passenger flows and costs are derived. It is shown that Lyapunov functions associated with the dynamics can be obtained and guarantee the desirable solution properties of existence, uniqueness, and global stability of the equilibria. In terms of dealing with stochastic equilibrium with explicit capacity constraints and non-separable link cost functions, the present theoretical analysis is a generalization of the existing day-to-day dynamics in the context of general traffic assignment.Comment: 26 pages, 3 figure

Pressure-Induced Antiferromagnetic Bulk Superconductor EuFe2_2As2_2

We present the magnetic and superconducting phase diagram of EuFe$_2$As$_2$ for $B \parallel c$ and $B \parallel ab$. The antiferromagnetic phase of the Eu$^{2+}$ moments is completely enclosed in the superconducting phase. The upper critical field vs. temperature curves exhibit strong concave curvatures, which can be explained by the Jaccarino-Peter compensation effect due to the antiferromagnetic exchange interaction between the Eu$^{2+}$ moments and conduction electrons.Comment: submitted to the proceedings of the M2S-IX Toky

Cyclotron resonance and mass enhancement by electron correlation in KFe2_2As2_2

Cyclotron resonance (CR) measurements for the Fe-based superconductor KFe$_2$As$_2$ are performed. One signal for CR is observed, and is attributed to the two-dimensional $\alpha$ Fermi surface at the $\Gamma$ point. We found a large discrepancy in the effective masses of CR [(3.4$\pm$0.05)$m_e$ ($m_e$ is the free electron mass)] and de-Haas van Alphen (dHvA) results, a direct evidence of mass enhancement due to electronic correlation. A comparison of the CR and dHvA results shows that both intra- and interband electronic correlations contribute to the mass enhancement in KFe$_2$As$_2$.Comment: 5 pages, 4 figure

Quasi-Two-Dimensional Fermi Surfaces and Coherent Interlayer Transport in KFe2_2As2_2

We report the results of the angular-dependent magnetoresistance oscillations (AMROs), which can determine the shape of bulk Fermi surfaces in quasi-two-dimensional (Q2D) systems, in a highly hole-doped Fe-based superconductor KFe$_2$As$_2$ with $T_c \approx$ 3.7 K. From the AMROs, we determined the two Q2D FSs with rounded-square cross sections, corresponding to 12% and 17% of the first Brillouin zone. The rounded-squared shape of the FS cross section is also confirmed by the analyses of the interlayer transport under in-plane fields. From the obtained FS shape, we infer the character of the 3d orbitals that contribute to the FSs.Comment: 4 pages, 4 figures, accepted in Phys. Rev. Let

Stochastic stability of dynamic user equilibrium in unidirectional networks: Weakly acyclic game approach

The aim of this study is to analyze the stability of dynamic user equilibrium (DUE) with fixed departure times in unidirectional networks. Specifically, stochastic stability, which is the concept of stability in evolutionary dynamics subjected to stochastic effects, is herein considered. To achieve this, a new approach is developed by synthesizing the three concepts: the decomposition technique of DUE assignments, the weakly acyclic game, and the asymptotic analysis of the stationary distribution of perturbed dynamics. Specifically, we first formulate a DUE assignment as a strategic game (DUE game) that deals with atomic users. We then prove that there exists an appropriate order of assigning users for ensuring equilibrium in a unidirectional network. With this property, we establish the relationship between DUE games in unidirectional networks and weakly acyclic games. The convergence and stochastic stability of better response dynamics in the DUE games are then proved based on the theory of weakly acyclic games. Finally, we observe the properties of the convergence and stability from numerical experiments. The results show that the strict improvement of users’ travel times by the applied evolutionary dynamics is important for ensuring the existence of a stochastically stable equilibrium in DUE games

Integer spin-chain antiferromagnetism of the 4d oxide CaRuO3 with post-perovskite structure

A quasi-one dimensional magnetism was discovered in the post-perovskite CaRuO3 (Ru4+: 4d4, Cmcm), which is iso-compositional with the perovskite CaRuO3 (Pbnm). An antiferromagnetic spin-chain function with -J/kB = 350 K well reproduces the experimental curve of the magnetic susceptibility vs. temperature, suggesting long-range antiferromagnetic correlations. The anisotropic magnetism is probably owing to the dyz - 2p- dzx and dzx - 2p- dyz superexchange bonds along a-axis. The Sommerfeld coefficient of the specific heat is fairly small, 0.16(2) mJ mol-1 K-2, indicating that the magnetism reflects localized nature of the 4d electrons. As far as we know, this is the first observation of an integer (S = 1) spin-chain antiferromagnetism in the 4d electron system.Comment: Accepted for publication in Phys. Rev.