Control of a lane-drop bottleneck through variable speed limits

In this study, we formulate the VSL control problem for the traffic system in a zone upstream to a lane-drop bottleneck based on two traffic flow models: the Lighthill-Whitham-Richards (LWR) model, which is an infinite-dimensional partial differential equation, and the link queue model, which is a finite-dimensional ordinary differential equation. In both models, the discharging flow-rate is determined by a recently developed model of capacity drop, and the upstream in-flux is regulated by the speed limit in the VSL zone. Since the link queue model approximates the LWR model and is much simpler, we first analyze the control problem and develop effective VSL strategies based on the former. First for an open-loop control system with a constant speed limit, we prove that a constant speed limit can introduce an uncongested equilibrium state, in addition to a congested one with capacity drop, but the congested equilibrium state is always exponentially stable. Then we apply a feedback proportional-integral (PI) controller to form a closed-loop control system, in which the congested equilibrium state and, therefore, capacity drop can be removed by the I-controller. Both analytical and numerical results show that, with appropriately chosen controller parameters, the closed-loop control system is stable, effect, and robust. Finally, we show that the VSL strategies based on I- and PI-controllers are also stable, effective, and robust for the LWR model. Since the properties of the control system are transferable between the two models, we establish a dual approach for studying the control problems of nonlinear traffic flow systems. We also confirm that the VSL strategy is effective only if capacity drop occurs. The obtained method and insights can be useful for future studies on other traffic control methods and implementations of VSL strategies.Comment: 31 pages, 14 figure

Relativistic Hartree-Fock theory. Part I: density-dependent effective Lagrangians

Effective Lagrangians suitable for a relativistic Hartree-Fock description of nuclear systems are presented. They include the 4 effective mesons $\sigma, \omega, \rho$ and $\pi$ with density-dependent meson-nucleon couplings. The criteria for determining the model parameters are the reproduction of the binding energies in a number of selected nuclei, and the bulk properties of nuclear matter (saturation point, compression modulus, symmetry energy). An excellent description of nuclear binding energies and radii is achieved for a range of nuclei encompassing light and heavy systems. The predictions of the present approach compare favorably with those of existing relativistic mean field models, with the advantage of incorporating the effects of pion-nucleon coupling.Comment: 26 pages, 5 table

Neutron star properties in density-dependent relativistic Hartree-Fock theory

With the equations of state provided by the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory for hadronic matter, the properties of the static and $\beta$-equilibrium neutron stars without hyperons are studied for the first time, and compared to the predictions of the relativistic mean field (RMF) models and recent observational data. The influences of Fock terms on properties of asymmetric nuclear matter at high densities are discussed in details. Because of the significant contributions from the $\sigma$- and $\omega$-exchange terms to the symmetry energy, large proton fractions in neutron stars are predicted by the DDRHF calculations, which strongly affect the cooling process of the star. The critical mass about 1.45 $M_\odot$, close to the limit 1.5 $M_\odot$ determined by the modern soft X-ray data analysis, is obtained by DDRHF with the effective interactions PKO2 and PKO3 for the occurrence of direct Urca process in neutron stars. The maximum masses of neutron stars given by the DDRHF calculations lie between 2.45 M$_\odot$ and 2.49 M$_\odot$, which are in reasonable agreement with high pulsar mass $2.08 \pm 0.19 M_\odot$ from PSR B1516+02B. It is also found that the mass-radius relations of neutron stars determined by DDRHF are consistent with the observational data from thermal radiation measurement in the isolated neutron star RX J1856, QPOs frequency limits in LMXBs 4U 0614+09 and 4U 1636-536, and redshift determined in LMXBs EXO 0748-676.Comment: 28 pages, 11 figure

Shell Structure and ρ\rho-Tensor Correlations in Density-Dependent Relativistic Hartree-Fock theory

A new effective interaction PKA1 with $\rho$-tensor couplings for the density-dependent relativistic Hartree-Fock (DDRHF) theory is presented. It is obtained by fitting selected empirical ground state and shell structure properties. It provides satisfactory descriptions of nuclear matter and the ground state properties of finite nuclei at the same quantitative level as recent DDRHF and RMF models. Significant improvement on the single-particle spectra is also found due to the inclusion of $\rho$-tensor couplings. As a result, PKA1 cures a common disease of the existing DDRHF and RMF Lagrangians, namely the artificial shells at 58 and 92, and recovers the realistic sub-shell closure at 64. Moreover, the proper spin-orbit splittings and well-conserved pseudo-spin symmetry are obtained with the new effective interaction PKA1. Due to the extra binding introduced by the $\rho$-tensor correlations, the balance between the nuclear attractions and the repulsions is changed and this constitutes the physical reason for the improvement of the nuclear shell structure.Comment: 20 pages, 11 figures, 6 table

Pairing phase transition: A Finite-Temperature Relativistic Hartree-Fock-Bogoliubov study

Background: The relativistic Hartree-Fock-Bogoliubov (RHFB) theory has recently been developed and it provides a unified and highly predictive description of both nuclear mean field and pairing correlations. Ground state properties of finite nuclei can accurately be reproduced without neglecting exchange (Fock) contributions. Purpose: Finite-temperature RHFB (FT-RHFB) theory has not yet been developed, leaving yet unknown its predictions for phase transitions and thermal excitations in both stable and weakly bound nuclei. Method: FT-RHFB equations are solved in a Dirac Woods-Saxon (DWS) basis considering two kinds of pairing interactions: finite or zero range. Such a model is appropriate for describing stable as well as loosely bound nuclei since the basis states have correct asymptotic behaviour for large spatial distributions. Results: Systematic FT-RH(F)B calculations are performed for several semi-magic isotopic/isotonic chains comparing the predictions of a large number of Lagrangians, among which are PKA1, PKO1 and DD-ME2. It is found that the critical temperature for a pairing transition generally follows the rule $T_c = 0.60\Delta(0)$ for a finite-range pairing force and $T_c = 0.57\Delta(0)$ for a contact pairing force, where $\Delta(0)$ is the pairing gap at zero temperature. Two types of pairing persistence are analysed: type I pairing persistence occurs in closed subshell nuclei while type II pairing persistence can occur in loosely bound nuclei strongly coupled to the continuum states. Conclusions: This first FT-RHFB calculation shows very interesting features of the pairing correlations at finite temperature and in finite systems such as pairing re-entrance and pairing persistence.Comment: 13 pages, 11 figures, accepted version in Phys. Rev.

KS0−KL0K_S^0-K_L^0 Asymmetries and CPCP Violation in Charmed Baryon Decays into Neutral Kaons

We study the $K^0_S-K^0_L$ asymmetries and $CP$ violations in charm-baryon decays with neutral kaons in the final state. The $K^0_S-K^0_L$ asymmetry can be used to search for two-body doubly Cabibbo-suppressed amplitudes of charm-baryon decays, with the one in $\Lambda^+_c\to pK^0_{S,L}$ as a promising observable. Besides, it is studied for a new $CP$-violation effect in these processes, induced by the interference between the Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with the neutral kaon mixing. Once the new CP-violation effect is determined by experiments, the direct $CP$ asymmetry in neutral kaon modes can then be extracted and used to search for new physics. The numerical results based on $SU(3)$ symmetry will be tested by the experiments in the future.Comment: 15 pages, 3 tables. Version published in JHE