2,515 research outputs found
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 and 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 -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 - and
-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 , close
to the limit 1.5 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 and
2.49 M, which are in reasonable agreement with high pulsar mass 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 -Tensor Correlations in Density-Dependent Relativistic Hartree-Fock theory
A new effective interaction PKA1 with -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 -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 -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 for a finite-range pairing force and for a contact pairing force, where 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.
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