Equilibrium Speed Research Articles

Stability analysis of nonlinear inviscid microscopic and macroscopic traffic flow models of bidirectional cruise-controlled vehicles

Abstract The paper introduces a new bidirectional microscopic inviscid Adaptive Cruise Control (ACC) model that uses only spacing information from the preceding and following vehicles in order to select the proper control action to avoid collisions and maintain a desired speed. $KL$ estimates that guarantee uniform convergence of the ACC model to the set of equilibria are provided. Moreover, the corresponding macroscopic model is derived, consisting of a conservation equation and a momentum equation that contains a nonlinear relaxation term. It is shown that, if the density is sufficiently small, then the macroscopic model has a solution that approaches exponentially the equilibrium speed (in the sup norm) while the density converges exponentially to a traveling wave. Numerical simulations are also provided, illustrating the properties of the microscopic and macroscopic inviscid ACC models.

G modes of neutron stars with hadron-to-quark crossover transitions

We perform the first study of the principal core $g$-mode oscillation in hybrid stars containing quark matter, utilizing a crossover model for the hadron-to-quark transition inspired by lattice QCD. The ensuing results are compared with our recent findings of $g$-mode frequencies in hybrid stars with a first-order phase transition using Gibbs constructions. We find that models using Gibbs construction yield $g$-mode amplitudes and the associated gravitational energy radiated that dominate over those of the chosen crossover model owing to the distinct behaviors of the equilibrium and adiabatic sound speeds in the various models. Based on our results, we conclude that were $g$-modes to be detected in upgraded LIGO and Virgo detectors it would indicate a first-order phase transition akin to a Gibbs construction.

The “backward-looking” effect in the continuum model considering a new backward equilibrium velocity function

In this paper, a new continuum traffic model is developed considering the backward-looking effect through a new positive backward equilibrium speed function. As compared with the conventional full velocity difference model, the backward equilibrium velocity function, which is largely acceptably grounded from mathematical and physical perspectives, plays an important role in significantly enhancing the stability of the traffic flow field. A linear stability condition is derived to demonstrate the flow neutralization capacity of the model, whereas the Korteweg–de Vries–Burgers equation and the attendant analytical solution are deduced using nonlinear analysis to observe the traffic flow behavior near the neutral stability condition. A numerical simulation, used to determine the flow stability enhancement efficiency of the model, is also conducted to verify the theoretical results.

Transient study of series-connected pumps working as turbines in off-grid systems

In the current world economic environment where reducing energy costs is a high priority, it is not surprising that sustainable water and energy management are key topics among the water and electric industry. Specifically, water suppliers, pump manufacturers, and operatives of small hydropower systems, all recognize that pumps working as turbines can be an efficient, simple, and economic approach to generating power and recover the excess of energy in water pressurized systems. In both, variable operating flow rate conditions (ex: presence of different water users) impose the need to augment the range of a proper pump as turbine system. One solution is to associate several pumps as turbines in series to increase the recovered energy. In that context, this work assesses their reliability at transient off-grid conditions by two pumps as turbines connected in series. Each one has an identical self-excited induction generator feeding a three-phase and balanced resistive load. Changes (increase/decrease in values) were applied to the resistive loads and the bank of capacitors at one group only, which allowed examining how changes affect the overall two-group system dynamics. Results show that one change in the first pump as turbine group will significantly affect the other group dynamics. For example, a decrease in load of the first group will affect the flow and head of the other system, until reaching a new equilibrium point. However, as both groups are not mechanically connected, they can achieve different equilibrium speeds. Furthermore, the highest impact occurred in the group where no changes were imposed. The first group maintained its global efficiency value, while the second had its efficiency decreased by about 8%. Similarly, an increase in the capacitance value caused a reduction in its efficiency (lesser but around 2%). Finally, a numerical model was developed and validated through experimental tests to be an applicable prediction model.

A multi-class first-order traffic flow model to explain the disordered behaviour of vehicles

Disordered traffic streams are generally characterised by the presence of numerous vehicle classes having different sizes and operational characteristics. Unlike homogeneous traffic flow, smaller vehicles percolate between the bigger ones, invalidating the lane discipline and therefore requiring a different modelling approach. Each vehicle traverses through a series of opportunities created by other vehicles that are not only viable but also accessible, thus defining a permeable medium. Our objective is to develop an analytical traffic flow model that quantifies such opportunities for individual vehicle classes to traverse downstream. Equilibrium speed functions have been redefined based on a new metric termed as traversable distance. The inter-class flow dynamics of small-sized vehicles has further resulted in a significant reduction in their travel time.

Insights on features' contribution to desalination dynamics and capacity of capacitive deionization through machine learning study

Parameter optimization in designing a rational capacitive deionization (CDI) process is usually performed to achieve both high electrosorption capacity and speed. This necessitates a clear understanding of system behavior and discriminating the features' role on desalination capacity from its dynamic. Machine learning (ML) modeling is widely employed for understanding various systems' behavior as an alternative for physics-based extrapolation models. Herein, various ML models are implemented with reasonable accuracies to unveil CDI electrode and operational features' local and global impacts on equilibrium desalination capacity, speed, and duration. Electrode specific surface area and electrolyte ionic concentration are determined to play the most significant roles in CDI by synergistically enhancing desalination capacity and speed. Increasing electrode micropore volume is detected to inhibit desalination and make ion removal sluggish. According to the established models, electrode nitrogen content extends desalination capacity without improving its dynamic. In addition, unlike the complex impacts from electrodes oxygen content on desalination capacity, it is shown that electrode oxygen content clearly elongates desalination time. This study demonstrates the strong abilities of the established ML models in explaining the underlying complex mechanisms in the CDI process.

G -mode oscillations in hybrid stars: A tale of two sounds

We study the principal core g-mode oscillation in hybrid stars containing quark matter and find that they have an unusually large frequency range ($\approx$ 200 - 600 Hz) compared to ordinary neutron stars or self-bound quark stars of the same mass. Theoretical arguments and numerical calculations that trace this effect to the difference in the behaviour of the equilibrium and adiabatic sound speeds in the mixed phase of quarks and nucleons are provided. We propose that the sensitivity of core g-mode oscillations to non-nucleonic matter in neutron stars could be due to the presence of a mixed quark-nucleon phase. Based on our analysis, we conclude that for binary mergers where one or both components may be a hybrid star, the fraction of tidal energy pumped into resonant g-modes in hybrid stars can exceed that of a normal neutron star by a factor of 2-3, although resonance occurs during the last stages of inspiral. A self-bound star, on the other hand, has a much weaker tidal overlap with the g-mode. The cumulative tidal phase error in hybrid stars, $\Delta\phi\cong$ 0.5 rad, is comparable to that from tides in ordinary neutron stars, presenting a challenge in distinguishing between the two cases. However, should the principal g-mode be excited to sufficient amplitude for detection in a post-merger remnant with quark matter in its interior, its frequency would be a possible indication for the existence of non-nucleonic matter in neutron stars.

Freeway tunnel effect of travel time based-on a double lane traffic model

Speed limit of freeway tunnel restricts car driving behaviors. To explore the tunnel effect of travel time, a double lane traffic model is put forward, and a compensative function of mean travel time is simply introduced in this paper. The model describes the net lane-changing rate using the ratio of characteristic lane changing time to traffic relaxation time, assumes that the cars on both lanes of the tunnel have the same equilibrium speed, but the speeds on both lanes of normal section are different. It is assumed that the road length is 100 km, and the tunnel length is 7.5 km except for the case of seeking tunnel length effects. The model is used to build a simulation platform. Numerical results indicated that when the initial road density normalized by jam density is above 0.2, the tunnel causes a congestion region just upstream the tunnel inlet, provides a smooth region just downstream the tunnel outlet, can affect the traffic flow pattern significantly. But the tunnel effect of travel time is small, as the tunnel can merely slightly increase the mean travel time. The on/off ramp flows play a crucial role in the formation of traffic flow pattern.

Crossover from static to dynamic Non-Condon effecton charge Transport in Organic Semiconductors

The computed charge transport key parameters like, charge transfer integral, site energy and reorganization energy are used to study the hole and electron transport in dialkyl substituted thienothiophene caped benzobisthiazole (BDHTT-BBT) and methyl-substituted dicyanovinyl-capped quinquethiophene (DCV5T-Me) molecular crystals. The effect of structural fluctuation on charge transport in these molecules is analysed by Monte-Carlo simulations. To estimate the equilibrium speed during the charge transport process in these molecular solids, we have introduced the parameters such as, potential equilibrium rate and density flux rate. Here, the density flux rate is directly related with the drift force which facilitates the charge transfer along the consequential hopping sites. Our theoretical study reveals that the charge transfer up to the crossover point (or disorder drift time) is exponential, non-dispersive and it follows the static non-Condon effect. Beyond the disorder drift time, the charge transfer is partially exponential, dispersive and it follows the dynamic non-Condon principle. The expressions of density flux and diffusion shows their dependency on dynamic disorder and is in agreement with the Troisi’s model on diffusion limited by thermal disorder.

From homogeneous to heterogeneous traffic flows: [formula omitted] String stability under uncertain model parameters

This paper shows that the heterogeneity of drivers’ and vehicles characteristics makes platoons, on average, more string-unstable. However, the string instability degree of unstable platoons is much higher in a homogeneous flow than in a heterogeneous one. These results are based on an L∞ characterization of string stability, which is shown to be the most appropriate one from a traffic safety viewpoint. Mechanisms and conditions are discussed in which an L2 characterization is not able to capture the amplification of a speed drop through a string of vehicles. An analytical sufficient condition for the L∞ string stability of heterogeneous vehicles, which move according to a general class of car-following models, is derived. Above all, a thorough comparison of L∞ and L2 string stability characterizations between a homogeneous and a heterogenous flow, is performed. To this aim, the Lp norms of heterogeneous platoons are calculated within a quasi-Monte Carlo framework. The variability of the Lp norm values due to the platoon length, the equilibrium speed, and the probability distribution model of the uncertain vehicle parameters, is analysed. Overall, it is shown that the platoon stability behaviour sensibly changes with the shape and the correlation structure of vehicle model parameter distributions. Therefore, traffic heterogeneity needs to be modelled in order to correctly characterize the string stability of a mixed traffic flow.

Acoustics of a viscoelastic medium with encapsulated bubbles

In this paper, a modified Rayleigh-Lamb equation is derived that takes into account the radial vibrations of a gas bubble coated with a viscoelastic shell and located in an elastic medium. For small oscillations of inclusion, the problem of heat exchange between a gas, a liquid phase, a viscoelastic shell, and an elastic medium is solved. The energy integral is determined. In the case of small disturbances, the dispersion relation is found from the Rayleigh-Lamb equations, energy, and the known wave equation for the bubbly medium. An analytical expression of the equilibrium speed of sound is written out and its dependence on the size of the viscoelastic shell and the disturbance frequency is established. An example of a mixture of polydimethylsiloxane with air bubbles coated with a rubber shell illustrates the influence of the elasticity of the carrier medium and the shell of the bubbles on the dependence of the phase velocity and attenuation coefficient on the perturbation frequency. For a mixture of water with air bubbles coated with a rubber shell, the influence of the dependences of the shear modulus and viscosity of butyl rubber on the frequency of disturbances at different temperature on the dispersion curves is shown. A comparison of the theory with experimental data is given.

Modeling multi-class disordered traffic flow subject to varying vehicle composition using the concept of traversable distance

Disordered traffic stream at the microscopic level can be described as a permeable medium. Each vehicle is considered to traverse through a series of lateral gaps created by other vehicles. We develop a multi-class traffic flow model that considers such viable and accessible gaps for individual vehicle classes to traverse downstream. The model accounts for the varying shares of different vehicle classes. The concept of traversable distance and modified equilibrium speed functions are used to model the interplay among multiple vehicle classes. Using a higher order finite volume approximation method, evolution for a two-class traffic stream is shown. This model replicates prominent empirical characteristics exhibited by multi-class disordered traffic such as overtaking and creeping. Varying shares of smaller vehicles affect queue formation and discharge characteristics, and have significant impacts on roadway capacity. The model also could compute dynamic class-specific travel times at different vehicular compositions more realistically.

Why are highway speed limits really justified? An equilibrium speed choice analysis

Speed externalities – the impacts that a driver’s speed choice imposes on others – are usually quoted to justify highway speed regulation in the form of maximum speed limits. However, speed externalities could already be internalized if a pre-existing policy were in place that is related to speed, questioning the traditional rationale supporting speed limits. Given the relationship between speed and fuel consumption and the omnipresence of fuel taxes around the world, it comes as a surprise that pre-existing taxes on motor fuel are completely missing in the debate on the general appropriateness of speed regulation. In this paper we develop an economic equilibrium model of highway speed choice accounting for (i) a market failure – speeding externalities capturing the fact that drivers do not internalize the adverse consequences of speeding on other highway users and the society as a whole; (ii) a famous speed related behavioral anomaly – causing adverse effects drivers impose on themselves by falsely predicting the time saving potential of speed; (iii) a pre-existing fuel tax – closing the wedge between the privately and socially optimal speed. The latter creates a ‘government feedback effect’ reflecting the positive feedback effect of speed on fuel tax revenue and so the broader beneficial fiscal impacts of speed choice ignored by drivers. Numerical computations for Germany indicate a dominant ‘government feedback effect’ ((iii) outweighs (i)) for mean speeds up to around 120 km/h presuming fully variable travel time budgets and beyond that speed level when drivers put (some of the) travel time savings from speeding into more highway traveling. This implies that speed externalities are largely internalized and that the externality rationale in favor of speed regulation does not apply to the majority of drivers. Nevertheless, a moderate speed limit on German highways of 130 km/h would probably not compromise economic efficiency, at least as long as the share of diesel cars is significant. Generally, when drivers are subject to lack of rationality leading to excess speeding, (iii) is not able to outweigh (i). Then, speed limits remain highly warranted provided that appropriate “nudging” is not available. The numerical finding is likely to hold for a large number of European countries too but probably not for North American countries where fuel taxes are considerably lower.

Research on a balanced circuit and control strategy

Abstract For reducing the inconsistent state of charges (SOC) of lithium-ion battery cells and making the full use of battery packs, effective battery balancing technology should be used. In order to achieve the goal of balancing any single cell in the battery pack expediently and considering the cost and the balance efficiency, a balanced circuit is proposed. By changing the action state of single-pole double-throw relay connected to each of the single cell battery, the balanced single-cell battery is in a state of non-load power supply, at this point, the balanced battery is in `charging’ state compared with other batteries in the battery pack, thus achieving the balance target of the battery pack. On this basis, this paper also proposes a new balancing control strategy; it is different from the traditional control strategy to balance the SOC of the single cell to the SOC average of the battery pack, considering the different SOC change rates of the cells with different capacity in the battery pack. The balanced control strategy proposed in this paper allows the set condition of the single cell to end the equilibrium process in advance so as to reduce the unnecessary balance time and then improve the equilibrium speed. In order to verify the feasibility of the proposed circuit and control strategy, 18 650 batteries with different initial SOC in series are experimentally verified. The experimental results show that the balanced circuit proposed in this paper can well balance the cell of each single cell and make the battery pack reach a balanced state.

A fully implicit, scalable, conservative nonlinear relativistic Fokker–Planck 0D-2P solver for runaway electrons

Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic ‘runaway’ electrons (∼ MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. For this purpose, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker–Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron–ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham–Lorentz–Dirac reaction term. However, our implementation improves on these earlier studies by (1) ensuring exact conservation properties for electron collisions, (2) strictly preserving positivity, and (3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams–Karney potentials (Braams and Karney, 1987), and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.

Empirical Study on the Properties of Adaptive Cruise Control Systems and Their Impact on Traffic Flow and String Stability

Adaptive cruise control (ACC) systems are standard equipment in many commercially available vehicles. They are considered the first step of automation, and their market penetration rate is expected to rise, along with the interest of researchers worldwide to assess their impact in relation to traffic flow and stability. These properties are currently discussed mainly through microsimulation studies and empirical observations, with the first being the most common. Experimental observations can draw safer conclusions about the behavior of such systems, but the literature is limited. In this work, an experimental campaign with five vehicles equipped with ACC was conducted at the proving ground of AstaZero in Sweden to improve understanding on the properties of ACC systems and their functionality under real driving conditions. The main parameters under investigation are the response time of controllers, the available time headway settings, and the stability of the car-platoon. The results show that the response time range for the controllers is between 1.7 and 2.5 s, significantly longer than the values reported in the literature. The range of the time headway settings was found to be quite broad. Finally, a dataset of perturbations on a variety of equilibrium speeds of the car-platoon and of variable magnitudes was created. Results clearly highlight the instability of the car-platoon. Instability is also displayed even for slight perturbations derived by variability in the road gradient. Numerical differentiation on the altitude shows a negative correlation with the speed trajectory of the leading vehicle.

Modelling multi-class disordered traffic streams using traversable distance: a concept analogous to fluid permeability

In multi-class disordered traffic conditions, the presence of numerous classes of vehicles having different size and operational characteristics invalidates the behaviour of lane discipline. Each vehicle traverses through a series of both viable as well as accessible gaps created by other vehicles, thus defining a permeable medium. In this paper, a plausible way to incorporate the disordered behaviour on macroscopic traffic stream modelling is discussed. A new metric termed as traversable distance has been formulated for characterising this behaviour, based on field observations. Based on class-specific traversable distances that correspond to a set of incommensurate density measures, equilibrium speed functions have been redefined. Disordered stream behaviour significantly affects the scatter in the equilibrium speed–density relationship which is a key input to macroscopic traffic flow models. Results from the modified speed functions based on traversable distance proved that the proposed methodology could considerably explain the scatter observed in the fundamental diagram.

Oil volatility pass through and real exchange misalignment in leading commodity exporting countries

Past research has shown how real Exchange rates follow a univariate nonlinear process that approximates their behavior in terms of transaction costs. However, little or nothing has been said about alternative sources of nonlinearity in commodity exporting countries. Our paper investigates the missing link between the Real Exchange Rate Commodity Prices equilibrium by employing an oil price volatility measure as an external source of short-term fluctuations. Our estimates show that the Real Exchange Rate Commodity price relationship appears to be nonlinear with respect to oil price variation, and that the goodness of fit of the nonlinear specifications appears to outperform that of the equivalent linear models. The equilibrium speed of adjustment appears to be different in the two branches of the relationship: in the majority of the threshold models, the negative volatility regime presents a faster speed of adjustment and in some cases a most significant one.

Acoustics of a Two-fractional Polydisperse Bubbly Liquid with Phase Transitions

A mathematical model that determines the propagation of acoustic waves in a two-fractional mixture of a liquid with polydisperse vapor-gas bubbles of different sorts, taking into account the phase transitions in each fraction is presented. A system of integro-differential equations of the disturbed motion of a two-phase mixture is written, and a dispersion equation is obtained. In particular cases, for gas-liquid and vapor-liquid mixtures, expressions for the equilibrium speed of sound are obtained.

Control Strategy for Active Hierarchical Equalization Circuits of Series Battery Packs

Most series battery active equalization circuits implement the equalization first within the series and then between the series, which restricts the equilibrium speed. A hierarchical equalization circuit topology based on the Buck-Boost module is applied in this paper. The equalization is divided into two different equalization processes according to the equilibrium energy flow. The two equalization processes can be performed simultaneously, and the currents in the different hierarchical circuits do not affect each other, thus achieving simultaneous equalizations within the series and between the series. An equalization condition of the terminal voltage is applied and simulations and experiments on charge, discharge, and static equalizations in the four series-connected ternary lithium-ion batteries are performed.