Mixed traffic flow model considering illegal lane-changing behavior: Simulations in the framework of Kerner’s three-phase theory

This paper studies the mixed motorized vehicle (m$m$-vehicle) and non-motorized vehicle (nm$nm$-vehicle) traffic flow in the m$m$-vehicle lane. We study the formation mechanism of the nm$nm$-vehicle illegal lane-changing behavior (NILB) by considering the overtaking motivation and the traffic safety awareness. In the framework of Kerner’s three-phase theory, we propose a model for the mixed traffic flow by introducing a new set of rules. A series of simulations are carried out in order to reveal the formation, travel process and influence of the mixed traffic flow. The simulation results show that the proposed model can be used to study not only the travel characteristic of the mixed traffic flow, but also some complex traffic problems such as traffic breakdown, moving synchronized flow pattern (MSP) and moving jam. Moreover, the results illustrate that the proposed model reflects the phenomenon of the mixed flow and the influence of the MSP caused by the NILB, which is consistent with the actual traffic system, and thus this work is helpful for the management of the mixed traffic flow.     

A cellular automaton model based on empirical observations of a driver’s oscillation behavior reproducing the findings from Kerner’s three-phase traffic theory

In this paper, we propose a new cellular automaton model based on the well known three-phase traffic theory. The model takes into account the mechanism of a driver’s oscillation behavior obtained from engineering experiments in real traffic conditions. This mechanism shows the inner competition between speed adaptation and distance adjustment effects. The speed adaptation effect leads to synchronized flow, whereas a pinch region emerges, associated with the spontaneous occurrence of wide moving jams, due to distance over-adjustment. Numerical simulations are carried out both with periodic and with open boundary conditions in order to investigate the spatiotemporal features of traffic flow. The results indicate that our model is able to reproduce the three distinct traffic phases and exhibit the four congested patterns upstream of an isolated on-ramp, which is in good consistency with the results predicted from the three-phase theory.     

Cellular automaton model within the fundamental-diagram approach reproducing some findings of the three-phase theory

We propose a simple cellular automaton for traffic flow within the fundamental diagram, which could reproduce aspects of the three-phase theory. This so-called average space gap model (ASGM) is based on the Nagel–Schreckenberg model with additional slow-to-start and anticipation rules. The anticipation rule takes into account the average space gap of multiple leading vehicles and conveys to the model its three-phase property. Due to the anticipation rule, ASGM can show the transition from free flow to synchronized flow. Due to the slow-to-start rule, ASGM can show the spontaneous wide moving jam emerges in the synchronized flow. Simulations are carried out for periodic and open boundary conditions. Under periodic boundary condition, the fundamental diagram, and the properties of synchronized flow are studied. Under open boundary condition, different congested patterns induced by an on-ramp are analyzed. We found that the ASGM produces the same spatiotemporal dynamics as many of the more complex three-phase models. Due to its simplicity and its close relation to conventional slow-to-start models, this model can shed light on the relation between ‘two-phase’ and three-phase models.     

Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system

In this paper, a new lattice hydrodynamic traffic flow model is proposed by considering the driver’s anticipation effect in sensing relative flux (DAESRF) for two-lane system. The effect of anticipation parameter on the stability of traffic flow is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear analysis. The theoretical findings have been verified using numerical simulation which confirms that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model for two-lane traffic.     

A different method for calculation of the deflection angle of light passing close to a massive object by Fermat’s principle

We introduce a method for calculating the amount of deflection angle of light passing close to a massive object. It is based on Fermat’s principle. The varying refractive index of medium around the massive object is obtained from the Buckingham pi-theorem.     

A dispersion relation for the density of states with application to the Casimir effect

The trace of a function of a Schrödinger operator minus the same for the Laplacian can be expressed in terms of the determinant of its scattering matrix. The naive formula for this determinant is divergent. Using a dispersion relation, we find another expression for it which is convergent, but needs one piece of information beyond the scattering matrix: the spatial integral of the potential. Except for this ‘anomaly’, we can express the Casimir energy of a compact body in terms of its optical scattering matrix, without assuming any rotational symmetry for its shape.     

Magnetic properties of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system: Green’s function study

The magnetic behaviors of a mixed spin-1 and spin-2 Heisenberg ferrimagnetic system on a square lattice are studied by using the double-time temperature-dependent Green’s function technique. In order to decouple the higher order Green’s functions, Anderson and Callen’s decoupling and random phase approximations have been used. The system is described in the presence of an external magnetic field. We illustrate the influences of the nearest- and next-nearest-neighbor interactions and the single-ion anisotropies with an external magnetic field on compensation and critical temperatures. We found that the system that includes only the nearest-neighbor interaction and the single-ion anisotropies does not have a compensation temperature. When the next-nearest-neighbor interactions exceed a certain minimum value, a compensation temperature begins to appear. For some negative values of single-ion anisotropies, there exist first-order phase transitions. The system has first-order phase transition properties when it is under the influence of an external magnetic field.     

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Mar?enko–Pastur distribution.     

Bödeker’s effective theory: From Langevin dynamics to Dyson–Schwinger equations

The dynamics of weakly coupled, non-abelian gauge fields at high temperature is non-perturbative if the characteristic momentum scale is of order |k|g²T. Such a situation is typical for the processes of electroweak baryon number violation in the early Universe. Bödeker has derived an effective theory that describes the dynamics of the soft field modes by means of a Langevin equation. This effective theory has been used for lattice calculations so far [G.D. Moore, Nucl. Phys. B568 (2000) 367. Available from: <hep-ph/9810313>; G.D. Moore, Phys. Rev. D62 (2000) 085011. Available from: <hep-ph/0001216>]. In this work we provide a complementary, more analytic approach based on Dyson–Schwinger equations. Using methods known from stochastic quantitation, we recast Bödeker’s Langevin equation in the form of a field theoretic path integral. We introduce gauge ghosts in order to help control possible gauge artefacts that might appear after truncation, and which leads to a BRST symmetric formulation and to corresponding Ward identities. A second set of Ward identities, reflecting the origin of the theory in a stochastic differential equation, is also obtained. Finally, Dyson–Schwinger equations are derived.     

Phase diagrams of a ferroelectric superlattice: A Green’s function technique study

A Fermi-type Green’s function method has been used to investigate the phase transition properties of a ferroelectric superlattice with two alternating materials on the basis of the transverse Ising model. By performing a higher-order decoupling to the equations of motion for the Green’s functions, the eigenfrequencies of the infinite ferroelectric superlattice are obtained. Moreover, we discuss the dependence of the phase diagrams on the interface coupling strength, the transverse field, and the thicknesses of two slabs. The comparison between the Green’s function technique and the usual mean-field approximation is illustrated.     

Revisiting Maxwell’s accommodation coefficient: A study of nitrogen flow in a silica microtube across all flow regimes

Gas flows have been studied quantitatively for more than a hundred years and have relevance in modern fields such as the control of gas inputs to processes, the measurement of leak rates and the separation of gaseous species. Cha and McCoy have derived a convenient formula for the flow of an ideal gas applicable across a wide range of Knudsen numbers (Kn) that approaches the Navier–Stokes equations at small Kn and the Smoluchowski extension of the Knudsen flow equation at large Kn  . Smoluchowski’s result relies on the Maxwell definition of the tangential momentum accommodation coefficient α$\alpha$, recently challenged by Arya et al. We measure the flow rate of nitrogen gas in a smooth walled silica tube across a wide range of Knudsen numbers from 0.0048 to 12.4583. We find that the nitrogen flow obeys the Cha and McCoy equation with a large value of α$\alpha$, unlike carbon nanotubes which show flows consistent with a small value of α$\alpha$. Silica capillaries are therefore not atomically smooth. The flow at small Kn   has α=0.91$\alpha =0.91$ and at large Kn   has α$\alpha$ close to one, consistent with the redefinition of accommodation coefficient by Arya et al., which also resolves a problem in the literature where there are many observations of α$\alpha$ of less than one at small Kn and many equal to one at large Kn. Silica capillaries are an excellent choice for an accurate flow control system.     

Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot’s and multiple scattering models

This article quantitatively investigates ultrasound propagation in numerical anisotropic porous media with finite-difference simulations in 3D. The propagation media consist of clusters of ellipsoidal scatterers randomly distributed in water, mimicking the anisotropic structure of cancellous bone. Velocities and attenuation coefficients of the ensemble-averaged transmitted wave (also known as the coherent wave) are measured in various configurations. As in real cancellous bone, one or two longitudinal modes emerge, depending on the micro-structure. The results are confronted with two standard theoretical approaches: Biot’s theory, usually invoked in porous media, and the Independent Scattering Approximation (ISA), a classical first-order approach of multiple scattering theory. On the one hand, when only one longitudinal wave is observed, it is found that at porosities higher than 90% the ISA successfully predicts the attenuation coefficient (unlike Biot’s theory), as well as the existence of negative dispersion. On the other hand, the ISA is not well suited to study two-wave propagation, unlike Biot’s model, at least as far as wave speeds are concerned. No free fitting parameters were used for the application of Biot’s theory. Finally we investigate the phase-shift between waves in the fluid and the solid structure, and compare them to Biot’s predictions of in-phase and out-of-phase motions.     

Kinetic Monte Carlo simulations of electrodeposition: Crossover from continuous to instantaneous homogeneous nucleation within Avrami’s law

The influence of lateral adsorbate diffusion on the dynamics of the first-order phase transition in a two-dimensional Ising lattice gas with attractive nearest-neighbor interactions is investigated by means of kinetic Monte Carlo simulations. For example, electrochemical underpotential deposition proceeds by this mechanism. One major difference from adsorption in vacuum surface science is that under control of the electrode potential and in the absence of mass-transport limitations, local adsorption equilibrium is approximately established. We analyze our results using the theory of Kolmogorov, Johnson and Mehl, and Avrami (KJMA), which we extend to an exponentially decaying nucleation rate. Such a decay may occur due to a suppression of nucleation around existing clusters in the presence of lateral adsorbate diffusion. Correlation functions prove the existence of such exclusion zones. By comparison with microscopic results for the nucleation rate I and the interface velocity of the growing clusters v, we can show that the KJMA theory yields the correct order of magnitude for Iv². This is true even though the spatial correlations mediated by diffusion are neglected. The decaying nucleation rate causes a gradual crossover from continuous to instantaneous nucleation, which is complete when the decay of the nucleation rate is very fast on the time scale of the phase transformation. Hence, instantaneous nucleation can be homogeneous, producing negative minima in the two-point correlation functions. We also present in this paper an n-fold way Monte Carlo algorithm for a square lattice gas with adsorption/desorption and lateral diffusion.     

A new quantitative evaluation method of spiral drawing for patients with Parkinson’s disease based on a polar coordinate system with varying origin

Parkinson’s disease (PD) is a common disease of the central nervous system among the elderly, and its complex symptoms bring up challenges for the clinical diagnosis. In this paper, a new method based on a polar coordinate system with varying origin was proposed in order to quantitatively evaluate the performance in spiral drawing tasks for patients with Parkinson’s disease, since this method can assess the movement ability of spiral drawing before and after deep brain stimulation (DBS) among the patients. In this paper, three normal subjects and twelve PD patients participated in spiral drawing experiment. The hand movements of patients, before and after DBS, were recorded by a digitized tablet respectively in this experiment. And the variation of origin, radius, degree and other characteristics of hand movements were evaluated by introducing a set of parameters for feature extraction. The result showed that the proposed polar coordinate system embraced good performance in the quantitative evaluation of spiral drawing. Therefore, the proposed method overcame the limitation of data processes with fixed origin for diagnosis and evaluation, and by combining with extraction and analysis of characteristic parameters it had clinical significance in measuring the effectiveness of operation or treatment for the PD patients.     

Study of nonlinear dissipative pulse propagation under the combined effect of two-photon absorption and gain dispersion: A variational approach involving Rayleigh’s dissipation function

We try to derive some explicit equations for predicting the laws which govern the evolution of different parameters of a propagating optical pulse in a nonlinear medium under the combined influence of two-photon absorption and gain dispersion. Using the generalized Euler-Lagrange equation, the dynamics of different pulse parameters are generated. The Rayleigh’s dissipation function is incorporated in order to take recourse to the dissipative part, with an analogy with the non-conservative frictional problem in classical mechanics. It appears from the study that the influence of the dissipative part can well be explained using the proposed model. The analytically predicted results are compared with the numerical data obtained from direct simulation of the Ginzburg-Landau equation and the results are found to be quite satisfactory, supporting the prediction.     

Proposal to Test a Transient Deviation from Quantum Mechanics’ Predictions for Bell’s Experiment

Quantum mechanics predicts correlations between measurements performed in distant regions of a spatially spread entangled state to be higher than allowed by intuitive concepts of Locality and Realism. These high correlations forbid the use of nonlinear operators of evolution (which would be desirable for several reasons), for they may allow faster-than-light signaling. As a way out of this situation, it has been hypothesized that the high quantum correlations develop only after a time longer than L/c has elapsed (where L is the spread of the entangled state and c is the velocity of light). In shorter times, correlations compatible with Locality and Realism would be observed instead. A simple hidden variables model following this hypothesis is described. It is based on a modified Wheeler–Feynman theory of radiation. This hypothesis has not been disproved by any of the experiments performed to date. A test achievable with accessible means is proposed and described. It involves a pulsed source of entangled states and stroboscopic record of particle detection during the pulses. Data recorded in similar but incomplete optical experiments are analyzed, and found consistent with the proposed model. However, it is not claimed, in any sense, that the hypothesis has been validated. On the contrary, it is stressed that a complete, specific test is absolutely needed.     

Dilemma game structure hidden in traffic flow at a bottleneck due to a 2 into 1 lane junction

Following Yamauchi’s study [A. Yamauchi, J. Tanimoto, A. Hagishima, H. Sagara, Dilemma game structure observed in traffic flow at a 2-to-1 lane junction, Physical Review E 79 (2009) 036104], we find that several social dilemma structures are represented by n-person Prisoner’s Dilemma (n-PD) games in certain traffic flow phases at a bottleneck caused by a lane-closing section. In this study, the stochastic Nishinari-Fukui-Schadschneider (S-NFS) model was adopted as a cellular automaton traffic model. In the system, two classes of driver-agents coexist: C-Agents (cooperative strategy) always driving in the first lane, and D-Agents (defective strategy) trying to drive in a lower-density lane, whether the first or the second lane. In relatively high-density flow phases, such as the metastable phase and the high-density phase, we found n-PD games, where D-Agents’ interruption into the first lane from the second just before the lane-closing section creates a heavier traffic jam, which reduces social efficiency. This could be solved by decreasing the interruption probability, which can be realized by a provision where drivers in the first lane firmly refuse interruptions.