Upper Bounds for the Critical Car Densities in Traffic Flow Problems

In most models of traffic flow, the car density $p$ is the only free parameter in determining the average car velocity $\langle v \rangle$. The critical car density $p_c$, which is defined to be the car density separating the jamming phase (with $\langle v \rangle = 0$) and the moving phase (with $\langle v \rangle > 0$), is an important physical quantity to investigate. By means of simple statistical argument, we show that $p_c < 1$ for the Biham-Middleton-Levine model of traffic flow in two or higher spatial dimensions. In particular, we show that $p_{c} \leq 11/12$ in 2 dimension and $p_{c} \leq 1 - \left( \frac{D-1}{2D} \right)^D$ in $D$ ($D > 2$) dimensions.Comment: REVTEX 3.0, 5 pages with 1 figure appended at the back, Minor revision, to be published in the Sept issue of J.Phys.Soc.Japa

Complex Dynamics of Bus, Tram and Elevator Delays in Transportation System

It is necessary and important to operate buses and trams on time. The bus schedule is closely related to the dynamic motion of buses. In this part, we introduce the nonlinear maps for describing the dynamics of shuttle buses in the transportation system. The complex motion of the buses is explained by the nonlinear-map models. The transportation system of shuttle buses without passing is similar to that of the trams. The transport of elevators is also similar to that of shuttle buses with freely passing. The complex dynamics of a single bus is described in terms of the piecewise map, the delayed map, the extended circle map and the combined map. The dynamics of a few buses is described by the model of freely passing buses, the model of no passing buses, and the model of increase or decrease of buses. The nonlinear-map models are useful to make an accurate estimate of the arrival time in the bus transportation

Spontaneous Time Asymmetry due to Horizon

We show that quantized matter fields in the presence of background metrics with Horizon exhibit spontaneous time asymmetry. All quantized matter fields have to vanish at the horizon. Some phenemenological applications of this in the context of black holes and early universe are considered.Comment: 4 pages, Revte

Towards a variational principle for motivated vehicle motion

We deal with the problem of deriving the microscopic equations governing the individual car motion based on the assumptions about the strategy of driver behavior. We suppose the driver behavior to be a result of a certain compromise between the will to move at a speed that is comfortable for him under the surrounding external conditions, comprising the physical state of the road, the weather conditions, etc., and the necessity to keep a safe headway distance between the cars in front of him. Such a strategy implies that a driver can compare the possible ways of his further motion and so choose the best one. To describe the driver preferences we introduce the priority functional whose extremals specify the driver choice. For simplicity we consider a single-lane road. In this case solving the corresponding equations for the extremals we find the relationship between the current acceleration, velocity and position of the car. As a special case we get a certain generalization of the optimal velocity model similar to the "intelligent driver model" proposed by Treiber and Helbing.Comment: 6 pages, RevTeX

Solvable Optimal Velocity Models and Asymptotic Trajectory

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine $T$ and $v_B$ (the backward velocity of the pattern), the global parameters associated with vehicles' collective motion in a congested flow, in terms of parameters such as the sensitivity $a$, which appeared in the original coupled equations.Comment: 25 pages, 15 eps figures, LaTe

Kinetics of Clustering in Traffic Flows

We study a simple aggregation model that mimics the clustering of traffic on a one-lane roadway. In this model, each ``car'' moves ballistically at its initial velocity until it overtakes the preceding car or cluster. After this encounter, the incident car assumes the velocity of the cluster which it has just joined. The properties of the initial distribution of velocities in the small velocity limit control the long-time properties of the aggregation process. For an initial velocity distribution with a power-law tail at small velocities, \pvim as $v \to 0$, a simple scaling argument shows that the average cluster size grows as n \sim t^{\va} and that the average velocity decays as v \sim t^{-\vb} as $t\to \infty$. We derive an analytical solution for the survival probability of a single car and an asymptotically exact expression for the joint mass-velocity distribution function. We also consider the properties of spatially heterogeneous traffic and the kinetics of traffic clustering in the presence of an input of cars.Comment: 18 pages, Plain TeX, 2 postscript figure

The radiative lepton flavor violating decays in the split fermion scenario in the two Higgs doublet model

We study the branching ratios of the lepton flavor violating processes \mu -> e \gamma, \tau -> e \gamma and \tau -> \mu\gamma in the split fermion scenario, in the framework of the two Higgs doublet model. We observe that the branching ratios are relatively more sensitive to the compactification scale and the Gaussian widths of the leptons in the extra dimensions, for two extra dimensions and especially for the \tau -> \mu \gamma decay.Comment: 19 pages, 7 Figure

Two-dimensional cellular automaton model of traffic flow with open boundaries

A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and average velocity have flicker noises in a jamming phase. The low density behavior are discussed with simple jam-free approximation.Comment: 14 pages, Phys. Rev. E in press, PostScript figures available at ftp://hirose.ai.is.saga-u.ac.jp/pub/documents/papers/1996/2DTR/ OpenBoundaries/Figs.tar.g

Charged Lepton Flavor Physics and Extra Dimensions

We estimate the charged lepton electric dipole moments and the branching ratios of radiative lepton flavor violating decays in the framework of the two Higgs doublet model with the inclusion two extra dimensions. Here, we consider that the new Higgs doublet is accessible to one of the extra dimensions with a Gaussian profile and the fermions are accessible to the other extra dimension with uniform zero mode profile. We observe that the numerical values of the physical quantities studied enhance with the additional effects due to the extra dimensions and they are sensitive to the new Higgs localization.Comment: 23 pages, 13 page