A Two-Lane Cellular Automata Model with Influence of Next-Nearest Neighbor Vehicle

In this paper, we propose a new two-lane cellular automata model in which the influence of the next-nearest neighbor vehicle is considered. The attributes of the traffic system composed of fast-lane and slow-lane are investigated by the new traffic model. The simulation results show that the proposed two-lane traffic model can reproduce some traffic phenomena observed in real traffic, and that maximum flux and critical density are close to the field measurements.Moreover, the initial density distribution of the fast-lane and slow-lane has much influence on the traffic flow states.With the ratio between the densities of slow lane and fast lane increasing the lane changing frequency increases, but maximum flux decreases. Finally, the influence of the sensitivity coefficients is discussed.     

Classical analogue of the statistical operator

We advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system.     

Extended speed gradient model for traffic flow on two-lane freeways

In this paper, the speed gradient (SG) model is extended to describe the traffic flow on two-lane freeways. Terms related to lane change are added into the continuity equations and velocity dynamic equations. The empirically observed two-lane phenomena, such as lane usage inversion and lane change rate versus density, are reproduced by extended SG model. The local cluster effect is also investigated by numerical simulations.     

A cellular automata model for urban traffic with multiple roundabouts

Urban transportation with multiple roundabouts is facing significant challenges such as traffic congestion, gridlock and traffic accidents. In order to understand these behaviors, we propose a two-dimensional cellular automata (CA) model, where all streets are two-way, with one lane in each direction. To allow the turning movement, a roundabout is designed for each intersection where four roads meet. The distance between each pair of roundabouts is configured with the parameter K while the turning behavior of drivers is modeled by a parameter γ. To study the impact of these different parameters on the urban traffic, several traffic metrics are considered such as traffic flow, average velocity, accident probability and waiting time at the entrance of roundabout. Our simulation results show that the urban traffic is in free flow state when the vehicle’s density is low enough. However, when the density exceeds a critical density ρ_c, the urban traffic will be in gridlock state whenever γ is nonzero. In the case where $\gamma =0,$ the urban traffic presents a phase transition between free flow and congested state. Furthermore, detailed analysis of the traffic metrics shows that the model parameters (γ, K) have a significant effects on urban traffic dynamics.     

Mathematics of gravitational lensing: multiple imaging and magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.     

Local information‐distance thermodynamics of molecular fragments

The Fisher information contained in a probability distribution is summarized. The corresponding measures of the information distance, relative to the reference probability density, are introduced and discussed. These concepts are designed as analogues of the Kullback‐Leibler directed divergence and Kullback's divergence. For these alternative measures of the missing information the equilibrium (“stockholder”) scheme of Hirshfeld, of a division of the molecular electron density into the subsystem components, is derived from the minimum principle of the local or global entropy deficiency relative to the free‐subsystem (“promolecule”) reference. The local information distance densities are used to describe instantaneous electron distributions in molecular subsystems within a thermodynamic‐like approach to the density fluctuations and irreversible processes. The key concepts of such a local irreversible “thermodynamics” are introduced. They include the corresponding local affinities (forces) and the conjugate fluxes (responses), which together determine the local entropy deficiency source. These quantities depend on the adopted measure of the information distance and selected state‐parameters. For each such representation the relevant Onsager‐type reciprocity relations can be derived, which reflect the symmetries between the linear effects of affinities on fluxes.     

Traffic states induced by slowdown sections on two-lane highway

We study the traffic states and jams occurring on a two-lane highway with a few slowdown sections. We derive the fundamental diagrams (flow-density diagrams). The fundamental diagrams on first and second lanes depend highly on the configuration of slowdown sections. The occupancy fraction of vehicles on first and second lanes varies with configuration of slowdown sections and also changes with density for the definite configuration. When a jam is formed on a lane, the flow (current) saturates on the lane. The saturated flow is given by the maximal value of the current of the slowdown section. The relationship between the densities before and after the jam is derived analytically. The dependence of jam lengths on density is derived numerically and analytically.     

Surface nucleation and growth in the system of interacting particles

Recent experiments on epitaxial growth of metals on graphene have shown a strong dependence of island densities on coverage. These investigations cannot be explained by the standard mean-field nucleation theories. To understand them, we extend to higher coverage the former theory of rate equations developed for the initial state of nucleation, in a system where adsorbate interaction is included. We account for that, in the case of high coverage, the repulsive interaction influences both the attachment of monomers to clusters and the mobility of atoms. In our work we analyze the modification of the dependence of the island density on coverage, temperature and F/D ratio. In some regimes our theory results in the experimentally observed substantial growth of island density with coverage for a high deposited amount and a weak dependence on deposition rate F. We also find out the local maxima in temperature dependence of island density, as a consequence of long-range repulsive interactions.     

Liouville and Fokker–Planck dynamics for classical plasmas and radiation

We consider a nonequilibrium statistical system formed by many classical non‐relativistic particles of opposite electric charges (plasma) and by the classical dynamical electromagnetic (EM) field. The charges interact with one another directly through instantaneous Coulomb potentials and with the dynamical degrees of freedom of the transverse EM field. The system may also be subject to external influences of: i) either static, but spatially inhomogeneous, electric and magnetic fields (case 1)), or ii) weak distributions of electric charges and currents (case 2)). The particles and the dynamical EM field are described, for any time t > 0, by the classical phase‐space probability distribution functional (CPSPDF) f and, at the initial time (t = 0), by the initial CPSPDF f_in. The CPSPDF f and f_in, multiplied by suitable Hermite polynomials (for particles and field) and integrated over all canonical momenta, yield new moments. The Liouville equation and f_in imply a new nonequilibrium linear infinite hierarchy for the moments. In case 1), f_in describes local equilibrium but global nonequilibrium, and we propose a long‐time approximation in the hierarchy, which introduces irreversibility and relaxation towards global thermal equilibrium. In case 2), the statistical system, having been at global thermal equilibrium, without external influences, for t ≤ 0, is subject to weak external charge‐current distributions: then, new hierarchies for moments and their long‐time behaviours are discussed in outline. As examples, approximate mean‐field (Vlasov) approximations are treated for both cases 1) and 2).     

Information theories for time-dependent harmonic oscillator

Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville–von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.     

晶粒细化对MgB_2超导临界电流密度的作用

在多晶系统的MgB2超导体中存在晶粒间较小的整体电流和晶粒内大的局域电流.用改变升温速率的方法制备了不同晶粒大小和晶粒连接性的MgB2样品,并对它们的晶粒大小进行了统计.采用一种测量超导临界电流密度的Campbell法,分别测量和计算得到了它们的整体电流和局域电流密度.研究表明:长时间的烧结造成晶粒变大,材料有较大的整体临界电流密度,而短时间烧结的样品则相反;同时发现晶粒细化只提高了样品的局域临界电流密度,而且样品内部缺陷、杂质及晶界等因素是影响MgB2超导体整体电流传输的主要因素.     

Out of equilibrium dynamics of supersymmetry at high energy density

We investigate the out of equilibrium dynamics of global chiral supersymmetry at finite energy density. We concentrate on two specific models. The first is the massive Wess–Zumino model which we study in a self-consistent one-loop approximation. We find that for energy densities above a certain threshold, the fields are driven dynamically to a point in field space at which the fermionic component of the superfield is massless. The state, however, is found to be unstable, indicating a breakdown of the one-loop approximation. To investigate further, we consider an O(N) massive chiral model which is solved exactly in the large N limit. For sufficiently high energy densities, we find that for late times the fields reach a nonperturbative minimum of the effective potential degenerate with the perturbative minimum. This minimum is a true attractor for O(N) invariant states at high energy densities, and this provides a mechanism for determining which of the otherwise degenerate vacua is chosen by the dynamics. The final state for large energy density is a cloud of massless particles (both bosons and fermions) around this new nonperturbative supersymmetric minimum. By introducing boson masses which softly break the supersymmetry, we demonstrate a see-saw mechanism for generating small fermion masses. We discuss some of the cosmological implications of our results.     

The asymmetric single-impurity Anderson model – the modified perturbation theory

We investigate the single-impurity Anderson model by means of the recently introduced modified perturbation theory. This approximation scheme yields reasonable results away from the symmetric case. The agreement with exactly known results for the symmetric case is checked, and results for the non-symmetric case are presented. With decreasing conduction band occupation, the breakdown of the screening of the local moment is observed. In the crossover regime between Kondo limit and mixed-valence regime, an enhanced zero-temperature susceptibility is found.     

Subconscious Effect on Pedestrian Counter Flow

We propose an extended lattice gas model with different maximum velocities to simulate pedestrian counter flow by considering the subconscious behaviour of walkers. Four types of walkers including faster right walkers, slower right walkers, faster left walkers and slower left walkers are involved in the simulation. The simulation results show that our model can capture some essential features of pedestrian counter flows, such as the lane formation, segregation effect and phase separation at higher densities. We also find that the subconscious effect can reduce the occurrence of jam cluster evidently compared with the ease of un-subeonscious effect. At large maximum velocity, the critical density corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.     

Extreme fluctuation events in a simple high-density traffic model

We revisit a simple car-following model adapting it for simulating high-density traffic dynamics. Simulations in continuum space and discrete time are presented for the case of a single traffic lane, using periodic boundary conditions. The model parameters are fitted to empirical data for the mean car speed versus car density for densities higher than . The time evolution of the car ensemble is studied upon application of different types of random perturbations yielding strong speed fluctuations in all cases, the latter characterized by probability distribution functions displaying fat tails. We attempt to study the phenomenon of stop-and-go along the lane in the absence of perturbations by assuming a stopping cutoff speed, and find the resulting behavior of the ensemble both in space and time.     

Variational formulation of Chern–Simons theory for arbitrary Lie groups

We show that the Chern–Simons theory for a principal G-bundle P over a three-dimensional manifold, with G an arbitrary Lie group, can be formulated as a variational problem defined by local data on the bundle of connections C(P) of P. By means of the theory of variational problems defined by local data we prove that the Euler–Lagrange operator and the differential of the Poincaré–Cartan form can be intrinsically expressed in terms of the symplectic form and the curvature morphism of C(P). These facts and the theory of the global inverse problem of the Calculus of Variations allow us to prove that there is indeed a global Lagrangian density for these theories. We also prove that every infinitesimal automorphism of P produces in a natural way an infinitesimal symmetry of the variational problem defined by the Chern–Simons theory. We therefore conclude that the algebra of infinitesimal symmetries of these theories is infinite dimensional.     

Layering and position-dependent diffusive dynamics of confined fluids

We study the diffusive dynamics of a hard-sphere fluid confined between parallel smooth hard walls. The position-dependent diffusion coefficient normal to the walls is larger in regions of high local packing density. High density regions also have the largest available volume, consistent with the fast local diffusivity. Indeed, local and global diffusivities as a function of the Widom insertion probability approximately collapse onto a master curve. Parallel and average normal diffusivities are strongly coupled at high densities and deviate from bulk fluid behavior.     

On the validity of pre-equilibrium model assumptions

The Hartree-Fock calculation is performed for nuclear matter using the Skyrme interaction. It is shown that a stable density wave periodic in only one direction exists at densities below about one-third of the normal nuclear density. The critical densityρ _c below which the energy of the density wave is lower than that of the Fermi gas is determined for Skyrme interactions SKI to SKVI. It is further shown that even at densities slightly higher thanρ _c the density wave still exists as ametastable state in the sense that its energy is a local minimum in the variation parameter space. The density wave solution suddenly disappears at a higher density, since there the local minimum changes to an inflection point.     

Persistence of magnetic moments at high density in disordered systems near the metal insulator transition

Abstract

Spontaneous moment formation has been observed in disordered narrow band systems like doped semiconductors, or the liquid alloy Cs-Au. A recent model has provided a natural origin for this behaviour in a disordered system whenever the conduction band is almost empty. The intimate interplay between correlation, localization and magnetic properties characterizes this regime, and makes it different from the usual half filled band correlated system.

In this work we investigate the behaviour of the model at high density. Precisely correlation effects are strongly enhanced in the limit of low filling of the band, giving rise to persistent local moments even at high density. Conversely in the well studied case of a half filled band local nioments vanish at high density, and correlation effects become negligible in this limit.

At the light of the model we argue that the observed magnetic properties should persist at higher densities provided that only a few per cent electrons populate the conduction band.     

Vacuum local and global electromagnetic self-energies for a point-like and an extended field source

We consider the electric and magnetic energy densities (or equivalently field fluctuations) in the space around a point-like field source in its ground state, after having subtracted the spatially uniform zero-point energy terms, and discuss the problem of their singular behavior at the source’s position. We show that the assumption of a point-like source leads, for a simple Hamiltonian model of the interaction of the source with the electromagnetic radiation field, to a divergence of the renormalized electric and magnetic energy density at the position of the source. We analyze in detail the mathematical structure of such a singularity in terms of a delta function and its derivatives. We also show that an appropriate consideration of these singular terms solves an apparent inconsistency between the total field energy and the space integral of its density. Thus the finite field energy stored in these singular terms gives an important contribution to the self-energy of the source. We then consider the case of an extended source, smeared out over a finite volume and described by an appropriate form factor. We show that in this case all divergences in local quantities such as the electric and the magnetic energy density, as well as any inconsistency between global and space-integrated local self-energies, disappear.