An Improved Car-Following Model for Multiphase Vehicular Traffic Flow and Numerical Tests

This paper attempts to introduce an improved difference model that modifies a car-following model, which takes the next-nearest-neighbor interaction into account. The hnprovement of this model over the previous one lies in that it performs more realistically in the dynamical motion for small delay time. The traffic behavior of the improved model is investigated with analytic and numerical methods with the finding that the new consideration could further stabilize traffic flow. And some simulation tests verify that the proposed model can demonstrate some complex physical features observed recently in real traffic such as the existence of three phases： free flow, coexisting flow, and jam flow; spontaneous formation of density waves; sudden flow drop in flow-density plane; traffic hysteresis in transition between the free and the coexisting flow. Furthermore, th.e improved model also predicts that the stable state to relative density in the coexisting flow is insusceptible to noise.     

Visualization of a rotating flow under large-deformed free surface using anisotropic flakes

This study aims to clarify the relationship between the deformation of a free surface and flow transition in a “switching phenomenon” process. In a flow driven by a rotating disk in a cylindrical open vessel, the free surface irregularly changes its shape from axisymmetric to nonaxisymmetric and vice versa with repeating up-and-down motion (so-called “switching phenomenon”). The flow under the free surface was visualized by anisotropic flakes. When the free surface assumes a parabolic shape, the flow is distinguished by three regions; local circulation region, rigid vortex region and meridional circulation region. The flow transition in the switching phenomenon was shown by snapshots and movies of the visualized flow; the flow near the free surface is laminar even if the shape of the free surface changes to nonaxisymmetric during the time at which the free surface attaches to the bottom of the vessel. After the free surface detaches from the disk, the flow near the free surface becomes turbulent. When the free surface changes to axisymmetric while descending to the bottom, the flow changes from turbulent to laminar flow and the local circulation region reemerges at the center of the vessel.     

Molecular-dynamics simulations with explicit hydrodynamics II: On the collision of polymers with molecular obstacles

We present a study of the dynamics of single polymers colliding with molecular obstacles using Molecular-dynamics simulations. In concert with these simulations we present a generalized polymer-obstacle collision model which is applicable to a number of collision scenarios. The work focusses on three specific problems: i) a polymer driven by an external force colliding with a fixed microscopic post; ii) a polymer driven by a (plug-like) fluid flow colliding with a fixed microscopic post; and iii) a polymer driven by an external force colliding with a free polymer. In all three cases, we present a study of the length-dependent dynamics of the polymers involved. The simulation results are compared with calculations based on our generalized collision model. The generalized model yields analytical results in the first two instances (cases i) and ii)), while in the polymer-polymer collision example (case iii)) we obtain a series solution for the system dynamics. For the case of a polymer-polymer collision we find that a distinct V-shaped state exists as seen in experimental systems, though normally associated with collisions with multiple polymers. We suggest that this V-shaped state occurs due to an effective hydrodynamic counter flow generated by a net translational motion of the two-chain system.     

Random turn walk on a half line with creation of particles at the origin

We consider a version of random motion of hard core particles on the semi-lattice 1,2,3,… , where in each time instant one of three possible events occurs, viz., (a) a randomly chosen particle hops to a free neighboring site, (b) a particle is created at the origin (namely, at site 1) provided that site 1 is free and (c) a particle is eliminated at the origin (provided that the site 1 is occupied). Relations to the BKP equation are explained. Namely, the tau functions of two different BKP hierarchies provide generating functions respectively (I) for transition weights between different particle configurations and (II) for an important object: a normalization function which plays the role of the statistical sum for our non-equilibrium system. For time t→∞ we obtain the asymptotic configuration of particles obtained from the initial empty state (the state without particles).     

Aeroelastic dynamic response and control of an airfoil section with control surface nonlinearities

Nonlinearities in aircraft mechanisms are inevitable, especially in the control system. It is necessary to investigate the effects of them on the dynamic response and control performance of aeroelastic system. In this paper, based on the state-dependent Riccati equation method, a state feedback suboptimal control law is derived for aeroelastic response and flutter suppression of a three degree-of-freedom typical airfoil section. With the control law designed, nonlinear effects of freeplay in the control surface and time delay between the control input and actuator are investigated by numerical approach. A cubic nonlinearity in pitch degree is adopted to prevent the aeroelastic responses from divergence when the flow velocity exceeds the critical flutter speed. For the system with a freeplay, the responses of both open- and closed-loop systems are determined with Runge-Kutta algorithm in conjunction with Henon’s method. This method is used to locate the switching points accurately and efficiently as the system moves from one subdomain into another. The simulation results show that the freeplay leads to a forward phase response and a slight increase of flutter speed of the closed-loop system. The effect of freeplay on the aeroelastic response decreases as the flow velocity increases. The time delay between the control input and actuator may impair control performance and cause high-frequency motion and quasi-periodic vibration.     

Irregular scattering of particles confined to ring-bounded cavities

The classical motion of a free particle that scatters elastically from ring-bounded cavities is analyzed numerically. When the ring is a smooth circle the scattering follows a regular and periodic pattern. However, for rings composed ofN scatterers the flow is irregular, of Lyapunov type. The Lyapunov exponent is found to depend logarithmically withN, which is consistent with the theoretical derivation of Chernov for polygon-shaped billiard systems. The escape time from cavities bounded by a ring ofN separated scatterers is demonstrated to follow a geometric distribution as a function of the aperture size. An empirical scaling is proposed between the Lyapunov exponent, the escape time, andN.     

Presence of many stable nonhomogeneous states in an inertial car-following model

We present a single lane car- following model of traffic flow which is inertial and free of collisions. It demonstrates observed features of traffic flow such as existence of three regimes: free, nonhomogeneous congested (NHC) or synchronized, and homogeneous congested (HC) or jammed flow; bistability of free and NHC flow states in a range of densities, hysteresis in transitions between these states; jumps in the density-flux plane in the NHC regime; gradual spatial transition from synchronized to free flow; long survival time of jams in the HC regime. The model predicts that in the NHC regime there exist many stable states with different wavelengths, and noise can cause transitions between them.     

Correlation time and diffusion coefficient imaging: application to a granular flow system

A parametric method for spatially resolved measurements for velocity autocorrelation functions, R(u)(tau) = , expressed as a sum of exponentials, is presented. The method is applied to a granular flow system of 2-mm oil-filled spheres rotated in a half-filled horizontal cylinder, which is an Ornstein-Uhlenbeck process with velocity autocorrelation function R(u)(tau) = e(- ||tau ||/tau(c)), where tau(c) is the correlation time and D = tau(c) is the diffusion coefficient. The pulsed-field-gradient NMR method consists of applying three different gradient pulse sequences of varying motion sensitivity to distinguish the range of correlation times present for particle motion. Time-dependent apparent diffusion coefficients are measured for these three sequences and tau(c) and D are then calculated from the apparent diffusion coefficient images. For the cylinder rotation rate of 2.3 rad/s, the axial diffusion coefficient at the top center of the free surface was 5.5 x 10(-6) m(2)/s, the correlation time was 3 ms, and the velocity fluctuation or granular temperature was 1.8 x 10(-3) m(2)/s(2). This method is also applicable to study transport in systems involving turbulence and porous media flows.     

The dynamics of clusters of flexible cylinders in axial flow: Theory and experiments

This paper presents an outline of the theory for the dynamics of clusters of independently supported flexible cylinders in axial flow, and an extensive discussion of the behaviour of such systems with increasing flow velocity, with special emphasis placed on the modal forms of free coupled motions of the cylinders and on the onset of instabilities. Results of an experimental study of the problem are also presented, involving systems of two, three or four cylinders supported at both ends and positioned symmetrically in the cylindrical test section of a water tunnel; experiments were conducted with different inter-cylinder gaps and support conditions. Both theory and experiment show that with increasing flow the system loses stability by buckling in one of its coupled modes, commonly in a pattern where cylinders move towards one another symmetrically, maximum displacement occurring just downstream of their midpoints. With increasing flow, theory predicts that other buckling instabilities are superimposed on the first; in the experiments the system remains buckled, changing modal patterns constantly; some of them correspond to those predicted by theory. At sufficiently high flow, oscillatory motion is observed, corresponding to theoretical flutter. Theory and experiment agree qualitatively in most essential features of the dynamical behaviour of the system, and quantitative agreement in the critical flow velocities for the onset of the first buckling instability is remarkably good.     

Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations

The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for the motion of shallow water, from the Navier-Stokes system for incompressible flows with a moving free surface [14]. These compressible systems are degenerate when vacuum state appears. We study initial-boundary-value problems for such systems for both bounded spatial domains or periodic domains. The dynamics of weak solutions and vacuum states are investigated rigorously. First, it is proved that the entropy weak solutions for general large initial data satisfying finite initial entropy exist globally in time. Next, for more regular initial data, there is a global entropy weak solution which is unique and regular with well-defined velocity field for short time, and the interface of initial vacuum propagates along the particle path during this time period. Then, it is shown that for any global entropy weak solution, any (possibly existing) vacuum state must vanish within finite time. The velocity (even if regular enough and well-defined) blows up in finite time as the vacuum states vanish. Furthermore, after the vanishing of vacuum states, the global entropy weak solution becomes a strong solution and tends to the non-vacuum equilibrium state exponentially in time.     

Theory of Gravitational-Inertial Field of Universe. II. On Critical Systems in Universe

Application of the equations of the gravitational-inertial field to the problem of free motion in the inertial field (to the cosmologic problem) leads to results according to which 1. all Galaxies in the Universe “disperse” from each other according to Hubble's law, 2. the “dispersion” of bodies represents a free motion in the inertial field and Hubble's law represents a law of motion of free body in the inertial field, 3. for arbitrary mean distribution densities of space masses different from zero the space is Lobachevskian. All critical systems (with Schwarzschild radius) are specific because they exist in maximalinertial and gravitational potentials. The Universe represents a critical system, it exists under the Schwarzschild radius. In high-potential inertial and gravitational fields the material mass in a static state or in motion with deceleration is subject to an inertial and gravitational “annihilation”. At the maximal value of inertial and gravitational potentials (= c²) the material mass is being completely “evaporated” transforming into radiation mass. The latter is being concentrated in the “horizon” of the critical system. All critical systems-black holes-represent geon systems, i.e. local formations of gravitational-electromagnetic radiations, held together by their own gravitational and inertial fields. The Universe, being a critical system, is “wrapped” in a geon crown.     

Statistical mechanics of Arakawa’s discretizations

The results of statistical analysis of simulation data obtained from long time integrations of geophysical fluid models greatly depend on the conservation properties of the numerical discretization used. This is illustrated for quasi-geostrophic flow with topographic forcing, for which a well established statistical mechanics exists. Statistical mechanical theories are constructed for the discrete dynamical systems arising from three discretizations due to Arakawa [Arakawa, Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I. J. Comput. Phys. 1 (1966) 119–143] which conserve energy, enstrophy or both. Numerical experiments with conservative and projected time integrators show that the statistical theories accurately explain the differences observed in statistics derived from the discretizations.     

Dynamics of a camphoric acid boat at the air–water interface

We report experiments on an agarose gel tablet loaded with camphoric acid (c-boat) spontaneously set into motion by surface tension gradients on the water surface. We observe three distinct modes of c-boat motion: harmonic mode where the c-boat speed oscillates sinusoidally in time, a steady mode where the c-boat maintains constant speed, and an intermittent mode where the c-boat maintains near-zero speed between sudden jumps in speed. Whereas all three modes have been separately reported before in different systems, controlled release of Camphoric Acid (CA) from the agarose gel matrix allowed the observation of all the three modes in the same system. These three modes are a result of a competition between the driving (surface tension gradients) and drag forces acting on the c-boat. Moreover we suggest that there exist two time scales corresponding to spreading of CA and boat motion and the mismatch of these two time scales give rise to the three modes in boat motion. We reproduced all the modes of motion by varying the air–water interfacial tension using Sodium Dodecyl Sulfate (SDS).     

Natural patterns of energy dispersal

Universal patterns such as power-law dependences, skewed distributions, tree-like structures, networks and spirals are associated with energy dispersal processes using the principle of least action. Also ubiquitous temporal courses such as sigmoid growth, bifurcations and chaos are ascribed to the decrease of free energy in the least time. Moreover, emergence of natural standards such as the common genetic code and chirality consensus of amino acids are understood to follow from the quest to maximize the dispersal of energy. Many mathematical functions that model natural patterns and processes are found as approximations of the evolutionary equation of motion that has been derived from statistical physics of open systems. The evolutionary processes can be described as flows of energy that run from high energy sources to low energy sinks in the least time. However, the equation of evolution cannot be solved in general because the flows of energy and their driving forces are inseparable. Since the energy of the system keeps changing, the paths of evolution cannot be integrated from a given initial state to a final state. Although evolutionary courses of these non-Hamiltonian systems with two or more alternative ways of dissipation cannot be predicted, the flows of energy will search and naturally select paths of least action, known as geodesics, to consume free energy in the least time. The scale-invariant natural patterns follow from this natural law that impinges on processes at all scales of space and time.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dlmensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling fit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic depinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

Numerical Study on Depinning Dynamics of Fluids Interacting with Disorder

We investigate the depinning of two-dimensional fluids interacting with quenched disorder, based on Langevin simulations. For weak disorder the fluids depin elastically and flow in an ordered state. A power-law scaling lit between velocity and driving force can be obtained for the onset of motion in the elastic regime. This is in good agreement with that of colloid, charge density wave, and superconducting vortex systems. With an increasing strength of the disorder, we find a sharp crossover to plastic de. Pinning, accompanied by a substantial increase in the depinning force. The scaling fit obtained in the elastic regime becomes invalid when plastic flow occurs. In the plastic regime, the fluids flow in channels and the hexatic order decays exponentially with drives.     

水陆两栖飞机静水面高速滑行性能数值计算与试验分析

针对水陆两栖飞机静水面高速滑行过程的运动响应大、流场强非线性等问题，提出了一种基于传统动网格技术的"状态预估——精确计算"的数值模拟方法:通过求解Reynolds平均N-S方程结合运动方程来模拟飞机静水面滑行时的流场特征和运动特性，数值模拟方法为隐式有限体积法，湍流模型采用k-ω（SST Menter）结合壁函数进行处理，自由液面捕捉采用VOF方法；数值计算时，首先采用粗网格对简化后的飞机在不同航速下的姿态和升沉进行快速预估，再将飞机置于预估状态下进行精确网格划分，最后进行精确数值计算分析.为了验证数值模拟结果的正确性，在物理水池中进行了静水拖曳试验，将数值计算结果与试验结果进行对比分析可得:数值计算与水池试验的流场特征吻合，且阻力、姿态和升沉的计算精度达到90%，验证了数值模拟方法的可行性.