Floating car data of car-following behavior in cities were compared to existing microsimulation models, after their parameters had been calibrated to the experimental data. With these parameter values, additional simulations have been carried out, e.g. of a moving car which approaches a stopped car. It turned out that, in order to manage such kinds of situations without producing accidents, improved traffic models are needed. Good results have been obtained with the proposed generalized force model. 02.70.Ns,34.10.+x,05.70.Ln,89.40.+k

We investigate the motion of Brownian particles which have the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy. The resulting Langevin equation includes an additional acceleration term. The motion of the Brownian particles in a parabolic potential is discussed for two different cases: (i) continuous take-up of energy and (ii) take-up of energy at localized sources. If the take-up of energy is above a critical value, we found a limit-cycle motion of the particles, which, in case (ii), can be interrupted by stochastic influences. Including reflecting obstacles, we found for the deterministic case a chaotic motion of the particle. [S0031-9007(98)06328-5] PACS numbers: 05.40. + j, 05.45. + b, 05.60. + w, 87.10. + eActive motion is based on energy consumption. For biological systems, an external supply of energy is crucial, e.g., to maintain metabolism and to perform movement [1]. For a spatially inhomogeneous supply of energy, the organism needs to store energy internally, in order to overcome periods of starvation, e.g., during the search for new sources. But even provided the homogeneous supply of energy, the organism needs to convert the energy taken up from the environment into kinetic energy. Dependent on the level of biological organization, the take-up, storage, and conversion of energy is a rather complex process.In the following, we consider the motion of microscopic biological objects, such as cells or bacteria, which can be sufficiently described by a Langevin dynamics. Stochastic differential equations have long been used to describe the motion of organisms [2,3]. In order to derive a simplified model of active biological motion, we study Brownian particles with an internal energy depot. The motion of simple Brownian particles in a space-dependent potential, U͑r͒ can be described by the Langevin equation:where g 0 is the friction coefficient of the particle at position r, moving with velocity y. F ͑t͒ is a stochastic force with strength S and a d-correlated time dependenceRecently, Brownian motion models attracted much attention for describing nonequilibrium transport on the microscale [4]. In addition to the dynamics described above, the Brownian particles discussed here are active particles [5] to the effect that they have the ability to take up energy from the environment and to store it in an internal depot, which is considered a new element of the model. Further, the particles are able to convert internal energy into kinetic energy. Considering also internal dissipation, the resulting balance equation for the internal energy de-pot, e, of an active particle is given by d dt e͑t͒ q͑r͒ 2 c e͑t͒ 2 d͑y͒ e͑t͒ .( 3) q͑r͒ is the space-dependent take-up of energy and c describes the internal dissipation assumed to be proportional to the depot energy. d͑y͒ is the rate of conversion of internal into kinetic energy which should be a function of the actual velocity of the particle. A simple ansatz for d͑y͒ reads: d͑y͒ d 2 y 2 ; ...

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We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the takeup/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of nonequilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e., for active motion, and (b) interactions between the particles based on global couplings. We derive analytical expressions for the nonequilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.

A model of Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion, is discussed. The general dynamics outlined in Sect. 2 is investigated for the deterministic and stochastic particle's motion in a non-fluctuating ratchet potential. First, we discuss the attractor structure of the ratchet system by means of computer simulations. Dependent on the energy supply, we find either periodic bound attractors corresponding to localized oscillations, or one/two unbound attractors corresponding to directed movement in the ratchet potential. Considering an ensemble of particles, we show that in the deterministic case two currents into different directions can occur, which however depend on a supercritical supply of energy. Considering stochastic influences, we find the current only in one direction. We further investigate how the current reversal depends on the strength of the stochastic force and the asymmetry of the potential. We find both a critical value of the noise intensity for the onset of the current and an optimal value where the net current reaches a maximum. Eventually, the dynamics of our model is compared with other ratchet models previously suggested.