Nonlocal Interaction Term Research Articles

Macroscopic dynamics of multilane traffic.

We present a macroscopic model of mixed multilane freeway traffic that can be easily calibrated to empirical traffic data, as is shown for Dutch highway data. The model is derived from a gas-kinetic level of description, including effects of vehicular space requirements and velocity correlations between successive vehicles. We also give a derivation of the lane-changing rates. The resulting dynamic velocity equations contain nonlocal and anisotropic interaction terms which allow a robust and efficient numerical simulation of multilane traffic. As demonstrated by various examples, this facilitates the investigation of synchronization patterns among lanes and effects of on ramps, off ramps, lane closures, or accidents.

Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.

Thermal properties of spacetime foam

Spacetime foam can be modeled in terms of nonlocal effective interactions in a classical nonfluctuating background. Then, the density matrix for the low-energy fields evolves, in the weak-coupling approximation, according to a master equation that contains a diffusion term. Furthermore, it is argued that spacetime foam behaves as a quantum thermal field that, apart from inducing loss of coherence, gives rise to effects such as gravitational Lamb and Stark shifts as well as quantum damping in the evolution of the low-energy observables. These effects can be, at least in principle, experimentally tested.

Spacetime Foam as a Quantum Thermal Bath

An effective model for the spacetime foam is constructed in terms of nonlocal interactions in a classical background. In the weak-coupling approximation, the evolution of the low-energy density matrix is determined by a master equation that predicts loss of quantum coherence. Moreover, spacetime foam can be described by a quantum thermal field that, apart from inducing loss of coherence, gives rise to effects such as gravitational Lamb and Stark shifts as well as quantum damping in the evolution of the low-energy observables.

Some remarks on nonlocal interactions and hysteresis in phase transitions

This paper examines models of shape memory alloys in which the usual multiwell, nonconvex elastic energy is modified by the addition of a nonlocal interaction term. It is shown that minimizing such an energy over uniform Young-measures yields a good prediction of hysteresis in a material subjected to biaxial loading. In addition, the relationship between the nonlocal interaction energy and the coherency energy is discussed.

A minimax problem for semilinear nonlocal competitive systems

A two-sided game for the control of a stationary semilinear competitive system with autonomous sources is considered, where the controls are the kernels of the nonlocal interaction terms. The saddle point (the optimal solution of the game) is characterized as the unique solution of the associated optimality system, which is solved by an iterative scheme.

Variational approach for competitive systems with obstacles

We prove existence and uniqueness results for competitive systems consisting of two parabolic equations supplemented with positivity constraints. The coupling terms include local and nonlocal interaction terms. Monotone iteration schemes are used to obtain solutions in a variational approach. The solutions of the system are compared with the solution of a simplified ordinary differential system.

Fem calculation of the elastic H-H interaction energy for hydrogen in metals

A method of calculating the elastic contribution to the hydrogen chemical potential and the mean elastic interaction energy for hydrogen atoms dissolved in metals is presented. The method, which is based on the Finite-Element Method (FEM), makes it possible to solve the elastic problem for the metal-hydrogen system in arbitrary geometries and for arbitrary boundary conditions. Two examples are presented: In the first example the method is applied to calculate the mean hydrogen-hydrogen interaction energy in substrate-supported PdH x films. Results from this calculation indicate a decreased strength of the elastic interaction for thin PdH x films as compared to free bulk PdH x , which is in qualitative agreement with recent experiments. In the second example the anomalous “up-hill” diffusion of hydrogen in Pd-Pt alloys is examined. Results here support a previously reported model calculation which has shown that the unusual diffusion behaviour can be explained in terms of non-local elastic interactions between the dissolved hydrogen atoms.

Quantum and nonlocal coherent effects in Boltzmann gases.

Quantum coherent phenomena in Boltzmann gases are studied on the basis of the generalized Waldmann-Snider kinetic equation. The equation takes into account the effects of quantum identity of particles. The conditions are formulated for the propagation of different collective modes in gases of particles with arbitrary internal degrees of freedom. Collective coherent effects are macroscopic manifestations of the molecular field for the transverse (off-diagonal) elements of particle distribution in a ``polarized'' system (a system with a nonuniform population of internal energy levels in an unperturbed state). The simplest results are obtained for particles with equidistant internal-energy levels exploiting the analogy with spin-polarized quantum gases. The accurate study of nonlocal interaction terms permits one to compare classical-kinetic and Fermi-liquid approaches to kinetic phenomena in dilute gases, and shows the limitations of both approaches. In the case of collective modes, more accurate schemes of derivation of the kinetic equation must be accompanied by the simultaneous calculations of nonlocal contributions.

Zum Aufbau der Quantenfeldtheorie ohne Lagrangeformalismus

It is investigated to what extent the quantum theory of elementary particles can be built up by using the following principle only: « There exists an irreducible representation of the algebra of creation-and annihilation operatorsa+,a, and the infinitesimal transformations of the inhomogeneous Lorentz group can be constructed out of them. » The representation of the inhomogeneous Lorentz group can then be split up in irreducible ones classified byWigner and describing different sorts of elementary particles. Space-time dependence of all operators is introduced by a unitary transformation of thea+,a. Energy-momentumtensors and charge-current vectors are found without use of fields. Fields and field-equations, corresponding to the various sorts of elementary particles, may also be set up but are dispensable. Interactions are introduced as unitary transformations of thea+,a, mixing the irreducible representations of the Lorentz group. This corresponds to in general non-local interaction terms in the Lagrange formalism.