Jamming transition of high-dimensional traffic dynamics

Time-dependent Ginzburg–Landau equation in a car-following model considering the driver’s physical delay

In this paper, a new anticipation driving car-following model (AD-TVDM) is presented based on the two velocity difference model (TVDM)[1], taking into the effect of anticipation driving behavior in real world. The nature of the model is investigated by using linear and nonlinear analysis method. A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow and the time-dependent Ginzburg-Landau (TDGL) equation is derived to describe the traffic flow near the critical point.

Phase transition and critical phenomenon in traffic flow model with velocity-dependent sensitivity

Phase transition and critical phenomena in magnetic multilayer systems are studied in terms of Ginzburg–Landau mean-field theory. Detailed calculations are carried out for a system consisting of a layer of finite thickness coupled to a semi-infinite bulk magnet. Correlation functions are derived and the shift in critical point with the overlayer thickness and coupling between the neighboring layer is evaluated. A new critical exponent ν̃=1 is derived for the divergence of the effective extrapolation length at the interface with temperature and/or layer thickness.

Critical conditions are obtained for bifurcation phenomena in nonequilibrium systems (chemical instabilities) which are appropriate for transitions between homogeneous steady states as well as for symmetry-breaking transitions to static structures. In the case of symmetry-breaking instabilities these criteria enable the theory to be applied to systems in any number of spatial dimensions, eliminating a restriction to one-dimensional systems encountered in other treatments. These critical conditions allow for the derivation of time-dependent Ginzburg-Landau (TDGL)-type equations for the critical-mode amplitude (the order parameter) that grows into the new macrostate beyond the critical point. For homogeneous transitions the usual TDGL equation is obtained. For the case of intrinsic symmetry breaking, TDGL equations are found for coupled order parameters corresponding to different directions in $k$ space. In both the intrinsic and the extrinsic cases the TDGL equations are found to have nonlinear transport terms. When the TDGL equations are turned into Langevin equations, Ginzburg criteria (defining the region where meanfield theory breaks down) are derived. The critical dimensionality thus determined is 4 for homogeneous and intrinsic symmetry-breaking transitions, and 6 for the extrinsic symmetry-breaking case (under given mild technical conditions). Expressions for the size of the nonclassical critical regions are obtained for the different transitions in terms of characteristic parameters. For chemical instabilities these regions are in principle accessible.

A dynamical model of traffic is proposed to take into account the effect of acceleration delay. In the limit of no delay, the model reproduces the optimal velocity model of traffic. When the delay is small, it is shown that the phase transition among the freely moving phase, the coexisting phase, and the uniform congested phase occurs below the critical point. Above the critical point, no phase transition occurs. The value ${a}_{c}$ of the critical point increases with increasing delay time $1/b,$ where $a$ is the friction coefficient (or sensitivity parameter). When the delay time is longer than $\frac{1}{2},$ the critical point disappears and the phase transition always occurs. The linear stability theory and nonlinear analysis are applied. The critical point predicted by the linear stability theory agrees with the simulation result. The modified Korteweg--de Vries (KdV) equation is obtained from the nonlinear analysis near the critical point. The phase separation line obtained from the modified KdV equation is consistent with the simulation result.

Phase transition phenomenon: A compound measure analysis

Critical behavior of the Ising model under strong shear: The conserved case

In a Multi-Agent System (MAS), there usually exist system-level goals that agents are collectively trying to attain. Generally speaking, the local behaviours and performances of individual agents directly determine which global characteristics of an MAS, for example, the global performance and/or patterns, will emerge and how the system-level goals will be attained. In most cases, such a local?global relationship is neither obvious nor straightforward. In this paper, we will address several issues on modelling emergent complex behaviours in MAS. In particular, we will focus on the local?global relationship in a Self-Organising MAS (SOMAS), and discuss the phenomena of Self-Organised Criticality (SOC) and phase transition in SOMAS.

Thermodynamics of phase transition in Reissner–Nordström–de Sitter spacetime

An effect is studied of the crystal field on a system of rotors under the conditions of quantum orientational melting. It is shown that even very small crystal fields can substantially change the behavior of the system: at a certain positive value of the crystal field, a critical point appears at the “classical” side of the phase separation line; another critical point appears at the “quantum” side with further increasing of the field; then these critical points degenerate into a multicritical point and then the phase separation line disappears. For negative crystal fields stable states of the system of rotors can exist with a negative order parameter which can be treated as the orientational analog of the easy-plane-type ordering in magnets.

This is the first part of a study, by the Monte Carlo method, of one-dimensional and two-dimensional steady-state Ising systems. We examine phase transitions and critical behavior at equilibrium (for reference) and steady state. The primary model is a 10×10 or 100×1 periodic square lattice of M=100 interacting, two-state, cycling enzyme molecules. We use a flat top on P (N2) (the probability N2 out of M molecules are in state 2) as a criterion to locate the approximate ’’critical point’’ in these finite systems. At equilibrium, cases M=10×10, 5×5, and 12 have been examined. Reducing M increases the nearest-neighbor correlation function c1 at fixed T and increases the critical temperature. At steady state, with M=100 in either one or two dimensions, the cooperativity of the system may be either enhanced or reduced compared to equilibrium, depending on the choice of certain kinetic parameters. With the rather conservative choices of parameters used here, phase transition behavior at steady state is qualitatively similar to that at equilibrium except, of course, the enzyme flux is involved in the steady-state cases but not at equilibrium. We confirm a number of qualitative predictions of the Bragg–Williams (mean field) approximation. Hysteresis and nucleation kinetics can be studied by the Monte Carlo method, but we do not pursue these topics here. We plan to study the noise power spectrum in N2 in future work.

Traffic Flow as Physics of Many-Body System

A geometric foundation of thermo-statistics is presented with only the axiomatic assumption of Boltzmann’s principle S(E, N, V) = k In W. This relates the entropy to the geometric area e S(E,N,V) of the manifold of constant energy in the (finite) N-body phase space. From this principle, all of thermodynamics and especially all phenomena of phase transitions and critical phenomena can be unambiguously identified for even small systems. Within Boltzmann’s principle, Statistical Mechanics becomes a geometric theory addressing the whole ensemble or the manifold of all points in phase space which are consistent with the few macroscopic conserved control parameters. This interpretation leads to a straight derivation of irreversibility and the second law of thermodynamics out of the time-reversible microscopic mechanical dynamics. It is the whole ensemble that spreads irreversibly over the accessible phase space not the single N-body trajectory. This is all possible without invoking the thermodynamic limit, extensivity, or concavity of S(E, N, V). Without the thermodynamic limit or at phase-transitions the systems are usually not self-averaging, i.e. do not have a single peaked distribution in phase space. The main obstacle against the second law, the conservation of the phase-space volume due to Liouville, is overcome by realizing that a macroscopic theory like Thermodynamics cannot distinguish a fractal distribution in phase space from its closure.

Ground-state magnetic properties of the spin- [formula omitted] transverse Ising model