We describe a bottom–up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy...

Using a straightforward extension of the Onsager-theory for hard rods, we consider the thermodynamic stability of the isotropic (I) and nematic (N) phase of binary mixtures of thick and thin hard rods of the same length. We show that such mixtures not only exhibit the expected I–N ordering...

The ferromagnetic spin-1 Ising model with a transverse crystal field is studied within the framework of the effective field theory on honeycomb, square and cubic lattices. We have investigated the effect of the transverse crystal field on the magnetization and quadrupolar moments, and phase...

We study the dynamics of a coupled two-channel ASEP in which intra-channel transition rates are dependent on the configuration of neighboring channel. The binding constant k, which signifies the ratio of inter-channel transition rates, is introduced and the symmetric and asymmetric coupling...

Necessary and sufficient conditions from optimal control theory that are typically used when studying finite and infinite horizon natural resource economics problems are stated. In the finite horizon case their use is demonstrated by deriving an explicit solution of a model describing the...

We propose a simple cellular automaton model to study the traffic dynamics in a roundabout. Both numerical and analytical results are presented. We are able to obtain exact solutions in the full parameter space. Exact phase diagrams are derived. When the traffic from two directions mixed, there...

The influence of elastic interactions on the phase diagram of a two-dimensional model binary alloy with antiferromagnetic nearest and ferromagnetic next-nearest-neighbor-type interactions is studied by Monte Carlo simulations and finite size scaling techniques. The elastic interaction leads to a...

The continuum Heisenberg model of spin fluid is considered. The pair correlation functions and the single-particle distribution function of ferromagnetic state are obtained by the self-consistent solution of the Ornstein–Zernike and the Lovett equations in the mean spherical approximation. On...

We study the traffic congestion and dispersion of vehicles occurring on a single lane highway in Hurricane evacuation. The traffic congestion depends on both sensitivity and speed of the leading vehicle. When the leading vehicle moves with low speed, the vehicular traffic exhibits the stop and...