Critical System Size Research Articles

Energy dissipation and clustering for a cooling granular material on a substrate

We experimentally study the dynamics of a cooling two-dimensional granular system of steel spheres moving radially inward on an aluminum substrate. We find that the cooling process in this system differs significantly from model calculations that include realistic restitutional losses and rolling (hence, weak) friction. A likely explanation for the experimental observations is the fact that particles typically slide on the substrate for some time after each collision, losing energy rapidly. Using results from an MD simulation as a reference point, we consider detailed experimental results for the cooling of systems of spheres on a substrate as a function of the system size, N. For systems with more than N=300 particles, we find that final spatial configurations consist primarily of dense central clusters, and that the velocity distributions, which have an exponential character, are only weakly dependent on system size. Thus, there is a critical system size above which a majority of particles come to rest in a densely packed lattice. We also find evidence of a spatial ordering size scale in the cooled state that is much smaller than the system size. Velocity distributions in the cooling system are nearly Maxwell–Boltzmann (MB)-like at early times, but show significant differences from a MB distribution after particles have undergone a moderate number of collisions.

System-Size Effects on the Collective Dynamics of Cell Populations with Global Coupling

Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells subject to small additive noise. As the population size is changed, the system shows a phase-transitionlike behavior. That is, there exits a well-defined critical system size above which the system stays in a monostable state with high-frequency activity while below which a new phase characterized by alternation of high- and low frequency activities appears. The mean field motion obeys a stochastic process with state-dependent noise, and the above phenomenon can be interpreted as a noise-induced transition characteristic to such processes. Coexistence of high- and low frequency activities observed in finite size systems is reported by N. Cohen, Y. Soen and E. Braun[Physica A249, 600 (1998)] in the experiments of cultivated heart cells. The present report gives the first qualitative interpretation of their experimental results.

Fermion current-current interactions and orthogonality in two dimensions

Abstract The wavefunction renormalization Z of a two-dimensional Fermi gas with current-current interaction mediated by an unscreened transverse gauge field is discussed within a simple Hartree approximation for self-field effects. In the case of a three-dimensional gauge field, a critical coupling strength is required before level crossing and strict orthogonality occur. In the case of a two-dimensional gauge field, any finite coupling guarantees orthogonality beyond a critical system size.

Critical parameters for nucleation in finite systems

We consider a supersaturated vapor in a closed and finite system. The conditions for the existence of a stable droplet of the liquid phase in this system are in principle determined by the thermodynamic parameters ( N, V, T). It is shown that in deviation from the nucleation theory of infinite systems the nucleation in finite systems occurs in a smaller region of thermodynamic values. We investigate critical values of this parameters, e.g., the critical system size, the critical overall particle number, and the critical temperature, where it becomes impossible for a stable droplet to exist in the finite system. The critical parameters are discussed in terms of the initial supersaturation.