In this study, we investigate the critical dynamics of sound wave propagation in the BC model with bimodal crystal field by combining the statistical equilibrium theory and the thermodynamics of linear irreversible processes.

The present study is devoted to critical dynamics of sound propagation in BC model with a random single anisotropy by using a method that combines the statistical equilibrium theory of phase transitions with the linear response theory of irreversible thermodynamics.

To shed light onto the initial condition sensitivity inside the MPI attractor in the RE model, the leading Lyapunov exponent is numerically estimated for 500 cycles starting after 5 days into integration, when the simulated vortex roughly reaches its statistical equilibrium (Fig.

For example, a 500-day idealized experiment in the study by Hakim (2011) using a different axisymmetric model captured intensity variation as large as 12 m [s.sup.-1] at the statistical equilibrium, whereas numerical simulations with a full-physics model by Yang et al.

* The photon population of the frequency states has to be adapted to a

statistical equilibrium, under the constraint of a finite and given total energy density.

Once these distributions are known, each cluster can be hadronized on the basis of

statistical equilibrium, leading to the calculation of averages in the microcanonical ensemble, enforcing the exact conservation of energy and charges of each cluster.

Indeed, recognition of the importance of heterogeneity leads Pareto to introduce

statistical equilibrium as a complement to the theoretical equilibrium that results from a balance of economic forces.

When all of these properties of the LGM system are so specified, the CSM 1.4 model delivers

statistical equilibrium results for the Atlantic MOC (Peltier and Solheim 2004; Fig.

Another, which they called the nuclear

statistical equilibrium, or e-process, operates only at staggeringly high temperatures and pressures and favors elements near iron in the periodic table, because these are the toughest, most stable nuclei.

Using a

statistical equilibrium concept such as the QRE, one can derive the statistical version of a model of conflict in extensive form that directly incorporates the structure of the strategic interaction.

Rivier sees the scaling state as a "

statistical equilibrium," meaning that shifts in individual parts of the system preserve its overall properties.