Nonergodicity

Even if a system is formally ergodic, its behavior during computer simulations may resemble those of nonergodic systems. This means that the system does not properly explore phase space, and, therefore, the calculated statistical averages might... 

One reason for the inefficiencies of constraint methods is that they may prevent an efficient sampling of the set (x) = . This is illustrated by Fig. 4.2. It is common that many pathways separated by high energy barriers exist to go from A to B. In constrained simulation, the system can get trapped in one of the pathways. In the most serious cases, this leads to quasi-nonergodic effect where only a part of the set (x) is effectively explored. In less serious cases, the convergence is quite slow. 

Dependence of the Nonergodicity Parameter in Polybutadiene in the Neighborhood of the Glass Transition. 

Study of Nonergodicity Transitions Gelation in Colloidal Systems with Short-Range Attractions. 

For Moore (1984), this identity between the velocity and the multiplier is unlikely to hold in a real nonergodic economy, where expectations are continually changing. It should be emphasized, however, that Marx s reproduction schema provides a limiting extreme in which unlikely conditions such as those associated with balanced growth are assumed to hold. 

Cerda, B.A. Horn, D.M. Breuker, K. Carpenter, B.K. McLafferty, F.W. Electron Capture Dissociation of Multiply-Charged Oxygenated Cations. A Nonergodic Process. Eur. Mass Spectrom. 1999, 5,335-338. 

In general multiscale network, two type of obstacles can violate approximate equality t 1 /k.. Following the zero-one law for nonergodic multiscale networks (previous subsection) we can split the set of all vertices into two subsets. Hi and H2. The dominant reaction network dom mod( ) is a union of networks on sets without any link between sets. 

R. A. Zubarev, N. L. Kelleher, and F. W. McLafferty, Electron capture dissociation of multiply charged protein cations. A nonergodic process, J. Am. Chem. Soc., 120 (1998) 3265-3266. 

Detailed high-frequency (terahertz) dynamical studies of glasses have been probed by inelastic X-ray scattering (IXS) [139], The advantage of this technique is that with reliable measurements it allows determination of the so-called nonergodicity parameter f(q, T) as a function of wavevector q this quantity is defined by the long time limit of the density-density correlation function F(q, t) divided by the static structure factor [15],... 

The quantity e w is the Debye-Waller factor, while Sis(q) is the structure factor due to packing statistics or the inherent structure. The contributions from the anharmonic vibrational degrees of freedom about the inherent structure are denoted by Finei(q,t). In the longtime limit, the nonergodicity parameter becomes [139]... 

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