Damping region

Multipole fluctuation strength of the cosmic microwave background radiation as a function of the spherical harmonic index I. The location and the height of the first minimum favors a spatially flat Universe, while the level of the fluctuations in the higher multipoles (/ > 400) Indicates the presence of a low-density baryonic component (<5%). The measurements cover already the damping region (/ > 1,000). Wilkinson Microwave Anisotropy Probe (WMAP) data are displayed together with results of earlier balloon observations (Reprinted from Nolta et al. 2009 with kind permission of the first author, the WMAP Science Team, and AAS)... 

The instability of the assembly and the near resonance of the upstream, B4, bellows with the forcing fluid flow initiates fatigue damage, which accumulates in the most highly stressed, and least damped, regions of the unit. 

Figure 5 Approach curve to a gold surface with a hydrophilic S-H monolayer, showing linearity in the appropriate damping region with a slope AF/A (% damping) of 0.099.

As in Section 2.7 we now formulate as a condition for the onset of the limit cycle that the oscillator in (6.24) is not damped but amplified, i.e., x < 0, but still A > 0. We expect that x as defined in (6.23) is some function of the external parameters of the network such that at least near the thermodynamic equilibrium we have X > 0 and only for sufficiently strong nonequilibrium conditions for the external parameters X becomes negative. This behaviour is typically reflected by the conditions (2.75) and (2.76) for our model in Section 2.7. At the critical point, the so-called bifurcation point, which separates the damped region from the amplifying one, we have X = 0 and thus from the definition of x in (6.23) opposite signs of and 2 2 2 2 other hand we... 

The most commonly used BC methods can be classified into three main categories the exact nonreflective BC, the approximated nonreflective BC (also called the variational BC or VBC), and the damping region BC. In principle, exact nonreflective BCs can be obtained via numerical computation for crystalline systems under certain assumptions.One possible formulation of this type of BC is discussed below. However, exact BCs are not local in both space and time, meaning that information about all of the boundary atoms at all times is, in principle, necessary to compute them. Because the decay of the history dependence is rather slow, implementing such a BC scheme can be computationally very expensive. To reduce such a computational cost, E and co-workers introduced the VBC scheme. 

Figure 12 Schematic representation of (a) damping region BC (the region of interest is surrounded by a border region where damping of the outgoing waves takes place), and (b) coupled system for exact nonreflective BC (P is the region of interest and may contain inhomogeneities, while Q is the defect-free medium that surrounds it).

Absorption of wave packet amplitude that approaches the edges of the computational grid can be accomplished by periodically damping out the wave packet in small regions at the grid edges [10]. Suppose A represents this (real) operation. Instead of Eq. (2), one has... 

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