Finite volume collapse

In these equations fi is the coluirm mass of dry air, V is the velocity (u, v, w), and (jf) is a scalar mixing ratio. These equations are discretized in a finite volume formulation, and as a result the model exactly (to machine roundoff) conserves mass and scalar mass. The discrete model transport is also consistent (the discrete scalar conservation equation collapses to the mass conservation equation when = 1) and preserves tracer correlations (c.f. Lin and Rood (1996)). The ARW model uses a spatially 5th order evaluation of the horizontal flux divergence (advection) in the scalar conservation equation and a 3rd order evaluation of the vertical flux divergence coupled with the 3rd order Runge-Kutta time integration scheme. The time integration scheme and the advection scheme is described in Wicker and Skamarock (2002). Skamarock et al. (2005) also modified the advection to allow for positive definite transport. 

Earthquake Focal Mechanisms Earthquake focal mechanisms describe the nature of deformation at the earthquake source. Most VT earthquakes are double-couple, indicative of shear motion on a fault plane. The orientation of focal mechanism describes the stress field at the source. Rotations of the focal mechanism with time from, for example, strike-slip to reverse, have been reported before some eruptions and interpreted in terms of magma pressurization changing the orientations of the principal stresses in the vicinity of the magma body (Roman and Cashman 2006). Non-double-couple earthquakes indicate a more complex source, including tensile failure and events associated with finite volume changes, such as explosions or collapses. In Iceland, for example, such sources have been associated with tensile failure during the opening of subsurface cracks. 

When a voltage of sufficient magnitude (>Vs for dc) is suddenly applied to a gas-insulated electrode gap, or a gas-insulated conductor, breakdown does not occur instantaneously, but after a finite time t = ts T The 4 is called the statistical time lag and is the time that elapses between the application of the voltage V (>Vs) and the occurrence of a free electron in the stressed gas volume which initiates the breakdown process. The tf is called the formative time lag and is the time interval between the occurrence of the free electron and the collapse of the voltage (i.e., breakdown). 

Even though the simulation timescale accessible with atomistic MD is short, some authors succeed in modeling micelle formation starting from an initially random distribution of monomers [64]. Provided the ability to frequently repeat this computer experiment, that is, formation of an isolated micelle (or cluster), with varying number of monomers in the simulation cell, it is possible to observe the dependence of micelle shape on monomer concentration. Usually such simulations are carried out for coarse-grained molecules [65]. But even then equilibration is difficult. The collapse of randomly distributed monomers into a condensed structure may be fast however, the transformation of this structure into an equilibrium structure may be very slow. In addition, finite size effects may strongly influence the results, because often the characteristic dimensions of the observed structures usually are comparable to the size of the simulation volume. 

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