Scale simulation

Fig. 2.10. Use of the dump option to simulate scaling. The pore fluid is initially in equilibrium with minerals in the formation. As the fluid enters the wellbore, the minerals are isolated (dumped) from the system. The fluid then follows a polythermal, sliding-fugacity path as it ascends the wellbore toward lower temperatures and pressures, depositing scale.

Figure 4.3. Sketch of computational domain used in the LEM for homogeneous flows. The circumference of the circular domain scales as L L . Thus, the number of grid points required for fully resolved simulations scales as Sc1/2 Re /4.

Trosset J-Y, Scheraga HA (1999) Flexible docking simulations scaled collective variable Monte Carlo minimization approach using Bezier splines, and comparison with a standard Monte Carlo algorithm. J Comp Chem 20 244-252... 

The computer time per reaction of this algorithms scales with system size as 0(log S) where S is the number of sites in the system. (Note that for all kMC algorithms the total number of reactions in a system is of the order 0(S). So for the first-reaction method the computer time for a whole simulation scales as 0(S log 5).) This logarithmic dependence originates from the data-structures, which are normally trees, that are used to store the reactions and their times. 

When process conditions change, the VLE and efficiency errors no longer offset each other equally. If the true relative volatility is higher than simulated, then the scale-up will be conservative. If the true relative volatility is lower than simulated, scale-up will be optimistic. A detailed discussion is found in Kister, Distillation Design, McGraw-Hill, New York, 1992. 

Simulations Scaled Collective Variable Monte Carlo Minimization Approach Using Bezier Splines, and Comparison with a Standard Monte Carlo Algorithm. 

To obtain a quick overview, we can bundle them together into a three-dimensional space which we call the simulation scale phase space. The range of these numbers vary several orders of magnitudes so it makes good sense to use logarithmic scale in each direction of the space. To define and use the first two dimensions N and T) is straightforward, while the third is fairly difficult to measure exactly. However, for our purposes, reasonable estimates are quite sufficient. 

Figure 1 Simulation scale phase space. The intersection points of the computational horizons with the N, T, F) axes move towards larger values over time because large simulations become possible to perform.

In the simulated scaling strategy [26], a biasing potential (or a biasing weight function) is employed as in the following equation ... 

Li, H.Z., Fajer, M., Yang, W. Simulated scaling method for localized enhanced sampling and simultaneous "alchemical" free energy simulations A general method for molecular mechanical, quantum mechanical, and quantum mechanical/molecular mechanical simulations. J. Chem. Phys. 2007,126, 024106. 

Figure 3. DC circuit analog to simulate scaling according to electrochemical...

The enterprise shall mitigate system-level risks to include products risks that were assessed to be critical to system development during concept selection. For critical risks associated with products, the enterprise utilizes simulation, scale-model tests, or prototype tests to demonstrate mitigation of risks to an acceptable level. The enterprise should assess subsystem risks and prioritize critical risks based upon probabihty of occurrence and related consequences to cost, schedule, and/or performance. 

In this paper, numerical simulation, scaling theory and experiments have been used in order to study the recovery mechanism operating in the polymer flooding of macroscopically layered systems. All of the work has centred on vertical sweep improvement in which the local water/oll mobility ratio has been close to unity. The main conclusions are as follows ... 

As discussed in Sect. 2.1, the solvent is treated as purely viscous (as opposed to viscoelastic) in LD and BD simulations. This approximation will be valid when solvent relaxation times are much shorter than all relevant relaxation processes of the polymer chain. In BD simulations, an additional approximation is made by ignoring inertial effects. A consequence of these approximations is that all relaxation times in a BD simulation scale linearly with the solvent viscosity r. ... 

The wavemaker stroke and maximum velocity are important because they determine the height and wavelength of the wave that can be simulated (scale factor again). Of course, larger waves can be simulated as the stroke increases. Wavemakers are computer-controlled to (a) perform digital to analog (D/A) conversion for paddle(s) at run time, (b) monitor paddle displacement and feedback. 

Table 3 shows a summary of means and standard deviations for the simulated scale parameter of the Power Law process, for each size of asset group. Since ai were generated for each asset from a gamma distribution, T a,b), the mean and standard deviation, respectively, should be... 

The simulated domain is 5 x 5 mm square flow field with 100 x 100 grids. Extended boundary condition is applied to the upper gas-liquid interface periodic and bounce-back boundary conditions are chosen, respectively, for the two side walls and solid bottom. The simulated scale is Ax = 5 x 10 m and At = 5 X 10 s. An uniform distributed higher solute concentration is set in the width of 1 mm at the interface at r = 0. During the diffusion process, both Marangoni and Rayleigh convections are simultaneously coupling the former is created at the surface, and the latter is formed perpendicular to the interface. Figure 9.5 shows the simulated results at different times ... 

The scaled particle theory of fluids is a theory that offers an excellent conceptual framework with which to understand solvent effects. The theory was originally designed to give the thermodynamic properties of a fluid of hard spheres, but experimentally determined parameters can be introduced to treat real liquids. The treatment of simple liquids is better than the treatment of structured liquids such as water. The theory has been applied extensively to certain aspects of hydrophobic solvation and interactions. In some studies of hydrophobic solvation based on molecular dynamics or Monte Carlo simulations, scaled particle theory has provided useful guidelines for analysis of the results. ... 

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