Flow algorithm

Molecular dynamics, in contrast to MC simulations, is a typical model in which hydrodynamic effects are incorporated in the behavior of polymer solutions and may be properly accounted for. In the so-called nonequilibrium molecular dynamics method [54], Newton s equations of a (classical) many-particle problem are iteratively solved whereby quantities of both macroscopic and microscopic interest are expressed in terms of the configurational quantities such as the space coordinates or velocities of all particles. In addition, shear flow may be imposed by the homogeneous shear flow algorithm of Evans [56]. 

The second approach is a fractional-step method we call asymptotic timestep-splitting. It is developed by consideration of the specific physics of the problem being solved. Stiffness in the governing equations can be handled "asymptotically" as well as implicitly. The individual terms, including those which lead to the stiff behavior, are solved as independently and accurately as possible. Examples of such methods include the Selected Asymptotic Integration Method (4,5) for kinetics problems and the asymptotic slow flow algorithm for hydrodynamic problems where the sound speed is so fast that the pressure is essentially constant (6, 2). ... 

These equilibrium fluctuation estimates have been cross checked by using the heat flow algorithm (3.5). The results agree very well. It has been possible to find an interval where the heat field is large enough to prevail over thermal fluctuations and small enough not to violate the linear response relation (2.17). 

Comparison of the thermal conductivities of prolate (p) and oblate (o) nematic liquid crystals. The entries for zero field have been obtained by using the Green-Kubo relation (3.3). The entries for finite field have been obtained by applying the heat flow algorithm (3.5). Note that the EMD GK estimates and the NEMD estimates agree within the statistical error. 

The strategy generally applied in a diagnostic clarification in the case of suspected liver tumour is outlined later in a flow algorithm, (s. p. 196) (s. fig. 9.4)... 

Mercle CL, Athavale M (1987) Time-Accurate Unsteady Incompressible Flow Algorithms Based on Artificial Compressibility. AIAA Paper 87-1137, AIAA Press Washington, DC... 

The two-fluid model discretization procedure outlined in this appendix is to a large extent based on the single phase flow algorithm implemented in the pioneering TEACH-T code [8]. In order to simulate two phase bubble driven flow in bubble columns, the original TEACH-T code was extended to enable solution of the two-fluid model described previously in this appendix. 

Lipid production Maximizing the productivity and yield of lipid for an optimum composition of the culture medium. Diploid Genetic Algorithm (DGA) Net flow algorithm was used for ranking the Pareto-optimal solutions obtained by DGA. Muniglia et al. (2004)... 

The FUGSE blends the liquid-flow algorithm for high-pressure ratios with a choking equation valid at low valve pressure ratios by using a sine function, the argument of which is chosen to be proportional to the square root of the fractional pressure drop, =... 

A feasible solution is obtained in step 3, using a minimum-cost-flow algorithm (Ahuja et td. 1993) sequentially for each trailer type that needs to balance. First, for each building the excess or deficit of trailers of each type that has to balance is computed. Then a minimum-cost-flow algorithm is applied for each trailer type that obtains the optimal movements of trailers from each node of excess to each node of deficit. This may be the movement of a single empty trailer, the movement of an empty trailer that gets attached to an already used trailer to make up a permitted combination, or the... 

Typical calculations. In this section, we will perform a suite of validation runs designed to demonstrate the stability and physical correctness of the two-phase flow algorithm. In the calculations, a borehole radius of 0.2 ft and an... 

Heat-flow algorithm for rigid polyatomic molecules... 

The gas transmission network model is based on maximum flow algorithm well known in graph theory (Deo, 2008). The algorithm was modified to reflect gas transport property to have lower pressure at the points far from the supply source. This means that in case of disruption and lack of gas in the network, consumers that are closer to the source have better chances to be served rather than those that are located far away. Therefore, the maximum flow algorithm was modified to distribute gas first to the consuming nodes close to the supply source and distance from the nearest source was used as a priority criteria. 

This case is similar to failure mode 2, in that failure of the FACTS device can cause the grid to fail, even when all physical components are functioning correctly. However, instead of pushing the flow in the transmission line bearing the FACTS device to its capacity, as in mode 2, the failure results in the flow being set to 80% of what would have been the correct value. This fault could occur due to malfunction of the maximum flow algorithm used to calculate the appropriate settings for the FACTS devices [17]. 

In the advanced electric power grid presented in this paper, the cyber control is intended to prevent failures through control of the power flow in specific lines. The cyber network of FACTS devices runs a distributed version of the maximum flow algorithm [17] to determine appropriate settings for these transmission lines. 

The main task of a FACTS device is to set the power flow in its transmission line to some predetermined value, but another very important contribution made by each FACTS device is to help determine that value. The network of interconnected FACTS devices collectively executes the maximum flow algorithm, in a distributed fashion. Three types of faults can contribute to failure in the operation of a FACTS device ... 

The next stage of the research described in this paper will include injection of all three types of faults into the cyber network, as it executes the maximum flow algorithm, and investigate the effect of such faults on the operation of the FACTS devices. We anticipate that faults injected into the system will cause the FACTS device to operate in of the three failure modes discussed in Section 4. Additional failure modes are also possible. One objective of this research is comprehensive identification of the failure modes for cyber control of the grid, which will facilitate determination of the causes of failure. Our reliability model will be refined and improved as a result, and we anticipate valuable insight into increasing the efficacy of cyber control of the grid. 

The two-fluid model discretization procedure outlined in this appendix is to a large extent based on the single phase flow algorithm implemented in the pioneering... 

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