RESPECT computer code

Let us clarify the above two statements. MOD-FLOW is an example of an internationally respected computer code for three-dimensional groundwater flow. Like other models, it is based on Jacob s development of the continuity equation. As used in MODFLOW, McDonald and Harbaugh s (1988) algebraic formulation of the continuity equation is... 

The pseudopotential density-functional technique is used to calculate total energies, forces on atoms and stress tensors as described in Ref. 13 and implemented in the computer code CASTEP. CASTEP uses a plane-wave basis set to expand wave-functions and a preconditioned conjugate gradient scheme to solve the density-functional theory (DFT) equations iteratively. Brillouin zone integration is carried out via the special points scheme by Monkhorst and Pack. The nonlocal pseudopotentials in Kleynman-Bylander form were optimized in order to achieve the best convergence with respect to the basis set size. 5... 

The partial differential equations describing the catalyst particle are discretized with central finite difference formulae with respect to the spatial coordinate [50]. Typically, around 10-20 discretization points are enough for the particle. The ordinary differential equations (ODEs) created are solved with respect to time together with the ODEs of the bulk phase. Since the system is stiff, the computer code of Hindmarsh [51] is used as the ODE solver. In general, the simulations progressed without numerical problems. The final values of the rate constants, along with their temperature dependencies, can be obtained with nonlinear regression analysis. The differential equations were solved in situ with the backward... 

The uncertainty in the predicted CHF of rod bundles depends on the combined performance of the subchannel code and the CHF correlation. Their sensitivities to various physical parameters or models, such as void fraction, turbulent mixing, etc., are complementary to each other. Therefore, in a comparison of the accuracy of the predictions from various rod bundle CHF correlations, they should be calculated by using their respective, accompanied computer codes.The word accompanied here means the particular code used in developing the particular CHF correlation of the rod bundle. To determine the individual uncertainties of the code or the correlation, both the subchannel code and the CHF correlation should be validated separately by experiments. For example, the subchannel code THINC II was validated in rod bundles (Weismanet al., 1968), while the W-3 CHF correlation was validated in round tubes (Tong, 1967a). 

In problems in which there are n variables and m equality constraints, we could attempt to eliminate m variables by direct substitution. If all equality constraints can be removed, and there are no inequality constraints, the objective function can then be differentiated with respect to each of the remaining (n — m) variables and the derivatives set equal to zero. Alternatively, a computer code for unconstrained optimization can be employed to obtain x. If the objective function is convex (as in the preceding example) and the constraints form a convex region, then any stationary point is a global minimum. Unfortunately, very few problems in practice assume this simple form or even permit the elimination of all equality constraints. 

The long-term goal in the science of thermochemical conversion of a solid fuel is to develop comprehensive computer codes, herein referred to as a bed model or CFSD (computational fluid-solid dynamics). Firstly, this CFSD code must be able to simulate basic conversion concepts, with respect to the mode, movement, composition and configuration of the fuel bed. The conversion concept has a great effect on the behaviour of the thermochemical conversion process variables, such as the molecular composition and mass flow of conversion gas. Secondly, the bed model must also consider the fuel-bed structure on both micro- and macro-scale. This classification refers to three structures, namely interstitial gas phase, intraparticle gas phase, and intraparticle solid phase. Commonly, a packed bed is referred to as a two-phase system. 

Also most significant is the fact that experimental values of K in Eq. (1) [obtained by dividing P pti by ( rbXpoa)3 average 15.83 0,84 for the 80 data sets and 15.78 0.66 for the best 72 6f 80 data sets (last column in Table I). These differ by only +1.6% and + 1.3%, respectively, from the K — 15.58 value derived from an analysis of the K-W equation and the ruby %. computer code,6 and they confirm that the experimental results bracket the predicted values reasonably equally. 

The numerical values differences with respect to the previously published paper, [20] are due to the different computational code used. 

The formulas derived above, despite their cumbersome look, are very practical. Indeed, they present the nonlinear initial susceptibilities of a superparamagnetic particulate medium as analytical expressions of arbitrary accuracy. Another remarkable feature of the formulas of Section III.B.6 is that with respect to the frequency behavior they give the exact structure of the susceptibilities and demonstrate that those dependencies are quite simple. This makes our formulas a handy tool for analytical studies. Yet they are more convenient for numerical work because with their use the difficult and time-consuming procedure of solving the differential equations is replaced by a plain summation of certain power series. For example, if to employ Eqs. (4.194)-(4.200), a computer code that fits simultaneously experimental data on linear and a reasonable set of nonlinear susceptibilities (say, the 3th and the 5th) taking into account the particle polydispersity of any kind (easy-axes directions, activation volume, anisotropy constants) becomes a very fast procedure. 

Equations 5-137, 5-146, 5-149, and 5-152 can be incorporated respectively in the subprogram of a computer code as follows... 

Our miscible-displacement modeling approach was modified in order to describe S04 effluent from the BS (as well as BC) layers. We adjusted the computer code to account for a variable concentration of the input pulse rather than a constant one as is commonly accepted in most column experiments and mathematical solutions. In all our simulations presented here, for each soil column, the S04 input concentrations from our experimental results were incorporated as inputs to the model. In addition, presentations of relative concentrations (C/C0) were based on the respective C0 of the applied solution to the top layer (E). 

To optimise the geometry, the energy must be expressed as a function of atomic displacements. This yields the partial derivatives crucial to automatic minimisation algorithms. The expressions for the total energy derivatives with respect to atomic displacements are quite complex for ab initio and semi-empirical methods but trivial for empirical schemes like Molecular Mechanics (MM). Virtually all modern computer codes provide extensive, efficient facilities for determining ground state molecular geometries. 

Although I have been involved with linear methods for a long time, I was by no means the first to make working LMTO programmes. I have in this respect benefitted greatly from early access to the computer codes generated by my predecessors Ove Jepsen and Uffe Kim Poulsen. In this context, I should also mention that Ove Jepsen performed the first calculations of the canonical bands for the fee, bcc, and hep crystal structures which are included in this book. 

The first stage of any lattice simulation is to equilibrate the structure, i.e. bring it to a state of mechanical equilibrum. The simplest procedure is to equilibrate under conditions of constant volume, i.e. with invariant cell dimensions. Extensions to the procedure were introduced by Parker (1982, 1983) who introduced the use of constant pressure minimization in the computer code METAPOCS, in which lattice energy minimization was performed with respect... 

Dalle Donne [80] notes that at a Reynolds number of 105, for two-dimensional roughness, Stanton numbers are typically increased by a factor of 2 while the corresponding increase in friction factor is 4. He also cites data for two three-dimensional roughnesses that indicate that the Stanton number increased by 3 and 4 with friction factor ratios of 8 and 12, respectively. The first roughness is depicted in Fig. 11.11. Large-scale computer codes such as SAGAPO [81] are required to accurately predict the thermal-hydraulic behavior of roughened fuel element bundles. 

Four research teams—AECB, CLAY, KIPH and LBNL—studied the task with different computational models. The computer codes applied to the task were ROCMAS, FRACON, THAMES and ABAQUS-CLAY. All of them were based on the finite-element method (FEM). Figure 6 presents an overview of the geometry and the boundary conditions of respective models, including the nearfield rock, bentonite buffer, concrete lid, and heater. The LBNL model is the largest and explicitly includes nearby drifts as well as three main fractures... 

However, the codes were pretty machine-dependent and certainly could not be used as black boxes. In these respects the codes were no better (and no worse) than any others available in the United States and elsewhere. Computational chemistry codes became portable in a routine way only in the 1980s, when also their operation became transparent to users, with the widespread use of free-format input, made interactive on an interface with suitable graphics. In fact, free-format input was actually a feature of the ATMOL suite, and so it was rather ahead of its time. 

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