# Generalized Newtonian approach

Ultimately, the compromise between the realized speedup and the accuracy obtained for the governing dynamic model should depend on the applications for which the dynamic simulations are used for. For very detailed dynamic pathways, only the Newtonian approach is probably adequate. For general conformational sampling questions, many other simulation methodologies can work well. In particular, if a weak coupling to a phenomenological heat bath, as in the LN method, is tolerated, the general efficiency of force splitting methods can be combined with the long-timestep stability of methods that resolve harmonic and anharmonic motions separately (such as LIN) to alleviate severe resonances and yield speedup. The speedup achieved in LN might be exploited in general thermodynamic studies of macromolecules, with possible extensions into enhanced sampling methods envisioned. [c.257]

In general, the model-based reasoning approach is best appHed, not as a method in itself, but as an add-on to a knowledge-based system. The main reason is that modeling is hard, and problem-solving based solely on fundamental models is computationally complex (41). Using the hybrid approach can take advantage of the efficiency of compiled knowledge in rapidly focusing on the solution, while retaining the robustness of models when confronted with the need for behavioral detail. Several recent research papers in the chemical engineering Hterature have explored this hybrid problem-solving notion (42,43). For more information on model-based reasoning in general see References 44 and 45. [c.536]

Chapter 4 describes in general terms the processing methods which can be used for plastics. All the recent developments in this area have been included and wherever possible the quantitative aspects are stressed. In most cases a simple Newtonian model of each of the processes is developed so that the approach taken to the analysis of plastics processing is not concealed by mathematical complexity. [c.517]

Chapter 4 describes in general terms the processing methods which can be used for plastics and wherever possible the quantitative aspects are stressed. In most cases a simple Newtonian model of each of the processes is developed so that the approach taken to the analysis of plastics processing is not concealed by mathematical complexity. Chapter 5 deals with the aspects of the flow behaviour of polymer melts which are relevant to the processing methods. The models are developed for both Newtonian and Non-Newtonian (Power Law) fluids so that the results can be directly compared. [c.520]

Molecular dynamics has emerged as an application to molecules of the general method of point particles, with Cartesian coordinates and Newton s equations, and it was first applied to flexible polymeric molecules more than 20 years ago [29,26,30]. It was already clear at that time that harmonic potentials that keep bond lengths and bond angles close to their standard values severely limited the time step and that it would be desirable to get rid of these uninteresting degrees of freedom. No wonder, therefore, that early attempts to apply internal coordinates with the standard geometry approximation in MD were made at the same time [19,31]. This way, however, appeared too complicated and has been abandoned in favor of an alternative approach proposed by Ryckaert et al. [32], which consists in imposing holonomic distance constraints upon a system of point particles governed by Newton s equations. Their method, now called constraint dynamics, is reviewed elsewhere in this book. However, although it seemed initially that not only bond lengths but also bond angles, dihedral angles, and larger rigid groups could be fixed by using triangulation, this was found to be true only for very small molecules. In large complex polymers such as proteins, even bond angles cannot be fixed in this way [12]. [c.122]

Yet another difficulty was encountered in the numerical integration of dynamics equations. The general structure of the internal coordinate equations precludes the use of familiar Verlet or leapfrog algorithms, and that is why, at first, general-purpose predictor-corrector and Runge-Kutta integrators were used [8,36,39,40]. The results, however, clearly indicated that the quality of trajectories is much inferior to the conventional MD, even though the possibility of a considerable increase in time step length was demonstrated on some examples [36,39,40]. This difficulty could not be anticipated, because only recently was it realized that the exceptional stability of the integrators of the Stdnner-Verlet-leapfrog group is bound to their symplectic property, which in turn is due to the fact that the Newtonian equations are essentially Hamiltonian. A very recent approach [42] seems to overcome this difficulty, and it has been demonstrated that ICMD is able to give a net gain in terms of computations per picosecond of dynamics. [c.123]

See pages that mention the term

**Generalized Newtonian approach**:

**[c.126] [c.47] [c.1034] [c.846] [c.462]**

Practical aspects of finite element modelling of polymer processing (2002) -- [ c.14 , c.79 ]