Dynamic simulation open-chain

Using the first-principles molecular-dynamics simulation, Munejiri, Shimojo and Hoshino studied the structure of liquid sulfur at 400 K, below the polymerization temperature [79]. They found that some of the Ss ring molecules homolytically open up on excitation of one electron from the HOMO to the LUMO. The chain-like diradicals S " thus generated partly recombine intramolecularly with formation of a branched Sy=S species rather than cyclo-Ss- Furthermore, the authors showed that photo-induced polymerization occurs in liquid sulfur when the Ss chains or Sy=S species are close to each other at their end. The mechanism of polymerization of sulfur remains a challenging problem for further theoretical work. 

FIG. 23 Surface pressure vs. area/molecule isotherms at 300 K from molecular dynamics simulations of Karaborni et al. (Refs. 362-365). All are for hydrocarbon chains with carboxylate-like head groups, (a) (filled squares) A 20-carbon chain, (b) (filled circles) A 16-carbon chain with a square simulation box the curve is shifted 5 A to the right, (c) (open squares) A 16-carbon chain with a nonsquare box with dimensions in the ratio xly = (3/4) to fit a hexagonal lattice the curve is shifted 5 A to the right. (Reproduced with permission from Ref. 365. Copyright 1993 American Chemical Society.)... 

Computer simulation studies by Stillinger and Rahman (1974) suggest that the pentamer is the most likely structure to spontaneously arise in water at many temperatures, followed in frequency by hexamers, and squares. In a review of water, Frank (1970) noted that closed rings of bonds are always more stable than the most stable open chains of the same cluster number, due to the extra energy of the hydrogen bond. Through molecular dynamics studies of many five-molecule clusters, Plummer and Chen (1987) argued that the cyclic pentamer that comprises many hydrate cavities is the only stable five-member cluster above 230 K. 

Previous research in the dynamic simulation of robotic mechanisms includes the examination of both open-chain mechanisms [2,3,12,42] and closed-chain configurations [4, 16, 22, 31, 33, 39]. Although many of these earli results are useful and impextant, further improvements in the computational efficiency of dynamic simulation algorithms are necessary for real-time implementation. 

Although the details may be quite different, every research effort in the area of dynamic simulation faces a common task — the efficient and accurate solution of the Direct Dynamics problem. In the development of algorithms for Direct Dynamics, two basic approaches have emerged for both open- and closed-chain systems. The first utilizes the inversion of the x manipulator joint space inertia matrix to solve for the joint accelerations. More accurately, the accelerations are found via the solution of a system of linear algebraic equations, but the... 

Recently there has been considerable interest in the phase transition of polymerized (tethered) membranes with attractive interactions [1-4]. In a pioneer work [1], Abraham and Nelson found by molecular dynamics simulations that the introduction of attractive interactions between monomers leads to a collapsed membrane with fractal dimension 3 at a sufficiently low temperature. Subsequently, Abraham and Kardar [2] showed that for open membranes with attractive interactions, as the temperature decreases, there exists a well-defined sequence of folding transitions and then the membrane ends up in the collapsed phase. They also presented a Landau theory of the transition. Grest and Petsche [4] extensively carried out molecular dynamics simulations of closed membranes. They considered flexible membranes the nodes of the membrane are connected by a linear chain of n monomers. For short monomer chains, n = 4, there occurs a first-order transition from the high-temperature flat phase to... 

In this paper, an algorithm for dynamic simulation based on the concept of velocity transformations is presented. This algorithm may be applied to the analysis of open and closed-chain systems. The equations of motion for open chain systems are derived using a direct velocity transformation, called open chain velocity trarvrformation. Closed chain systems are analyzed in two steps. First, they are converted into open chain systems by removing some joints and the open chain velocity transformation is applied then, the closed loop conditions are imposed through a second velocity transformation. The implementation of the proposed algorithm was carried out on a SGI 4D/240 workstation and the results obtained for a series of illustrative examples are presented. 

In the next section we describe the basic models that have been used in simulations so far and summarize the Monte Carlo and molecular dynamics techniques that are used. Some principal results from the scaling analysis of EP are given in Sec. 3, and in Sec. 4 we focus on simulational results concerning various aspects of static properties the MWD of EP, the conformational properties of the chain molecules, and their behavior in constrained geometries. The fifth section concentrates on the specific properties of relaxation towards equilibrium in GM and LP as well as on the first numerical simulations of transport properties in such systems. The final section then concludes with summary and outlook on open problems. 

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