Bead method, description

A macrostate of a macromolecule can be described with the help of the end-to-end distance R. To give a more detailed description of the macromolecule, one should use a method introduced by the pioneering work reported by Kargin and Slonimskii (1948) and by Rouse (1953), whereby the macromolecule is divided into N subchains of length M/N. One can consider the ends of the macromolecule and the points, at which the subchains join to form the entire chain, as a particles (the beads), labelled 0 to N respectively, and their positions will be represented by r°, r1,..., rN. 

During the 50 years that have passed since the pubhcation of these classical studies, numerous research groups examined the salt and, in particular, acid retardation processes in ion exchanger, but no new ideas have been suggested for the explanation of the non-trivial phenomenon of electrolytes discrimination. Interestingly, a more or less adequate mathematical description of experimental data is possible both in terms of selfassociation of acids in the homogeneous resin phase and association of acid molecules with the functional groups of the resin [122] and in frames of a two-phase model of the resin bead [123]. However, both approaches are based on the above ideas that have been formulated, considered, and rejected by the pioneers of the method. Indeed, mathematical models may well fit experimental data into equations, but they do not prove the reality of the concept they are based on. 

The first term In the bracket of Equation 19 refers to the moles of substrate In the bulk phase and the second term refers to the moles of substrate in the catalyst beads. Equation 19 Is the most general description of the slope of a plot of experimentally determined conversion versus time for reaction in a solvent-swollen polymer-immobilized catalyst. Numerical methods may be required to solve Equation 8 the solution to Equation 8 Is needed to evaluate the Integral in Equation 19. 

Fig. 12 Description of the magnetic capture hybridization method. Hybridization is first performed between RNA and biotin-labeled probes. The hybridized RNA is separated from the unhybridized RNA using streptavidin-coated magnetic beads...

Other Generic Models. The lattice methods that have been briefly considered are but one example of what we are calling generic methods. These methods lose atomic detail through a coarse-graining procedure or ad hoc parameterization. The traditional Rouse spring-bead model is an example of this type of model. Clearly, a description of this kind is useful only to the extent that the properties one seeks to describe are generic. Thus, the Rouse model has been extremely... 

Arsenic occurs in seawater in a variety of chemical species, the most abundant of which are arsenate, arsenite, methylarsonate and dimethylarsinate Andreae, 1979 Cullen and Reimer, 1989). The method described here permits the individual determination of these four species. It provides high sensitivity (limit of detection 4.0pmol/L) and adequate precision (5-10 % relative standard deviation). In seawater and most natural waters, interferences are absent or minimal. This method was first published by Andreae (1977) and has been modified subsequently Andreae, 1983). It has been used successfully by numerous workers, often with minor modifications. Some improvements have been proposed recently, such as the addition of cysteine to the reaction mixture Le et al, 1994 Howard and Salou, 1996) and the use of glass beads etched with hydrofluoric acid in the cold trap Howard and Comber, 1992).The following description represents the procedure followed in the author s laboratory. 

Dissipative particle dynamics (DPD) is a meshless, coarse-grained, particle-based method used to simulate systems at mesoscopic length and timescales (Coveney and Espafiol 1997 Espafiol and Warren 1995). In simple terms, DPD can be interpreted as coarse-grained MD. Atoms, molecules, or monomers are grouped together into mesoscopic clusters, or beads, that are acted on by conservative, dissipative, and random forces. The interaction forces are pairwise additive in nature and act between bead centers. Connections between DPD and the macroscopic (hydrodynamic, Navier-Stokes) level of description (Espanol 1995 Groot and Warren 1997), as well as microscopic (atomistic MD) have been well established (Marsh and Coveney 1998). DPD has been used to model a wide variety of systems such as lipid bilayer membranes (Groot and Rabone 2001), vesicles (Yamamoto et al. 2002), polymersomes (Ortiz et al. 2005), binary immiscible fluids (Coveney and Novik 1996), colloidal suspensions (Boek et al. 1997), and nanotube polymer composites (Maiti etal.2005). 

As the DPD method has been detailed extensively elsewhere [55], here we provide only a brief description of the technique. Similar to MD simulations, DPD captures the time evolution of a many-body system through the numerical integration of Newton s equation of motion, dvi/dt = 5, where the mass m of a bead of any species is set to 1. (We use the term bead to refer to a single point particle in the numerical simulation, and the term particle to refer to a nanoparticle, the interaction of which with a membrane is studied here.) Unlike MD simulations,... 

An advantage of a soft, coarse-grained, off-lattice model is the ability to simultaneously and accurately calculate the pressure, p, and the chemical potential, p. Abandoning the lattice-description allows a precise calculation of the pressure, p, and simulations at constant pressure or tension. This is also possible in off-lattice models with harsh excluded volume interactions (e.g., a Lennard-Jones bead-spring model). The accurate calculation of the chemical potential by particle insertion methods. 

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