Numerical modelling interaction assembly

DPMs offer a viable tool to study the macroscopic behavior of assemblies of particles and originate from MD methods. Initiated in the 1950s by Alder and Wainwright (1957), MD is by now a well-developed method with thousands of papers published in the open literature on just the technical and numerical aspects. A thorough discussion of MD techniques can be found in the book by Allen and Tildesley (1990), where the details of both numerical algorithms and computational tricks are presented. Also, Frenkel and Smit (1996) provide a comprehensive introduction to the recipes of classical MD with emphasis on the physics underlying these methods. Nearly all techniques developed for MD can be directly applied to discrete particles models, except the formulation of particle-particle interactions. Based on the mechanism of particle-particle interaction, a granular system may be modeled either as hard-spheres or as soft-spheres. ... 

GPCR interactions with ligand and G protein are represented by the ternary complex formalism (Fig. 2A Christopoulos and Kenakin, 2002 De Lean et al, 1980 Sam am a et al, 1993). The quantitative analysis of the soluble assembly system formally requires inclusion of soluble G protein due to the use of a crude receptor preparation. These soluble G proteins compete with the G protein attached to the G-beads for the solubilized receptor as shown in Fig. 2C (Simons et al, 2003, 2004). Experimental values from G-beads (Fig. 3) were fitted with the calculations of bead-bound receptors (RG k..i< + ARG k. i< ) based on this model, which includes soluble G proteins. Simulations were made by Mathematica , numerically solving the series of... 

The thermodynamic model of micellization, presented here, describes the association of any amphiphilic molecules, including low molecular weight surfactants or polymeric amphiphiles. The physical origin of the minimum in the free energy, as a function of p, is specified by the molecular architecture and the interactions between amphiphilic molecules involved in the assembly, and will be discussed in the corresponding sections. An extension of the model for the case of a continuous distribution of micelles with respect to aggregation number (polydispersity of the aggregates) involves the value of d Fp/dp. If this quantity is small in the vicinity of p = Po, then the micelle distribution is wide, and vice versa [37]. The approximation of micelle monodispersity is essential for application of the numerical SCF model which is discussed in Sect. 9. 

The solution to the model of the flow interaction with a fibrous assembly requires application of numerical methods collectively known as computational fluid dynamics (CFD) implemented in computer software packages which use finite-element methods. 

After the discovery of the first mesoporous silicas through external templating, a lot of work has been done to understand and rationalize the formation mechanisms of these materials. Numerous research groups employed a variety of techniques (e.g., NMR spectroscopy. X-ray diffraction, cryo-TEM, electron paramagnetic resonance, and fluorescence) toward this objective. Several models have been proposed [10] and two of them are generally accepted the liquid crystal templating approach and the cooperative self-assembly approach. In both models, the interactions between the surfactant molecules and the inorganic species direct the formation of the ordered solid. 

---