Scaling dynamics functions

The understanding of structure-dynamics-function relationships in oligonucleotides or oligonucleotide/protein complexes calls for biophysical methods that can resolve the structure and dynamics of such systems on the critical nanometer length scale. A modern electron paramagnetic resonance (EPR) method called pulsed electron-electron double resonance (PELDOR or DEER) has been shown to reliably and precisely provide distances and distance distributions in the range of 1.5-8 nm. In addition, recent experiments proved that a PELDOR experiment also contains information on the orientation of labels,... 

Particle dynamics are a critical component of animal viruses and appear to fall into two broad categories fluctuations about an equilibrium point and large-scale dynamics that lead to a change in particle morphology. The former are essential for virus interactions with a cell and its uncoating. The latter are necessary for complex virus structures that cannot directly assemble into the final functional form. 

The discussion of the details of these models is not within the scope of this book. We mention here only the following. It is evident that models of the first type are the simplest one, while large-scale dynamic models simulate reality most closely. However, the differential equations in these complicated models pan only be integrated numerically which involves serious computer problems. Furthermore, in simulating climate (minimum time scale is one week) the interaction of atmosphere and ocean also has to be considered. That is, the model must contain equations which relate changes in the state of the ocean to atmospheric parameters. Unfortunately the variations of the state of the ocean as a function of time are not well understood as a result the parameterization of the effect of the ocean is particularly difficult. 

Jarymowycz VA, Stone MJ (2006) East time scale dynamics of protein backbones NMR relaxation methods, applications, and functional consequences. Chem Rev 106 1624—1671... 

The structures and dynamics of supramolecular assemblies are usually complex and cannot be completely characterized by a single technique. This is particularly true for functional systems, which require a minimum size of a few nanometers and a certain balance between flexibility and rigidity to allow for reproducible changes of their states. The difficulties in characterizing such systems are readily apparent for a natural class of supramolecular systems, namely, membrane proteins that are functional when embedded in a lipid bilayer and tend to be extremely difficult to crystallize. To understand structure-dynamics-function relationships of such systems, many pieces of information on length scales between 1 A and several nanometers and time scales between picoseconds and milliseconds have to be assembled and interpreted. The samples are often macroscopically disordered systems, and the conformation of the molecules is distributed to some extent. Techniques for local characterization of structures and dynamics at selected sites are required to reduce the complexity of the problem. 

Mechanistic interpretations The results of the dynamic and equilibrium displacement experiments are used to evaluate and further define mechanisms by which alkaline floods increase the displacement and recovery of acidic oil in secondary mode and the tertiary mode floods. The data sets used in the mechanistic interpretations of alkaline floods are (a) overall and incremental recovery efficiencies from dynamic and equilibrium displacement experiments, (b) production and effluent concentration profiles from dynamic displacement experiments, (c) capillary pressure as a function of saturation curves and conditions of wettability from equilibrium displacement experiments, (d) interfacial tension reduction and contact angle alteration after contact of aqueous alkali with acidic oil and, (e) emulsion type, stability, size and mode of formation. These data sets are used to interpret the results of the partially scaled dynamic experiments in terms of two-stage phase alteration mechanisms of emulsification followed by entrapment, entrainment, degrees and states of wettability alteration or coalescence. 

The use of a simple polynomial form as a surrogate model decreases the computational cost of the objective function evaluation by orders of magnitude. Not only does it make the solution of the inverse problem possible for large-scale dynamic models, but it also allows one to use more elaborate numerical methods of optimization, enables a rigorous statistical analysis of confidence regions [30,31], and ties in closely with a more general approach to model analysis. Data Collaboration, discussed later in the text. 

Embedded Divide-and-Conquer Algorithm on Hierarchical Real-Space Grids Parallel Molecular Dynamics Simulation Based on Linear-Scaling Density Functional Theory. 

Alexander S., Courtens E., Vacher R. Vibrations of fractals dynamic scaling, couelation functions and inelastic light scattering. Physica A 1993 195 286-318... 

It is not surprising that the two main classes of microscopic simulations have evolved quite independently. Aside from the obvious problem of calculating potential energy functions (surfaces), the greatest computational difficulty arises in treating systems with multiple time scales. Dynamical simulations within class A are feasible because the bulk properties of interest can be determined on a time scale corresponding to a computationally finite number of molecular collisions. When the most important events are rare on this time scale, one rapidly reaches the limits of feasibility for detailed molecular dynamics... 

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