Mesoscale methods

Because mesoscale methods are so new, it is very important to validate the results as much as possible. One of the best forms of validation is to compare the computational results to experimental results. Often, experimental results are not available for the system of interest, so an initial validation calculation is done for a similar system for which experimental results are available. Results may also be compared to any other applicable theoretical results. The researcher can verify that a sulficiently long simulation was run by seeing that the same end results are obtained after starting from several different initial configurations. 

In principle, mesoscale methods can provide a means for connecting one type of simulation to another. For example, a molecular simulation can be used to describe a lipid. One can then derive the parameters for a lipid-lipid potential. These parameters can then be used in a simulation that combines lipids to form a membrane, which, in turn, can be used to compute parameters describing a membrane as a flexible sheet. Such parameters could be used for a simulation with many cells in order to obtain parameters that describe an organ, which could be used for a whole-body biological simulation. Each step, in theory, could be modeled in a different way using parameters derived not from experiment but from a more low-level form of simulation. This situation has not yet been realized, but it is representative of one trend in computational technique development. 

Commercially produced elastic materials have a number of additives. Fillers, such as carbon black, increase tensile strength and elasticity by forming weak cross links between chains. This also makes a material stilfer and increases toughness. Plasticizers may be added to soften the material. Determining the effect of additives is generally done experimentally, although mesoscale methods have the potential to simulate this. 

Some of the most widely used computational approaches will be briefly described below, namely some quantum chemical methods, classical simulations by Monte Carlo and Molecular Dynamics techniques and a few mesoscale methods. 

Simulation and Modeling of Aerogels Using Atomistic and Mesoscale Methods... 

A problem area that is not so amenable to mesoscale methods is polymer crystallization. This has proven to be one of the most difficult computational challenges in all of polymer science because the pertinent phenomena operate simultaneously over a wide range of length scales. The pol5uner crystallizes into a particular space group because of atomic detail, and the mechanical properties of the crystallites are determined by, and can only be calculated reliably with, atomic force fields with all atoms represented (126,127). Yet the size of the crystallites or spherulites is so large as to require mesoscopic methods for comprehension. But a crystalline polymer is almost never 100% crystalline. The interphases between crystalline and amorphous domains, with the possibilities for adjacent or nonadjacent reentry and tie-chain distributions, are critical to the properties of semicrystalline polymers. Only recently have models been developed (203) to rigorously address this problem area. 

Molecular simulation techniques can obtain the microscopic information that cannot be detected by current experimental conditions, but the conventional simulation methods stiU have inherent limitations with special mesoscopic scales of various complex forces and complex structure. It is necessary to establish a new mesoscale method that considers the chemical reaction and transport to the larger system at the same time. The roughness and chemical properties of catalyst supporting interface have great influence on chemical and physical adsorption stability of clusters. The problem is that the system is too large for traditional simulation in nano-/micro-/mesoscale. We need a new mesoscale method to study the effect of interface roughness on physical/chemistry phenomena. 

Mesoporous Ti02 surface is very complex it has a mesoporous structure and a variety of crystal planes as an active support. The catalyst loading by mesoporous Ti02 has multiple mesoscale structures and relative phenomena in heterogenous catalysis. Thus, unconventional mesoscale method is needed to study these structures and phenomena. 

The new mesoscale method for large systems takes account of chemical reaction, and transport should be estabHshed to examine the reaction mechanism quantitatively and the relationship with the changes of concentration of reactants and products. AFM study shows that the interfacial roughness of catalyst support has a significant impact for clusters on its chemical and physical adsorption stabdity this problem is in the nanometer and micrometer mesoscale traditional simulation also met the problem that studied system is too big to handle. A new medium-scale method is needed to be established to study effects of interfacial roughness on chemical and physical phenomena. 

As a typical multiphase and multiscale process, the research of MTO process spanning molecules, zeohtes, catalyst particles, microscale reactors, and pilot-scale reacton to industrial equipments, cross a wide time and length scales. The development of efficient mesoscale methods are expected for further optimizing the DMTO process and improving fluidized bed reactor design and operation. 

This is one of the simple and most commonly used method to perform multiscale simulation. By definition calculation of parameters for classical MD simulation from quantum chemical calculation is also a multiscale simulation. Therefore, most of the force filed e.g., OPLS," AMBER, GROMOS available for simulations of liquid, polymers, biomolecules are derived from quantum chemical calculations can be termed as multiscale simulation. To bridge scales from classical MD to mesoscale, different parameter can be calculated and transferred to the mesoscale simulation. One of the key examples will be calculation of solubiUty parameter from all atomistic MD simulations and transferring it to mesoscale methods such dissipative particle dynamics (DPD) or Brownian dynamics (BD) simulation. Here, in this context of multiscale simulation only DPD simulation along with the procedure of calculation of solubility parameter from all atomistic MD simulation will be discussed. 

Spatial multi-scale methods are based on the paradigm that in many real situations the atomic description is only required within small parts of the simulation domain whereas for the majority the continuum model is still valid. This allows one to apply concurrent continuum and molecular simulations for the respective parts of the simulation domain using a coupling scheme that permits to connect between the two domains. The majority of the spatial domain is calculated by continuum solvers (computational fluid dynamics) which are very fast and only the active part is calculated using molecular simulation methods. In some cases several other coarser-grained (mesoscale) methods than the atomic simulations ones are used as interfaces between the molecular simulation and the continuum domains. Such approaches are called hybrid molecular-continuum methods and allow the simulation of problems that are not accessible either by continuum or by pure molecular simulation methods. 

One of the first approaches employed to impose a non-slip boundary condition at an external wall or at a moving object in a MFC solvent was to use ghost or wall particles [36,81]. In other mesoscale methods such as LB, no-slip conditions are modeled using the bounce-back rule the velocity of the particle is inverted from v to -V when it intersects a wall. For planar walls which coincide with the boundaries of the collision cells, the same procedure can be used in MFC. However, the walls will generally not coincide with, or even be parallel to, the cell walls. Furthermore, for small mean free paths, where a shift of the cell lattice is required to guarantee Galilean invariance, partially occupied boundary cells are unavoidable, even in the simplest flow geometries. 

In this section we briefly summarize the Brownian dynamics algorithm and its close cousin Stokesian Dynamics. We then outline the motivation and development of several mesoscale methods, some of which are reviewed elsewhere in this series. 

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