Multi-domain method

There are generally two main approaches for handling the mushy region in multi-domain methods. The first approach considers the planar interface between the solid and liquid regions and solves only transport equations for the liquid and solid phases. The interface is tracked explicitly with appropriate boundary conditions [87,89-92],... 

The boundary conditions are essentially the same for all the methods reviewed above. However, the multiphase and multi-domain methods need extra boundary conditions due to the additional equations solved. Therefore the general boundary conditions employed in control volume methods and FEMs are discussed together and additional boundary conditions required for other methods are given in subsequent sections. 

Studies employing the multi-domain method usually consider solidification problems cooled from the bottom. There are primarily three approaches for treating boundary conditions between the mush-melt and solid-mush interfaces in the multi-domain approach,. The first model to be considered is that used by Worster [2] and Chen et al. [97] in which the Darcy s equation is employed as the momentum equation in the mushy layer and the Navier-Stokes equation as the momentum equation in the fluid layer and no-slip boundary condition is prescribed at the melt-mushy interface. 

RDC methods used to probe the structural dynamics between relatively large molecular fragments such as domains in multi-domain proteins can be... 

W.F. Florez. Multi-domain dual reciprocity method for the solution of nonlinear flow problems. PhD thesis, University of Wales, Wessex Institute of Technology, Southampton, 2000. 

Park, J., and S. A. Teichmann. 1998. DIVCLUS An automatic method in the GEAN-FAMMER package that finds homologous domains in single- and multi-domain proteins. Bioinformatics 14 144—50. 

Fig. 1 Three representative cases of wPPIs. Case I a weak protein-protein interaction found in a locally highly crowded manner. Case II a weak domain-domain interaction, exemplified by A-B pair, as part of a tight multi-domain complex. Such weak binary domain-domain interaction may be undetectable by many conventional methods including deletion mapping, yeast-hybrid approach, immunoprecipitation, etc., but become apparent when the tertiary structure of the tight complex is challengingly determined. However, NMR may be able to pick this interaction at early stage of the characterization. Case III a weak protein-protein interaction as a part of multi-protein complex. Similar to II), a weak A-D pair may not be detectable in isolated manner by any conventional techniques except NMR...

Besides the aforementioned time-domain approaches, many frequency-domain methods have also been developed and widely used. Examples are the complex curve fitting method [153], the maximum entropy method [4,263], the pole/zero assignment technique [271], the simultaneous frequency-domain approach [62], the rational fraction polynomial approach [219], the orthogonal polynomial approach [264], the polyreference frequency-domain approach [73], the multi-reference simultaneous frequency-domain approach [64] and the best-fit reciprocal vectors method [173]. 

The stability analysis for parametrically excited systems with delay can be performed by numerical techniques. Such a technique is the semi-discretization method (Insperger and Stepan 2011), which is a time-domain method, or the multi-frequency solution... 

Shyy W, Francois M, Udaykumar HS (2001) Cartesian and curvilinear grid methods for multi-domain, moving boundary problems. In Debit M et al (eds) Thirteenth international conference on domain decomposition method. CIMNE, Barcelona... 

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