Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions.
A series of useful theories and methods have been proposed to explore stochastic differential equations, such as invariant manifolds [1 3], averaging principle [3 12], homogenization principle, and so on.
In addition to the principles of homogenization and internal diversification, the constitution of the field of study was also based on the criteria of theoretical relevance, intrinsic quality of cases, exemplarity and accessibility (Pirès, 1997).
The elastic properties of porous materials with a disordered pore structure are estimated using the mean-field Eshelby homogenization scheme together with the principle of recurrence to generate a cascade of effective microstructures as a function of the porosity and the cascade level n.
Therefore, we determine an effective material law by means of energetic homogenization using the Hill-Mandel-principle [36, 42].
The viscoelastic Hill and localization tensors as well as the homogeneous viscoelastic stiffness tensors are firstly derived by combining the homogenization theory of elasticity and the correspondence principle.
The fully thermomechanical model is based on free energy principles combined with stochastic homogenization techniques.
The properties were determined by three methods that exploited the 3D elastic homogenization formulas: (i) quasi-elastic method, (ii) correspondence principle, and (iii) direct time integration of the incremental viscoelastic equations.
So, at least, in principle, by measuring the extent of "homogenization" of evolutionary rates of domains in multidomain proteins, it should be possible to disentangle and compare the contributions of translation rate-mediated factors and translation-independent, intrinsic ones.
The model is derived by means of the "second-order" homogenization theory, which makes use of suitably designed variational principles utilizing the idea of a "linear comparison composite".
The proposed model is generated by means of the "second-order" homogenization method, which makes use of suitably designed variational principles utilizing the idea of a "linear comparison composite".
