They are upscaled with superior accuracy from a detailed Discrete Fracture Network Model (DFN) sector model, where orthogonal hydraulic fractures are explicitly discretized.
Fractures, which are longer than the threshold value, are explicitly discretized in the domain using tetrahedral elements and the fluid-flow is modeled using the discrete fracture approach.
Fractures, with radius longer than the threshold value, are explicitly discretized in the domain by using the triangular elements, and the fluid flow is modelled using the discrete fracture approach.
Locally dual porosity models are implemented to characterize the heterogeneity of small-scale natural fractures, and large-scale fractures are represented explicitly by discrete fracture models.
This also indicates that continuum-based modeling of unsaturated flow in fractured rock at mesoscale or a larger scale is not necessarily conditional explicitly on discrete fracture patterns.
Making no assumption on the integrability of πλ, we describe explicitly a discrete subset Γ of G and a vector f∈L2(M,dμM) such that πλf is a tight frame for L2(M,dμM).
Second, we refrained from explicitly modeling discrete sensorimotor input generated by the movement itself, because the central motor control adopts a continuous "whole-field control" rather than monitoring particular aspects of each submovement during repetitive movements with a high repetition rate (Siebner et al. 2001).
Although this model is framed in terms of a quantitative trait and does not explicitly incorporate discrete epigenetic states, if we imagine an environment as inducing the epigenetic state 1 in our model, then the parameter ν from Tal et al. (2010) would be equivalent to μ1→0 + μ0→1.
Life reduced to discrete, stark images.
Make it quick and discrete.
