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The example presented here demonstrates that auxin can also be recruited to coordinate a heterogeneous group of cells to commit to a program, which imposes homogeneous identity to them.
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Globalization does not mean imposing homogeneous solutions in a pluralistic world.
A volume penalization method for imposing homogeneous Neumann boundary conditions in advection diffusion equations is presented.
There are many ways of numerically defining the basis functions, one of which being to impose homogeneous boundary conditions on each of the three surfaces.
At last, for (s geq0) the space (H^{s}) will denote a closed subspace of the Sobolev space (H^{s} ( 0,1) ), defined e.g. by imposing homogeneous boundary conditions at one or both endpoints, and for (s < 0) the space (H^{s}) will denote the dual space (H^{s} := (H ^{-s})').
Therefore, we impose homogeneous Neumann boundary conditions for the cell densities to supplement model equations (1a), (1b), (1c) and (2).
We consider two possible descriptions of the volume variation process: either by imposing a homogeneous volumetric strain (biological growth) or through migration of solvent molecules inside a solid network (swelling).
Can we impose the homogeneous boundary condition u x,t)=0,quad (x,t inpartialOmegatimes 0,T), (1.3) as usual?
The key is to determine the portion of the boundary on which we can impose the homogeneous boundary value.
In addition, we will impose discrete, homogeneous Neumann boundary data for each of the three functions of interest.
To this aim, we restrict the prey species to living in a spatial domain (xin[0, L]) and (L= 15), and impose an homogeneous Neumann boundary condition at (x = L).
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