Spatial distributions for 100-µm2-stiffness of type I collagen gels were measured by wide-range scanning probe microscopy. A cantilever being attached to the tip of a glass bead of 100 µm diameter was used to reduce local stress during measurements. This method enabled the cantilever to be in contact with the gel surface in a manner of a Hertzian contact model regardless of the rough meshwork formation of collagen gels. Stiffness images of collagen gels showed stiff domain structures with a size of 20 µm. The more the concentration of collagen increased, the more the stiffness increased with the growth of stiff domain structures. Immunostaining for collagen molecules showed highly concentrated fibril structures as large as the stiff domain structures. These results indicate that the structure of collagen gel is nonuniform in the range of 100 µm□, but it is heterogeneous because of collagen fibril aggregation.
We consider an N = 1 U(N ) gauge theory with matter in the antisymmetric representation and its conjugate, with a tree level superpotential containing at least quartic interactions for these fields. We obtain the effective glueball superpotential in the classically unbroken case, and show that it has a non-trivial N -dependence which does not factorize. We also recover additional contributions starting at order S N from the dynamics of Sp (0) factors. This can also be understood by a precise map of this theory to an Sp(2N − 2) gauge theory with antisymmetric matter.
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