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Magnetic-resonance-imaging rheometrical experiments show that concentrated suspensions or emulsions cannot flow steadily at a uniform rate smaller than a critical value (gamma(c)). As a result, a "liquid" region (sheared rapidly, i.e., at a rate larger than gamma(c)) and a "solid" region (static) coexist. The behavior of the fluid in the liquid region follows a simple power-law model, while the extent of the solid region increases with the degree of jamming of the material.