Introduction to the theory of normal metals by A. A. Abrikosov
By A. A. Abrikosov
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It should be noticed that beyond the universal characteristics of these patterns (spots, stripes), the precise initial conditions at the time of activation of the reaction–diffusion mechanism determine the individuality of the patterns. Such individuality is important for kin and group recognition among animals. The role the pattern plays in survival differs between different species. If it does play a role, the time of activation in the embryonic phase should be well controlled. These remarks may give some hints regarding the fact that, although the basic mechanism behind pattern formation sounds rather simple, its robust implementation in a biological context raises a number of challenging questions for future research.
20 H. Meyer-Ortmanns • The covariant derivatives correspond to each other; from an abstract point of view, the idea behind their construction and their transformation behavior is the same. • The ﬁeld strength tensor F lm;cc0 ðxÞ corresponds to the Riemann curvature tensor Rikmn . The overarching mathematical structure between gauge theories and general relativity is formulated in the theory of ﬁber bundles. The standard model of particle physics has been conﬁrmed experimentally to a very high level of accuracy.
Our examples of a scalar ﬁeld theory and an Ising model are simple dynamical systems. In the vicinity of critical points, the conjecture of self-similar actions over the spatial scales could be suggested, for example, by visualizing the blocks of aligned spins: at the critical point the linear block size varies overall length scales, so it is natural to deﬁne the block spin in such a way as to represent a whole block by another spin. In general, block variables should be representative of the whole block, in the sense that they project onto the appropriate degrees of freedom.