@article{1445891,
      recid = {1445891},
      author = {Kunihiro, Teiji, and Kikuchi, Yuta, and Tsumura, Kyosuke,},
      title = {Geometrical formulation of renormalization-group method as  an asymptotic analysis : with applications to derivation of  causal fluid dynamic /},
      pages = {1 online resource (1 volume) :},
      abstract = {This book presents a comprehensive account of the  renormalization-group (RG) method and its extension, the  doublet scheme, in a geometrical point of view. It extract  long timescale macroscopic/mesoscopic dynamics from  microscopic equations in an intuitively understandable way  rather than in a mathematically rigorous manner and  introduces readers to a mathematically elementary, but  useful and widely applicable technique for analyzing  asymptotic solutions in mathematical models of nature. The  book begins with the basic notion of the RG theory,  including its connection with the separation of scales.  Then it formulates the RG method as a construction method  of envelopes of the naive perturbative solutions containing  secular terms, and then demonstrates the formulation in  various types of evolution equations. Lastly, it describes  successful physical examples, such as stochastic and  transport phenomena including second-order relativistic as  well as nonrelativistic fluid dynamics with causality and  transport phenomena in cold atoms, with extensive numerical  expositions of transport coefficients and relaxation times.  Requiring only an undergraduate-level understanding of  physics and mathematics, the book clearly describes the  notions and mathematical techniques with a wealth of  examples. It is a unique and can be enlightening resource  for readers who feel mystified by renormalization theory in  quantum field theory.},
      url = {http://library.usi.edu/record/1445891},
      doi = {https://doi.org/10.1007/978-981-16-8189-9},
}