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Fueling Innovation and Discovery The Mathematical Sciences in the 21st Century (2012) / Chapter Skim
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Probability and Statistical Physics / Connecting Microscopic and Macroscopic
Pages 53-58

The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.


From page 53...
... It is surprisingly common for random microscopic events to produce predictable effects at a macroscopic level. The Brownian motion of any single particle of smoke is highly unpredictable, yet smoke spreads in a room at a predictable rate.
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From page 54...
... The intensity of the jiggling is described by the parameter k; larger values of k correspond to more intense jiggling and to more jagged cracks. The basic idea of Schramm-Loewner evolution converts any two dimensional, conformally invariant random process into 25 / Schramm-Loewner evolution for different values a one-dimensional Brownian motion.
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From page 55...
... It is likely also that the critical exponents describing the correlation of nearby molecules are not as simple as they are in the two-dimensional case. So 21st century mathematical scientists still have their work cut out for them as they try to explain phase transitions in our three-dimensional world.
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From page 56...
... This patent is for a "monolithic" A basic statistical method for determining how silicon chip that can compute closely related two paired sets of data are. FFT's; such chips are used An optical scanner locates a "bull's-eye" on in digital image processing, a label by finding the correlation between speech recognition, and scanned pixel sequences and the expected transmission as in cell phones.
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From page 57...
... 6446205 (2002) Citibank This patent proposes the Schwarz triply periodic minimal surface as a scaffold for regenerating human bone and organ tissue.
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From page 58...
... FUELING innovation and discovery 58
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Key Terms

  • mathematical sciences
  • phase transitions
  • industry standard
  • random process
  • rotation invariance

  • random processes
  • explain phase
  • mathematical scientists
  • single parameter
  • called maximum

  • conformally invariant
  • maximum likelihood
  • critical percolation
  • cell phones
  • mathematical transition

  • invariant random
  • microscopic disorder
  • united parcel
  • cal technique
  • allows precise

  • representing smooth
  • spins spontaneously
  • routinely jolted
  • statistical method
  • invariant processes

  • macroscopic level
  • predictable effects
  • conjugate gradient
  • mathematical construct
  • albert einstein


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