TERMIUM Plus®

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HARMONIC MEASURE [2 records]

Filter results by subject field Alphabetical list of terms

Filter results by subject field

Alphabetical list of terms

Record 1 2011-08-17

English

Subject field(s)
  • Analytical Functions (Math.)
  • Surveying
  • Mathematical Geography
DEF

Any solution of the Laplace equation which has continuous derivatives of first and second order.

CONT

... it is quite natural to look at GSPD as a fractal measure ... with infinitely many types of singularities. Probing the surface with many random walks is equivalent to the estimation of the corresponding solutions of Laplace's equation ... which are usually called harmonic functions. Consequently, the name harmonic measure is also used for GSPD.

OBS

To calculate the harmonic measure and its characteristic properties one can follow two numerical methods. i) After having generated a DLA cluster one releases further particles ... whose diffusional motion is simulated by the same technique ... which is used for growing the aggregate. These probe particles, however, are eliminated when they arrive at the surface, and a record is kept of how many times each of the surface sites is contacted in this way. The normalized number of contacts is then regarded as the growth probability.

French

Domaine(s)
  • Fonctions mathématiques analytiques
  • Arpentage
  • Géographie mathématique
DEF

Fonction formée par quatre points d'une droite, d'un faisceau de droites, d'une moyenne, etc.

Spanish

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Record 2 1994-05-11

English

Subject field(s)
  • Mathematics
  • Computer Graphics
CONT

DLA and the Harmonic Measure. How can we best characterise the surface or perimeter of ... fractal structures? The harmonic measure affords a method of quantitatively characterising such surfaces. This (probability) measure is defined (with respect to a particular cluster) as the probability, ... of a random walker approaching the cluster from infinity first striking the cluster between the points ... along the boundary of the cluster.

French

Domaine(s)
  • Mathématiques
  • Infographie

Spanish

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