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HARMONIC MEASURE [5 fiches]

Fiche 1 2015-11-23

Anglais

Subject field(s)
  • Music
CONT

Pitched instruments are those that have a well-defined pitch or fundamental frequency-in this case, normally the "pitch"(a subjective frequency measure) matches the "fundamental frequency"(an objective frequency measure). For that reason, it is common that both terms be used interchangeably. Most pitched instruments are also harmonic, meaning that their partials... are close to being harmonics... However, some percussion instruments have a defined pitch, but their partials tend to be nonharmonic.

Français

Domaine(s)
  • Musique

Espagnol

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Fiche 2 2015-07-10

Anglais

Subject field(s)
  • General Mechanics (Physics)
  • Plant Biology
DEF

... a measure of how much a structure resists motion when subjected to a harmonic force.

CONT

Root elongation in drying soil is generally limited by a combination of mechanical impedance and water stress.

Français

Domaine(s)
  • Mécanique générale (Physique)
  • Biologie végétale
DEF

[...] mesure de la résistance opposée à un mouvement par une structure soumise à une force donnée.

Espagnol

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Fiche 3 2011-08-17

Anglais

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.

Français

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.

Espagnol

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Fiche 4 2000-08-29

Anglais

Subject field(s)
  • Mathematics
  • Computer Graphics
CONT

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.... ii) solving the Laplace equation... with boundary conditions.... For small clusters the Green's function method can be used to solve Laplace's equation... yielding GSPD free of any effects....

Terme(s)-clé(s)
  • Green method

Français

Domaine(s)
  • Mathématiques
  • Infographie
DEF

Méthode de simulation numérique de la croissance d'un agrégat limité par diffusion, par résolution d'équations laplaciennes.

Espagnol

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Fiche 5 1994-05-11

Anglais

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.

Français

Domaine(s)
  • Mathématiques
  • Infographie

Espagnol

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