Discussion:Nombre de Deborah

message: Les juges chapitre 5 verset 5
Le mot נָזְלוּ
est traduit par "coulèrent" dans l'article et de façon analogue dans plusieurs traductions.
Belle image que celle de la montagne qui se liquifie, cela fait penser à la lave des volcans...Mais d'autres traductions sont plus éloignées.
On lit quelquefois "ruisselèrent" qui évoque les torrents des montagnes.
Ci-après le texte en hébreu et une des traductions
ה הָרִים נָזְלוּ, מִפְּנֵי יְהוָה:  {ס}  זֶה  {ר}  סִינַי--מִפְּנֵי, יְהוָה אֱלֹהֵי יִשְׂרָאֵל.  {ס}   5 
Les monts ruisselèrent à la vue du Seigneur, le Sinaï tressaillit à l’aspect du Dieu d’Israël. 
D'autres traductions sont encore plus éloignées.
Ci-après un lien qui cite quelques traductions :
http://saintebible.com/judges/5-5.htm
"les montagnes fondirent" dans la version Darby traduit bien l'idée d'une liquéfaction des montagnes.
Mais "les montagne s'ébranlèrent" dans la version Louis Segond n'évoque absolument pas une notion de liquide.
Le lien suivant en anglais cite les différentes nuances dans la bible ,dans l'emploi du mot "couler" נָזְלוּ en hébreu. Pour juges 5:5 il est écrit: melted , fondu, qui traduit bien l'idée de liquéfaction :
http://lexiconcordance.com/hebrew/5140.html
V - flood 3, flow 3, stream 2, pour out 1, distil 1, melted 1,
      drop 1, running waters 1, flow out 1, pour down 1, gush out 1; 16
    distil
Deuteronomy 32:2.
    down
Isaiah 45:8.
    drop
Job 36:28.
    floods
Exodus 15:8. Psalms 78:44. Isaiah 44:3.
    flow
Psalms 147:18. Isaiah 48:21.
    flowing
Jeremiah 18:14.
    melted
Judges 5:5.
    out
Numbers 24:7. Song of Songs 4:16. Jeremiah 9:18.
    pour
Numbers 24:7.
    streams
Psalms 78:16. Song of Songs 4:15.
    waters
Proverbs 5:15.
...........................................................................
Nahum chaptre 1 verset 5 évoque la même image selon certaines traductions :
1,5
Les montagnes tremblent devant lui et les collines se liquéfient. La terre se soulève à son aspect, l'univers et tout ce qui l'habite.
ה הָרִים רָעֲשׁוּ מִמֶּנּוּ, וְהַגְּבָעוֹת הִתְמֹגָגוּ; וַתִּשָּׂא הָאָרֶץ מִפָּנָיו, וְתֵבֵל וְכָל-יוֹשְׁבֵי בָהּ. 
Le mot en hébreu traduit par fondre ou liquéfier est différent de celui de juges 5:5:
http://scholarsgateway.com/parse/%D7%94%D6%B4%D7%AA%D6%B0%D7%9E%D6%B9%D7%92%D6%B8%D7%92%D7%95%D6%BC
Word Parsed:	
הִתְמֹגָגוּ
Parts of Speech:	Verb Hithpolel Perfect 3rd Com. Pl.
Root:	
מוג
Strong's Number:	H4127
Infinitive Definition:	1. to melt, cause to melt
  a. (Qal) 1. to
   melt, faint 2. to...
Transliteration:	
First occurance in each book:
Nahum 1:5
הָרִים רָעֲשׁוּ מִמֶּנּוּ וְהַגְּבָעֹות הִתְמֹגָגוּ וַתִּשָּׂא הָאָרֶץ מִפָּנָיו וְתֵבֵל וְכָל־יֹשְׁבֵי בָֽהּ׃
En tout 17 occurrences dans la bible:
    * מוּג
    * mug (556a); a prim. root; to melt:—
    * NASB - disheartened(1), dissolve(2), dissolved(2), melt(3), melted(2), melted away(4), melts(1), soften(1).
—NAS Exhaustive Concordance of the Bible with Hebrew-Aramaic and Greek Dictionaries
Copyright © 1981, 1998 by The Lockman Foundation — All rights reserved — http://www.lockman.org
 AV - melt 5, dissolve 4, faint 3, melt away 2, consumed 1,
      fainthearted 1, soft 1; 17
    away
Exodus 15:15. 1 Samuel 14:16.
    consumed
Isaiah 64:7.
    dissolved
Psalms 75:3. Isaiah 14:31. Nahum 2:6.
    dissolvest
Job 30:22.
    faint
Joshua 2:9, 24. Ezekiel 21:15.
    fainthearted
Jeremiah 49:23.
    melt
Amos 9:5, 13. Nahum 1:5.
    melted
Psalms 46:6; 107:26.
    soft
Psalms 65:10.
....................................................................
Michée 1 4
Traduction analogue:
ד וְנָמַסּוּ הֶהָרִים תַּחְתָּיו, וְהָעֲמָקִים יִתְבַּקָּעוּ, כַּדּוֹנַג מִפְּנֵי הָאֵשׁ, כְּמַיִם מֻגָּרִים בְּמוֹרָד. 
4 Sous ses pas, les montagnes se liquéfient, lés vallées se crevassent: ainsi la cire fond sous l'action du feu et les eaux se précipitent sur une pente.
Word Parsed:
וְנָמַסּוּ 
Parts of Speech:
Verb Niphal Perfect 3rd Com. Pl.
Root:
מסס 
Strong's Number:
H4549
Infinitive Definition:
1. to dissolve, melt
 a. (Qal) to
 waste away
 b....
Transliteration:
First occurance in each book:
--------------------------------------------------------------------------------
Isaiah 34:3
וְחַלְלֵיהֶם יֻשְׁלָכוּ וּפִגְרֵיהֶם יַעֲלֶה בָאְשָׁם וְנָמַסּוּ הָרִים מִדָּמָֽם׃
Micah 1:4
וְנָמַסּוּ הֶֽהָרִים תַּחְתָּיו וְהָעֲמָקִים יִתְבַּקָּעוּ כַּדֹּונַג מִפְּנֵי הָאֵשׁ כְּמַיִם מֻגָּרִים בְּמֹורָֽד׃
Strong's Number H4549 matches the Hebrew מָסַס(macac ),
 which occurs 24 times in 20 verses in the Hebrew concordance of the NASB
(More Info)
Exo 16:21
Morning by morning they gathered it, each as much as he could eat; but when the sun grew hot, it melted. 
Deu 1:28
Whither are we going up? Our brethren have made our hearts melt, saying, "The people are greater and taller than we; the cities are great and fortified up to heaven; and moreover we have seen the sons of the Anakim there."' 
Deu 20:8
And the officers shall speak further to the people, and say, 'What man is there that is fearful and fainthearted? Let him go back to his house, lest the heart of his fellows melt as his heart.' 
Jos 2:11
And as soon as we heard it, our hearts melted, and there was no courage left in any man, because of you; for the LORD your God is he who is God in heaven above and on earth beneath. 
Jos 5:1
When all the kings of the Amorites that were beyond the Jordan to the west, and all the kings of the Canaanites that were by the sea, heard that the LORD had dried up the waters of the Jordan for the people of Israel until they had crossed over, their heart melted, and there was no longer any spirit in them, because of the people of Israel. 
Jos 7:5
and the men of Ai killed about thirty-six men of them, and chased them before the gate as far as Sheb'arim, and slew them at the descent. And the hearts of the people melted, and became as water. 
Jdg 15:14
When he came to Lehi, the Philistines came shouting to meet him; and the Spirit of the LORD came mightily upon him, and the ropes which were on his arms became as flax that has caught fire, and his bonds melted off his hands. 
1Sa 15:9
But Saul and the people spared Agag, and the best of the sheep and of the oxen and of the fatlings, and the lambs, and all that was good, and would not utterly destroy them; all that was despised and worthless they utterly destroyed. 
2Sa 17:10
Then even the valiant man, whose heart is like the heart of a lion, will utterly melt with fear; for all Israel knows that your father is a mighty man, and that those who are with him are valiant men. 
Psa 22:14
I am poured out like water, and all my bones are out of joint; my heart is like wax, it is melted within my breast; 
Psa 68:2
As smoke is driven away, so drive them away; as wax melts before fire, let the wicked perish before God! 
Psa 97:5
The mountains melt like wax before the LORD, before the Lord of all the earth. 
Psa 112:10
The wicked man sees it and is angry; he gnashes his teeth and melts away; the desire of the wicked man comes to nought. 
Isa 10:18
The glory of his forest and of his fruitful land the LORD will destroy, both soul and body, and it will be as when a sick man wastes away. 
Isa 13:
Therefore all hands will be feeble, and every man's heart will melt, 
Isa 19:1
An oracle concerning Egypt. Behold, the LORD is riding on a swift cloud and comes to Egypt; and the idols of Egypt will tremble at his presence, and the heart of the Egyptians will melt within them. 
Isa 34:3
Their slain shall be cast out, and the stench of their corpses shall rise; the mountains shall flow with their blood. 
Eze 21:7
And when they say to you, 'Why do you sigh?' you shall say, 'Because of the tidings. When it comes, every heart will melt and all hands will be feeble, every spirit will faint and all knees will be weak as water. Behold, it comes and it will be fulfilled,'" says the Lord GOD. 
Mic 1:4
And the mountains will melt under him and the valleys will be cleft, like wax before the fire, like waters poured down a steep place. 
Nah 2:10
Desolate! Desolation and ruin! Hearts faint and knees tremble, anguish is on all loins, all faces grow pale! 
Frydman Charles (discuter) 8 mai 2014 à 09:27 (CEST)
thread_title:  Les montagnes coulèrent devant le seigneur ? 

message: Selon l'article de Wikipédia :
http://fr.wikipedia.org/wiki/Grandeur_sans_dimension
Ces 2 nombres ont la même définition, en réalité il semble qu'il y ait une différence. Le nombre de Weissenberg est défini par : \text{Wi} = \dot{\gamma} \lambda.\, produit du temps de relaxation et du quotient entre la vitesse de déformation et la distance entre deux repères.
Je corrige l'article sur les "grandeurs sans dimension".
selon la définition sur wikipédia du shear rate en anglais:
https://en.wikipedia.org/wiki/Shear_rate
:\dot\gamma = \frac{v}{h},
where: 
*\dot\gamma is the shear rate, measured in reciprocal seconds;
*v is the velocity of the moving plate, measured in meters per second;
*h is the distance between the two parallel plates, measured in meters.
Selon Wikipédia en Anglais:
http://en.wikipedia.org/wiki/Weissenberg_number
While Wi is similar to the Deborah number and is often confused with it in technical literature, they have different physical interpretations. The Weissenberg number indicates the degree of anisotropy or orientation generated by the deformation, and is appropriate to describe flows with a constant stretch history, such as simple shear. In contrast, the Deborah number should be used to describe flows with a non-constant stretch history, and physically represents the rate at which elastic energy is stored or released.
En fait dans certains cas les deux formules se rejoignent:
Formule de Déborah:
 De = \frac{t_\mathrm{c}}{t_\mathrm{p}}
où tc est le temps caractéristique de relaxation du matériau et tp est le temps caractéristique de l'expérience.
On remarque que si d est la distance entre les deux repères (les deux plaques) , et v la vitesse :
V/d=1/tp
Et donc :
\text{Wi} = \frac{t_\mathrm{c}}{t_\mathrm{p}}
http://pcwww.liv.ac.uk/~robpoole/PAPERS/POOLE_45.pdf
Le nombre de Déborah a été cité au 4ème congrès de rhéologie en  1964 , des souvenirs de 1928 , l'année de la création du mot rhéologie  ,y sont évoqués . Mais si le nombre de Deborah fait référence aux souvenirs de 1928, il semble n'avoir été introduit qu'en 1964 ?
books.google.fr/books?isbn=2804102483
Mr Richard Taillet, ‎Mr Pascal Febvre, ‎Mr Loïc Villain - 2009 - ‎Science Deborah number) Nombre sans dimension intervenant en rhéologie, introduit par Markus Reiner (1886—1976) en 1964, et défini comme le rapport entre le ...
http://perso.ens-lyon.fr/thomas.gibaud/pdf/reiner_DeborahNumber.pdf
le nombre de Weissenberg probablement de 1948, présenté au 1er congrès de Rhéologie.
Karl Weissenberg s'est rendu au Technion de Haïfa en 1966 pour y publer une étude:
http://weissenberg.bsr.org.uk/Publications/Publications.htm
(K.W.) A Rheological Approach to Research in Microcirculation, Technicon, Haifa, Israel, 1966
Frydman Charles (discuter) 8 mai 2014 à 17:14 (CEST)
thread_title:  Nombre de Déborah et nombre de Weissenberg 

message: — Une discussion a été initié au coin café du labo : Typographie des nombres adimensionnels .
— Ellande  (Disc.) 8 mars 2024 à 12:51 (CET)
thread_title:  Typographie : De ou ''De''