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rarefaction

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rarefaction
rarefaction (rɛərɪ-, rærɪˈfækʃən) Also 7–8 rari-. [Noun of action f. L. rārēfacĕre: see rarefy v. Cf. F. raréfaction (14th c., Oresme).] The action of rarefying, or process of being rarefied; diminution of density. (Now chiefly of the air or gases, or Path. of bones.)1603 Holland Plutarch's Mor. 131... Oxford English Dictionary
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Rarefaction
Rarefaction is the reduction of an item's density, the opposite of compression. Rarefaction waves expand with time (much like sea waves spread out as they reach a beach); in most cases rarefaction waves keep the same overall profile wikipedia.org
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Rarefaction (ecology)
Rarefaction allows the calculation of species richness for a given number of individual samples, based on the construction of so-called rarefaction curves References External links Rarefaction Calculator EcoSim Professional Rarefaction Software PAST (PAlaeontological STatistics) Biodiversity Measurement wikipedia.org
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rarefactional
rarefactional, a. (rɛərɪˈfækʃənəl) [f. rarefaction + -al.] Characterized by rarefaction.1909 in Cent. Dict. Suppl. 1971 I. G. Gass et al. Understanding Earth xix. 272/1 On either side of the fault, the first waves to leave the source are compressions in the direction of motion and rarefactions away ... Oxford English Dictionary
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rarefication
rarefiˈcation rare. Also 7–8 rari-. [Noun of action, after L. types, from rarefy v.] = rarefaction.1616 in Bullokar Eng. Expos. 1727 Bradley Fam. Dict. s.v. Bee hive, Its Whiteness is increased by this Rarification. 1794 Sullivan View Nat. I. 209 It carries the point of greater rarefication on the o... Oxford English Dictionary
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Absorption (acoustics)
Additionally, the cycle of compression and rarefaction exhibits hysteresis of pressure waves in most materials which is a function of frequency, so for every compression there is a rarefaction, and the total amount of energy dissipated due to hysteresis changes with frequency. wikipedia.org
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rarifaction
rarifaction, -fy see rarefaction, rarefy. Oxford English Dictionary
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Zeldovich–Taylor flow
Thus, the rarefaction motion occurs for and there is no fluid motion for . It can be shown that the relation not only holds for small , but throughout the rarefaction wave. wikipedia.org
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rarefaction（Rarefaction and Its Importance in Biodiversity Analysis）
Jan 11, 2024Rarefaction and Its Importance in Biodiversity AnalysisIntroduction: Rarefaction is a commonly used statistical technique in biodiversity analysis. It allows re,爱他生活 www.ito-co.com
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singular shock solutions for strictly hyperbolic system of conservation law Shallow water equation \begin{eqnarray} \rho_t+q_x=0\\\ q_t + \left(q^2 +\frac{\rho ^2}{2} \right)_x=0 \end{eqnarray} being a strictly hyperb...
The procedure explained in "Numeric approximations of hyperbolic systems of conservation laws" by Godlewsky and Raviart is applicable for strictly hyperbolic systems provided $U_L$ and $U_R$ are sufficiently close. The method in general is not applicable for any $U_L$ and $U_R.$ Strict hyperbolicity...
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Sod shock tube
Namely the rarefaction wave, the contact discontinuity and the shock discontinuity. The first one is the position of the beginning of the rarefaction wave while the other is the velocity of the propagation of the shock. wikipedia.org
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densation
† denˈsation Obs. [ad. L. densātiōn-em, n. of action from densāre: see prec.] Thickening, condensation.1615 Crooke Body of Man 263 The Densation, Rarefaction, and Contraction of the matter of the parts. 1655–60 Stanley Hist. Philos. (1701) 7/1 Densation, or rarefaction. 1729 G. Shelvocke Artillery i... Oxford English Dictionary
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Mechanical index
It is defined as where Pr is the peak rarefaction pressure of the ultrasound wave (MPa), derated by an attenuation factor to account for in-tissue acoustic wikipedia.org
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纵波
纵波（longitudinal waves）又称疏密波（rarefaction waves），是指在传播介质中质点的振动方向与波的传播方向平行的一类波，形成的波是疏密相间的波形。 wikipedia.org
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A generalised Cauchy problem with Burgers' differential equation Consider the following: $$u_t+uu_x=0, ~~ t>0$$ and the initial data: $$ u(x,0)=\begin{cases} 1,&\text{ if }x\in[0,1]\text{ and } \\\ 0,&\text{ otherwis...
After $t=2$ you have that the rarefaction segment $0<x<a(t)$ where $u(x,t)=x/t$ is directly followed by the "unchanged" segment with $u(x,t)=0$ on $a(t See Burgers' equation after rarefaction wave catches up with the shock for a more extensive discussion of this situation.
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