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1

Goligorsky, Michael S. "Microvascular rarefaction." Organogenesis 6, no. 1 (January 2010): 1–10. http://dx.doi.org/10.4161/org.6.1.10427.

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2

Joshi, Vivek, Yogesh Kumar, Neetu Jindal, and Renu Aggarwal. "An In Vivo Comparative Evaluation of Postoperative Complications in Single- versus Multiple-Visit Endodontic Therapy: 18-Month Follow-Up." Dental Journal of Advance Studies 07, no. 02 (August 2019): 066–73. http://dx.doi.org/10.1055/s-0039-1697208.

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Abstract Objective The goal of root canal therapy is thorough disinfection and obturation of the root canal system in all its dimensions. Success of endodontic treatment is highly related to the elimination of postendodontic pain, tenderness, and swelling.Single-visit endodontic therapy has several advantages such as increased patient acceptance, less overhead costs, and only single time local anesthesia administration is required.Multiple-visit endodontic (MVE) treatment allows the clinician to determine the effect of the therapy on the inflamed tissues and shorter appointments.This in vivo study was undertaken to compare the postoperative incidence of pain, swelling, tenderness, and radiographic evaluation of periapical pathology following single- versus multiple-visit endodontic therapy in vital as well as nonvital teeth. Materials and Methods A total of 60 subjects in the age group of 15 to 50 years were selected for the study. The patients were divided into four groups:• Group 1 (n = 15): Single-visit endodontic (SVE) therapy with vital pulp involvement without periapical rarefaction.• Group 2 (n = 15): SVE therapy of asymptomatic pulpless teeth with periapical rarefaction as observed in radiographic evaluation.• Group 3 (n = 15): MVE of vital pulp involvement without periapical rarefactions.• Group 4 (n = 15): MVE therapy of asymptomatic pulpless teeth with periapical rarefaction as observed radiographically.Access cavity was prepared, working length was taken. Biomechanical preparation was done with Protaper universal rotary file system and obturation was done immediately in single-visit cases.In multivisit cases, Ca (OH)2 is placed as an intracanal medicament and obturation was done with the help of AH plus sealer and gutta-percha.Postobturation pain levels, swelling, and tenderness on percussion were assessed till 6 weeks. The radiographic parameter was studied till 18 months follow-up. Results Among the different experimental groups, maximum patients in MVE without periapical rarefaction showed no pain according to visual analog scale (VAS) scale, swelling, and tenderness and in SVE with periapical rarefaction showed maximum number of patients reported with pain, tenderness, and swelling.At 4 and 6 weeks postoperatively, patients in all the groups exhibited no pain, swelling, and tenderness to percussion.As periapical rarefaction, healing of periapical lesion was evident in all the patients after 18 months.
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3

Yunfei, Fu, Han Zhaoyuan, and Gong Minwei. "Condensation induced by rarefaction waves and reflected rarefaction waves." Advances in Atmospheric Sciences 12, no. 4 (November 1995): 507–12. http://dx.doi.org/10.1007/bf02657008.

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4

Morère, Jean-François. "Normalization, inhibition, rarefaction?" Targeted Oncology 2, no. 3 (July 10, 2007): 133. http://dx.doi.org/10.1007/s11523-007-0055-4.

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5

Pullicino, Patrick, Peter Ostrow, Lucia Miller, Wendy Snyder, and Frederick Munschauer. "Pontine ischemic rarefaction." Annals of Neurology 37, no. 4 (April 1995): 460–66. http://dx.doi.org/10.1002/ana.410370408.

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6

Afsar, Baris, Rengin E. Afsar, Tuncay Dagel, Ege Kaya, Suat Erus, Alberto Ortiz, Adrian Covic, and Mehmet Kanbay. "Capillary rarefaction from the kidney point of view." Clinical Kidney Journal 11, no. 3 (November 28, 2017): 295–301. http://dx.doi.org/10.1093/ckj/sfx133.

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ABSTRACT Capillary rarefaction is broadly defined as a reduction in vascular density. Capillary rarefaction in the kidneys is thought to promote hypoxia, impair hemodynamic responses and predispose to chronic kidney disease (CKD) progression and hypertension development. Various mechanisms have been suggested to play a role in the development of capillary rarefaction, including inflammation, an altered endothelial-tubular epithelial cell crosstalk, a relative deficiency in angiogenic growth factors, loss of pericytes, increased activity of Transforming growth factor -β1 and thrombospondin-1, vitamin D deficiency, a link to lymphatic neoangiogenesis and INK4a/ARF (Cylin-dependent kinase inhibitor 2a; CDKN2A). In this review, we summarize the tools available to monitor capillary rarefaction noninvasively in the clinic, the contribution of capillary rarefaction to CKD and hypertension, the known mechanisms of capillary rarefaction, and potential future strategies to attenuate capillary rarefaction and reduce its negative impact. Therapeutic strategies to be explored in more detail include optimization of antihypertensive therapy, vitamin D receptor activators, sirtuin 1 activators, Hypoxia inducible factor prolyl hydroxylase inhibitors and stem cell therapy.
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7

Jenssen, Helge Kristian. "On Exact Solutions of Rarefaction-Rarefaction Interactions in Compressible Isentropic Flow." Journal of Mathematical Fluid Mechanics 19, no. 4 (December 5, 2016): 685–708. http://dx.doi.org/10.1007/s00021-016-0309-y.

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8

Frisbee, Jefferson C., Adam G. Goodwill, Stephanie J. Frisbee, Joshua T. Butcher, Robert W. Brock, I. Mark Olfert, Evan R. DeVallance, and Paul D. Chantler. "Distinct temporal phases of microvascular rarefaction in skeletal muscle of obese Zucker rats." American Journal of Physiology-Heart and Circulatory Physiology 307, no. 12 (December 15, 2014): H1714—H1728. http://dx.doi.org/10.1152/ajpheart.00605.2014.

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Evolution of metabolic syndrome is associated with a progressive reduction in skeletal muscle microvessel density, known as rarefaction. Although contributing to impairments to mass transport and exchange, the temporal development of rarefaction and the contributing mechanisms that lead to microvessel loss are both unclear and critical areas for investigation. Although previous work suggests that rarefaction severity in obese Zucker rats (OZR) is predicted by the chronic loss of vascular nitric oxide (NO) bioavailability, we have determined that this hides a biphasic development of rarefaction, with both early and late components. Although the total extent of rarefaction was well predicted by the loss in NO bioavailability, the early pulse of rarefaction developed before a loss of NO bioavailability and was associated with altered venular function (increased leukocyte adhesion/rolling), and early elevation in oxidant stress, TNF-α levels, and the vascular production of thromboxane A2 (TxA2). Chronic inhibition of TNF-α blunted the severity of rarefaction and also reduced vascular oxidant stress and TxA2 production. Chronic blockade of the actions of TxA2 also blunted rarefaction, but did not impact oxidant stress or inflammation, suggesting that TxA2 is a downstream outcome of elevated reactive oxygen species and inflammation. If chronic blockade of TxA2 is terminated, microvascular rarefaction in OZR skeletal muscle resumes, but at a reduced rate despite low NO bioavailability. These results suggest that therapeutic interventions against inflammation and TxA2 under conditions where metabolic syndrome severity is moderate or mild may prevent the development of a condition of accelerated microvessel loss with metabolic syndrome.
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9

Kida, Yujiro. "Peritubular Capillary Rarefaction: An Underappreciated Regulator of CKD Progression." International Journal of Molecular Sciences 21, no. 21 (November 4, 2020): 8255. http://dx.doi.org/10.3390/ijms21218255.

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Peritubular capillary (PTC) rarefaction is commonly detected in chronic kidney disease (CKD) such as hypertensive nephrosclerosis and diabetic nephropathy. Moreover, PTC rarefaction prominently correlates with impaired kidney function and predicts the future development of end-stage renal disease in patients with CKD. However, it is still underappreciated that PTC rarefaction is a pivotal regulator of CKD progression, primarily because the molecular mechanisms of PTC rarefaction have not been well-elucidated. In addition to the established mechanisms (reduced proangiogenic factors and increased anti-angiogenic factors), recent studies discovered significant contribution of the following elements to PTC loss: (1) prompt susceptibility of PTC to injury, (2) impaired proliferation of PTC, (3) apoptosis/senescence of PTC, and (4) pericyte detachment from PTC. Mainly based on the recent and novel findings in basic research and clinical study, this review describes the roles of the above-mentioned elements in PTC loss and focuses on the major factors regulating PTC angiogenesis, the assessment of PTC rarefaction and its surrogate markers, and an overview of the possible therapeutic agents to mitigate PTC rarefaction during CKD progression. PTC rarefaction is not only a prominent histological characteristic of CKD but also a central driving force of CKD progression.
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10

van Dinther, Maud, Paulien HM Voorter, Jacobus FA Jansen, Elizabeth AV Jones, Robert J. van Oostenbrugge, Julie Staals, and Walter H. Backes. "Assessment of microvascular rarefaction in human brain disorders using physiological magnetic resonance imaging." Journal of Cerebral Blood Flow & Metabolism 42, no. 5 (January 26, 2022): 718–37. http://dx.doi.org/10.1177/0271678x221076557.

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Cerebral microvascular rarefaction, the reduction in number of functional or structural small blood vessels in the brain, is thought to play an important role in the early stages of microvascular related brain disorders. A better understanding of its underlying pathophysiological mechanisms, and methods to measure microvascular density in the human brain are needed to develop biomarkers for early diagnosis and to identify targets for disease modifying treatments. Therefore, we provide an overview of the assumed main pathophysiological processes underlying cerebral microvascular rarefaction and the evidence for rarefaction in several microvascular related brain disorders. A number of advanced physiological MRI techniques can be used to measure the pathological alterations associated with microvascular rarefaction. Although more research is needed to explore and validate these MRI techniques in microvascular rarefaction in brain disorders, they provide a set of promising future tools to assess various features relevant for rarefaction, such as cerebral blood flow and volume, vessel density and radius and blood-brain barrier leakage.
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11

Bai, Xiang, Lin-An Li, and Xiaojing Xu. "Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment." Nonlinearity 37, no. 6 (May 7, 2024): 065014. http://dx.doi.org/10.1088/1361-6544/ad422b.

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Abstract In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment.
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12

Ikeda, Sadamichi, Katsuro Iwasaki, and Toshibumi Eto. "Bone rarefaction after gastrectomy." Orthopedics & Traumatology 38, no. 3 (1990): 1143–51. http://dx.doi.org/10.5035/nishiseisai.38.1143.

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13

Liu, Tai-Ping, and Haitao Wang. "Viscous Scalar Rarefaction Waves." SIAM Journal on Mathematical Analysis 49, no. 3 (January 2017): 2061–100. http://dx.doi.org/10.1137/16m1063927.

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14

Ricotta, Carlo, Alicia T. R. Acosta, Giovanni Bacaro, Marta Carboni, Alessandro Chiarucci, Duccio Rocchini, and Sandrine Pavoine. "Rarefaction of beta diversity." Ecological Indicators 107 (December 2019): 105606. http://dx.doi.org/10.1016/j.ecolind.2019.105606.

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15

Longwei, Lin, and Xie Feipeng. "Perturbation of rarefaction waves." Acta Mathematica Sinica 8, no. 2 (June 1992): 122–34. http://dx.doi.org/10.1007/bf02629933.

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16

Smith, Eric P., Paul M. Stewart, and John Cairns. "Similarities between rarefaction methods." Hydrobiologia 120, no. 2 (January 1985): 167–70. http://dx.doi.org/10.1007/bf00032138.

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17

Deift, Percy, Spyridon Kamvissis, Thomas Kriecherbauer, and Xin Zhou. "The Toda rarefaction problem." Communications on Pure and Applied Mathematics 49, no. 1 (January 1996): 35–83. http://dx.doi.org/10.1002/(sici)1097-0312(199601)49:1<35::aid-cpa2>3.0.co;2-8.

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18

Li, Dening. "On the initial-boundary value problem for the Euler equations in presence of a rarefaction wave." Journal of Hyperbolic Differential Equations 16, no. 02 (June 2019): 271–92. http://dx.doi.org/10.1142/s0219891619500103.

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We study the initial-boundary value problem for the general non-isentropic 3D Euler equations with data which are incompatible in the classical sense, but are “rarefaction-compatible”. We show that such data are also rarefaction-compatible of infinite order and the initial-boundary value problem has a piece-wise smooth solution containing a rarefaction wave.
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19

Greene, A. S., P. J. Tonellato, J. Lui, J. H. Lombard, and A. W. Cowley. "Microvascular rarefaction and tissue vascular resistance in hypertension." American Journal of Physiology-Heart and Circulatory Physiology 256, no. 1 (January 1, 1989): H126—H131. http://dx.doi.org/10.1152/ajpheart.1989.256.1.h126.

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The purpose of this study was to quantitatively estimate the relative contribution of arteriolar rarefaction (disappearance of microvessels) and arteriolar constriction to the increases in total peripheral resistance and changes in the patterns of flow distribution observed in hypertension. A mathematical model of the hamster cheek pouch intraluminal microcirculation was constructed based on data from the literature and observations from our own laboratory. Separate rarefaction and constriction of third-order (3A) and fourth-order (4A) arterioles were performed on the model, and the results were quantified based on the changes of the computed vascular resistance. The degree of increase in resistance depended both on the number and the order of vessels rarefied or constricted and also on the position of those vessels in the network. The maximum increases in resistance obtained in the model runs were 21% for rarefaction and 75% for constriction. Rarefaction, but not constriction, produced large increases in the degree of heterogeneity of blood flow in the various vessel orders. These results demonstrate that vessel rarefaction significantly influences tissue blood flow resistance to a degree comparable with vessel constriction; however, unlike constriction, microvascular rarefaction markedly altered blood flow distribution in our model of the hamster cheek pouch vascular bed. These findings conform with the hypothesis that a significant component of the increase in total peripheral resistance in hypertension may be due to vessel rarefaction.
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20

ZAMFIRESCU, CALIN, ALBERTO GUARDONE, and PIERO COLONNA. "Admissibility region for rarefaction shock waves in dense gases." Journal of Fluid Mechanics 599 (March 6, 2008): 363–81. http://dx.doi.org/10.1017/s0022112008000207.

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In the vapour phase and close to the liquid–vapour saturation curve, fluids made of complex molecules are expected to exhibit a thermodynamic region in which the fundamental derivative of gasdynamic Γ is negative. In this region, non-classical gasdynamic phenomena such as rarefaction shock waves are physically admissible, namely they obey the second law of thermodynamics and fulfil the speed-orienting condition for mechanical stability. Previous studies have demonstrated that the thermodynamic states for which rarefaction shock waves are admissible are however not limited to the Γ<0 region. In this paper, the conditions for admissibility of rarefaction shocks are investigated. This results in the definition of a new thermodynamic region – the rarefaction shocks region – which embeds the Γ<0 region. The rarefaction shocks region is bounded by the saturation curve and by the locus of the states connecting double-sonic rarefaction shocks, i.e. shock waves in which both the pre-shock and post-shock states are sonic. Only one double-sonic shock is shown to be admissible along a given isentrope, therefore the double-sonic states can be connected by a single curve in the volume–pressure plane. This curve is named the double sonic locus. The influence of molecular complexity on the shape and size of the rarefaction shocks region is also illustrated by using the van der Waals model; these results are confirmed by very accurate multi-parameter thermodynamic models applied to siloxane fluids and are therefore of practical importance in experiments aimed at proving the existence of rarefaction shock waves in the single-phase vapour region as well as in future industrial applications operating in the non-classical regime.
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21

GUARDONE, ALBERTO. "Three-dimensional shock tube flows for dense gases." Journal of Fluid Mechanics 583 (July 4, 2007): 423–42. http://dx.doi.org/10.1017/s0022112007006313.

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The formation process of a non-classical rarefaction shock wave in dense gas shock tubes is investigated by means of numerical simulations. To this purpose, a novel numerical scheme for the solution of the Euler equations under non-ideal thermodynamics is presented, and applied for the first time to the simulation of non-classical fully three-dimensional flows. Numerical simulations are carried out to study the complex flow field resulting from the partial burst of the shock tube diaphragm, a situation that has been observed in preliminary trials of a dense gas shock tube experiment. Beyond the many similarities with the corresponding classical flow, the non-classical wave field is characterized by the occurrence of anomalous compression isentropic waves and rarefaction shocks propagating past the leading rarefaction shock front. Negative mass flow through the rarefaction shock wave results in a limited interaction with the contact surface close to the diaphragm, a peculiarity of the non-classical regime. The geometrical asymmetry does not prevent the formation of a single rarefaction shock front, though the pressure difference across the rarefaction wave is predicted to be weaker than the one which would be obtained by the complete burst of the diaphragm.
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22

Werber, Andrew H., MaryPat C. Fitch-Burke, David G. Harrington, and Jina Shah. "No rarefaction of cerebral arterioles in hypertensive rats." Canadian Journal of Physiology and Pharmacology 68, no. 4 (April 1, 1990): 476–79. http://dx.doi.org/10.1139/y90-067.

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A reduction in the density of small arterioles (rarefaction) has been reported in several vascular beds of the spontaneously hypertensive rat (SHR). There have been conflicting reports on the existence of rarefaction in the pial vasculature of SHR. In this study, we determined whether there was rarefaction of pial arterioles in several models of hypertension. We studied SHR; two-kidney, one-clip Goldblatt hypertensive rats; deoxycorticosterone–salt hypertensive rats; and Dahl salt-sensitive rats fed high salt diet. The two groups of normotensive controls were Wistar–Kyoto rats and Dahl salt-sensitive rats fed low salt diet. The duration of hypertension was about 2 months. Density of first-, second-, third-, and fourth-order arterioles was determined by counting the number of vessels from enlarged photographs. We also measured the lengths of segments of the arterioles. We did not observe any evidence of rarefaction of arterioles in the pial vasculature in any of the hypertensive groups of rats. We conclude that (i) rarefaction of arterioles does not occur in the pial microvasculature after approximately 2 months of hypertension and (ii) rarefaction of pial arterioles does not account for abnormalities in the cerebral circulation of hypertensive rats such as protection of the blood–brain barrier or changes in autoregulation of cerebral blood flow.Key words: microcirculation, brain, vascular density.
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23

Paavonsalo, Satu, Sangeetha Hariharan, Madeleine H. Lackman, and Sinem Karaman. "Capillary Rarefaction in Obesity and Metabolic Diseases—Organ-Specificity and Possible Mechanisms." Cells 9, no. 12 (December 14, 2020): 2683. http://dx.doi.org/10.3390/cells9122683.

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Obesity and its comorbidities like diabetes, hypertension and other cardiovascular disorders are the leading causes of death and disability worldwide. Metabolic diseases cause vascular dysfunction and loss of capillaries termed capillary rarefaction. Interestingly, obesity seems to affect capillary beds in an organ-specific manner, causing morphological and functional changes in some tissues but not in others. Accordingly, treatment strategies targeting capillary rarefaction result in distinct outcomes depending on the organ. In recent years, organ-specific vasculature and endothelial heterogeneity have been in the spotlight in the field of vascular biology since specialized vascular systems have been shown to contribute to organ function by secreting varying autocrine and paracrine factors and by providing niches for stem cells. This review summarizes the recent literature covering studies on organ-specific capillary rarefaction observed in obesity and metabolic diseases and explores the underlying mechanisms, with multiple modes of action proposed. It also provides a glimpse of the reported therapeutic perspectives targeting capillary rarefaction. Further studies should address the reasons for such organ-specificity of capillary rarefaction, investigate strategies for its prevention and reversibility and examine potential signaling pathways that can be exploited to target it.
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24

FERGASON, S. H., T. L. HO, B. M. ARGROW, and G. EMANUEL. "Theory for producing a single-phase rarefaction shock wave in a shock tube." Journal of Fluid Mechanics 445 (October 16, 2001): 37–54. http://dx.doi.org/10.1017/s0022112001005444.

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Although predicted early in the 20th century, a single-phase vapour rarefaction shock wave has yet to be demonstrated experimentally. Results from a previous shock tube experiment appear to indicate a rarefaction shock wave. These results are discussed and their interpretation challenged. In preparation for a new shock tube experiment, a global theory is developed, utilizing a van der Waals fluid, for demonstrating a single-phase vapour rarefaction shock wave in the incident flow of the shock tube. The flow consists of four uniform regions separated by three constant-speed discontinuities: a rarefaction shock, a compression shock, and a contact surface. Entropy jumps and upstream supersonic Mach number conditions are verified for both shock waves. The conceptual van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations. The analysis predicts a small region of initial states that may be used to unequivocally demonstrate the existence of a single-phase vapour rarefaction shock wave. Simulation results in the form of representative sets of thermodynamic state data (pressure, density, Mach number, and fundamental derivative of gas dynamics) are presented.
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25

Gasanenko, V. A., and A. B. Roitman. "Rarefaction of moving diffusion particles." Ukrainian Mathematical Journal 56, no. 5 (May 2004): 835–39. http://dx.doi.org/10.1007/pl00022200.

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26

Zolghadri, Marc, Sid-Ali Addouche, Claude Baron, Amel Soltan, and Kevin Boissie. "Obsolescence, rarefaction and their propagation." Research in Engineering Design 32, no. 4 (August 9, 2021): 451–68. http://dx.doi.org/10.1007/s00163-021-00372-x.

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27

Palin, V. V., and E. V. Radkevich. "Bifurcations of Critical Rarefaction Waves." Journal of Mathematical Sciences 202, no. 2 (September 9, 2014): 245–58. http://dx.doi.org/10.1007/s10958-014-2044-3.

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28

Azhishchev, N. A., V. A. Antipin, A. A. Borisov, and V. A. Samoilov. "Rarefaction waves in free charges." Journal of Engineering Physics 52, no. 1 (January 1987): 9–12. http://dx.doi.org/10.1007/bf00870193.

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29

Mailybaev, Alexei A., and Dan Marchesin. "Hyperbolicity singularities in Rarefaction Waves." Journal of Dynamics and Differential Equations 20, no. 1 (June 2, 2007): 1–29. http://dx.doi.org/10.1007/s10884-007-9070-5.

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30

Elperin, T., O. Igra, and G. Ben-Dor. "Rarefaction waves in dusty gases." Fluid Dynamics Research 4, no. 4 (December 1988): 229–38. http://dx.doi.org/10.1016/0169-5983(88)90026-3.

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31

Hauge, Sindre B., Boris V. Balakin, and Pawel Kosinski. "Dust lifting behind rarefaction waves." Chemical Engineering Science 191 (December 2018): 87–99. http://dx.doi.org/10.1016/j.ces.2018.06.056.

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32

Brewer, Andrew, and Mark Williamson. "A new relationship for rarefaction." Biodiversity and Conservation 3, no. 4 (June 1994): 373–79. http://dx.doi.org/10.1007/bf00056509.

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33

Gasanenko, V. A., and A. B. Roitman. "Rarefaction of moving diffusion particles." Ukrainian Mathematical Journal 56, no. 5 (May 2004): 835–39. http://dx.doi.org/10.1007/s11253-005-0108-8.

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34

Chiarucci, A., G. Bacaro, D. Rocchini, C. Ricotta, M. Palmer, and S. Scheiner. "Spatially constrained rarefaction: incorporating the autocorrelated structure of biological communities into sample-based rarefaction." Community Ecology 10, no. 2 (December 2009): 209–14. http://dx.doi.org/10.1556/comec.10.2009.2.11.

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35

FAN, HAITAO, and HAILIANG LIU. "PATTERN FORMATION, WAVE PROPAGATION AND STABILITY IN CONSERVATION LAWS WITH SLOW DIFFUSION AND FAST REACTION." Journal of Hyperbolic Differential Equations 01, no. 04 (December 2004): 605–26. http://dx.doi.org/10.1142/s0219891604000275.

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The limiting behavior of the solution of a scalar conservation law with slow diffusion and fast bistable reaction is considered. In a short time the solution develops transition patterns connected by shock layers and rarefaction layers, when the initial data has finitely many monotone pieces. The existence and uniqueness of the front profiles for both shock layers and rarefaction layers are established. A variational characterization of wave speeds of these profiles is derived. These profiles are shown to be stable. Furthermore, it is proved that solutions with monotone initial data approach the shock layer or rarefaction layer waves as time goes to infinity.
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36

Ben-Ami, Y., and A. Manela. "The sound of a pulsating sphere in a rarefied gas: continuum breakdown at short length and time scales." Journal of Fluid Mechanics 871 (May 24, 2019): 668–93. http://dx.doi.org/10.1017/jfm.2019.329.

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The pressure field of a pulsating sphere is a canonical problem in classical acoustics, used to illustrate the acoustic efficiency of a monopole source at continuum conditions. We consider the counterpart vibroacoustic and thermoacoustic problems in a rarefied gas, to investigate the effect of continuum breakdown on monopole radiation. Focusing on small-amplitude normal-to-boundary mechanical and heat-flux excitations, the perturbation field is analysed in the entire range of gas rarefaction and input frequencies. Numerical calculations are carried out via the direct simulation Monte Carlo method, and are used to validate analytical predictions in the free-molecular and near-continuum regimes. In the latter, the regularized thirteen moments model (R13) is applied, to capture the system response at states where the Navier–Stokes–Fourier (NSF) description breaks down. Comparing with the continuum inviscid solution, the results quantitate the dampening effect of gas rarefaction on source point-wise strength and acoustic power. At near-continuum conditions, the acoustic field is composed of exponentially decaying ‘compression’, ‘thermal’ and ‘Knudsen-layer’ modes, reflecting thermoviscous and higher-order rarefaction effects. With reducing rarefaction, the contributions of the latter two modes vanish, and the former degenerates into the ideal-flow inverse-to-distance decaying wave. Stronger attenuation is obtained with increasing rarefaction, where boundary sphericity results in a ‘geometric reduction’ of the molecular layer affected by the source. Notably, while the R13 model at low frequencies appears valid up to moderate gas rarefaction rates, both the NSF and R13 descriptions break down at common low Knudsen numbers at higher frequencies. Further study should therefore be carried out to extend the applicability of moment models to unsteady flows with short time scales.
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37

von Kopylow, Kathrein, Hannah Staege, Andrej-Nikolai Spiess, Wolfgang Schulze, Hans Will, Michael Primig, and Christiane Kirchhoff. "Differential marker protein expression specifies rarefaction zone-containing human Adark spermatogonia." REPRODUCTION 143, no. 1 (January 2012): 45–57. http://dx.doi.org/10.1530/rep-11-0290.

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It is unclear whether the distinct nuclear morphologies of human Adark(Ad) and Apale(Ap) spermatogonia are manifestations of different stages of germ cell development or phases of the mitotic cycle, or whether they may reflect still unknown molecular differences. According to the classical description by Clermont, human dark type A spermatogonium (Ad) may contain one, sometimes two or three nuclear ‘vacuolar spaces’ representing chromatin rarefaction zones. These structures were readily discerned in paraffin sections of human testis tissue during immunohistochemical and immunofluorescence analyses and thus represented robust morphological markers for our study. While a majority of the marker proteins tested did not discriminate between spermatogonia with and without chromatin rarefaction zones, doublesex- and mab-3-related transcription factor (DMRT1), tyrosine kinase receptor c-Kit/CD117 (KIT) and proliferation-associated antigen Ki-67 (KI-67) appeared to be restricted to subtypes which lacked the rarefaction zones. Conversely, exosome component 10 (EXOSC10) was found to accumulate within the rarefaction zones, which points to a possible role of this nuclear domain in RNA processing.
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CHEN, GUI-QIANG, and JUN CHEN. "STABILITY OF RAREFACTION WAVES AND VACUUM STATES FOR THE MULTIDIMENSIONAL EULER EQUATIONS." Journal of Hyperbolic Differential Equations 04, no. 01 (March 2007): 105–22. http://dx.doi.org/10.1142/s0219891607001070.

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We are interested in properties of the multidimensional Euler equations for compressible fluids. Rarefaction waves are the unique solutions that may contain vacuum states in later time, in the context of one-dimensional Riemann problem, even when the Riemann initial data are away from the vacuum. For the multidimensional Euler equations describing isentropic or adiabatic fluids, we prove that plane rarefaction waves and vacuum states are stable within a large class of entropy solutions that may contain vacuum states. Rarefaction waves and vacuum states are also shown to be global attractors of entropy solutions in L∞, provided initial data are L∞ ∩ L1 perturbations of Riemann initial data. Our analysis applies to entropy solutions with arbitrarily large oscillation, and no bounded variation regularity is required.
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39

Zhuang, Zhihong, Dawen Xue, Zhihua Chen, and Xiaohai Jiang. "The eruption of a high-pressure cylindrical heavy gas cloud." Canadian Journal of Physics 91, no. 10 (October 2013): 850–54. http://dx.doi.org/10.1139/cjp-2013-0014.

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The physical explosion of a high-pressure and cylindrical dense gas (SF6) cloud has been simulated with the use of large eddy simulation (LES), and hybrid high-order schemes have been employed to solve the LES equations. Our results show that, while the shockwave is exploding from the SF6 to the air, it bifurcates into the reflected rarefaction wave and the transmitted shock, and a reverse shock also appears. The rarefaction wave moves inward first, the Richtmyer–Meshkov (RM) instabilities occur as the transmitted shock accelerates the interface between the SF6 and the air. Later, the rarefaction wave merges with the reverse shock, and finally converges at the origin of the cloud, which generates a strong circular reflected shock, and makes the flow field complex.
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40

Fan, Lili, Guiqiong Gong, and Shaojun Tang. "Asymptotic stability of viscous contact wave and rarefaction waves for the system of heat-conductive ideal gas without viscosity." Analysis and Applications 17, no. 02 (March 2019): 211–34. http://dx.doi.org/10.1142/s0219530518500239.

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This paper is concerned with the Cauchy problem of heat-conductive ideal gas without viscosity, where the far field states are prescribed. When the corresponding Riemann problem for the compressible Euler system has the solution consisting of a contact discontinuity and rarefaction waves, we show that if the strengths of the wave patterns and the initial perturbation are suitably small, the unique global-in-time solution exists and asymptotically tends to the corresponding composition of a viscous contact wave with rarefaction waves, which extended the results by Huang–Li–Matsumura [Asymptotic stability of combination of viscous contact wave with rarefaction waves for one-dimensional compressible Navier–Stokes system, Arch. Ration. Mech. Anal. 197 (2010) 89–116.], where they treated the viscous and heat-conductive ideal gas.
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41

Warrington, Junie P., Anna Csiszar, Daniel A. Johnson, Terence S. Herman, Salahuddin Ahmad, Yong Woo Lee, and William E. Sonntag. "Cerebral microvascular rarefaction induced by whole brain radiation is reversible by systemic hypoxia in mice." American Journal of Physiology-Heart and Circulatory Physiology 300, no. 3 (March 2011): H736—H744. http://dx.doi.org/10.1152/ajpheart.01024.2010.

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Whole brain radiation therapy (WBRT) leads to cognitive impairment in 40–50% of brain tumor survivors following treatment. Although the etiology of cognitive deficits post-WBRT remains unclear, vascular rarefaction appears to be an important component of these impairments. In this study, we assessed the effects of WBRT on the cerebrovasculature and the effects of systemic hypoxia as a potential mechanism to reverse the microvascular rarefaction. Transgenic mice expressing green fluorescent protein driven by the Acta2 (smooth muscle actin) promoter for blood vessel visualization were randomly assigned to control or radiated groups. Animals received a clinical series of 4.5 Gy WBRT two times weekly for 4 wk followed by 1 mo of recovery. Subsequently, mice were subjected to 11% (hypoxia) or 21% (normoxia) oxygen for 1 mo. Capillary density in subregions of the hippocampus revealed profound vascular rarefaction that persisted despite local tissue hypoxia. Nevertheless, systemic hypoxia was capable of completely restoring cerebrovascular density. Thus hippocampal microvascular rarefaction post-WBRT is not capable of stimulating angiogenesis and can be reversed by chronic systemic hypoxia. Our results indicate a potential shift in sensitivity to angiogenic stimuli and/or the existence of an independent pathway of regulating cerebral microvasculature.
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42

Bae, Jang-Whan. "Hypertension, Vascular Rarefaction and Angiopoietin-1." Korean Circulation Journal 41, no. 10 (2011): 575. http://dx.doi.org/10.4070/kcj.2011.41.10.575.

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43

Solow, Andrew R., and David L. Roberts. "Museum collections, species distributions, and rarefaction." Diversity Distributions 12, no. 4 (July 2006): 423–24. http://dx.doi.org/10.1111/j.1366-9516.2006.00259.x.

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44

Hiers, Robert. "Rarefaction Effects in Small Particle Combustion." Journal of Thermophysics and Heat Transfer 11, no. 2 (April 1997): 232–38. http://dx.doi.org/10.2514/2.6227.

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45

Lewicka, Marta. "Stability Conditions for Strong Rarefaction Waves." SIAM Journal on Mathematical Analysis 36, no. 4 (January 2005): 1346–69. http://dx.doi.org/10.1137/s0036141003429517.

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46

Krejčí, P. "Hysteresis rarefaction in the Riemann problem." Journal of Physics: Conference Series 138 (November 1, 2008): 012010. http://dx.doi.org/10.1088/1742-6596/138/1/012010.

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47

Chao, Anne, Chun‐Huo Chiu, T. C. Hsieh, Thomas Davis, David A. Nipperess, and Daniel P. Faith. "Rarefaction and extrapolation of phylogenetic diversity." Methods in Ecology and Evolution 6, no. 4 (September 25, 2014): 380–88. http://dx.doi.org/10.1111/2041-210x.12247.

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48

Kono, Ichiyo, Yoshihiro Ueda, Yukitaka Gotoh, Hidenori Kawaguchi, and Kenji Nakajimam. "Clinical significance of pontine ischemic rarefaction." Nosotchu 19, no. 1 (1997): 40–45. http://dx.doi.org/10.3995/jstroke.19.40.

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49

Münch, A., and A. L. Bertozzi. "Rarefaction–undercompressive fronts in driven films." Physics of Fluids 11, no. 10 (October 1999): 2812–14. http://dx.doi.org/10.1063/1.870177.

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50

Diebold, D., N. Hershkowitz, and S. Eliezer. "Rarefaction shock in the near wake." Physics of Fluids 30, no. 10 (1987): 3308. http://dx.doi.org/10.1063/1.866462.

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