Relevant bibliographies by topics / Non-collapsing

Academic literature on the topic 'Non-collapsing'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Non-collapsing"

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Swaminathan, Sundararaman, Donna J. Lager, Xiang Qian, Mark D. Stegall, Timothy S. Larson, and Matthew D. Griffin. "Collapsing and non-collapsing focal segmental glomerulosclerosis in kidney transplants." Nephrology Dialysis Transplantation 21, no. 9 (May 16, 2006): 2607–14. http://dx.doi.org/10.1093/ndt/gfl225.

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Andrews, Ben, Mat Langford, and James McCoy. "Non-collapsing in fully non-linear curvature flows." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 30, no. 1 (January 2013): 23–32. http://dx.doi.org/10.1016/j.anihpc.2012.05.003.

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Dey, Agnish, and Arunava Mukherjea. "Collapsing of non-homogeneous Markov chains." Statistics & Probability Letters 84 (January 2014): 140–48. http://dx.doi.org/10.1016/j.spl.2013.10.002.

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Floratos, E. G., and G. K. Leontaris. "Non-collapsing membrane instantons in higher dimensions." Physics Letters B 545, no. 1-2 (October 2002): 190–96. http://dx.doi.org/10.1016/s0370-2693(02)02550-9.

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Moulay, Emmanuel. "Non-collapsing wave functions in an infinite universe." Results in Physics 4 (2014): 164–67. http://dx.doi.org/10.1016/j.rinp.2014.08.010.

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Li, Haozhao, and Kai Zheng. "Kähler non-collapsing, eigenvalues and the Calabi flow." Journal of Functional Analysis 267, no. 5 (September 2014): 1593–636. http://dx.doi.org/10.1016/j.jfa.2014.06.001.

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Menahem, S., C. Chan, and T. Quach. "Collapsing FSGS Post Non Renal Solid Organ Transplantation." Transplantation Journal 94, no. 10S (November 2012): 370. http://dx.doi.org/10.1097/00007890-201211271-00684.

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Menahem, S., C. Chan, and T. Quach. "Collapsing FSGS Post Non Renal Solid Organ Transplantation." Transplantation Journal 94, no. 10S (November 2012): 767. http://dx.doi.org/10.1097/00007890-201211271-01501.

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Sakai, Masahiko, and Mizuhito Ogawa. "Weakly-non-overlapping non-collapsing shallow term rewriting systems are confluent." Information Processing Letters 110, no. 18-19 (September 2010): 810–14. http://dx.doi.org/10.1016/j.ipl.2010.06.015.

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Liu, Yannan, and Hongjie Ju. "Non-collapsing for a fully nonlinear inverse curvature flow." Communications on Pure & Applied Analysis 16, no. 3 (2017): 945–52. http://dx.doi.org/10.3934/cpaa.2017045.

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Dissertations / Theses on the topic "Non-collapsing"

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Faria, Mary Frances Veloz. "A non-traditional way to manage change : collapsing hierarchy temporarily to allow for collective knowledge work /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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Deruelle, Alix. "Géométrie à l'infini de certaines variétés riemanniennes non-compactes." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENM068.

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On s'intéresse à la géométrie globale et asymptotique de certaines variétés riemanniennes non compactes. Dans une première partie, on étudie la topologie et la géométrie à l'infini des variétés riemanniennes à courbure (de Ricci) positive ayant un rapport asymptotique de courbure fini. On caractérise le cas non effondré via la notion de cône asymptotique et on donne des conditions suffisantes sur le groupe fondamental pour garantir un non effondrement. La seconde partie est dédiée à l'étude des solutions de Type III du flot de Ricci à courbure positive et aux solitons gradients de Ricci expansifs (points fixes de Type III) présentant une décroissance quadratique de la courbure. On montre l'existence et l'unicité des cônes asymptotiques de tels points fixes. On donne également des conditions suffisantes de nature algébrique et géométrique pour garantir une géométrie de révolution de tels solitons. Dans une troisième partie, on caractérise la géométrie des solitons gradients de Ricci stables à courbure positive et à croissance volumique linéaire. Puis, on s'intéresse au non effondrement des variétés riemanniennes de dimension trois à courbure de Ricci positive ayant un rapport asymptotique de courbure fini
We study the global and asymptotic geometry of non-compact Riemannian manifolds. First, we study the topology and geometry at infinity of Riemannian manifolds with nonnegative (Ricci) curvature and finite asymptotic curvature ratio. We focus on the non-collapsed case with the help of asymptotic cones and we give sufficient conditions on the fundamental group to guarantee non-collapsing. The second part is dedicated to the study of (non-negatively curved) Type III Ricci flow solutions. We mainly analyze the asymptotic geometry of Type III self-similar solutions (expanding gradient Ricci soliton) with finite asymptotic curvature ratio. We prove the existence and uniqueness of their asymptotic cones. We also give algebraic and geometric sufficient conditions to guarantee rotational symmetry of such metrics. In the last part, we characterize the geometry of steady gradient Ricci solitons with nonnegative sectional curvature and linear volume growth. Finally, we study the non-collapsing of three dimensional Riemannian manifold with nonnegative Ricci curvature and finite asymptotic curvature ratio
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Hung, Pei-Ken, and 洪培根. "The Non-collapsing Property for Mean Curvature flow in S^{n+1}." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/59127804385027422218.

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碩士
國立臺灣大學
數學研究所
100
Following the same computation in [1], we use certain subelliptic operator and maximal principle to prove non-collapsing for mean curvature flow in $S^{n+1}$. We also use similar method to prove the preservation of convexity for mean curvature flow in the hyperbolic space.
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Langford, Mat. "Motion of hypersurfaces by curvature." Phd thesis, 2014. http://hdl.handle.net/1885/14119.

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It is well-known that solutions of such flows necessarily suffer finite time singularities. On the other hand, under various natural conditions, singularities are characterised by a curvature blow-up. Our first main area of study concerns the asymptotic behaviour of the curvature at a singularity. We first prove a quantitative convexity estimate for positive solutions (that is, solutions moving with inward normal speed everywhere positive) under one of the following additional assumptions: either the evolving hypersurfaces are of dimension two, or the flow speed is a convex function of the curvature. Roughly speaking, the convexity estimate states that, for positive solutions, the normalised Weingarten curvature operator is asymptotically non-negative at a singularity. We then prove a family of cylindrical estimates for flows by convex speed functions. Roughly speaking, these estimates state that, for $(m+1)$-positive solutions (that is, solutions with $(m+1)$-positive Weing! arten curvature), the Weingarten curvature is asymptotically $m$-cylindrical at a singularity unless it becomes $m$-positive. The convexity and cylindrical estimates yield a detailed description of the possible singularities which may form under surface flows and flows by convex speeds. Moreover, they are uniform across the class of solutions with given dimension, flow speed, and initial volume, diameter and curvature hull, which should make them useful for applications such as the development of flows with surgeries. Our second main area of study concerns the development, in the fully non-linear setting, of the recently discovered {\it non-collapsing} phenomena for the mean curvature flow; namely, we prove that embedded solutions of flows by concave speeds are {\it interior non-collapsing}, whilst embedded solutions of flows by convex or inverse-concave speeds are {\it exterior non-collapsing}. The non-collapsing results complement the above curvature estimates by ruling out certain types of asymptotic behaviour which the curvature estimates do not. (This is mainly due to the non-local nature of the non-collapsing estimates.) As a particular application, we show how non-collapsing gives rise to a particularly efficient proof of the Andrews--Huisken theorem on the convergence of convex hypersurfaces to {\it round points} under such flows.
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Li, Chi-Hao, and 李其澔. "Using Discrete Particle Swarm Optimization to Find Optimal Non-collapsing and Space-filling Experimental Designs." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/88927815990054632981.

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碩士
國立臺灣大學
數學研究所
102
Uniformity of experimental designs is an important issue in computer experiments recent years. To reduce the cost of handling experiment, we need to find usable designs effectively and effeciently. A design with good space-filling and non-collapsing properties may help us get the most information under some specific cost. Since a lot amount of real problems require grid discretization, based on the framework of the discrete particle swarm optimization (DPSO), we try several strategies and propose several applied methods to discuss the multi-objective issue, and will illustrate it by handling experiments on several regular and irregular feasible domains by some DPSO-based algorithms.
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Books on the topic "Non-collapsing"

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Garner, Justin, and David Treacher. Intensive care unit and ventilation. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780199657742.003.0009.

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Acute lung injury (ALI) and acute respiratory distress syndrome (ARDS) are characterized by rapidly developing hypoxaemic respiratory failure and bilateral pulmonary infiltrates on chest X-ray. ALI/ARDS are a relatively frequent diagnosis in protracted-stay patients in the intensive care unit. The pathology is a non-specific response to a wide variety of insults. Impaired gas exchange, ventilation-perfusion mismatch, and reduced compliance ensue. Mechanical ventilation is the mainstay of management, along with treatment of the underlying cause. Mortality remains very high at around 40%. The condition is challenging to treat. Injury to the lungs, indistinguishable from that of ARDS, has been attributed to the use of excessive tidal volumes, pressures, and repeated opening and collapsing of alveoli. Lung-protective strategies aim to minimize the effects of ventilator-induced lung injury. Use of low tidal volume ventilation has been shown to improve mortality. Emerging ventilatory therapies include high-frequency oscillatory ventilation and extracorporeal membrane oxygenation.
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Book chapters on the topic "Non-collapsing"

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Bisnovatyi-Kogan, G. S., and O. Y. Tsupko. "The dynamics of non-symmetrically collapsing stars." In Chaos in Astronomy, 461–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75826-6_47.

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Maleva, Olga. "Point Preimages under Ball Non-Collapsing Mappings." In Lecture Notes in Mathematics, 148–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-36428-3_13.

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Sakai, Masahiko, Michio Oyamaguchi, and Mizuhito Ogawa. "Non-E-Overlapping, Weakly Shallow, and Non-Collapsing TRSs are Confluent." In Automated Deduction - CADE-25, 111–26. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21401-6_7.

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Némethi, András, and Ágnes Szilárd. "The Collapsing Main Algorithm." In Milnor Fiber Boundary of a Non-isolated Surface Singularity, 131–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23647-1_12.

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Seibel, Wolfgang. "Politicization of the Non-politicizable: The Collapse of the Ice Skating Rink in Bad Reichenhall on 2 January 2006." In Collapsing Structures and Public Mismanagement, 129–55. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-67818-0_5.

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AbstractAfter heavy snowfall, the skating rink of the city of Bad Reichenhall collapsed on 2 January 2006. Fifteen people, twelve children between the age of 7 and 15 and three mothers, were killed by the falling debris of the roof, 34 people were injured. Court trials came to the conclusion that the City of Bad Reichenhall, over a long period of time, had seriously neglected the maintenance of the hall despite clear indication of water ingress and related weak points in the roof structure. The Lord Mayor admitted before court to have purposefully obstructed the decision of the municipal parliament to renovate the hall since he had intended to have the hall dismantled anyway and to build a modern pastime and wellness center instead.
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Seibel, Wolfgang. "Evaporated Responsibility: The Collapse of the West Gate Bridge in Melbourne on 15 October 1970." In Collapsing Structures and Public Mismanagement, 13–53. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-67818-0_2.

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AbstractOn 15 October 1970, at 11:50AM, part of the West Gate Bridge in Melbourne, span 10-11 of 367 feet length, disintegrated and triggered the collapse of the bridge. Thirty-five men were killed in the disaster. The bridge was still under construction, all those killed were workers or engineers employed on the construction site. The investigation of a Royal Commission revealed a mismatch between an ambitious structural design of the bridge plus an unconventional method of erection and a fragmented, conflict-ridden construction management whose detrimental effects remained unchecked by public authorities. Regulatory powers and enforcement competence had been delegated to a QUANGO—a quasi-non-governmental organization—which diluted responsibility structures and decisively weakened the coordination and control capacity of the agency.
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"Large Eddy Simulation of a Collapsing Vapor Bubble Containing Non-Condensable Gas." In Proceedings of the 10th International Symposium on Cavitation (CAV2018), 656–59. ASME Press, 2018. http://dx.doi.org/10.1115/1.861851_ch125.

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Johnson, Julian. "Prologue: Music and language." In After Debussy, 1–28. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190066826.003.0001.

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The Prologue explores the tension between language and music and the place that musicology might occupy as a way of thinking through that tension. Rather than collapsing this difference into the assumption that language deals adequately with music or that, conversely, music remains ineffable to language, the relationship is explored as one of non-identity that is mutually constitutive – in other words, that we understand both music and language better through an exploration of their non-identical proximity. Music is taken here to mount a challenge to philosophy – specifically, that music embodies a kind of thinking through particularity rather than thinking through the abstraction of the concept. It sets out the rationale for a musical focus on Debussy and later French composers, and a parallel exploration of French writers from Mallarmé and Bergson to Derrida and Nancy.
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Jacobsen, Jesper Lykke. "Integrability in statistical physics and quantum spin chains." In Integrability: From Statistical Systems to Gauge Theory, 1–59. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198828150.003.0001.

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This chapter illustrates basic concepts of quantum integrable systems on two important models of statistical physics: the Q-state Potts model and the O(n) model. Both models are transformed into loop and vertex models that provide representations of the dense and dilute Temperley–Lieb algebras. The identification of the corresponding integrable R-matrices leads to the solution of both models by the algebraic Bethe Ansatz technique. Elementary excitations are discussed in the critical case and the link to conformal field theory in the thermodynamic limit is established. The concluding sections outline the solution of a specific model of the theta point of collapsing polymers, leading to a continuum limit with a non-compact target space.
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Sagar, Rahul. "Hindu Nationalists and the Cold War." In India and the Cold War, 229–54. University of North Carolina Press, 2019. http://dx.doi.org/10.5149/northcarolina/9781469651163.003.0011.

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It is widely believed that at the time of Independence there was in India a broad consensus on non-alignment. This consensus, crafted by India’s first Prime Minister, Jawaharlal Nehru, is depicted as having steadily weakened over subsequent decades, eventually collapsing when diplomatic isolation and near bankruptcy toward the end of the Cold War prompted India to revitalize relations with the West. The evidence does not support this narrative, however. Drawing on a variety of sources, including Constituent Assembly debates and prominent essays, this essay shows that there were throughout the Cold War voices—often Hindu nationalists otherwise suspicious of modernity—calling for closer relations with the West. Though these voices were subdued, recollecting them reveals that post-Cold War declarations of a “natural alliance” between India and America in particular are not a new development, but instead the fruition of a longer view of the West’s significance.
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Conference papers on the topic "Non-collapsing"

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Clauss, Philippe, Ervin Altintas, and Matthieu Kuhn. "Automatic Collapsing of Non-Rectangular Loops." In 2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS). IEEE, 2017. http://dx.doi.org/10.1109/ipdps.2017.34.

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Brizuela, David, Kerstin E. Kunze, Marc Mars, and Miguel Angel Vázquez-Mozo. "Non-linear perturbations of a spherically collapsing star." In PHYSICS AND MATHEMATICS OF GRAVITATION: Proceedings of the Spanish Relativity Meeting 2008. AIP, 2009. http://dx.doi.org/10.1063/1.3141259.

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Liu, H., Z. Ren, and Y. Jia. "Refitting and Pathway Expanding Techniques for Casing Deformed Wells With Small Non-Collapsing Pathways." In Canadian International Petroleum Conference. Petroleum Society of Canada, 2002. http://dx.doi.org/10.2118/2002-183-ea.

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Ma, Jingsen, Chao-Tsung Hsiao, and Georges L. Chahine. "Euler-Lagrange Simulations of Bubble Cloud Dynamics Near a Wall." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65191.

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We present in this paper a two-way coupled Eulerian-Lagrangian model to study the dynamics of microbubble clouds exposed to incoming pressure waves and the resulting pressure loads on a nearby rigid wall. The model simulates the two-phase medium as a continuum and solves the N-S equations using Eulerian grids with a time and space varying density. The microbubbles are modeled as interacting spherical bubbles, which follow a modified Rayleigh-Plesset-Keller-Herring equation and are tracked in a Lagrangian fashion. A two-way coupling between the Euler and Lagrange components is realized through the local mixture density associated with the bubbles volume change and motion. Using this numerical framework, simulations involving a large number of bubbles were conducted under driving pressures of different frequencies. The results show that the frequency of the driving pressure is critical in determining the overall dynamics: either a collective strongly coupled cluster behavior or non-synchronized weaker multiple bubble oscillations. The former creates extremely high pressures with peak values orders of magnitudes higher than that of the excitation pressures. This occurs when the driving frequency matches the natural frequency of the bubble cloud. The initial distance between the bubble cloud and the wall is also critical on the resulting pressure loads. A bubble cloud collapsing very close to the wall exhibits a cascading collapse with the bubbles farthest from the wall collapsing first and the nearest ones collapsing last, thus the energy accumulates and then results in very violent pressure peaks at the wall. Farther from the wall, the bubble cloud collapses quasi spherically with the cloud center collapsing last.
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Oweis, Ghanem F., Jaehyug Choi, and Steven L. Ceccio. "Dynamics and Noise Emission of Laser Induced Bubbles in a Vortical Flow Field." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45484.

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The sound produced by the collapse of discreet cavitation bubbles was examined. Laser-generated cavitation bubbles were produced in both a quiescent and a vortical flow. The sound produced by the collapse of the cavitation bubbles was recorded, and its spectral content was determined. It was found that the rise time of the sound pulse produced by the collapse of single, spherical cavitation bubbles in quiescent fluid exceeded that of the slew-rate of the hydrophone, which is consistent with previously published results. It was found that, as the collapsing bubbles were deformed by the vortical flow, the acoustic impulse of the bubbles was reduced. Collapsing non-spherical bubbles often created a sound pulse with a rise time that exceeded that of the hydrophone slew-rate, although the acoustic impulse created by the bubbles was influenced largely by the degree to which the bubbles became non-spherical before collapse. The noise produced by the growth of cavitation bubbles in the vortex core was not measurable. These results have implications for the interpretation of hydrodynamic cavitation noise.
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Zhang, Shengming. "Buckling and Ultimate Strength Assessments of Ship Structures." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-11137.

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This paper presents buckling and ultimate strength assessment methods for ship structures. Buckling and collapsing analysis approaches for plates, stiffened panels and hull girders are described and their development history and employments in ship design assessments are reviewed and discussed. Examples using non-linear finite (FE) element analysis are given and comparisons between results obtained by formulae and FE analysis are carried out. Lloyd’s Register’s recent research and development work on ultimate strength and its applications to existing oil tankers and bulk carriers are also presented.
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Sato, Keiichi, Shigemasa Shimojo, and Jun Watanabe. "Observations of Chain-Reaction Behavior at Bubble Collapse Using Ultra High Speed Video Camera." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45002.

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Collapsing behavior of cavitation bubbles is a very short phenomenon. In this study a new ultra-high-speed video camera with the maximum frame speed of 106 fps is used to observe the detailed aspects of three cavitation patterns such as separated vortex cavitation in a convergent-divergent channel, Karman-vortex-like cavitation in the wake flow of a circular cylinder and vibratory cavitation in an ultrasonic vibratory apparatus. For a convergent-divergent channel, the re-entrant motion within the separation zone was observed together with bubble collapse in the divergent part. It was found that minute bubbles collapsed in a chain-reaction manner inside the separated zone with the re-entrant motion after the shedding of cavitation cloud. For the wake flow of a circular cylinder, a collapsing motion of cavitation was observed as an axial-collapse type. The successive bubble collapses after the collapse of main bubble were caused due to pressure wave near the flow field. For cavitation in a vibratory apparatus, cavitation bubbles on the vibratory disk surface were examined in detail, especially from the viewpoint of a non-cavitation ring. The disappearance of bubbles spread radially toward the outer region through the motion of vibratory horn.
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Li, Zhijian, Chao Zhang, Hui Qian, Xin Du, and Lingwei Peng. "SHPOS: A Theoretical Guaranteed Accelerated Particle Optimization Sampling Method." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/372.

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Recently, the Stochastic Particle Optimization Sampling (SPOS) method is proposed to solve the particle-collapsing pitfall of deterministic Particle Variational Inference methods by ultilizing the stochastic Overdamped Langevin dynamics to enhance exploration. In this paper, we propose an accelerated particle optimization sampling method called Stochastic Hamiltonian Particle Optimization Sampling (SHPOS). Compared to the first-order dynamics used in SPOS, SHPOS adopts an augmented second-order dynamics, which involves an extra momentum term to achieve acceleration. We establish a non-asymptotic convergence analysis for SHPOS, and show that it enjoys a faster convergence rate than SPOS. Besides, we also propose a variance-reduced stochastic gradient variant of SHPOS for tasks with large-scale datasets and complex models. Experiments on both synthetic and real data validate our theory and demonstrate the superiority of SHPOS over the state-of-the-art.
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Ferreira, V. C. S., C. S. S. M. Cordeiro, and J. W. Kaehler. "Computational Studies for the Exhausted Flue Gas." In ASME 2005 Pressure Vessels and Piping Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/pvp2005-71024.

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Pulverized coal with low average heating, producing ashes with high percentage of silica, is fired inside the furnaces of a Thermal Power Plant (TPP) of Candiota, State of Rio Grande do Sul, Brazil. The produced hot flue gas heats the water of the ECONOMIZER 01 (ECO 01) placed inside the exhausted duct. Distorted velocity profile at inlet of ECO 01 and high concentration of abrasive particles of flue gas cause drastic erosion. So intensive has been the abrasive action that some well-identified tubes end up collapsing. The unpredictable fail has caused many non-scheduled stops of the TPP. A study focused on the reduction this effect, was set up years ago. The paper shows part of this study end present results, obtained from the numerical simulation analysis of the flue gas flow. Some technical solutions are suggested to reduce the erosion of tubes providing that avoiding it showed be impossible.
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Nabika, Ryo, and Mitsuhiro Matsumoto. "MD-CFD Hybrid Simulation for Microbubble Dynamics." In ASME/JSME 2011 8th Thermal Engineering Joint Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajtec2011-44397.

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We have developed a hybrid numerical simulation code to investigate the dynamics of nanobubbles. The idea is based on a combination of a molecular dynamics (MD) technique for the region containing a bubble and surrounding area, and the lattice Boltzmann method (LBM) for the region well away from the bubble. The boundary between the two regions is movable and driven by their pressure difference. As a test of the developed code, we have performed a simulation of a collapsing nanobubble. After equilibrating the system, we introduce a uniaxial pressure wave in the continuum region far from the bubble. The pressure wave propagates through the LBM region, and the pressure difference deforms the MD-LBM boundary. As the MD region deforms, the bubble inside the region starts to collapse non-spherically. We have analyzed the bubble collapse dynamics with several different pressure waves. Vapor bubbles and bubbles containing noncondensable particles are compared.
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