On the Aboav–Weaire law

Vincze, Gyula; Zsoldos, Ibolya; Szász, András

doi:10.1016/j.geomphys.2003.08.003

Cited by 13 publications

(6 citation statements)

References 24 publications

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“…Even if the scattering is high (R = 0.335), it can be noted that the slope of the linear regression curve calculated from our data (s = −0.168) is very close to that reported by Vincze et al (s ′ = −1/6, with a coefficient of determination even lower, R ′ = 0.21 [49]). In figure 6 the variation of ρ (quotient a/µ 2 ) as a function of µ 2 (with µ 2 ranging from 0.14 to 4.3) is plotted, for various natural structures including our crack networks.…”

Section: Relations Between Topological Quantitiessupporting

confidence: 89%

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Topological and metric properties of microscopic crack patterns: application to thermal fatigue of high temperature tool steels

Roux¹,

Rézaï-Aria²

2013

J. Phys. D: Appl. Phys.

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The topological properties of heat-checking patterns, produced on the oxidized surface of high temperature tool steels under thermal fatigue experiments, are investigated using image analysis methods. All crack networks are composed of polygonal cells with a mean number of sides close to 6. Whatever the thermal cycling conditions, the semi-empirical Aboav-Weaire's and Lewis' laws are quite well verified. The least-squares fit parameters of these laws are discussed and compared with values reported in the literature for other random cellular structures. It is shown that the heat-checking cells undergo a strong shrinkage and that the cellular organization is rather disordered at the beginning of the fragmentation process. The heat-checking networks evolve towards a more stable and ordered state upon cycling. Most disordered cellular networks are obtained at low maximal temperatures and low heating rates. The slope of Lewis' law is mainly dependent on the maximum heat-flux density applied to the specimen during the heating period. Whatever the test conditions, the stabilized heat-checking networks obey a unique normalized Lewis' law.

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Section: Relations Between Topological Quantitiessupporting

confidence: 89%

“…It seems that the parameters of Aboav-Weaire's law (a and µ 2 ) are interdependent [40,49]. Figure 5 shows that there is a tendency for the decrease of the system-constant a when the variance µ 2 becomes larger:…”

Section: Relations Between Topological Quantitiesmentioning

confidence: 97%

Topological and metric properties of microscopic crack patterns: application to thermal fatigue of high temperature tool steels

Roux¹,

Rézaï-Aria²

2013

J. Phys. D: Appl. Phys.

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“…n is the second central moment of the distribution of n, and γ is a constant that may decrease as σ 2 n increases [44,45], or may be independent of σ 2 n [46]. This relation has been commonly used to explore the topology of tessellations and arrangements in cellular assemblies [40,47,48].…”

Section: Universal Topology Of Homeostatic Statesmentioning

confidence: 99%

On the mechanical regulation of epithelial tissue homeostasis

Kaliman

Hubert

Wollnik

et al. 2021

Preprint

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Despite recent efforts to understand homeostasis in epithelial tissues, there are many unknowns surrounding this steady state. It is considered to be regulated by mechanoresponse, but unlike for single cells, this remains heavily debated for tissues. Here, we show that changes in matrix stiffness induce a non-equilibrium transition from tubular to squamous Madin-Darby Canine Kidney II tissues. Nonetheless, despite different cell morphologies and densities, all homeostatic tissues display equivalent topologies, which, hence, must be actively targeted and regulated. On the contrary, the mechanoresponse induces dramatic changes in the large-scale organization of the colonies. On stiff gels, this yields an unreported cooperative state of motile cells displaying higher densities than in the arrested homeostatic state. This suggests a more complex relation between cell density and motility than previously anticipated. Our results unequivocally relate the mechanosensitive properties of individual cells to the evolving macroscopic structures, an effect that could be important for understanding the emergent pathologies of living tissues.

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“…The morphology is an important factor of the cellular organization, [37], and varies by kind of tissues. Cellular structures have coordination constrains preferring special coordination arrangements [38], and form self-organized collectivity [39] [40]. The tendency of proliferation is low in the population having small number of cells [41].…”

Section: Method-selection Parameters In Nanoscopic Rangementioning

confidence: 99%

Bioelectromagnetic Paradigm of Cancer Treatment—Modulated Electro-Hyperthermia (mEHT)

Szász¹

2019

OJBIPHY

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One of the most frequently applied bioelectromagnetic effects is the deep heating of the living species with EMF energy. Despite its long history, hyperthermia is a rarely applied oncotherapy. The reason is its controversial results and complicated control. One of the solutions is concentrating the electromagnetic energy nanoscopically on the parts of the malignant cells instead of heating up the complete tumor-mass. This approach is a kind of non-uniform energy absorption, providing energy liberation only in the selected regions. The energy-absorption of the malignant cells targets the membranes and creates a situation far from thermal equilibrium. The selection of the malignant cells is based on their decided differences from their healthy counterparts. The distinguishing parameters are the electromagnetic properties of the components of the malignant tissue which are the physiologic differences between the malignant cells and their healthy counterparts. The targets realize nano-range heating, using natural nanoclusters on the cell-membrane without artificially implementing them. This energy absorption generates consequent reactions, like programmed cell-death (apoptosis) continued by immunogenic cell-death involving extended immune reactions. The applied radiofrequency current is amplitude modulated by time-fractal modulation pattern. The accurately matched impedance realizes the self-selective mechanisms which are promoted by stochastic resonances. This complex method is a new kind of hyperthermia, named mEHT. Our objective is to analyze the problems of the selective, non-equilibrium energy absorption, and present a solution by the electromagnetic mechanisms for an effective and controllable hyperthermia in oncology.

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On the Aboav–Weaire law

Cited by 13 publications

References 24 publications

Topological and metric properties of microscopic crack patterns: application to thermal fatigue of high temperature tool steels

Topological and metric properties of microscopic crack patterns: application to thermal fatigue of high temperature tool steels

On the mechanical regulation of epithelial tissue homeostasis

Bioelectromagnetic Paradigm of Cancer Treatment—Modulated Electro-Hyperthermia (mEHT)

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