Quasi-isotropic and locked grain growth dynamics in a three-phase eutectic system

In vivo tumours are highly heterogeneous entities which often comprise intratumoural regions of hypoxia and widespread necrosis. In this paper, we develop a new three phase model of nutrient-limited, avascular tumour growth to investigate how dead material within the tumour may influence the tumour’s growth dynamics. We model the tumour as a mixture of tumour cells, dead cellular material and extracellular fluid. The model equations are derived using mass and momentum balances for each phase along with appropriate constitutive equations. The tumour cells are viewed as a viscous fluid pressure, while the extracellular fluid phase is viewed as inviscid. The physical properties of the dead material are intermediate between those of the tumour cells and extracellular fluid, and are characterised by three key parameters. Through numerical simulation of the model equations, we reproduce spatial structures and dynamics typical of those associated with the growth of avascular tumour spheroids. We also characterise novel, non-monotonic behaviours which are driven by the internal dynamics of the dead material within the tumour. Investigations of the parameter sub-space describing the properties of the dead material reveal that the way in which non-viable tumour cells are modelled may significantly influence the qualitative tumour growth dynamics.

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Grain Growth Dynamics in Winter Wheat Crops

Annals of Botany ◽

10.1093/oxfordjournals.aob.a087577 ◽

1988 ◽

Vol 61 (4) ◽

pp. 459-472 ◽

Cited By ~ 5

Author(s):

Z. S. CHALABI ◽

W. DAY ◽

V. B. A. WILLINGTON ◽

P. V. BISCOE

Keyword(s):

Winter Wheat ◽

Grain Growth ◽

Growth Dynamics

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Creep characteristics of alumina, nickel aluminate spinel, zirconia composites

Journal of Materials Research ◽

10.1557/jmr.2008.0071 ◽

2008 ◽

Vol 23 (2) ◽

pp. 556-564 ◽

Cited By ~ 3

Author(s):

R. Peter Dillon ◽

Dong-Kyu Kim ◽

Joy E. Trujillo ◽

Waltraud M. Kriven ◽

Martha L. Mecartney

Keyword(s):

High Temperature ◽

Grain Growth ◽

Mechanical Stability ◽

True Strain ◽

Tetragonal Zirconia ◽

Ceramic Composites ◽

High Temperature Deformation ◽

Temperature Deformation ◽

Nickel Aluminate ◽

Three Phase

Fine grained, three-phase ceramic composites that exhibit favorable toughness, hardness, and high room-temperature strength were evaluated for high-temperature mechanical stability. A 50vol%Al2O3–25vol%NiAl2O4–25vol%3 mol%yttria-stabilized tetragonal zirconia polycrystal (3Y–TZP) and a 33vol%Al2O3–33vol%NiAl2O4–33vol%3Y-TZP composite were compression creep tested at temperatures between 1350 and 1450 °C under constant stresses of 20–45 MPa. The three-phase microstructure effectively limited grain growth (average d0 = 1.3 μm, average df = 1.6 μm after 65% true strain). True strain rates were 10−4 to 10−6 s−1 with stress exponents n = 1.7 to 1.8 and a grain-size exponent p = 1.3. A method for compensating for grain growth is presented using stress jump tests. The apparent activation energy for high-temperature deformation for 50vol%Al2O3–25vol%NiAl2O4–25vol%3Y–TZP was found to be 373 kJ/mol-K.

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Preparation of zinc oxide seed grains

Journal of Materials Research ◽

10.1557/jmr.1994.0164 ◽

1994 ◽

Vol 9 (1) ◽

pp. 164-167 ◽

Cited By ~ 1

Author(s):

Wang Liangbin ◽

Li Xiao-Guang ◽

Xiang Xinyu ◽

Chen Chun ◽

Zhang Yuheng

Keyword(s):

Zinc Oxide ◽

Grain Boundary ◽

Grain Growth ◽

Boundary Diffusion ◽

Classical Model ◽

Growth Dynamics ◽

Energy Difference ◽

Weight Percent ◽

Boiling Water ◽

Square Root

ZnO seed grains are derived from washing ZnO-BaO sintered disks in boiling water. The grain growth of ZnO results from the energy difference across a curved grain boundary. The growth dynamics of ZnO grains and the dissolution of BaO in the boiling water are studied. The classical model shows that the growth of ZnO grains depends on grain boundary diffusion. The dissolution of BaO in boiling water can be considered as the diffusion of BaO in boiling water. The weight percent of BaO dissolved in boiling water varies linearly with the thickness of ZnO-BaO sintered disks and the reciprocal of the square root of the boiling time.

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