{1 1 1} facet growth laws and grain competition during silicon crystallization

This paper describes a 3D structure-imitation computer model of evolution of the powder compact during sinteringand recrystallization without nucleation. At the initial stages of the evolution processes (sintering until a mosaic structure of boundaries is formed) the model particles are spheres, and two-particle interaction laws control their evolution. During sintering the degree of mutual penetration of the particles increases, regions where spherical particles are wholly facetted by contacts with neighboring particles are formed and grow. These particles are described using the formalism of Voronoi radical polyhedra, and grain growth laws govern their evolution. The model predicts the time dependencies of the following structure parameters of the polyhedra: average polyhedron size and dispersion, total surface of the facets of the polyhedra and total lenght of the edges of the polyhedra.

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Simple growth laws and selection consequences

Trends in Ecology & Evolution ◽

10.1016/0169-5347(91)90228-p ◽

1991 ◽

Vol 6 (11) ◽

pp. 366-370 ◽

Cited By ~ 49

Author(s):

Eörs Szathmáry

Keyword(s):

Growth Laws ◽

Simple Growth

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Emergence of protocellular growth laws

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2007.2076 ◽

2007 ◽

Vol 362 (1486) ◽

pp. 1841-1845 ◽

Cited By ~ 19

Author(s):

Tristan Rocheleau ◽

Steen Rasmussen ◽

Peter E Nielsen ◽

Martin N Jacobi ◽

Hans Ziock

Keyword(s):

Kinetic Studies ◽

Product Inhibition ◽

Replication Process ◽

Gene Replication ◽

Math Biol ◽

Curr Opin Cell Biol ◽

Growth Laws ◽

Internal Gene ◽

The Many ◽

The Individual

Template-directed replication is known to obey a parabolic growth law due to product inhibition (Sievers & Von Kiedrowski 1994 Nature 369 , 221; Lee et al . 1996 Nature 382 , 525; Varga & Szathmáry 1997 Bull. Math. Biol . 59 , 1145). We investigate a template-directed replication with a coupled template catalysed lipid aggregate production as a model of a minimal protocell and show analytically that the autocatalytic template–container feedback ensures balanced exponential replication kinetics; both the genes and the container grow exponentially with the same exponent. The parabolic gene replication does not limit the protocellular growth, and a detailed stoichiometric control of the individual protocell components is not necessary to ensure a balanced gene–container growth as conjectured by various authors (Gánti 2004 Chemoton theory ). Our analysis also suggests that the exponential growth of most modern biological systems emerges from the inherent spatial quality of the container replication process as we show analytically how the internal gene and metabolic kinetics determine the cell population's generation time and not the growth law (Burdett & Kirkwood 1983 J. Theor. Biol . 103 , 11–20; Novak et al . 1998 Biophys. Chem . 72 , 185–200; Tyson et al . 2003 Curr. Opin. Cell Biol . 15 , 221–231). Previous extensive replication reaction kinetic studies have mainly focused on template replication and have not included a coupling to metabolic container dynamics (Stadler et al . 2000 Bull. Math. Biol . 62 , 1061–1086; Stadler & Stadler 2003 Adv. Comp. Syst . 6 , 47). The reported results extend these investigations. Finally, the coordinated exponential gene–container growth law stemming from catalysis is an encouraging circumstance for the many experimental groups currently engaged in assembling self-replicating minimal artificial cells (Szostak 2001 et al . Nature 409 , 387–390; Pohorille & Deamer 2002 Trends Biotech . 20 123–128; Rasmussen et al . 2004 Science 303 , 963–965; Szathmáry 2005 Nature 433 , 469–470; Luisi et al . 2006 Naturwissenschaften 93 , 1–13). 1

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Creep crack growth laws in heat-resistant steels

Engineering Fracture Mechanics ◽

10.1016/0013-7944(91)90178-4 ◽

1991 ◽

Vol 40 (6) ◽

pp. 1147-1163 ◽

Cited By ~ 2

Author(s):

V.A. Vainshtok ◽

M.V. Baumshtein ◽

I.A. Makovetskaya ◽

I.V. Kramarenko

Keyword(s):

Crack Growth ◽

Creep Crack Growth ◽

Creep Crack ◽

Heat Resistant ◽

Growth Laws ◽

Heat Resistant Steels

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Handling Uncertainty in the Remnant Fatigue Life Assessment of Offshore Process Pipework

Volume 14: Emerging Technologies; Materials: Genetics to Structures; Safety Engineering and Risk Analysis ◽

10.1115/imece2016-65504 ◽

2016 ◽

Cited By ~ 2

Author(s):

Arvind Keprate ◽

R. M. Chandima Ratnayake

Keyword(s):

Fatigue Life ◽

Crack Growth ◽

Life Assessment ◽

Assessment Process ◽

Linear Elastic ◽

Fatigue Life Assessment ◽

Process Piping ◽

Growth Laws ◽

Elastic Fracture ◽

Offshore Industry

A typical procedure for a remnant fatigue life (RFL) assessment is stated in the BS-7910 standard. The aforementioned standard provides two different methodologies for estimating RFL; these are: the S-N curve approach and the crack growth laws (i.e. using Linear Elastic Fracture Mechanics (LEFM) principles) approach. Due to its higher accuracy, the latter approach is more commonly used for RFL assessment in the offshore industry. Nevertheless, accurate prediction of RFL using the deterministic LEFM approach (stated in BS-7910) is a challenging task, as RFL prediction is afflicted with a high number of uncertainties. Furthermore, BS-7910 does not provide any recommendation in regard to handling the uncertainty in the deterministic RFL assessment process. The most common way of dealing with the aforementioned uncertainty is to employ Probabilistic Crack Growth (PCG) models for estimating the RFL. This manuscript explains the procedure for addressing the uncertainty in the RFL assessment of process piping with the help of a numerical example. The numerically obtained RFL estimate is used to demonstrate a calculation of inspection interval.

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Bacterial growth laws reflect the evolutionary importance of energy efficiency

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1421138111 ◽

2014 ◽

Vol 112 (2) ◽

pp. 406-411 ◽

Cited By ~ 87

Author(s):

Arijit Maitra ◽

Ken A. Dill

Keyword(s):

Energy Efficiency ◽

Bacterial Growth ◽

Growth Conditions ◽

High Energy ◽

Fast Growth ◽

Growth Speed ◽

Energy Costs ◽

Extensive Literature ◽

E Coli ◽

Growth Laws

We are interested in the balance of energy and protein synthesis in bacterial growth. How has evolution optimized this balance? We describe an analytical model that leverages extensive literature data on growth laws to infer the underlying fitness landscape and to draw inferences about what evolution has optimized inEscherichia coli. IsE. colioptimized for growth speed, energy efficiency, or some other property? Experimental data show that at its replication speed limit,E. coliproduces about four mass equivalents of nonribosomal proteins for every mass equivalent of ribosomes. This ratio can be explained if the cell’s fitness function is the the energy efficiency of cells under fast growth conditions, indicating a tradeoff between the high energy costs of ribosomes under fast growth and the high energy costs of turning over nonribosomal proteins under slow growth. This model gives insight into some of the complex nonlinear relationships between energy utilization and ribosomal and nonribosomal production as a function of cell growth conditions.

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