Simplified Procedures for Fitting a Gompertz Curve and a Modified Exponential Curve

Sherman, Jack E.; Morrison, Winifred J.

doi:10.2307/2280430

Cited by 2 publications

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“…An example of population dynamics is the law of Benjamin Gompertz, 1825. 12 This selflimiting growth function has been used to describe growth and mortality of populations [13][14][15][16][17][18][19][20] like humans, animals or bacteria. In contrast to the symmetric logistic function, which found its way into physics and chemistry, Gompertz's function is hardly known outside the population dynamics community, 19 perhaps due to its strange double exponential approach and its asymmetry.…”

Section: Introductionmentioning

confidence: 99%

Kinetics of bulk polymerisation and Gompertz's law

Schmitt

Schulze-Pillot

Hempelmann

2011

Phys. Chem. Chem. Phys.

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The kinetics of bulk photo-polymerisation of multifunctional monomers, leading to highly cross-linked polymers, has been investigated by in situ real-time Raman spectroscopy. The decrease with time of the monomer content is described by a modified Gompertzian function originally developed for population dynamics. This function is flexible enough to take into account inhibitor effect, gel effect and glass effect which are characteristic for curing of technical polymer coatings. Layers of commercial acrylic resins with a thickness of 50 μm, with commercial initiators, are taken as model systems for the UV-curing. The proof-of-concept is presented that the combination of Raman hardware and Gompertzian software enables systematic laboratory tests of curable systems.

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Section: Introductionmentioning

confidence: 99%

Kinetics of bulk polymerisation and Gompertz's law

Schmitt

Schulze-Pillot

Hempelmann

2011

Phys. Chem. Chem. Phys.

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“…where k has mutatis mutandis the same meaning as M , the carrying capacity, in the Verhulst approach. Fits to Gompertz double exponential law can be searched for with different techniques [20,21,22,23,24,25,26], still imposing the amplitude y M to be an integer. It has occurred after much simulations that two distinct regimes must be considered, exactly as in the analysis along Verhulst approach: one at low time, i.e.…”

Section: Evolution Study Gompertz Equationmentioning

confidence: 99%

Another Analytic View About Quantifying Social Forces

Ausloos¹

2013

Advs. Complex Syst.

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Montroll had considered a Verhulst evolution approach for introducing a notion he called "social force", to describe a jump in some economic output when a new technology or product outcompetes a previous one. In fact, Montroll's adaptation of Verhulst equation is more like an economic field description than a "social force". The empirical Verhulst logistic function and the Gompertz double exponential law are used here in order to present an alternative view, within a similar mechanistic physics framework. As an example, a "social force" modifying the rate in the number of temples constructed by a religious movement, the Antoinist community, between 1910 and 1940 in Belgium is found and quantified. Practically, two temple inauguration regimes are seen to exist over different time spans, separated by a gap attributed to a specific "constraint", a taxation system, but allowing for a different, smooth, evolution rather than a jump. The impulse force duration is also emphasized as being better taken into account within the Gompertz framework. Moreover, a "social force" can be as here, attributed to a change in the limited need/capacity of some population, coupled to some external field, in either Verhulst or Gompertz equation, rather than resulting from already existing but competing goods as imagined by Montroll.

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Simplified Procedures for Fitting a Gompertz Curve and a Modified Exponential Curve

Cited by 2 publications

References 0 publications

Kinetics of bulk polymerisation and Gompertz's law

Kinetics of bulk polymerisation and Gompertz's law

Another Analytic View About Quantifying Social Forces

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