Power laws in biology: Between fundamental regularities and useful interpolation rules

Schuster, Peter

doi:10.1002/cplx.20366

Cited by 5 publications

(5 citation statements)

References 19 publications

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“…In this context, it is worth remarking that when bed expansion data have to be treated with the Richardson-Zaki equation, then the form (2) has to be studied instead but not U = U t e n . Simultaneous determination of both U t and the exponent n through regression analysis is physically and mathematically incorrect [19][20][21]. Many readers will be confused by this statement, but we will clarify it.…”

Section: Scaling Approach In the Richardson-zaki Equationmentioning

confidence: 93%

The Richardson‐Zaki Equation Reconsidered: Derivation of the Power Law for Aerated Particle Beds

Hristov

2022

Chemie Ingenieur Technik

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Ing. Joachim Werther on the occasion of his 80th birthdayAnalytical derivations of the Richardson-Zaki power law in the case of aeratable fine particle beds where the interparticle forces allow the creation of expanded beds, known also as meta-states, with fixed structures, but not yet fluidized, have been developed. The analysis is based on the concept that the fluid flow through such beds is governed by the porous media equations such as Darcy's and Forchheimer models, upon the assumption of deformable bed structures (driven by the fluid flow) and fluid velocity independent pressure drop.

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Section: Scaling Approach In the Richardson-zaki Equationmentioning

confidence: 93%

The Richardson‐Zaki Equation Reconsidered: Derivation of the Power Law for Aerated Particle Beds

Hristov

2022

Chemie Ingenieur Technik

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“…In biology, the value β = ¾ was often proposed wrongly as a universal constant. The pace of live decreases with increasing mass 23 . In biology a broad spectrum of phenomena scale over an immense range of mass with .…”

Section: Exponential Growth and (Generalized) Logistic Growthmentioning

confidence: 96%

“…It shows the Eqs. (19)(20)(21)(22)(23) and (19c), (20c), for 'slow' decay with τ decay = 2τ growth and Eqs. (19a) and (20a) for 'fast' decay, with τ decay = τ growth /2 .…”

Section: The Verhulst Model For Limited Growth Verhulst Proposed Thementioning

confidence: 99%

Similarities between pandemics and cancer in growth and risk models

Vandamme

Hingh

Fonseca

et al. 2021

Sci Rep

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Cancer and pandemics are leading causes of death globally, with severe socioeconomic repercussions. To better understand these repercussions, we investigate similarities between pandemics and cancer and describe the limited growth in number of infections or cancer cells, using mathematical models. For a pandemic, the analysis shows that in most cases, the initial fast growth is followed by a slower decay in the recovery phase. The risk of infection increases due to the airborne virus contact crossing a risk-threshold. For cancers caused by carcinogens, the increasing risk with age and absorbed dose of toxins that cross a risk-threshold, may lead to the disease onset. The time scales are different for both causes of death: years for cancer development and days to weeks for contact with airborne viruses. Contamination by viruses is on a time scale of seconds or minutes. The risk-threshold to get ill and the number-threshold in cancer cells or viruses, may explain the large variability in the outcome. The number of infected persons per day is better represented in log–lin plots instead of the conventional lin–lin plots. Differences in therapies are discussed. Our mathematical investigation between cancer and pandemics reveals a multifactorial correlation between both fragilities and brings us one step closer to understand, timely predict and ultimately diminish the socioeconomic hurdle of both cancer and pandemics.

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“…We can consider the power‐law form of memory fading and power‐law memory functions due to the following reasons. Power laws and power‐law functions play an important role in different life and social sciences 59 : Biology 59,61,62 ; Ecology 59,63 ; Population dynamics 59,64 ; Victimology 59,60 ; Economics 59,65,66 ; Finance 66 The power‐law memory function can be considered as an approximation of the generalized memory functions.…”

Section: Lotka‐volterra Model With Kicks and Memorymentioning

confidence: 99%

“…Power laws and power‐law functions play an important role in different life and social sciences 59 : Biology 59,61,62 ; Ecology 59,63 ; Population dynamics 59,64 ; Victimology 59,60 ; Economics 59,65,66 ; Finance 66 …”

Section: Lotka‐volterra Model With Kicks and Memorymentioning

confidence: 99%

Predator‐prey models with memory and kicks: Exact solution and discrete maps with memory

Tarasov

2021

Math Methods in App Sciences

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In this paper, we proposed new predator‐prey models that take into account memory and kicks. Memory is understood as the dependence of current behavior on the history of past behavior. The equations of these proposed models are generalizations of the Lotka‐Volterra and Kolmogorov equations by using the Caputo fractional derivative of non‐integer order and periodic kicks. This fractional derivative allows us to take into account memory with power‐law fading. The periodic kicks, which are described by Dirac delta‐functions, take into account short duration of interaction between predators and prey. For the proposed equations, which are fractional differential equations with kicks, we obtain exact solutions that describe behaviors of predator and prey with power‐law fading memory. Using these exact solutions, we derive, without using any approximations, new discrete maps with memory that represent the proposed predator‐prey models with memory.

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Power laws in biology: Between fundamental regularities and useful interpolation rules

Abstract: 1 Allometry is the study of the relationship between size and shape. The original meaning of the term has been extended to all kinds of size and body mass related properties. 6C O M P L E X I T Y Q

Cited by 5 publications

References 19 publications

The Richardson‐Zaki Equation Reconsidered: Derivation of the Power Law for Aerated Particle Beds

The Richardson‐Zaki Equation Reconsidered: Derivation of the Power Law for Aerated Particle Beds

Similarities between pandemics and cancer in growth and risk models

Predator‐prey models with memory and kicks: Exact solution and discrete maps with memory

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