scholarly journals The role of order and disorder in thermal and material sciences part 2: Scientific world and new insights

2003 ◽  
Vol 39 (3-4) ◽  
pp. 407-425
Author(s):  
Jaroslav Sesták
Keyword(s):  
Open Systems ◽  
Thermal Environment ◽  
Reaction Diffusion ◽  
Big Bang ◽  
Alternative Theory ◽  
Order And Disorder ◽  
Self Organized ◽  
Reaction Diffusion Model ◽  
Basic Ideas ◽  
The Impact

The notion of heat is thoroughly analyzed and its historical links are search particularly with relation to both the Greek philosophy (Mile in print sians Pythagoreans, atomists, etc) and the in the present day thermal physics. Fluctuation, spontaneity and chaos is discussed. Thermodynamics is reviewed in the relation to both the traditional development and the modern description of disequilibria (open systems). Effect of dissipation is shown often to provide new, self-organized structures. Exploitation of fire and its conscious use as a manufacturing power are analyzed in terms of generalized engines to act in the sense of as the information transducers. The part 2 reveals the impact of mathematics as explained on some simple cases showing development of basic ideas (vibration, topology, bifurcations etc). Earth thermal environment is discussed in relation to the existence of life (antropy principles). Alternative theory of reaction-diffusion model of the space-time is put in contrast with big bang hypothesis and related to the herewith-discussed specialty of self-catalyzed chemical reactions. The text gives a consistent view to various historical and modern concepts that emerged during the gradual understanding of order and disorder.

scholarly journals The influence of density in population dynamics with strong and weak Allee effect

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kamrun Nahar Keya ◽  
Md. Kamrujjaman ◽  
Md. Shafiqul Islam
Keyword(s):  
Population Dynamics ◽  
Allee Effect ◽  
Global Bifurcation ◽  
Reaction Diffusion ◽  
Logistic Growth ◽  
Allee Effects ◽  
Reaction Diffusion Model ◽  
Positive Steady States ◽  
The Stability ◽  
The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

scholarly journals Self-organized criticality and pattern emergence through the lens of tropical geometry

2018 ◽  
Vol 115 (35) ◽  
pp. E8135-E8142 ◽  
Author(s):  
N. Kalinin ◽  
A. Guzmán-Sáenz ◽  
Y. Prieto ◽  
M. Shkolnikov ◽  
V. Kalinina ◽  
...  
Keyword(s):  
Mirror Symmetry ◽  
Tropical Geometry ◽  
Scaling Limit ◽  
Reaction Diffusion ◽  
Auction Theory ◽  
Discrete Models ◽  
Self Organized ◽  
Reaction Diffusion Model ◽  
Pure Mathematics ◽  
Self Organized Criticality

Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation.

scholarly journals Microbial competition reduces interaction distances to the low µm-range

2020 ◽  
Author(s):  
Rinke J. van Tatenhove-Pel ◽  
Tomaž Rijavec ◽  
Aleš Lapanje ◽  
Iris van Swam ◽  
Emile Zwering ◽  
...  
Keyword(s):  
Effective Interaction ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Dimensional System ◽  
Cellular Interactions ◽  
Natural Ecosystems ◽  
Concentration Gradients ◽  
Reaction Diffusion Model ◽  
The Impact ◽  
Three Dimensional System

AbstractMetabolic interactions between cells affect microbial community compositions and hence their function in ecosystems. It is well-known that under competition for the exchanged metabolite, concentration gradients constrain the distances over which interactions can occur. However, interaction distances are typically quantified in two-dimensional systems or without accounting for competition or other metabolite-removal, conditions which may not very often match natural ecosystems. We here analyze the impact of cell-to-cell distance on unidirectional cross-feeding in a three-dimensional system with competition for the exchanged metabolite. Effective interaction distances were computed with a reaction-diffusion model and experimentally verified by growing a synthetic consortium of 1 µm-sized metabolite producer, receiver and competitor cells in different spatial structures. We show that receivers cannot interact with producers ∼15 µm away from them, as product concentration gradients flatten close to producer cells. We developed an aggregation protocol and created variants of the receiver cells’ import system, to show that within producer-receiver aggregates even low affinity receiver cells could interact with producers. These results show that competition or other metabolite-removal of a public good in a three-dimensional system reduces the interaction distance to the low micrometer-range, highlighting the importance of concentration gradients as physical constraint for cellular interactions.

scholarly journals The role of order and disorder in thermal and material sciences part 1: Heat and society

2002 ◽  
Vol 38 (1-2) ◽  
pp. 1-22 ◽  
Author(s):  
J. Sesták
Keyword(s):  
Open Systems ◽  
Greek Philosophy ◽  
Thermal Physics ◽  
Order And Disorder ◽  
Self Organized ◽  
Material Sciences

The notion of heat is thoroughly analyzed and its historical links are searched particularly with relation to both the Greek philosophy (Milesians, Pythagoreans, atomists, etc.) and in the present day thermal physics. Fluctuation, spontaneity and chaos are discussed. Thermodynamics is reviewed in the relation to both the traditional development and the modern description of disequilibria (open systems). Effect of dissipation is shown often to provide new, self-organized structures. Exploitation of fire and its conscious use as a manufacturing power are analyzed in terms of generalized engines to act in the sense of the information transducers.

scholarly journals Why microbes secrete molecules to modify their environment: the case of iron-chelating siderophores

2019 ◽  
Vol 16 (150) ◽  
pp. 20180674 ◽  
Author(s):  
Gabriel E. Leventhal ◽  
Martin Ackermann ◽  
Konstanze T. Schiessl
Keyword(s):  
Iron Uptake ◽  
Large Fraction ◽  
Reaction Diffusion ◽  
Iron Particles ◽  
Diffusion Limitation ◽  
Iron Solubility ◽  
Reaction Diffusion Model ◽  
Particulate Iron ◽  
The Impact ◽  
Release Strategy

Many microorganisms secrete molecules that interact with resources outside of the cell. This includes, for example, enzymes that degrade polymers like chitin, and chelators that bind trace metals like iron. In contrast to direct uptake via the cell surface, such release strategies entail the risk of losing the secreted molecules to environmental sinks, including ‘cheating’ genotypes. Nevertheless, such secretion strategies are widespread, even in the well-mixed marine environment. Here, we investigate the benefits of a release strategy whose efficiency has frequently been questioned: iron uptake in the ocean by secretion of iron chelators called siderophores. We asked the question whether the release itself is essential for the function of siderophores, which could explain why this risky release strategy is widespread. We developed a reaction–diffusion model to determine the impact of siderophore release on iron uptake from the predominant iron sources in marine environments, colloidal or particulate iron, formed due to poor iron solubility. We found that release of siderophores is essential to accelerate iron uptake, as secreted siderophores transform slowly diffusing large iron particles to small, quickly diffusing iron–siderophore complexes. In addition, we found that cells can synergistically share their siderophores, depending on their distance and the size of the iron sources. Our study helps understand why release of siderophores is so widespread: even though a large fraction of siderophores is lost, the solubilization of iron through secreted siderophores can efficiently increase iron uptake, especially if siderophores are produced cooperatively by several cells. Overall, resource uptake mediated via release of molecules transforming their substrate could be essential to overcome diffusion limitation specifically in the cases of large, aggregated resources. In addition, we find that including the reaction of the released molecule with the substrate can impact the result of cooperative and competitive interactions, making our model also relevant for release-based uptake of other substrates.

scholarly journals Effect of Bulk Composition on the Heterogeneous Oxidation of Semi-Solid Atmospheric Aerosols

Atmosphere ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 791
Author(s):  
Hanyu Fan ◽  
Fabien Goulay
Keyword(s):  
Atmospheric Aerosols ◽  
Bulk Composition ◽  
Particle Surface ◽  
Reaction Diffusion ◽  
Solid Particles ◽  
Molar Ratio ◽  
Heterogeneous Oxidation ◽  
Reaction Diffusion Model ◽  
Semi Solid ◽  
The Impact

The OH-initiated heterogeneous oxidation of semi-solid saccharide particles with varying bulk compositions was investigated in an atmospheric pressure flow tube at 30% relative humidity. Reactive uptake coefficients were determined from the rate loss of the saccharide reactants measured by mass spectrometry at different monosaccharide (methyl-β-d-glucopyranoside, C7H14O6) and disaccharide (lactose, C12H22O11) molar ratios. The reactive uptake for the monosaccharide was found to decrease from 0.53 ± 0.10 to 0.05 ± 0.06 as the mono-to-disaccharide molar ratio changed from 8:1 to 1:1. A reaction–diffusion model was developed in order to determine the effect of chemical composition on the reactive uptake. The observed decays can be reproduced using a Vignes relationship to predict the composition dependence of the reactant diffusion coefficients. The experimental data and model results suggest that the addition of the disaccharide significantly increases the particle viscosity leading to slower mass transport phenomena from the bulk to the particle surface and to a decreased reactivity. These findings illustrate the impact of bulk composition on reactant bulk diffusivity which determines the rate-limiting step during the chemical transformation of semi-solid particles in the atmosphere.

Pattern Formation and Oscillations in Reaction–Diffusion Model with p53-Mdm2 Feedback Loop

2019 ◽  
Vol 29 (14) ◽  
pp. 1930040 ◽  
Author(s):  
Qianqian Zheng ◽  
Jianwei Shen ◽  
Zhijie Wang
Keyword(s):  
Pattern Formation ◽  
Feedback Loop ◽  
Reaction Diffusion ◽  
Vital Role ◽  
Reaction Diffusion Equation ◽  
Biological Mechanism ◽  
Reaction Diffusion Model ◽  
The Impact ◽  
Theoretical Results ◽  
Diffusive System

P53 plays a vital role in DNA repair, and several mathematical models of the p53-Mdm2 feedback loop were used to explain the biological mechanism. In this paper, a p53-Mdm2 model described by a delay reaction–diffusion equation is studied both analytically and numerically. This research aims to provide an understanding of the impact of delay and sustained pressure on the p53-Mdm2 dynamics and tries to explain some biological mechanism. It is found that the type of pattern formation is affected by Hopf bifurcation. Also, the amplitude equation in delay diffusive system is derived and it is shown that sustained stress plays an essential role in the function of p53. Finally, simulation is used to verify the theoretical results.

scholarly journals Meta-modeling on detailed geography for accurate prediction of invasive alien species dispersal

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Nick Pepper ◽  
Luca Gerardo-Giorda ◽  
Francesco Montomoli
Keyword(s):  
Invasive Species ◽  
Alien Species ◽  
Temporal Dynamics ◽  
Coupled Model ◽  
Reaction Diffusion ◽  
Model Complexity ◽  
Model Parameters ◽  
Northern Spain ◽  
Reaction Diffusion Model ◽  
The Impact

Abstract Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematical approaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on the assumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can be considered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in different situations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC) to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suited to handle important landscape heterogeneities as elevation and the complex geometries associated with the boundaries of an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing the uncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain.

scholarly journals Pattern formation on a growing oblate spheroid. an application to adult sea urchin development

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Deborah Lacitignola ◽  
Massimo Frittelli ◽  
Valerio Cusimano ◽  
Andrea De Gaetano
Keyword(s):  
Sea Urchin ◽  
Adult Stage ◽  
Reaction Diffusion ◽  
Oblate Spheroid ◽  
Gene Control ◽  
Control Networks ◽  
Model Driven ◽  
Reaction Diffusion Model ◽  
The Impact ◽  
Theoretical Results

<p style='text-indent:20px;'>In this study, the formation of the adult sea urchin shape is rationalized within the Turing's theory paradigm. The emergence of protrusions from the expanding underlying surface is described through a reaction-diffusion model with Gray-Scott kinetics on a growing oblate spheroid. The case of slow exponential isotropic growth is considered. The model is first studied in terms of the spatially homogenous equilibria and of the bifurcations involved. Turing diffusion-driven instability is shown to occur and the impact of the slow exponential growth on the resulting Turing regions adequately discussed. Numerical investigations validate the theoretical results showing that the combination between an inhibitor and an activator can result in a distribution of spot concentrations that underlies the development of ambulacral tentacles in the sea urchin's adult stage. Our findings pave the way for a model-driven experimentation that could improve the current biological understanding of the gene control networks involved in patterning.</p>

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