scholarly journals Prebiotic Aggregates (Tissues) Emerging from Reaction–Diffusion: Formation Time, Configuration Entropy and Optimal Spatial Dimension

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 124
Author(s):  
Juan Cesar Flores
Keyword(s):  
Diffusion Coefficient ◽  
Structural Parameters ◽  
Reaction Diffusion ◽  
Spatial Dimension ◽  
Formation Time ◽  
Spatial Region ◽  
Configuration Entropy ◽  
Selection Processes ◽  
Practical Tool ◽  
Basic Concepts

For the formation of a proto-tissue, rather than a protocell, the use of reactant dynamics in a finite spatial region is considered. The framework is established on the basic concepts of replication, diversity, and heredity. Heredity, in the sense of the continuity of information and alike traits, is characterized by the number of equivalent patterns conferring viability against selection processes. In the case of structural parameters and the diffusion coefficient of ribonucleic acid, the formation time ranges between a few years to some decades, depending on the spatial dimension (fractional or not). As long as equivalent patterns exist, the configuration entropy of proto-tissues can be defined and used as a practical tool. Consequently, the maximal diversity and weak fluctuations, for which proto-tissues can develop, occur at the spatial dimension 2.5.

scholarly journals Insights into the interactions and dynamics of a DES formed by phenyl propionic acid and choline chloride

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Parisa Jahanbakhsh Bonab ◽  
Alireza Rastkar Ebrahimzadeh ◽  
Jaber Jahanbin Sardroodi
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Phase ◽  
Propionic Acid ◽  
Structural Parameters ◽  
Choline Chloride ◽  
Self Diffusion ◽  
Phenyl Propionic Acid ◽  
Donor And Acceptor ◽  
Experimental Values ◽  
Self Diffusion Coefficient

AbstractDeep eutectic solvents (DESs) have received much attention in modern green chemistry as inexpensive and easy to handle analogous ionic liquids. This work employed molecular dynamics techniques to investigate the structure and dynamics of a DES system composed of choline chloride and phenyl propionic acid as a hydrogen bond donor and acceptor, respectively. Dynamical parameters such as mean square displacement, liquid phase self-diffusion coefficient and viscosity are calculated at the pressure of 0.1 MPa and temperatures 293, 321 and 400 K. The system size effect on the self-diffusion coefficient of DES species was also examined. Structural parameters such as liquid phase densities, hydrogen bonds, molecular dipole moment of species, and radial and spatial distribution functions (RDF and SDF) were investigated. The viscosity of the studied system was compared with the experimental values recently reported in the literature. A good agreement was observed between simulated and experimental values. The electrostatic and van der Waals nonbonding interaction energies between species were also evaluated and interpreted in terms of temperature. These investigations could play a vital role in the future development of these designer solvents.

scholarly journals A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine

2002 ◽  
Vol 7 (1) ◽  
pp. 27-40 ◽  
Author(s):  
Victor Kardashov ◽  
Shmuel Einav
Keyword(s):  
Nonlinear Diffusion ◽  
Structural Parameters ◽  
Deterministic Chaos ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Novel Approach ◽  
Dynamics Models ◽  
And Control

This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions).

Stability of reaction-diffusion fronts

1994 ◽  
Vol 446 (1928) ◽  
pp. 517-528 ◽  
Keyword(s):  
Growth Rate ◽  
Diffusion Coefficient ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Reaction Rate ◽  
Reaction Diffusion ◽  
Two Dimensional ◽  
Isothermal Reaction ◽  
Analytic Expression ◽  
Cubic Autocatalysis

Horvath, Petrov, Scott and Showalter (1993) have shown that isothermal reaction-diffusion fronts with cubic autocalysis are linearly unstable to two-dimensional disturbances if the ratio, δ , of the diffusion coefficient of the reactant to that of the autocatalyst, is sufficiently large. However, they were only able to obtain an analytic expression for the growth rate by assuming an infinitely thin reaction zone, which is a poor approximation for cubic autocatalysis. We have carried out a linear stability analysis of such fronts with a finite reaction rate, and find that the critical δ for instability is unchanged, but the range of unstable wavenumbers is larger and increases rather than decreases with δ .

Stability of Turing-Type Patterns in a Reaction–Diffusion System with an External Gradient

2017 ◽  
Vol 27 (01) ◽  
pp. 1750003 ◽  
Author(s):  
Tilmann Glimm ◽  
Jianying Zhang ◽  
Yun-Qiu Shen
Keyword(s):  
Diffusion Coefficients ◽  
Chemical Species ◽  
Reaction Diffusion ◽  
Spatial Dimension ◽  
Reaction Diffusion Equations ◽  
Generic Model ◽  
Bifurcation Diagrams ◽  
Analytic Approximations ◽  
Small Parameters ◽  
The Stability

We investigate the stability of Turing-type patterns in one spatial dimension in a system of reaction–diffusion equations with a term depending linearly on the spatial position. The system is a generic model of two interacting chemical species where production rates are dependent on a linear external gradient. This is motivated by mathematical models in developmental biology. In a previous paper, we found analytic approximations of Turing-like steady state patterns. In the present article, we derive conditions for the stability of these patterns and show bifurcation diagrams in two small parameters related to the slope of the external gradient and the ratio of the diffusion coefficients.

scholarly journals Nanoferrofluid Materials: Advanced Structure Monitoring Using Optical Transmission in a Magnetic Field

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Serhii Shulyma ◽  
Bogdan Tanygin ◽  
Valery Kovalenko ◽  
Michail Petrychuk
Keyword(s):  
Magnetic Field ◽  
Optical Transmission ◽  
Structural Parameters ◽  
Aggregate Size ◽  
Spatial Dimension ◽  
Laser Wavelength ◽  
Time Interval ◽  
Field Pulse ◽  
Optical Extinction ◽  
Nanoparticle Aggregates

The optical transmission of a thin ferrofluid layer was investigated at various optical radiation wavelengths. The turning on of the durable external magnetic field pulse leads to nonmonotonic changes of the optical transmission value with minimal value during the field pulse. This phenomenon is related to the formation of columnar nanoparticle aggregates and transformation in the ferrofluid bulk. It was shown that time interval corresponding to the optical transmission minimum is proportional to the laser wavelength, which can be explained with Mie-like optical extinction on the ferrofluid aggregates and its dependence on the diameters of columnar aggregates. Hence, a simple experimental approach was proposed to measure and control the ferrofluid aggregates diameters in submicron spatial dimension ranges. Particularly, this approach could be used for the formation of composite nanomaterials consisting of polymers and magnetic nanoparticles with controlled structural parameters. These materials could be reused after parameters changes (e.g., lattice constant, aggregate size, and magnetic permeability tensor) with a heating/cooling cycle without the need for preparation of a new material from scratch.

scholarly journals Stochastic simulation of the spatio-temporal dynamics of reaction-diffusion systems: the case for the bicoid gradient

2010 ◽  
Vol 7 (1) ◽  
Author(s):  
Paola Lecca ◽  
Adaoha E. C. Ihekwaba ◽  
Lorenzo Dematté ◽  
Corrado Priami
Keyword(s):  
Diffusion Coefficient ◽  
Stochastic Simulation ◽  
Diffusion Coefficients ◽  
Temporal Dynamics ◽  
Concentration Field ◽  
Reaction Diffusion ◽  
Local Concentration ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Spatio Temporal

SummaryReaction-diffusion systems are mathematical models that describe how the concentrations of substances distributed in space change under the influence of local chemical reactions, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose solution predicts how diffusion causes the concentration field to change with time. This change is proportional to the diffusion coefficient. If the solute moves in a homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and solute. However, in nonhomogeneous and structured media the assumption of constant intracellular diffusion coefficient is not necessarily valid, and, consequently, the diffusion coefficient is a function of the local concentration of solvent and solutes. In this paper we propose a stochastic model of reaction-diffusion systems, in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces. We then describe the software tool Redi (REaction-DIffusion simulator) which we have developed in order to implement this model into a Gillespie-like stochastic simulation algorithm. Finally, we show the ability of our model implemented in the Redi tool to reproduce the observed gradient of the bicoid protein in the Drosophila Melanogaster embryo. With Redi, we were able to simulate with an accuracy of 1% the experimental spatio-temporal dynamics of the bicoid protein, as recorded in time-lapse experiments obtained by direct measurements of transgenic bicoidenhanced green fluorescent protein.

scholarly journals The influence of autotoxicity on the dynamics of vegetation spots

2020 ◽  
Author(s):  
Annalisa Iuorio ◽  
Frits Veerman
Keyword(s):  
Dynamical System ◽  
Reaction Diffusion ◽  
Homoclinic Orbits ◽  
Spatial Dimension ◽  
Travelling Wave ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Scaling Analysis ◽  
Water Models ◽  
Vegetation Water

AbstractPlant autotoxicity has proved to play an essential role in the behaviour of local vegetation. We analyse a reaction-diffusion-ODE model describing the interactions between vegetation, water, and autotoxicity. The presence of autotoxicity is seen to induce movement and deformation of spot patterns in some parameter regimes, a phenomenon which does not occur in classical biomass-water models. We aim to analytically quantify this novel feature, by studying travelling wave solutions in one spatial dimension. We use geometric singular perturbation theory to prove the existence of symmetric, stationary and non-symmetric, travelling pulse solutions, by constructing appropriate homoclinic orbits in the associated 5-dimensional dynamical system. In the singularly perturbed context, we perform an extensive scaling analysis of the dynamical system, identifying multiple asymptotic scaling regimes where (travelling) pulses may or may not be constructed. We discuss the agreement and discrepancy between the analytical results and numerical simulations. Our findings indicate how the inclusion of an additional ODE may significantly influence the properties of classical biomass-water models of Klausmeier/Gray–Scott type.

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