scholarly journals Nonclassical Kinetics in Constrained Geometries: Initial Distribution Effects

1998 ◽  
Vol 08 (05) ◽  
pp. 853-868 ◽  
Author(s):  
K. Lindenberg ◽  
A. H. Romero ◽  
J. M. Sancho
Keyword(s):  
Initial Density ◽  
Reaction Diffusion ◽  
Initial Distribution ◽  
Density Fluctuations ◽  
Time Behavior ◽  
Numerical Work ◽  
Irreversible Reaction ◽  
Long Wavelength ◽  
Reaction Diffusion Model

We present a detailed study of the effects of the initial distribution on the kinetic evolution of the irreversible reaction A+B→0 in one dimension. Our analytic as well as numerical work is based on a reaction–diffusion model of this reaction. We focus on the role of initial density fluctuations in the creation of the macroscopic patterns that lead to the well-known kinetic anomalies in this system. In particular, we discuss the role of the long wavelength components of the initial fluctuations in determining the long-time behavior of the system. We note that the frequently studied random initial distribution is but one of a variety of possible distributions leading to interesting anomalous behavior. Our discussion includes an initial distribution with correlated A-B pairs and one in which the initial distribution forms a fractal pattern. The former is an example of a distribution whose long wavelength components are suppressed, while the latter exemplifies one whose long wavelength components are enhanced, relative to those of the random distribution.

Initial Distribution Effects on Diffusion-Limited Reactions in Constrained Geometries

1996 ◽  
Vol 464 ◽  
Author(s):  
Katja Lindenberg ◽  
A. H. Romero ◽  
J. M. Sancho
Keyword(s):  
Initial Density ◽  
Initial Distribution ◽  
Anomalous Behavior ◽  
Density Fluctuations ◽  
Low Dimensions ◽  
Long Wavelength ◽  
Diffusion Limited ◽  
The Creation ◽  
Initial Distributions

ABSTRACTWe present a study of the effects of the initial distribution on the kinetic evolution of irreversible binary reactions in low dimensions. We focus on the role of initial density fluctuations and, in particular, on the role of the long wavelength components of the initial fluctuations, in the creation of the macroscopic patterns that lead to the well-known kinetic anomalies in this system. The frequently studied random initial distribution is but one of a variety of possible distributions leading to interesting anomalous behavior. Our discussion includes initial distributions that suppress and ones that enhance the initial long wavelength components.

MIXING IN REACTION-DIFFUSION PROBLEMS

1991 ◽  
Vol 05 (20) ◽  
pp. 3127-3164 ◽  
Author(s):  
I.M. SOKOLOV ◽  
A. BLUMEN
Keyword(s):  
Time Evolution ◽  
Geometrical Structure ◽  
Reaction Diffusion ◽  
Initial Distribution ◽  
Present Review ◽  
Viscous Liquids ◽  
Irreversible Reaction ◽  
Diffusion Problems

Mixing of two viscous liquids often produces arrays of alternating striations. The geometrical structure of these arrays controls the course of the reactions between the liquids, both when the reaction occurs after mixing and also when mixing and reaction take place simultaneously. In the present review we consider some aspects of the problem for the A+B→0 irreversible reaction under stoichiometric conditions. We focus on the influence of the initial distribution of striation thicknesses, on the time evolution of this distribution, on the structure of the reaction layers and on the role of mixing.

scholarly journals A Reaction-Diffusion Model for Interference in Meiotic Crossing Over

Genetics ◽  
2002 ◽  
Vol 161 (1) ◽  
pp. 365-372 ◽  
Author(s):  
Youhei Fujitani ◽  
Shintaro Mori ◽  
Ichizo Kobayashi
Keyword(s):  
Genetic Distance ◽  
Diffusion Model ◽  
Genetic Model ◽  
Initial Density ◽  
Reaction Diffusion ◽  
Crossover Point ◽  
Random Walker ◽  
Random Walkers ◽  
Reaction Diffusion Model ◽  
Two Parameters

Abstract One crossover point between a pair of homologous chromosomes in meiosis appears to interfere with occurrence of another in the neighborhood. It has been revealed that Drosophila and Neurospora, in spite of their large difference in the frequency of crossover points, show very similar plots of coincidence—a measure of the interference—against the genetic distance of the interval, defined as one-half the average number of crossover points within the interval. We here propose a simple reaction-diffusion model, where a “randomly walking” precursor becomes immobilized and matures into a crossover point. The interference is caused by pair-annihilation of the random walkers due to their collision and by annihilation of a random walker due to its collision with an immobilized point. This model has two parameters—the initial density of the random walkers and the rate of its processing into a crossover point. We show numerically that, as the former increases and/or the latter decreases, plotted curves of the coincidence vs. the genetic distance converge on a unique curve. Thus, our model explains the similarity between Drosophila and Neurospora without parameter values adjusted finely, although it is not a “genetic model” but is a “physical model,” specifying explicitly what happens physically.

scholarly journals Reaction-diffusion model as framework for understanding the role of riboflavin in “eye defence” formulations

RSC Advances ◽  
2020 ◽  
Vol 10 (25) ◽  
pp. 14965-14971
Author(s):  
Francesca Di Nezza ◽  
Ciro Caruso ◽  
Ciro Costagliola ◽  
Luigi Ambrosone
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Eye Drops ◽  
Reaction Diffusion Model ◽  
Visible Spectra ◽  
Uv Visible

Analysis of UV-visible spectra, performed on commercial riboflavin-based eye drops, showed that absorbance is a saturating function of vitamin concentration.

Role of dark excitations in the nonequilibrium condensation of exciton polaritons in optically-pumped organic single crystal microcavities

2015 ◽  
Vol 29 (22) ◽  
pp. 1550157 ◽  
Author(s):  
Svitlana Zaster ◽  
Eric R. Bittner
Keyword(s):  
Reaction Diffusion ◽  
Optically Pumped ◽  
Reaction Diffusion Model ◽  
Exciton Polaritons ◽  
Organic Single Crystal ◽  
Dielectric Mirrors ◽  
Dynamical Regimes ◽  
Nonequilibrium Condensation ◽  
External Driving

We present a reaction/diffusion model for the formation of a lower polariton condensate in a microcavity containing an organic semiconducting molecular crystalline film. Our model–based upon an anthracene film sandwiched between two reflecting dielectric mirrors–consists of three coupled fields corresponding to a gas of excitons created by an external driving pulse, a reservoir of dark states formed by the nonemissive decay of excitons in to nearby electronic states, and a lower polariton condensate. We show that at finite temperature, the presence of the dark reservoir can augment the exciton population such that a lower critical pumping threshold is required to achieve the critical exciton densities required to sustain a stable condensate population. Using linear-stability analysis, we show that a variety of dynamical regimes can emerge depending upon the characteristics of the cavity and the lattice temperature.

Initially Separated Reaction-Diffusion Systems

1994 ◽  
Vol 366 ◽  
Author(s):  
Haim Taitelbaum ◽  
Baruch Vilensky ◽  
Yong-Eun Lee Koo ◽  
Andrew Yen ◽  
Anna Lin ◽  
...  
Keyword(s):  
Reaction Front ◽  
Theoretical Study ◽  
Initial Density ◽  
Reaction Diffusion ◽  
Time Behavior ◽  
Reaction Diffusion Systems ◽  
System Parameters ◽  
Diffusion Systems ◽  
Reaction Constant ◽  
Asymptotic Time

ABSTRACTCharacteristics of the A + B → C reaction-diffusion system with initially separated components are studied theoretically and experimentally. When the reaction is slow, the two species will mix before reacting. This leads to a series of crossovers from a rich initial behavior to an asymptotic time behavior. The crossovers depend on the system parameters, such as the diffusion coefficients and initial densities of the two species. In this paper we review our recent studies on this system. We elaborate on a theoretical study of momentum effects, and then focus on theoretical explanations of two experimental phenomena: 1) Non-universal and non-monotonic motion of the reaction front center. The latter occurs when one of the reactants has larger diffusion coefficient but smaller initial density. 2) Existence of more than one front. This occurs when two different transformations of the same reactant (on one of the sides of the system), react with the reactant on the other side with a different reaction constant - the majority slowly, but the minority much faster.

scholarly journals Source-sink dynamics can maintain mismatched range and bioclimatic limits even at large spatial scales

2020 ◽  
Author(s):  
Nikunj Goel ◽  
Timothy H. Keitt
Keyword(s):  
Spatial Scales ◽  
Reaction Diffusion ◽  
Dispersal Distance ◽  
Life Strategy ◽  
Stepping Stones ◽  
Reaction Diffusion Model ◽  
Primary Determinant ◽  
Source Sink ◽  
Bioclimatic Envelope

AbstractBioclimatic models assume that at broad spatial scales, climate is the primary determinant of species distribution. Meanwhile, processes such as source-sink dynamics can be ignored because they are thought to manifest at length scales comparable to species mean dispersal distance. We present a reaction-diffusion model to show species can use sink patches near the bioclimatic (or niche) limit as stepping-stones to occupy sinks much further than the mean dispersal distance, thereby extending the distribution far beyond the bioclimatic envelope. This mismatch between geographical and bioclimatic limits is mediated by the shape of the bioclimatic limit and may be significant for low growth sensitivity and fast dispersal life strategy. These findings challenge one of the core assumptions of the bioclimatic models. Therefore, we advocate that biogeographers consider the role of dispersal when using bioclimatic models to generate inferences about the ecological and evolutionary processes that determine the distribution of biota.

scholarly journals The Role of Cytoplasmic Interactions in the Collective Polarization of Tissues and its Interplay with Cellular Geometry

2018 ◽  
Author(s):  
Shahriar Shadkhoo ◽  
Madhav Mani
Keyword(s):  
Large Scale ◽  
Planar Cell Polarity ◽  
Reaction Diffusion ◽  
Directional Information ◽  
Collective Response ◽  
Reaction Diffusion Model ◽  
Necessary And Sufficient ◽  
Molecular Components ◽  
Theory And Experiments

AbstractPlanar cell polarity (PCP), the ability of a tissue to polarize coherently over multicellular length scales, provides the directional information that guides a multitude of developmental processes at cellular and tissue levels. While it is manifest that cells utilize both intra-cellular and intercellular mechanisms, how they couple together to produce the collective response remains an active area of investigation. Exploring a phenomeno-logical reaction-diffusion model, we predict a crucial, and novel, role for cytoplasmic interactions in the large-scale correlations of cell polarities. We demonstrate that finite-range (i.e. nonlocal) cytoplasmic interactions are necessary and sufficient for the robust and long-range polarization of tissues — even in the absence of global cues — and are essential to the faithful detection of weak directional signals. Strikingly, our model re-capitulates an observed influence of anisotropic tissue geometries on the orientation of polarity. In order to facilitate a conversation between theory and experiments, we compare five distinct classes of in silico mutants with experimental observations. Within this context, we propose quantitative measures that can guide the search for the participant molecular components, and the identification of their roles in the collective polarization of tissues.

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