A+B→0 AND A+A→0 CHEMICAL REACTIONS UNDER ENHANCED DIFFUSION CONDITIONS THROUGH THOMPSON'S METHOD

2001 ◽  
Vol 15 (26) ◽  
pp. 1205-1215 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA

In this work we use Thompson's method to study both A+B→0 and A+A→0 reactions under anomalous diffusion regimes. We consider a general action encompassing the two kinds of reactions, by including a non-brownian (γ<2) superdiffusion mechanism, for instance, Levy-mixing. Such a kind of mechanism leads to a continuous mixing of the reactants, which homogenizes the system, thereby partially suppressing the fluctuations. We show that for [Formula: see text], the segregation disappears in d=3 in the A+B→0 reaction in agreement with previous results of Zumofen, Klafter and Shlesinger. This last result can be interpreted as the erosion of the segregation in d=3. In the A+A→0 reaction, the superdiffusion mechanism leads to the decreasing of the upper critical dimension (d c ). We also show that, at d c , we always obtain logarithmic corrections both for the reactant concentrate decays (<∊>) and for the reaction rates (<K>).

2021 ◽  
pp. 1-12
Author(s):  
Andrey Viktorovich Podlazov

I investigate the nature of the upper critical dimension for isotropic conservative sandpile models and calculate the emerging logarithmic corrections to power-law distributions. I check the results experimentally using the case of Manna model with the theoretical solution known for all statement starting from the two-dimensional one. In addition, based on this solution, I construct a non-trivial super-universal indicator for this model. It characterizes the distribution of avalanches by time the border of their region needs to pass its width.


2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marco Panero ◽  
Antonio Smecca

Abstract We present a high-precision Monte Carlo study of the classical Heisenberg model in four dimensions. We investigate the properties of monopole-like topological excitations that are enforced in the broken-symmetry phase by imposing suitable boundary conditions. We show that the corresponding magnetization and energy-density profiles are accurately predicted by previous analytical calculations derived in quantum field theory, while the scaling of the low-energy parameters of this description questions an interpretation in terms of particle excitations. We discuss the relevance of these findings and their possible experimental applications in condensed-matter physics.


2021 ◽  
Vol 2 (1) ◽  
pp. 168-186
Author(s):  
Bahareh Vafakish ◽  
Lee D. Wilson

The nanoreactor concept and its application as a modality to carry out chemical reactions in confined and compartmentalized structures continues to receive increasing attention. Micelle-based nanoreactors derived from various classes of surfactant demonstrate outstanding potential for chemical synthesis. Polysaccharide (glycan-based) surfactants are an emerging class of biodegradable, non-toxic, and sustainable alternatives over conventional surfactant systems. The unique structure of glycan-based surfactants and their micellar structures provide a nanoenvironment that differs from that of the bulk solution, and supported by chemical reactions with uniquely different reaction rates and mechanisms. In this review, the aggregation of glycan-based surfactants to afford micelles and their utility for the synthesis of selected classes of reactions by the nanoreactor technique is discussed. Glycan-based surfactants are ecofriendly and promising surfactants over conventional synthetic analogues. This contribution aims to highlight recent developments in the field of glycan-based surfactants that are relevant to nanoreactors, along with future opportunities for research. In turn, coverage of research for glycan-based surfactants in nanoreactor assemblies with tailored volume and functionality is anticipated to motivate advanced research for the synthesis of diverse chemical species.


Author(s):  
Tom Hutchcroft

AbstractWe study long-range Bernoulli percolation on $${\mathbb {Z}}^d$$ Z d in which each two vertices x and y are connected by an edge with probability $$1-\exp (-\beta \Vert x-y\Vert ^{-d-\alpha })$$ 1 - exp ( - β ‖ x - y ‖ - d - α ) . It is a theorem of Noam Berger (Commun. Math. Phys., 2002) that if $$0<\alpha <d$$ 0 < α < d then there is no infinite cluster at the critical parameter $$\beta _c$$ β c . We give a new, quantitative proof of this theorem establishing the power-law upper bound $$\begin{aligned} {\mathbf {P}}_{\beta _c}\bigl (|K|\ge n\bigr ) \le C n^{-(d-\alpha )/(2d+\alpha )} \end{aligned}$$ P β c ( | K | ≥ n ) ≤ C n - ( d - α ) / ( 2 d + α ) for every $$n\ge 1$$ n ≥ 1 , where K is the cluster of the origin. We believe that this is the first rigorous power-law upper bound for a Bernoulli percolation model that is neither planar nor expected to exhibit mean-field critical behaviour. As part of the proof, we establish a universal inequality implying that the maximum size of a cluster in percolation on any finite graph is of the same order as its mean with high probability. We apply this inequality to derive a new rigorous hyperscaling inequality $$(2-\eta )(\delta +1)\le d(\delta -1)$$ ( 2 - η ) ( δ + 1 ) ≤ d ( δ - 1 ) relating the cluster-volume exponent $$\delta $$ δ and two-point function exponent $$\eta $$ η .


1984 ◽  
Vol 55 (6) ◽  
pp. 1646-1648 ◽  
Author(s):  
Susan R. McKay ◽  
A. Nihat Berker

Author(s):  
Yongkang Peng ◽  
Xiaoyue Chen ◽  
Yeqiang Deng ◽  
Lan Lei ◽  
Zhan Haoyu ◽  
...  

Abstract The traditional corona discharge fluid model considers only electrons, positive and negative ions, and the discharge parameters are determined using the simplified weighting method involving the partial pressure ratio. Atmospheric pressure discharge plasma in humid air involves three main neutral gas molecule types: N2, O2, and H2O(g). However, in these conditions, the discharge process involves many types of particles and chemical reactions, and the charge and substance transfer processes are complex. At present, the databases of plasma chemical reaction equations are still expanding based on scholarly research. In this study, we examined the key particles and chemical reactions that substantially influence plasma characteristics. In summarizing the chemical reaction model for the discharge process of N2–O2–H2O(g) mixed gases, 65 particle types and 673 chemical reactions were investigated. On this basis, a global model of atmospheric pressure humid air discharge plasma was developed, with a focus on the variation of charged particles densities and chemical reaction rates with time under the excitation of a 0–200 Td pulsed electric field. Particles with a density greater than 1% of the electron density were classified as key particles. For such particles, the top ranking generation or consumption reactions (i.e., where the sum of their rates was greater than 95% of the total rate of the generation or consumption reactions) were classified as key chemical reactions On the basis of the key particles and reactions identified, a simplified global model was derived. A comparison of the global model with the simplified global model in terms of the model parameters, particle densities, reaction rates (with time), and calculation efficiencies demonstrated that both models can adequately identify the key particles and chemical reactions reflecting the chemical process of atmospheric pressure discharge plasma in humid air. Thus, by analyzing the key particles and chemical reaction pathways, the charge and substance transfer mechanism of atmospheric pressure pulse discharge plasma in humid air was revealed, and the mechanism underlying water vapor molecules’ influence on atmospheric pressure air discharge was elucidated.


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