scholarly journals Heterogeneous Pair Approximation of Methanol Oxidation on TiO2 Reveals Two Reaction Pathways

2021 ◽  
Author(s):  
Changhae Andrew Kim ◽  
Troy Van Voorhis
Keyword(s):  
Methanol Oxidation ◽  
Rate Constants ◽  
Mean Field ◽  
Pair Approximation ◽  
Static Disorder ◽  
Pairwise Correlation ◽  
Dynamic Correlation ◽  
Activity Group ◽  
Hole Scavenger ◽  
Novel Method

We propose a novel method to simulate the chemical kinetics of methanol oxidation on the rutile TiO2(110) surface. This method must be able to capture the effects of static disorder (site-to-site variations in the rate constants), as well as dynamic correlation (interdependent probabilities of finding reactants and products next to each other). Combining the intuitions of the mean-field steady state (MFSS) method and the pair approximation (PA), we consider representative pairs of sites in a self-consistent bath of the average pairwise correlation. Pre-averaging over the static disorder in one site of each pair makes this half heterogeneous pair approximation (HHPA) efficient enough to simulate systems of several species and calibrate rate constants. According to the simulated kinetics, a static disorder in the hole transfer steps suffices to reproduce the stretched exponentials in the observed kinetics. The identity of the dominant hole scavenger is found to be temperature-dependent -- the methoxy anion at 80 K and the methanol molecule at 180 K. Moreover, two distinct groups of 5-coordinate titanium (Ti5c) sites emerge -- a high-activity group and a low-activity group -- even though no such division exists in the rate constants. Since the division is quite insensitive to the type of static disorder, the emergence of the two groups might play a significant role in a variety of photocatalytic processes on TiO2.

scholarly journals Pair approximation model for the vaccination game: predicting the dynamic process of epidemic spread and individual actions against contagion

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200769
Author(s):  
Kazuki Kuga ◽  
Masaki Tanaka ◽  
Jun Tanimoto
Keyword(s):  
Dynamic Process ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pair Approximation ◽  
Order Effects ◽  
Epidemic Spread ◽  
Underlying Network ◽  
Individual Actions ◽  
Individual Decisions

We successfully establish a theoretical framework of pairwise approximation for the vaccination game in which both the dynamic process of epidemic spread and individual actions in helping prevent social behaviours are quantitatively evaluated. In contrast with mean-field approximation, our model captures higher-order effects from neighbours by using an underlying network that shows how the disease spreads and how individual decisions evolve over time. This model considers not only imperfect vaccination but also intermediate protective measures other than vaccines. Our analytical predictions are validated by multi-agent simulation results that estimate random regular graphs at varying degrees.

Determination of Hydrogen Density of States in Amorphous Silicon Using Fractional Evolution Experiments

1997 ◽  
Vol 467 ◽  
Author(s):  
A. J. Franz ◽  
W. B. Jackson ◽  
J. L. Gland
Keyword(s):  
Amorphous Silicon ◽  
Density Of States ◽  
Silicon Film ◽  
Mean Field ◽  
Frequency Factor ◽  
Silicon Films ◽  
Hydrogen Density ◽  
Heating And Cooling ◽  
Novel Method

ABSTRACTHydrogen plays an important role in the electronic behavior, structure and stability of amorphous silicon films. Therefore, determination of the hydrogen density of states (DOS) and correlation of the hydrogen DOS with the electronic film properties are important research goals. We have developed a novel method for determination of hydrogen DOS in silicon films, based on fractional evolution experiments. Fractional evolution experiments are performed by subjecting a silicon film to a series of linear, alternating heating and cooling ramps, while monitoring the hydrogen evolution rate. The fractional evolution data can be analyzed using two complementary memods, the fixed frequency factor approach and Arrhenius analysis. Using a rigorous, mean-field evolution model, we demonstrate the applicability of the two approaches to obtaining the hydrogen DOS in silicon films. We further validate both methods by analyzing experimental fractional evolution data foran amorphous silicon carbide film. Both types of analysis yield a similar double peaked density of states for the a-Si:C:H:D film.

Symmetry-preserving mean field theory for electrostatics at interfaces

2014 ◽  
Vol 50 (92) ◽  
pp. 14397-14400 ◽  
Author(s):  
Zhonghan Hu
Keyword(s):  
Field Theory ◽  
Computer Simulations ◽  
Mean Field Theory ◽  
Mean Field ◽  
Molecular Liquids ◽  
Novel Method

A novel method is developed for complex nonuniform electrostatics in computer simulations of molecular liquids at interfaces.

Relative rate constants for reactions of hydroxyl radicals from the reaction of Fe(II) or Ti(III) with H2O2

1969 ◽  
Vol 47 (20) ◽  
pp. 3737-3744 ◽  
Author(s):  
W. A. Armstrong
Keyword(s):  
Hydrogen Peroxide ◽  
Hydroxyl Radicals ◽  
Rate Constants ◽  
Relative Rate ◽  
Chloride Ion ◽  
Strong Electron ◽  
Spin Resonance ◽  
Relative Rate Constants ◽  
Novel Method ◽  
Hydroxyl Radical Scavengers

In an attempt to clarify the reactions of ferrous sulfate and titanous sulfate with hydrogen peroxide, a novel method has been developed to determine the relative rate constants for reactions of the oxidizing species generated in these systems. These species react with hydrogen peroxide to give perhydroxyl radicals which combine with titanium(IV) ions to form the relatively stable TiOO•3+ radical. This radical gives a strong electron spin resonance signal and the competition between hydrogen peroxide and a scavenger for the oxidizing species can be followed by measuring the amplitude of this signal in the presence of various concentrations of scavenger. The relative rate constants calculated in this way for both the Fe(II)–H2O2 and Ti(III)–H2O2 systems at pH 1.0 agree with those reported for the reactions of hydroxyl radicals in γ-irradiated thymine solutions. This supports the view that hydroxyl radicals are formed in these cases.Under conditions of acidity favoring the hydrolysis of Fe(II) to FeOH+ ions, hydroxyl radical scavengers do not compete with hydrogen peroxide for the precursors of the TiOO•3+ radical. It is suggested that the FeOH+ ions react with hydrogen peroxide to give a different oxidizing species, possibly the ferryl ion.Scavengers investigated were thymine, methanol, ethanol, formic acid, acetic acid, chloride ion, and several amino acids.

scholarly journals Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes

2018 ◽  
Vol 97 (1) ◽  
Author(s):  
Charalampos Kyriakopoulos ◽  
Gerrit Grossmann ◽  
Verena Wolf ◽  
Luca Bortolussi
Keyword(s):  
Mean Field ◽  
Pair Approximation ◽  
Contact Processes

The Critical Behavior of the General Spin Blume–Capel Model

1998 ◽  
Vol 12 (20) ◽  
pp. 2045-2061 ◽  
Author(s):  
D. Peña Lara ◽  
J. A. Plascak
Keyword(s):  
Phase Diagram ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Mean Field Theory ◽  
Mean Field ◽  
Pair Approximation ◽  
Temperature Anisotropy ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
The Mean

The general spin-S Blume–Capel model is studied within two different approaches: the pair approximation for the free energy, and Monte Carlo simulations. The global phase diagram in the temperature-anisotropy plane is obtained for general values of S in the pair approximation and the results are qualitatively the same as those of the usual mean field theory. Special interest is given in the low temperature region of the phase diagram where a number of first-order lines emerge from a multiphase point at the ground state. Monte Carlo simulations for S=1, 3/2, and 2 on simple cubic lattices also confirm the general trend of the mean field like approach, and in the special S=3/2 case the present results are in disagreement with previous Monte Carlo simulations, as well as renormalization group calculations on corresponding two-dimensional lattices.

A novel method to clarify nonlinear equivalent circuits of tunnel diodes by extracting rate constants for nonequilibrium electrons

2011 ◽  
Vol 9 (2) ◽  
pp. 278-281
Author(s):  
Kiyoto Asakawa ◽  
Yuji Kurakami ◽  
Mitsufumi Saito ◽  
Michihiko Suhara
Keyword(s):  
Rate Constants ◽  
Equivalent Circuits ◽  
Tunnel Diodes ◽  
Novel Method
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