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

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.

How Local Interactions Impact the Dynamics of an Epidemic

Susceptible–Infected–Recovered (SIR) models have long formed the basis for exploring epidemiological dynamics in a range of contexts, including infectious disease spread in human populations. Classic SIR models take a mean-field assumption, such that a susceptible individual has an equal chance of catching the disease from any infected individual in the population. In reality, spatial and social structure will drive most instances of disease transmission. Here we explore the impacts of including spatial structure in a simple SIR model. We combine an approximate mathematical model (using a pair approximation) and stochastic simulations to consider the impact of increasingly local interactions on the epidemic. Our key development is to allow not just extremes of ‘local’ (neighbour-to-neighbour) or ‘global’ (random) transmission, but all points in between. We find that even medium degrees of local interactions produce epidemics highly similar to those with entirely global interactions, and only once interactions are predominantly local do epidemics become substantially lower and later. We also show how intervention strategies to impose local interactions on a population must be introduced early if significant impacts are to be seen.

Spatial social dilemmas promote diversity

Cooperative investments in social dilemmas can spontaneously diversify into stably coexisting high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation, we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual-based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be understood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavorable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

Hysteretic dipolar and quadrupolar properties of the spin-1 Blume–Emery–Griffiths model under pair approximation

As a continuation of previously published work [A. Erdinç and M. Keskin, Int. J. Mod. Phys. B 18, 1603 (2004), doi:10.1142/S0217979204024823] the hysteretic properties of magnetization ([Formula: see text]) and quadrupolar moment ([Formula: see text] have been investigated for the spin-1 Blume–Emery–Griffiths model using pair approximation. The magnetic field ([Formula: see text]) dependence of [Formula: see text] is produced for different values of the lattice coordination number ([Formula: see text]), biquadratic interaction ([Formula: see text]) and single-ion anisotropy ([Formula: see text]). The ([Formula: see text]) loops show different and novelty properties when [Formula: see text]. We also observed the hysteresis cycles in the ([Formula: see text], ([Formula: see text] and ([Formula: see text]) planes. These curves strongly depend on biquadratic interaction [Formula: see text]. Our results are found to be in good agreement with the other theoretical findings.

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

We study the binary q-voter model with generalized anticonformity on random Erdős–Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence $$q_c$$ q c in case of conformity is independent from the size of the source of influence $$q_a$$ q a in case of anticonformity. For $$q_c=q_a=q$$ q c = q a = q the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for $$q_c \ge q_a + \Delta q$$ q c ≥ q a + Δ q , where $$\Delta q=4$$ Δ q = 4 for $$q_a \le 3$$ q a ≤ 3 and $$\Delta q=3$$ Δ q = 3 for $$q_a>3$$ q a > 3 . In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree $$\langle k\rangle \le 150$$ ⟨ k ⟩ ≤ 150 observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of $$\langle k\rangle$$ ⟨ k ⟩ . Moreover, we show that for $$q_a < q_c - 1$$ q a < q c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for $$q_a \ge q_c - 1$$ q a ≥ q c - 1 pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to $$\langle k\rangle$$ ⟨ k ⟩ , as long as the pair approximation indicates correctly the type of the phase transition.

Thermodynamic Optimization of the Ternary Ga-Sn-Te System Using Modified Quasichemical Model

Thermoelectric (TE) materials are of great interest to many researchers because they directly convert electric and thermal energy in a solid state. Various materials such as chalcogenides, clathrates, skutterudites, eutectic alloys, and intermetallic alloys have been explored for TE applications. The Ga-Sn-Te system exhibits promising potential as an alternative to the lead telluride (PbTe) based alloys, which are harmful to environments because of Pb toxicity. Therefore, in this study, thermodynamic optimization and critical evaluation of binary Ga-Sn, binary Sn-Te, and ternary Ga-Sn-Te systems have been carried out over the whole composition range from room temperature to above liquidus temperature using the CALPHAD method. It is observed that Sn-Te and Ga-Te liquids show the strong negative deviation from the ideal solution behavior. In contrast, the Ga-Sn liquid solution has a positive mixing enthalpy. These different thermodynamic properties of liquid solution were explicitly described using Modified Quasichemical Model (MQM) in the pair approximation. The asymmetry of ternary liquid solution in the Ga-Sn-Te system was considered by adopting the toop-like interpolation method based on the intrinsic property of each binary. The solid phase of SnTe was optimized using Compound Energy Formalism (CEF) to explain the high temperature homogeneity range, whereas solid solution, Body-Centered Tetragonal (BCT) was optimized using a regular solution model. Thermodynamic properties and phase diagram in the Ga-Sn-Te and its sub-systems were reproduced successfully by the optimized model parameters. Using the developed database, we also suggested several ternary eutectic compositions for designing TE alloy with improved properties.

Origin of diversity in spatial social dilemmas

Cooperative investments in social dilemmas can spontaneously diversify into stably co-existing high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be under-stood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavourable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.