How Accurate Is the Mean-Field Approximation for Catalytic Kinetics?

Modelling catalytic kinetics is indispensable for the design of reactors and chemical processes. Currently, the majority of kinetic models employ mean-field approximations and are formulated as ordinary differential equations, which leads to an approximate description of catalytic kinetics by omitting spatial correlations. On the other hand, kinetic Monte Carlo (KMC) approaches provide a discrete-space continuous-time stochastic formulation that enables a detailed treatment of spatial correlations in the adlayer, but at a significant computation expense. Such spatial correlations arise from slow diffusion in tandem with 2-site reactions, or from adsorbate-adsorbate lateral interactions, and have been shown to markedly affect the observed kinetics. It is thus well known that mean-field models are limited, as they neglect such correlations; yet, due to their computational efficiency, such approaches are ideal in multiscale modelling frameworks (for instance as chemistry modules in computational fluid dynamics). However, it is possible to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail but at the cost of higher computational effort. In this study, we assess the error and computational efficiency of mean-field and higher order approximations for kinetics in catalytic systems with strongly interacting adsorbates. We thus focus on a model for NO oxidation incorporating first nearest neighbor lateral interactions and construct a sequence of approximate models of progressively higher accuracy, starting from the mean-field treatment and continuing with a sequence of Bethe-Peierls models with increasing cluster sizes. By comparing the turnover frequencies of these models with those obtained from KMC simulation, we show that the mean-field predictions deviate by several orders of magnitude from the KMC simulation results. The Bethe-Peierls model, with a cluster incorporating sites up to 2nd nearest neighbors, performs well for predicting coverages; however, due to the exponential dependence of reaction rate on activation energy, the turnover frequency predictions are still inadequate. One requires Bethe-Peierls approximations with clusters of 4th or higher nearest neighbors, in order to faithfully reproduce the KMC predictions. We show that such approximations, while more computationally intense than the mean-field treatment, still enable significant computational savings compared to a KMC simulation, thereby paving the road for employing them in multiscale modelling frameworks

Experimental and Theoretical Studies of the Environmental Sensitivity of the Absorption Spectra and Photochemistry of Nitenpyram and Analogs

Neonicotinoid (NN) pesticides have widespread use, largely replacing other pesticides such as the carbamates. Hence, there is a need to understand their environmental fates at a molecular level in various media, especially water. We report here the studies of a nitroenamine NN, nitenpyram (NPM), in aqueous solution where the absorption cross sections in the actinic region above 290 nm are observed to dramatically decrease compared to those in nonaqueous solvents. Quantum chemical calculations show that addition of a proton to the tertiary amine nitrogen in NPM breaks the conjugation in the chromophore, shifting the absorption to shorter wavelengths, consistent with experiment. However, surprisingly, adding a proton to the secondary amine nitrogen leads to its immediate transfer to the NO2 group, preserving the conjugation. This explains why the UV absorption of ranitidine (RAN), which has a similar chromophore but only secondary amine nitrogens, does not show a similar large blue shift in water. Photolysis quantum yields in aqueous NPM solutions were measured to be φ = 0.18 ± 0.07 at 254 nm, (9.4 ± 1.6) × 10-2 with broadband radiation centered at 313 nm and (5.2 ± 1.1) × 10-2 for broadband radiation centered at 350 nm (errors are 2σ). The major products in aqueous solutions are an imine that was also formed in the photolysis of the solid and a carboxylic acid derivative that is unique to the photolysis in water. Combining the larger quantum yields in water with the reduced absorption cross sections results in a calculated lifetime of NPM of only 5 min at a solar zenith angle of 35°, typical of 40°N latitude on April 1. The products do not absorb in the actinic region and hence will be long-lived with respect to photolysis

Feedback-induced nonlinearity and superconducting on-chip quantum optics

Quantum coherent feedback has been proven to be an efficient way to tune the dynamics of quantum optical systems and, recently, those of solid-state quantum circuits. Here, inspired by the recent progress of quantum feedback experiments, especially those in mesoscopic circuits, we prove that superconducting circuit QED systems, shunted with a coherent feedback loop, can change the dynamics of a superconducting transmission line resonator, i.e., a linear quantum cavity, and lead to strong on-chip nonlinear optical phenomena. We find that bistability can occur under the semiclassical approximation, and photon anti-bunching can be shown in the quantum regime. Our study presents new perspectives for engineering nonlinear quantum dynamics on a chip.Comment: 10 pages, 9 figure

A Computational Study of the Weak Galerkin Method for Second-Order Elliptic Equations

The weak Galerkin finite element method is a novel numerical method that was first proposed and analyzed by Wang and Ye for general second order elliptic problems on triangular meshes. The goal of this paper is to conduct a computational investigation for the weak Galerkin method for various model problems with more general finite element partitions. The numerical results confirm the theory established by Wang and Ye. The results also indicate that the weak Galerkin method is efficient, robust, and reliable in scientific computing.Comment: 19 page

Oral tolerance to cancer can be abrogated by T regulatory cell inhibition

Oral administration of tumour cells induces an immune hypo-responsiveness known as oral tolerance. We have previously shown that oral tolerance to a cancer is tumour antigen specific, non-cross-reactive and confers a tumour growth advantage. We investigated the utilisation of regulatory T cell (Treg) depletion on oral tolerance to a cancer and its ability to control tumour growth. Balb/C mice were gavage fed homogenised tumour tissue – JBS fibrosarcoma (to induce oral tolerance to a cancer), or PBS as control. Growth of subcutaneous JBS tumours were measured; splenic tissue excised and flow cytometry used to quantify and compare systemic Tregs and T effector (Teff) cell populations. Prior to and/or following tumour feeding, mice were intraperitoneally administered anti-CD25, to inactivate systemic Tregs, or given isotype antibody as a control. Mice which were orally tolerised prior to subcutaneous tumour induction, displayed significantly higher systemic Treg levels (14% vs 6%) and faster tumour growth rates than controls (p<0.05). Complete regression of tumours were only seen after Treg inactivation and occurred in all groups - this was not inhibited by tumour feeding. The cure rates for Treg inactivation were 60% during tolerisation, 75% during tumour growth and 100% during inactivation for both tolerisation and tumour growth. Depletion of Tregs gave rise to an increased number of Teff cells. Treg depletion post-tolerisation and post-tumour induction led to the complete regression of all tumours on tumour bearing mice. Oral administration of tumour tissue, confers a tumour growth advantage and is accompanied by an increase in systemic Treg levels. The administration of anti-CD25 Ab decreased Treg numbers and caused an increase in Teffs. Most notably Treg cell inhibition overcame established oral tolerance with consequent tumor regression, especially relevant to foregut cancers where oral tolerance is likely to be induced by the shedding of tumour tissue into the gut

Marked long-term decline in ambient CO mixing ratio in SE England, 1997–2014:Evidence of policy success in improving air quality

Atmospheric CO at Egham in SE England has shown a marked and progressive decline since 1997, following adoption of strict controls on emissions. The Egham site is uniquely positioned to allow both assessment and comparison of ‘clean Atlantic background’ air and CO-enriched air downwind from the London conurbation. The decline is strongest (approximately 50ppb per year) in the 1997–2003 period but continues post 2003. A ‘local CO increment’ can be identified as the residual after subtraction of contemporary background Atlantic CO mixing ratios from measured values at Egham. This increment, which is primarily from regional sources (during anticyclonic or northerly winds) or from the European continent (with easterly air mass origins), has significant seasonality, but overall has declined steadily since 1997. On many days of the year CO measured at Egham is now not far above Atlantic background levels measured at Mace Head (Ireland). The results are consistent with MOPITT satellite observations and ‘bottom-up’ inventory results. Comparison with urban and regional background CO mixing ratios in Hong Kong demonstrates the importance of regional, as opposed to local reduction of CO emission. The Egham record implies that controls on emissions subsequent to legislation have been extremely successful in the UK

Quantitative model for inferring dynamic regulation of the tumour suppressor gene p53

Background: The availability of various "omics" datasets creates a prospect of performing the study of genome-wide genetic regulatory networks. However, one of the major challenges of using mathematical models to infer genetic regulation from microarray datasets is the lack of information for protein concentrations and activities. Most of the previous researches were based on an assumption that the mRNA levels of a gene are consistent with its protein activities, though it is not always the case. Therefore, a more sophisticated modelling framework together with the corresponding inference methods is needed to accurately estimate genetic regulation from "omics" datasets. Results: This work developed a novel approach, which is based on a nonlinear mathematical model, to infer genetic regulation from microarray gene expression data. By using the p53 network as a test system, we used the nonlinear model to estimate the activities of transcription factor (TF) p53 from the expression levels of its target genes, and to identify the activation/inhibition status of p53 to its target genes. The predicted top 317 putative p53 target genes were supported by DNA sequence analysis. A comparison between our prediction and the other published predictions of p53 targets suggests that most of putative p53 targets may share a common depleted or enriched sequence signal on their upstream non-coding region. Conclusions: The proposed quantitative model can not only be used to infer the regulatory relationship between TF and its down-stream genes, but also be applied to estimate the protein activities of TF from the expression levels of its target genes

Complexity without chaos: Plasticity within random recurrent networks generates robust timing and motor control

It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent dynamics for two main reasons: nonlinear recurrent networks often exhibit chaotic behavior and most known learning rules do not work in robust fashion in recurrent networks. Here we address both these problems by demonstrating how random recurrent networks (RRN) that initially exhibit chaotic dynamics can be tuned through a supervised learning rule to generate locally stable neural patterns of activity that are both complex and robust to noise. The outcome is a novel neural network regime that exhibits both transiently stable and chaotic trajectories. We further show that the recurrent learning rule dramatically increases the ability of RRNs to generate complex spatiotemporal motor patterns, and accounts for recent experimental data showing a decrease in neural variability in response to stimulus onset

Evolution of Cooperation and Coordination in a Dynamically Networked Society

Situations of conflict giving rise to social dilemmas are widespread in society and game theory is one major way in which they can be investigated. Starting from the observation that individuals in society interact through networks of acquaintances, we model the co-evolution of the agents' strategies and of the social network itself using two prototypical games, the Prisoner's Dilemma and the Stag Hunt. Allowing agents to dismiss ties and establish new ones, we find that cooperation and coordination can be achieved through the self-organization of the social network, a result that is non-trivial, especially in the Prisoner's Dilemma case. The evolution and stability of cooperation implies the condensation of agents exploiting particular game strategies into strong and stable clusters which are more densely connected, even in the more difficult case of the Prisoner's Dilemma.Comment: 18 pages, 14 figures. to appea