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This paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically,novel techniques are developed for the transient data obtained through the Temporal Analysis of Products (TAP) reactor. The methodology allows distinguishing between two domains of diffusion transport in heterogeneous catalytic systems, i.e., Knudsen and non-Knudsen diffusion, using statistical fingerprints, and finding the transition domain. Two distribution parameters were obtained that directly result in coefficients that correspond to the concentration and the rate of transport. Using a linear relationship between the rate and concentration coefficients, Knudsen diffusion is revealed when the rate of transport is constant and non-Knudsen diffusion is confirmed when the rate of transport coefficient is a function of the concentration coefficient. As a result, accurate transport information is obtained while in the presence of instrument drift or noise while investigating higher pressure pulse responses. As such, experiments where the influence of gas phase reactions can be more directly studied.

We consider reaction-transport processes in open reactors in which systems of first order reactions involving a number of gas species and solid catalysts can occur at localized active regions. Reaction products flow out of the reactor into vacuum conditions and are collected at an exit boundary. The output composition problem (OCP) is to determine the composition (molar fractions) of the collected gas after the reactor is fully emptied. We provide a solution to this problem in the form of a boundary-value problem for a system of time-independent partial differential equations. We then consider network-like reactors, which can be approximated by a network consisting of a collection of nodes and 1-dimensional branches, with reactions taking place at nodes. For these, it is possible to solve the OCP in a simple and effective way, giving explicit formulas for the output composition as a function of the reaction coefficients and parameters associated with the geometric configuration of the system. Several examples are given to illustrate the method.

The Maxwell-Smoluchowski (MS) theory of gas diffusion is revisited here in the context of gas transport in straight channels in the Knudsen regime of large mean free path. This classical theory is based on a phenomenological model of gas-surface interaction that posits that a fraction $\vartheta$ of molecular collisions with the channel surface consists of diffuse collisions, i.e., the direction of post-collision velocities is distributed according to the Knudsen Cosine Law, and a fraction $1-\vartheta$ undergoes specular reflection. From this assumption one obtains the value $\mathcal{D}=\frac{2-\vartheta}{\vartheta}\mathcal{D}_K$ for the self-diffusivity constant, where $\mathcal{D}_K$ is a reference value corresponding to $\vartheta=1$. In this paper we show that $\vartheta$ can be expressed in terms of micro- and macro-geometric parameters for a model consisting of hard spheres colliding elastically against a rigid surface with prescribed microgeometry. Our refinement of the MS theory is based on the observation that the classical surface scattering operator associated to the microgeometry has a canonical velocity space diffusion approximation by a generalized Legendre differential operator whose spectral theory is known explicitly. More specifically, starting from an explicit description of the effective channel surface microgeometry -- a concept which incorporates both the actual surface microgeometry and the molecular radius -- and using this operator approximation, we show that $\vartheta$ can be resolved into easily obtained geometric parameters., Comment: 19 pages, 5 figures

The Transiting Exoplanet Survey Satellite (TESS) mission is providing the scientific community with millions of light curves of stars spread across the whole sky. Since 2018 the telescope has detected thousands of planet candidates that need to be meticulously scrutinized before being considered amenable targets for follow-up programs. We present the second catalog of the Plant Patrol citizen science project containing 999 uniformly-vetted exoplanet candidates within the TESS ExoFOP archive. The catalog was produced by fully exploiting the power of the Citizen Science Planet Patrol project. We vetted TESS Objects of Interest (TOIs) based on the results of Discovery And Vetting of Exoplanets DAVE pipeline. We also implemented the Automatic Disposition Generator, a custom procedure aimed at generating the final classification for each TOI that was vetted by at least three vetters. The majority of the candidates in our catalog, $752$ TOIs, passed the vetting process and were labelled as planet candidates. We ruled out $142$ candidates as false positives and flagged $105$ as potential false positives. Our final dispositions and comments for all the planet candidates are provided as a publicly available supplementary table., Comment: 17 pages, 11 figures, 5 tables. Accepted for publication on MNRAS

The Transiting Exoplanet Survey Satellite (TESS) has detected thousands of exoplanet candidates since 2018, most of which have yet to be confirmed. A key step in the confirmation process of these candidates is ruling out false positives through vetting. Vetting also eases the burden on follow-up observations, provides input for demographics studies, and facilitates training machine learning algorithms. Here we present the TESS Triple-9 (TT9) catalog -- a uniformly-vetted catalog containing dispositions for 999 exoplanet candidates listed on ExoFOP-TESS, known as TESS Objects of Interest (TOIs). The TT9 was produced using the Discovery And Vetting of Exoplanets pipeline, DAVE, and utilizing the power of citizen science as part of the Planet Patrol project. More than 70% of the TOIs listed in the TT9 pass our diagnostic tests, and are thus marked as true planetary candidates. We flagged 144 candidates as false positives, and identified 146 as potential false positives. At the time of writing, the TT9 catalog contains ~20% of the entire ExoFOP-TESS TOIs list, demonstrates the synergy between automated tools and citizen science, and represents the first stage of our efforts to vet all TOIs. The DAVE generated results are publicly available on ExoFOP-TESS., Comment: 15 pages, 11 figures. Accepted on MNRAS

The temporal analysis of products reactor provides a vast amount of transient kinetic information that may be used to describe a variety of chemical features including the residence time distribution, kinetic coefficients, number of active sites, and the reaction mechanism. However, as with any measurement device, the TAP reactor signal is convoluted with noise. To reduce the uncertainty of the kinetic measurement and any derived parameters or mechanisms, proper preprocessing must be performed prior to any advanced analysis. This preprocessing consists of baseline correction, i.e., a shift in the voltage response, and calibration, i.e., a scaling of the flux response based on prior experiments. The current methodology of preprocessing requires significant user discretion and reliance on previous experiments that may drift over time. Herein we use machine learning techniques combined with physical constraints to convert the raw instrument signal to chemical information. As such, the proposed methodology demonstrates clear benefits over the traditional preprocessing in the calibration of the inert and feed mixture products without need of prior calibration experiments or heuristic input from the user.

Understanding the set of elementary steps and kinetics in each reaction is extremely valuable to make informed decisions about creating the next generation of catalytic materials. With physical and mechanistic complexity of industrial catalysts, it is critical to obtain kinetic information through experimental methods. As such, this work details a methodology based on the combination of transient rate/concentration dependencies and machine learning to measure the number of active sites, the individual rate constants, and gain insight into the mechanism under a complex set of elementary steps. This new methodology was applied to simulated transient responses to verify its ability to obtain correct estimates of the micro-kinetic coefficients. Furthermore, experimental CO oxidation data was analyzed to reveal the Langmuir-Hinshelwood mechanism driving the reaction. As oxygen accumulated on the catalyst, a transition in the mechanism was clearly defined in the machine learning analysis due to the large amount of kinetic information available from transient reaction techniques. This methodology is proposed as a new data driven approach to characterize how materials control complex reaction mechanisms relying exclusively on experimental data.

A new steady-state kinetic model of ammonia decomposition is presented and analyzed regarding the electronic properties of metal catalysts. The model is based on the classical Temkin-Ertl mechanism and modified in accordance with Wolkenstein electronic theory by implementing participation of free electrons of the catalyst to change the chemical nature of adsorbed species. Wolkenstein original theory only applied to semiconductors but by including the d-band model, the electronic theory can be extended to metals. For both simplified and full reaction mechanisms, including electronic steps, we present a steady-state rate equation where the dependence on the Fermi level of the metal creates a volcano-shaped dependence. According to the kinetic model, an increasing Fermi level of the catalyst, that approaching the antibonding state with adsorbed nitrogen molecules, will increase the fraction of neutral nitrogen molecules and enhance their the desorption. Concurrently, strong chemisorption of ammonia molecules proceeds easily through participation of additional free catalyst electrons in the adsorbate bond. As a result, the reaction rate is enhanced and reaches its maximum value. A further increasing Fermi level of the catalyst that approaches the antibonding state with ammonia molecules will result in a smaller fraction of negatively charged ammonia molecules and less dehydrogenation. Concurrently, the desorption of neutral nitrogen molecules occurs without impairment. As a result, the reaction rate decreases. The detailed kinetic model is compared to recent experimental measurements of ammonia decomposition on iron, cobalt and CoFe bimetallic catalysts.

Three epochs in development of chemical dynamics are presented. We try to understand the modern research programs in the light of classical works. Three eras (or waves) of chemical dynamics can be revealed in the flux of research and publications. These waves may be associated with leaders: the first is the van't Hoof wave, the second may be called the Semenov--Hinshelwood wave and the third is definitely the Aris wave. Of course, the whole building was impossible without efforts of hundreds of other researchers. Some of of them are mentioned in our brief review., Comment: A brief review of chemical dynamics with 45 references

A computational procedure is developed for determining the conversion probability for reaction-diffusion systems in which a first-order catalytic reaction is performed over active particles. We apply this general method to systems on metric graphs, which may be viewed as 1-dimensional approximations of 3-dimensional systems, and obtain explicit formulas for conversion. We then study numerically a class of 3-dimensional systems and test how accurately they are described by model formulas obtained for metric graphs. The optimal arrangement of active particles in a 1-dimensional multiparticle system is found, which is shown to depend on the level of catalytic activity: conversion is maximized for low catalytic activity when all particles are bunched together close to the point of gas injection, and for high catalytic activity when the particles are evenly spaced.

A concept of "critical" simplification was proposed by Yablonsky and Lazman in 1996 for the oxidation of carbon monoxide over a platinum catalyst using a Langmuir-Hinshelwood mechanism. The main observation was a simplification of the mechanism at ignition and extinction points. The critical simplification is an example of a much more general phenomenon that we call \emph{a bifurcational parametric simplification}. Ignition and extinction points are points of equilibrium multiplicity bifurcations, i.e., they are points of a corresponding bifurcation set for parameters. Any bifurcation produces a dependence between system parameters. This is a mathematical explanation and/or justification of the "parametric simplification". It leads us to a conjecture that "maximal bifurcational parametric simplification" corresponds to the "maximal bifurcation complexity." This conjecture can have practical applications for experimental study, because at points of "maximal bifurcation complexity" the number of independent system parameters is minimal and all other parameters can be evaluated analytically or numerically. We illustrate this method by the case of the simplest possible bifurcation, that is a multiplicity bifurcation of equilibrium and we apply this analysis to the Langmuir mechanism. Our analytical study is based on a coordinate-free version of the method of invariant manifolds (proposed recently in 2006 ). As a result we obtain a more accurate description of the "critical (parametric) simplifications." With the help of the "bifurcational parametric simplification" kinetic mechanisms and reaction rate parameters may be readily identified from a monoparametric experiment (reaction rate vs. reaction parameter)., Comment: 23 pages, 4 figures

The century of complexity has come. The face of science has changed. Surprisingly, when we start asking about the essence of these changes and then critically analyse the answers, the result are mostly discouraging. Most of the answers are related to the properties that have been in the focus of scientific research already for more than a century (like non-linearity). This paper is Preface to the special issue "Grasping Complexity" of the journal "Computers and Mathematics with Applications". We analyse the change of era in science, its reasons and main changes in scientific activity and give a brief review of the papers in the issue., Comment: 8 pages, 3 figures, bibliography 52 items

For many real physico-chemical complex systems detailed mechanism includes both reversible and irreversible reactions. Such systems are typical in homogeneous combustion and heterogeneous catalytic oxidation. Most complex enzyme reactions include irreversible steps. The classical thermodynamics has no limit for irreversible reactions whereas the kinetic equations may have such a limit. We represent the systems with irreversible reactions as the limits of the fully reversible systems when some of the equilibrium concentrations tend to zero. The structure of the limit reaction system crucially depends on the relative rates of this tendency to zero. We study the dynamics of the limit system and describe its limit behavior as $t \to \infty$. If the reversible systems obey the principle of detailed balance then the limit system with some irreversible reactions must satisfy the {\em extended principle of detailed balance}. It is formulated and proven in the form of two conditions: (i) the reversible part satisfies the principle of detailed balance and (ii) the convex hull of the stoichiometric vectors of the irreversible reactions does not intersect the linear span of the stoichiometric vectors of the reversible reactions. These conditions imply the existence of the global Lyapunov functionals and alow an algebraic description of the limit behavior. The thermodynamic theory of the irreversible limit of reversible reactions is illustrated by the analysis of hydrogen combustion., Comment: 23 pages, extended version with figs

The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. homogeneous combustion, heterogeneous catalytic oxidation, most enzyme reactions etc), detailed mechanisms include both reversible and irreversible reactions. In this case, the principle of detailed balance cannot be applied directly. We represent irreversible reactions as limits of reversible steps and obtain the principle of detailed balance for complex mechanisms with some irreversible elementary processes. We proved two consequences of the detailed balance for these mechanisms: the structural condition and the algebraic condition that form together the extended form of detailed balance. The algebraic condition is the principle of detailed balance for the reversible part. The structural condition is: the convex hull of the stoichiometric vectors of the irreversible reactions has empty intersection with the linear span of the stoichiometric vectors of the reversible reaction. Physically, this means that the irreversible reactions cannot be included in oriented pathways. The systems with the extended form of detailed balance are also the limits of the reversible systems with detailed balance when some of the equilibrium concentrations (or activities) tend to zero. Surprisingly, the structure of the limit reaction mechanism crucially depends on the relative speeds of this tendency to zero., Comment: The final version (minor corrections and editing), accepted for publication in Chemical Engineering Science

We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, $\dot{x}=Kx$, the kinetic operator $K$ is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, $\exp (Kt)$, is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the $i$th pure state and measure the probability $p_j(t)$ of the $j$th state ($j\neq i$), and, similarly, measure $p_i(t)$ for the process, which starts at the $j$th pure state, then the ratio of these two probabilities $p_j(t)/p_i(t)$ is constant in time and coincides with the ratio of the equilibrium probabilities. We study similar and more general reciprocal relations between the kinetic curves. The experimental evidence provided as an example is from the reversible water gas shift reaction over iron oxide catalyst. The experimental data are obtained using Temporal Analysis of Products (TAP) pulse-response studies. These offer excellent confirmation within the experimental error., Comment: 6 pages, 1 figure, the final version

In contrast to common opinion, it is shown that equilibrium constants determine the time-dependent behavior of particular ratios of concentrations for any system of reversible first-order reactions. Indeed, some special ratios actually coincide with the equilibrium constant at any moment in time. This is established for batch reactors, and similar relations hold for steady-state plug-flow reactors, replacing astronomic time by residence time. Such relationships can be termed time invariants of chemical kinetics.

Everything that is not prohibited is permissible. So, what is prohibited in the course of chemical reactions, heat transfer and other dissipative processes? Is it possible to "overshoot" the equilibrium, and if yes, then how far? Thermodynamically allowed and prohibited trajectories of processes are discussed by the example of effects of equilibrium encircling. The complete theory of thermodynamically accessible states is presented. The space of all thermodynamically admissible paths is presented by projection on the "thermodynamic tree", that is the tree of the related thermodynamic potential (entropy, free energy, free enthalpy) in the balance polyhedron. The stationary states and limit points for open systems are localized too., Comment: IMACS2005 extended abstract

It is known that many constructions arising in the classical Gaussian infinite dimensional analysis can be extended to the case of more general measures. One such extension can be obtained through biorthogonal systems of Appell polynomials and generalized functions. In this paper, we consider linear continuous operators from a nuclear Frechet space of test functions to itself in this more general setting. We construct an isometric integral transform (biorthogonal CS-transform) of those operators into the space of germs of holomorphic functions on a locally convex infinite dimensional nuclear space. Using such transform, we provide characterization theorems and give biorthogonal chaos expansion for operators., Comment: 13 pages