Theory Of Reactions Research Articles

The Theory and Computation of the Semi-Linear Reaction–Diffusion Equation with Dirichlet Boundaries

The Theory and Computation of the Semi-Linear Reaction–Diffusion Equation with Dirichlet Boundaries

A methodology of quantifying membrane permeability based on returning probability theory and molecular dynamics simulation.

We propose a theoretical approach to estimate the permeability coefficients of substrates (permeants) for crossing membranes from donor (D) phase to acceptor (A) phase by means of molecular dynamics (MD) simulation. A fundamental aspect of our approach involves reformulating the returning probability (RP) theory, a rigorous bimolecular reaction theory, to describe permeation phenomena. This reformulation relies on the parallelism between permeation and bimolecular reaction processes. In the present method, the permeability coefficient is represented in terms of the thermodynamic and kinetic quantities for the reactive (R) phase that exists within the inner region of a membrane. One can evaluate these quantities using multiple MD trajectories starting from phase R. We apply the RP theory to the permeation of ethanol and methylamine at different concentrations (infinitely dilute and 1 mol % conditions of permeants). Under the 1 mol% condition, the present method yields a larger permeability coefficient for ethanol (0.12 ± 0.01cms-1) than for methylamine (0.069 ± 0.006cms-1), while the values of the permeability coefficient are satisfactorily close to those obtained from the brute-force MD simulations (0.18 ± 0.03 and 0.052 ± 0.005cms-1 for ethanol and methylamine, respectively). Moreover, upon analyzing the thermodynamic and kinetic contributions to the permeability, we clarify that a higher concentration dependency of permeability for ethanol, as compared to methylamine, arises from the sensitive nature of ethanol's free-energy barrier within the inner region of the membrane against ethanol concentration.

Minimum Principles for Sturm–Liouville Inequalities and Applications

A minimum principle for a Sturm–Liouville (S-L) inequality is obtained, which shows that the minimum value of a nonconstant solution of a S-L inequality never occurs in the interior of the domain (a closed interval) of the solution. The minimum principle is then applied to prove that any nonconstant solutions of S-L inequalities subject to separated inequality boundary conditions (IBCs) must be strictly positive in the interiors of their domains and are increasing or decreasing for some of these IBCs. These positivity results are used to prove the uniqueness of the solutions of linear S-L equations with separated BCs. All of these results hold for the corresponding second-order differential inequalities (or equations), which are special cases of S-L inequalities (or equations). These results are applied to two models arising from the source distribution of the human head and chemical reactor theory. The first model is governed by a nonlinear S-L equation, while the second one is governed by a nonlinear second-order differential equation. For the first model, the explicit solutions are not available, and there are no results on the existence of solutions of the first model. Our results show that all the nonconstant solutions are increasing and are strictly positive solutions. For the second model, many results on the uniqueness of the solutions and the existence of multiple solutions have been obtained before. Our results are applied to prove that all the nonconstant solutions are decreasing and strictly positive.

Physical Chemistry Lab for Data Analysis of COVID-19 Spreading Kinetics in Different Countries.

The COVID-19 pandemic has passed. It gives us a real-world example of kinetic data analysis practice for our undergraduate physical chemistry laboratory class. It is a great example to connect this seemingly very different problem to the kinetic theories for chemical reactions that the students have learned in the lecture class. At the beginning of the spring 2023 semester, we obtained COVID-19 kinetic data from the "Our World in Data" database, which summarizes the World Health Organization (WHO) data reported from different countries. We analyzed the effective spreading kinetics based on the susceptible-infectious-recovered-vaccinated (SIR-V) model. We then compared the effective rate constants represented by the real-time reproduction numbers ( ) underlining the reported data for these countries and discussed the results and the limitations of the model with the students.

Features of a gas turbine combustion chamber in operation with gaseous ammonia

Achieving climate neutrality requires the use of alternative hydrogen carriers for energy purposes, with ammonia currently being considered. One potential application in the energy sector is gas turbine systems, for which combustion chambers need to be designed to efficiently combust ammonia within an airflow. This paper focuses on theoretical investigations of fuel combustion completeness and environmental cleanliness of a gas turbine combustion chamber with a thermal power output of 1.0 MW, operating on gaseous ammonia. A prospective scheme for organizing processes is proposed, based on pre-mixing ammonia with a portion of air in a special pre-chamber, the sequential introduction of the remaining air through a radial-axial swirler and a series of holes in the flame tube, ensuring stable fuel combustion. Two approaches were used for modeling combustion processes in such a combustion chamber: one based on chemical reactor theory and the other on three-dimensional hydrodynamic analysis. After conducting a detailed kinetic analysis, it was concluded that to maintain stable ammonia combustion while varying the air excess coefficient in the primary combustion zone from 1.4 to 2.0, the reactants need to remain in this zone for a duration exceeding 0.025 s. Based on these parameters, design schemes for two combustion chamber variants were developed, differing in combustion tube length and air distribution pattern, for operation with an ammonia flow rate of approximately 50 g/s and a pressure of 0.3 MPa, determining a gas outlet temperature of 1490 K. Three-dimensional calculations of aerodynamic flow structures, ammonia combustion, and formation of toxic components were conducted, revealing that the proposed process organization scheme ensures complete ammonia combustion and small nitrogen oxide emissions. These results have potential applications in the development of new gas turbine combustion chamber designs for decarbonized energy systems, including those integrated with solid oxide fuel cells.

Nonstatistical Unimolecular Decay of the CH2OO Criegee Intermediate in the Tunneling Regime.

Unimolecular decay of the formaldehyde oxide (CH2OO) Criegee intermediate proceeds via a 1,3 ring-closure pathway to dioxirane and subsequent rearrangement and/or dissociation to many products including hydroxyl (OH) radicals that are detected. Vibrational activation of jet-cooled CH2OO with two quanta of CH stretch (17-18 kcal mol-1) leads to unimolecular decay at an energy significantly below the transition state barrier of 19.46 ± 0.25 kcal mol-1, refined utilizing a high-level electronic structure method HEAT-345(Q)Λ. The observed unimolecular decay rate of 1.6 ± 0.4 × 106 s-1 is 2 orders of magnitude slower than that predicted by statistical unimolecular reaction theory using several different models for quantum mechanical tunneling. The nonstatistical behavior originates from excitation of a CH stretch vibration that is orthogonal to the heavy atom motions along the reaction coordinate and slow intramolecular vibrational energy redistribution due to the sparse density of states.

Measurement of nuclear interaction cross sections towards neutron-skin thickness determination

The accuracy of reaction theories used to extract properties of exotic nuclei from scattering experiments is often unknown or not quantified, but of utmost importance when, e.g., constraining the equation of state of asymmetric nuclear matter from observables as the neutron-skin thickness. In order to test the Glauber multiple-scattering model, the total interaction cross section of ▪ on carbon targets was measured at initial beam energies of 400, 550, 650, 800, and 1000 MeV/nucleon. The measurements were performed during the first experiment of the newly constructed R3B (Reaction with Relativistic Radioactive Beams) experiment after the start of FAIR Phase-0 at the GSI/FAIR facility with beam energies of 400, 550, 650, 800, and 1000 MeV/nucleon. The combination of the large-acceptance dipole magnet GLAD and a newly designed and highly efficient Time-of-Flight detector enabled a precise transmission measurement with several target thicknesses for each initial beam energy with an experimental uncertainty of ±0.4%. A comparison with the Glauber model revealed a discrepancy of around 3.1% at higher beam energies, which will serve as a crucial baseline for the model-dependent uncertainty in future fragmentation experiments.

Nuclear reactions in gaseous stars: Perspectives from kinetic theory and thermodynamics

In the Standard Model of gaseous stars, temperature is primary both in the initiation of thermonuclear reactions to form heavier elements and the emission of radiation. These processes have been described using thermodynamic expressions. However, within any given thermodynamic relation, not only must units balance on each side, but so must thermodynamic character. Temperature, whether or not equilibrium conditions are established, must always be intensive in macroscopic thermodynamics, and mass must be extensive. This ensures that the laws of thermodynamics are respected. The theory of temperatures and nuclear reactions within gaseous stars is constructed from the kinetic theory of an ideal gas, by which temperature is introduced, in combination with gravitational and Coulomb forces. The resulting thermodynamic relations impart a nonintensive character to temperature and a nonextensive character to mass. Consequently, the theory of nuclear reactions in gaseous stars is invalid. Deprived of the only theoretical means by which the Standard Model justifies stellar nuclear reactions, the theory of gaseous stars is not viable. The most reasonable alternative rests in lattice confinement fusion and the recognition that the stars are comprised of condensed matter, namely metallic hydrogen.

Soliton solutions of nonlinear stochastic Fitz-Hugh Nagumo equation

This study deals with the stochastic Fitz-Hugh Nagumo (FHN) equation and its multiple soliton solutions. The underlying model has numerous applications in neuroscience that express the pulse behavior of neurons. In general, different kinds of noise affect neurons, e.g., oscillations in the opening and closing of ion stations within cell membranes and the fluctuations of the different conductivities in the system. This fluctuation creates a sequence of stochastic excitation. Various applications are branching Brownian motion process, flame propagation, nuclear reactor theory, autocatalytic chemical reaction, mobility in neurons, population growth in the open environment, and liquid environment. So, need of the hour to consider the FHN equation under the impact of noise. The ϕ6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^6$$\\end{document}-model expansion method is used to extract the analytical solutions that give a dynamic attitude of the transmission for the nerve impulses of a nervous system. The different constraint conditions for the existence of these solutions are also discussed. The solutions of this model are represented in hyperbolic, trigonometric, and rational forms. The 2 and 3-dimensional behavior of these solutions are depicted by choosing the different values of parameters. The impact of noise on the physical system is analyzed and its real-world applications are discussed. The spikes in the solutions are controlled through the Borel function. These important results will open a new horizon of research for the young researchers.

Impact of Food Processing Techniques on Nutritional Content in Brazil

Purpose: The aim of the study was to analyze the impact of food processing techniques on nutritional content in Brazil. Methodology: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries. Findings: In Brazil, studies show that food processing techniques affect nutritional content, with traditional methods like fermentation enhancing nutrient bioavailability, while modern methods like high-temperature cooking reduce vitamins and minerals. This impact raises concerns about the nutritional quality of the Brazilian diet, prompting a shift towards techniques that preserve nutritional value. Unique Contribution to Theory, Practice and Policy: Maillard reaction theory, enzyme inactivation theory & degradation and retention theory may be used to anchor future studies on analyze the impact of food processing techniques on nutritional content in Brazil. Food manufacturers should strive to optimize processing techniques to minimize nutrient losses while achieving other objectives such as safety, taste, and texture. Policymakers should collaborate with industry stakeholders to develop evidence-based guidelines and standards for food processing.

Analysis of volatiles from the thermal decomposition of Amadori rearrangement products in the cysteine-glucose Maillard reaction and density functional theory study

The Amadori rearrangement products are an important flavor precursor in the Maillard reaction. Its thermal decomposition products usually contribute good flavors in foods. Therefore, investigating the thermal breakdown of Amadori products is significant for understanding the flavor forming mechanism in the Maillard reaction. In this study, volatiles from thermal decomposition of Amadori products in cysteine and glucose Maillard reaction was investigated by a thermal desorption cryo-trapping system combined with gas chromatography-mass spectrometry (GC-MS). A total of 60 volatiles were detected and identified. Meanwhile, the forming mechanism of 2-methylthiophene, a major decomposition product, was also investigated by using density functional theory. Seventeen reactions, 12 transition states, energy barrier and rate constant of each reaction were finally obtained. Results reveal that it is more likely for Amadori products of cysteine and glucose to undergo decomposition under neutral or weakly alkaline conditions.

Theory of Majorana-Type Heavy Ion Double Charge Exchange Reactions by Pion–Nucleon Isotensor Interactions

The theory of heavy ion double charge exchange (DCE) reactions proceeding by effective rank-2 isotensor interactions is presented. Virtual pion–nucleon charge exchange interactions are investigated as the source for induced isotensor interactions, giving rise to the Majorana DCE (MDCE) reaction mechanism. MDCE is of a generic character, proceeding through pairs of complementary (π±,π∓) reactions in the projectile and target nucleus. The dynamics of the elementary processes is discussed, where the excitation of pion–nucleon resonances are of central importance. Investigations of initial and final state ion–ion interactions show that these effects are acting as vertex renormalizations. In closure approximation, well justified by the finite pion mass, the second-order transition matrix elements reduce to pion potentials and effective two-body isotensor DCE interactions, giving rise also to two-body correlations in either of the participating nuclei. Connections to neutrinoless Majorana double beta decay (MDBD) are elucidated at various levels of the dynamics, from the underlying fundamental electro-weak and QCD scales to the physical scales of nuclear MDBD and MDCE physics. It is pointed out that heavy ion MDCE reactions may also proceed by competing electro-weak charge exchange processes, leading to lepton MDCE by electrons, positrons, and neutrinos.

Preparation and Structural Analysis of a Water-Soluble Aminated Lignin.

Lignin is insoluble in water, thereby limiting its use in the synthesis of adhesives. Therefore, in this study, an aminated lignin compound was prepared through a lignin amination reaction to increase the amount of raw lignin material that can be used in the synthesis of adhesives; moreover, structural analysis was conducted. The main result of this was the introduction of amino groups into phenolic hydroxyl groups in the hydrolyzing lignin from the raw lignin materials, thus generating the product of aminated lignin. The resulting particle sizes were about 100 nm, the average molecular weight was 57,627 g/mol, and the water solubility of the aminated lignin was about 0.45 g/100 mL. Therefore, the water solubility of raw lignin was greatly improved. The proposed reaction mechanism of phenolic hydroxyl groups and carboxylic acid groups in lignin is a reaction with ammonia molecules; thus, the successful introduction of amino groups generated the aminated lignin compounds. Hence, this article enriches the scientific theory of lignin reactions and provides a reference for the widespread application of raw lignin materials in the field of adhesives.

A novel electrochemical aptamer biosensor for lead (Ⅱ) ion detection utilizing GO/PAMAM @Au and Au/MB as dual signal amplifiers

A competitive electrochemical aptamer biosensor for the selective detection of Pb2+ was developed in this study. The PAMAM@Au hybrid materials and the bioprobe MB-GNPs-ssDNA were synthesized with chemical methods. Modified electrode with carboxylated graphene oxide was prepared via electrodeposition. PAMAM@Au was immobilized on the modified electrode using the EDC/NHS crosslinker, and aptamer (Apt) was bound to PAMAM@Au hybrid materials using the glutaraldehyde crosslinker. The assembly of MB-GNPs-ssDNA/Apt/PAMAM@Au/GO/SPCE biosensors was achieved through immobilizing bioprobe onto electrodes, based on the theory of aptamer-complementary chain reactions. The fabricated biosensor was characterized through electrochemical experiments, SEM, AFM, TEM, XPS and FTIR. The biosensor's performance was evaluated in a series of Pb2+ aqueous solutions by differential pulse voltammetry (DPV), and the results demonstrated this biosensor had excellent repeatability, stability, and specificity. The detection range spanned from 0.5 pM/L to 500 nM/L, with a detection limit of 5 fM/L. Consequently, the proposed biosensor can serve as a reliable analytical tool for the sensitive detection of lead ions.

Toxicity of persistent organic pollutants: a theoretical study

ContextPolychlorinated biphenyls (PCBs) and polybrominated diphenyl ethers (PBDEs) are two families of persistent organic pollutants that are dangerous as they remain in the atmosphere for long periods and are toxic for humans and animals. They are found all over the world, including the penguins of Antarctica. One of the mechanisms that explains the toxicity of these compounds is related to oxidative stress. The main idea of this theoretical research is to use conceptual density functional theory as a theory of chemical reactivity to analyze the oxidative stress that PCBs and PBDEs can produce. The electron transfer properties as well as the interaction with DNA nitrogenous bases of nine PCBs and ten PBDEs found in Antarctic penguins are investigated. From this study, it can be concluded that compounds with more chlorine or bromine atoms are more oxidizing and produce more oxidative stress. These molecules also interact directly with the nitrogenous bases of DNA, forming hydrogen bonds, and this may be an explanation for the toxicity. Since quinone-type metabolites of PCBs and PBDEs can cause neurotoxicity, examples of quinones are also investigated. Condensed Fukui functions are included to analyze local reactivity. These results are important as the reactivity of these compounds helps to explain the toxicity of PCBs and PBDEs.MethodsAll DFT computations were performed using Gaussian16 at M06-2x/6–311 + g(2d,p) level of theory without symmetry constraints. Electro-donating (ω-) and electro-accepting (ω +) powers were used as global response functions and condensed Fukui functions as local parameters of reactivity.

Chemical reactivity theory to analyze possible toxicity of microplastics: Polyethylene and polyester as examples.

Micro- and nanoplastics are widespread throughout the world. In particular, polyethylene (PE) and polyethylene terephthalate or polyester (PET) are two of the most common polymers, used as plastic bags and textiles. To analyze the toxicity of these two polymers, oligomers with different numbers of units were used as models. The use of oligomers as polymeric templates has been used previously with success. We started with the monomer and continued with different oligomers until the chain length was greater than two nm. According to the results of quantum chemistry, PET is a better oxidant than PE, since it is a better electron acceptor. Additionally, PET has negatively charged oxygen atoms and can promote stronger interactions than PE with other molecules. We found that PET forms stable complexes and can dissociate the guanine-cytosine nucleobase pair. This could affect DNA replication. These preliminary theoretical results may help elucidate the potential harm of micro- and nanoplastics.

A chemical kinetics theory for interpreting the non-monotonic temperature dependence of enzymatic reactions

Abstract. One notable observation of enzymatic chemical reactions is that, for a given abundance of enzymes and substrates, temperature increases cause reaction rates to first increase consistent with the Arrhenius relationship, then plateau, and finally fall off quickly to zero at high temperatures. While many mathematical functions have been used to describe this pattern, we here propose a chemical kinetics theory which successfully replicates this observation and provides insights into the processes responsible for these dynamics. The chemical kinetics theory combines the law of mass action, von Smoluchowski's diffusion-limited chemical reaction theory, and Eyring's transition state theory. This new theory reveals that the thermally reversible enzyme denaturation ensured by the ceaseless thermal motion of molecules and ions in an enzyme solution explains the plateau and subsequent decrease in chemical reaction rates with increasing temperature. The temperature-dependent affinity parameter (K) that relates enzymes and substrates through their binding also affects the shape of the emergent temperature response. We demonstrate that with an increase in substrate availability, K shifts the optimal temperature, where reaction rates plateau, towards higher values. Further, we show that the chemical kinetics theory accurately represents 12 sets of published enzyme assay data and includes the popular mechanistic model by Ratkowsky et al. (2005) as a special case. Given its good performance and solid theoretical underpinning, we believe this new theory will facilitate the construction of more mechanistic-based environmental biogeochemical models.

The 50th anniversary of the coupled channels Born approximation (CCBA) and the coupled reaction channels (CRC) theories of nucleon transfer reactions (a unique interplay between theory, experiment and computer technology, conducted during the most tumultuous period in modern American society)

Nucleon transfer reactions have played a fundamental role in understanding the single-particle components, shell structure and collective properties of atomic nuclei. The conventional distorted wave Born approximation (DWBA) envisioned the nucleon transfer reaction as a one-step process, which proceeds directly from the ground state of the target nucleus to a state of the residual nucleus. The coupled channels Born approximation (CCBA) and coupled reaction channels (CRC) theories evolved because a number of nucleon transfer reaction cross sections could not be reconciled within the DWBA. These coupled channels models revealed that, in addition to the “one-step” process of the DWBA, “multi-step” nucleon transfer processes involving accessary pathways can participate in populating the final nuclear state. In the CCBA, the auxiliary pathways involved inelastic excitations of the target and/or residual nucleus, whereas, in the CRC, the pathways included sequential nucleon transfer passing through nuclear states of an intermediate partition. Coherent addition of contributions from one-step and multi-step nucleon transfer processes resulted in dramatic alterations in reaction cross sections, which were experimentally confirmed. The CCBA and CRC linked the structure of the nuclei participating in a reaction to modalities of nucleon transfer arising during the relative motion between the interacting ions. These complementary theories inexorably changed physicists’ interpretations of nucleon transfer reactions and, in doing so, heralded in the new field of direct heavy-ion reactions.

Influence phase of a dS observer. Part I. Scalar exchange

Inspired by real-time computations in AdS black holes, we propose a method to obtain the influence phase of a cosmological observer by calculating the on-shell action on a doubled spacetime geometry. The influence phase is the effective action for an open system: for a dS static patch observer coupled to a scalar field it incorporates the radiation reaction due to the bulk fields and their dS Hawking radiation. For a general extended source in dS, we describe how to account for finite size effects. In the long-time limit, we get a Markovian open quantum system susceptible to cosmological fluctuations, whereas the short-time limit reproduces the worldline theory of flat-space radiation reaction. We also present a fully covariantised form for the cubic corrections to the radiation reaction in even spacetime dimensions, including Hubble contributions, and find an intriguing recursive structure across dimensions.

Localisation of stress-affected chemical reactions in solids described by coupled mechanics-diffusion-reaction models

Chemical reactions in solids can induce chemical expansion of the solid that causes the emergence of the mechanical stresses, which, in turn, can affect the rate of the reaction. A typical example of this is the reaction of Si lithiation, where the stresses can inhibit the reaction up to the reaction locking. The reactions in solids can take place within some volume (bulk reactions) or localise at a chemical reaction front (localised reactions). These cases are typically described by different thermo-chemo-mechanical theories that contain the source/sink terms either in the bulk or at the propagating infinitely-thin interface, respectively. However, there are reactions that can reveal both regimes; hence, there is a need to link the theories describing the bulk and the localised (sharp-interface) reactions. The present paper bridges this gap and shows that when a certain structure of the Helmholtz free energy density is adopted (based on the ideas from the phase-field methods), it is possible to obtain (in the limit) the same driving force for the chemical reaction (hence, the same reaction kinetics) as derived within the theory of the sharp-interface chemical reactions based on the chemical affinity tensor.