Variational Theory Research Articles

Theoretical study of H-abstraction and addition reactions of cyclohexene with H, OH and HO2

Reactions with small radicals are of essential significance for alkene oxidation. In this work, the potential energy surfaces and rate constants of cyclohexene plus H, OH, HO2 radicals were thoroughly investigated. The molecular geometries and vibrational frequencies were calculated for all stationary points at BHandHLYP/6-311++G(d,p) level, and then the single point energies were refined at DLPNO-CCSD(T)/CBS level. It contained secondary alkyl, allylic, vinyl H-abstraction and addition channels. The axial and equatorial carbon sites were calculated separately. The reactant and product complexes for allylic H-abstraction and addition channels by OH and HO2 were located with lower energies than the path entrance or exit. In contrast, those complexes for pathways with H-atom had higher energies than reactants or products. The barrierless formation process of reactant complex for cyclohexene plus OH/HO2 was consider to evaluate the influences on rate constants. Rate constants were determined using canonical variational transition state theory in consideration of quantum transmission effects. Notable tunneling effects are observed for H-abstraction reactions with H and HO2 radicals, of which low-temperature rate constants are enhanced, whereas variational and recrossing coefficients of channels with OH deviate far from unity, rendering lower rate constants than those obtained at conventional transition state theory. Comparison of rate constants with similar reactions published in literatures showed that fairly agreements were achieved for H-abstraction and addition channels with H and HO2, but great gaps are noted for those with OH radical. Branching ratio analysis exhibited that addition reactions dominated at T < 1000 K and allylic H-abstraction reactions turned more significant as temperature increased.

Simplifying the variational iteration method: A new approach to obtain the Lagrange multiplier

The variational iteration method (VIM) has been in the last two decades, one of the most used semi-analytical techniques for approximating nonlinear differential equations. The notion of VIM is based on the identification of the Lagrange multiplier using the variational theory. The performance of the method is highly dependent on how the Lagrange multiplier is determined. In this paper, a novel method for calculating the Lagrange multiplier is provided, making the VIM more efficient in solving a variety of nonlinear problems. To illustrate the effectiveness of the new approach, a standard nonlinear oscillator problem is tested and the results demonstrate that only one iteration leads to an excellent outcome.

Sociolectal and Dialectal Variation in Prosody.

As in many linguistics subfields, studies of prosody have mainly focused on majority languages and dialects and on speakers who hold power in social structures. The goal of this Special Issue is to diversify prosody research in terms of the languages and dialects being investigated, as well as the social structures that influence prosodic variation. The Special Issue brings together prosody researchers and researchers exploring sociological variation in prosody, with a focus on the prosody of marginalized dialects and on prosodic differences based on gender, sexuality, race, and ethnicity. The papers in this volume don't just advance our understanding of critical issues in sociolinguistics, but they also challenge some of the received wisdom in the exploration of sociolinguistic influences on prosody. Not only does this collection highlight the value of this work to informing theories of prosodic variation and change, but the collected papers also provide examples of methodological innovations in the field that will be valuable for all prosody researchers.

Feynman integrals in dimensional regularization and extensions of Calabi-Yau motives

We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the example of multi-loop banana integrals. For example, we show how Griffiths transversality, known from the theory of variation of mixed Hodge structures, leads quite generically to a set of quadratic relations among maximal cut integrals associated to Calabi-Yau motives. These quadratic relations then naturally lead to a compact expression for l-loop banana integrals in D = 2 dimensions in terms of an integral over a period of a Calabi-Yau (l − 1)-fold. This new integral representation generalizes in a natural way the known representations for l ≤ 3 involving logarithms with square root arguments and iterated integrals of Eisenstein series. In a second part, we show how the results obtained by some of the authors in earlier work can be extended to dimensional regularization. We present a method to obtain the differential equations for banana integrals with an arbitrary number of loops in dimensional regularization without the need to solve integration-by-parts relations. We also present a compact formula for the leading asymptotics of banana integrals with an arbitrary number of loops in the large momentum limit. This generalizes the novel hat{Gamma} -class introduced by some of the authors to dimensional regularization and provides a convenient boundary condition to solve the differential equations for the banana integrals. As an application, we present for the first time numerical results for equal-mass banana integrals with up to four loops and up to second order in the dimensional regulator.

A Study of Formal Features of Chu Ci Translation and Research Texts in English Based on Variational Translation Theory

The dissemination works of Chu Ci (楚辞) in Western countries can roughly be divided into three groups: translation works, research works and literary works. The formal features of the dissemination works are intimately related to and determined by the variational translation methods which include adaptation translation, selective translation, translation and comment, translation and writing, introduction-translation, edited translation, reference translation, condensed translation, and so on. Research on the textual features of Chu Ci dissemination works in the West is of great help to the globalization of Chinese culture, especially to ancient Chinese literary and cultural classics’ going global which is an important national policy of the Chinese government.

Didaktik attention. Preschool teaching from a didaktik and variation theory perspective using examples of mathematical aspects of programming

This article is based on a partial study of an R&amp;D programme with various theory-informed teaching arrangements aimed at describing and further developing knowledge of what characterizes preschool teaching. The aim of this study is to contribute knowledge about how teachers and children can create attention in relation to an example when teaching focuses on mathematical aspects and programming from a didaktik and variation theory perspective. The guiding question is: What can characterize attention-forming acts of teaching in preschool? The analysed material in this article consists of an example with just over ten minutes of audio-visual data – videos of teaching. An abductive analysis has been carried out. Preschool teachers’ interactions with children while teaching is studied and analysed based on didaktik questions and with a didaktik triangle as the didaktik model and based on three dimensions representations of attention: sharing, creating and alternating attention and attention-forming acts. Concepts of variation theory is connec­ted to the didaktik questions and didaktik triangle. Overall, the representations of sharing, creating and alternating attention and attention-forming acts of teaching can be summarized in the concept of didaktik attention.

Flash pyrolysis mechanism of trimethylchlorosilane

The thermal decomposition mechanism of trimethylchlorosilane at temperatures up to 1400 K was investigated using flash pyrolysis microreactor coupled with vacuum ultraviolet (118.2 nm) photoionization time-of-flight mass spectrometry. The main initiation reaction of the parent molecule was identified to be HCl molecular elimination producing Me2Si=CH2, and its onset temperature was estimated to be around 1210 K. The methyl loss channel was also observed at an onset temperature of ∼1280 K. Other possible initiation pathways such as chlorine atom loss and methane molecular elimination were considered to be insignificant. Quantum chemistry calculations at the UCCSD(T)/cc-pVTZ//UM05–2X/aug-cc-pVDZ level of theory were performed to study the energetics of the possible initiation pathways. The theoretical calculations revealed that the HCl elimination channel via a van der Waals intermediate was the most energetically favored pathway among all the initiation channels, in agreement with the experimental observations. Transition state theory (TST) and variational transition state theory (VTST) calculations were employed to calculate unimolecular dissociation rate constants of the initiation reactions at elevated temperatures. The results supported the experimental observations and reaction energetics calculations that the HCl molecular elimination reaction was the most prominent initiation reaction and the CH3 loss channel was a significant initiation reaction channel. Secondary reactions of the initial products were identified, and the possible mechanisms were proposed.

Quantitative Kinetics of the Reaction between CH2OO and H2O2 in the Atmosphere.

Criegee intermediates (CIs) are generated from the ozonolysis of unsaturated hydrocarbons in the atmosphere. They have an important role in determining the implications of atmospheric bimolecular reactions with other atmospheric species. The reaction between CH2OO and H2O2 plays a crucial role in understanding how CIs impact the HOx budget in the atmosphere. The reaction mechanism and kinetics are critical to atmospheric modeling, which is a prominent challenge in present-day climate change modeling. This is particularly true for bimolecular reactions that involve complex reaction sequences. Here, we report the mechanism and quantitative kinetics of the CH2OO + H2O2 reaction by using a novel dual-level strategy that contains W3X-L//CCSD(T)-F12a/cc-pVTZ-F12 for the transition state theory and M11-L/MG3S functional method for direct dynamics calculations using canonical variational transition state theory with small-curvature tunneling to obtain both recrossing effects and tunneling. The present work shows that the CH2OO + H2O2 reaction has a negative temperature dependency with the decrease in the rate constant of CH2OO + H2O2 from 1.31 × 10-13 cm3 molecule-1 s-1 to 3.80 × 10-14 cm3 molecule-1 s-1 between 200 and 350 K. The calculated results also show that the CH2OO + H2O2 reaction can have an impact on the H2O2 profile under certain atmospheric conditions. The present findings should have implications for the quantitative kinetics of Criegee intermediates with other hydroperoxides.

A direct method for the extension of FastSim under non-Hertzian contact conditions

In wheel-rail contact mechanics, there coexist different models characterised by their ability to reproduce the real phenomenon and the time associated with computing the solution. In simulation of the vehicle dynamics, the increase in the computational performance places researchers close to a horizon in which it is possible to implement the most realistic theories (Variational Theory or finite elements), although at present the use of these models is mainly limited to offline calculations, far from real-time simulation. In this context, this work presents a tangential contact theory that is an intermediate point between simplified models (unable to model non-Hertzian contact) and more realistic models (whose complexity triggers simulation times). The tangential contact model proposed is based on the FastSim algorithm, whose precision comes from the algorithm convergence to the results of an exact adhesion theory (i.e. when creepages tend to zero). The impossibility of considering Kalker’s Linear Theory as an adjustment method when the hypotheses of the Hertzian model are not fulfilled leads to the adoption of the Kalker’s steady-state CONTACT version in adhesion conditions. The calculations presented through the proposed algorithm provide errors for creep forces lower than 4% with computational times one order lower than the Variational Theory.

Electronic modulation of metal-support interactions improves polypropylene hydrogenolysis over ruthenium catalysts

Ruthenium (Ru) is the one of the most promising catalysts for polyolefin hydrogenolysis. Its performance varies widely with the support, but the reasons remain unknown. Here, we introduce a simple synthetic strategy (using ammonia as a modulator) to tune metal-support interactions and apply it to Ru deposited on titania (TiO2). We demonstrate that combining deuterium nuclear magnetic resonance spectroscopy with temperature variation and density functional theory can reveal the complex nature, binding strength, and H amount. H2 activation occurs heterolytically, leading to a hydride on Ru, an H+ on the nearest oxygen, and a partially positively charged Ru. This leads to partial reduction of TiO2 and high coverages of H for spillover, showcasing a threefold increase in hydrogenolysis rates. This result points to the key role of the surface hydrogen coverage in improving hydrogenolysis catalyst performance.

Phonological and Semantic Variations in Tsonga Spoken in Zimbabwe and South Africa

Tsonga is a cross-border language spoken in South Africa, Mozambique, Zimbabwe, and Eswatini. This article focuses on variations of Tsonga spoken in Zimbabwe and South Africa. The aim of this article is to discuss the phonological and semantic differences between Tsonga spoken in South Africa and Zimbabwe using a comparative approach. Interviews were conducted among 20 Tsonga first language speakers from Zimbabwe and South Africa. Document analysis was also used. Labov's (1972) variation theory, which points out that there is variation in any given language, was employed. The article discusses differences in places of articulation of consonants found in certain lexical items, highlighting phonological processes such as labialisation versus palatalisation, velarisation versus labialisation, nasalisation versus non- nasalisation, and aspiration versus non-aspiration. Semantic variations are also discussed. It was found that there are phonological and semantic similarities and differences between Tsonga spoken in Zimbabwe and South Africa.

Experimental and Theoretical Investigation of Reactions of Formyl (HCO) Radicals in the Gas Phase: (I) Kinetics of HCO Radicals with Ethyl Formate and Ethyl Acetate in Tropospherically Relevant Conditions.

Formyl (HCO) radicals were generated in situ in the gas phase via the photolysis of glyoxal in N2 at 248 nm using the pulsed laser photolysis-cavity ring-down spectrometry technique, and the absorption cross-section of the radical was measured to be σHCO = (5.3 ± 0.9) × 10-19 cm2 molecule-1 at 298 K and 615.75 nm, which was the probing wavelength. The kinetics of the reactions of HCO radicals with ethyl formate (EF) and ethyl acetate (EA) were investigated experimentally in the temperature range of 260-360 (±2) K at a pressure of 60 Torr/N2. The absolute rate coefficient for the reaction between HCO and EF was measured to be (298 K) = (1.39 ± 0.30) × 10-14 cm3 molecule-1 s-1 at ambient temperature, whereas that for the reaction of HCO with EA was measured tobe (298 K) = (2.05 ± 0.43) × 10-14 cm3 molecule-1 s-1. The reaction of HCO with EA was faster than that with EF, which might be due to the greater stability of the formed radical intermediate due to hyperconjugative and inductive effects. The dependency of the measured kinetics on experimental pressures and laser fluences was examined within a certain range. To complement the experiments, kinetics of the title reactions in the temperature range of 200-400 K were deciphered theoretically via the canonical variational transition-state theory with small-curvature tunneling and interpolated single-point energy (CVT/SCT/ISPE) method using a dual-level approach at the CCSD(T)/cc-pVTZ//MP2/6-311++G(d,p) level of theory/basis set. A good degree of agreement was detected between the rate coefficients measured experimentally and those calculated theoretically both at room temperature and throughout the range of temperatures studied. The kinetic branching ratios and thermochemistry of the reactions were investigated to understand the thermodynamic feasibility and kinetic lability of each pathway throughout the studied temperatures. Atmospheric implications of these reactions of HCO radicals are also discussed.

A structure-preserving algorithm for time-scale non-shifted Hamiltonian systems

The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus. Not only can the combination of Δ and ∇ derivatives be beneficial to obtaining higher convergence order in numerical analysis, but also it prompts the time-scale numerical computational scheme to have good properties, for instance, structure-preserving. In this letter, a structure-preserving algorithm for time-scale non-shifted Hamiltonian systems is proposed. By using the time-scale discrete variational method and calculus theory, and taking a discrete time scale in the variational principle of non-shifted Hamiltonian systems, the corresponding discrete Hamiltonian principle can be obtained. Furthermore, the time-scale discrete Hamilton difference equations, Noether theorem, and the symplectic scheme of discrete Hamiltonian systems are obtained. Finally, taking the Kepler problem and damped oscillator for time-scale non-shifted Hamiltonian systems as examples, they show that the time-scale discrete variational method is a structure-preserving algorithm. The new algorithm not only provides a numerical method for solving time-scale non-shifted dynamic equations but can be calculated with variable step sizes to improve the computational speed.

A NOVEL COMPUTATIONAL APPROACH FOR FRACTAL NONLINEAR POCHHAMMER–CHREE MODEL

The purpose of this paper is to establish a novel algorithm to find the fractal solitary wave solution for fractal nonlinear Pochhammer–Chree model based on fractal variational theory, which is called variational transform method (VTM). The numerical examples are given to reveal the effectiveness and simplicity of the proposed method. Finally, some physical properties of the obtained fractal traveling wave solutions are illustrated by some graphs. The novel method sheds a new light on the fractal soliton theory.

Stability of a flattened dipolar binary condensate: Emergence of the spin roton

We develop a theory for a two-component miscible dipolar condensate in a planar trap. Using numerical solutions and a variational theory we solve for the excitation spectrum and identify regimes where density- and spin-roton excitations are favored. We characterize the various instabilities that can emerge in this system over a wide parameter regime and present results for the stability phase diagram. Importantly this allows us to identify the parameter regimes where a novel roton-immiscibility transition can occur, driven by the softening of the spin-roton excitation.

Relationships, power, and ambiguity: how do U.S. intelligence officer responses to toxicity affect support to the core mission?

ABSTRACT Research has explored U.S. intelligence core teams at the cultural and functional levels. How intelligence officers respond to toxic interpersonal relationships remains unexplored. A May 2021 grounded theory and situational analysis study of variations of responses to workplace toxicity in the core mission identified nine response patterns and three impacts to mission support. The study also found that power, agency, and acumen played central roles, along with relational ambiguity and toxic memory as contextual factors. The findings generated five research propositions.

Evaluating the three-network theory of creativity: Effects of music listening on resting state EEG

Research evidences the ability of music listening to transiently improve performance on creative cognition. However, the mechanism for cognitive improvements as a result of music listening is still contested. Research has asserted that three networks neatly map onto the well-known theory of blind variation and selective retention (BVRT); the default mode, cognitive control, and salience networks (SNs). This study investigates the activation in these networks after participants listen to music that has previously been shown to increase creative cognition. Using 128-channel high-density array, we measured resting state electroencephalography (EEG) in 26 participants before and after listening to the 2011 single “Can’t Hold Us.” Findings demonstrate that activation is increased in the default mode, cognitive control, and SNs, as indicated by increases in spectral frequency power for whole-brain beta, parietal theta, and whole-brain gamma. Here, we find support for the idea that music might facilitate creative cognition by activating networks deemed important in the creative process, providing novel methodology for investigating network activation in a creative cognition framework using resting state EEG.

Thermal decomposition of isopentanol: A theoretical calculation and kinetic modeling analysis

Isopentanol (3-methyl-1-butanol, 3M1B) is a prospective bioderived fuel with advantages over ethanol that make it a suitable substitute for gasoline. Although there have been studies on the combustion properties of 3M1B, reaction kinetics for its thermal decomposition is scarce. This study explores the reaction pathways for the thermal decomposition of 3M1B through theoretical calculations. Six reactions with tight transition states, and nine bond dissociation reactions (i.e., barrierless reactions) were considered. For reactions with tight transition states, the CCSD(T)/CBS//M06–2X-D3(0)/def2-TZVP method was used, and the MRCISD(+Q)/CBS//CASPT2/cc-pVDZ method was adopted for the bond dissociation reactions. The conventional transition state theory (CTST), including multi-structural torsional anharmonicity (MS-T) correction, addressed those reactions with tight transition states. The MS-T method thoroughly examined the co-effect of the multiple structures and torsional anharmonicity. Direct bond-breaking reactions were studied using the variational transition state theory (VTST). Subsequently, system-specific quantum Rice-Ramsperger-Kassel (SS-QRRK) theory and Rice-Ramsperger-Kassel-Marcus/Master Equation (RRKM/ME) were employed to obtain the rate constants for reactions with tight transition states and direct bond-breaking reactions at different temperatures and pressures (T/P) regimes (T = 298–2400 K, P = 0.01–100 atm), respectively. The results showed that water elimination and C-C bond dissociation play a significant role for 3M1B unimolecular decomposition, other molecular elimination and bond dissociation channels can be ignored. Combining the reaction pathways and the corresponding pressure dependent rate constants into the kinetic model resulted in good predictions of the speciation profiles during 3M1B pyrolysis. These data are valuable for the development of the combustion models of 3M1B.

Reactions of hydrazine with the amidogen radical and atomic hydrogen

The rate coefficient k1 for NH2 + N2H4 was measured to be (5.4 ± 0.4) × 10−14 cm3 molecule−1 s−1 at 296 K. NH2 was generated by pulsed laser photolysis of NH3 at 193 nm, and monitored as a function of time by pulsed laser-induced fluorescence excited at 570.3 nm under pseudo-first order conditions in the presence of excess N2H4 in an Ar bath gas. This reaction was also investigated computationally, with geometries and scaled frequencies obtained with M06-2X/6-311+G(2df,2p) theory, and single-point energies from CCSD(T)-F12b/cc-pVTZ-F12 theory, plus a term to correct approximately for electron correlation through CCSDT(Q). Three connected transition states are involved and rate constants were obtained via Multistructural Improved Canonical Variational Transition State Theory with Small Curvature Tunneling. Combination of experiment and theory leads to a recommended rate coefficient for hydrogen abstraction of k1 = 6.3 × 10−23 T3.44 exp(+289 K/T) cm3 molecule−1 s−1. The minor channel for H + N2H4 forming NH2 + NH3 was characterized computationally as well, to yield 5.0 × 10−19 T2.07 exp(-4032 K/T) cm3 molecule−1 s−1. These results are compared to several discordant prior estimates, and are employed in an overall mechanism to compare with measurements of half-lives of hydrazine in a shock tube.

Thermally-Activated Tunneling in the Two-Water Bridge Catalyzed Tautomerization of Phosphinylidene Compounds.

Phosphinylidenes are an important class of organophosphorus compounds that can exhibit tautomerization between tricoordinated P(III) hydroxide (R1 R2 POH) and a pentacoordinated P(V) oxide (R1 R2 P(O)H) form. Herein we show, using the canonical variational transition state theory combined with multidimensional small-curvature tunneling approximation, the dominance of proton tunneling in the two-water-bridged tautomerizations of phosphinous acid and model phosphinylidenes comprising phosphosphinates, H-phosphonates, H-phosphinates and secondary phosphine oxides. Based on the studied system, the contribution of thermally-activated tunneling is predicted to speed up the semiclassical reaction rate by ca. threefold to as large as two orders of magnitude at 298.15 K in the gas phase. The large KIE and the concavity in the Arrhenius plots are further fingerprints of tunneling. The simulations also predicted that the rapid tunneling rate and short half-life span for the forward reaction, as opposed to the reverse reaction in fluorinated secondary phosphine oxides, would result in P(V) being elusive and only P(III) being isolable, which agrees with previous experiments where only P(III) was detected by IR and NMR spectroscopy. We also explored the role of solvent and predicted tunneling to be substantial.