Variational Theory Research Articles

Application of variation theory in STEM education: A comprehensive guideline for STEM teachers

Incorporating appropriate pedagogical strategies has been instrumental in the development of a favorable learning environment for holistic learning, particularly in Science, Technology, Engineering, and Mathematics (STEM) education. However, there is growing evidence of the need to advance the existing methods, through more robust and comprehensive fieldwork grounded in design study. It has been shown that the lack of guidance in lesson planning using variation theory is also thought to require particular attention, as the accuracy of the student learning relies significantly on the planning of the lesson. However, little research has outlined the strategy to be followed for incorporating variation theory. This article proposes a method of preparing lesson plans to systematically implement the variation theory in STEM classrooms. The method seeks to design and implement current techniques as follows:•According to variation theory, teachers must create the necessary conditions for learning for the students to recognize what they are expected to learn.•To create the necessary conditions for learning, teachers define the key aspects of the topic to be covered and use different patterns of variations in teaching those contents, such as contrast, separation, generalization, and fusion.•Finally, teachers focus on the key aspects one by one or simultaneously to grab students’ attention.

When the Sun is Out of the Picture: Exploring a Variation Theory Key to Children’s Imagination in a Picturebook Reading Activity

The purpose of this study is to explore a theoretical idea in relation to a body of empirical material from a reading activity involving a picturebook on shadow. The theoretical idea, sprung from variation theory, entails children’s discernment through synchronic simultaneity as a key to their ability to imagine. To explore this idea, an analysis has been conducted on how 5-year-olds, in words and actions, express themselves in a reading activity involving The Black Rabbit (Leathers, 2014) in regard to discerning and imagining about shadow as a light phenomenon. Vygotsky describes children’s previous experiences as a key to their ability to imagine. The results of this study imply that children’s discernment in the moment, with synchronic simultaneity, appears to be another key that unlocks their ability to imagine explicit depictions in a picturebook. The results also show that when children’s discernment with both synchronic and diachronic simultaneity (i.e., discernment in the moment and before the moment) is missing, their ability to imagine remains untapped, as none of the keys to their imagination, which might unlock their ability to imagine implicit depictions in a picturebook, are used.

Mahler’s question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory

Mahler’s question for intrinsic Diophantine approximation on triadic Cantor set: the divergence theory

An application to formable transform: Novel numerical approach to study the nonlinear oscillator

Numerical methods in the area of nonlinear systems are extensively implemented for computing their approximate solutions because these systems are very difficult to tackle analytically. There are various numerical techniques available in the literature to find the solutions of nonlinear oscillators. Variational iteration method (VIM) is one of these approaches which is convenient to implement for these kinds of problems. In this work, our study aims to identify the numerical solution of nonlinear oscillator by making use of variational iteration method associated with Formable transformation. For the smooth utilization of this approach, we have to formulate the Lagrange multiplier through variational theory. Furthermore, we develop a new unified iterative scheme for the correction functional of VIM, considering the Formable transformation. Several new schemes of correction functional can be deduced from the newly proposed method considering the duality relation of Formable transform. In support of our primary finding, we discuss numerical example as application. A number of Physical applications of nonlinear oscillators are available in the field of vibrations and oscillations but in recent times nonlinear oscillators are used to describe complicated systems or to address mechanical, electrical, and other engineering phenomenon.

Method for extracting the free vibration response of transmission tower

The analysis of the free vibration in transmission towers is aimed at better evaluating their health status. Due to the non-stationarity of the height of non-uniform wind-induced vibration, there is a sustained forced vibration response in the vibration signal of transmission towers. This will lead to a decrease in the stability of vibration characteristics, which brings great difficulty to transmission tower status identification. In order to solve this problem, this paper proposes a method for extracting the free vibration response of transmission towers. By using Void–Kalman filtering (VKF) and generalized demodulation transform (GDT) for modal frequency tracking and pseudo-peak elimination, the signal is maximally cleaned while retaining all modal information. In addition, this paper combines variational theory and time-frequency domain features to decompose all effective modal orders in the vibration response. This not only solves the errors that exist when GDT and VKF directly process the original signal, but also makes the extraction of frequency parameters of each modal orders more convenient. The effectiveness of this approach is demonstrated by extracting the free vibration response of a 110 kV cat-head type tower. And by comparing it with existing mainstream signal processing methods using the example of bolt loosening faults. The results show that the signal processed by this approach can more stably and accurately capture the fault characteristics, providing a new idea for the extraction of free vibration response in the field of transmission tower health monitoring.

Variational field theory of macroscopic forces in coulomb fluids.

Based on the variational field theory framework, we extend our previous mean-field formalism [Y. A. Budkov and A. L. Kolesnikov, JStatMech 2022, 053205.2022], taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an additional term that depends on the autocorrelation function of the local electric field fluctuations. Utilizing the derived total stress tensor and applying the mechanical equilibrium condition, we establish a general expression for the disjoining pressure of the Coulomb fluids, confined in a pore with a slit-like geometry. Using this equation, we derive an asymptotic expression for the disjoining pressure in a slit-like pore with non-electrified conductive walls. Present theory is the basis for future modeling of the mechanical stresses that occur in electrode pores with conductive charged walls, immersed in liquid phase electrolytes beyond the mean-field theory.

Deformation behaviors in light of dislocation core characteristics with respect to the compositional-dependent misfit potentials of aluminum alloys

Dislocation core dominates dislocation mobility and mechanical properties of crystalline solids. To date, a complete landscape for describing dislocation with narrow core in metals like aluminum (Al) remains elusive, and thus deformation mechanisms of Al alloys are still unclear. This work investigates the dislocation core structure and deformation behaviors of Al alloyed with solutes X (X = Mg, Si, Cu, Zn, and Fe) within the framework of semi-discrete variational theory combined with first-principles calculations. Depending on the dislocation core characteristics, the deformation modes of Al alloys are governed by the compositional-dependent misfit potentials. Except for Fe, all other solutes in Al decrease the intrinsic SF energy, with considerable effects being Mg and Si. The deformation tends to occur via cross-slip of dislocations in Al alloyed with Mg, whereas Si additions can benefit to deform via emission of partial dislocations. Our investigation offers theoretical guidance for choosing solutes favorable to mechanical performances of Al alloys.

Toward an Accurate Black-Box Tool for the Kinetics of Gas-Phase Reactions Involving Barrier-less Elementary Steps.

An enhanced computational protocol has been devised for the accurate characterization of gas-phase barrier-less reactions in the framework of the reaction-path (RP) and variable reaction coordinate variational transition-state theory. In particular, the synergistic combination of density functional theory and Monte Carlo sampling to optimize reactive fluxes led to a reliable yet effective computational workflow. A black-box strategy has been developed for selecting the most suited density functional with reference to a high-level one-dimensional reference potential. At the same time, different descriptions of hindered rotations are automatically selected, depending on the corresponding harmonic frequencies along the RP. The performance of the new tool is investigated by means of two prototypical reactions involving different degrees of static and dynamic correlation, namely, H2S + Cl and CH3 + CH3. The remarkable agreement of the computed kinetic parameters with the available experimental data confirms the accuracy and robustness of the proposed approach. Together with their intrinsic interest, these results also pave the way toward systematic investigations of gas-phase reactions involving barrier-less elementary steps by a reliable, user-friendly tool, which can be confidently used also by nonspecialists.

Thermodynamically consistent variational theory of porous media with a breaking component

Thermodynamically consistent variational theory of porous media with a breaking component

Optimal Control Theory and Calculus of Variations in Mathematical Models of Chemotherapy of Malignant Tumors

Optimal Control Theory and Calculus of Variations in Mathematical Models of Chemotherapy of Malignant Tumors

“The Clash of Theoretizations”: the Case of the Ottoman Empire in the XVIIIth century

Article deals with some common theoretical questions and theories regarding the Ottoman Empire as an interesting matter to prove them right or wrong, and how they work on particular historical material. For such reasons several key theories will be used: modernization theory, world-system analysis, divergence theory, historical sociology, class struggle theory, another point of view is Ray Dalio’s concept of “big curve” and economic cycles theory, depicted in Clement Juglar, Tugan-Baranovsky and Nikolai Kondratiev works along with Oded Lagor’s theory of unified growth. Author tries to imply how these theories explain or could explain the magistral way of development in the XVIII century and how Ottoman history is comparable to other states. Main results are next: from modernization theory prospects Ottomans faced couple short periods of what we can call modernization (improvement or reestablishing institutions and the way they perform their strict duties) during the “Tulip Era” (1703-1730), during major confrontations with European powers (1750-1770) and by the beginning or reign of Selim III from 1789. All those endeavors were different in spheres. lasting and methods, but pursuing one goal – to emulate European experience using Islamic and strictly Ottoman background – creating a well-organized state, able to withstand Europe. Due to world-system analysis in the XVIII century Ottoman Empire inadvertently lost its superpower status, diminishing to regional power. Also, they shifted from semi-periphery to periphery, a process which has been proceeding for all of the XVIII century and ended in 1839. From a sociological point of view, Ottoman society began to polarize – both in territorial and functional ways. Territorial – local elites began to grow in wealth and question central government power, creating local myths, dealing with non-Muslim and tribal minorities. Functional – due to absence of large-scale industrial manufacturing and consequently absence of middle class in European view, Ottoman trading elites profited as mediators for Europeans and consequently didn’t grow as “Third power” to provide pressure on their government. Ray Dalio’s “big curve” concept was chosen due to its nearly absence in current research, and it is shown that it is too abstract and uses non-qualified criteria to make any probable conclusion, whether state is fine or on the verge of collapse. Economic activity cycles concept shows that Ottomans situated in the wholesale trend of the XVIII century – diminishing prices for grain and rising activity in the credit sphere.

Nonlinear polyharmonic boundary value problems in the punctured unit ball

In this paper we investigate the existence and the asymptotic behavior of positive continuous solutions for a class of nonlinear polyharmonic boundary value problems in the punctured unit ball of . Our arguments are based on potential theory associated to the polyharmonic operator , where m is a positive integer less than , properties of functions in the Kato class , Karamata regular variation theory tools and the Schauder fixed point theorem.

Discovering stochastic partial differential equations from limited data using variational Bayes inference

We propose a novel framework for discovering Stochastic Partial Differential Equations (SPDEs) from data. The proposed approach combines the concepts of stochastic calculus, variational Bayes theory, and sparse learning. We propose the extended Kramers–Moyal expansion to express the drift and diffusion terms of an SPDE in terms of state responses and use Spike-and-Slab priors with sparse learning techniques to efficiently and accurately discover the underlying SPDEs. The proposed approach has been applied to three canonical SPDEs, (a) stochastic heat equation, (b) stochastic Allen–Cahn equation, and (c) stochastic Nagumo equation. Our results demonstrate that the proposed approach can accurately identify the underlying SPDEs with limited data. This is the first attempt at discovering SPDEs from data, and it has significant implications for various scientific applications, such as climate modeling, financial forecasting, and chemical kinetics.

Theoretical Kinetics Predictions for Reactions on the NH2O Potential Energy Surface.

Recent modeling studies of ammonia oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies among the existing literature mechanisms. In this study, high-level theoretical kinetics predictions have been obtained for reactions on the NH2O potential energy surface, including the NH2 + O, HNO + H, and NH + OH reactions. These reactions have previously been highlighted as important reactions in NH3 oxidation with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations, including large basis sets and high-level corrections to yield high-accuracy (∼0.2 kcal/mol 2σ uncertainty) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature- and pressure-dependent kinetics. For radical-radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constants as well as the branching ratios. We find that the NO + H2 channel contributes 10% of the total NH2 + O flux at combustion temperatures, although this channel is not included in modern NH3 oxidation mechanisms. Modeling is used to illustrate the ramifications of these rate predictions on the kinetics of NH3 oxidation and NOx formation. The present results for NH2 + O are important for predicting the chain branching and formation of NO in the oxidation of NH3 and thermal DeNOx.

Exploring patterns of collaboration among professionals, organisations, patients and communities that meet complex challenges and promote patient well-being

Managing the well-being of a super-ageing society requires effective collaboration and communication between professionals, organisations, patients and families. Alongside education and training, the importance of a comprehensive understanding of interprofessional competencies cannot be understated. Professor Junji Haruta is building on his personal experience as a physician dealing with family illnesses to conduct research that promotes a holistic approach to medicine. He believes primary care professionals will play a crucial role in providing optimal care for the elderly population in communities for the next 20 years. Haruta is developing resources, including models and theories linked to education on complex issues in primary care, to promote effective interprofessional education. These can be utilised by individuals, universities, organisations and the wider community as a comprehensive system and facilitate the development of solutions to the increasingly complex challenges associated with healthcare, promoting individual and societal well-being. Haruta employs empirical generalisation, which explores relationships between two or more variables observed across different conditions and involves collecting findings from various cases and specific contexts to identify patterns. In one study, he and his collaborators investigated the learning process of medical students in an online community diagnostics programme using a realist approach, which involves theory-driven evaluation, to identify patterns of learning within this programme using the Context (C), Mechanism (M) and Outcome (O) framework. They found that the students acquired knowledge about communities through four distinct learning patterns, and the community diagnosis programme facilitated a deeper understanding of communities through the application of discovery learning, variation theory and cognitive flexibility theory.

Mechanistic study on the effect of ammonia co-firing with pulverized coal on NO formation and reduction

In this study, the heterogeneous formation and reduction mechanisms of NO by ammonia (NH3) were determined to evaluate the performance of NH3 co-firing with coal in NO emissions by density functional theory and canonical variational transition-state theory. NO formation is initialized by the dissociative adsorption of O2 on the char, and the subsequent dehydrogenation reactions after NH3 adsorption are prioritized. NO reduction via char synergism with NH3 are also elucidated by the NNH dissociation or ONNH conversion. Thermodynamic and kinetic results indicate that introducing NH3 has the advantage of promoting heterogeneous NO reduction, which is characteristic of the synergistic effect afforded by the properties of char and reducing agent NH3. The reduction effect of NH3 on NO is more significant than its oxidation effect for NO formation at elevated temperatures, which provides theoretical evidence for the potential advantages of NH3 co-firing on NO emissions in coal-fired boilers.

Kinetics of the Simplest Criegee Intermediate Reaction with Water Vapor: Revisit and Isotope Effect.

The kinetics of the simplest Criegee intermediate (CH2OO) reaction with water vapor was revisited. By improving the signal-to-noise ratio and the precision of water concentration, we found that the kinetics of CH2OO involves not only two water molecules but also one and three water molecules. Our experimental results suggest that the decay of CH2OO can be described as d[CH2OO]/dt = -kobs[CH2OO]; kobs = k0 + k1[water] + k2[water]2 + k3[water]3; k1 = (4.22 ± 0.48) × 10-16 cm3 s-1, k2 = (10.66 ± 0.83) × 10-33 cm6 s-1, k3 = (1.48 ± 0.17) × 10-50 cm9 s-1 at 298 K and 300 Torr with the respective Arrhenius activation energies of Ea1 = 1.8 ± 1.1 kcal mol-1, Ea2 = -11.1 ± 2.1 kcal mol-1, Ea3 = -17.4 ± 3.9 kcal mol-1. The contribution of the k3[water]3 term becomes less significant at higher temperatures around 345 K, but it is not ignorable at 298 K and lower temperatures. By quantifying the concentrations of H2O and D2O with a Coriolis-type direct mass flow sensor, the kinetic isotope effect (KIE) was investigated at 298 K and 300 Torr and KIE(k1) = k1(H2O)/k1(D2O) = 1.30 ± 0.32; similarly, KIE(k2) = 2.25 ± 0.44 and KIE(k3) = 0.99 ± 0.13. These mild KIE values are consistent with theoretical calculations based on the variational transition state theory, confirming that the title reaction has a broad and low barrier, and the reaction coordinate involves not only the motion of a hydrogen atom but also that of an oxygen atom. Comparing the results recorded under 300 Torr (N2 buffer gas) with those under 600 Torr, a weak pressure effect of k3 was found. From quantum chemistry calculations, we found that the CH2OO + 3H2O reaction is dominated by the reaction pathways involving a ring structure consisting of two water molecules, which facilitate the hydrogen atom transfer, while the third water molecule is hydrogen-bonded outside the ring. Furthermore, analysis based on dipole capture rates showed that the CH2OO(H2O) + (H2O)2 and CH2OO(H2O)2 + H2O pathways will dominate in the three water reaction.

A density functional theory study of the molecular structure, reactivity, and spectroscopic properties of 2-(2-mercaptophenyl)-1-azaazulene tautomers and rotamers

Five stable tautomer and rotamers of the 2-(2-Mercaptophenyl)-1-azaazulene (thiol, thione, R1, R2, and R3) molecules were studied using density functional theory (DFT). The geometries of the studied tautomer and rotamers were fully optimized at the B3LYP/6-31G(d,p) level. Thermodynamic calculations were performed at M06-2X/6-311G++(2d,2p) and ωB97XD/6-311G++(2d,2p) in the gas phase and ethanol solution conditions modeled by the solvation model based on density (SMD). The kinetic constant of tautomer and rotamers conversion was calculated in the temperature range 270–320 K using variational transition state theory (VTST) accompanied by one-dimensional wigner tunneling correction. Energy refinement at CCSD(T)/6–311++G(2d,2p) in the gas phase has been calculated. All the studied DFT methods qualitatively give similar tautomer stability orders in the gas phase. The ethanol solvent causes some reordering of the relative stability of 2-(2-Mercaptophenyl)-1-azaazulene conformers. The transition states for the 2-(2-Mercaptophenyl)-1-azaazulene tautomerization and rotamerization processes were also determined. The reactivity, electric dipole moment, and spectroscopic properties of the studied tautomer and rotamers were computed. The hyper-Rayleigh scattering (βHRS), and depolarization ratio (DR) exhibited promising optical properties when nonlinear optical properties were calculated.

Customer relational benefit: A second‐order meta‐analysis and an alternative framework

AbstractPrevious literature uses first‐order meta‐analyses to overcome the divergent theories about customer relational benefit, which produced mixed results in terms of the associations found. Originally conceptualised as unidimensional, customer relational benefit is an integrative multidimensional concept that includes trust, commitment, loyalty, satisfaction, word of mouth, and other constructs involved in long‐term relational exchanges. The authors conduct a second‐order meta‐analysis on 41 first‐order meta‐analyses on customer relational benefits, generating 3.8 million observations and 3462 independent samples, resulting in an overall generalisation of the relationships between these constructs. We test three theoretical models and propose an alternative rival framework. Main results indicate that the product‐ versus consumer‐related model generates strong variance in loyalty. Second, the cognitive–affective–conative–behavioural model is not superior in terms of explaining and predicting loyalty, but our three‐stage model performs better. Third, the service‐profit chain model is an alternative in terms of generating a sequence of effects (serial perspective). Fourth, our new alternative framework (a three‐stage model based on the temporal sequence of loyalty) works better for explaining some constructs.

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement