Variational Theory Research Articles

Positioning Accuracy Characterization Approach in Micro-scale Displacement for Precise Linear Stage Based on Stream of Variation Theory

Positioning Accuracy Characterization Approach in Micro-scale Displacement for Precise Linear Stage Based on Stream of Variation Theory

A NEW FRACTAL MODIFIED BENJAMIN–BONA–MAHONY EQUATION: ITS GENERALIZED VARIATIONAL PRINCIPLE AND ABUNDANT EXACT SOLUTIONS

In this paper, we derive a new fractal modified Benjamin–Bona–Mahony equation (MBBME) that can model the long wave in the fractal dispersive media of the optical illusion field based on He’s fractal derivative. First, we apply the semi-inverse method (SIM) to develop its fractal generalized variational principle with the aid of the fractal two-scale transforms. The obtained fractal generalized variational principle reveals the conservation laws via the energy form in the fractal space. Second, Wang’s Bäcklund transformation-based method, which combines the Bäcklund transformation and the symbolic computation with the ansatz function schemes, is used to study the abundant exact solutions. Some new solutions in the form of the rational function-type, double-exp function-type, Sin-Cos function-type and the Sinh-Cosh function-type are successfully constructed. The impact of the fractal orders on the behaviors of the different solutions is elaborated in detail via the 3D plots, 2D contours and 2D curves, where we can find that: (1) When the fractal order [Formula: see text], the direction of wave propagation tends to be more vertical to the [Formula: see text]-axis, on the other hand, it tends to be more parallel to the [Formula: see text]-axis when [Formula: see text]; (2) The fractal order cannot impact the peak amplitude of the waveform; (3) For the periodic waveform, the fractal orders can affect its period, that is, the period becomes smaller when the fractal order [Formula: see text]. The obtained results show that the proposed methods are effective and powerful, and can construct the abundant exact solutions, which are expected to give some new enlightenment to study the variational theory and traveling wave solutions of the fractal partial differential equations.

Multistructural partition function truncation and its effect on the thermal rate constants.

Thermal rate constants for the hydrogen abstraction reaction of methyl pentanoate were calculated using the multistructural canonical variational theory with small-curvature tunneling (MS-CVT/SCT). The conformational search for the stationary points generated by these reactions was performed with an algorithm that combines systematic and stochastic searches at dual-level. At the high-level (MPWB1K/6-31+G(d,p)), 244 geometries for methyl pentanoate and transition states were found. A systematic estimative of the efficiency of the truncation of multistructural rovibrational partition functions and its effects on thermal rate constants was carried out. In this analysis, we observed that rotation about -OCH3 group (ϕ4) of the ester generates unstable structures with little contribution to the magnitude of the partition function. We also estimate that the truncation of the partition functions in a small set of conformations can produce deviations up to 75% compared to converged theoretical results.

An analytical solution of the fractal toda oscillator

In this paper, the fractal Toda oscillator is established by using the fractal variational theory and the exact analytical solution is obtained by the non-perturbative method. Also, trigonometric series and He’s frequency formula are applied to determine the approximate analytical solution. To illustrate the operability and effectiveness of these methods, the solution processes are described in detail, and the analytical solutions are compared with numerical ones, showing good agreement. It should be noted that the relative errors produced by He's frequency formula and the trigonometric series method are all small. The results show that the non-perturbative method and He's frequency formula are extremely effective and simple for fractal differential equations. Finally, the effect of fractal derivative order on the vibration characteristics is briefly explained graphically. The non-perturbative method provides additional advantages for quickly testing the frequency property of fractal nonlinearity vibration, which is of great significance in the study of the vibration characteristics of nonlinear oscillators.

Atmospheric chemistry of methoxyflurane: Reaction with Cl atoms and further degradation

AbstractA dual‐level direct dynamics technique is used to explore the kinetic properties of the reaction of Cl atoms with methoxyflurane (CH3OCF2CHCl2). The energy profiles of two reaction channels of the two conformers are refined with the interpolated single‐point energies (ISPE) method at the CCSD(T)/M06‐2X level. The canonical variational transition state theory (CVT) with a small‐curvature tunneling (SCT) correction is used to assess the rate coefficients over a wide temperature range (250–500 K) in order to get accurate results. At a temperature of 296 K, the calculated CVT/SCT rate coefficient kCl = 2.71 × 10−13 cm3 molecule−1 s−1 is found to be in reasonably good agreement with the experimental result. Our calculations demonstrate that CH3OCF2CHCl2 + Cl → CH2OCF2CHCl2 + HCl (R1) reaction is the key pathway and a prominent conduit for CH3OCF2CHCl2 degradation in the troposphere. The atmospheric loss of C•H2OCF2CHCl2 and CH3OCF2C•Cl2 radicals are discussed. The rate coefficient value of the oxidation of the primary product HC(O)OCF2CHCl2 with the Cl atoms is 1.8 × 10−14 cm3 molecule−1 s−1, and for the first time, the rate coefficient of HC(O)OCF2CHCl2 + OH reaction has also been reported here.

Structurational Divergence, Implicit Orientations to Active Followership, and Employees’ Selection of Upward Dissent Strategies and Silence

This study investigated dissent strategy selection as a product of structurational divergence (SD) and individuals’ lay theories of leader and follower roles. A survey of working adults ( N = 338) revealed that employees who reported experiencing structurational divergence in their workplace were more likely to engage in circumvention, threatening resignation, and defensive silence. Analysis also indicated that employees with an active followership mindset were more likely to report engaging in prosocial and repetition dissent strategies. Meanwhile, they were less likely to report engaging in circumvention, threatening resignation, and defensive silence. Importantly, perceptions of SD were negatively associated with members’ implicit belief that a good follower is an active follower. Implications for structurational divergence theory, implicit theories of followership, and organizational dissent conclude the paper.

Superconductivity in the twisted bilayer transition metal dichalcogenide WSe2 : A quantum cluster study

The observation of flat energy bands in transition metal dichalcogenide bilayers such as twisted ${\mathrm{WSe}}_{2}$ makes those materials interesting prospects for reproducing the behavior observed in graphene-based systems. We use an effective Hubbard model providing a description of twisted ${\mathrm{WSe}}_{2}$ to explore the presence of superconductivity, which was previously reported in experiments. Using both the variational cluster approximation and cluster dynamical mean-field theory, we predict the existence of chiral superconductivity of type $d\ifmmode\pm\else\textpm\fi{}id$ that can be tuned by the twist angle and by the application of a perpendicular displacement field in both electron- and hole-doped systems.

Improved lightweight corrugated network design to auxetic perforated metamaterial

Auxetic metamaterials with peanut-shaped perforations are superior for durable morphing control applications due to its extremely low stress concentration level and controllable auxetic capability. However, there are some issues to be concerned for such metamaterials with complex cellular features, including (1) improving structure topology for higher material efficiency, (2) tunable Poisson's ratio from positive to negative, (3) characterization of full elastic properties. To this end, an improved lightweight design with orthogonal corrugated beams is proposed in this study to approximate the perforated auxetic structure and then its full anisotropic elastic constants are characterized by a distinctive computational homogenization model based on the eigenfunction expansion variational theory with simple implementation technique of periodic displacement constraints. The numerical model is verified by the experimental tests of three specimens with different geometrical topologies. Subsequently, the dependence of structural elastic responses on the microstructural configuration is highlighted towards an elevated understanding of cell-structure-property relationship. It is demonstrated that the local in-plane rotation of interconnected regions in unit cell under uniaxial loading contributes to the structural auxetic behavior. Also, it is feasible to achieve tailorable mechanical properties through flexible microstructural adjustment and a design criterion of the crucial zero Poisson's ratio is given by a polynomial in terms of the normalized amplitude and thickness of the curved beam. The results pave a way to the design and analysis of novel metamaterials with tunable mechanical properties.

Theoretical Study of the Atmospheric Chemistry of Methane Sulfonamide Initiated by OH Radicals and the CH3S(O)2N•H + 3O2 Reaction

In the present work, we have revisited the reaction mechanism of the atmospheric oxidation of methane sulfonamide (CH3S(═O)2NH2; MSAM) initiated by hydroxyl (OH) radicals in the gas phase. The present reaction has been studied for the first time using quantum calculations combined with chemical kinetic modeling. The abstraction of an H-atom from the -NH2 group of MSAM by OH radical to form the products CH3S(═O)2N•H + H2O was found to be a major path with a barrier height of ∼2.3 kcal mol-1 relative to the energy of the separated MSAM + •OH starting reactants. This study is the first to identify the reaction of MSAM with •OH as exclusively generating N-centered MSAM radicals. The chemical kinetic calculations for various paths associated with the MSAM + •OH reaction were performed under pre-equilibrium approximation conditions using canonical variational transition state theory, employing the small curvature tunneling method in the temperature range of 200-400 K. A recent experimental study reported that OH radical-mediated degradation of MSAM proceeds via the formation of the C-centered MSAM radical (•CH2S(═O)2NH2) product. However, the energetics and rate coefficient calculations in the present work suggest that the formation of the N-centered MSAM radical is a major path compared to that which proceeds via the C-centered MSAM radical. The overall rate coefficient for the MSAM + •OH reaction was calculated in the 200-400 K temperature range. The overall rate coefficient for the MSAM + •OH reaction was estimated to be k = 1.2 × 10-13 cm3 molecule-1 s-1 at 298 K. This rate coefficient at 298 K agrees well with the reported experimental value (1.4 × 10-13 cm3 molecule-1 s-1) at the same temperature. We also provide branching ratios for each path associated with the MSAM + •OH reaction. In addition, the atmospheric implications for the title reactions are discussed. The oxidation mechanism of the MSAM + •OH reaction suggests that the formed CH3S(═O)2N•H further reacts with atmospheric oxygen (3O2) to form the corresponding RO2 radical adduct. The downstream products of the CH3S(═O)2N•H + 3O2 reaction in the present work indicate that sulfur dioxide (SO2), carbon monoxide (CO), carbon dioxide (CO2), nitric acid (HNO3), nitrous oxide (N2O), and formic acid [HC(O)OH] are formed as final products.

Theoretical Simulations of Kinetic Isotope Effects on Decarboxylation of 3-Carboxybenzisoxazole.

Kinetic isotope effect values on the decarboxylation of 3-carboxybenzisoxazole have been computed using the second-order Kleinert's variational perturbation theory in the framework of Feynman's path integrals along with the potential energy surface obtained at the MP2/6-31+G(d) level. Good agreement with the experimental data was obtained, demonstrating that this novel computational approach for computing KIE values of organic reaction is a viable alternative to the traditional method employing the Bigeleisen equation and harmonic vibrational frequencies. Compared with the experimental measurements, consideration of anharmonicity and tunneling effects can significantly improve the calculated KIE values, reducing the root-mean-square deviation from 1.19 % for traditional method to 0.20 % for path-integral method.

The Comparison Between Kerinci Siulak and Kerinci Rawang Dialect

The Kerinci dialect has various variations in almost every region. These dialects also have differences, both at the phonological and lexical levels between dialects. However, speakers and interlocutors understand each other when speaking in their respective dialects so that it does not prevent the Kerinci people from communicating with each other. The purpose of the research was to describe the differences in language variation between the Kerinci Siulak dialect and the Kerinci Rawang dialect. This research uses Jeff Siegel's theory of language and dialect variations. In reviewing the data of this study using qualitative methods, while data collection used interview methods with recording techniques. This research was conducted in Hamparan Rawang Village and in Siulak Village, Kerinci Regency with 5 informants. The results showed that based on the available data, in the Kerinci language, the Siulak dialect and the Rawang dialect, there are sounds which are phonemes that can be grouped into three groups, namely vowels, diphthongs, and consonants. The Siulak and Rawang dialects have 23 sounds, with 5 vowels, 10 consonants, and 8 diphthongs. The correspondence phonemes of the two dialects are 35 which are at the initial, middle and final syllable caused by geographical, sociocultural and social status factors.

The roles of heteromorphic crystals and organic compounds in the formation of the submandibular stones

ObjectiveThe study aimed to analyze the formation process of submandibular stones based on the theory of biological mineralization and inorganic crystal structure variation. Study designFrom January 2021 to December 2021, patients with submandibular stones treated in the Affiliated Hospital of Stomatology, Sun Yat-sen University (Guangzhou, China) were selected. According to the criterion of maximum transverse diameter ≥3 mm, a total of five submandibular stones meeting the requirement were included. After the surface of sample stones were washed, they were cut along the maximum transverse diameter. Next, the study employed Scanning Electron Microscope (SEM), Energy Dispersive X-ray Spectroscopy (EDS), and polycrystalline X-ray Diffraction (XRD) to analyze the composition and structure of submandibular stones. ResultsFive submandibular stones were included. The organic and inorganic compounds showed a rhythmic or irregular distribution. Submandibular stones were highly occupied with carbon (C), oxygen (O), calcium (Ca), and phosphorus (P). Hydroxyapatite (HAP) was the primary inorganic component. In addition, the precursor of HAP, namely Amorphous Calcium Phosphate (ACP), was also found. Tetrahedral Substitution Index (TSI) and Ca/P ratio reflected the degree of structural variation in HAP crystal, which fluctuated from 5.62-90.71 and 1.10–1.35, respectively. ConclusionsThe development of submandibular stones was influenced by inorganic crystals’ chemical and structural variation as well as the organics’ regulation towards the inorganic. The isomorphic substitution was accompanied by the occurrence of inorganic crystals, resulting in the crystal structure change. Organics might influence the appearance, aggregation, and mineralization of HAP during its formation.

Temperature and pressure dependent rate constants of the reactions of OH• with cyclopentene from variational TST and SS-QRRK methods.

In this work, the pressure- and temperature-dependent reaction rate constants for the hydrogen abstraction and addition of hydroxyl radicals to the unsaturated cyclopentene were studied. Geometries and vibrational frequencies of reactants, products, and transition states were calculated using density functional theory, with single-point energy corrections determined at the domain-based local pair natural orbital-coupled-cluster single double triple/cc-pVTZ-F12 level. The high-pressure limit rate constants were calculated using the canonical variational transition state theory with the small-curvature tunneling approximation. The vibrational partition functions were corrected by the effects of torsional and ring-puckering anharmonicities of the transition states and cyclopentene, respectively. Variational effects are shown to be relevant for all the hydrogen abstraction reactions. The increasing of the rate constants by tunneling is significant at temperatures below 500K. The pressure dependence on the rate constants of the addition of OH• to cyclopentene was calculated using the system-specific quantum Rice-Ramsperger-Kassel model. The high-pressure limit rate constants decrease with increasing temperature in the range 250-1000K. The falloff behavior was studied at several temperatures with pressures varying between 10-3 and 103 bar. At temperatures below 500K, the effect of the pressure on the addition rate constant is very modest. However, at temperatures around and above 1000K, taking pressure into account is mandatory for an accurate rate constant calculation. Branching ratio analyses reveal that the addition reaction dominates at temperatures below 500K, decreasing rapidly at higher temperatures. Arrhenius parameters are provided for all reactions and pressure dependent Arrhenius parameters are given for the addition of OH• to cyclopentene.

Human Interference with the Earth Has Abolished the Next Ice Age but Overdosing with Carbon Dioxide Emissions Could Have Catastrophic Consequences

Around 1600 AD the carbon dioxide content of the earth’s atmosphere started to rise, even whilst according to the Milankovitch [1] astronomical theory of climate variation it was due to fall. On the natural earth the carbon dioxide count of the atmosphere is a delayed response and an enhancing feedback on the basic cause of the Milankovitch astronomical cycle, the intensity of the June sunshine. If the Milankovitch cycle had continued its natural course, the medevial cold period known as the little ice age. Human interference with the earth has abolished or delayed the next ice age but overdosing with carbon dioxide emissions could have catastrophic consequences.

Semi-discrete Lagrangian 2-forms and the Toda hierarchy

We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is an extension of the ideas known by the names ‘Lagrangian multiforms’ and ‘Pluri-Lagrangian systems’, which have previously been established in both the fully discrete and fully continuous cases. The main feature of these ideas is to capture a hierarchy of commuting equations in a single variational principle. Semi-discrete Lagrangian multiforms provide a new way to relate differential-difference equations and partial differential equations. We discuss this relation in the context of the Toda lattice, which is part of an integrable hierarchy of differential-difference equations, each of which involves a derivative with respect to a continuous variable and a number of lattice shifts. We use the theory of semi-discrete Lagrangian multiforms to derive PDEs in the continuous variables of the Toda hierarchy, which hold as a consequence of the differential-difference equations, but do not involve any lattice shifts. As a second example, we briefly discuss the semi-discrete potential Korteweg-de Vries equation, which is related to the Volterra lattice.

Precise ground state of multiorbital Mott systems via the variational discrete action theory

Determining the ground state of multi-orbital Hubbard models is critical for understanding strongly correlated electron materials, yet existing methods struggle to simultaneously reach zero temperature and infinite system size. The \textit{de facto} standard is to approximate a finite dimension multi-orbital Hubbard model with a $d=\infty$ version, which can then be formally solved via the dynamical mean-field theory (DMFT), though the DMFT solution is limited by the state of unbiased impurity solvers for zero temperature and multiple orbitals. The recently developed variational discrete action theory (VDAT) offers a new approach to solve the $d=\infty$ Hubbard model, with a variational ansatz that is controlled by an integer $\mathcal{N}$, and monotonically approaches the exact solution at an increasing computational cost. Here we propose a decoupled minimization algorithm to implement VDAT for the multi-orbital Hubbard model in $d=\infty$ and study $\mathcal{N}=2-4$ . At $\mathcal{N}=2$, VDAT rigorously recovers the multi-orbital Gutzwiller approximation, reproducing known results. At $\mathcal{N}=3$, VDAT precisely captures the competition between the Hubbard $U$, Hund $J$, and crystal field $\Delta$ in the two orbital Hubbard model over all parameter space, with a negligible computational cost. For sufficiently large $U/t$ and $J/U$, we show that $\Delta$ drives a first-order transition within the Mott insulating regime. In the large orbital polarization limit with finite $J/U$, we find that interactions have a nontrivial effect even for small $U/t$. VDAT will have far ranging implications for understanding multi-orbital model Hamiltonians and strongly correlated electron materials.

Deflection assessment of prestressed steel-concrete–steel sandwich panel: experiment and numerical simulation

A steel-concrete-steel sandwich panel with prestressed reinforcement was developed, named prestressed steel-concrete–steel sandwich panel. Nine specimens where the loading mode, top steel plate thickness, spacing of connectors and prestressed reinforcement arrangement were varied were experimentally tested to explore the failure mode, ultimate strength, ductility and deflection of the structure. The results show that prestressing enhanced the ultimate strength and ductility of the structure. Finite element analysis predictions were consistent with test results in terms of crack characteristics, load-displacement curve and ultimate strength. Deflection prediction analysis of the prestressed panels was also developed based on variational theory which provided good agreement with the finite element results.

PERIODIC WAVE STRUCTURE OF THE FRACTAL GENERALIZED FOURTH-ORDER BOUSSINESQ EQUATION TRAVELING ALONG THE NON-SMOOTH BOUNDARY

In this study, we present a fractal generalized fourth-order Boussinesq equation which can describe the shallow water waves with the non-smooth boundary (such as the fractal boundary). Aided by the semi-inverse method, we establish its variational principle, which is proved to have a strong minimum condition via the He–Weierstrass theorem. Then, two powerful approaches namely the variational method (VM) and energy balance theory (EBT) are utilized to search for the periodic wave solutions. As expected, the results obtained by the two methods are almost the same. Furthermore, the impact of the fractal orders on the periodic wave structure is illustrated via the 3D plot and 2D curve. The results of this paper are expected to provide a reference for the study of periodic wave theory in fractal space.

The new formulation of Hamiltonian second order continuous systems of Riemann-Liouville fractional derivatives

In this study, we first generalized the Hamilton formulation for continuous systems with second-order fractional derivatives and applied it to Podolsky’s generalized electrodynamics. Then, we compared the outcomes to those obtained using Dirac’s approach. This approach was primarily intended to validate Podolsky’s generalized electrodynamics. Using this technique, a combined Riemann-Liouville fractional derivative operator and a fractional variational theory are produced. Fractional Euler equations and fraction Hamilton equations are created using the fraction variational notion. The Hamiltonian equations of motion are compatible with the Euler–Lagrange equations.

Anything but Cookbook Medicine: Exploring the Influence of Supervisor Practice Variability on Resident Learning in Thrombosis Medicine

Introduction Clinical practice variability is characterized by two or more expert clinicians who make different treatment decisions despite encountering a similar case. Thrombosis Medicine is an example of a specialty that has a large evidence base to support decision-making and where practice variability is common. Our objective was to explore how residents experience and interpret inter-supervisor clinical practice variability in Thrombosis Medicine, and how these variations influence learning. Methods Seventeen senior residents in Internal Medicine, Hematology or Thrombosis Medicine (Postgraduate Year [PGY] 3-6) participated in semi-structured interviews. Data collection and analysis occurred iteratively and concurrently in a manner consistent with constructive grounded theory methodology. Variation theory was used as a sensitizing concept. A central tenet of this theory is that learning occurs by experiencing three sequential patterns of variation: contrast, generalization, and fusion. All transcripts were coded in duplicate by paired members of the study team. Participants were recruited purposively with regard to their field of training until thematic saturation was reached. The primary investigator maintained an audit trail and reflexivity journal. Member checking was performed. Dedoose (version 8.0.35) was used for all analyses. The Hamilton Integrated Research Ethics Board reviewed the study. Results Clinical practice variability was common and generally viewed positively. Residents attributed clinical practice variability to supervisor personality differences, inter-institutional differences, availability and interpretation of evidence, differences in patient preferences and characteristics, and their own participation in the decision-making process. Inherent differences between supervisors, including personality traits, risk tolerance, and prior educational and clinical experiences were a major contributor. Clinical practice variability was felt to be most common when the clinical problem had scant or conflicting evidence to guide practice, for example, in the treatment of subsegmental pulmonary embolism or splanchnic vein thrombosis. Supervisors and learners often took patient preferences into account when making a decision, especially when the net clinical benefit of anticoagulation was uncertain. Supervisor-learner discussions were critical to learning from clinical practice variability. Through these interactions, residents asked clarifying questions, and supervisors shared tacit knowledge, elaborated on their prior experiences, compared and contrasted similar cases, and articulated their clinical reasoning. Residents endorsed the view that a certain baseline level of knowledge is required to appreciate the nuances that are uncovered by clinical practice variability. Junior residents (PGY 2-4) were often assessment-focused and made note of practice patterns between their supervisors in order to predict their supervisors' preferences for future cases. More experienced residents (PGY 5-6), especially those pursuing advanced training in Thrombosis Medicine, were more likely to view clinical practice variability as a means to improve their own decision-making skill in preparation for independent practice. Consistent with variation theory, clinical practice variability helped residents to discern critical aspects that influenced decision-making (contrast), group similar cases together so that the appropriate evidence could be applied (generalization), and weigh multiple variables to make a treatment decision (fusion). Observing practice variability was more helpful for senior learners and less so for junior learners as inexperience and knowledge gaps made it difficult to reconcile differences. Conclusion Residents had a generally positive perception of clinical practice variability in the workplace. Practice variability helped residents discern critical aspects, group similar patients together and practice individualized medicine. Reflection, literature review, and case discussions were felt to maximize learning from practice variability. Clinical supervisors and curriculum designers can promote learning from practice variability through first and second order scaffolding, modeling, coaching, and thinking aloud.