Elementary Case Research Articles

Approximate bound state solutions of the Dunkl-Schrödinger equation for a hyperbolic double-well interaction

We construct approximate solutions to the stationary, one-dimensional Schrödinger equation for a hyperbolic double-well potential within the Dunkl formalism. Our approximation is applied to an inverse quadratic term contributed by the Dunkl formalism in the effective potential. The solutions we obtain are given in terms of confluent Heun functions. We establish parity of these solutions, discuss their elementary cases, and present an example of a system admitting bound states.

Section force calculation in flexible substructures modelled by wind turbine design tool Bladed

Aeroelastic simulation tools are widely used to predict the coupled response for onshore, offshore and floating wind turbines. A key output of the analysis is the section forces in the flexible substructures, such as blades, towers, and floating foundations. Individual substructures are typically modelled as a single linear flexible body, which is a part of a multibody system used for modelling the complete wind turbine. However, in some floating foundation concepts, in particular those with pre-tensioned cables, geometric non-linearities in the substructure can have a significant effect. With the conventional method for calculating section forces, such non-linearities are not captured accurately. In this paper, a new equilibrium-based method for calculation of section forces is presented, as part of the wind turbine design tool Bladed. This method relies on equilibrium between the section forces and the applied loads. The section forces are determined in terms of Lagrange multipliers, which represent the internal constraint forces in the structural elements. This method is valid even when significant geometric non-linearities are present, with reduced order models, and for statically indeterminate substructures. A case study is presented demonstrating the self-consistency of the new method for the OC4 semi-submersible floating platform, modified to include pre-tensioned cables. A verification against ANSYS is also presented for some elementary cases.

초등학교 운동장 개선 사례를 통해 본 유아교육기관 바깥놀이터 개선방안 탐색

Purpose: To examine the characteristics of elementary school playground improvement cases and to explore ways to improve outdoor playgrounds of early childhood institutions. Method: The characteristics improvement cases were identified and the improvement plan for the outdoor playground of early childhood institutions was derived. Results: The playground with water and grass, with hills and tunnels, with a small forest, and built by the Ministry of Education, the Metropolitan Office of Education, students, teachers, parents, and experts. Based on this, the outdoor playground should be able to contain eco-friendly life and various plays, second, a space that can provide ecological education and rest, third, created by the educational entities together. Conclusion: Practical support policies from the municipal education offices are needed, and it should be improved by actively reflecting the needs of infants, teachers, and early childhood education experts.

Learning Transformation in the Post-Pandemic Era: Synergy of Teacher and Parent Collaboration in Elementary Schools

Changes in educational paradigms and practices after the COVID-19 pandemic are a reflection of educational improvements, examples of good practices, and predictions for the future. This research aims to investigate learning transformation in the post-COVID-19 pandemic era, focusing on the synergy of collaboration between teachers and parents at the elementary school level. The research method used was descriptive qualitative using an elementary school case study method. The research subjects involved teachers and parents of fifth-grade students at the State Elementary School of Wanasari 05 Cibitung Sub-district, who were involved in collaborative efforts. The data collection instruments in this research were interviews and observation. The data obtained would be analyzed using the Miles and Huberman model, with a data analysis process that included data reduction, where the data obtained was compiled, selected, and focused on aspects relevant to the research objectives. The research results demonstrated a transformation in post-pandemic learning approaches, especially through collaboration between teachers and parents. These collaborative practices covered strategies such as regular meetings and utilizing communication technology. It was also found that the synergy between teachers and parents positively impacted the quality of student learning, particularly in terms of motivation, understanding of the material, and social support.

A sequential inverse approach for draping simulations of woven fabrics with anisotropic hyperelastic behavior laws

Simulations of the draping of woven fabrics for the manufacturing of composite parts with complex geometries rely on either the geometrical method, which does not consider the shearing stresses and the external forces, or incremental finite element analyses, which require substantial CPU times. In this study, the one-step finite element method, also referred as the inverse approach in the literature, commonly used for sheet metal forming, is adapted to the woven fabric draping. The main issue of one-step simulations is the convergence of the Newton–Raphson scheme, which relies on an appropriate initial solution estimation. This problem is addressed by a sequential initial solution estimation, based on successive sub-problems with increasing difficulty up to the actual one. Applications of the proposed method on elementary test cases show fast and robust convergence, with CPU times comparable to those of the geometrical method. The proposed method is able to predict the influence of external forces and material hyperelastic mechanical behavior laws on the strain components of interest of woven fabrics, such as the shearing angles between yarns and the yarn elongations.

Value Distributions of Perfect Nonlinear Functions

In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions in the most general setting, generalizing several results that were achieved under specific constraints. For the particularly interesting elementary abelian case, we derive several new strong conditions and classification results on the value distributions. Moreover, we show that most of the classical constructions of perfect nonlinear functions have very specific value distributions, in the sense that they are almost balanced. Consequently, we completely determine the possible value distributions of vectorial Boolean bent functions with output dimension at most 4. Finally, using the discrete Fourier transform, we show that in some cases value distributions can be used to determine whether a given function is perfect nonlinear, or to decide whether given perfect nonlinear functions are equivalent.

Computing maximum matchings in temporal graphs

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph G, a temporal graph is represented by assigning a set of integer time-labels to every edge e of G, indicating the discrete time steps at which e is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) (e,t) such that no vertex is matched more than once within any time window of Δ consecutive time slots, where Δ∈N is given. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases, as well as fixed-parameter algorithms with respect to natural parameters and polynomial-time approximation algorithms.

Explicit infinite families of bent functions outside the completed Maiorana–McFarland class

During the last five decades, many different secondary constructions of bent functions were proposed in the literature. Nevertheless, apart from a few works, the question about the class inclusion of bent functions generated using these methods is rarely addressed. Especially, if such a “new” family belongs to the completed Maiorana–McFarland ({{{mathcal {M}}}{{mathcal {M}}}}^#) class then there is no proper contribution to the theory of bent functions. In this article, we provide some fundamental results related to the inclusion in {{{mathcal {M}}}{{mathcal {M}}}}^# and eventually we obtain many infinite families of bent functions that are provably outside {{{mathcal {M}}}{{mathcal {M}}}}^#. The fact that a bent function f is in/outside {{{mathcal {M}}}{{mathcal {M}}}}^# if and only if its dual is in/outside {{{mathcal {M}}}{{mathcal {M}}}}^# is employed in the so-called 4-decomposition of a bent function on {mathbb {F}}_2^n, which was originally considered by Canteaut and Charpin (IEEE Trans Inf Theory 49(8):2004–2019, 2003) in terms of the second-order derivatives and later reformulated in (Hodžić et al. in IEEE Trans Inf Theory 65(11):7554–7565, 2019) in terms of the duals of its restrictions to the cosets of an (n-2)-dimensional subspace V. For each of the three possible cases of this 4-decomposition of a bent function (all four restrictions being bent, semi-bent, or 5-valued spectra functions), we provide generic methods for designing bent functions provably outside {{{mathcal {M}}}{{mathcal {M}}}}^#. For instance, for the elementary case of defining a bent function h(textbf{x},y_1,y_2)=f(textbf{x}) oplus y_1y_2 on {mathbb {F}}_2^{n+2} using a bent function f on {mathbb {F}}_2^n, we show that h is outside {{{mathcal {M}}}{{mathcal {M}}}}^# if and only if f is outside {{{mathcal {M}}}{{mathcal {M}}}}^#. This approach is then generalized to the case when two bent functions are used. More precisely, the concatenation f_1||f_1||f_2||(1oplus f_2) also gives bent functions outside {{{mathcal {M}}}{{mathcal {M}}}}^# if f_1 or f_2 is outside {{{mathcal {M}}}{{mathcal {M}}}}^#. The cases when the four restrictions of a bent function are semi-bent or 5-valued spectra functions are also considered and several design methods of constructing infinite families of bent functions outside {{{mathcal {M}}}{{mathcal {M}}}}^# are provided.

A fine-grained distinction of coarse graining

This paper aims to distinguish two main types of coarse graining, and reveal the relationship between the notions of coarse graining and emergence. In physics, some forms of coarse graining seem to be indispensable to show a physical property, and the other merely changes our descriptions of the system. To clarify the notion of coarse graining, this article investigates the cases of the renormalization group method and irreversibility, both of which have been important topics in philosophy of science, and the case of the rigid body in classical mechanics, which is an elementary case including coarse graining. The case studies reveal the distinction between substantial and mere coarse-graining. This distinction clarifies the relationships between the notions of coarse graining and emergence and further provides some implications for the issues about emergence.

A new anisotropic bending model for nonlinear shells: Comparison with existing models and isogeometric finite element implementation

A new nonlinear hyperelastic bending model for shells formulated directly in surface form is presented, and compared to four existing prominent bending models. Through an essential set of elementary nonlinear bending test cases, the membrane and bending stresses of each model are examined analytically. Only the proposed bending model passes all the test cases, while the other bending models either fail or only pass the test cases for small deformations. The proposed new bending model can handle large deformations and initially curved surfaces. It is based on the principal curvatures and their directions in the initial configuration, and it thus can have different bending moduli along those directions. These characteristics make it flexible in modeling a given material, while it does not suffer from the pathologies of existing bending models. Further, the bending models are compared computationally through four classical benchmark examples and one contact example. As the underlying shell theory is based on Kirchhoff–Love kinematics, isogeometric NURBS shape functions are used to discretize the shell surface. The linearization and efficient finite element implementation of the proposed new model are also provided.

Raising the benchmark potential of a simple alcohol-ketone intermolecular balance.

2-Butanone offers two hydrogen bond docking variants to a solvating methanol which are cleanly separated by supersonic jet infrared absorption spectroscopy in the OH-stretching range, resolving earlier action spectroscopy indeterminacies for this elementary case of an intermolecular alcohol-ketone balance. The solvent preference for the shorter chain side is unambiguously derived from the spectra of homologous compounds. It is analysed in terms of competing steric and dispersion interactions and the resulting energy differences across a low interconversion barrier. Fortuitous cancellations are discussed and quantitative energy deficiencies of the employed DFT approaches are suggested. Some benchmarkable experimental observations: at low temperature, a single methanol molecule prefers the methyl-sided oxygen lone pair of 2-butanone over the ethyl-sided lone pair by 1-2 kJ mol-1, the trans butane backbone is conserved in both low-lying isomers, the OH-stretching fundamentals differ by 47(2) cm-1.

Electromagnetic Transients in Multiconductor Transmission Lines

The theory of multiconductor transmission lines is based on the principle of superposition. According to this principle, any electric or magnetic field can be represented as the sum of individual electric or magnetic fields. This theory is used to analyze and design electrical systems involving multiple conductors. In this work, the procedures for analyzing electromagnetic transients in 3-conductor transmission lines are presented, which is the last step for generalization in the case of lines to “n” conductors. The paper presents elementary cases and a more general one to illustrate such an approach.

Central limit theorem for bifurcating markov chains under L2-ergodic conditions

AbstractBifurcating Markov chains (BMCs) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMCs under $L^2$ -ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As an application, we study the elementary case of a symmetric bifurcating autoregressive process, which justifies the nontrivial hypothesis considered on the kernel transition of the BMCs. We illustrate in this example the phase transition observed in the fluctuations.

Effect of the BOPPPS model combined with case-based learning versus lecture-based learning on ophthalmology education for five-year paediatric undergraduates in Southwest China

BackgroundTo investigate the effect of the bridge-in, objective, preassessment, participatory learning, post assessment, and summary (BOPPPS) model combined with case-based learning (CBL) on ophthalmology teaching for five-year paediatric undergraduates.MethodsThe effects of the BOPPPS model combined with CBL (BOPPPS-CBL) and traditional lecture-based learning (LBL) on ophthalmology teaching were compared among students in a five-year programme. The questionnaire surveys of the students were collected and statistically analysed after the class. The final examination scores, including on elementary knowledge and case analysis, in the two groups were analysed.ResultsThere were no statistically significant differences between the teachers and students in the baseline data. More students agreed that the BOPPPS-CBL model helped develop their problem-solving skills, analytical skills and motivation for learning better than the LBL model. There was no significant difference in learning pressure between the two groups. The final examination scores of the BOPPPS-CBL group were significantly higher than those of the LBL group. The overall course satisfaction of the BOPPPS-CBL group was obviously higher than that of the LBL group.ConclusionsThe BOPPPS-CBL model is an effective ophthalmology teaching method for five-year paediatric undergraduates.

Towards random and enumerative testing for OCaml and WhyML properties

Deductive program verification greatly improves software quality, but proving formal specifications is difficult, and this activity can only be partially automated. It is therefore relevant to supplement deductive verification tools, such as Why3, with the ability to test the properties to be verified. We present a methodological study and a prototype for the random and enumerative testing of properties written either in the Why3 input language WhyML or in the OCaml programming language used by Why3 to run programs written in WhyML. An originality is that we propose enumerative testing based on data generators themselves written in WhyML and formally verified with Why3. Another specificity is that the development effort is reduced by exploiting Why3’s extraction mechanism to OCaml and an existing random testing tool for OCaml. These design choices are applied in a prototypal implementation of a tool, called AutoCheck. The prototype and the paper are designed with simplicity and usability in mind, in order to make them accessible to the widest audience. Starting from the most elementary cases, a tutorial illustrates the implemented features with many examples presented in increasing complexity order.

Nonlinear material identification of heterogeneous isogeometric Kirchhoff–Love shells

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for describing incompressible material behavior as well as initially curved shells. The material distribution is discretized by bilinear elements such that the nodal values are the design variables to be identified. Independent FE analysis and material discretization, as well as flexible incorporation of experimental data, offer high robustness and control. Three elementary test cases and one application example, which exhibit large deformations and different challenges, are considered: uniaxial tension, pure bending, sheet inflation, and abdominal wall pressurization. Experiment-like results are generated from high-resolution simulations with the subsequent addition of up to 4% noise. Local optimization based on the trust-region approach is used. The results show that with a sufficient number of experimental measurements, design variables and analysis elements, the algorithm is capable to reconstruct material distributions with high precision even in the presence of large noise. The proposed formulation is very general, facilitating its extension to other material models, optimization algorithms and meshing approaches. Adapted material discretizations allow for an efficient and accurate reconstruction of material discontinuities by avoiding overfitting due to superfluous design variables. For increased computational efficiency, the analytical sensitivities and Jacobians are provided.

A dispersion of a droplet flow on crossing wires in an air counterflow

Liquid dispersion on a wire mesh is a phenomenon that is utilized in many industrial applications, such as rotating packed beds. It is a very simple method of liquid atomization without a need for complex nozzles. This research focuses on an elementary case of a liquid dispersion on a crossing of two wires. Experiments were carried out in a wind tunnel to elucidate the influence of counterflow air velocity on a liquid sheet and droplets. High-speed camera was used to capture the impact of droplets on the crossing. Images were then processed using MATLAB® addon PIVlab. The effect of the input parameters, including a liquid flow rate in the range of 3.8 to 12 kg/h and air flow velocity varying from 0 to 9 m/s on the angle and velocity of dispersed droplets downstream of the crossing, was investigated. Finally, a qualitative description of the dispersion was evaluated. Results show that with an increasing liquid flow rate, the droplets dispersed in a wider angle. On the other hand, the influence of the air counterflow is significant only for low liquid flow rates. The atomization rate, determined by the number of small droplets, was better for higher liquid flow rates.

Computing Maximum Matchings in Temporal Graphs

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the discrete time steps at which $e$ is active. We introduce and study the complexity of a natural temporal extension of the classical graph problem Maximum Matching, taking into account the dynamic nature of temporal graphs. In our problem, Maximum Temporal Matching, we are looking for the largest possible number of time-labeled edges (simply time-edges) $(e,t)$ such that no vertex is matched more than once within any time window of $\Delta$ consecutive time slots, where $\Delta \in \mathbb{N}$ is given. The requirement that a vertex cannot be matched twice in any $\Delta$-window models some necessary recovery period that needs to pass for an entity (vertex) after being paired up for some activity with another entity. We prove strong computational hardness results for Maximum Temporal Matching, even for elementary cases. To cope with this computational hardness, we mainly focus on fixed-parameter algorithms with respect to natural parameters, as well as on polynomial-time approximation algorithms.

미래교육에 대응하는 초등학교 단위학습공간에 관한 연구 - 일본 초등학교 사례분석을 중심으로 -

The school space, which will be required in the rapidly changing future society, should be composed of a unit learning space including various programs to enable lifelong learning. Therefore, in this study, the type of unit learning space and arrangement type is derived by analyzing the case of elementary school with future education type spatial composition, and the characteristics of each are considered. In order to respond to future education in the future, we present basic data for the composition of a unit learning space including a student-centered creative educational space plan. The scope of the study was selected as an elementary school case planned as a future education type in order to derive common characteristics of unit learning spaces. In addition, considering the cultural similarity of school management methods and wearing indoor shoes, it was limited to elementary school cases built in Japan among advanced overseas cases. The period was analyzed as cases constructed within 15 years, and cases with low connectivity between the interior and exterior spaces were excluded. The results of the study are as follows. First, in the type analysis of unit learning space, the type varies depending on the usability of the multi-purpose space connected with the classroom, and the extended type expands the width of the hallway and naturally flows into movement to connect the space. Second, in the arrangement analysis of unit learning space, there is an external activity space that naturally occurs according to the configuration of two or more unit learning spaces, and there are a type having an individual external space and a type having a common external space. Depending on the purpose of this, the layout will be different. Third, in the analysis of the combination of type and arrangement of unit learning space, there is a type of combination that induces various activities in the internal and external space through the common external space. In addition, there is a type of combination that has excellent connection between interior and exterior spaces in both directions.

Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

The present article proposes a mortar-type finite element formulation for consistently embedding curved, slender beams into 3D solid volumes. Following the fundamental kinematic assumption of undeformable cross-section s, the beams are identified as 1D Cosserat continua with pointwise six (translational and rotational) degrees of freedom describing the cross-section (centroid) position and orientation. A consistent 1D-3D coupling scheme for this problem type is proposed, requiring to enforce both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions within the 3D solid. While the rotation tensor defined by the polar decomposition of the deformation gradient appears as a natural choice and will even be demonstrated to represent these material directions in a L_2-optimal manner, several alternative triad definitions are investigated. Such alternatives potentially allow for a more efficient numerical evaluation. Moreover, objective (i.e. frame-invariant) rotational coupling constraints between beam and solid orientations are formulated and enforced in a variationally consistent manner based on either a penalty potential or a Lagrange multiplier potential. Eventually, finite element discretization of the solid domain, the embedded beams, which are modeled on basis of the geometrically exact beam theory, and the Lagrange multiplier field associated with the coupling constraints results in an embedded mortar-type formulation for rotational and translational constraint enforcement denoted as full beam-to-solid volume coupling (BTS-FULL) scheme. Based on elementary numerical test cases, it is demonstrated that a consistent spatial convergence behavior can be achieved and potential locking effects can be avoided, if the proposed BTS-FULL scheme is combined with a suitable solid triad definition. Eventually, real-life engineering applications are considered to illustrate the importance of consistently coupling both translational and rotational degrees of freedom as well as the upscaling potential of the proposed formulation. This allows the investigation of complex mechanical systems such as fiber-reinforced composite materials, containing a large number of curved, slender fibers with arbitrary orientation embedded in a matrix material.