Search results for: boundary play

Authors: Guohua Tu, Zhi Fu, Zhiwei Hu, Neil D Sandham, Jianqiang Chen

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Tripping of boundary-layers from laminar to turbulent flow, which may be necessary in specific practical applications, requires high amplitude disturbances to be introduced into the boundary layers without large drag penalties. As a possible improvement on fixed trip devices, a technique based on vortex shedding for enhancing supersonic flow transition is demonstrated in the present paper for a Mach 1.5 boundary layer. The compressible Navier-Stokes equations are solved directly using a high-order (fifth-order in space and third-order in time) finite difference method for small-scale cylinders suspended transversely near the wall. For cylinders with proper diameter and mount location, asymmetry vortices shed within the boundary layer are capable of tripping laminar-turbulent transition. Full three-dimensional simulations showed that transition was enhanced. A parametric study of the size and mounting location of the cylinder is carried out to identify the most effective setup. It is also found that the vortex shedding can be suppressed by some factors such as wall effect.

Keywords: boundary layer instability, boundary layer transition, vortex shedding, supersonic flows, flow control

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Authors: Shamsul Chowdhury

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The objective of this paper is to present the detailed analysis of the turbulent wave boundary layer produced by progressive finite-amplitude waves theory. Most of the works have done for the mass transport in the turbulent boundary layer assuming the eddy viscosity is not time varying, where the sediment movement is induced by the mean velocity. Near the ocean bottom, the waves produce a thin turbulent boundary layer, where the flow is highly rotational, and shear stress associated with the fluid motion cannot be neglected. The magnitude and the predominant direction of the sediment transport near the bottom are known to be closely related to the flow in the wave induced boundary layer. The magnitude of water particle velocity at the Crest phase differs from the one of the Trough phases due to the non-linearity of the waves, which plays an important role to determine the sediment movement. The non-linearity of the waves become predominant in the surf zone area, where the sediment movement occurs vigorously. Therefore, in order to describe the flow near the bottom and relationship between the flow and the movement of the sediment, the analysis was done using the non-linear boundary layer equation and the finite amplitude wave theory was applied to represent the velocity fields in the turbulent wave boundary layer. At first, the calculation was done for turbulent wave boundary layer by two-dimensional model where throughout the calculation is non-linear. But Stokes second order wave profile is adopted at the upper boundary. The calculated profile was compared with the experimental data. Finally, the calculation is done based on various modes of the velocity and turbulent energy. The mean velocity is found to differ from condition of the relative depth and the roughness. It is also found that due to non-linearity, the absolute value for velocity and turbulent energy as well as Reynolds stress are asymmetric. The mean velocity of the laminar boundary layer is always positive but in the turbulent boundary layer plays a very complicated role.

Keywords: wave boundary, mass transport, mean velocity, shear stress

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Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

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We study the existence of positive solutions to the three points difference summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: positive solution, boundary value problem, fixed point theorem, cone

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Authors: Sherri Franklin-Guy

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The emergence of language in young children has been well-documented and play-based activities that support its continued development have been utilized in the clinic-based setting. Speech-language pathologists have long used such activities to stimulate the production of language in children with speech and language disorders via modeling and elicitation tasks. This presentation will examine the importance of play in the development of language in young children, including social and pragmatic communication. Implications for clinicians and educators will be discussed.

Keywords: language development, language stimulation, play-based activities, symbolic play

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

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Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Aziz Sezgin

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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems

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Authors: Dhahri Maher, Aouinet Hana

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The presence of bubbles in the boundary layer introduces corrections into the log law, which must be taken into account. In this work, a logarithmic wall law was presented for bubbly two phase flows. The wall law presented in this work was based on the postulation of additional turbulent viscosity associated with bubble wakes in the boundary layer. The presented wall law contained empirical constant accounting both for shear induced turbulence interaction and for non-linearity of bubble. This constant was deduced from experimental data. The wall friction prediction achieved with the wall law was compared to the experimental data, in the case of a turbulent boundary layer developing on a vertical flat plate in the presence of millimetric bubbles. A very good agreement between experimental and numerical wall friction prediction was verified. The agreement was especially noticeable for the low void fraction when bubble induced turbulence plays a significant role.

Keywords: bubbly flows, log law, boundary layer, CFD

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Authors: Md. Fazlul Karim, Ahmad Izani Md. Ismail, Mohammed Ashaque Meah

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This paper focuses on the development of a 2-D Boundary Fitted and Nested Grid (BFNG) model to compute the tsunami propagation of Indonesian tsunami 2004 along the coastal region of Penang in Peninsular Malaysia. In the presence of a curvilinear coastline, boundary fitted grids are suitable to represent the model boundaries accurately. On the other hand, when large gradient of velocity within a confined area is expected, the use of a nested grid system is appropriate to improve the numerical accuracy with the least grid numbers. This paper constructs a shallow water nested and orthogonal boundary fitted grid model and presents computational results of the tsunami impact on the Penang coast due to the Indonesian tsunami of 2004. The results of the numerical simulations are compared with available data.

Keywords: boundary fitted nested model, tsunami, Penang Island, 2004 Indonesian Tsunami

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Authors: D. M. W. Munasinghe

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This study focuses on how teachers view and use play to influence creativity in preschool children. Play is strongly featured in most of the discussions about creativity in young children. Hence, it was noted through direct observation that most preschool teachers are not concerned with promoting play to develop the child’s creativity. Therefore, this study attempts to investigate how the teachers use play, for the development of creativity in the preschool environment. The survey method was used as the research design and interviews, observations and document perusal were used as data collection methods. The sample consisted of 20 preschools from selected administrative divisions in the Colombo district. It was revealed that a majority of preschool teachers used folk games as a means of involving children in play. Teachers assume that this type of guided play will motivate the child learn new words, memorization and provide enjoyment. Eighty percent of the preschool teachers used the play equipment installed in the preschool premises to encourage children to get involved in activities calculated at promoting the physical development of the child. In 40% of the preschools visited it was noticed that when children were given their break they created their own forms of free play and enjoyed themselves thoroughly in the little time available to them. Also, about 20% of preschool teachers promoted imaginative play with their preschoolers. There was also the situation where the role of play was interpreted negatively by the teachers who assigned the children to copy letters and numerals during the time assigned for play. This has a negative impact on the child’s creativity. In conclusion, it was felt that the teachers do not make the best use of the opportunity available to use the child’s enthusiasm to stimulate creative actions his/her and that there is no suitable environment to develop creativity through play.

Keywords: creativity, preschool children, preschool environment, play method

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Authors: Esra Orum Cattik

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This study evaluated the effects of using video modeling procedures on the iPad to teach play skills to children with autism spectrum disorders. A male student with autism spectrum disorders participated in this study. A multiple baseline-across-skills single-subject design was used to evaluate the effects of using video modeling procedures on the iPad. During baseline, no prompts were presented to participants. In the intervention phase, the teacher gave video model on iPad to the first skill and asked play with toys for him. When the first play skill completed the second play skill began intervention. This procedure continued till all three play skill completed intervention. Finally, the participant learned all three play skills to use video modeling presented on the iPad. Based upon findings of this study, suggestions have been made to future researches.

Keywords: autism spectrum disorders, play, play skills, video modeling, single subject design

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Authors: Alsaidi M. Altaher, Mohd Tahir Ismail

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Wavelet thresholding has been a power tool in curve estimation and data analysis. In the presence of outliers this non parametric estimator can not suppress the outliers involved. This study proposes a new two-stage combined method based on the use of the median filter as primary step before applying wavelet thresholding. After suppressing the outliers in a signal through the median filter, the classical wavelet thresholding is then applied for removing the remaining noise. We use automatic boundary corrections; using a low order polynomial model or local polynomial model as a more realistic rule to correct the bias at the boundary region; instead of using the classical assumptions such periodic or symmetric. A simulation experiment has been conducted to evaluate the numerical performance of the proposed method. Results show strong evidences that the proposed method is extremely effective in terms of correcting the boundary bias and eliminating outlier’s sensitivity.

Keywords: boundary correction, median filter, simulation, wavelet thresholding

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Authors: Végh Ádám, Mekler Csaba, Dezső András, Szabó Dávid, Stomp Dávid, Kaptay György

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Grain boundary segregation transition (GBST) has been calculated by a thermodynamic model in binary alloys. The method is used on cementite (Fe3C) segregation in base-centered cubic (ferrite) iron (Fe) in the Fe-C binary system. The GBST line is shown in the Fe3C lacking part of the phase diagram with high solvent (Fe) concentration. At a lower solute content (C) or at higher temperature the grain boundary is composed mostly of the solvent atoms (Fe). On higher concentration compared to the GBST line or at lower temperature a phase transformation occurs at the grain boundary, the latter mostly composed of the associates (Fe3C). These low-segregation and high-segregation states are first order interfacial phase transitions of the grain boundary and can be transformed into each other reversibly. These occur when the GBST line is crossed by changing the bulk composition or temperature.

Keywords: GBST, cementite, segregation, Fe-C alloy

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Authors: Thelma Mort

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Currently, in South African schools, under the fast-paced and content-heavy CAPS curriculum, the notion of play is being lost in the foundation phase. Even in Grade R, aimed at improving the quality of education, there is a focus on mathematical literacy, language, and life skills (DoE, 2001). This is largely due to the dichotomizing of play and learning. And although the play is meant to be the primary means of achieving these skills, it somehow loses its playfulness in the face of early academic pressure. Student teachers similarly have not been trained to use play in the early years of schooling. This action research study shares findings from the “Learn to Play” intervention in teacher training at one university in which student teachers were given substantial training in types of play, the ways they could use and promote play, and the changing roles of teachers in play-based learning. Using observation focus group interviews, reflections, student teacher engagement in learning communities, and Theories of Change, the study measures the changes made by the intervention in student teachers’ approaches and attitudes to play in the classroom. Key findings were that the student teachers learned new skills, had better relationships with pupils, and became more confident in their foundation phase settings.

Keywords: action research, foundation phase, South Africa, student teacher training

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Authors: Zhenjie Liu

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This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method. The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

Keywords: mixed monotone operator, boundary value problem, time scale, green's function, positive solution, singularity

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Authors: Fiona Armstrong, David Gaul, Michael Barrett, Lorraine D'Arcy

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Playing is an instinctive and universal human behavior, is a child’s way of learning and an outlet for their innate need of activity. Risky play can be defined as any play that is thrilling or exciting involving the risk of injury. The benefits of risky play have been acknowledged as helping children to explore and conquer fears, develop confidence, reduce anxiety, and develop risk-management skills. Studies indicate that children learn sound judgment by assessing and confronting risks in relation to their own capabilities through exposure to carefully managed play experiences. Risky play has been associated with danger and increased risk of injury, with families focusing on risk aversion and protecting children from the risks inherent in the modern world. Despite children needing cultural, social, emotional, physical, and geographical space to play, the opportunity for children to play is diminishing. Aim: This study explores play behaviors and risky play in an Irish context by investigating parental attitudes to risky play. Methodology: This is a mixed methods study involving the State of Play survey and semi-structured interviews exploring parental attitudes to risky play. Data will be quantitatively analyzed using descriptive and inferential statistics using IBM SPSS and qualitatively analyzed via thematic analysis using NVivo. Conclusion: The information gathered could advise stakeholders regarding the creation and provision of developmentally appropriate, challenging, stimulating, adaptable, accessible, and safe as necessary outdoor play areas. This research can inform parents, planners, architects, and authorities involved in creating environments for play and contribute to policy development.

Keywords: child development, parental attitudes, play opportunities, risky play

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Authors: Chinsuk Hong

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This paper investigates the characteristics of wall pressure fluctuations in naturally developing boundary layer flows on axisymmetric bodies experimentally. The axisymmetric body has a modified ellipsoidal blunt nose. Flush-mounted microphones are used to measure the wall pressure fluctuations in the boundary layer flow over the body. The measurements are performed in a low noise wind tunnel. It is found that the correlation between the flow regime and the characteristics of the pressure fluctuations is distinct. The process from small fluctuation in laminar flow to large fluctuation in turbulent flow is investigated. Tollmien-Schlichting wave (T-S wave) is found to generate and develop in transition. Because of the T-S wave, the wall pressure fluctuations in the transition region are higher than those in the turbulent boundary layer.

Keywords: wall pressure fluctuation, boundary layer flow, transition, turbulent flow, axisymmetric body, flow noise

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Authors: Rana Alghamdi

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This study explored teachers’ perceptions of rough-and-tumble (R&T) play in early childhood education in Saudi Arabia. The literature on rough-and-tumble play in Saudi Arabia is limited in scope, and more research is needed to explore teachers’ perceptions on this type of play for early learners. The pertinent literature reveals that R&T play, which includes running, jumping, fighting, wrestling, chasing, pulling, pushing, and climbing, among other rough playful activities, can positively impact learning and development across psychosocial, emotional, and cognitive domains. Teachers’ understanding of R & T play is key, and the attitudes of Saudi early childhood teachers who are responsible for implementing curriculum-based play have not been fully researched. Four early childhood teachers from an urban Saudi preschool participated in the study. The data collected in this study were interpreted through a sociocultural lens. Data sources included in-depth interviews, photo-elicitation interviews, and participant-generated drawings. Three overarching themes emerged: teachers’ concerns about rough-and-tumble play, teachers’ perceptions about the benefits of rough-and-tumble play, and teachers’ expression of gender roles in R & T play as contextualized within Saudi culture. Saudi teachers’ perceptions are discussed in detail, and implications of the findings and recommendations for future research are put forth.

Keywords: rough and tumble play, gender, culture, early childhood, Saudi Arabia

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Authors: Bo Wan, Xiu Wen, Lingling An, Xiaoling Ding

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The paper describes a Chinese shadow play animation system based on Kinect. Users, without any professional training, can personally manipulate the shadow characters to finish a shadow play performance by their body actions and get a shadow play video through giving the record command to our system if they want. In our system, Kinect is responsible for capturing human movement and voice commands data. Gesture recognition module is used to control the change of the shadow play scenes. After packaging the data from Kinect and the recognition result from gesture recognition module, VRPN transmits them to the server-side. At last, the server-side uses the information to control the motion of shadow characters and video recording. This system not only achieves human-computer interaction, but also realizes the interaction between people. It brings an entertaining experience to users and easy to operate for all ages. Even more important is that the application background of Chinese shadow play embodies the protection of the art of shadow play animation.

Keywords: hadow play animation, Kinect, gesture recognition, VRPN, HCI

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Authors: Benjamin Cramer, Josephine Chau, Helen Little, Erica Randle

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Play Streets provide a safe and open space for children to play and adults to socialize by closing residential streets to through traffic. While research on Play Streets has typically focused on physical activity outcomes in children, there is limited research on the psychosocial health externalities for the wider community. Charles Sturt, a local government area in Adelaide, South Australia, has been hosting Play Streets for several years. The current study is a mixed-methods evaluation of the Charles Sturt Play Streets, concerned with the perceived psychological and social impacts that Play Streets impact on the community. A combination of semi-structured interviews of Play Street organizers and participants will be conducted and analyzed using inductive thematic analysis. Pre-existing survey data will also be analyzed quantitatively and qualitatively to triangulate the findings of the qualitative interviews. The implications of this research are far-reaching, from informing local councils of any additional health benefits of Play Streets, expanding the growing literature on Play Streets beyond childhood physical activity, informing the development of city infrastructure, and advancing the Sustainability Development Goals of Good Health and Wellbeing, Reduced Inequalities, and Sustainable Cities and Communities.

Keywords: play streets, mental health, social health, community health

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Authors: Mingxi Xiao

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This case study focused on a bilingual child named Emma and her play. Emma was a four-year-old girl born in Australia while her parents were both Chinese. Emma could speak fluent English, while her Mandarin was not as good as her spoken English. With the research question to figure out whether creative play had an impact on children’s bilingualism, this case study mainly used the anecdotes method to observe Emma’s play and this report presented five observations of Emma, describing detailed information about her play and recording her language use. Based on Emma’s interests and daily activities, this case study chose her creative play for observation, which incorporates a whole range of activities from dancing to drawing, as well as playing instruments. From the five observations, it could be seen that Emma often mixed languages to help her express her meaning. It could be seen that Emma made an effort to use her bilingualism in her creative play. In other words, play encouraged Emma to use the two languages. In conclusion, the observations with Emma showed that although her Mandarin was not good enough, she displayed confidence in speaking both languages and had gradually shifted from mixing languages to code-switching. Recommendations were provided to support Emma’s bilingual abilities for further development in the end.

Keywords: bilingual, case study, code-switching, creative play, early childhood

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Authors: Jayashree S. Bhat, Megha Mohan

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Play is any activity spontaneously chosen, inherently motivated, and personally directed. There is a wide range of literature and research supporting the concept of play in promoting healthy development in young children. Modern children are experiencing nurture that has more structure and adult involvement than previous generations and free, unstructured, and child directed play is under peril. Play behaviors serve as a reflection of a child’s cultural and ethnic background and can be an index of a child’s development. The influence and impact of culture in children’s play is diverse. The culturally variable dimensions of play includes the choice of objects, the involvement of specific play partners, the amount of child initiations of social pretend play with caregivers along with its the components, and sequences and specific themes involved during play. India is a country well known for its cultural diversity. In this study, a cross sectional study design with convenient sampling was adopted. The mother child free play interaction was video clipped at their residence among typically developing children between 12 to 24 months in an urban city from South India. It was ascertained that all the children were first born and mothers were unemployed belonging to middle socioeconomic status. The video clippings were coded and analysed using SPSS software version 17. The results revealed interesting behaviors demonstrated by the mother as well as the child during the play interaction. The results high light the need for focusing on the play behaviors of children during their developmental assessment, especially so for children with challenges.

Keywords: culture, free play, interaction, typically developing

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Authors: Janaka B. Lewis

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“Narratives of Slavery and the Culture of Play” examines how play is discussed in early African American literature by both men and women to illustrate ways that they negotiated the hierarchy and oppression of enslavement. Reading narratives categorized as “slave narratives,” including those written by Frederick Douglass, Harriet Jacobs, and Olaudah Equiano, through the lens of play theory offers an illuminated analysis of the significance of play culture in these texts. It then reads late nineteenth-century play culture (or absence thereof) portrayed in literature as a lens for more contemporary African American oral and literary culture. These discussions of social constructions through literature bridge analyses of African American-authored texts and create a larger conversation about print media as a tool of activism and resistance. This essay also contributes to a larger body of analysis of nineteenth-century African American culture through literature.

Keywords: childhood, slavery, consciousness of play, 19th century African American culture

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Authors: Po-Chun Wang, Yan-Ru Lai, Sophia I. C. Lin, Alvin W. Y. Su

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The Generative Theory of Tonal Music (GTTM) provides systematic approaches to recognizing local boundaries of music. The rules have been implemented in some automated melody segmentation algorithms. Besides, there are also deep learning methods with GTTM features applied to boundary detection tasks. However, these studies might face constraints such as a lack of or inconsistent label data. The GTTM database is currently the most widely used GTTM database, which includes manually labeled GTTM rules and local boundaries. Even so, we found some problems with these labels. They are sometimes discrepancies with GTTM rules. In addition, since it is labeled at different times by multiple musicians, they are not within the same scope in some cases. Therefore, in this paper, we examine this database with musicians from the aspect of classical music and relabel the scores. The relabeled database - GTTM Database v2.0 - will be released for academic research usage. Despite the experimental and statistical results showing that the relabeled database is more consistent, the improvement in boundary detection is not substantial. It seems that we need more clues than GTTM rules for boundary detection in the future.

Keywords: dataset, GTTM, local boundary, neural network

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Authors: Stephen Kirkup

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This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: boundary element method, Laplace’s equation, vector calculus, simulation, education

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Yigal Rosen, Garrett Jaeger, Michelle Newstadt, Ilia Rushkin, Sara Bakken

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All children are capable of advancing their creative thinking skills and engaging in creative play. Creative play puts children in charge of exploring ideas, relationships, spaces and problems. Supported by The LEGO Foundation, the creative thinking formative assessment is designed to provide valid, reliable and informative measurement to support the development of creative skills while children are engaged in Learning through Play. In this paper we provide an overview of the assessment framework underpinned the assessment of creative thinking and report the results from the 2022 pilot study demonstrating promising evidence on the ability to measure creative skills in a conceptually and ecologically valid way to inform the development of creative skills.

Keywords: creativity, creative thinking, assessment, learning through play, creative play, learning progressions

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Authors: S. Kida

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We consider the flow of an incompressible viscous fluid in a precessing sphere whose spin and precession axes are orthogonal to each other. The flow is characterized by two non-dimensional parameters, the Reynolds number Re and the Poincare number Po. For which values of (Re, Po) will the flow approach a steady state from an arbitrary initial condition? To answer it we are searching the instability boundary of the steady states in the whole (Re, Po) plane. Here, we focus the rapidly rotating and weakly precessing limit, i.e., Re >> 1 and Po << 1. The steady flow was obtained by the asymptotic expansion for small ε=Po Re¹/² << 1. The flow exhibits nearly a solid-body rotation in the whole sphere except for a thin boundary layer which develops over the sphere surface. The thickness of this boundary layer is of O(δ), where δ=Re⁻¹/², except where two circular critical bands of thickness of O(δ⁴/⁵) and of width of O(δ²/⁵) which are located away from the spin axis by about 60°. We perform the linear stability analysis of the steady flow. We assume that the disturbances are localized in the critical bands and make an expansion analysis in terms of ε to derive the eigenvalue problem for the growth rate of the disturbance, which is solved numerically. As the solution, we obtain an asymptote of the stability boundary as Po=28.36Re⁻⁰.⁸. This agrees excellently with the corresponding laboratory experiments and numerical simulations. One of the most popular instability mechanisms so far is the parametric instability, which turns out, however, not to give the correct stability boundary. The present instability is different from the parametric instability.

Keywords: boundary layer, critical band, instability, precessing sphere

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Authors: Erin Louise Robinson, Emily Elsa Freeman

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Rough-and-tumble play (RTP) is a physical and competitive type of play that parents engage in with their children. While past research has reported RTP to be the preferred play type for western fathers, the frequency of these interactions in Australian families have not been explored. With parental perceptions of play importance playing a major role in the frequency of activity engagement, the present study investigated how perceptions and parent gender impact on RTP play frequency. By utilising child gender in our approach, we also examined the historical trend of boys receiving more physical play interactions with their parents. Three hundred and seventy-nine respondents completed the study with their 0–10-year-old children. The results indicated that, in line with past research, parents engaged more frequently in RTP with their sons than their daughters. While, both mothers and fathers participated in RTP with their children, fathers perceived RTP to be of greater important to their child’s development than mothers did. Moreover, supporting previous findings, this more positive perception of the play was related to greater frequency of RTP in these father-child dyads. Although RTP literature remains heavily focussed on fathers, the fact that mothers are engaging in these interactions as well, establishes the need to explore maternal influences in future research.

Keywords: parenting, play, child development, family, Australia

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Authors: Manana Chumburidze, David Lekveishvili

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We have considered the harmonic oscillations and general dynamic (pseudo oscillations) systems of theory generalized Green-Lindsay of couple-stress thermo-elasticity for isotropic, homogeneous elastic media. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed.

Keywords: the couple-stress thermoelasticity, boundary value problems, dynamic problems, approximate solution

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Authors: Shuang Luo, Er-Xiang Song

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Many problems in geotechnical engineering, such as foundation deformation, groundwater seepage, seismic wave propagation and geothermal transfer problems, may involve analysis in the ground which can be seen as extending to infinity. To that end, consideration has to be given regarding how to deal with the unbounded domain to be analyzed by using numerical methods, such as finite element method (FEM), finite difference method (FDM) or finite volume method (FVM). A simple artificial boundary approach derived from the analytical solutions for transient radial seepage problems, is introduced. It should be noted, however, that the analytical solutions used to derive the artificial boundary are particular solutions under certain boundary conditions, such as constant hydraulic head at the origin or constant pumping rate of the well. When dealing with unbounded domains with unsteady boundary conditions, a more sophisticated artificial boundary approach to deal with the infinity of the domain is presented. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global artificial boundary conditions (ABCs) are simplified to local ones so that the computational efficiency is enhanced significantly. The introduced two local ABCs are implemented in a finite element computer program so that various seepage problems can be calculated. The two approaches are first verified by the computation of a one-dimensional radial flow problem, and then tentatively applied to more general two-dimensional cylindrical problems and plane problems. Numerical calculations show that the local ABCs can not only give good results for one-dimensional axisymmetric transient flow, but also applicable for more general problems, such as axisymmetric two-dimensional cylindrical problems, and even more general planar two-dimensional flow problems for well doublet and well groups. An important advantage of the latter local boundary is its applicability for seepage under rapidly changing unsteady boundary conditions, and even the computational results on the truncated boundary are usually quite satisfactory. In this aspect, it is superior over the former local boundary. Simulation of relatively long operational time demonstrates to certain extents the numerical stability of the local boundary. The solutions of the two local ABCs are compared with each other and with those obtained by using large element mesh, which proves the satisfactory performance and obvious superiority over the large mesh model.

Keywords: transient seepage, unbounded domain, artificial boundary condition, numerical simulation

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