Search results for: Robert Christopher Hamilton

Authors: Nayak Amar, Turner Naomi, Gobina Edward

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The Scottish Higher Education Institutes must report their scope 1 & 2 emissions, whereas reporting scope 3 is optional. Scope 3 is indirect emissions which embodies a significant component of total carbon footprint and therefore it is important to record, measure and report it accurately. Robert Gordon University (RGU) reported only business travel, grid transmission and distribution, water supply and transport, and recycling scope 3 emissions. This study estimates the RGUs total scope 3 emissions by comparing it with a similar HEI in scale. The scope 3 emission reporting of sixteen Scottish HEI was studied. Glasgow Caledonian University was identified as the nearest neighbour by comparing its students' full time equivalent, staff full time equivalent, research-teaching split, budget, and foundation year. Apart from the peer, data was also collected from the Higher Education Statistics Agency database. RGU reported emissions from business travel, grid transmission and distribution, water supply, and transport and recycling. This study estimated RGUs scope 3 emissions from procurement, student-staff commute, and international student trip. The result showed that RGU covered only 11% of the scope 3 emissions. The major contributor to scope 3 emissions were procurement (48%), student commute (21%), international student trip (16%), and staff commute (4%). The estimated scope 3 emission was more than 14 times the reported emissions. This study has shown the relative importance of each scope 3 emissions source, which gives a guideline for the HEIs, on where to focus their attention to capture maximum scope 3 emissions. Moreover, it has demonstrated that it is possible to estimate the scope 3 emissions with limited data.

Keywords: HEI, university, emission calculations, scope 3 emissions, emissions reporting

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Authors: Tadeusz Nowicki, Radosław Pytlak, Robert Waszkowski, Jerzy Bertrandt, Anna Kłos

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This paper presents methods for formal modeling of activities in the area of sanitary inspectors outbreak of food-borne diseases. The models allow you to measure the characteristics of the activities of sanitary inspection and as a result allow improving the performance of sanitary services and thus food security.

Keywords: food-borne disease, epidemic, sanitary inspection, mathematical models

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Bayan Bevrani, Robert L. Burdett, Prasad K. D. V. Yarlagadda

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This article focuses upon multi-modal transportation systems (MMTS) and the issues surrounding the determination of system capacity. For that purpose a multi-objective framework is advocated that integrates all the different modes and many different competing capacity objectives. This framework is analytical in nature and facilitates a variety of capacity querying and capacity expansion planning.

Keywords: analytical model, capacity analysis, capacity query, multi-modal transportation system (MMTS)

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Authors: Robert L. Burdett, Bayan Bevrani

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Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways, these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

Keywords: capacity analysis, capacity expansion, railways, track sub division, track duplication

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Authors: Min Dai, Hong Liu, Shuaijie Qian

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We study a portfolio selection problem of an investor who faces constraints on rebalancing frequency, which is common in pension fund investment. We formulate it as a multiple optimal stopping problem and utilize the dynamic programming principle. By numerically solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we find a series of free boundaries characterizing optimal strategy, and the constraints significantly impact the optimal strategy. Even in the absence of transaction costs, there is a no-trading region, depending on the number of the remaining trading chances. We also find that the equivalent wealth loss caused by the constraints is large. In conclusion, our model clarifies the impact of the constraints on transaction frequency on the optimal strategy.

Keywords: portfolio selection, rebalancing frequency, optimal strategy, free boundary, optimal stopping

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Authors: Onyeka Nkwonta, Christopher Iheukwumere

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It is a waste to irrigate with great quantities of drinking water when plants thrive on used water containing small bits of compost. Unlike a lot of ecological stopgap measures, greywater reuse is a part of the fundamental solution to many ecological problems and will probably remain essentially unchanged in the distant future. Water is abused and wasted by both the wealthy and the poor. Education about water conservation is also needed. This study gives an outline of the sources of grey water in our home and provides a process of creating awareness on the importance of re-using grey water in our home, in order to achieve the 7th aim of the millennium development goals by 2015, which is ensuring environmental sustainability.

Keywords: tickling filter, education, grey water, environmental sustainability

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Authors: Zelal Çınar

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This paper aims to expose the effects of the ideological program of Turkish Republic on city planning, through the first plan of Ankara. As the new capital, Ankara was planned to be the ‘showcase’ of modern Turkey. It was to represent all new ideologies and the country’s cultural similarities with the west. At the same time it was to underline the national identity and independence of Turkish republic. To this end, a new plan for the capital was designed by German city planner Carl Christopher Lörcher. Diametrically opposed with the existing fabric of the city, this plan was built on the basis of papers and plans, on ideological aims. On the contrary, this paper argues that the city is a machine of possibilities, rather than a clear, materialized system.

Keywords: architecture, ideology, modernization, urban planning

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Authors: Prabhvir Singh Marway, Kai Lok Chan, Maria-Ruxandra Jinga, Rachel Bok Ying Lee, Matthew Bok Kit Lee, Krishan Nandapalan, Sze Yi Beh, Harry Carr, Christopher Kui

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We piloted a structured series of online workshops on the 3D segmentation of anatomical structures from CT scans. 33 participants were recruited from four UK universities for two-day workshops between 2020 and 2021. Open-source software (3D-Slicer) was used. We hypothesized that active participation via real-time screen-sharing and voice-communication via Discord would enable improved engagement and learning, despite national lockdowns. Written feedback indicated positive learning experiences, with subjective measures of anatomical understanding and software confidence improving.

Keywords: medical education, workshop, segmentation, anatomy

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Authors: Oláh Gál Róbert, Veress Bágyi Ibolya

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The scientific public has relatively little knowledge about the Hungarian János Bolyai, one of the greatest thinkers of all times. Few people know that apart from being the founder of the non-Euclidean geometry he was also interested in sociology, philosophy, epistemology and linguistics. According to the renowned Hungarian psychoanalytic Imre Hermann, who lives in France, János Bolyai was mentally deranged. However, this is incorrect. The present article intends to prove that he was completely sane until the moment of his death.

Keywords: Imre Hermann, insane, János Bolyai, mathematics, non-Euclidean geometry, psyphoanalytic

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Authors: Elizabeth Hartney, Keith Borkowsky, Jo Axe, Doug Hamilton

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The aim of this research is to develop a grounded theory of educational leadership development, using an approach to initiating and maintaining professional growth in school principals and vice principals termed generative dialogue. The research was conducted in a relatively affluent, urban school district in Western Canada. Generative dialogue interviews were conducted by a team of consultants, and anonymous data in the form of handwritten notes were voluntarily submitted to the research team. The data were transcribed and analyzed using grounded theory. The results indicate that a key focus of educational leadership development is focused on navigating relationships within the school setting and that the generative dialogue process is helpful for principals and vice principals to explore how they might do this. Applicability and limitations of the study are addressed.

Keywords: generative dialogue, school principals, grounded theory, leadership development

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: functionally graded beam, free vibration, elastic foundation, Engesser-Timoshenko beam theory

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Authors: Piyanud Chompookard

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This research aims to study the effect of self-compassion techniques for individuals with depression (A pilot study). A quasi-experimental research with pretest-posttest is used to design this work. The research includes 30 participants, divided into the experimental group (ten samples) and the control group (twenty samples). The experimental group received a self-compassion techniques with an appropriate treatment for a total six times. The control group received an appropriate treatment. The measurement of this study using the Hamilton Rating Scale for Depression (Thai version). There are significant differences in levels of depression after received a self-compassion techniques with an appropriate treatment (p<.01). And there are significant differences in levels of depression between the experimental group and the control group (p<.01).

Keywords: depression, self compassion techniques, psychotherapy, pilot study

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Authors: M. Najafi, F. Rahimi Dehgolan

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In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: non-linear vibration, stability, axially moving beam, bifurcation, multiple scales method

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Authors: Christopher Hardly Joseph, Nicola Pelagalli, Davide Mencarelli, Luca Pierantoni

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In this contribution, we report the electromagnetic response of a split ring resonator (SRR) based magnetic metamaterial unit cell in free space nature by means of a full-wave electromagnetic simulation. The effective parameters of these designed structures have been analyzed. The structures have been specifically designed to work at high frequency considering the development of many microwave and lower mm-wave devices. In addition to that, the application of the designed metamaterial structures is also proposed, namely metamaterial loaded planar transmission lines, potentially useful to optimize size and quality factor of circuit components and radiating elements.

Keywords: CPW, Microwave Components, Negative Permeability, Split Ring Resonator (SRR)

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Authors: Piotr-Robert Lazik, Harald Garrecht

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Many concrete technologists are looking for a solution to replace Fly Ashes that would be unavailable in a few years as an element that occurs as a major component of many types of concrete. The importance of such component is clear - it saves cement and reduces the amount of CO₂ in the atmosphere that occurs during cement production. Wood Ashes from electrostatic filter can be used as a valuable substitute in concrete. The laboratory investigations showed that the wood ash concrete had a compressive strength comparable to coal fly ash concrete. These results indicate that wood ash can be used to manufacture normal concrete.

Keywords: wood ashes, fly ashes, electric filter, replacement, concrete technology

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Authors: Vathya Anindita Putri, Henny Saptatia Drajati Nugrahani

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This research aims to explore the representation of Nordic mythology in the commercial film titled “Thor” produced by the Marvel Cinematic Universe. First, the Nordic mythology adaptation and representation in “Thor” compared to other media. Second, the importance of using the mise en scene technique, the comprehensive portrayal of Nordic mythology and the audience's experiences in enjoying the film. This research is conducted using qualitative methods. The two research questions are analyzed using three theories: Adaptation theory by Robert Stam, Mise en Scene theory by Jean-Luc Godard, and Cultural Criticism theory by Michel Foucault. Robert Stam emphasizes the importance of social and historical in understanding film adaptations. Film adaptations always occur in a specific cultural and historical context; therefore, authors and producers must consider these factors when creating a successful adaptation. Jean-Luc Godard uses the “politiques des auteurs” approach to understand that films are not just cultural products made for entertainment, but they are works of art by authors and directors. It is important to explore how authors and directors convey their ideas and emotions in their films, in this case, a film set in Nordic mythology. Foucault takes an approach to analyzing power that considers how power operates and influences social relationships in a specific context. Foucault’s theory is used to analyze how the representation of Nordic mythology is used as an instrument of power by the Marvel Cinematic Universe to influence how the audience views Nordic mythology. The initial findings of this research are that the fusion of Nordic mythology with modern superhero storytelling in the film “Thor” produced by Marvel, is successful. The film contains conflicts in the modern world and represents the symbolism of Nordic mythology. The rich and interesting atmosphere of Nordic mythology is presented through epic battle scenes, captivating character roles, and the use of visual effects that make the film more vivid and real.

Keywords: adaptation theory, cultural criticism theory, film criticism, Marvel cinematic universe, Mise en Scene theory, Nordic mythology

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Authors: Ruijia Hu, Susanna T.Y. Tong

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Light detection and ranging (LiDAR) and four-channel red, green, blue, and near-infrared (RGBI) remote sensed imageries allow an accurate quantification and contiguous measurement of vegetation characteristics and forest structures. This information facilitates the generation of habitat structure variables for forest species distribution modelling. However, applications of remote sensing data, especially the combination of structural and spectral information, to support evidence-based decisions in forest managements and conservation practices at local scale are not widely adopted. In this study, we examined the habitat requirements of pileated woodpecker (Dryocopus pileatus) (PW) in Hamilton County, Ohio, using ecologically relevant forest structural and vegetation characteristics derived from LiDAR and RGBI data. We hypothesized that the habitat of PW is shaped by vegetation characteristics that are directly associated with the availability of food, hiding and nesting resources, the spatial arrangement of habitat patches within home range, as well as proximity to water sources. We used 186 PW presence or absence locations to model their presence and absence in generalized additive model (GAM) at two scales, representing foraging and home range size, respectively. The results confirm PW’s preference for tall and large mature stands with structural complexity, typical of late-successional or old-growth forests. Besides, the crown size of dead trees shows a positive relationship with PW occurrence, therefore indicating the importance of declining living trees or early-stage dead trees within PW home range. These locations are preferred by PW for nest cavity excavation as it attempts to balance the ease of excavation and tree security. In addition, we found that PW can adjust its travel distance to the nearest water resource, suggesting that habitat fragmentation can have certain impacts on PW. Based on our findings, we recommend that forest managers should use different priorities to manage nesting, roosting, and feeding habitats. Particularly, when devising forest management and hazard tree removal plans, one needs to consider retaining enough cavity trees within high-quality PW habitat. By mapping PW habitat suitability for the study area, we highlight the importance of riparian corridor in facilitating PW to adjust to the fragmented urban landscape. Indeed, habitat improvement for PW in the study area could be achieved by conserving riparian corridors and promoting riparian forest succession along major rivers in Hamilton County.

Keywords: deadwood detection, generalized additive model, individual tree crown delineation, LiDAR, pileated woodpecker, RGBI aerial imagery, species distribution models

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Authors: Tai-Ping Chang

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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: Robert Lenzie

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Transcranial electrical stimulation (tES) is significant in the research literature. However, the effects of tES on brain activity are still poorly understood at the surface level, the Brodmann Area level, and the impact on neural networks. Using a method like electroencephalography (EEG) in conjunction with tES might make it possible to comprehend the brain response and mechanisms behind published observed alterations in more depth. Using a method to directly see the effect of tES on EEG may offer high temporal resolution data on the brain activity changes/modulations brought on by tES that correlate to various processing stages within the brain. This paper provides unpublished information on a cutting-edge methodology that may reveal details about the dynamics of how the human brain works beyond what is now achievable with existing methods.

Keywords: tACS, frequency, EEG, optimal

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Authors: Christopher Deekia Nwimae, Nigel Simms, Liyun Lao

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Erosion in pipe bends caused by particles is a major obstacle in the oil and gas fields and might cause the breakdown of production equipment. This work studied the effects imposed by flow velocity and impact of solid particles diameter in an elbow; erosion rate was verified with experimental data using the computational fluid dynamics (CFD) approach. Two-way coupled Euler-Lagrange and discrete phase model was employed to calculate the air/solid particle flow in an elbow. One erosion model and three-particle rebound models were used to predict the erosion rate on the 90° elbows. The generic erosion model was used in the CFD-based erosion model, and after comparing it with experimental data, results showed agreement with the CFD-based predictions as observed.

Keywords: erosion, prediction, elbow, computational fluid dynamics

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Authors: Gholamreza Koochaki

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This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions.

Keywords: buckling, functionally graded beams, Hamilton's principle, Euler-Bernoulli beam

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Authors: Maryam Kamali Nezhad

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The Robert-Bourassa development (LG-2), the first to be built on the Grande Rivière, comprises two sets of eight turbines- generator units each, the East and West powerhouses. Each powerhouse has two tailrace tunnels with an average length of about 1178 m. The LG-2A powerhouse houses 6 turbine-generator units. The water is discharged through two tailrace tunnels with a length of about 1330 m. The objective of this work, at RB (LG-2), is; 1) to establish a new maximum transient level in the surge chamber, 2) to define the new maximum equipment flow rate for the future turbine-generator units, 3) to ensure safe access to various intervention locations in the surge chamber. The transient levels under normal operating conditions at the RB plant were determined in 2001 by the Hydraulics Unit of HQE using the "Chamber" software. It is a one-dimensional mass oscillation calculation software; it is used to determine the variation of the water level in the equilibrium chamber located downstream of a power plant during the load shedding of the power plant units; it can also be used in the case of an equilibrium stack upstream of a power plant. The RB (LG-2) plant study is based on the theoretical nominal geometry of the chamber and the tailrace tunnels and the flow-level relationship at the outlet of the galleries established during design. The software is used in such a way that the results have an acceptable margin of safety, especially with respect to the maximum transient level (e.g., resumption of flow at an inopportune time), to take into account the turbulent and three-dimensional aspects of the actual flow in the chamber. Note that the transient levels depend on the water levels in the river and in the steady-state equilibrium chambers. These data are established in the HQP CRP database and updated from time to time. The maximum transient levels in the RB-East and RB-West powerhouses surge chamber were revised based on the latest update (set 4) of in-river rating curves and steady-state surge chamber water levels. The results of the revision were also used to update the technical advice on the operating conditions for the aforementioned surge chamber access while considering revisions to the calculated water levels.

Keywords: generating station, surge chamber, maximum transient level, hydroelectric power station, turbine-generator, reservoir

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Authors: Justin M. Swanson, Anna Nelson, Daniel Handysides, Patti Herring, Christopher Hill

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Not only may social media use have a psychological impact, but increased use may be tied to decreases in physical activity and influencing sedentary behaviors. Social media can be used to share physically active lifestyles and possibly influence others to participate. In contrast, social media use may have adverse effects by decreasing participation in exercise. This study used a qualitative design to examine the relationship between social media use and exercise patterns. Participants were asked questions about their social media habits and how it might impact their physical activity behaviors. Self-reported exercise seemed to increase after viewing others engage in relatable activities or viewing someone that has overcame challenges. To increase the likelihood of engaging in exercise, exercise related posts should be low in difficulty, require few materials, or displayed progress from the individual posting.

Keywords: social media, exercise, physical activity, adults

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Authors: Bo Yang, Christopher Monterola

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Urban intersection control without the use of the traffic light has the potential to vastly improve the efficiency of the urban traffic flow. For most proposals in the literature, such lightless intersection control depends on the mass market commercialization of highly intelligent autonomous vehicles (AV), which limits the prospects of near future implementation. We present an efficient lightless intersection traffic control scheme that only requires Level 1 AV as defined by NHTSA. The technological barriers of such lightless intersection control are thus very low. Our algorithm can also accommodate a mixture of AVs and conventional vehicles. We also carry out large scale numerical analysis to illustrate the feasibility, safety and robustness, comfort level, and control efficiency of our intersection control scheme.

Keywords: intersection control, autonomous vehicles, traffic modelling, intelligent transport system

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Authors: Korosh Khorshidi

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Due to the increasing use of different materials, such as auxetic structures, it is necessary to investigate mechanical phenomena, such as vibration, in structures made of these types of materials. This paper examines the forced vibrations of a three-layer cylindrical shell containing inviscid fluid under shock load. All three layers are made of aluminum, and the central layer is made of a re-entrant honeycomb cell structure. Using high-order shear deformation theories (HSDT) and Hamilton’s principle, the governing equations of the system have been extracted and solved by the Galerkin weighted residual method. The outputs of the Abaqus finite element software are used to validate the results. The system is investigated with both simple and clamped support conditions. Finally, this study investigates the influence of the geometrical parameters of the shell and the auxetic structure, as well as the type, intensity, duration, and location of the load, and the effect of the fluid on the dynamic and time responses.

Keywords: force vibration, cylindrical shell, auxetic structure, inviscid fluid

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Authors: Grace karimi Muriithi, Behnaz Papari, Ali Arsalan, Christopher Shannon Edrington

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Complexity and nonlinearity of the control system design is increasing for DC microgrid applications when the cyber concept associated with the technology constraints will added to the picture. Controllers’ functionality during the critical operation mode is required to guaranteed specifically for a high profile applications such as NAVY DC ship power system (SPS) as an small-scaled DC microgrid. Thus, SPS is susceptible to cyber-attacks and, accordingly, can provide the disastrous effects. In this study, a machine learning (ML) approach is demonstrated to offer the promising performance of SPS for developing an effective and robust functionality over attacks time. Simulation results analysis demonstrate that the proposed method can improve the controllability successfully.

Keywords: controlability, cyber attacks, distribute control, machine learning

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Authors: Robert Roznowski

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The thought process of the character is never more evident than when singing alone onstage. The composer scores the emotional state and the lyricist voices the inner conflict as the character shares with an audience her or his deepest feelings. It is at these moments that a character may be thought of as voicing her or his inner monologue. Using examples from several musical theatre songs, this presentation will look at a codified approach to analyze a song from a more psychological perspective. Using the clues from the score, traditional character analysis and a psychological-based scoring method an actor may explore more fully inhabit and express the sung and unsung thoughts of the character. The approach yields a richer and more complex approach to acting the song.

Keywords: acting, analysis, musical theatre, psychology

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Authors: M. Najafi, S. Bab, F. Rahimi Dehgolan

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The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: super harmonic resonances, non-linear vibration, axially moving beam, Galerkin method

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