scholarly journals Re-Evaluating the Classical Falling Body Problem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 553 ◽  
Author(s):  
Essam R. El-Zahar ◽  
Abdelhalim Ebaid ◽  
Abdulrahman F. Aljohani ◽  
José Tenreiro Machado ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Inertial Frame ◽  
Analytic Solution ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Rotating Frame ◽  
Dimensional Model ◽  
Three Dimensional Model

This paper re-analyzes the falling body problem in three dimensions, taking into account the effect of the Earth’s rotation (ER). Accordingly, the analytic solution of the three-dimensional model is obtained. Since the ER is quite slow, the three coupled differential equations of motion are usually approximated by neglecting all high order terms. Furthermore, the theoretical aspects describing the nature of the falling point in the rotating frame and the original inertial frame are proved. The theoretical and numerical results are illustrated and discussed.

scholarly journals A Three-Dimensional Polar Ice-Sheet Model

1977 ◽  
Vol 18 (80) ◽  
pp. 373-389 ◽  
Author(s):  
D. Jenssen
Keyword(s):  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Phase Changes ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Polar Ice ◽  
Three Dimensional Model ◽  
Temperature Dependent ◽  
Mass Depletion

AbstractA three-dimensional model of the temperature and velocity distribution within any arbitrary-shaped ice mass is described. There is a mutual interaction in the model between the flow of the ice and its thermodynamics, since the flow law used in the model is temperature-dependent.Ice growth in three dimensions is governed by mass accumulation through precipitation, by mass depletion through loss of ice over the ocean, and by continuity requirements. Phase changes at the base of the ice are accounted for. The model has been applied in art exploratory manner to the Greenland ice sheet. Changes in the ice shape and temperature are presented and discussed. The basic shortcoming of the model as here presented appears primarily due to the coarse finite-difference mesh used, and to an unsophisticated approach to modelling the boundary ice.

scholarly journals COORDINATE SYSTEM FOR REPRESENTATION OF MULTIDIMENSIONAL DATA

2018 ◽  
pp. 40-44
Author(s):  
A. B. Lachikhina ◽  
K. N. Soldatov
Keyword(s):  
Three Dimensional ◽  
Data Representation ◽  
Three Dimensions ◽  
Multidimensional Data ◽  
Independent Data ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Proposed Model ◽  
Multidimensional Array ◽  
Number Of Faces

Visualization of analyzing multidimensional data is often required in order to improve perception and visibility. The purpose of this research is a multidimensional array of data representation. It is proposed to use a three-dimensional model as a tool. The methods used to represent an array of data with more than three dimensions are presented. The principle of constructing a multidimensional array cell is considered. An example of the constructed hypercube cell is given. The formulas for calculating the number of faces of the figure, the number of triangles that can be built through points, the number of internal triangles are obtained. The approach of visualization of aggregates is described. The use of color gradation to improve the convenience of perception of the cell in the analysis of the cube cells. It is concluded that the proposed model allows us to perceive each cell as an independent data element in the construction of charts for the analyzed indicators.

Towards a Three-Dimensional Model of Planning Behaviour

1971 ◽  
Vol 3 (3) ◽  
pp. 253-266 ◽  
Author(s):  
A Faludi
Keyword(s):  
Decision Making ◽  
Three Dimensional ◽  
Complex Model ◽  
Learning Systems ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Planning Systems ◽  
Three Dimensional Model ◽  
Disjointed Incrementalism ◽  
Planning Problems

This paper develops conceptual tools for the analysis of planning behaviour. These are, firstly, a model of planning systems as learning systems, and then three dimensions of planning behaviour, each described by defining a pair of dichotomous concepts at their far ends: ‘blueprint’ versus ‘process’ modes of planning; ‘rational-deductive’ decision-making versus ‘disjointed incrementalism’; ‘normative’ versus ‘functional’ planning. Each of these concepts is discussed in detail, and some indicators for the analysis of planning behaviour are suggested. Finally, a more complex model is constructed which combines the three dimensions. Elements of this model are firstly the level at which planning is conducted within a hierarchy of planning systems, and secondly, the ‘planning sub-structurel, that is the technology-image reflecting the nature of planning problems and available planning technologies. From this model one can derive a number of researchable hypotheses about planning behaviour.

Quasi-three-dimensional simulation of crescent-shaped waves

2020 ◽  
Author(s):  
Alexander Dosaev ◽  
Yuliya Troitskaya
Keyword(s):  
Water Waves ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Rogue Waves ◽  
Boundary Integral ◽  
Main Direction ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Wave Interactions

<p>Many features of nonlinear water wave dynamics can be explained within the assumption that the motion of fluid is strictly potential. At the same time, numerically solving exact equations of motion for a three-dimensional potential flow with a free surface (by means of, for example, boundary integral method) is still often considered too computationally expensive, and further simplifications are made, usually implying limitations on wave steepness. A quasi-three-dimensional model, put forward by V. P. Ruban [1], represents another approach at reducing computational cost. It is, in its essence, a two-dimensional model, formulated using conformal mapping of the flow domain, augmented by three-dimensional corrections. The model assumes narrow directional distribution of the wave field and is exact for two-dimensional waves. It was successfully applied by its author to study a nonlinear stage of of Benjamin-Feir instability and rogue waves formation.</p><p>The main aim of the present work is to explore the behaviour of the quasi-three-dimensional model outside the formal limits of its applicability. From the practical point of view, it is important that the model operates robustly even in the presence of waves propagating at large angles to the main direction (although we do not attempt to accurately describe their dynamics). We investigate linear stability of Stokes waves to three-dimensional perturbations and suggest a modification to the original model to eliminate a spurious zone of instability in the vicinity of the perpendicular direction on the perturbation wavenumber plane. We show that the quasi-three-dimensional model yields a qualitatively correct description of the instability zone generated by resonant 5-wave interactions. The values of the increment are reasonably close to those obtained from the exact equations of motion [2], despite the fact that the corresponding modes of instability consist of harmonics that are relatively far from the main direction. Resonant 5-wave interactions are known to manifest themselves in the formation of the so-called “horse-shoe” or “crescent-shaped” wave patterns, and the quasi-three-dimensional model exhibits a plausible dynamics leading to formation of crescent-shaped waves.</p><p>This research was supported by RFBR (grant No. 20-05-00322).</p><p>[1] Ruban, V. P. (2010). Conformal variables in the numerical simulations of long-crested rogue waves. <em>The European Physical Journal Special Topics</em>, <em>185</em>(1), 17-33.</p><p>[2] McLean, J. W. (1982). Instabilities of finite-amplitude water waves. <em>Journal of Fluid Mechanics</em>, <em>114</em>, 315-330.</p>

scholarly journals A Three-Dimensional Polar Ice-Sheet Model

1977 ◽  
Vol 18 (80) ◽  
pp. 373-389 ◽  
Author(s):  
D. Jenssen
Keyword(s):  
Three Dimensional ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Phase Changes ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Polar Ice ◽  
Three Dimensional Model ◽  
Temperature Dependent ◽  
Mass Depletion

Abstract A three-dimensional model of the temperature and velocity distribution within any arbitrary-shaped ice mass is described. There is a mutual interaction in the model between the flow of the ice and its thermodynamics, since the flow law used in the model is temperature-dependent. Ice growth in three dimensions is governed by mass accumulation through precipitation, by mass depletion through loss of ice over the ocean, and by continuity requirements. Phase changes at the base of the ice are accounted for. The model has been applied in art exploratory manner to the Greenland ice sheet. Changes in the ice shape and temperature are presented and discussed. The basic shortcoming of the model as here presented appears primarily due to the coarse finite-difference mesh used, and to an unsophisticated approach to modelling the boundary ice.

Control of Meloidogyne incognita in three-dimensional model systems and pot experiments by the attract-and-kill effect of furfural acetone

Plant Disease ◽  
2020 ◽  
Author(s):  
Wanli Cheng ◽  
Zhen Chen ◽  
Li Zeng ◽  
Xue Yang ◽  
Dian Huang ◽  
...  
Keyword(s):  
Meloidogyne Incognita ◽  
Large Scale ◽  
Three Dimensional ◽  
Control Agent ◽  
Three Dimensions ◽  
Model Systems ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Moist Sand ◽  
Attract And Kill

Meloidogyne incognita causes large-scale losses of agricultural crops worldwide. The natural metabolite furfural acetone has been reported to attract and kill M. incognita, but whether the attractant and nematicidal activities of furfural acetone on M. incognita function simultaneously in the same system, especially in three dimensions or in soil, is still unknown. Here, we used 23% pluronic F-127 gel and a soil simulation device to demonstrate that furfural acetone has a significant attract-and-kill effect on M. incognita in both three-dimensional model systems. At 24 h, the chemotaxis index and corrected mortality of nematodes exposed to 60 mg/mL furfural acetone in 23% pluronic F-127 gel were as high as 0.82 and 74.44%, respectively. Soil simulation experiments in moist sand showed that at 48 h, the chemotaxis index and corrected mortality of the nematode towards furfural acetone reached 0.63 and 82.12%, respectively, and the effect persisted in the presence of tomato plants. In choice experiments, nematodes selected furfural acetone over plant roots and were killed subsequently. In pot studies, furfural acetone had a control rate of 82.80% against M. incognita. Collectively, these results provide compelling evidence for further investigation of furfural acetone as a novel nematode control agent.

Three-dimensional model predictive controller design for approach to landing with microburst encounter

2017 ◽  
Vol 232 (11) ◽  
pp. 2034-2047 ◽  
Author(s):  
A Hassanpour ◽  
Seid H Pourtakdoust
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Model Predictive Controller ◽  
Predictive Controller ◽  
Lateral Displacements ◽  
Alternative Routes

Microburst is considered an extreme powerful hazard for aircrafts, especially during takeoff, approach and landing phases of flight. Current airborne piloting practices involve taking alternative routes, if early detection of microburst wind shear (MBW) for its effective avoidance is possible. In this respect, design and analysis of precision automatic flight path control systems for microburst penetration are of outmost importance whose success can significantly reduce crash risks and thus enhance the flight safety. The current study is focused on the design and analysis of a three-dimensional model predictive controller for a wide body transport type aircraft encountering MBW in approach to landing phase of flight. This task is performed utilizing the full nonlinear six degrees of freedom aircraft equations of motion and the most complete 3D model of the MBW and its gradients. The results are promising for online applications as the proposed model predictive controller-based controller has effectively guided and kept the aircraft on the approach glide path with negligible deviations against aircraft initial lateral displacements, sharp edge gust disturbance as well as the MBW.

scholarly journals Are narcissists resilient? Examining grandiose and vulnerable narcissism in the context of a three-dimensional model of resilience

2021 ◽  
Author(s):  
Michał Sękowski ◽  
Łukasz Subramanian ◽  
Magdalena Żemojtel-Piotrowska
Keyword(s):  
Adaptive Capacity ◽  
Three Dimensional ◽  
Stressful Events ◽  
Self Report ◽  
Three Dimensions ◽  
Ecological Resilience ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Grandiose Narcissism ◽  
Vulnerable Narcissism

AbstractIn this paper, we focused on the poorly understood and rarely researched relationship between resilience and narcissism, adopting the adjective-based measures of narcissism. We examine how levels of resilience are related to grandiose and vulnerable narcissism, based on a three-dimensional model of resilience (i.e., ecological resilience, engineering resilience, and adaptive capacity). Using self-report, cross-sectional data from a general Polish sample (N = 657), we found that grandiose narcissism was positively related to all three dimensions of resilience, while vulnerable narcissism was negatively related to them. Grandiose narcissism was most strongly associated with adaptive capacity where vulnerable narcissism was mostly strongly associated with engineering resilience. We discuss our findings in relation to the function of two forms of narcissism may yield different capacities for stress management and recovery after experiencing stressful events. Therefore, this research is focused on self-report and we look forward to expand our research by behavioral indices in the future.

scholarly journals Aspects of the polynomial affine model of gravity in three dimensions

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
Oscar Castillo-Felisola ◽  
Oscar Orellana ◽  
José Perdiguero ◽  
Francisca Ramírez ◽  
Aureliano Skirzewski ◽  
...  
Keyword(s):  
Tensor Field ◽  
Affine Connection ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Metric Tensor ◽  
Affine Model ◽  
Cosmological Solutions ◽  
Affine Gravity

AbstractThe polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently truncated sectors. Using the cosmological ansatz for the connection, we scan the cosmological solutions on the truncated sectors. We discuss the emergence of different kinds of metrics.

scholarly journals Detailed Description on the Three Dimensions of Deprivation

2020 ◽  
Vol 13 (1) ◽  
pp. 37-55
Author(s):  
Hakan Ünal ◽  
Csilla Obádovics ◽  
Emese Bruder
Keyword(s):  
Human Life ◽  
Three Dimensional ◽  
Measuring Method ◽  
Living Conditions ◽  
Three Dimensions ◽  
Standard Of Living ◽  
Multidimensional Approach ◽  
The European Union ◽  
Dimensional Model ◽  
Three Dimensional Model

This study introduces a method for measuring standard of living, based on a three-dimensional model. The authors argue that their proposed indicators (and items) can more realistically capture people’s inability to afford an adequate way of living than the ones Eurostat uses and recommends. The commonly used deprivation measuring method has a unidimensional perspective and provides only a general overview of those living in deprivation. The authors’ multidimensional approach, however, considers not only the well-known aspects of human life but also others, giving a more extensive view of individuals’ needs. The calculations are based on the European Union Statistics on Income and Living Conditions database provided by Eurostat and the relevant Turkish data¬base from the Turkish Statistical Office. The decomposite method introduced in the study measures standard of living using three dimensions, economic strain, living conditions, and housing and environmental conditions.

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