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Loeb, Sarah J., and Douglas B. West. "Fractional and circular separation dimension of graphs." European Journal of Combinatorics 69 (March 2018): 19–35. http://dx.doi.org/10.1016/j.ejc.2017.09.001.
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Liou, J. L., and J. F. Lin. "A Microcontact Model Developed for Asperity Heights with a Variable Profile Fractal Dimension, A Surface Fractal Dimension, Topothesy, and Non-Gaussian Distribution." Journal of Mechanics 25, no. 1 (2009): 103–15. http://dx.doi.org/10.1017/s1727719100003646.
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AbstractThe cross sections formed by the contact asperities of two rough surfaces at an interference are islandshaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying with the mean separation (or the interference at the rough surface) between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformations are derived and the inceptions of the elastoplastic deformation regime and the fully plastic deformation regime are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). The contact parameters, including the total contact force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and Ds parameters in these deformation regimes increased with increasing the mean separation (d*). The initial plasticity index before contact deformation (ψ)0 is also a factor of importance to the predictions of the contact load (F*t) and contact area (At*) between the model of variable D and G, non-Gaussian asperity heights and circular contact area and the present model of variable D and G, non-Gaussian asperity heights and fractal contact area.
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Bartram, Lyn, and Colin Ware. "Filtering and Brushing with Motion." Information Visualization 1, no. 1 (2002): 66–79. http://dx.doi.org/10.1057/palgrave.ivs.9500005.
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Visualizing information in user interfaces to complex, large-scale systems is difficult due to visual fragmentation caused by an enormous amount of inter-related data distributed across multiple views. New display dimensions are required to help the user visually integrate and filter such spatially distributed and heterogeneous information. Motion holds promise in this regard as a perceptually efficient display dimension. It has long been known to have a strong grouping effect, suggesting it has potential for filtering and brushing techniques. However, there is little known about which properties of motion are most effective. This paper reviews the prior literature relating to the use of motion for display and discusses the requirements for how motion can be usefully applied to these problems, especially for visualizations incorporating multiple groups of data objects. Results from previous research by the authors suggested motion type was a strong distinguishing feature. Three types of motions in pairwise combinations were compared: linear, circular and expansion/contraction. Combinations of linear directions were also compared to evaluate how great angular separation needs to be to enforce perceptual distinction. The results showed that motion can effectively group objects that are otherwise dissimilar. Type differentiation is more effective than directional differences (except for 90°). Of the three types studied, circular demands the most attention. Angular separation must be 90° to be equally effective. These results suggest that motion can be usefully applied to both filtering and brushing. They also provide the beginnings of a vocabulary of simple motions that can be applied to information visualization.
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Zhang, Hui, Zixin Liu, and Jun Zhang. "An efficient finite element method based on dimension reduction scheme for a fourth-order Steklov eigenvalue problem." Open Mathematics 20, no. 1 (2022): 666–81. http://dx.doi.org/10.1515/math-2022-0032.
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Abstract In this article, an effective finite element method based on dimension reduction scheme is proposed for a fourth-order Steklov eigenvalue problem in a circular domain. By using the Fourier basis function expansion and variable separation technique, the original problem is transformed into a series of radial one-dimensional eigenvalue problems with boundary eigenvalue. Then we introduce essential polar conditions and establish the discrete variational form for each radial one-dimensional eigenvalue problem. Based on the minimax principle and the approximation property of the interpolation operator, we prove the error estimates of approximation eigenvalues. Finally, some numerical experiments are provided, and the numerical results show the efficiency of the proposed algorithm.
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Yon, Hamizan, Nurul Huda Abd Rahman, Mohd Aziz Aris, et al. "Development of C-Shaped Parasitic MIMO Antennas for Mutual Coupling Reduction." Electronics 10, no. 19 (2021): 2431. http://dx.doi.org/10.3390/electronics10192431.
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In the 5G system, multiple-input multiple-output (MIMO) antennas for both transmitting and receiving ends are required. However, the design of MIMO antennas at the 5G upper band is challenging due to the mutual coupling issues. Many techniques have been proposed to improve antenna isolation; however, some of the designs have impacts on the antenna performance, especially on the gain and bandwidth reduction, or an increase in the overall size. Thus, a design with a detailed trade-off study must be implemented. This article proposes a new C-shaped parasitic structure around a main circular radiating patch of a MIMO antenna at 16 GHz with enhanced isolation features. The proposed antenna comprises two elements with a separation of 0.32λ edge to edge between radiation parts placed in a linear configuration with an overall dimension of 15 mm × 26 mm. The C-shaped parasitic element was introduced around the main radiating antenna for better isolation. Based on the measurement results, the proposed structure significantly improved the isolation from −23.86 dB to −32.32 dB and increased the bandwidth from 1150 MHz to 1400 MHz. For validation, the envelope correlation coefficient (ECC) and the diversity gain (DG) were also measuredas 0.148 dB and 9.89 dB, respectively. Other parameters, such as the radiation pattern, the total average reflection coefficient and the mean effective gain, were also calculated to ensure the validity of the proposed structure. Based on the design work and analysis, the proposed structure was proven to improve the antenna isolation and increase the bandwidth, while maintaining the small overall dimension.
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Zabala-Quintero, Camilo, Jesus Ramirez-Pastran, and Maria Josefina Torres. "Performance Characterization of a New Model for a Cyclone Separator of Particles Using Computational Fluid Dynamics." Applied Sciences 11, no. 12 (2021): 5342. http://dx.doi.org/10.3390/app11125342.
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In the present study, through Computational Fluid Dynamics techniques, the performance characterization of a new Stairmand-type separator cyclone was carried out using the commercial software ANSYS Fluent. Four models for the geometrical cyclone separator were built, namely model A as per the dimensions reported in the literature and models B, C, and D by applying square and circular shape cavities as a passive flow control technique on the surface of its cylindrical section. The Navier-Stokes equations with the RSM turbulence model were formulated to solve the continuous phase of the cyclone separator and, the Lagrangian approach was adopted to track the solid particles with one way-coupling. The proposed model’s separation efficiency and pressure drop were compared against those recorded in the previous studies reported in the literature. Model D was the cyclone separator that stood out as the most valuable by demonstrating a separation efficiency and pressure drop decrement of 0.42% and 6.01%, respectively.
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VERHOFF, A. "Two-dimensional potential flow solutions with separation." Journal of Fluid Mechanics 657 (July 21, 2010): 238–64. http://dx.doi.org/10.1017/s0022112010001448.
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A procedure for constructing two-dimensional incompressible potential flowfield solutions with separation and a recirculation region is presented. It naturally makes use of complex variable theory and other analysis techniques such as conformal mapping and the generalized Poisson integral formula. Flowfield determination is reduced to solution of a boundary value problem in various simple domains. The entire velocity field is described analytically; stream function and velocity potential contour maps are readily constructed. Example solutions are presented. Solutions for sharp leading edge airfoils at arbitrary angle of attack are completely determined, including the limiting angle of attack for upper-surface flow re-attachment. For other configurations (e.g. circular cylinder, backward-facing step) the analytical solution contains one or more free parameters, whose values may be inferred from boundary layer theory or experiment.
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Xue, Xiao Feng, Hua Bai, Yu Li, Wei Li, and Sai Gong. "Test Study on Aerodynamic Performance of Three-Dimensional Stayed Cables in Two-Dimensional Flow Field." Advanced Materials Research 532-533 (June 2012): 469–73. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.469.
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Cables, distributed with diversity spatially angle, are rich in wind direction. Circular cross sectional shape is sensitive to the Reynolds number. This paper studed the aerodynamic performance of three-dimentional stayed cable under two-dimensional flow field in Chang'an University wind tunnel by Pitot tube, electronic pressure scanning valve, data conversion and collection systems. The following conclusions are obtained: (1)The stagnation point and the upper and lower airflow separation point clockwise goes on with the wind angle increases. Absolute value of pressure coefficient at stagnation point and separation point are biggest at 0°wind angle.(2)The absolute value of pressure coefficient at upper and lower separation point increase with the increase of wind speed.(3) Pressure stagnation point,and upper and lower airflow separation point don’t changed with the parameters of helix,while pressures near helix changed irregularlly. Drag coefficient decrease with the increase of helix distance and the deduce of helix height. Meaningful references are provided for the further refinement research on aerodynamic performance of cable-stayed with suppressing vibration measures.
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Jabbar, Tahseen, Rafi M. Qasim, and Bassam A. Mohammed. "Vane Angle Influence on the Flow Pattern around a Circular Pier." U.Porto Journal of Engineering 8, no. 6 (2022): 189–209. http://dx.doi.org/10.24840/2183-6493_008.006_0014.
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This paper intends to numerically analyze the hydrodynamic characteristics of the flow pattern that surrounds the circular pier near the vane angle. These include flow velocity, turbulent intensity, and pressure. A computational fluid dynamic is proposed to simulate the two-dimensional model by using the finite volume method, while the k - ε turbulence model is used to describe the turbulent model. The vane is located upstream of the pier, with its dimensions as function of the pier diameter. The distance between the vane and the pier center is equal to the pier diameter, the angle of the vane is put with a range from 60o to 180o, and the pier diameter is equal to 10 mm. The turbulent flow has a Reynolds number that varies from 20000 to 50000. The existence of the vane angle leads to two different processes, which are flow separation and flow dissipation, which have a direct effect on flow velocity, turbulent intensity, and pressure. From the current numerical results, the relationships between Reynolds number and average flow velocity, maximum flow velocity, turbulent intensity, and maximum turbulent intensity are more sensitive to flow separation and flow dissipation along the vane. Also, positive and negative pressure distributions have a higher influence on flow separation and flow dissipation.
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Chang, Hsuan-Ting, Tzu-Yao Lin, Chih-Hao Chuang, Chien-Yu Chen, Chian C. Ho, and Chuan-Yu Chang. "Separation of Two-Dimensional Mixed Circular Fringe Patterns Based on Spectral Projection Property in Fractional Fourier Transform Domain." Applied Sciences 11, no. 2 (2021): 859. http://dx.doi.org/10.3390/app11020859.
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In this paper, a method for automatically separating the mixed circular fringe patterns based on the fractional Fourier transform (FrFT) analysis is proposed. Considering the mixed two-dimensional (2-D) Gaussian-based circular fringe patterns, detected by using an image sensor, we propose a method that can efficiently determine the number and parameters of each separated fringe patterns by using the FrFT due to the observed higher sparsity in the frequency domain than that in the spatial domain. First, we review the theory of FrFT and the properties of the 2-D circular fringe patterns. By searching the spectral intensities of the various fractional orders in the FrFT projected along both the frequency axes, the proposed method can automatically determine the total fringe number, the central position, binary phase, and the maximum fringe width of each 2-D circular fringe pattern. In the experimental results, both the computer-simulated and optically mixed fringe patterns are used to verify the proposed method. In addition, the additive Gaussian noise effects on the proposed method are investigated. The proposed method can still successfully separate the mixed fringe pattern when the signal-to-noise ratio is higher than 7 dB.
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Agbaglah, G., and C. Mavriplis. "Three-dimensional wakes behind cylinders of square and circular cross-section: early and long-time dynamics." Journal of Fluid Mechanics 870 (May 10, 2019): 419–32. http://dx.doi.org/10.1017/jfm.2019.265.
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The flow in the near wake of a square cylinder at Reynolds numbers of 205 and 225, corresponding to three-dimensional wake instability modes $A$ and $B$, respectively, and that of the square’s circumscribed circular cylinder are examined by using three-dimensional Navier–Stokes numerical simulations. At small times, prior to the streamwise vortex shedding, a self-similar velocity is observed in the wake and no significant difference is observed in the dynamics of the flows past the square and the circular cylinders. The exponential growth of the three-dimensional instability reaches a saturation regime during this early time for the considered Reynolds numbers. Vortical structures in the wake at long times and shedding frequencies are very close for the square and the circular cylinders. The flow separation on the forward top and bottom corners of the square cylinder have the effect of increasing its effective width, making it comparable with the diameter of the circumscribed circular cylinder. Thus, Floquet multipliers and modes of the associated three-dimensional instabilities are shown to be very close for the two cylinders when using the circumscribed circular cylinder as the basis for a characteristic length scale. Most importantly, the wavenumber with the maximum growth rate, for modes $A$ and $B$, is approximately identical for the two cylinders.
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Chunguang, Wang, Chen Cong, Ren Quanbin, and Chen Ke. "Investigation on metal diaphragm of pulse separation device in dual-pulse solid rocket motor." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 3 (2016): 444–51. http://dx.doi.org/10.1177/0954410016638876.
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The theories of circular plates with large deflection and fracture mechanics were employed to investigate the calculating formula of stress intensity factor on prefab gap. The relationship of the opening pressure with physical dimensions of hard pulse separation device (PSD) was analyzed to achieve the feasible configuration of metal diaphragm, which could play a very important role in dual-pulse solid rocket motor. Moreover, six specific single-term tests of the metal diaphragm were conducted to validate the computing precision of designing formula. In addition, three kinds of scale experiments, e.g. the bearing test, opening test, and associated test were performed to explore the working characters of hard pulse separation device. The results indicate that the error between the experimental results and designing results is 4.4%, and the method can be applied to design the physical dimensions of metal diaphragm. The performances of bearing ability, sealability, opening and melt of PSD have been demonstrated. The results show that this kind of PSD can satisfy the requirements of dual-pulse solid rocket motor very well.
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Bai, Mingsian R., and Chang-Sheng Lai. "Localization and separation of acoustic sources by using a 2.5-dimensional circular microphone array." Journal of the Acoustical Society of America 139, no. 4 (2016): 2019–20. http://dx.doi.org/10.1121/1.4949957.
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Bai, Mingsian R., Chang-Sheng Lai, and Po-Chen Wu. "Localization and separation of acoustic sources by using a 2.5-dimensional circular microphone array." Journal of the Acoustical Society of America 142, no. 1 (2017): 286–97. http://dx.doi.org/10.1121/1.4994291.
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YAGITA, Miki, Ichiro KANO, and Masato SEINO. "On Unstableness of Separation of Two-dimensional Wall Jetalong Circular Cylinder with Coanda Effect." Transactions of the Japan Society of Mechanical Engineers Series B 70, no. 691 (2004): 594–601. http://dx.doi.org/10.1299/kikaib.70.594.
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Golovachov, Yu P., and N. V. Leont’eva. "Numerical investigation of cross-flow separation in three-dimensional supersonic flows around circular cones." Technical Physics 43, no. 10 (1998): 1154–59. http://dx.doi.org/10.1134/1.1259170.
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Yu, Tai-Ho, Shin-Yueh Yang, Chen-Liang Lee, and Ching-Chung Yin. "Bi-dimensional finite element analysis for modal separation of a circular cylindrical WW-USM." Finite Elements in Analysis and Design 47, no. 7 (2011): 635–42. http://dx.doi.org/10.1016/j.finel.2011.01.006.
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BALACHANDAR, S., R. MITTAL, and F. M. NAJJAR. "Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies." Journal of Fluid Mechanics 351 (November 25, 1997): 167–99. http://dx.doi.org/10.1017/s0022112097007179.
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The properties of the time- and span-averaged mean wake recirculation region are investigated in separated flows over several different two-dimensional bluff bodies. Ten different cases are considered and they divide into two groups: cylindrical geometries of circular, elliptic and square cross-sections and the normal plate. A wide Reynolds number range from 250 to 140000 is considered, but in all the cases the attached portion of the boundary layer remains laminar until separation. The lower Reynolds number data are from direct numerical simulations, while the data at the higher Reynolds number are obtained from large-eddy simulation and the experimental work of Cantwell & Coles (1983), Krothapalli (1996, personal communication), Leder (1991) and Lyn et al. (1995). Unlike supersonic and subsonic separations with a splitter plate in the wake, in all the cases considered here there is strong interaction between the shear layers resulting in Kármán vortex shedding. The impact of this fundamental difference on the distribution of Reynolds stress components and pressure in relation to the mean wake recirculation region (wake bubble) is considered. It is observed that in all cases the contribution from Reynolds normal stress to the force balance of the wake bubble is significant. In fact, in the cylinder geometries this contribution can outweigh the net force from the shear stress, so that the net pressure force tends to push the bubble away from the body. In contrast, in the case of normal plate, owing to the longer wake, the net contribution from shear stress outweighs that from the normal stress. At higher Reynolds numbers, separation of the Reynolds stress components into incoherent contributions provides more insight. The behaviour of the coherent contribution, arising from the dominant vortex shedding, is similar to that at lower Reynolds numbers. The incoherent contribution to Reynolds stress, arising from small-scale activity, is compared with that of a canonical free shear layer. Based on these observations a simple extension of the wake model (Sychev 1982; Roshko 1993a, b) is proposed.
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Tahir, N. A., V. V. Kim, A. V. Matvechev, et al. "High energy density and beam induced stress related issues in solid graphite Super-FRS fast extraction targets." Laser and Particle Beams 26, no. 2 (2008): 273–86. http://dx.doi.org/10.1017/s0263034608000347.
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AbstractSurvival of the production target in successive experiments (with a repetition rate of 1 Hz) over an extended period of time is one of the key problems encountered in designing the Super-FRS (Superconducting Fragment Separator) at the future Facility forAntiprotons and Ion Research (FAIR). Because of the difficulties involved in construction of a liquid jet metal target, it is highly desirable to employ a solid production target at the Super-FRS. However, with the high beam intensities that will be available at the FAIR, the production target may be destroyed in a single experiment due to high specific energy deposition by the beam in the target material. The level of specific energy deposition can be reduced to an acceptable value by increasing the beam focal spot area. However, the spot size is limited by requirements of achieving good isotope resolution and sufficient transmission of the secondary beam through the system. The resolving power of the fragment separator is inversely proportional to the X-dimension of the focal spot whereas the transmission depends on Y-dimension only. It has been previously shown [Tahir et al., 2005c] that an elliptic focal spot with appropriate dimensions, will fulfill the above two conditions simultaneously and will also have a large enough area to reduce the specific energy deposition to an acceptable level for certain beam intensities of interest. In this paper we present numerical simulations of thermodynamic and hydrodynamic behavior of a solid graphite target that is irradiated by 1 GeV/u uranium beam in the intensity range of 1010 –1011 ions per bunch with a bunch length = 50 ns. These simulations have been carried out using a three-dimensional computer code, PIC3D, that includes elastic-plastic effects. This theoretical work has shown that up to a beam intensity of 1011 ions/bunch, one can employ a solid target while for higher intensities the target will be destroyed due to thermal stresses induced by the beam. It has also been found that a circular focal spot leads to minimum thermal stresses as it generates minimum pressure gradients compared to an elliptic focal spot, for the same specific energy deposition. Moreover, the stress level increases with an increase in the ellipticity of the focal spot. It is therefore recommended that one should use a circular focal spot for lower intensities provided that the criteria for isotope resolution and transmission are fulfilled.
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Eckerle, W. A., and J. K. Awad. "Effect of Freestream Velocity on the Three-Dimensional Separated Flow Region in Front of a Cylinder." Journal of Fluids Engineering 113, no. 1 (1991): 37–44. http://dx.doi.org/10.1115/1.2926493.
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Details of the horseshoe vortex formation around a cylinder were studied to determine the flow parameters that affect the flow separation in front of the cylinder. An experimental setup consisting of a circular cylinder vertically mounted on the floor of the wind tunnel test section was assembled. The approaching turbulent boundary layer was four centimeters thick. Pressures were measured on the cylinder surface and the tunnel floor with surface static pressure taps. Surface flow visualizations were accomplished to locate singlar points and the size of separation region on the endwall surface. Interior mean and fluctuating velocity data and Reynolds stresses in front of the cylinder were nonintrusively measured with a two-component Laser Doppler Anemometer system. Freestream stagnation at the endwall/cylinder surface occurred in all cases, but two types of separation were identified in this investigation. The flow pattern in the separation region depends on the freestream momentum and the boundary layer displacement thickness. A large-scale fully developed vortex was formed in the plane of symmetry for low approaching freestream velocities. A fully developed vortex was not present at higher approach velocities. Maximum production of turbulent kinetic energy was measured around the core of the vortex when fully formed.
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LAWRENCE, T., I. A. TRAIL, and J. NOBLE. "Morphological Measurements of the Proximal Interphalangeal Joint." Journal of Hand Surgery 29, no. 3 (2004): 242–47. http://dx.doi.org/10.1016/j.jhsb.2004.01.010.
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The morphology of the proximal interphalangeal joint was determined using a photographic technique. The head of the proximal phalanx, viewed end on, has a complex trapezoid appearance characteristic for each named digit. The asymmetric condyles diverge from one another and are separated by an intercondylar groove that increases in depth from the dorsal to the palmar surface. Saggital sections of the head of the proximal phalanx are not circular, but, sections taken in the plane of maximum dimensions of the condyle are circular with a radius of curvature of approximately one half of the height of the condyles. The articular surface of the base of the middle phalanx is not circular in outline in either the saggital or coronal plane. In coronal sections the articular surface is biconcave convex with a prominent median ridge separating the two adjacent concave articular surfaces. The implications of this varied morphology on implant design are discussed.
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Wang, Zijian, and Pizhong Qiao. "Backward wave separation method in a single transmitter and multi-receiver sensor array for improved damage identification of two-dimensional structures." International Journal of Damage Mechanics 26, no. 2 (2017): 229–50. http://dx.doi.org/10.1177/1056789517694477.
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In this paper, a backward wave separation method is proposed. Since the first backward wave can be considered as the damage reflection, the damage reflected wave peaks are artificially amplified by appropriately shifting and summing signals collected from a series of sensing points aligned along the wave propagating direction. This shifting and summing process aims to present the damage reflected wave peaks more distinctively while offsets randomly distributed environmental interferences. Due to the high signal-to-noise ratio of the treated signal, the application of backward wave separation is able to attain baseline-free damage detection. A circular single transmitter and multi-receiver sensor array is then deployed on a metal plate to identify the crack-like damage. Signals collected by the sensor array with and without the treatment of the backward wave separation method are, respectively, imported to the delay-and-sum imaging algorithm to yield individual damage contours. The comparisons between these contours demonstrate that the backward wave separation method is able to significantly improve the damage identification performance of the sensor array with respect to the damage localization accuracy, noise immunity, and damage sensitivity. Both the finite element modeling and laser measurement are conducted to validate the effectiveness of the proposed backward wave separation method.
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Perdana, B. Endo Gauh. "Circular Economy of Used Cooking Oil in Indonesia: Current Practices and Development in Special Region of Yogyakarta." Journal of World Trade Studies 6, no. 1 (2021): 28–39. http://dx.doi.org/10.22146/jwts.v6i1.1541.
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Used Cooking Oil (UCO) has become an inherent lifestyle of Indonesian people as frying is the main cooking method. As UCO ways of disposal have not been properly managed, the question on how UCO should be managed contributes to the adaptability of circular economy strategies moving away from throw-away culture. This study adopts desk research methods collecting relevant information from articles, journals, and books. Utilizing six dimensions – governmental, economic, environmental, technological, societal, and behavioural – of CE research for built-in environment and its conceptual limitations, this study finds that the absence of UCO governance networks contributes to the establishment of UCO collection initiatives from private sectors and community-based programs. The adoption of CE in terms of its definition and conceptual frameworks are accentuated with varying levels of emphasis on waste separation and collection systems. This study also argues that the dimensions of CE and its limitations in terms of governance and management, and social and cultural definitions are strictly attributed to incentivized UCO collection models while business sectors tend to foster limited energy recovery of UCO.
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Egorov, Nickolay V., and Ekaterina M. Vinogradova. "Mathematical modeling of a field emitter with a hyperbolic shape." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 16, no. 3 (2020): 238–48. http://dx.doi.org/10.21638/11701/spbu10.2020.302.
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This article is devoted to modeling a field emission diode system. The emitter surface is a hyperboloid of rotation. The anode surface is a part of the hyperboloid of rotation, in a particular case, a circular diaphragm. A boundary value problem is formulated for the Laplace equation with non-axisymmetric boundary conditions of the first kind. A 3D solution was found by the variable separation method in the prolate spheroidal coordinates. The electrostatic potential distribution is presented in the form of the Legendre functions expansions. The calculation of the expansion coefficients is reduced to solving a system of linear equations with constant coefficients. All geometric dimensions of the system are the parameters of the problem.
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Reinaud, Jean N. "Three-dimensional quasi-geostrophic vortex equilibria with -fold symmetry." Journal of Fluid Mechanics 863 (January 22, 2019): 32–59. http://dx.doi.org/10.1017/jfm.2018.989.
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We investigate arrays of $m$ three-dimensional, unit-Burger-number, quasi-geostrophic vortices in mutual equilibrium whose centroids lie on a horizontal circular ring; or$m+1$ vortices where the additional vortex lies on the vertical ‘central’ axis passing through the centre of the array. We first analyse the linear stability of circular point vortex arrays. Three distinct categories of vortex arrays are considered. In the first category, the $m$ identical point vortices are equally spaced on a circular ring and no vortex is located on the vertical central axis. In the other two categories, a ‘central’ vortex is added. The latter two categories differ by the sign of the central vortex. We next turn our attention to finite-volume vortices for the same three categories. The vortices consist of finite volumes of uniform potential vorticity, and the equilibrium vortex arrays have an (imposed) $m$-fold symmetry. For simplicity, all vortices have the same volume and the same potential vorticity, in absolute value. For such finite-volume vortex arrays, we determine families of equilibria which are spanned by the ratio of a distance separating the vortices and the array centre to the vortices’ mean radius. We determine numerically the shape of the equilibria for $m=2$ up to $m=7$, for each three categories, and we address their linear stability. For the $m$-vortex circular arrays, all configurations with $m\geqslant 6$ are unstable. Point vortex arrays are linearly stable for $m<6$. Finite-volume vortices may, however, be sensitive to instabilities deforming the vortices for $m<6$ if the ratio of the distance separating the vortices to their mean radius is smaller than a threshold depending on $m$. Adding a vortex on the central axis modifies the overall stability properties of the vortex arrays. For $m=2$, a central vortex tends to destabilise the vortex array unless the central vortex has opposite sign and is intense. For $m>2$, the unstable regime can be obtained if the strength of the central vortex is larger in magnitude than a threshold depending on the number of vortices. This is true whether the central vortex has the same sign as or the opposite sign to the peripheral vortices. A moderate-strength like-signed central vortex tends, however, to stabilise the vortex array when located near the plane containing the array. On the contrary, most of the vortex arrays with an opposite-signed central vortex are unstable.
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Perrey-Debain, E., R. Maréchal, and J. M. Ville. "A Special Boundary Integral Method for the Numerical Simulation of Sound Propagation in Flow Ducts Lined with Multi-Cavity Resonators." Journal of Computational Acoustics 24, no. 03 (2016): 1650012. http://dx.doi.org/10.1142/s0218396x16500120.
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In this work, acoustic performances of a liner concept based on perforated screens backed by air cavities are investigated numerically for circular ducts with mean flow. Dimensions of the cavity are chosen to be of the order or bigger than the wavelength so acoustic waves within the liner can propagate parallel to the duct surface. In this case, the liner becomes nonlocally reacting and this gives rise to additional resonance effects which renders the attenuation more effective over a broader frequency range. In order to predict the mufflers’ acoustic performances, a special boundary integral method is presented. Using a tailored Green’s function for hard wall circular ducts containing uniform mean flow, the numerical technique only requires the discretization of the acoustic velocity potential on both sides of the perforated screen separating the central channel from the air cavities. Comparisons with finite element results show that the proposed method allows accurate results for a relatively modest computational cost. Influence of the mean flow in the central airway, the dimensions of the cavity as well as the nature of the incident field on acoustic performances are also shown and discussed.
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Hu, Ying, Gui Qiang Liu, Xiang Nan Zhang, and Zheng Jie Cai. "A New Two-Dimensional Photonic Crystal Channel Drop Filter Based on Two-Resonant Cavities." Advanced Materials Research 760-762 (September 2013): 397–400. http://dx.doi.org/10.4028/www.scientific.net/amr.760-762.397.
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In this paper, a channel drop filter (CDF) is composed of two cubic lattice circular ring resonator cavities and point micro-cavities in a two-dimensional photonic crystal. The photonic band gap is calculated using the plane wave expansion (PWE) method and the optical characteristics of proposed structure are studying by the finite difference time domain (FDTD) method with perfectly matched layers (PMLs) acting as the boundary conditions . Two different wavelengths centered at 1773 nm and 1742 nm have been successful separation in this CDF. These demonstrate that our proposed structure is suitable for photonic integrated circuits (PICs) and coarse wavelength division multiplexing (WDM) optical communication systems.
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Campos, Luís Braga, and Joaquim Guerreiro Marques. "On the Kinematics of Vehicles Relevant to Conflict Detection and Resolution." Journal of Advanced Transportation 2018 (August 19, 2018): 1–14. http://dx.doi.org/10.1155/2018/2918026.
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The paper presents methods to determine the time, positions, and distance of closest approach for two vehicles following arbitrary trajectories in two or three dimensions. The distance of closest approach of two vehicles following arbitrary curved trajectories is determined by two conditions: (i) the relative velocity must be orthogonal to the relative position in order for the distance to be a nonzero extremum; (ii) the radial acceleration including centripetal terms must have a direction that increases the separation for the extremum to be a minimum. This theorem on the distance of closest approach simplifies in the case of uniform motion along rectilinear trajectories. Three examples are given: (i) the two-dimensional motion of surface vehicles changing the velocity of one of them so as to enforce a given minimum separation distance; (ii) the three-dimensional motion of two aircraft, one flying horizontally and the other climbing, changing the vertical velocity of the latter to ensure a minimum separation distance set “a priori”; (iii) the case of an aircraft flying with constant velocity in a straight line so that its closest approach to another aircraft flying in a circular holding pattern in the same plane occurs at a given time chosen “a priori”.
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BOUHAIRIE, SALEM, and VINCENT H. CHU. "Two-dimensional simulation of unsteady heat transfer from a circular cylinder in crossflow." Journal of Fluid Mechanics 570 (January 3, 2007): 177–215. http://dx.doi.org/10.1017/s0022112006002941.
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The heat transfer from the surface of a circular cylinder into a crossflow has been computed using a two-dimensional model, for a range of Reynolds numbers from Re=200 to 15550. The boundary-layer separation, the local and overall heat-transfer rates, the eddy- and flare-detachment frequencies and the width of the flares were determined from the numerical simulations. In this range of Reynolds numbers, the heat-transfer process is unsteady and is characterized by a viscous length scale that is inversely proportional to the square root of the Reynolds number. To ensure uniform numerical accuracy for all Reynolds numbers, the dimensions of the computational mesh were selected in proportion to this viscous length scale. The small scales were resolved by at least three nodes within the boundary layers. The frequency of the heat flares increases, and the width of each flare decreases, with the Reynolds number, in proportion to the viscous time and length scales. Despite the presence of three-dimensional structures for the range of Reynolds numbers considered, the two-dimensional model captures the unsteady processes and produced results that were consistent with the available experimental data. It correctly simulated the overall, the front-stagnation and the back-to-total heat-transfer rates.
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Maleki, Erfan, and Hani Sadrhosseini. "Numerical Study of External Flow over Ducts with Various Cross-Sections." Defect and Diffusion Forum 366 (April 2016): 10–16. http://dx.doi.org/10.4028/www.scientific.net/ddf.366.10.
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In this article a comprehensive numerical study is performed to compare the effect of fluid flow across a duct with various cross sectional shapes and with different velocities of the flow. Circular, elliptical and rectangular cross sections have been chosen for the ducts and air flows across them with four values of low Reynolds numbers in the range of Re = 1 to Re = 1000. Continuity and momentum equations with proper boundary conditions are solved in two dimensions. Streamlines, pressure distribution and Velocity profiles are obtained and creation of vortices, boundary layers, separation region, wake region, reattachment point and stagnation points are studied in detail and the results are compared for various cases. The value of the Reynolds number which the flow transits from steady to unsteady has been compared for the different cross sectional shapes.
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Wang, Xiaofeng, and Andrey P. Jivkov. "Combined Numerical-Statistical Analyses of Damage and Failure of 2D and 3D Mesoscale Heterogeneous Concrete." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/702563.
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Generation and packing algorithms are developed to create models of mesoscale heterogeneous concrete with randomly distributed elliptical/polygonal aggregates and circular/elliptical voids in two dimensions (2D) or ellipsoidal/polyhedral aggregates and spherical/ellipsoidal voids in three dimensions (3D). The generation process is based on the Monte Carlo simulation method wherein the aggregates and voids are generated from prescribed distributions of their size, shape, and volume fraction. A combined numerical-statistical method is proposed to investigate damage and failure of mesoscale heterogeneous concrete: the geometrical models are first generated and meshed automatically, simulated by using cohesive zone model, and then results are statistically analysed. Zero-thickness cohesive elements with different traction-separation laws within the mortar, within the aggregates, and at the interfaces between these phases are preinserted inside solid element meshes to represent potential cracks. The proposed methodology provides an effective and efficient tool for damage and failure analysis of mesoscale heterogeneous concrete, and a comprehensive study was conducted for both 2D and 3D concrete in this paper.
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Mittal, S. "Three-Dimensional Instabilities in Flow Past a Rotating Cylinder." Journal of Applied Mechanics 71, no. 1 (2004): 89–95. http://dx.doi.org/10.1115/1.1631032.
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Flow past a spinning circular cylinder placed in a uniform stream is investigated via three-dimensional computations. A stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. The Reynolds number based on the cylinder diameter and freestream speed of the flow is 200. The nondimensional rotation rate, α, (ratio of the surface speed and freestream speed) is 5. It is found that although the two-dimensional flow for α=5 is stable, centrifugal instabilities exist along the entire span in a three-dimensional set-up. In addition, a “no-slip” side-wall can result in separation of flow near the cylinder ends. Both these effects lead to a loss in lift and increase in drag. The end conditions and aspect ratio of the cylinder play an important role in the flow past a spinning cylinder. It is shown that the Prandtl’s limit on the maximum lift generated by a spinning cylinder in a uniform flow does not hold.
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Lee, Sang Woo, Seong Kuk Joo, and Joon Sik Lee. "Flow Characteristics Inside Circular Injection Holes Normally Oriented to a Crossflow: Part II—Three-Dimensional Flow Data and Aerodynamic Loss." Journal of Turbomachinery 123, no. 2 (2000): 274–80. http://dx.doi.org/10.1115/1.1348016.
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Presented are three-dimensional mean velocity components and aerodynamic loss data inside circular injection holes. The holes are normally oriented to a crossflow and each hole has a sharp square-edged inlet. Because of their importance to flow behavior, three different blowing ratios, M=0.5, 1.0, and 2.0, and three hole length-to-diameter ratios, L/D=0.5, 1.0, and 2.0, are investigated. The entry flow is characterized by a separation bubble, and the exit flow is characterized by direct interaction with the crossflow. The uniform oncoming flow at the inlet undergoes a strong acceleration and a subsequent gradual deceleration along a converging–diverging flow passage formed by the inlet separation bubble. After passing the throat of the converging–diverging passage, the potential core flow, which is nearly axisymmetric, decelerates on the windward side, but tends to accelerate on the leeward side. The presence of the crossflow thus reduces the discharge of the injectant on the windward side, but enhances its efflux on the leeward side. This trend is greatly accentuated at M=0.5. In general, there are strong secondary flows in the inlet and exit planes of the injection hole. The secondary flow within the injection hole, on the other hand, is found to be relatively weak. The inlet secondary flow is characterized by a strong inward flow toward the injection-hole center. However, it is not completely directed inward since the crossflow effect is superimposed on it. Past the throat, secondary flow is observed such that the leeward velocity component induced by the crossflow is superimposed on the diverging flow. Short L/D usually results in an exit discharging flow with a steep velocity gradient as well as a strong deceleration on the windward side, as does low M. The aerodynamic loss inside the injection hole originates from the inlet separation bubble, wall friction and interaction of the injectant with the crossflow. The first one is considered as the most dominant source of loss, even in the case of L/D=2.0. At L/D=0.5, the first and third sources are strongly coupled with each other. Regardless of L/D, the mass-averaged aerodynamic loss coefficient has an increasing tendency with increasing M.
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Zhang, Xiang-Fei, Juan-Cheng Yang, Ming-Jiu Ni, Nian-Mei Zhang, and Xin-Gang Yu. "Experimental and numerical studies on the three-dimensional flow around single and two tandem circular cylinders in a duct." Physics of Fluids 34, no. 3 (2022): 033610. http://dx.doi.org/10.1063/5.0084764.
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Experimental and numerical investigations are conducted in order to understand the flow around identical tandem circular cylinders confined in a duct (blockage ratio b = 0.1 and aspect ratio a = 5). In this work, the Reynolds number Re ranges from 40 to 200 and the spacing ratio (distance between two centers of tandem circular cylinders to diameter, L/ d) from 0 to 8. When fluid flows around a single cylinder placed symmetrically in the duct ([Formula: see text]), it is found that the Strouhal numbers St and mean drag coefficients [Formula: see text] increase with the increase in Re, although the separation angle θs decreases. For the flows around two tandem circular cylinders, the research is focused on examining the coupling effect of Re and L/ d on St, flow structures, θs, [Formula: see text] and reverse region length Lr. Based on numerical results, the mathematical descriptions are established, [Formula: see text], and [Formula: see text]. The dependence of flow structures, drag forces, θs and Lr, on L/ d is described in detail with the help of approaching velocity profiles, pressure coefficient Cp, and vorticity [Formula: see text] distribution on a cylinder's surface. Through numerical simulations, the detailed mechanisms about influences of these factors on the flow properties are revealed. The experimental results evidence the occurrence of three flow modes, i.e., no vortex shedding mode, single body mode, and reattachment mode, which are determined practically by the Reynolds number and space ratio. Both the measured St based on the dominate frequencies of vortex shedding and the visual flow field match well with numerical simulations.
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Agui, J. H., and J. Andreopoulos. "Experimental Investigation of a Three-Dimensional Boundary Layer Flow in the Vicinity of an Upright Wall Mounted Cylinder (Data Bank Contribution)." Journal of Fluids Engineering 114, no. 4 (1992): 566–76. http://dx.doi.org/10.1115/1.2910069.
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The flow of a three-dimensional boundary layer approaching an upright wall mounted circular cylinder has been experimentally investigated by means of instantaneous flow visualization techniques using a laser sheet and time resolved measurements of the wall pressure, the gradients of which are related to the vorticity flux away from the wall. The mean separation point of the oncoming boundary layer is located on the plane of symmetry, 0.76 and 0.82 diameters upstream of the cylinder for the two investigated Reynolds numbers, based on the cylinder diameter, of 1.0 × 105 and 2.2 × 105, respectively. The present flow visualization studies have shown that there is always a primary vortex present in the flow which induces an eruption of wall fluid. Very often, this eruption results in the formation of counter rotating or mushroom vortices. A secondary vortex further upstream has been observed occasionally. This vortex, as well as the vortices formed by the fast eruption of wall fluid evolve quickly in time and space and therefore cannot be obtained from time-average measurements. The primary vortex consists of several large scale structures which have originated in the oncoming boundary layer and which have acquired substantial additional vorticity. Point measurements indicate that the r.m.s. pressure fluctuations increase as separation is approached and reach a maximum near reattachment. A low degree of space-time correlation and longer integral time scales were also observed downstream of separation. A bimodal probability density function of the fluctuating pressure was observed in the vicinity of the mean separation point, close to the corner region and in the wake of the cylinder. Quasi periodic vortex shedding from the cylinder with a Strouhal number 0.13 was also observed.
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YOKOI, Yoshifumi, and Kyoji KAMEMOTO. "Initial Stage of a Three-Dimensional Vortex Structure Existing in a Two-Dimensional Boundary Layer Separation Flow : Observation of Laminar Boundary Layer Separation over a Circular Cylinder by Flow Visualization." JSME international journal. Ser. 2, Fluids engineering, heat transfer, power, combustion, thermophysical properties 35, no. 2 (1992): 189–95. http://dx.doi.org/10.1299/jsmeb1988.35.2_189.
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NAMKOONG, KAK, JUNG YUL YOO, and HYOUNG G. CHOI. "Numerical analysis of two-dimensional motion of a freely falling circular cylinder in an infinite fluid." Journal of Fluid Mechanics 604 (May 14, 2008): 33–53. http://dx.doi.org/10.1017/s0022112008001304.
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The two-dimensional motion of a circular cylinder freely falling or rising in an infinite fluid is investigated numerically for the range of Reynolds number Re, < 188 (Galileo number G < 163), where the wake behind the cylinder remains two-dimensional, using a combined formulation of the governing equations for the fluid and the dynamic equations for the cylinder. The effect of vortex shedding on the motion of the freely falling or rising cylinder is clearly shown. As the streamwise velocity of the cylinder increases due to gravity, the periodic vortex shedding induces a periodic motion of the cylinder, which is manifested by the generation of the angular velocity vector of the cylinder parallel to the cross-product of the gravitational acceleration vector and the transverse velocity vector of the cylinder. Correlations of the Strouhal–Reynolds-number and Strouhal–Galileo-number relationship are deduced from the results. The Strouhal number is found to be smaller than that for the corresponding fixed circular cylinder when the two Reynolds numbers based on the streamwise terminal velocity of the freely falling or rising circular cylinder and the free-stream velocity of the fixed one are the same. From numerical experiments, it is shown that the transverse motion of the cylinder plays a crucial role in reducing the Strouhal number. The effect of the transverse motion is similar to that of suction flow on the low-pressure side, where a vortex is generated and then separates, so that the pressure on this side recovers with the vortex separation retarded. The effects of the transverse motion on the lift, drag and moment coefficients are also discussed. Finally, the effect of the solid/fluid density ratio on Strouhal–Reynolds-number relationship is investigated and a plausible correlation is proposed.
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Prosser, Daniel T., and Marilyn J. Smith. "Numerical characterization of three-dimensional bluff body shear layer behaviour." Journal of Fluid Mechanics 799 (June 21, 2016): 1–26. http://dx.doi.org/10.1017/jfm.2016.344.
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Three-dimensional bluff body aerodynamics are pertinent across a broad range of engineering disciplines. In three-dimensional bluff body flows, shear layer behaviour has a primary influence on the surface pressure distributions and, therefore, the integrated forces and moments. There currently exists a significant gap in understanding of the flow around canonical three-dimensional bluff bodies such as rectangular prisms and short circular cylinders. High-fidelity numerical experiments using a hybrid turbulence closure that resolves large eddies in separated wakes close this gap and provide new insights into the unsteady behaviour of these bodies. A time-averaging technique that captures the mean shear layer behaviours in these unsteady turbulent flows is developed, and empirical characterizations are developed for important quantities, including the shear layer reattachment distance, the separation bubble pressure, the maximum reattachment pressure, and the stagnation point location. Many of these quantities are found to exhibit a universal behaviour that varies only with the incidence angle and face shape (flat or curved) when an appropriate normalization is applied.
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Levy, C., M. Perl, and Q. Ma. "The Influence of Multiple Axial Erosions on a Three-Dimensional Crack in Determining the Fatigue Life of Autofrettaged Pressurized Cylinders." Journal of Pressure Vessel Technology 124, no. 1 (2001): 1–6. http://dx.doi.org/10.1115/1.1386656.
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Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from an erosion’s deepest point in a multiply eroded, autofrettaged, pressurized, thick-walled cylinder are investigated. The problem is solved via the finite element method (FEM). Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs are evaluated for a variety of relative crack depths, a0/t=0.01-0.40, and crack ellipticities, a0/c=0.5-1.5, emanating from the tip of erosions of different geometry, namely: (a) semi-circular erosions of relative depths of 1–10 percent of the cylinder’s wall thickness, t; (b) arc erosions for several dimensionless radii of curvature, r′/t=0.05-0.4; and (c) semi-elliptical erosions with ellipticities of d/h=0.3-2.0. The erosion separation angle, α, is taken from 7 to 360 deg. Deep cracks are found to be almost unaffected by the erosion. The effective SIF for relatively short cracks is enhanced by the presence, separation distance and geometry of the erosion, as well as the crack geometry, and may result in a significant decrease in the vessel’s fatigue life of up to an order of magnitude.
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Persinger, Michael A. "Relating Casimir to Magnetic Energies Results in Spatial Dimensions that Define Biology Systems." International Letters of Chemistry, Physics and Astronomy 39 (October 2014): 160–65. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.39.160.
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The volume-independence that occurs when Casimir and magnetic energies were equated wasemployed to solve for optimal spatial separations. For the magnetic moments of a proton and anelectron in the presence of a magnetic field strength that produced the energy associated with theneutral hydrogen line, the distances were 1 nm and 24 nm or the width of an ion channel in a plasmacell membrane and the average synaptic width, respectively. The small discrepancies in orbit-spinmagnetic moments of the electron with the magnetic moment of the proton emerged as relevant.Calculation of the radius in the bound (circular) system associated with the required magnetic fieldstrength for the ~3.41·10-27 A·m2 discrepancy solved as the Compton wavelength of the electron.Applications of the approach allowed quantitative convergence between universal photon densitieswithin 1 nm widths as well as integration of the energy from acceleration for estimated upper limits ofresting photon masses with Planck’s constant. The results suggest that the physical and chemicalproperties that define biological systems, particularly the brain, reflect astronomical principles.
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Persinger, Michael A. "Relating Casimir to Magnetic Energies Results in Spatial Dimensions that Define Biology Systems." International Letters of Chemistry, Physics and Astronomy 39 (October 2, 2014): 160–65. http://dx.doi.org/10.56431/p-n490wt.
Pełny tekst źródłaStreszczenie:
The volume-independence that occurs when Casimir and magnetic energies were equated wasemployed to solve for optimal spatial separations. For the magnetic moments of a proton and anelectron in the presence of a magnetic field strength that produced the energy associated with theneutral hydrogen line, the distances were 1 nm and 24 nm or the width of an ion channel in a plasmacell membrane and the average synaptic width, respectively. The small discrepancies in orbit-spinmagnetic moments of the electron with the magnetic moment of the proton emerged as relevant.Calculation of the radius in the bound (circular) system associated with the required magnetic fieldstrength for the ~3.41·10-27 A·m2 discrepancy solved as the Compton wavelength of the electron.Applications of the approach allowed quantitative convergence between universal photon densitieswithin 1 nm widths as well as integration of the energy from acceleration for estimated upper limits ofresting photon masses with Planck’s constant. The results suggest that the physical and chemicalproperties that define biological systems, particularly the brain, reflect astronomical principles.
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Nilsson, Erik, Nikolaos-Georgios Vardaxis, Sylvain Ménard, and Delphine Bard Hagberg. "Sound Reduction of Ventilation Ducts through Walls: Experimental Results and Updated Models." Acoustics 3, no. 4 (2021): 695–716. http://dx.doi.org/10.3390/acoustics3040044.
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Ventilation ducts can have a negative effect on the sound reduction index between two rooms if they pass through the dividing structure without treatments. The overall sound reduction of a ventilation duct is dependent on several factors including the transmission loss when sound is breaking in and out from the duct. This study aims to model the sound reduction of a combined system with a separating wall and a ventilation duct through it. Three walls, characterized according to ISO 717-1, are combined with three different ventilation ducts, two circular and one rectangular with different dimensions. Laboratory measurement data are used to determine the sound reduction of the different configurations and the type of treatments needed for each configuration. A proposed model with existing theory for describing sound transmission losses of circular and rectangular ventilation ducts predicts the shape of the measurement data for many frequency bands. A new theory part is developed through an iterative process for circular ducts, which is based on measurements with previous methods and studies as a guide because the existing prediction scheme is somewhat perplexing. For rectangular ducts, the existing theory has been updated to better match measurement data. The application of the proposed theory and model in this article shows similar results when compared to measurements. The difference in weighted sound reduction index between developed theories and measurement data is 0–1 dB for every configuration.
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YOKOI, Yoshifumi, and Kyoji KAMEMOTO. "The initial stage of a three-dimensional vortex structure existing in a two-dimensional boundary layer separation flow. The observation of laminar boundary layer separation over a circular cylinder by flow visualization." Transactions of the Japan Society of Mechanical Engineers Series B 57, no. 534 (1991): 427–33. http://dx.doi.org/10.1299/kikaib.57.427.
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Nezhad, Hossein, and Rahim Shamsoddini. "Numerical three-dimensional analysis of the mechanism of flow and heat transfer in a vortex tube." Thermal Science 13, no. 4 (2009): 183–96. http://dx.doi.org/10.2298/tsci0904183n.
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A fully three-dimensional computational fluid dynamic model is used to analyze the mechanism of flow and heat transfer in a vortex tube. Vortex tube is a simple circular tube with interesting function and several industrial applications and contains one or more inlets and two outlets. It is used as a spot cooling device in industry. The past numerical investigations of vortex tube have been performed with the two-dimensional axisymmetric assumption but in the present work this problem is studied fully three-dimensional without making that assumption. Using this model, appropriate numerical results are presented to clarify physical understanding of the flow and energy separation inside the vortex tube. It is observed that there are considerable differences between the results of the two aforementioned models, and that the results of fully three-dimensional model are more accurate and agree better with available experimental data. Moreover, the parameters affecting the cooling efficiency of the vortex tube are discussed.
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Papavassiliou, Dario, and Gareth P. Alexander. "Exact solutions for hydrodynamic interactions of two squirming spheres." Journal of Fluid Mechanics 813 (January 20, 2017): 618–46. http://dx.doi.org/10.1017/jfm.2016.837.
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We provide exact solutions of the Stokes equations for a squirming sphere close to a no-slip surface, both planar and spherical, and for the interactions between two squirmers, in three dimensions. These allow the hydrodynamic interactions of swimming microscopic organisms with confining boundaries, or with each other, to be determined for arbitrary separation and, in particular, in the close proximity regime where approximate methods based on point-singularity descriptions cease to be valid. We give a detailed description of the circular motion of an arbitrary squirmer moving parallel to a no-slip spherical boundary or flat free surface at close separation, finding that the circling generically has opposite sense at free surfaces and at solid boundaries. While the asymptotic interaction is symmetric under head–tail reversal of the swimmer, in the near field, microscopic structure can result in significant asymmetry. We also find the translational velocity towards the surface for a simple model with only the lowest two squirming modes. By comparing these to asymptotic approximations of the interaction we find that the transition from near- to far-field behaviour occurs at a separation of approximately two swimmer diameters. These solutions are for the rotational velocity about the wall normal, or common diameter of two spheres, and the translational speed along that same direction, and are obtained using the Lorentz reciprocal theorem for Stokes flows in conjunction with known solutions for the conjugate Stokes drag problems, the derivations of which are demonstrated here for completeness. The analogous motions in the perpendicular directions, i.e. parallel to the wall, currently cannot be calculated exactly since the relevant Stokes drag solutions needed for the reciprocal theorem are not available.
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GARNAUD, XAVIER, and CHIANG C. MEI. "Wave-power extraction by a compact array of buoys." Journal of Fluid Mechanics 635 (September 2, 2009): 389–413. http://dx.doi.org/10.1017/s0022112009007411.
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The majority of existing single-unit devices for extracting power from sea waves relies on resonance at the peak frequency of the incident wave spectrum. Such designs usually call for structural dimensions not too small compared to a typical wavelength and yield high efficiency only within a limited frequency band. A recent innovation in Norway departs from this norm by gathering many small buoys in a compact array. Each buoy is too small to be resonated in typical sea conditions. In this article a theoretical study is performed to evaluate this new design. Within the framework of linearization, we consider a periodic array of small buoys with similarly small separation compared to the typical wavelength. The method of homogenization (multiple scales) is used to derive the equations governing the macroscale behaviour of the entire array. These equations are then applied to energy extraction by an infinite strip of buoys, and by a circular array. In the latter case, advantages are found when compared to a single buoy of equal volume.
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Yuan, Jiade, Yujie Li, Zhimeng Xu, and Jiamin Zheng. "A Compact CPW-Fed Low-Profile Wideband Circularly Polarized Slot Antenna with a Planar Ring Reflector for GNSS Applications." International Journal of Antennas and Propagation 2019 (October 31, 2019): 1–12. http://dx.doi.org/10.1155/2019/6463101.
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A compact low-profile wideband circularly polarized slot antenna for global navigation satellite system (GNSS) is presented. The antenna comprises a planar slot radiator with a coplanar waveguide (CPW) feed and a modified ring-shaped reflector to achieve unidirectional radiation. The modified reflector is an inner square patch with four slantly cut corners, a center ring, and an outer ring with a notch; they significantly reduce the separation between the antenna radiator and reflector and therefore the overall antenna height. The overall dimensions are λ0/3 × λ0/3 × λ0/30 (λ0 denotes the free space wavelength at lower frequency). The measured −10 dB bandwidth of |S11|, 3-dB axial ratio (AR) bandwidth, and maximum gain are of 1.53–2.28 GHz, 1.558–1.672 GHz, and 5.87 dBi, respectively. The proposed antenna is simple without any additional feeding networks or shorting probes.
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Yokoi, Yoshifumi, and Kyoji Kamemoto. "Initial Stage of a Three-Dimensional Vortex Structure Existing in a Two-Dimensional Boundary Layer Separation Flow. Visual Observation of Laminar Boundary Layer Separation over a Circular Cylinder from the Side of a Separated Region." JSME International Journal Series B 36, no. 2 (1993): 201–6. http://dx.doi.org/10.1299/jsmeb.36.201.
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Albadri, Raed Ashraf Kamil, and Khalid Saeed Lateef Al-Badri. "Simulation Study of Perfect Dual Band Microwave Metasurface Absorber." NeuroQuantology 20, no. 3 (2022): 160–65. http://dx.doi.org/10.14704/nq.2022.20.3.nq22055.
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This study presents analytical results using the CST software for a very simple design of an electromagnetic wave absorber with a negative refractive index, a copper circular-shape printed on an insulating layer separating it from a flat ground layer of copper. This design provides two absorption bands with an absorption capacity of 97.55%. This absorption is due to the dipole oscillation. Also, controlling the shape dimensions and thickness of the insulating layer leads to good results in the synthesis of the resonant frequency that contributes to the applications of energy collection and protection from the effects of electromagnetic waves. The results gave the highest value of absorption with dielectric thickness h = 0.5 mm) and by selecting a proper the gap value for g = 0.3 mm. It is also worth noting that the design can be developed to operate in a wide range of frequencies such as microwaves, terahertz, up to optical frequencies, which may contribute to potential applications in many engineering and optical technologies.
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Kiswanto, Gandjar, Poly, Yolanda Rudy Johan, and Tae Jo Ko. "Preliminary Design of Two Dimensional Vibration Assisted Machining System for Multi-Axis Micro-Milling Application." Key Engineering Materials 846 (June 2020): 105–9. http://dx.doi.org/10.4028/www.scientific.net/kem.846.105.
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Vibration assisted machining (VAM) is a method that is widely used in improving the performance of machined products. External vibrations with high frequency to ultrasonic range along with an meso-micrometer amplitude are given to the cutting tool or workpiece. This will result in a periodic separation phenomenon, hence reducing the cutting force which has positive impacts on increasing tool life and machined surface quality. Among the high-precision machining processes, micro-milling which has the ability to produce complex components with 2D and 3D features, can also be applied with the vibration assisted method, known as vibration assisted micro-milling (VAMM). Based on the direction of vibration given in the machining process, there are 1D VAMM with linear vibrations and 2D VAMM with circular or elliptical trajectory vibrations. However to date, neither developed 1D nor 2D VAMM systems are still limited to the research of planar surfaces cutting using linear movement axes, meanwhile vibration assisted in inclination cutting of micro-milling using the rotational movement axes is still very rare. Therefore the purpose of this paper is to present the preliminary model in designing a 2D VAMM system for a 5-axis micro-milling machine. The system is powered using piezoelectric actuators as the vibration-producing actuators.