Journal articles on the topic 'Static equilibrium shapes'
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Sumesh, P. T., and Rama Govindarajan. "The possible equilibrium shapes of static pendant drops." Journal of Chemical Physics 133, no. 14 (October 14, 2010): 144707. http://dx.doi.org/10.1063/1.3494041.
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Szabó, Tímea, and Gábor Domokos. "A new classification system for pebble and crystal shapes based on static equilibrium points." Central European Geology 53, no. 1 (March 2010): 1–19. http://dx.doi.org/10.1556/ceugeol.53.2010.1.1.
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Kurniawan, A., J. R. Chaplin, M. R. Hann, D. M. Greaves, and F. J. M. Farley. "Wave energy absorption by a submerged air bag connected to a rigid float." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2200 (April 2017): 20160861. http://dx.doi.org/10.1098/rspa.2016.0861.
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A new wave energy device features a submerged ballasted air bag connected at the top to a rigid float. Under wave action, the bag expands and contracts, creating a reciprocating air flow through a turbine between the bag and another volume housed within the float. Laboratory measurements are generally in good agreement with numerical predictions. Both show that the trajectory of possible combinations of pressure and elevation at which the device is in static equilibrium takes the shape of an S. This means that statically the device can have three different draughts, and correspondingly three different bag shapes, for the same pressure. The behaviour in waves depends on where the mean pressure-elevation condition is on the static trajectory. The captured power is highest for a mean condition on the middle section.
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Vlachomitrou, M., and N. Pelekasis. "Dynamic simulation of a coated microbubble in an unbounded flow: response to a step change in pressure." Journal of Fluid Mechanics 822 (June 7, 2017): 717–61. http://dx.doi.org/10.1017/jfm.2017.301.
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A numerical method is developed to study the dynamic behaviour of an encapsulated bubble when the viscous forces of the surrounding liquid are accounted for. The continuity and Navier–Stokes equations are solved for the liquid, whereas the coating is described as a viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed for the spatial discretization of the flow domain surrounding the bubble, with the standard staggered grid arrangement that uses biquadratic and bilinear Lagrangian basis functions for the velocity and pressure in the liquid, respectively, coupled with a superparametric scheme with $B$-cubic splines as basis functions pertaining to the location of the interface. The spine method and the elliptic mesh generation technique are used for updating the mesh points in the interior of the flow domain as the shape of the interface evolves with time, with the latter being distinctly superior in capturing severely distorted shapes. The stabilizing effect of the liquid viscosity is demonstrated, as it alters the amplitude of the disturbance for which a bubble deforms and/or collapses. For a step change in the far-field pressure the dynamic evolution of the microbubble is captured until a static equilibrium is achieved. Static shapes that are significantly compressed are captured in the post-buckling regime, leading to symmetric or asymmetric shapes, depending on the relative dilatation to bending stiffness ratio. As the external overpressure increases, shapes corresponding to all the solution families that were captured evolve to exhibit contact as the two poles approach each other. Shell viscosity prevents jet formation by relaxing compressive stresses and bending moments around the indentation generated at the poles due to shell buckling. This behaviour is conjectured to be the inception process leading to static shapes with contact regions.
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Moon, K. W., W. J. Boettinger, M. E. Williams, D. Josell, B. T. Murray, W. C. Carter, and C. A. Handwerker. "Dynamic Aspects of Wetting Balance Tests." Journal of Electronic Packaging 118, no. 3 (September 1, 1996): 174–83. http://dx.doi.org/10.1115/1.2792149.
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The relationships between the force measured during wetting balance tests and the observed changes of contact angle and meniscus shape are studied. Experiments using silicone oil at 25, 50, and 100°C on glass plates as well as Pb-Sn eutectic solder on Au-coated glass plates are reported. Discrepancies between the measured force and height and those expected for a static meniscus are detailed. Equilibrium meniscus shapes are computed for wide plates using the elastica solution and for narrow plates using the public-domain software package, “Surface Evolver.” For room temperature experiments with oil, the measured force discrepancy disappears when the meniscus rise is complete. Thus, the force discrepancy may be due to shear stress exerted on the sample by fluid rising up the sample. For static menisci with heated liquids, force and meniscus height discrepancies do not disappear when the meniscus rise is complete. These discrepancies can be explained by Marangoni flow due to temperature gradients in the fluid for the oil experiments but not for the solder experiments.
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Kemmann, Guy, and Oliver Myers. "An Experimental Investigation of Combined Symmetric-Asymmetric Composite Laminates." Journal of Composites Science 3, no. 3 (July 10, 2019): 71. http://dx.doi.org/10.3390/jcs3030071.
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It has been found that certain asymmetric composite laminates exhibit bistability, where the composite laminate exhibits multiple stable static equilibrium states. If the bistable composite is actuated, it will snap to its secondary equilibrium state and then remain there without further actuation. This study investigates how the amount of symmetry in a combined symmetric asymmetric rectangular laminate under an imposed clamped edge boundary condition affects the bistability and the curvature of the laminate. Laminates with varying amounts of asymmetry were fabricated and then measured using a profilometer to capture the curvatures of the equilibrium shapes. The results showed that up to 20% symmetry can be introduced in the laminate without a substantial loss in snap through curvature, and that up to 83% symmetry can be introduced in the laminate before bistability is lost. Finite element simulations were conducted in Abaqus and showed good correlation with the experimental results.
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Psomopoulou, Efi, Daiki Karashima, Zoe Doulgeri, and Kenji Tahara. "Stable pinching by controlling finger relative orientation of robotic fingers with rolling soft tips." Robotica 36, no. 2 (August 14, 2017): 204–24. http://dx.doi.org/10.1017/s0263574717000303.
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SUMMARYThere is a large gap between reality and grasp models that are currently available because of the static analysis that characterizes these approaches. This work attempts to fill this need by proposing a control law that, starting from an initial contact state which does not necessarily correspond to an equilibrium, achieves dynamically a stable grasp and a relative finger orientation in the case of pinching an object with arbitrary shape via rolling soft fingertips. Controlling relative finger orientation may improve grasping force manipulability and allow the appropriate shaping of the composite object consisted of the distal links and the object, for facilitating subsequent tasks. The proposed controller utilizes only finger proprioceptive measurements and is not based on the system model. Simulation and experimental results demonstrate the performance of the proposed controller with objects of different shapes.
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Wilson, E. L., and A. Habibullah. "Static and Dynamic Analysis of Multi-Story Buildings, Including P-Delta Effects." Earthquake Spectra 3, no. 2 (May 1987): 289–98. http://dx.doi.org/10.1193/1.1585429.
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The P-Delta phenomenon is an area of concern to structural engineers. Traditional methods for incorporating P-Delta effects in analysis are based on iterative techniques. These techniques are time-consuming and are in general used for static analysis only. For building structures, the mass, which causes the P-Delta effect, is constant irrespective of the lateral loads and displacements. This information is used to linearize the P-Delta effect for buildings and solve the problem “exactly”, satisfying equilibrium in the deformed position, without iterations. An algorithm is developed that incorporates the P-Delta effects into the basic formulation of the structural stiffness matrix as a geometric stiffness correction. This procedure can be used for both static and dynamic analysis and will account for the lengthening of the structural time periods and changes in mode shapes due to P-Delta effects. The algorithm can be directly incorporated into building analysis programs.
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Arinicheva, I. V., I. V. Arinichev, and I. O. Sergeeva. "Application of elastic stability of flat and spatial shapes of rods in agriculture." IOP Conference Series: Earth and Environmental Science 949, no. 1 (January 1, 2022): 012050. http://dx.doi.org/10.1088/1755-1315/949/1/012050.
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Abstract In various elements of building structures, pipelines and tanks, ships and submarines, aircraft and spacecraft, in the oil and gas industry, in agriculture, elastic rods, shells and plates are widely used, for which the stability of the forms of equilibrium determines the conditions for their trouble-free operation. Today, the literature contains a huge number of works devoted to both the solution of individual particular problems and the development of general methods for analyzing the stability of equilibrium forms of elastic systems. Despite this, many problems still need to be studied. In particular, in the well-known works on the theory of stability of elastic systems, the most difficult problems include the problems of bending of heavy elastic rods, experiencing the joint action of inhomogeneous force factors. These tasks remain poorly understood, despite their importance for many agricultural and industrial processes. The article investigates the stability of elastic rods (stems), loaded at the ends by concentrated moments, and investigates the influence of the characteristics of distributed stiffness on the value of critical moments, which is a mathematical model of maintaining the stability of the stem of a cereal plant during lodging. For stems with the same bending stiffness in different planes, within the framework of the static approach, the influence of the variability of the distributions along the rods of bending stiff nesses on the critical values of the torques at which the loss of stability occurs is studied.
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Kołakowski, Zbigniew, and Andrzej Teter. "Coupled Static and Dynamic Buckling Modelling of Thin-Walled Structures in Elastic Range Review of Selected Problems." Acta Mechanica et Automatica 10, no. 2 (June 1, 2016): 141–49. http://dx.doi.org/10.1515/ama-2016-0023.
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AbstractA review of papers that investigate the static and dynamic coupled buckling and post-buckling behaviour of thin-walled structures is carried out. The problem of static coupled buckling is sufficiently well-recognized. The analysis of dynamic interactive buckling is limited in practice to columns, single plates and shells. The applications of finite element method (FEM) or/and analytical-numerical method (ANM) to solve interaction buckling problems are on-going. In Poland, the team of scientists from the Department of Strength of Materials, Lodz University of Technology and co-workers developed the analytical-numerical method. This method allows to determine static buckling stresses, natural frequencies, coefficients of the equation describing the post-buckling equilibrium path and dynamic response of the plate structure subjected to compression load and/or bending moment. Using the dynamic buckling criteria, it is possible to determine the dynamic critical load. They presented a lot of interesting results for problems of the static and dynamic coupled buckling of thin-walled plate structures with complex shapes of cross-sections, including an interaction of component plates. The most important advantage of presented analytical-numerical method is that it enables to describe all buckling modes and the post-buckling behaviours of thin-walled columns made of different materials. Thin isotropic, orthotropic or laminate structures were considered.
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Zhu, Yijun, and Huilin Shang. "Global Dynamics of the Vibrating System of a Tristable Piezoelectric Energy Harvester." Mathematics 10, no. 16 (August 12, 2022): 2894. http://dx.doi.org/10.3390/math10162894.
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Global dynamics of a piezoelectric energy harvester with tristable potential is investigated. The dynamical model of a cantilever beam energy harvester is considered; its static bifurcation is also discussed. Multiple intra-well attractors and their basins of attraction are presented to discuss the mechanism of multistability and its initial sensitivity. Moreover, the Melnikov method is applied to present the conditions for global bifurcations and the induced complex dynamics. The results show that the variation of coefficients of the polynomial may affect the number and shapes of potential wells, while the increase of the excitation amplitude may trigger multistability around one equilibrium, initial-sensitive jump, inter-well attractor and chaos. The results may provide some theoretical reference for increasing the working performance of energy harvesters.
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Mishchenko, A. "Longitudinal-transverse thermal- force bending and stability layered inhomogeneous profiled rod." Journal of Physics: Conference Series 2131, no. 2 (December 1, 2021): 022067. http://dx.doi.org/10.1088/1742-6596/2131/2/022067.
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Abstract The solution to the problem of the stress-strain state of an inhomogeneous profiled rod is based on the use of nonlinear equilibrium conditions and physical relations of a layered thermo elastic thin rod. A differential equation of bifurcation inhomogeneous rod stability of variable cross-section is obtained. The equation has variable functional coefficients. In the initial state, the rod is subjected to bending with the implementation of one of the asymmetric shapes. The critical state occurs under the action of a longitudinal load corresponding to one of the lowest symmetrical shapes, orthogonal to the initial shape. In the first series, numerical calculations of an inhomogeneous I-rod with a variable cross section height are performed. Shelves and wall I-rod are made of steel, aluminum and titanium alloys. The graphs of maximum deflection and normal stresses acting at the calculate points at the boundaries of the layers are plotted depending on the longitudinal load at the given levels of transverse loads and thermal field. A significant influence of the rod physical structure, the profiling its form and the factor of nonlinearity of static relations on the stress fields has been established. A homogeneous temperature field with a nominal value of 80°C creates fields of self-balanced stresses in an inhomogeneous rod. The components of normal stresses in this case reach 20-40% of the materials permissible resistance level. The presence of rod parts with a significant difference in the coefficients of thermal expansion in the composition enhances this effect. In the second, the stability analysis of an inhomogeneous I-rod with a variable width cross section was performed. The transition of the initial S-shaped bend to an unstable state is shown.
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Xie, Chang Chuan, Jia Zhen Leng, and Chao Yang. "Geometrical Nonlinear Aeroelastic Stability Analysis of a Composite High-Aspect-Ratio Wing." Shock and Vibration 15, no. 3-4 (2008): 325–33. http://dx.doi.org/10.1155/2008/957561.
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A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE) aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN), and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.
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Banerjee, S., R. Tewari, and G. K. Dey. "Omega phase transformation – morphologies and mechanisms." International Journal of Materials Research 97, no. 7 (July 1, 2006): 963–77. http://dx.doi.org/10.1515/ijmr-2006-0154.
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Abstract Various morphologies of the ω phase are observed in the α and the β phases of group-IV elements and their alloys where formation of this phase is induced by various means, namely, quenching from the β-phase field, isothermal annealing, under high static as well as dynamic pressure, and irradiation. The presence of various morphologies, such as ellipsoidal, cuboidal, granular or plate shapes, under different conditions is demonstrated. It is shown that various factors, including shuffling of atoms, shearing of atomic planes, long-range diffusion of solute atoms, change in volume during transformation, etc., influence the formation of different morphologies of the ω phase. The underlying mechanisms in each case are discussed. Ordered ω phases, which exist as equilibrium phases in various alloy systems, are shown as a case of superimposition of the concentration wave on the displacement wave.
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Zubair, M., Rabia Saleem, Yasir Ahmad, and G. Abbas. "Exact wormholes solutions without exotic matter in f(R,T) gravity." International Journal of Geometric Methods in Modern Physics 16, no. 03 (March 2019): 1950046. http://dx.doi.org/10.1142/s0219887819500464.
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This paper is aimed to evaluate the existence of wormholes in viable [Formula: see text] gravity models (where [Formula: see text] is the scalar curvature and [Formula: see text] is the trace of stress–energy tensor of matter). The exact solutions for energy–momentum tensor components depending on different shapes and redshift functions are calculated without some additional constraints. To investigate this, we consider static spherically symmetric geometry with matter contents as anisotropic fluid and formulate the Einstein field equations for three different [Formula: see text] models. For each model, we derive expression for weak and null energy conditions and graphically analyzed its violation near the throat. It is really interesting that wormhole solutions do not require the presence of exotic matter — like that in general relativity. Finally, the stability of the solutions for each model is presented using equilibrium condition.
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McGee, O. G., J. W. Kim, and A. W. Leissa. "Sharp Corner Functions for Mindlin Plates." Journal of Applied Mechanics 72, no. 1 (January 1, 2005): 1–9. http://dx.doi.org/10.1115/1.1795221.
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Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.
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Becze, Sigismund, and Gheorghe Ioan Vuscan. "Comparison study regarding bearing performance on 3 types of air bearingsusing Dyrobes software." MATEC Web of Conferences 299 (2019): 04001. http://dx.doi.org/10.1051/matecconf/201929904001.
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The gas bearings have low load capacity and high stiffness requirements beside the high precision which all are a concern in their development. The 2 large categories of gas bearings have each of them a drawback: the static gas bearing have the performances depending by the system which maintain the pressure, while the dynamic one's performances are increasing with speed. The article creates a comparison between 3 different type of dynamic gas bearing, using air as lubricant. While all 3 types of bearing having similar performances at max speed in term of eccentricity ratio vs. rpm, minimum film thickness and equilibrium locus, the cross-coupled damping and stiffness shown a rotor destabilization tendency. The 3 lobe rotor presented the highest pressure profiles at every speed. The pressure profiles present same shapes after 80000 rpm. The results shown potentially a multilobe rotor can over perform the plain bearing also in low speed.
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Engelmann, Ulrich M., Ahmed Shalaby, Carolyn Shasha, Kannan M. Krishnan, and Hans-Joachim Krause. "Comparative Modeling of Frequency Mixing Measurements of Magnetic Nanoparticles Using Micromagnetic Simulations and Langevin Theory." Nanomaterials 11, no. 5 (May 11, 2021): 1257. http://dx.doi.org/10.3390/nano11051257.
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Dual frequency magnetic excitation of magnetic nanoparticles (MNP) enables enhanced biosensing applications. This was studied from an experimental and theoretical perspective: nonlinear sum-frequency components of MNP exposed to dual-frequency magnetic excitation were measured as a function of static magnetic offset field. The Langevin model in thermodynamic equilibrium was fitted to the experimental data to derive parameters of the lognormal core size distribution. These parameters were subsequently used as inputs for micromagnetic Monte-Carlo (MC)-simulations. From the hysteresis loops obtained from MC-simulations, sum-frequency components were numerically demodulated and compared with both experiment and Langevin model predictions. From the latter, we derived that approximately 90% of the frequency mixing magnetic response signal is generated by the largest 10% of MNP. We therefore suggest that small particles do not contribute to the frequency mixing signal, which is supported by MC-simulation results. Both theoretical approaches describe the experimental signal shapes well, but with notable differences between experiment and micromagnetic simulations. These deviations could result from Brownian relaxations which are, albeit experimentally inhibited, included in MC-simulation, or (yet unconsidered) cluster-effects of MNP, or inaccurately derived input for MC-simulations, because the largest particles dominate the experimental signal but concurrently do not fulfill the precondition of thermodynamic equilibrium required by Langevin theory.
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Raper, S. C. B., O. Brown, and R. J. Braithwaite. "A geometric glacier model for sea-level change calculations." Journal of Glaciology 46, no. 154 (2000): 357–68. http://dx.doi.org/10.3189/172756500781833034.
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AbstractTowards accounting for the dynamic response of glaciers and ice caps in the estimation of their contribution to sea-level rise due to global warming, a mass-balance degree-day model is coupled to a geometric glacier model. The ice dynamics are treated implicitly in the geometric model by using scaling parameters that have been extensively investigated in the literature. The model is tested by presenting a case-study of the glacier Hintereisferner, Austrian Alps. The results are compatible with geomorphological data and other modelling studies. An estimate is made of the volume decrease due to initial disequilibrium. An extensive sensitivity study using generalized glacier shapes and sizes allows a comparison of results with dynamic theory. According to the geometric model, glaciers with a narrowing channel change more with a change in mass balance than glaciers with a widening channel, due to their shape and the way in which that shape changes with a changing climate. Also their response time is longer. As time progresses after a mass-balance perturbation, the longer response time for continental glaciers compared to glaciers with larger mass turnover offsets the effect of their smaller static sensitivity. Thus, although for the next century we may expect greater changes in volume from alpine glaciers, the equilibrium or committed change is greater for the continental glaciers.
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Jaikumar, Sankar, and Liu Yang. "Theoretical and experimental study of motion and sinking time of Saxon bowls." European Journal of Physics 43, no. 2 (February 4, 2022): 024001. http://dx.doi.org/10.1088/1361-6404/ac4b6a.
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Abstract This work focuses on investigating the time of sinking of a Saxon bowl proposed by ‘International Young Physicists’ Tournament in 2020. A quasi-static model is built to simulate the motion path of the bowl and predict the sinking time subsequently. The model assumes an open axisymmetric bowl with a hole in its base. The hole is modelled as a pipe for which the flow profile is governed by a modified Bernoulli’s equation which has a coefficient of discharge (C d) added to account for energy losses. The motion of the entire bowl is assumed to be in quasi-static equilibrium for an infinitesimal time interval to calculate the volumetric flow rate through the hole. The model is used to predict the sinking times of various bowls against independent variables—hole radius, bowl dimensions, mass of bowl, mass distribution of bowl, and coefficient of discharge—and predict the motion path of bowls of different, axisymmetric geometries. Characterisation of C d was done by draining a bowl filled with water and measuring the time taken to do so. Experimental verification was completed through measuring sinking times of 3D printed hemispherical bowls of the different variables in water. Motion tracking of bowls with different geometries was done using computational pixel tracking software to verify the model’s predictive power. Data from experiments for sinking time against the variables corroborate with the model to a great degree. The motion path tracked, matched the modelled motion path to a high degree for bowls of different shapes, namely a hemisphere, cylinder, frustum, and a free-form axisymmetric shape. The work is poised for an undergraduate level of readership.
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Liu, Peng-Fei, Wan-Ming Zhai, Kai-Yun Wang, Quan-Bao Feng, and Zai-Gang Chen. "Theoretical and experimental study on vertical dynamic characteristics of six-axle heavy-haul locomotive on curve." Transport 33, no. 1 (May 4, 2016): 291–301. http://dx.doi.org/10.3846/16484142.2016.1180638.
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This paper presents a method to study the vertical dynamic characteristics of a heavy-haul locomotive in curve. A quasi-static analysis model based on the static force equilibrium relationship is established to investigate the load bearing characteristics of suspension system when the locomotive runs through the curve. Then a locomotive–track coupled dynamics model is used to analyse the dynamic characteristics of wheel load in curves. Finally, a field test in curve is carried out to validate the simulated results. The theoretical analysis results indicate that due to the different twist shapes of track on the entry and exit transition curves, for some specific position in the suspension system or wheel arrangements, the corresponding vertical load along the curve length presents an asymmetry about the section of circular curve. The asymmetry is predominantly caused by the Superelevation Angle Differences (SADs) between car body, bogie frames and wheelsets. A distinct phenomenon is that the outer wheel–rail vertical load of the first axle increases when the locomotive enters the transition curve and then reduces when it exits. These results are expected to provide theoretical guidance to the design of the heavy-haul railways. It is suggested that the asymmetric characteristics of the wheel loads can be improved by some measures, such as adopting a low vertical stiffness in the secondary suspension and increasing the transition curve length.
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Ahmed, Gulraiz, Nektaria Koursari, Anna Trybala, and Victor M. Starov. "Sessile Droplets on Deformable Substrates." Colloids and Interfaces 2, no. 4 (November 6, 2018): 56. http://dx.doi.org/10.3390/colloids2040056.
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Wetting of deformable substrates has gained significant interest over the past decade due to a multiplicity of industrial and biological applications. Technological advances in the area of interfacial science have given rise to the ability to capture interfacial behavior between a liquid droplet and an elastic substrate. Researchers have developed several theories to explain the interaction between the two phases and describe the process of wetting of deformable/soft substrates. A summary of the most recent advances on static wetting of deformable substrates is given in this review. It is demonstrated that action of surface forces (disjoining/conjoining pressure) near the apparent three-phase contact line should be considered. Any consideration of equilibrium droplets on deformable (as well as on non-deformable) substrates should be based on consideration of the excess free energy of the system. The equilibrium shapes of both droplet and deformable substrate should correspond to the minimum of the excess free energy of the system. It has never been considered in the literature that the obtained equilibrium profiles must satisfy sufficient Jacobi’s condition. If Jacobi’s condition is not satisfied, it is impossible to claim that the obtained solution really corresponds to equilibrium. In recently published studies, equilibrium of droplets on deformable substrates: (1) provided a solution that corresponds to the minimum of the excess free energy; and (2) the obtained solution satisfies the Jacobi’s condition. Based on consideration of disjoining/conjoining pressure acting in the vicinity of the apparent three-phase contact line, the hysteresis of contact angle of sessile droplets on deformable substrates is considered. It is shown that both advancing and receding contact angles decrease as the elasticity of the substrate is increased and the effect of disjoining/conjoining pressure is discussed. Fluid inside the droplet partially wets the deformable substrate. It is shown that just these forces coupled with the surface elasticity determine the deformation of the deformable substrates.
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Jacobs, Verne L. "Polarized atomic radiative emission in electric and magnetic fields1This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas." Canadian Journal of Physics 89, no. 5 (May 2011): 533–49. http://dx.doi.org/10.1139/p10-115.
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A reduced density matrix approach is employed to provide a general theoretical description of polarized radiative emission during single-photon transitions from bound and auto-ionizing states of many-electron atomic systems in the presence of a general arrangement of static (or quasi-static) electric and magnetic fields. Polarized radiative emission from partially ionized atomic systems can occur as a result of the excitation of the radiating atomic states by electrons or ions with an anisotropic velocity distribution, which can be produced in an electron or ion beam experiment, and in a non-equilibrium plasma environment. Polarized radiative emission can also be produced or modified during the excitation of the atomic system in the presence of electric and magnetic fields, and electromagnetic fields. In electric and magnetic fields, the normally overlapping angular momentum projection components of atomic spectral lines can be substantially shifted from their field-free positions and split into spectroscopically resolvable (and inherently polarized) features. Because of the breakdown of the field-free angular momentum and parity selection rules, otherwise forbidden components of atomic spectral lines can be generated. Using a representation based on the field-free many-electron atomic states, the Stark–Zeeman patterns can be determined by a diagonalization of the atomic Hamiltonian in the presence of electric and magnetic fields. In the density operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic bound or auto-ionizing states. A general expression for the matrix elements of the detected-photon density operator is obtained and provides a unified framework for the analysis of the spectral intensity, angular distribution, and polarization of the Stark–Zeeman patterns. From a unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the more comprehensive reduced density matrix approach, the non-equilibrium atomic state kinetics and the homogeneous spectral line shapes can be systematically and self-consistently described.
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Randall, Alan. "Resource Scarcity and Sustainability—The Shapes Have Shifted but the Stakes Keep Rising." Sustainability 13, no. 10 (May 20, 2021): 5751. http://dx.doi.org/10.3390/su13105751.
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The objective is to provide an interpretive reading of the literature in resource scarcity and sustainability theory from the nineteenth century to the present time, focusing on shifts that have occurred in problem definition, conceptual framing, research tools applied, findings, and their implications. My reading shows, as one would expect, that the discourse has become more technical and the analysis more sophisticated; special cases have been incorporated into the mainstream of theory; and, where relevant, dynamic formulations have largely supplanted static analysis. However, that is barely scratching the surface. Here, I focus on more fundamental shifts. Exhaustible and renewable resource analyses were incorporated into the mainstream theory of financial and capital markets. Parallels between the resources and environmental spheres were discovered: market failure concepts, fundamental to environmental policy, found applications in the resources sector (e.g., fisheries), and renewable resource management concepts and approaches (e.g., waste assimilation capacity) were adopted in environmental policy. To motivate sustainability theory and assessment, there has been a foundational problem shift from restraining human greed to dealing with risk viewed as chance of harm, and a newfound willingness to look beyond stochastic risk to uncertainty, ambiguity, and gross ignorance. Newtonian dynamics, which seeks a stable equilibrium following a shock, gave way to a new dynamics of complexity that valued resilience in the face of shocks, warned of potential for regime shifts, and focused on the possibility of systemic collapse and recovery, perhaps incomplete. New concepts of sustainability (a safe minimum standard of conservation, the precautionary principle, and planetary boundaries) emerged, along with hybrid approaches such as WS-plus which treats weak sustainability (WS) as the default but may impose strong sustainability restrictions on a few essential but threatened resources. The strong sustainability objective has evolved from maintaining baseline flows of resource services to safety defined as minimizing the chance of irreversible collapse. New tools for management and policy (sustainability indicators and downscaled planetary boundaries) have proliferated, and still struggle to keep up with the emerging understanding of complex systems.
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Fleming, P. R., E. Faragher, and C. D. F. Rogers. "Laboratory and Field Testing of Large-Diameter Plastic Pipe." Transportation Research Record: Journal of the Transportation Research Board 1594, no. 1 (January 1997): 208–16. http://dx.doi.org/10.3141/1594-24.
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Flexible plastic pipe is increasingly being used in the United Kingdom for drainage and ducting (conduit) purposes. This increase in use is leading to the introduction of larger-diameter pipes. The U.K. Department of Transport (DoT) uses a recently developed, theoretical method to specify installation conditions in place of traditional techniques (e.g., Spangler’s Iowa method). The DoT design method is outlined. The extensive program of laboratory and field testing carried out at Lough-borough University to determine the performance of plastic pipes under a range of loading conditions that may be expected in practice is then described. Laboratory test results compared well with the results obtained in the field once the different boundary conditions were accounted for, thereby validating the laboratory test methods by suggesting how allowance for field conditions can be made. Some reference is made to the shapes of deformation (determined from circumferential strain data) and the effect of installation conditions upon them. Pipe deformations were found to be well within acceptable, conservative limits under all load regimens, and near equilibrium of the pipe-soil system was established relatively quickly following application of a static or a dynamic load sequence to it.
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Chen, Mingsong, Quan Chen, Yumin Lou, Yongcheng Lin, Hongbin Li, Guanqiang Wang, and Hongwei Cai. "Effect of Deformation Parameters of an Initial Aged GH4169 Superalloy on Its Microstructural Evolution during a New Two-Stage Annealing." Materials 15, no. 16 (August 11, 2022): 5508. http://dx.doi.org/10.3390/ma15165508.
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This study aims to explore the effect of deformation parameters on microstructure evolution during the new two-stage annealing method composed of an aging treatment (AT) and a cooling recrystallization annealing treatment (CRT). Firstly, the hot compressive tests with diverse deformation parameters were finished for an initial aged deformed GH4169 superalloy. Then, the same two-stage annealing method was designed and carried out for the deformed samples. The results show that the deformation parameters mainly affect the grain microstructure during CRT by influencing the content, distribution and morphology of the δ phase after deformation. The reason for this is that there is an equilibrium of the content of the δ phase and Nb atom. When the deformation temperature is high, the complete dissolution behavior of the δ phase nuclei promotes the dispersion distribution of the δ phase with rodlike and needle-like shapes during AT. Thus, the fine and heterogeneous microstructure is obtained after annealing because the recrystallization nucleation is enhanced in those dispersed δ phases during CRT. However, when the retained content of δ phase nuclei is high after deformation, the clusters of intragranular δ phases will form during AT, resulting in the pinning of the motion for dislocation. The elimination of the mixed grain microstructure is slowed down due to the low static recrystallization (SRX) nucleation rate within the deformed grain.
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Belotti, R., R. Caracciolo, I. Palomba, D. Richiedei, and A. Trevisani. "An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System." Shock and Vibration 2018 (September 16, 2018): 1–14. http://dx.doi.org/10.1155/2018/1797506.
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This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes.
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Jacobi, I., and B. J. McKeon. "Dynamic roughness perturbation of a turbulent boundary layer." Journal of Fluid Mechanics 688 (October 27, 2011): 258–96. http://dx.doi.org/10.1017/jfm.2011.375.
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AbstractThe zero-pressure-gradient turbulent boundary layer over a flat plate was perturbed by a temporally oscillating, spatial impulse of roughness, and the downstream response of the flow field was interrogated by hot-wire anemometry and particle-image velocimetry. The key features common to impulsively perturbed boundary layers, as identified in Jacobi & McKeon (J. Fluid Mech., 2011), were investigated, and the unique contributions of the dynamic perturbation were isolated by contrast with an appropriately matched static impulse of roughness. In addition, the dynamic perturbation was decomposed into separable large-scale and small-scale structural effects, which in turn were associated with the organized wave and roughness impulse aspects of the perturbation. A phase-locked velocity decomposition of the entire downstream flow field revealed strongly coherent modes of fluctuating velocity, with distinct mode shapes for the streamwise and wall-normal velocity components. Following the analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), the roughness perturbation was treated as a forcing of the Navier–Stokes equation and a linearized analysis employing a modified Orr–Sommerfeld operator was performed. The experimentally ascertained wavespeed of the input disturbance was used to solve for the most amplified singular mode of the Orr–Sommerfeld resolvent. These calculated modes were then compared with the streamwise and wall-normal velocity fluctuations. The discrepancies between the calculated Orr–Sommerfeld resolvent modes and those experimentally observed by phase-locked averaging of the velocity field were postulated to result from the violation of the parallel flow assumption of Orr–Sommerfeld analysis, as well as certain non-equilibrium effects of the roughness. Additionally, some difficulties previously observed using a quasi-laminar eigenmode analysis were also observed under the resolvent approach; however, the resolvent analysis was shown to provide reasonably accurate predictions of velocity fluctuations for the forced Orr–Sommerfeld problem over a portion of the boundary layer, with potential applications to designing efficient flow control strategies. The combined experimental and analytical effort provides a new opportunity to examine the non-equilibrium and forcing effects in a dynamically perturbed flow.
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HOŁYST, ROBERT, and PATRICK OSWALD. "DISLOCATIONS IN UNIAXIAL LAMELLAR PHASES OF LIQUID CRYSTALS, POLYMERS AND AMPHIPHILIC SYSTEMS." International Journal of Modern Physics B 09, no. 13n14 (June 30, 1995): 1515–73. http://dx.doi.org/10.1142/s0217979295000665.
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Dislocations in soft condensed matter systems such as lamellar systems of polymers, liquid crystals and ternary mixtures of oil, water and surfactant (amphiphilic systems) are described in the framework of continuum elastic theory. These systems are the subject of studies of physics, chemistry and biology. They also find applications in industry. Here we will discuss in detail the influence of dislocations on the bulk and surface properties of these lamellar phases. Especially the latter properties have only been recently studied in detail. We will present the experimental evidence of the existence of screw and edge dislocations in the systems and study their static properties such as: energy, line tension and core structure. Next we will show how the surface influences the equilibrium position of dislocations in the system. We will give the theoretical predictions and present the experimental results on thin copolymer films, free standing films of liquid crystals and smectic droplets shapes. In semi-infinite lamellar systems characterized by small surface tension the dislocation is stabilized at a finite distance, heq, from the surface, due to the surface bending elastic constant, Ks (for zero surface tension heq≈Ks/2K, where K is the bulk bending elastic constant). For large surface tension the edge dislocations are strongly repelled by the surface and the equilibrium location for finite symmetric systems such as free standing liquid crystal films shifts towards the center of the system. The surface is deformed by dislocations. These deformations are known as edge profiles. They will be discussed for finite systems with small and large surface tension. Surface deformations induce elastic interactions between edge dislocations, which decay exponentially with distance with decay length proportional to [Formula: see text] where D is the size of the system normal to lamellas. Two screw dislocations in finite system interact with the logarithmic potential, which is proportional to the surface tension and inversly proportional to D. The surface induced elastic interactions will be compared to, well-known, bulk deformation induced interactions. A new phenonenon discussed in our paper is the fluctuations induced interactions between edge dislocations, which follows from the Helfrich mechanism for flexible objects. At suitable conditions, edge dislocations can undergo an unbinding transition. Also a single dislocation loop can undergo an unbinding transition. We will calculate the properties of the loop inside finite system and discuss in particular the unbinding transition in freely suspended smectic films. We shall also compute the equilibrium size of the loop contained between two hard walls. Finally we will discuss the dynamical bulk properties of dislocations such as: mobility (climb and glide), permeation, and helical instability of screw dislocations. Lubrication theory will also be discussed.
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Wang, Zhi-Qian, Soon-Keat Tan, Nian-Sheng Cheng, and Keng-Wee Goh. "A simple relationship for crenulate-shaped bay in static equilibrium." Coastal Engineering 55, no. 1 (January 2008): 73–78. http://dx.doi.org/10.1016/j.coastaleng.2007.07.004.
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Neville, Robin M., Rainer M. J. Groh, Alberto Pirrera, and Mark Schenk. "Beyond the fold: experimentally traversing limit points in nonlinear structures." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2233 (January 2020): 20190576. http://dx.doi.org/10.1098/rspa.2019.0576.
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Recent years have seen a paradigm shift regarding the role of nonlinearities and elastic instabilities in engineering science and applied physics. Traditionally viewed as unwanted aberrations, when controlled to be reversible and well behaved, nonlinearity can enable novel functionalities, such as shape adaptation and energy harvesting. The analysis and design of novel structures that exploit nonlinearities and instabilities have, in part, been facilitated by advances in numerical continuation techniques. An experimental analogue of numerical continuation, on the other hand, has remained elusive. Traditional quasi-static experimental methods control the displacement or force at one or more load-introduction points over the test specimen. This approach fails at limit points in the control parameter, as the immediate equilibrium beyond limit points is statically unstable, causing the structure to snap to a different equilibrium. Here, we propose a quasi-static experimental path-following method that can continue along stable and unstable equilibria, and traverse limit points. In addition to controlling the displacement at the main load-introduction point, the technique relies on overall shape control of the structure using additional actuators and sensors. The proposed experimental method enables extended testing of the emerging class of structures that exploit nonlinearities and instabilities for novel functionality.
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Ruiz-Gutiérrez, Élfego, Ciro Semprebon, Glen McHale, and Rodrigo Ledesma-Aguilar. "Statics and dynamics of liquid barrels in wedge geometries." Journal of Fluid Mechanics 842 (March 6, 2018): 26–57. http://dx.doi.org/10.1017/jfm.2018.116.
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We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle $\unicode[STIX]{x1D703}_{e}$, confined in a solid wedge geometry of opening angle $\unicode[STIX]{x1D6FD}$. We focus on a mostly non-wetting regime, given by the condition $\unicode[STIX]{x1D703}_{e}-\unicode[STIX]{x1D6FD}>90^{\circ }$, where the droplet forms a liquid barrel – a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid–gas interface, we compute the changes to the surface energy and pressure distribution of the liquid upon a translation along the symmetry plane of the wedge. Our model is in good agreement with numerical calculations of the surface energy minimisation of static droplets deformed by gravity. Beyond the statics, we put forward a Lagrangian description of the droplet dynamics. We focus on the overdamped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact-line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales.
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Gainza, June, Ernesto Mauricio González, and Raúl Medina. "A process based shape equation for a static equilibrium beach planform." Coastal Engineering 136 (June 2018): 119–29. http://dx.doi.org/10.1016/j.coastaleng.2018.02.006.
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Weesakul, Sutat, and Somruthai Tasaduak. "EXPERIMENTAL INVESTIGATION ON DYNAMIC EQUILIBRIUM BAY SHAPE." Coastal Engineering Proceedings 1, no. 33 (October 25, 2012): 37. http://dx.doi.org/10.9753/icce.v33.sediment.37.
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Equilibrium bay is a bay that its shoreline is stable and does not change with time in long term. This concept can be applied for coastal protection. Experiments on dynamic equilibrium bay planform are conducted in a laboratory. There is one location of sediment supply source into a bay near upcoast headland and its magnitude vary from case to case. Wave obliquity varies from small to moderate values. These are two main parameters while wave condition is kept constant. The final bay planforms are investigated and recorded once they reach equilibrium with condition that sediment transport gradient approaches zero and no further shoreline change are observed. The parabolic equation similar to that for static equilibrium is newly proposed. The coefficients are originally derived and found to be a function of wave obliquity and the ratio of sediment supplied into bay to longshore sediment transport. The new dynamic equilibrium bay equation can be used and applied to study morphology change with variation of supplied sediment from inland.
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Kalu, Ebere Ume, Uchenna Florence Nwafor, Chinwe R. Okoyeuzu, and Vincent A. Onodugo. "Dynamics of energy consumption, real sector value added and growth in energy deficient economies." International Journal of Energy Sector Management 14, no. 5 (April 9, 2020): 1001–22. http://dx.doi.org/10.1108/ijesm-09-2019-0012.
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Purpose The purpose of this study is to investigate the energy–growth linkage in sub-Saharan Africa (SSA), with emphasis on real sectors’ contribution to aggregate growth using dynamic panel estimation techniques that are practically and conceptually superior to the static models. Design/methodology/approach Dynamic panel econometric techniques pooled mean group, mean group and dynamic fixed effect were used to investigate the linkage among energy consumption, real sector value added and economic growth from 1967 to 2016 in 48 SSA countries. Findings A strong empirical evidence in favor of energy dependence and growth hypothesis in the investigated SSA countries was found. The finding that real sector value added and overall growth rate adjust reasonably to the shocks and dynamics of the energy consumption variables makes energy consumption an enabler for growth. This indicates that well thought-out and implemented energy development policy will not only increase energy consumption but also elicit multi-sectoral growth while addressing the obvious energy deficiency in the SSA region. Research limitations/implications It is also important to note the policy implications of the high adjustment profiles indicated by the error correction representations. All the speeds of adjustment of the three models denominated in time are slightly above a year and are all within predictable limits (they fall below unity or 100%). We found that when agriculture value added, manufacturing value added and overall economic growth rate in our SSA panel estimation exceed equilibrium levels as a result of deviations arising from energy related variables, downward adjustments at 66%, 62% and 78% per year, respectively, take place. Practical implications The study indicates that well thought-out and implemented energy development policy will not only increase energy consumption but also elicit multi-sectoral growth while addressing the obvious energy deficiency in the SSA region. Social implications Much as this study has made some addition to the literature on energy-growth nexus in the SSA region, which undoubtedly is an unveiling of economic forces in a collection of developing and energy deficient economies, it will be of great research significance if the form and style of this study is adopted for other economic blocs in the shapes and sizes of the SSA region. Originality/value This study ensured currency of data, novelty of approach and disaggregated energy consumption into emerging sources, traditional sources and geographical access.
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Santana, Murillo V. B., Paulo B. Gonçalves, and Ricardo A. M. Silveira. "Static stability and load capacity of pyramidal trusses." MATEC Web of Conferences 148 (2018): 07005. http://dx.doi.org/10.1051/matecconf/201814807005.
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The analysis of pyramidal trusses has an immediate practical interest since these structures are currently used in many present-day civil constructions, either as main parts or a constitutive element. They can be used to represent tripod-like structures, cap of masts, tower cranes, big span roofs, and even a portion of a single-layer geodesic dome or of a generic-shaped reticulated shell. This paper examines the nonlinear static stability and load capacity for a simple class of space trusses in the shape of a regular pyramid. Joints located at the vertices of the base polygon are fixed while the joint at the apex is subjected to static loads acting in either the vertical direction, in the horizontal plane, or along a generic oblique direction. Despite their apparent simplicity, these structural systems exhibit a wide variety of post-critical responses, not exhausted by the classical snapping and bifurcation phenomena. In addition to regular primary and secondary branches, the equilibrium paths may include neutral branches, namely branches entirely composed of bifurcation or limit points. The analysis is conducted using the Finite Element Method together with a corotational formulation for the bars. The numerical results are validated in the elastic domain using the closed-form solutions found in literature.
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Ren, Hongru, Leining Zhang, Xiongying Li, Yifan Li, Weikang Wu, and Hui Li. "Interfacial structure and wetting properties of water droplets on graphene under a static electric field." Physical Chemistry Chemical Physics 17, no. 36 (2015): 23460–67. http://dx.doi.org/10.1039/c5cp04205d.
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McComb, Todd. "Calculation of the Rise and Pitch of a Three-Dimensional Low-Aspect-Ratio Flat Ship." Journal of Ship Research 35, no. 04 (December 1, 1991): 314–24. http://dx.doi.org/10.5957/jsr.1991.35.4.314.
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Using low-aspect-ratio flat ship theory, this paper defines a procedure to determine the position of a hull which is in equilibrium at some "fast" speed in terms of a given hull shape for the same hull at rest. This procedure is then used to find the equilibrium flow past a moving ship, when given the shape of the hull at rest. The method is then extended to find the hull configuration at various speeds based on either the configuration in the static case or at some other equilibrium speed, leading to a calculation of drag versus speed. Some general formulas and some simple examples are given.
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Accornero, Federico, and Alberto Carpinteri. "Funicularity in elastic domes: Coupled effects of shape and thickness." Curved and Layered Structures 8, no. 1 (January 1, 2021): 181–87. http://dx.doi.org/10.1515/cls-2021-0017.
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Abstract An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes. It is realized how the static and kinematic matrix operators are one the ad-joint of the other, and, on the other hand, it can be rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without ‚exural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membrane one.
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Lee, Juney, Caitlin Mueller, and Corentin Fivet. "Automatic generation of diverse equilibrium structures through shape grammars and graphic statics." International Journal of Space Structures 31, no. 2-4 (June 2016): 147–64. http://dx.doi.org/10.1177/0266351116660798.
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SHEN, SHUIFA, XIUJIE WANG, TINGDUN WEN, FENG PAN, JIANZHONG GU, LIHUA ZHU, XIAOGUANG WU, et al. "TRIAXIAL SHAPE IN Os–Pt REGION FROM GROUND STATES TO COLLECTIVE ROTATIONAL STATES." Modern Physics Letters A 25, no. 10 (March 28, 2010): 805–13. http://dx.doi.org/10.1142/s0217732310032329.
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In order to study the deformation of the nuclei which belongs to the transitional region between strongly deformed and spherical nuclei, the calculations of the total Routhian surfaces by means of the pairing-deformation-frequency self-consistent cranked shell model were carried out in order to investigate shape evolution in even-mass Os and Pt isotopes (176–202 Os and 182–204 Pt ) starting from the static nuclear ground states. It is found that some nuclear ground states such as in 196 Os and 188–194 Pt are neither oblate nor prolate. Instead, the ground-state minima in these nuclei are axially asymmetric in shape. In addition, a complementary approach is used to extract equilibrium γ0 value (nonaxially symmetric equilibrium shape parameter), which support our predictions.
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Petrolo, M., MH Nagaraj, E. Daneshkhah, R. Augello, and E. Carrera. "Static analysis of thin-walled beams accounting for nonlinearities." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 236, no. 6 (October 14, 2021): 2967–80. http://dx.doi.org/10.1177/09544062211032997.
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This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1 D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3 D finite elements (FE) are provided to assess the formulation’s accuracy and computational efficiency. It is shown how 1 D models based on Lagrange expansions of the displacement field are comparable to 3 D FE regarding the accuracy but require considerably fewer degrees of freedom.
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Gupta, Shikha, Fernando Carrillo, Medhi Balooch, Lisa Pruitt, and Christian Puttlitz. "Simulated Soft Tissue Nanoindentation: A Finite Element Study." Journal of Materials Research 20, no. 8 (August 1, 2005): 1979–94. http://dx.doi.org/10.1557/jmr.2005.0247.
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To address the growing interest in nanoindentation for biomaterials, the following finite element study investigated the influence of indentation testing protocol and substrate geometry on quasi-static and dynamic load-displacement behavior of linear viscoelastic materials. For a standard linear solid, the conventional quasi-static indentation modulus, EQS, fell between the instantaneous and equilibrium modulus of the model. EQS approached the equilibrium modulus only for indentation unloading times 1000 times greater than the characteristic relaxation time of the model. It was nearly insensitive to other changes in the indentation testing protocol, such as tip radius and penetration depth, exhibiting variations of only 5–10%. Dynamic nanoindentation provided a quantitatively accurate assessment of the complex dynamic modulus (within ±12%) for a range material of parameters at physiologically relevant testing parameters. Both quasi-static and dynamic moduli calculated from the irregular surfaces varied with the size and shape of the irregularities but were still within 10% of the smooth surface values for penetration depths larger than the dimensions of the surface irregularities.
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Shutyi A. M. and Sementsov D. I. "Dynamics of magnetization of a uniaxial nanoparticle in the region of noncollinear ferromagnetic resonance." Physics of the Solid State 64, no. 12 (2022): 1904. http://dx.doi.org/10.21883/pss.2022.12.54384.448.
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Resonance dynamics of the magnetic moment of a uniaxial ellipsoidal nanoparticle under its magnetic biasing along the symmetry axis and excitation by a transverse high-frequency field is studied with the parameters (frequency, magnetic bias field and shape parameter), corresponding to the noncollinear orientation of equilibrium magnetization and the external static field. We revealed the frequency regions where precession becomes nonlinear at a weak alternating field and dynamic bistability, as well as complex spatial attractors and chaos are implemented. Keywords: ellipsoidal nanoparticle, ferromagnetic resonance, static and high-frequency field, nonlinearity, effective anisotropy, bistability, regular and chaotic precession.
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Lim, Changbin, Jooyong Lee, and Jung Lyul Lee. "Simulation of Bay-Shaped Shorelines after the Construction of Large-Scale Structures by Using a Parabolic Bay Shape Equation." Journal of Marine Science and Engineering 9, no. 1 (January 4, 2021): 43. http://dx.doi.org/10.3390/jmse9010043.
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Among the various causes of coastal erosion, the installation of offshore breakwaters is considered the main cause that influences the most serious changes in shorelines. However, without a proper means for predicting such terrain changes, countries and regions continue to suffer from the aftermath of development projects on coastal land. It has been confirmed that the parabolic bay shape equation (PBSE) can accurately predict shoreline changes under the wave climate diffracted as a result of such development projects. This study developed a shoreline change model that has enhanced the previous shoreline change models by applying PBSE to shoreline changes into bay-shaped features. As an analytical comparison with the second term of the GENESIS model, which is an existing and well-known shoreline change model, a similar beach erosion width was obtained for a small beach slope. However, as the beach slope became larger, the result became smaller than that of the GENESIS model. The validity of the model was verified by applying it to satellite images that demonstrated the occurrence of shoreline changes caused by breakwaters for seaports on the eastern coast of Korea; Wonpyeong beach, Yeongrang beach, and Wolcheon beach. As a result, each studied site converged on the static equilibrium planform within several years. Simultaneously, the model enabled the coastal management of the arrangement of seaports to evaluate how the construction of structures causes serious shoreline changes by creating changes to wavefields.
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Banik, Deepayan, Kumar Gaurav, and Ishan Sharma. "Axisymmetric landslides on top-shaped asteroids." EPJ Web of Conferences 249 (2021): 03048. http://dx.doi.org/10.1051/epjconf/202124903048.
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Spin rates of minor planets or asteroids are known to have been affected by several agents including but not limited to tidal fly-bys, impacts and solar radiation. Surface processes like landslides occur as a result of such rotational changes. We study the evolution of landslides on top-shaped rubble pile asteroids like 101955 Bennu and 162173 Ryugu, with the underlying core modeled as two solid cones fused back to back. Using a depth averaged avalanche theory applicable to granular flows we solve for axisymmetric landslides occurring at various spin rates and regolith friction. Static regions on the surface corresponding to different spin rates are identified from an equilibrium analysis. We then solve for landslides initiated at different latitudes. It is found that landslides equilibrate at lower latitudes as the spin rate is increased. Beyond a critical spin rate regolith is shed from the equator. This critical spin is higher for a lower value of the semi-apex angle of the cone.
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Strzelecki, Stanisław. "STATIC CHARACTERISTICS OF OFFSET 8-LOBE JOURNAL BEARINGS." Tribologia 295, no. 1 (October 31, 2021): 39–51. http://dx.doi.org/10.5604/01.3001.0015.4899.
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The 8-lobe journal bearings have found application in the bearing systems of spindles of grinding machines. The design of bearings and the large number of lobes and oil grooves assures good cooling conditions of bearing. These bearings can be manufactured as the bearings with cylindrical, non-continuous operating surfaces separated by six lubricating grooves, bearings with the pericycloidal shape of the bearing bore, and as offset journal bearing. This paper presents the results of the computation of static characteristics of an offset 8-lobe journal bearing operating under the conditions of an aligned axis of journal and bush, adiabatic oil film, and at the static equilibrium position of journal. Different values of bearing length to diameter ratio, relative clearance, and lobe relative clearance were assumed. Reynolds' energy and viscosity equations were solved by means of an iterative procedure. Adiabatic oil film, laminar flow in the bearing gap, and aligned orientation of journal in the bearing were considered.
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Mitrishkin, Yuri V., Pavel S. Korenev, Artem E. Konkov, Valerii I. Kruzhkov, and Nicolai E. Ovsiannikov. "New Identification Approach and Methods for Plasma Equilibrium Reconstruction in D-Shaped Tokamaks." Mathematics 10, no. 1 (December 23, 2021): 40. http://dx.doi.org/10.3390/math10010040.
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The paper deals with the identification of plasma equilibrium reconstruction in D-shaped tokamaks on the base of plasma external magnetic measurements. The methods of such identification are directed to increase their speed of response when plasma discharges are relatively short, like in the spherical Globus-M2 tokamak (Ioffe Inst., St. Petersburg, Russia). The new approach is first to apply to the plasma discharges data the off-line equilibrium reconstruction algorithm based on the Picard iterations, and obtain the gaps between the plasma boundary and the first wall, and the second is to apply new identification methods to the gap values, producing plasma shape models operating in real time. The inputs for on-line robust identification algorithms are the measurements of magnetic fluxes on magnetic loops, plasma current, and currents in the poloidal field coils measured by the Rogowski loops. The novel on-line high-performance identification algorithms are designed on the base of (i) full-order observer synthesized by linear matrix inequality (LMI) methodology, (ii) static matrix obtained by the least square technique, and (iii) deep neural network. The robust observer is constructed on the base of the LPV plant models which have the novelty that the state vector contains the gaps which are estimated by the observer, using input and output signals. The results of the simulation of the identification systems on the base of experimental data of the Globus-M2 tokamak are presented.
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Karpov, V. V., and A. A. Semenov. "Mixed-Form Equations for Stiffened Orthotropic Shells of Arbitrary Canonical Shape with Static Loading." Journal of Mechanics 34, no. 4 (October 2, 2017): 469–74. http://dx.doi.org/10.1017/jmech.2017.82.
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AbstractThin-walled orthotropic shells of arbitrary form reinforced from the concave side by a cross-sectional stiffening system oriented in parallel to coordinate lines are examined. Geometrical nonlinearity and transverse shears are taken into account, but it is presumed that a shell is shallow.Mixed-form equations are more simplified equations of a shell theory as compared to displacement equations, but they are more convenient for some types of fixing of the shell edges (for example, for movable pin fixing).Forces are expressed using a stress function in a middle surface of a shell in such a way that the first two equilibrium equations are satisfied identically. Shell deformation is also expressed using this function.The third equation of strain compatibility is used to form one of the mixed-form equations. Curvature and torsion change functions for this equation are written in the same way as for the Kirchhoff–Love model, though also taking into account transverse shears.
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Vyas, D., F. Sayyad, M. Khardiwar, and Shailendra Kumar. "Physicochemical Properties of Briquettes from Different Feed Stock." Current World Environment 10, no. 1 (April 30, 2015): 263–69. http://dx.doi.org/10.12944/cwe.10.1.32.
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This study was undertaken to evaluate the Physico-chemical properties of eight different types of biomass feed stock and their briquettes were studied among that some properties which are influence their storage and combustion properties like Equilibrium moisture content (EMC %) and Relative humidity (%). Equilibrium moisture content are found out by static equilibrium technique using aqueous glycerol solutions of different concentrations in the relative humidity (RH) range of 40 to 90 % and at ambient temperature between 25 to 37 ºC. The Equilibrium moisture content of briquettes was lower than their feedstock by about 1 – 2.5 % in all the cases ranges from 40 to 70 % RH. At higher RH above 70%, the difference was between 2 - 4%. There was no change in the shape of the briquettes at all levels of RH. This was due to higher density of briquettes. This study showed during period of high humidity, the storage of briquettes will not create any problem and will be safer as compared to their feedstock.