Academic literature on the topic 'Static equilibrium shapes'
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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.
Dissertations / Theses on the topic "Static equilibrium shapes"
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Heptner, Nils. "Dynamics and non-equilibrium structure of colloidal dumbbell-shaped particles in dense suspensions." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2016. http://dx.doi.org/10.18452/17518.
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Neben ihrer Bedeutung in industriellen Anwendungen dienen Kolloide als Modellsysteme in Experimenten und in der Theorie, um die Struktur und Dynamik von kondensierter Materie zu untersuchen. Kürzlich wurde experimentell gezeigt, dass eine kleine Anisotropie ausreicht, um die viskoelastische Antwort im Vergleich zu harten Kugeln drastisch zu ändern. Die mikroskopischen Ursachen hierfür sind bisher nicht verstanden. In dieser Arbeit werden daher Nichtgleichgewichts-Brownsche-Dynamik-Simulationen (NEBD) von harten kolloidalen Dumbbells in oszillatorischen Scherfeldern entwickelt und eingesetzt, um diese Resultate mit Verbindung zu Rheologie- und Neutronenstreuexperimenten zu erklären. Weiterhin wird die Bedeutung der Anisotropie für Struktur und Dynamik von solchen Suspensionen im Gleichgewicht mit Hilfe von "Linear-Response"-Theorie und Brownsche-Dynamik-Simulationen analysiert. Im linearen Limit zeigt die Scherviskosität bei hohen Packungsdichten einen dramatischen Anstieg jenseits eines kritischen Anisotropieparameters. Dies weist darauf hin, dass schon bei den kleinen Anisotropien kollektive Rotations-Translations-Kopplungen für langsame Zeitskalen verantwortlich sind. Weiterhin wird ein Nichtgleichgewichtsübergang mittels NEBD-Simulationen von Suspensionen harter Dumbbells im PC unter oszillatorischer Scherung ersichtlich. Es wird gezeigt, dass der kontinuierliche Übergang nur für sehr kleine Aspektverhältnisse erhalten bleibt. Oberhalb eines bestimmten Aspektverhältnisses wird der Übergang durch einen ungeordneten Zustand vermittelt. Außerdem wird ein Sliding-Layer Zustand mit kollektiver Ordnung der Teilchenausrichtung bei hohen Scheramplituden beobachtet. Somit zeigt diese Arbeit, dass die NEBD-Simulationen Phänomene in Rheologie- und Streuexperimenten erklären. Angesichts dieser Experimente wird gezeigt, dass der Orientierungsfreiheitsgrad einen starken Einfluss auf den strukturellen Übergang bei steigenden Amplituden hat.Besides being important for industrial applications, colloidal suspensions have long served as model systems for investigating the structure and dynamics of condensed matter. Recently, it has been demonstrated experimentally that apparently a small particle anisotropy is sufficient to dramatically change the viscoelastic response under external shearing fields, of which the microscopic mechanisms are not yet sufficiently understood. In the present work, NEBD simulations of colloidal hard dumbbells in oscillatory shear fields are developed and employed to elucidate the novel findings in close connection with comprehensive rheology and SANS experiments. Furthermore, by utilising BD simulations and linear response theory, the impact of anisotropy on structure and dynamics of such suspensions in equilibrium is analysed. In the linear response limit, the shear viscosity exhibits a dramatic increase at high packing fractions beyond a critical anisotropy of the particles. This indicates that newly occurring, collective rotational-translational couplings must be made responsible for slow time scales appearing in the PC. Moreover, a non-equilibrium transition emerging at moderate aspect ratios is revealed by NEBD of plastic crystalline suspensions under oscillatory shear. This transition behaviour is systematically studied. It is demonstrated that the continuous nature of the transition is retained for very low aspect ratios only. Above a certain aspect ratio, the transition is mediated by an intermediate disordered state. Furthermore, a partially oriented sliding layer state featuring a finite collective order in the particles'' orientations is observed at high strains. Hence, this thesis demonstrates that the NEBD simulations explain novel phenomena in rheology and scattering experiments. In the light of these experiments, it is shown that the orientational degree of freedom has a vigorous impact on the structural transition under increasing oscillatory shear.
Books on the topic "Static equilibrium shapes"
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Escudier, Marcel. Linear momentum equation and hydrodynamic forces. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198719878.003.0009.
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In this chapter a method is shown for calculating the external reaction force which must be applied to a duct to counteract the hydrodynamic forces generated by a fluid flowing through it. Newton’s second law of motion applied to fluid flow through a duct of arbitrary shape leads to the linear momentum equation for fluid flow. This shows that the change in the momentum flowrate of the fluid is equal to the net force exerted on the fluid. The individual forces which contribute to the net force are the pressure forces at inlet and outlet, and the forces which arise due to the static pressure and shear stress distributed over the wetted interior surface of the duct. The condition of static equilibrium for the duct is used to relate the external restraining force to the force exerted by the flowing fluid on the wetted surface, which is termed the fluid-structure interaction force.
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D’Attoma, John. Explaining Italian Tax Compliance. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198796817.003.0005.
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It is well known that tax compliance is low in Italy. Many scholars have examined Italian taxpayer behavior, mainly using experiments and surveys. However, little attention has been given to the historical circumstances that have shaped divergent taxpayer behavior in Italy. This chapter uses historical data from Italian unification through the Second Republic to assess the effects of Italy’s major formal institutions (the Church, state, and political parties) and informal institutions (clientelism) on Italian tax behavior. It argues that nineteenth-century unification and Fascism had significant repercussions for the Italian state and how Italians perceive the state. Because of this, Italians lack trust in their government and their fellow citizens, which inhibits a willingness to pay taxes. The implication then is a low-trust/low-compliance equilibrium that becomes increasingly difficult to reverse.
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Sheppard, Eric. Heterodoxy as Orthodoxy: Prolegomenon for a Geographical Political Economy. Edited by Gordon L. Clark, Maryann P. Feldman, Meric S. Gertler, and Dariusz Wójcik. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198755609.013.9.
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For most geographers, thinking geographically about the economy means something very different than for mainstream/geographical economists: what is heterodox for the latter constitutes geographers’ orthodoxy. Nineteen propositions about geographical political economy demonstrate how thinking geographically disrupts core propositions about capitalism in mainstream economic theory. The spatiotemporality and relational nature of inter-sectoral commodity production, shaped by the socio-spatial dialectic, implies that commodity production generally is far from equilibrium, (re)produces uneven geographical development, and cannot be divorced from political processes. With respect to exchange, markets are socio-spatial constructs, profit rates are positive, free trade is inequalizing, and financialization matters. With respect to distribution, globalizing capitalism (re)produces socio-spatial inequality, an outcome modulated by the necessity of llabour politics and state intervention. Trajectories of globalizing capitalism co-evolve also with cultural and biophysical processes: its constitutional failure to deliver on the promise of equal opportunity for all makes it necessary to countenance more-than-capitalist alternatives.
Book chapters on the topic "Static equilibrium shapes"
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Ni, Wei-Ming, and Izumi Takagi. "On the Existence and Shape of Solutions to a Semilinear Neumann Problem." In Nonlinear Diffusion Equations and Their Equilibrium States, 3, 425–36. Boston, MA: Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0393-3_29.
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A. Bauer, Jacob, and Vladena Bauerová-Hlinková. "Normal Mode Analysis: A Tool for Better Understanding Protein Flexibility and Dynamics with Application to Homology Models." In Homology Molecular Modeling - Perspectives and Applications [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.94139.
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Molecular dynamics (MD) and normal mode analysis (NMA) are very useful methods for characterizing various dynamic aspects of biological macromolecules. In comparison to MD, NMA is computationally less expensive which facilitates the quick and systematic investigation of protein flexibility and dynamics even for large proteins and protein complexes, whose structure was obtained experimentally or in silico. In particular, NMA can be used to describe the flexible states adopted by a protein around an equilibrium position. These states have been repeatedly shown to have biological relevance and functional significance. This chapter briefly characterizes NMA and describes the elastic network model, a schematic model of protein shape used to decrease the computational cost of this method. Finally, we will describe the applications of this technique to several large proteins and their complexes as well as its use in enhancing protein homology modeling.
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Besley, Timothy, and Torsten Persson. "Fiscal Capacity." In Pillars of Prosperity. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691152684.003.0002.
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This chapter explores the forces that shape investments in fiscal capacity. It sets out a core model that shows how this aspect of state building is influenced by economic and political factors, such as common interests and political institutions. A key feature of the model has been to delineate the types of states that can emerge in equilibrium. It also shows that the model can be given microeconomic foundations and demonstrates how it can be extended in a number of directions that lead to more realism. The main focus of the chapter has been on the extractive role of government and on some of the issues raised in traditional public-finance models. This has laid the groundwork for the analyses to come.
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Henke, Marina E. "The Puzzle of Organizing Collective Action." In Constructing Allied Cooperation, 1–10. Cornell University Press, 2019. http://dx.doi.org/10.7591/cornell/9781501739699.003.0001.
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This introductory chapter discusses the importance of studying the process of coalition building. The puzzle of collective mobilization lies at the root of all politics. Studying the construction of multilateral military coalitions trains this puzzle on the context of international security—the one area of international cooperation that has traditionally been perceived as the most difficult to sustain a cooperative equilibrium. Moreover, the specific techniques used to build multilateral military coalitions affect how wars are fought. On the battlefield, coalition operations are supposedly more successful than non-coalition endeavors. Multilateral coalition building also affects the prospect for peace. Most peacekeeping deployments today are coalition endeavors, and research suggests that the stronger their participants, particularly in terms of personnel numbers and equipment, the more effective the missions are likely to be. Finally, coalitions unleash important socialization dynamics among participating states. They create common battle experiences and shape threat perceptions, military doctrine, and strategy for years to come. Sometimes, participation in a coalition can radically change a country's political trajectory. Thus, this book uses a social-institutional theory and evidence from over eighty multilateral military coalitions to explain coalition-building practices.
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Battersby, Paul. "Changing Patterns of Social Connection across Interventions: Unravelling Aberrant Globalisation." In Rethinking Humanitarian Intervention in the 21st Century, 94–114. Edinburgh University Press, 2017. http://dx.doi.org/10.3366/edinburgh/9781474423816.003.0005.
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International armed interventions in intrastate conflicts are planned with the expectation that order will be restored through the controlled application of limited military force. This persuasive orthodoxy, Paul Battersby argues in his Chapter Changing Patterns of Social Connection across Interventions: Unravelling Aberrant Globalisation, endures despite the erratic course of foreign interventions in the Middle East over the past two decades. Notions of order, equilibrium or stasis imply systemic balances that, where disturbed, can be restored through counteraction. Yet, while we can gather abundant conflict data, observe events from different vantage points, correlate variables and calibrate possibilities, the calculation of future trajectories of conflict events remains an imprecise and hazardous exercise. Thus, to anticipate only positive change from the rapid assertion of overwhelming military power into faraway places is to downplay the threads of happenings, decisions, ideas and beliefs that shape the subjective realities of global security. Globalisation is aberrant in its complexity, and global dynamics do not yield simple choices between binary opposites of order and disorder, control or chaos. The search for a more nuanced understanding of security leads inescapably towards the analysis of global patterns of connection and organisation that generate and sustain multiscalar supply chains of violence.
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Chankseliani, Maia. "Conclusion." In What Happened to the Soviet University?, 138—CC.P58. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192849847.003.0006.
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Abstract Soviet universities, similar to all other Soviet institutions, experienced considerable turmoil in the period following the dissolution of the Soviet Union. This was a time of revolutionary change across the region and brought about a radical break from the traditional Soviet university model in a number of countries. State withdrawal was used as an opportunity by universities to open up to market forces by introducing student fees, increasing student numbers, and engaging in commercial activities. Yet, in most contexts, the liberalisation was temporary, and newly formed states soon imposed various controls on their universities. Since the late 1990s, most of the changes at former Soviet universities have been evolutionary. This concluding chapter brings different thematic threads together and consolidates some of the key ideas pertaining to change and continuity as well as different types of change. It looks at the aspects of the Soviet university that experienced more prominent change and those that have changed less. All in all, these universities have remained flagship institutions in many contexts and demonstrated a remarkable capacity to regain equilibrium while undergoing incremental adaptations. The transformations have influenced the purposes and functions of universities, and shaped them as national institutions. While the Soviet university did not quite succeed in perpetuating the Soviet order for longer than 70 years, some of its characteristics remained resilient in the decades that followed the dissolution of the Soviet Union.
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Beris, Antony N., and Brian J. Edwards. "The Dynamical Theory of Liquid Crystals." In Thermodynamics of Flowing Systems: with Internal Microstructure. Oxford University Press, 1994. http://dx.doi.org/10.1093/oso/9780195076943.003.0016.
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Liquid crystals (LCs) present a state of matter with properties—as the name suggests—intermediate between those of liquids and crystalline solids. Liquid-crystalline materials, as all liquids, cannot support shear stresses at static equilibrium. Their molecules are characterized by an anisotropy in the shape and/or intermolecular forces. Thus, there is the potential for the formation of a separate phase(s), called a “mesophase(s),” where a partial order arises in the molecular orientation and/or location, which extends over macroscopic distances. This partial long-range molecular order, reminiscent of (but not equivalent to) the perfect order of solid crystals, in addition to the material fluidity, is primarily responsible for the many properties which are inherent characteristics of liquid-crystalline phases, such as a rapid response to electric and magnetic fields, anisotropic optical and rheological properties, etc.—see, for examples, the reviews by Stephen and Straley [1974] and Jackson and Shaw [1991], the monographs by de Gennes [1974], Chandrasekhar [1977], and Vertogen and de Jeu [1988], and the edited volumes by Ciferri et al. [1982] and Ciferri [1991]. The variety of the liquid-crystalline macroscopic properties is such that trying to derive a theory capable of describing the principal liquid-crystalline dynamic characteristics can be a very frustrating task if one does not approach the issue in a systematic fashion. Characteristically, the main two theories that have been advanced over the last thirty years for the description of the liquid-crystalline flow behavior—the Leslie/ Ericksen (LE) theory and the Doi theory—are essentially models developed from a set theoretical frame work—continuum mechanics and molecular theory, respectively. Nevertheless, each one of these theories has a limited domain of application. The description of the dynamic liquid-crystalline behavior through the bracket formalism, as seen in this chapter, leads naturally to a single conformation tensor theory with an extended domain of validity. This conformation theory consistently generalizes both previous theories, which can be recovered from it as particular cases. This offers additional evidence that the wealth of inherent information in LCs can only be appropriately handled when pursued in a systematic, fundamental manner.
Conference papers on the topic "Static equilibrium shapes"
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Towfighian, S., E. M. Abdel-Rahman, and G. R. Heppler. "Static and Dynamic Analysis of a Bistable Micro-Actuator." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67553.
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The static response of an electrostatic micro-catilever beam has been obtained by using Galerkin’s method. To make the system bi-stable, a controller has been added and the static response profile is presented using a multi-mode model for the beam. The number of mode shapes leading to convergence has been studied. The softening effect of adding more mode shapes has been investigated along with the effect of changing the system parameters on the static response. Decreasing the controller gain has been found to widen the voltage range of the bi-stability region and increasing the sensor amplification factor is shown to push the upper equilibrium point away from pull-in. Properly choosing these parameters can adjust the range of voltage for bi-stability. By doing a linearization about the stable fixed points, we also found the two natural frequencies for each stable equilibrium point. Finally, we have found the dynamic response of the bistable system using one- and three-mode-models. The basins of attraction for each stable fixed point and the exchange of energy between the two potential energy wells (equilibrium points), are demonstrated.
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Lee, Shong-Leih, and Chao-Fu Yang. "Detachment Criterion for Static Axisymmetric Bubbles on Horizontal Flat Surfaces." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78081.
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The static Young-Laplace equation is solved with the geometry method to yield the bubble shape on a horizontal flat surface under various contact angles. Multi-solution modes are found. Among the many possible equilibrium shapes of the bubble, however, only the fundamental solution mode could occur naturally. The value of VAR (volume to contact area ratio) could be a good measure for stability of equilibrium bubbles. The bubble becomes less stable when VAR increases. The numerical result reveals that in the course of bubble growth (i.e. volume increases) the VAR of the bubble increases linearly until the maximum contact area is reached. After that, VAR has a sharp increase due to a decreasing contact area. Beyond the maximum volume, equilibrium bubble does not seem possible. Based on the finding, it is postulated that bubble detachment occurs somewhere between the maximum contact area and the maximum volume according to perturbations from environment. However, the postulation seems to underestimate the stability of the bubble significantly for contact angles of larger than 160 degrees. A correction is proposed in the paper. Numerical result of bubble detachment criterion is fitted with polynomial functions of the contact angle.
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Fu, Gen, and Alexandrina Untaroiu. "A Study of the Effect of Various Recess Shapes on Hybrid Journal Bearing Using CFD and Response Surface Method." In ASME 2016 Fluids Engineering Division Summer Meeting collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/fedsm2016-7907.
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Hybrid bearings are mostly used in high speed and load situations due to their better stability and loading capacity. They are typically designed with recess grooves to enhance both static and dynamic performance of the bearing. Previous theoretical studies on the influence of the recess geometrical shapes often utilize the Reynolds equation method and most of the research focuses on thrust bearings. The aims of this paper is to analytically study the influence of various recess geometrical shapes on hybrid journal bearings. A 3-D CFD model of a hybrid journal bearing is built and a new method of response surface model is employed to determine the equilibrium position of the rotor. Based the response surface model, an optimization scheme is used to search around the equilibrium position to get a more accurate solution. The current analysis includes the recess geometry of rectangular, circular, triangular, elliptical and annular shapes. All these different shapes are studied assuming the same operating and loading conditions and bearing static properties are used as the indices of the bearing performance. The flow rate, fluid film thickness and recess flow pattern are analyzed for various recess shapes. The CFD model for the baseline bearing is validated against experimental data. The results show that the response surface model method is fast and robust in determining the rotor equilibrium position even though a 3-D CFD model is utilized. The results suggest that recess shape is a dominant factor in hybrid bearing design. This study proposed a new design process for a 3-D CFD bearing model with the ability of calculating equilibrium position and is expected to be useful to bearing designers.
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Alfosail, Feras K., Ali H. Nayfeh, and Mohammad I. Younis. "Natural Frequencies and Mode Shapes of Statically Deformed Inclined Risers." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66009.
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In this work, we investigate numerically the linear vibrations of inclined risers using the Galerkin approach. The riser is modeled as an Euler-Bernoulli beam accounting for the nonlinear mid-plane stretching and self-weight. After solving for the initial deflection of the riser due to self-weight, a Galerkin expansion of fifteen axially loaded beam mode shapes are used to solve the eigenvalue problem of the riser around the static equilibrium configuration. This yields the riser natural frequencies and exact mode shapes for various values of inclination angles and applied tension. The obtained results are validated against a boundary-layer analytical solution and are found in good agreement. This constructs a basis to study the nonlinear forced vibrations of inclined risers.
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Santillan, Sophia T., Lawrence N. Virgin, and Raymond H. Plaut. "Static and Dynamic Behavior of Highly-Deformed Risers and Pipelines." In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2007. http://dx.doi.org/10.1115/omae2007-29180.
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This paper models flexible risers and pipelines as slender elastica structures. The theoretical formulation leads to a type of nonlinear boundary value problem that can be solved numerically given appropriate boundary conditions. The offsetting effects of gravity and buoyancy are included in the analysis. These forces can provide considerable axial loading (as can thermal changes) and hence stability (buckling) is a major concern. Initial studies are based on the planar problem. A free-vibration analysis is also conducted for small-amplitude oscillations about various deflected equilibrium configurations in terms of natural frequencies and corresponding mode shapes [1]. Energy dissipation and fluid forces are a key issue in the forced problem, especially when large deformations are involved [2, 3]. Free vibration information is a vital prerequisite in understanding the response of these types of structures in practice [4].
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Pernot, Jean-Philippe, Ste´phane Guillet, Jean-Claude Le´on, Bianca Facidieno, and Franca Giannini. "A New Approach to Minimisations for Shape Control During Free-Form Surface Deformation." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/dac-48777.
Full textAbstract:
Even if researches on free-form surface deformation have produced a lot of various methods, very few of them are able to really control the shape in an adequately interactive way and most of them propose a unique solution to the underconstrained system of equations coming out of their deformation models. In our approach, where the deformation is performed through the static equilibrium modification of a bar network coupled to the surface control polyhedron, different minimizations have been proposed to overcome these limits and form a set of representative parameters that can be used to give access to the desired shape. In this paper, a reformulation of the optimization problem is presented thus enabling the generation of new shapes based on a common set of minimization criteria. Such a modification widens the variety of shapes still verifying the same set of constraints. When generalizing some of these minimizations the user has access to a continuous set of shapes while acting on a single parameter. Taking advantage of the reformulation, anisotropic surface behaviors are considered too and briefly illustrated. In addition, the possibility of defining several minimizations on different areas of a surface is sketched and aims at giving the user more freedom in local shape definition. The whole minimizations proposed are illustrated through examples resulting from our surface deformation software.
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Fukushige, Takashi, Seiichi Hata, Takehiko Hayashi, and Akira Shimokohbe. "Design and Driving Methodology of Out-of-Plane Electrostatic Microactuator With Extended Stable Motion Range." In ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems collocated with the ASME 2005 Heat Transfer Summer Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/ipack2005-73145.
Full textAbstract:
We present design and driving methodology of out-of-plane electro-static microactuator to extend stable motion range without any closed loop control system. The microactuator employed in this study is a curved cantilever microactuator, which consists of a curved cantilever moving electrode and a taper-shaped substrate electrode. A curved cantilever brings large deflection in the out-of-plane direction. Electrostatic and mechanical model of the device is derived. The equilibrium position and the stability of the cantilever are considered by calculating the stored electrostatic energy, the stored elastic energy and the lost energy from a power source due to the transfer of charges. The design methodology of the electrode shapes using the model is described and a prototype device is designed. The substrate electrode has tapered shape according to a function of distance from the anchor. The prototype is fabricated and its driving characteristics are examined. Stable motion range is extended to 65% of its full stroke by applying DC voltage and to 77% by square-wave AC voltage having a 2-kHz frequency. The calculated driving characteristics by a modified model that includes the existence of particles on insulator surface coincide with the measured one.
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Cheng, S. P., and N. C. Perkins. "Approximate Linear Theories for the Dynamics of Slack Cables Supporting a Discrete Mass." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0364.
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Abstract A continuum model is presented that describes the three-dimensional response of an elastic cable that supports a single attached mass. Two asymptotic forms of this model are analyzed for the free, linear response of slack suspensions having small equilibrium curvature (sag) and level supports. The first model, which is valid for relatively small attached masses, assumes that the cable stretches quasi-statically and results in uniform dynamic cable tension. The quasi-static stretching assumption is partially relaxed in the second model which accounts for spatially varying dynamic tension in an approximate manner. The eigen-solutions associated with free response are compared for the two models. Results indicate that the “small mass model” provides excellent approximations to the natural frequency spectrum and vibration mode shapes for most cables and modes of technical interest. A simple criterion is presented which governs the range of validity of the small mass model.
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Fan, W., and W. D. Zhu. "Dynamic Analysis of an Elevator Traveling Cable Using a Singularity-Free Beam Formulation." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68299.
Full textAbstract:
An elevator traveling cable is modeled using a singularity-free beam formulation and its static and dynamic behaviors are analyzed. The beam is assumed to be an extensible Euler-Bernoulli beam, and the configuration of the beam is described by Euler parameters, which can resolve the singularity problem of Euler angles, and the normal strain of the centroid line of the beam. The position of the centroid line of the beam is integrated from its slope. Governing equations of the beam and constraint equations are derived using Lagrange’s equations for systems with constraints. The current formulation is used to calculate the equilibrium and dynamic responses of an elevator traveling cable with arbitrarily moving ends. Equilibria of a traveling cable with different elevator car positions are calculated. Natural frequencies and corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by ABAQUS. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated using the current formulation and compared with those from commercial multibody dynamics software RecurDyn, and they are in good agreement with each other. Free responses of the traveling cable due to vertical motion of the car and forced responses with inplane and out-of-plane building sways are simulated, and their effects on dynamic responses of the traveling cable are investigated. While the vertical motion of the car can affect the in-plane lateral response of the traveling cable, it has almost no effect on its out-of-plane response. Building sways can affect both lateral and out-of-plane responses of the traveling cable, but they have little effect on its vertical response.
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Snow, Michael G., and Anil K. Bajaj. "Comprehensive Reduced-Order Models of Electrostatically Actuated MEMS Switches and Their Dynamics Including Impact and Bounce." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28590.
Full textAbstract:
As MEMS technology develops it is becoming better understood that MEMS designers must account for the large uncertainties characteristic of the relevant manufacturing processes. Uncertainty quantification tasks the designer with evaluating many different possible outcomes from the manufacturing process which creates a demand for models that are accurate and comprehensive, yet fast to evaluate. This work presents a comprehensive reduced-order model of electrostatically actuated switches incorporating a range of effects that are typically included only in FE modeling codes. Specifically, the model accounts for variable electrode geometry, stretching of centerline or large displacement effects, fringing field, squeeze film and rarefied gas damping, and allows for elastic contact with the dielectric substrate. Individual compact models for each of these effects are taken from literature and included in the model for the system. The dielectric substrate is modeled as an elastic foundation. The resulting partial differential equation for the switch modeled as a beam is discritized via a Galerkin method into ordinary differential equations for modal amplitudes. The Galerkin method uses the linear un-damped mode shapes of the beam to approximate the solution. Both cantilever and fixed-fixed type switches are analyzed. Static equilibrium solutions as a function of the applied voltage are developed along with their stability. Static pull-in voltages, first time of switch closure, and voltage for lift-off are studied with the model. To capture the contact dynamics, the contact condition is evaluated with the substrate divided into a large number of elements and the contact force is projected on to the beam basis functions. In the case of cantilever geometry and slow voltage variations, three stable regimes of contact configuration and hysteresis between them are demonstrated.