Topic
Hydrostatic equilibrium
About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.
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TL;DR: In this paper, photoelastic disks are released from an incline to create steady two-dimensional avalanches, which reveal the distribution of dynamic forces in the bulk of granular free-surface flows.
Abstract: In this study, we perform experiments that reveal the distribution of dynamic forces in the bulk of granular free-surface flows. We release photoelastic disks from an incline to create steady two-dimensional avalanches. These gravity-driven dry granular flows are in the slow to intermediate regime ($I\ensuremath{\le}1$), dense ($\ensuremath{\varphi}\ensuremath{\approx}0.8$), and thin ($h\ensuremath{\approx}10d$). The transition between solidlike (quasisteady) and fluidlike (inertial) regimes is observable for certain experimental settings. We measure constant density and quasilinear velocity profiles through particle tracking at several points down the chute, for two different basal topographies. The photoelastic technique allows the visualization and quantification of instantaneous forces transmitted between particles during individual collisions. From the measured forces we obtain coarse-grained profiles of all stress tensor components at various positions along the chute. The discreteness of the system leads to highly fluctuating individual force chains which form preferentially in the directions of the bulk external forces: in this case, gravity and shear. The behavior of the coarse-grained stress tensor within a dynamic granular flow is analogous to that of a continuous fluid flow, in that we observe a hydrostatic increase of the mean pressure with depth. Furthermore, we identify a preferential direction for the principal stress orientation, which depends on the local magnitudes of the frictional and gravitational forces. These results allow us to draw an analogy between discrete and continuous flow models.
11 citations
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TL;DR: In this article, the authors compare two commonly adopted strategies: going to very high order and reduce drastically the truncation errors on the equilibrium solution, or design a specific scheme that preserves by construction the equilibrium exactly, the so-called well-balanced approach.
Abstract: Equilibrium or stationary solutions usually proceed through the exact balance between hyperbolic transport terms and source terms. Such equilibrium solutions are affected by truncation errors that prevent any classical numerical scheme from capturing the evolution of small amplitude waves of physical significance. In order to overcome this problem, we compare two commonly adopted strategies: going to very high order and reduce drastically the truncation errors on the equilibrium solution, or design a specific scheme that preserves by construction the equilibrium exactly, the so-called well-balanced approach. We present a modern numerical implementation of these two strategies and compare them in details, using hydrostatic but also dynamical equilibrium solutions of several simple test cases. Finally, we apply our methodology to the simulation of a protoplanetary disc in centrifugal equilibrium around its star and model its interaction with an embedded planet, illustrating in a realistic application the strength of both methods.
11 citations
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TL;DR: The same model can be applied to study metre-scale waves, even beyond breaking, with results closely matching those obtained using small-scale Euler/Navier-Stokes models, and coastal or global scale dispersive waves, with an accuracy and efficiency comparable to extended Boussinesq wave models.
11 citations
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TL;DR: In this paper, the fluid-structure interactions model of oil hydrostatic guideways with annular slit restrictors is established based on the dynamic Reynolds equation on the land, the elastic deformation equation of the upper slideway and the table dynamic equilibrium equation.
Abstract: Oil hydrostatic guideways are widely applied in ultra-precision machine tools, the structural parts are often considered as rigid bodies without deformations in the process of design and calculation. In other words, the effects of the structural parts on the oil film thickness and the pressure distribution are ignored in the course of working. The fluid-structure interactions model of oil hydrostatic guideways with annular slit restrictors is established. This model is based on the dynamic Reynolds equation on the land, the elastic deformation equation of the upper slideway and the table dynamic equilibrium equation. The effects of fluid-structure interactions on the deformations, static and dynamic stiffness and settling time under the step load are explored. The results show that the deformations of the upper slideway increase linearly with recess pressure, the static and dynamic stiffness are decreased by the deformations, the settling time is extended by the deformations. Measured values of the static and dynamic stiffness agree well with the theoretical values with the deformations.
11 citations
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TL;DR: In this paper, the effects of modification of gravity on the problem of dynamical instability of the spherical relativistic anisotropic interiors were studied and a modified hydrostatic equation was constructed and then solved by using radial perturbation scheme.
Abstract: In this paper, we study the effects of modification of gravity on the problem of dynamical instability of the spherical relativistic anisotropic interiors. We have considered non-zero influence of expansion scalar throughout during the evolutionary phases of spherical geometry that led to the use of fluid stiffness parameter. The modified hydrostatic equation for the stellar anisotropic matter distributions is constructed and then solved by using radial perturbation scheme. Such a differential equation can be further used to obtain instability constraints at both weak field and post-Newtonian approximations after considering a particular Harrison-Wheeler equation of state. This approach allows us to deal with the effects of usual and effective matter variables on the stability exotic stellar of self-gravitating structures.
11 citations