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This paper evaluates the effects of uncertainties on the load capacity of a four-pad tilting-pad journal bearing, in which the pad radius, oil viscosity, and radial clearance are considered as uncertain information. The hydrodynam...
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This paper evaluates the effects of uncertainties on the load capacity of a four-pad tilting-pad journal bearing, in which the pad radius, oil viscosity, and radial clearance are considered as uncertain information. The hydrodynamic supporting forces at the bearing pads are obtained by solving the Reynolds equation. In this case, the uncertain parameters are modeled as fuzzy type-2 variables. Fuzzy type-2 sets have been widely used due to their ability to model higher orders of uncertainties as compared with the fuzzy type-1 approach. They allow for inaccurate knowledge to be included in the membership functions used to describe the uncertain parameters. In the present contribution, the so-called alpha-level optimization was associated with the fuzzy type-2 technique for uncertainty analysis purposes. A sensitivity analysis was also carried out as an additional assessment of the considered uncertain parameters. The numerical results allowed to understand how the uncertain parameters affect the bearing supporting forces for three shaft speeds, namely, 3000, 9000, and 15,000 rpm. It was demonstrated that the effect of the uncertain parameters on the supporting forces increases according to the shaft speed. Additionally, the load capacity revealed to be more sensitive to variations on the oil viscosity and radial clearance than to the pad radius concerning the adopted uncertain interval. Consequently, the obtained results can provide suitable information for the design, manufacturing, and maintenance of tilting-pad journal bearings.
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We consider smooth multimodal maps which have finitely many non-flat critical points. We prove the existence of real bounds. From this we obtain a new proof for the non-existence of wandering intervals, derive extremely useful imp...
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We consider smooth multimodal maps which have finitely many non-flat critical points. We prove the existence of real bounds. From this we obtain a new proof for the non-existence of wandering intervals, derive extremely useful improved Koebe principles, show that high iterates have 'negative Schwarzian derivative' and give results on ergodic properties of the map. One of the main complications in the proofs is that we allow f to have inflection points.
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The motion of a vortex near two circular cylinders of arbitrary radii-a problem of geophysical significance-is studied. The fluid motion is governed by the two-dimensional Euler equations and the flow is irrotational exterior to t...
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The motion of a vortex near two circular cylinders of arbitrary radii-a problem of geophysical significance-is studied. The fluid motion is governed by the two-dimensional Euler equations and the flow is irrotational exterior to the vortex. Two models are considered. First, the trajectories of a line vortex are obtained using conformal mapping techniques to construct the vortex Hamiltonian which respects the zero normal flow boundary condition on both cylinders. The vortex paths reveal a critical trajectory (i.e. separatrix) that divides trajectories into those that orbit both cylinders and those that orbit just one cylinder. Second, the motion of a patch of constant vorticity is computed using a combination of conformal mapping and the numerical method of contour surgery. Although the patch can deform, the results show that when the islands have comparable radii the patch remains remarkably coherent. Moreover, it is demonstrated that the trajectory of the centroid of the patch is well modelled by a line vortex. For the limiting case when one of the cylinders has infinite curvature (i.e. it becomes a straight line or wall) it is shown that the vortex patch, which propagates under the influence of its image in the wall, may undergo severe deformation as it collides with the smaller cylinder, with portions of the vortex passing around different sides of the cylinder. [References: 17]
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The study of the dynamics of an holomorphic map near a fixed point is a central topic in complex dynamical systems. In this paper, we will consider the corresponding random setting: given a probability measure nu with compact supp...
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The study of the dynamics of an holomorphic map near a fixed point is a central topic in complex dynamical systems. In this paper, we will consider the corresponding random setting: given a probability measure nu with compact support on the space of germs of holomorphic maps fixing the origin, we study the compositions f(n) circle ... circle f(1), where each f(i) is chosen independently with probability nu. As in the deterministic case, the stability of the family of the random iterates is mostly determined by the linear part of the germs in the support of the measure. A particularly interesting case occurs when all Lyapunov exponents vanish, in which case stability implies simultaneous linearizability of all germs in supp(nu).
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We present results from numerical experiments testing the behavior of cohesionless gravitational aggregates experiencing a gradual increase of angular momentum. The test bodies used in these numerical simulations are gravitational...
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We present results from numerical experiments testing the behavior of cohesionless gravitational aggregates experiencing a gradual increase of angular momentum. The test bodies used in these numerical simulations are gravitational aggregates of different construction, distinguished by the size distribution of the particles constituting them, parameterized in terms of the angle of friction (φ). Shape change and mass loss are found to depend strongly on φ, with results ranging from oblate spheroids forming binary systems to near-fluid behavior characterized by mass shedding bursts and no binary formation. Bodies with the highest angle of friction, φ ~40°, evolve to shapes with average axis ratios of c/. a~. 0.70 and b/. a~. 0.90 (a. b. c), and are efficient at forming satellites. Bodies with lower angle of friction, φ~. 20°, evolve to shapes with average axis ratios of c/. a~. 0.61 and b/. a~. 0.83, and are less efficient at forming satellites. The most fluid-like bodies tested, with φ near zero, become very elongated, with average axis ratios c/. a~. 0.40 and b/. a~. 0.56, and do not form satellites in any simulation. In all but 2 fluid-like cases out of 360, no more than 5% of the total mass was ejected in a single event. Bodies with substantial cores were also tested under slow spin-up, and cases with cores larger than ~30% of the total mass were successful at forming binaries.The binary systems created in all simulations are analyzed and compared against observed binary near-Earth asteroids and small Main Belt asteroids. The shape and rotation period of the primary, orbital and rotational period of the secondary, and the orbital semi-major axis and eccentricity are found to closely match the observed population.
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We present Pseudo-Symbolic Dynamic Modeling (PSDM), a novel method of deriving the closed-form equations of motion of a serial kinematic chain, using base inertial parameters. PSDM is a numerical algorithm, yet allows for model si...
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We present Pseudo-Symbolic Dynamic Modeling (PSDM), a novel method of deriving the closed-form equations of motion of a serial kinematic chain, using base inertial parameters. PSDM is a numerical algorithm, yet allows for model simplification and pre-computation generally only possible using symbolic software. In PSDM, we characterize the form of the dynamic equations to build a set of functions guaranteed to form a linear basis for the inverse dynamics function of the manipulator. Then, a two-step numerical analysis is performed to reduce this set into a minimal dynamic model, in regressor form. PSDM offers a fast and procedural method of generating simplified dynamic models. Extensions to the algorithm allow for fast real-time code generation, forward dynamic modeling, and increased model efficiency through the elimination of minimally important model elements. The algorithm is benchmarked on common robot configurations and shown to be attractive for the dynamic modeling of up to 7-DOF manipulators, in terms of derivation time and realtime evaluation speed. Additionally, a MATLAB implementation of the algorithm has been developed and is made available for general use. (C) 2020 Elsevier Ltd. All rights reserved.
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We study a family of population game dynamics under which each revising agent randomly selects a set of strategies according to a given test-set rule; tests each strategy in this set a fixed number of times, with each play of each...
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We study a family of population game dynamics under which each revising agent randomly selects a set of strategies according to a given test-set rule; tests each strategy in this set a fixed number of times, with each play of each strategy being against a newly drawn opponent; and chooses the strategy whose total payoff was highest, breaking ties according to a given tie-breaking rule. These dynamics need not respect dominance and related properties except as the number of trials become large. Strict Nash equilibria are rest points but need not be stable. We provide a variety of sufficient conditions for stability and for instability, and illustrate their use through a range of applications from the literature. (C) 2019 Elsevier Inc. All rights reserved.
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In this paper, synchronization dynamics of two different dynamical systems is investigated through the theory of discontinuous dynamical systems. The necessary and sufficient conditions for the synchronization, de-synchronization ...
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In this paper, synchronization dynamics of two different dynamical systems is investigated through the theory of discontinuous dynamical systems. The necessary and sufficient conditions for the synchronization, de-synchronization and instantaneous synchronization (penetration or grazing) are presented. Using such a synchronization theory, the synchronization of a controlled pendulum with the Duffing oscillator is systematically discussed as a sampled problem, and the corresponding analytical conditions for the synchronization are presented. The synchronization parameter study is carried out for a better understanding of synchronization characteristics of the controlled pendulum and the Duffing oscillator. Finally, the partial and full synchronizations of the controlled pendulum with periodic and chaotic motions are presented to illustrate the analytical conditions. The synchronization of the Duffing oscillator and pendulum are investigated in order to show the usefulness and efficiency of the methodology in this paper. The synchronization invariant domain is obtained. The technique presented in this paper should have a wide spectrum of applications in engineering. For example, this technique can be applied to the maneuvering target tracking, and the others.
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We discuss the generation of dynamical scalar fields within pure Yang-Mills theories, with an eye on possible implications for the actual Higgs physics. Such scalars are routinely introduced, in particular, within the dual-superco...
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We discuss the generation of dynamical scalar fields within pure Yang-Mills theories, with an eye on possible implications for the actual Higgs physics. Such scalars are routinely introduced, in particular, within the dual-superconductor model of confinement and there is plenty of lattice data on condensation of magnetic degrees of freedom in the Yang-Mills vacuum. We emphasize that the dynamical scalar fields of this type turn to be “soft” and avoid the problems of ultraviolet divergences. Moreover, generically their properties are close to the stringy scalars, like the thermal scalar. No immediate proposals for the Higgs particles are made.
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The dynamics of the collective excitations of a latticeBose gas at zero temperature is systematically investigated using the time-dependent Gutzwiller mean-field approach. The excitation modes are determined within the framework o...
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The dynamics of the collective excitations of a latticeBose gas at zero temperature is systematically investigated using the time-dependent Gutzwiller mean-field approach. The excitation modes are determined within the framework of the linear-response theory as solutions of the generalized Bogoliubov–de Gennes equations valid in the superfluid and Mott-insulator phases at arbitrary values of parameters. The expression for the sound velocity derived in this approach coincides with the hydrodynamic relation. We calculate the transition amplitudes for the excitations in the Bragg scattering process and show that the higher excitation modes make significant contributions. We simulate the dynamics of the density perturbations and show that their propagation velocity in the limit of week perturbation is satisfactorily described by the predictions of the linear-response analysis.
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