Arbitrary Initial Velocity Research Articles

Incompressible limit for compressible viscoelastic flows with large velocity

Abstract We are concerned with the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the three-dimensional compressible viscoelastic equations. The incompressibility is achieved by the large value of the volume viscosity, which is different from the low Mach number limit. To obtain the uniform estimates, we establish the estimates for the potential part and the divergence-free part of the velocity. As the volume viscosity goes to infinity, the dispersion associated with the pressure waves tends to disappear, but the large volume viscosity provides a strong dissipation on the potential part of the velocity forcing the flow to be almost incompressible.

Spherically symmetric stationary flows of a rarefied two-phase fluid

The spherically symmetric stationary flows of isothermal rarefied two-phase fluid are studied. The results of the research give a qualitative description such flows for arbitrary positive initial data. Namely, for arbitrary positive initial velocities and densities of the first and the second phase, which are set at the initial sphere of arbitrary radius, the obtained phase portrait gives a qualitative description of the distribution of characteristics at the spheres of other radii. A classification of all possible types of spherically symmetric stationary flows of isothermal two-phase fluid in a case of the spread of a substance has been carried out. In the work it is also described a bifurcation of a dynamical system. As a result of this bifurcation, some attracting set appears at the curve of singular points. The emergence of this set greatly changes a quantity of the types of two-phase flows. Another result of the study is a description of all types of continuous transonic spherically symmetric stationary flows at the investigating model of two-phase fluid. The study showed that if the ratio of the flows of the first and second phases through an initial sphere is bigger than 8, then there is a non-zero probability of a realization in two-phase fluid dynamics a continuous transition from supersonic mode to subsonic mode. There have been carried out different numerical experiments, which are illustrated the obtained results.

On Fast Jerk-Continuous Motion Functions with Higher-Order Kinematic Restrictions for Online Trajectory Generation

In robotics and automated manufacturing, motion functions for parts of machines need to be designed. Many proposals for the shape of such functions can be found in the literature. Very often, time efficiency is a major criterion for evaluating the suitability for a given task. If there are higher precision requirements, the reduction in vibration also plays a major role. In this case, motion functions should have a continuous jerk function but still be as fast as possible within the limits of kinematic restrictions. The currently available motion designs all include assumptions that facilitate the computation but are unnecessary and lead to slower functions. In this contribution, we drop these assumptions and provide an algorithm for computing a jerk-continuous fifteen segment profile with arbitrary initial and final velocities where given kinematic restrictions are met. We proceed by going systematically through the design space using the concept of a varying intermediate velocity and identify critical velocities and jerks where one has to switch models. The systematic approach guarantees that all possible situations are covered. We implemented and validated the model using a huge number of random configurations in Matlab, and we show that the algorithm is fast enough for online trajectory generation. Examples illustrate the improvement in time efficiency compared to existing approaches for a wide range of configurations where the maximum velocity is not held over a period of time. We conclude that faster motion functions are possible at the price of an increase in complexity, yet which is still manageable.

Negative mass effects of a spin soliton in Bose-Einstein condensates

We investigate the energy-velocity dispersion relation of spin solitons with arbitrary initial velocities. Based on the dispersion relation, we further characterize the inertial mass of a spin soliton and find two critical velocities to distinguish between the positive mass and negative mass. One critical velocity separates the initial negative and positive masses, and the other denotes the velocity for negative-positive mass transition during an acceleration process. With the aid of the two critical velocities, we further propose two possible ways to observe the pure negative mass effect of a spin soliton. Moreover, the relations between the soliton's width and its velocity are discussed according to the variational results. We report that the soliton width can become narrower with larger moving speed (when a spin soliton possesses positive mass), in sharp contrast to the dark solitons reported before. These results would motivate experiments to observe negative mass effects of solitons in Bose-Einstein condensates.

On the Schwarzschild solution in TEGR

Conserved currents, superpotentials and charges for the Schwarzschild black hole in the Teleparallel Equivalent of General Relativity (TEGR) are constructed. We work in the covariant formalism and use the Noether machinery to construct conserved quantities that are covariant/invariant with respect to both coordinate and local Lorentz transformations. The constructed quantities depend on the vector field ξ and we consider two different possibilities, when ξ is chosen as either a timelike Killing vector or a four-velocity of an observer. We analyze and discuss the physical meaning of each choice in different frames: static and freely falling Lemaitre frame. Moreover, a new generalized free-falling frame with an arbitrary initial velocity at infinity is introduced. We derive the inertial spin connection for various tetrads in different frames and find that the “switching-off” gravity method leads to ambiguities.

Formation control for unmanned aerial vehicle swarm with disturbances: A mission‐driven control scheme

SummaryDifferent formation controllers are to deal with different missions for unmanned aerial vehicle (UAV) swarm. The mission‐driven control scheme of the UAV swarm is necessary and worth exploring, leading to the main work of this article. Aiming at different requirements of UAV swarm, we proposed a mission‐driven control scheme, including a consensus‐based near‐optimal formation controller and a finite‐time precise formation controller. This control scheme can enable the swarm to reach its target position while maintaining consensus formation on the way. When the UAV swarm flies to the mission area, a consensus‐based near‐optimal formation controller based on adaptive neural networks is investigated to regulate the UAV states online. The controller drives the swarm from an arbitrary initial position and velocity to the desired target in an optimal manner while maintaining an expected formation with finite‐time consensus at the same time. When the UAV swarm approaches the mission area, a consensus‐based precise formation controller based on a fixed‐time disturbance observer (FDO) is designed to achieve an accurate and consensus formation within a limited time. The mission‐driven control scheme can better adapt to tasks and promote control optimization, formation precision, and system robustness. Finally, the efficiency of the proposed methodology is illustrated by numerical simulation.

On conserved quantities for the Schwarzschild black hole in teleparallel gravity

We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field xi and we consider two different options where xi is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained generalised freely falling frame with an arbitrary initial velocity. We also demonstrate how to determine an inertial spin connection for various tetrads used in our calculations, and find a certain ambiguity in the “switching-off” gravity method where different tetrads can share the same inertial spin connection.

Geodesic Structure of the Accelerated Stephani Universe

For the spherically symmetric Stephani cosmological model with an accelerated expansion, we investigate the main scenarios of the test particle and photon motion. We show that a comoving observer sees an appropriate picture. In the case of purely radial motion, the radial velocity decreases slightly with time due to the universe expansion. Both particles and photons spiral out of the center when the radial coordinate is constant. In the case of the motion with arbitrary initial velocity, the observable radial distance to the test particle can increase under negative observable radial velocity.

Effect of the electron motion on the Compton scattering of a twisted photon

We present theoretical and numerical results on the Compton scattering of a twisted Bessel photon by a plane-wave electron with an arbitrary initial velocity. Scattering of a photon prepared in a superposition of Bessel states is also explored. Specifically, we investigate how the electron motion affects the dependence of the angular distribution and polarization of the scattered photons on the twisted photon opening angle, projection of angular momentum, and on the superposition of angular-momentum projection. The motion of the electron is found to strongly influence the dependence of these quantities on the parameters of the twisted photon. Moreover, if the speed of a properly directed electron exceeds a critical value, various distributions, such as the degree of circular polarization of the scattered photons, undergo a nearly global reversal of sign that is absent from the scattering of a plane-wave photon under identical conditions. This behavior is found to correspond to the inversion of the twisted photon momentum cone in the rest frame of the electron.

Analytical investigation of rotationally symmetrical oscillating flows of viscoelastic fluids

This paper deals with the analytical investigation of rotationally symmetrical oscillating Couette flows of a viscoelastic Oldroyd-B fluid, taking the inertial force into account. The fluid is enclosed between two coaxial cylinders. One or both cylinders oscillate rotatingly. The periodic responses of the velocity distribution and the stress field are analytically obtained and graphically presented. The decaying transient motion of the fluid in respect of an arbitrary initial velocity field and the stationary cylinders is also acquired. The corresponding natural oscillations of the fluid system are also analyzed. The inertial, viscous and elastic effects on the flow behavior are extensively discussed with reference to the dimensionless parameters – Reynolds number, Deborah number, the ratio of the relaxation time to the retardation time and the ratio of the two cylinder radii. It is shown that with increasing inertial effect (increasing Reynolds number), and increasing fluid elasticity (increasing Deborah number) the fluid responds to the cylinder oscillation with an increasing phase shift, which increases further with the distance to the exciting cylinder, up to a phase shift of several periods. The resonance response of the flow system can be clearly identified in terms of various parameters and the corresponding eigenmodes are demonstrated.

Hierarchical Fuzzy Logic-Based Variable Structure Control for Vehicles Platooning

This paper proposes a variable structure control approach for vehicles platooning based on a hierarchical fuzzy logic. The leader-follower vehicle dynamics with model uncertainties is discussed from the viewpoint of a consensus problem. A practical two-layer fuzzy control for the platooning is designed by employing two common spacing policies to ensure system robustness in different scenarios. The two policies, i.e., constant distance and constant time headway, utilize the predecessor-successor information flow from the immediate predecessor and follower other than controlled vehicles. The first layer of the fuzzy system combines spacing control with velocity-acceleration control to achieve a rapid tracking for the desired control commands, and the second layer combines the sliding mode control to adaptively compensate for reducing the state errors caused by parameter uncertainties and disturbances. Shift between different controller parameters is based on performance boundaries to guarantee the stability of individual vehicle and platooning for arbitrary initial spacing and velocity errors. These performance boundaries can be determined by using a Lyapunov method with exponential stability. Simulation of a ten-vehicle large platooning with two spacing policies shows that the control performance of the newly proposed method is effective and promising.

Compressible Navier–Stokes system: Large solutions and incompressible limit

Here we prove the existence of global in time regular solutions to the two-dimensional compressible Navier–Stokes equations supplemented with arbitrary large initial velocity v0 and almost constant density ϱ0, for large volume (bulk) viscosity. The result is generalized to the higher dimensional case under the additional assumption that the strong solution of the classical incompressible Navier–Stokes equations supplemented with the divergence-free projection of v0, is global. The systems are examined in Rd with d≥2, in the critical B˙2,1s Besov spaces framework.

FIR filter-based online jerk-constrained trajectory generation

In the context of human–robot manipulation interaction for service or industrial robotics, the robot controller must be able to quickly react to unpredictable events in dynamic environments. In this paper, a FIR filter-based trajectory generation methodology is presented, combining the simplicity of the analytic second-order trajectory generation, i.e. acceleration-limited trajectory, with the flexibility and computational efficiency of FIR filtering, to generate on the fly smooth jerk-constrained trajectories. The proposed methodology can generate synchronized (fixed-time) and time-optimal jerk-limited trajectories from arbitrary initial velocity and acceleration conditions within 20 microsecond. Other jerk-constrained trajectories such as jerk-time fixed trajectories, which are particularly suitable for vibration reduction, can be easily generated. Experimental validations carried out on a seven axis Kuka LBR iiwa are presented.

Formation tracking control for multiple rigid bodies on matrix Lie groups: A system decomposition approach

SummaryThis paper addresses the finite‐time formation tracking control problem for multiple rigid bodies whose dynamics are defined on the matrix Lie groups, including the special Euclidean group SE(2),SE(3) as specific cases. The reference trajectory in a form of rotational and translational motions is generated offline in advance as the virtual leader for tracking. Moreover, the formation time is specified according to the task, and the desired formation shape is given a priori with respect to the virtual leader. By virtue of the system decomposition approach, intrinsic formation tracking laws are derived for arbitrary initial velocities for the rigid bodies. The tracking controllers are intrinsic meaning that the dynamics and controllers are developed in the body‐fixed frame without a global reference frame. Moreover, based on the geometric convex combination on SE(3), the result is extended to the distributed case where only the neighboring agents' state are used. Two numerical simulations on SE(2) and SE(3) are given respectively to illustrate the validity and robustness of the proposed controllers. Copyright © 2017 John Wiley & Sons, Ltd.

Numerical study on the effect of initial flow velocity on liquid film thickness of accelerated slug flow in a micro tube

Numerical simulation of air–water slug flows accelerated from steady states with different initial velocities in a micro tube is conducted. It is shown that the liquid film formed between the gas bubble and the wall in an accelerated flow is significantly thinner than that in a steady flow at the same instantaneous capillary number. Specifically, the liquid film thickness is kept almost unchanged just after the onset of acceleration, and then gradually increases and eventually converges to that of an accelerated flow from zero initial velocity. Due to the flow acceleration, the Stokes layer is generated from the wall, and the instant velocity profile can be given by superposition of the Stokes layer and the initial parabolic velocity profile of a steady flow. It is found that the velocity profile inside a liquid slug away from the bubble can be well predicted by the analytical solution of a single-phase flow with acceleration. The change of the velocity profile in an accelerated flow changes the balance between the inertia, surface tension and viscous forces around the meniscus region, and thus the resultant liquid film thickness. By introducing the displacement thickness, the existing correlation for liquid film thickness in a steady flow (Han and Shikazono, 2009) is extended so that it can be applied to a flow with acceleration from an arbitrary initial velocity. It is demonstrated that the proposed correlation can predict liquid film thickness at Re<4600 within the range of ±10% accuracy.

Representation of geodesics near the Schwarzschild radius

In our recent research work we considered gravitation in flat Minkowski space, and the result fits with all well-known gravitational experiments. In this paper we continue the research considering the shape of geodesics close to a gravitating center, assuming that the test body has a negligible mass. This is made for arbitrary initial velocity, including the trajectories of light rays. For each velocity there exists a characteristic sphere whose radius takes values in the segment [GM/c2; 3.7921 GM/c2]. For light rays, this radius is GM/c2. There are two possibilities: the test body has never been outside the Schwarzschild sphere or the test body has intersected the Schwarzschild sphere. Some geodesics have hyperbolic or parabolic shapes, and they do not pass inside the Schwarzschild sphere. Trajectories of elliptic type also do not intersect this sphere.

Numerical study of water mist centerline velocity in microgravity

With water mist regarded as a promising fire-extinguishing agent in spacecraft, it is necessary to investigate characteristics of water mist in microgravity. In this paper, FDS 6.0 is used to measure the centerline velocity of water mist with various initial velocities and the spray distance. The droplets will approach their terminal velocity after leaving the nozzle in normal-gravity, which agrees with the theoretical calculation. The velocity of water mist declines in microgravity. The polynomials of the velocity change are given in microgravity, which makes it possible to obtain the velocity with the spray distance increase when arbitrary initial velocity is given.

Higher order impact analysis of sandwich panels with functionally graded flexible cores

This study deals with dynamic model of composite sandwich panels with functionally graded flexible cores under low velocity impacts of multiple large or small masses using a new improved higher order sandwich panel theory (IHSAPT). In-plane stresses were considered for the functionally graded core and face sheets. The formulation was based on the first order shear deformation theory for the composite face sheets and polynomial description of the displacement fields in the core that was based on the second Frostig's model. Fully dynamic effects of the functionally graded core and face-sheets were considered in this study. Impacts were assumed to occur simultaneously and normally over the top and/or bottom of the face-sheets with arbitrary different masses and initial velocities. The contact forces between the panel and impactors were treated as internal forces of the system. Nonlinear contact stiffness was linearized with a newly presented improved analytical method in this paper. The results were validated by comparing the analytical, numerical and experimental results published in the latest literature.

Beam Response to Longitudinal Impact by a Pole

The linear response of a flexible longitudinal pole hitting a column or beam is investigated. Based on Timoshenko beam theory, an efficient analytical solution method using mode superposition for the coupled beam-pole system is presented. Any physical set of boundary conditions can be accommodated, such as a free pole impacting a column with arbitrary boundary conditions or a free-free beam hitting a pole that is either pinned or free at the opposite end. For the case of the free-free beam, it can have arbitrary initial translational and rotational velocities. Impact can occur anywhere within the beam span, although the contact is frictionless. It is shown that, when the beam response governs, the initial impact is likely governed by shear, and therefore, Euler-Bernoulli beam theory is not a good modeling choice in general. Results based on a wood log hitting concrete, steel, and wood columns reveal the behavior governing the impact force time history. A simple design formula for the initial maximum impact force is shown to be quite accurate. The impact duration is governed by either the longitudinal wave speed in the pole or the shear wave speed in the column. In addition, the energy transfer between translational and rotational kinetic energies and strain energies is used to analyze the impact vibrational motion; this analysis reveals both the initial dependence on shear deformation and the transfer of the associated energy to bending energy. The significance of including rotary inertia is also demonstrated.

Temporal evolution of bubble tip velocity in classical Rayleigh-Taylor instability at arbitrary Atwood numbers

In this research, the temporal evolution of the bubble tip velocity in Rayleigh-Taylor instability (RTI) at arbitrary Atwood numbers and different initial perturbation velocities with a discontinuous profile in irrotational, incompressible, and inviscid fluids (i.e., classical RTI) is investigated. Potential models from Layzer [Astrophys. J. 122, 1 (1955)] and perturbation velocity potentials from Goncharov [Phys. Rev. Lett. 88, 134502 (2002)] are introduced. It is found that the temporal evolution of bubble tip velocity [u(t)] depends essentially on the initial perturbation velocity [u(0)]. First, when the u(0)&amp;lt;C(1)uasp, the bubble tip velocity increases smoothly up to the asymptotic velocity (uasp) or terminal velocity. Second, when C(1)uasp≤u(0)&amp;lt;C(2)uasp, the bubble tip velocity increases quickly, reaching a maximum velocity and then drops slowly to the uasp. Third, when C(2)uasp≤u(0)&amp;lt;C(3)uasp, the bubble tip velocity decays rapidly to a minimum velocity and then increases gradually toward the uasp. Finally, when u(0)≥C(3)uasp, the bubble tip velocity decays monotonically to the uasp. Here, the critical coefficients C(1),C(2), and C(3), which depend sensitively on the Atwood number (A) and the initial perturbation amplitude of the bubble tip [h(0)], are determined by a numerical approach. The model proposed here agrees with hydrodynamic simulations. Thus, it should be included in applications where the bubble tip velocity plays an important role, such as the design of the ignition target of inertial confinement fusion where the Richtmyer-Meshkov instability (RMI) can create the seed of RTI with u(0)∼uasp, and stellar formation and evolution in astrophysics where the deflagration wave front propagating outwardly from the star is subject to the combined RMI and RTI.