Regimes Of Motion Research Articles

Rotating hematite cube chains.

Recently a two-dimensional chiral fluid was experimentally demonstrated. It was obtained from cubic-shaped hematite colloidal particles placed in a rotating magnetic field. Here we look at building blocks of that fluid by analyzing short hematite chain behavior in a rotating magnetic field. We find equilibrium structures of chains in static magnetic fields and observe chain dynamics in rotating magnetic fields. We find and experimentally verify that there are three planar motion regimes and one where the cube chain goes out of the plane of the rotating magnetic field. In this regime we observe interesting dynamics-the chain rotates slower than the rotating magnetic field. In order to catch up with the magnetic field, it rolls on an edge and through rotation in the third dimension catches up with the magnetic field. The same dynamics is also observable for a single cube when gravitational effects are explicitly taken into account.

INVESTIGATION OF TWO-SIDED SOFT IMPACTS

In various engineering devices used in robotics, transport and agricultural engineering two-sided impacts take place. In this paper two-sided soft impacts are investigated.
 Model of the investigated vibrating system with two-sided soft impacts is described in detail. Dynamics of the investigated system with two-sided soft impacts takes place according to the three typical regimes of motion: vibrating system is not connected with the supports, vibrating system is connected with the first support, vibrating system is connected with the second support.
 Results of numerical investigations are presented in the form of graphical relationships.
 Variation of displacement of the vibrating system, variation of velocity of the vibrating system, variation of displacement of the left support, variation of displacement of the right support, variation of the value of the force and variation of the quantity characterizing the regime of motion of the vibrating system as functions of time are investigated.
 Investigation of steady state regimes of motion for various stiffnesses of the supports is performed. Results for several typical values of stiffnesses of the supports are presented in the paper. The obtained graphical representations enable to understand the behavior of the investigated vibrating system with two-sided soft impacts in steady state regimes of motion for various stiffnesses of the supports.
 The obtained results of the performed investigation are applied in the process of design of pipe robots and other engineering devices.
 Keywords: two-sided impacts, soft impacts, harmonic excitation, nonlinear dynamics, left support, right support.

INVESTIGATION OF DYNAMICS OF A PIPE ROBOT WITH SELF-STOPPING MECHANISM

Pipe robots are used in agricultural engineering for transportation of various materials inside the pipe as well as for cleaning of internal surfaces of the pipes.
 In this paper a model of a pipe robot with self-stopping mechanism is proposed and described in detail. Numerical investigations are performed, and the obtained results are presented in the form of graphical relationships. Variations of displacements as well as variations of velocities of the exciting mass and of the case of the pipe robot as functions of time are investigated. Results for steady state regime of motion are presented.
 Displacement of the first degree of freedom, velocity of the first degree of freedom, displacement of the second degree of freedom, velocity of the second degree of freedom as functions of time in the steady state regime of motion are investigated. Also, difference of displacements as well as difference of velocities as functions of time in the steady state regime of motion are represented.
 Results for three typical values of the constant force are described in the paper: first the results when the constant force is assumed equal to zero are presented and then the results for the two typical nonzero values of the constant force are presented. From the obtained graphical representations, the influence of the value of the constant force to the dynamic behavior of the pipe robot can be seen.
 The obtained graphical representations enable to understand the behavior of the investigated pipe robot with self-stopping mechanism.
 Keywords: pipe robot, self-stopping mechanism, harmonic excitation, steady state motions, parameters of the system.

Shear rheology of a dilute suspension of thin rings

The rheology of suspensions of rings (tori) rotating in an unbounded low Reynolds number simple shear flow is calculated using numerical simulations at dilute particle number densities ( n ≪ 1 ). Suspensions of non-Brownian rings are studied by computing pair interactions that include hydrodynamic interactions modeled using slender body theory and particle collisions modeled using a short-range repulsive force. Particle contact and hydrodynamic interactions were found to have comparable influences on the steady-state Jeffery orbit distribution. The average tilt of the ring away from the flow-vorticity plane increased during pairwise interactions compared to the tilt associated with Jeffery rotation and the steady-state orbit distribution. Particle stresses associated with the increased tilt during the interaction were found to be comparable to the stresses induced directly by particle contact forces and the hydrodynamic velocity disturbances of other particles. The hydrodynamic diffusivity coefficients in the gradient and vorticity directions were also obtained and were found to be two orders of magnitude larger than the corresponding values in fiber suspensions at the same particle concentrations. Rotary Brownian dynamics simulations of isolated Brownian rings were used to understand the shear rate dependence of suspension rheology. The orbit distribution observed in the regime of weak Brownian motion, P e ≫ ϕ T − 3, was surprisingly similar to that obtained from pairwise interaction calculations of non-Brownian rings. Here, the Peclet number P e is the ratio of the shear rate and the rotary diffusivity of the particle and ϕ T is the effective inverse-aspect ratio of the particle (approximately equal to 2 π times the inverse of its non-dimensional Jeffery time period). Thus, the rheology results obtained from pairwise interactions should retain accuracy even for weakly Brownian rings ( n ≪ 1 and ϕ T − 3 ≪ P e ).

Nonlinear dynamics of a nearly taut cable subjected to parametric aerodynamic excitation due to a typical pulsatile wind flow

In this study, the dynamic response of a nearly taut nonlinear cable that is actuated by a pulsatile wind flow is investigated for the sake of obtaining the regime of motion and bifurcations of the system. The aerodynamic model is a general modelling of wind excitation including nonlinear cubic terms. Since realistic wind blows frequently and is not invariant, the velocity of the time-variant flow is considered to be a typical combination of a constant and a small harmonic perturbation. The equation of motion of the system has a simple form and is discretized by single-mode Galerkin method and by employing the method of multiple scales (MMS) the parametric resonance of the system is obtained. The results of bifurcations of the system assuming solely its first mode, exhibit a complicated behavior, whose occurrence in a simple dynamical system is interesting from the nonlinear dynamic point of view. Moreover, we show that as the frequency of the wind flow is decreased, the amplitude of the cable is also decreased. Also, as both constant and harmonic wind velocities are increased, the maximum amplitude of the system is not significantly influenced. Furthermore, the numerical-based bifurcation analyses show that for high values of constant wind velocity, small values of harmonic wind velocity, and excitation frequency, the system undergoes less chaos and actually unpredictable motions. The presented model can be evaluated more precisely to extend the above results to more realistic ones.

Numerical simulation of square shaped particle sedimentation

Direct numerical simulations of square particle sedimentation in a viscous incompressible fluid are presented to examine the effects of sharp edges for various particle-to-fluid density ratios and different initial inclination angles. The settling process exhibits four different motion regimes; non-oscillatory, non-uniform centered oscillatory, uniform off-centered oscillatory, and non-uniform off-centered (irregular) oscillatory. At moderate density ratios, we observe that the rotational motion of settling square particle varies with the initial inclination angle. We employ Dynamic Time Warping and Fast Fourier Transform to analyze translational and angular velocities. Oscillating systems are described using phase-space plots, and a chaotic phenomenon is observed at a higher density ratio.

A neglected history: The political figure of the Colombian migrant in Venezuela

AbstractThe aim of this article is to examine migration between Venezuela and Colombia by taking the long view and thus filling a gap in the literature. Building on Thomas Nail’s 2015 book, The Figure of the Migrant, the focus of the analysis is on regimes of social motion and the essentially political figure of the migrant. The article moves on to a more detailed empirical examination, analysing various topics such as the socio‐occupational insertion of migrants along with their demographic and economic impact, with some final thoughts about reverse migration. By offering an historical description of the process, the aim is to explore the multiple aspects of migration that manifest along this particular border.

Rotating quantum wave turbulence

Turbulence under strong influence of rotation is described as an ensemble of interacting inertial waves across a wide range of length scales. In macroscopic quantum condensates, the quasiclassical turbulent dynamics at large scales is altered at small scales, where the quantization of vorticity is essential. The nature of this transition remains an unanswered question. Here we expand the concept of wave-driven turbulence to rotating quantum fluids where the spectrum of waves extends to microscopic scales as Kelvin waves on quantized vortices. We excite inertial waves at the largest scale by periodic modulation of the angular velocity and observe dissipation-independent transfer of energy to smaller scales and the eventual onset of the elusive Kelvin wave cascade at the lowest temperatures. We further find that energy is pumped to the system through a boundary layer distinct from the classical Ekman layer and support our observations with numerical simulations. Our experiments demonstrate a regime of turbulent motion in quantum fluids where the role of vortex reconnections can be neglected, thus stripping the transition between the classical and the quantum regimes of turbulence down to its constituent components.

Dynamics of Elastic Systems with Particular Constrains by Means of the Small Parameter Approach

We study dynamics of elastic systems with external unilateral interaction (friction, recovering force), which is given as a function defined by inequalities relative to unknown variables. The analytical-numerical method for investigation oscillations of the mentioned systems was constructed. We consider transient regimes of the system motion. It was shown that the unilateral interaction promotes conditions for preventing development of resonance and it can be considered as a mean for active suppression of oscillations.

Diffusion mobility increases linearly on liquid binodals above triple point

Self-diffusion in fluids has been thoroughly studied numerically, but even for simple liquids just a few scaling relationships are known. Relations between diffusion, excitation spectra, and character of the interparticle interactions remain poorly understood. Here, we show that diffusion mobility of particles in simple fluids increases linearly on the liquid branch of the liquid–gas binodal, from the triple point almost up to the critical point. With molecular dynamics simulations, we considered bulk systems of particles interacting via a generalised Lennard–Jones potential, as well as ethane. Using a two-oscillator model for the analysis of excitations, we observed that the mobility (inverse diffusion) coefficient on the liquid–gas binodal increases linearly above the triple point until the dispersion of high-frequency spectra has a solid-like (oscillating) shape. In terms of a separate mode analysis (of longitudinal and transverse modes), this corresponds to crossed modes in the intermediate range of wavenumbers q, between the hydrodynamic regime (small q) and the regime of individual particle motion (large q). The results should be interesting for a broad community in physics and chemistry of fluids, since self-diffusion is among the most fundamental transport phenomena, important for prospective chemical technologies, micro-, nanofluidics, and biotechnologies.

Semi-Analytical Approach in BiER4BP for Exploring the Stable Positioning of the Elements of a Dyson Sphere

In this study, we present a new approach with semi-analytical and numerical findings for solving equations of motion of small orbiter m, which is moving under the combined gravitational attraction of three primaries, M1, M2, and M3, in case of the bi-elliptic restricted problem of four bodies (BiER4BP), where three such primaries, M1, M2, and M3, are moving on elliptic orbits with hierarchical configuration M3 << M2 << M1 within one plane as follows: third primary body M3 is moving on elliptical orbit around second M2, and second primary M2 is moving on elliptical orbit around first M1. Our aim for constructing the aforementioned quasi-planar motion of planetoid m is obtaining its coordinates supporting its orbit in a regime of close motion to the plane of orbiting the main bodies M1, M2, and M3. Meanwhile, the system of equations of motion was successfully numerically explored with respect to the existence and stable positioning of approximate solution for a Dyson sphere. As a result, the concept of the Dyson sphere for possible orbiting variety of solar energy absorbers was transformed to the elongated Dyson space net with respect to their trajectories for the successful process of absorbing the energy from the Sun; this can be recognized as symmetry reduction. We obtain the following: (1) the solution for coordinates {x, y} is described by the simplified system of two nonlinear ordinary differential equations of second order, depending on true anomaly f; (2) the expression for coordinate z is given by an equation of Riccati-type where small orbiter that quasi-oscillates close to the fixed plane {x,y,0}.

A switching Gaussian process latent force model for the identification of mechanical systems with a discontinuous nonlinearity

Abstract An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the sharp variations and multiple motion regimes introduced by these nonlinearities in the dynamic response, the partially known physics-based model and noisy measurements of the system’s response to a known input force are combined within a switching Gaussian process latent force model (GPLFM). In this grey-box framework, multiple Gaussian processes are used to model the unknown nonlinear force across different motion regimes and a resetting model enables the generation of discontinuities. The states of the system, nonlinear force, and regime transitions are inferred by using filtering and smoothing techniques for switching linear dynamical systems. The proposed switching GPLFM is applied to a simulated dry friction oscillator and an experimental setup consisting of a single-storey frame with a brass-to-steel contact. Excellent results are obtained in terms of the identified nonlinear and discontinuous friction force for varying: (i) normal load amplitudes in the contact; (ii) measurement noise levels, and (iii) number of samples in the datasets. Moreover, the identified states, friction force, and sequence of motion regimes are used for evaluating: (1) uncertain system parameters; (2) the friction force–velocity relationship, and (3) the static friction force. The correct identification of the discontinuous nonlinear force and the quantification of any remaining uncertainty in its prediction enable the implementation of an accurate forward model able to predict the system’s response to different input forces.

Friction, mobility, and thermophoresis of carbon nanoparticles on a graphene sheet

It is shown using the method of molecular dynamics that the motion of carbon nanoparticles (rectangular graphene flakes, spherical fullerenes of size $L<10$ nm) on the surface of a thermalized graphene sheet lying on a flat substrate can be described as the motion of particles in a viscous medium with a constant coefficient of friction, the value of which depends on the temperature and particle size. It has been shown that there are two types of effective friction: diffusion and ballistic. In ballistic regime of motion (at velocities $v>100$ m/s), deceleration occurs due to the interaction of moving nanoparticles with thermal out-of-plane bending vibrations of a graphene sheet. Because of this, with the increasing temperature, the coefficient of friction monotonically increases. In the diffusion regime of motion (at $v<10$ m/s), friction arises due to the need for the particle to overcome local energy barriers, therefore it decreases with increasing emperature. The difference between ballistic and diffusion friction is most pronounced at low temperatures, since the mobility of nanoparticles in the ballistic regime of motion decreases with increasing temperature, while in the diffusion regime it monotonously increases. It is shown that the presence of a normal force pressing the nanoparticle to the substrate leads to an increases in its friction with the substrate.

Vibration suppression of a linear oscillator by a chain of nonlinear vibration absorbers with geometrically nonlinear damping

Nonlinear energy sink (NES) is a lightweight vibration absorber that is coupled to linear primary structure for passive vibration mitigation. In this work, we aim to investigate the effects of geometrically nonlinear damping on the capacity of multiple-degree-of-freedom (MDOF) NES to mitigate forced responses of the impulsively and harmonically loaded linear oscillator (LO). For the system under applied shock excitation, extensive simulation results show that the internal use of nonlinear damping enables the MDOF NES to rapidly and effectively absorb, transfer and dissipate the shock-induced energy for a broad range of initially imparted energies, particularly for the high or very high energy levels. The effectiveness of the optimized MDOF NES is further improved since the large-amplitude oscillations of the LO are reduced to a sufficiently low level during initial regime of motion. When the LO is subjected to harmonic excitations, the analytical study is performed to obtain the slow invariant manifold (SIM) by means of complexification-averaging (CX-A) method. The complex geometry of SIM reveals the energy transfer paths when the system reaches steady state. The global system behavior (strongly modulated response or periodic oscillation regimes) is analytically predicted by the singular points and ordinary equilibrium points, and a close match is achieved between theoretical analysis and numerical results. It is found that the proposed MDOF NES with nonlinear damping can eliminate the upper closed high-amplitude isolated branch, and the frequency bandwidth of multiple steady-state responses also decreases, the robustness and capacity of vibration attenuation by the proposed NES is dramatically enhanced. The findings in this work facilitate the design and broad applications in diverse engineering fields for the protection and safe operation of mechanical structures.

Newtonian approximation in (1 + 1) dimensions

We study the possible existence of a Newtonian regime of gravity in 1 + 1 dimensions, considering metrics in both the Kerr-Schild and conformal forms In the former case, the metric gives the exact solution of the Poisson equation in flat space, but the weak-field limit of the solutions and the non-relativistic regime of geodesic motion are not trivial. We show that using harmonic coordinates, the metric is conformally flat and a weak-field expansion is straightforward. An analysis of the non-relativistic regime of geodesic motion remains non-trivial and the weak-field potential only satisfies the flat space Poisson equation approximately.

Nonlinear Analysis of Stability and Safety of Optimal Velocity Model Vehicle Groups on Ring Roads

In this work, we study a group of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> homogeneous vehicles travelling on a ring road by describing the collective vehicle dynamics via the so-called Optimal Velocity Model (OVM). We analyze the stability of the equilibrium motion regime in which all vehicles drive at the same speed and keep the same headway. First, stability is studied through linearization, thereby highlighting the roles of the model parameters. Next, we tackle the full nonlinear model and we determine ellipsoidal estimates of the equilibrium’s region of attraction by defining and solving suitable Linear Matrix Inequalities (LMIs). Finally, safety aspects are discussed, incorporated in our LMI formulation as lower bounds of the inter-vehicle distances, and illustrated via simulations.

Investigation of Soft Impacts in Elements of Pipe Robots

Vibrators with deformable impact support under harmonic excitation are especially useful in the case when their stationary regimes of motion are stable. This is useful in practice by applying those vibrators to single direction manipulators and various robots of space type.&#x0D; For practical application it is necessary to reveal dynamical qualities of the system from where it would be possible to determine optimal regimes. For this purpose investigations of dynamics of the system by numerical methods were performed.&#x0D; Investigation of dynamics of impact interactions in elements of robots is an important engineering problem. Dynamics of soft impacts in elements of manipulators and robots is investigated. The model of the investigated system is described. Numerical investigations for various parameters of the system are performed. Free and forced vibrations are investigated.&#x0D; From the presented results it can be noted that for the smaller values of the coefficient of stiffness of the support period of steady state motion coincides with the period of the exciting force, while for the higher values of the coefficient of stiffness of the support period of steady state motion is equal to two periods of the exciting force. Thus it is concluded that with the increase of the coefficient of stiffness of the support behavior of the investigated vibro impact system with soft impacts experiences essential changes.&#x0D; Main characteristics of steady state motion as functions of frequency of excitation are investigated. From the presented results the minimum and maximum inter impact intervals as functions of frequency of excitation, minimum and maximum velocities before impact as functions of frequency of excitation, minimum and maximum minimum displacements in inter impact intervals as functions of frequency of excitation are seen. Three resonant zones of expected single valued motions are observed in the presented results. They correspond to optimal regions of operation of the vibro impact system with soft impacts.&#x0D; Results of the performed analysis of dynamic interactions with soft impacts in the elements of manipulators and robots are used in the process of design of pipe robots of advanced type.

Exciton States and Optical Absorption in CdSe and PbS Nanoplatelets.

The exciton states and their influence on the optical absorption spectrum of CdSe and PbS nanoplatelets (NPLs) are considered theoretically in this paper. The problem is discussed in cases of strong, intermediate, and weak size quantization regimes of charge carrier motion in NPLs. For each size quantization regime, the corresponding potential that adequately describes the electron–hole interaction in this mode of space quantization of charge carriers is chosen. The single-particle energy spectra and corresponding wave functions for strong intermediate and weak size quantization regimes have been revealed. The dependence of material parameters on the number of monolayers in the sample has been considered. The related selection rules and the dependence of the absorption coefficient on the frequency and polarization direction of the incident light wave were obtained. The interband transition threshold energy dependencies were obtained for each size quantization regime. The effect of dielectric coefficient mismatch and different models of electron–hole interaction potentials have been studied in CdSe and PbS NPLs. It is also shown that with an increase in the linear dimensions of the structure, the threshold frequency of absorption decreases. The binding energies and absorption coefficient results for NPL with different thicknesses agree with the experimental data. The values of the absorption exciton peaks measured experimentally are close to our calculated values for CdSe and PbS samples.

Highly Anisotropic Tip-Induced Domain Growth in Polydomain Triglycine Sulfate

Ferroelectrics are widely used as modern functional materials for nonlinear optics, optoelectronics, nonvolatile data storage, and nanoelectronics. Most of these applications require creation of precise micron-scale domain patterns. We have studied the current limited wall motion regime driven by anisotropic bulk screening processes during local switching in polydomain triglycine sulfate single crystals. The field application using a conductive tip of a scanning probe microscope (SPM) in a dry atmosphere resulted in formation of a partially switched area, strongly elongated in the c crystallographic direction. At the same time, switching at high humidity led to a circular shape of the area. The calculation of the spatial distribution of the external field demonstrated the possibility of domain wall shift at distances up to hundreds of microns from the SPM tip. However, after external field switch-off the depolarization field in nonscreened areas led to reverse domain wall motion. Thus, the domain wall stabilization is possible only in the regions with sufficient screening of the depolarization field. We have shown that the growth of the area size with time obeys the same current-limited wall motion expressions that were derived previously for domain growth during local switching by a highly resistive electrode. The change in the area shape with humidity was attributed to the change in the governing screening mechanism from anisotropic bulk conductivity to isotropic surface conductivity through an adsorbed water layer. The obtained results demonstrate the essential role of the screening processes during periodical poling and pave the way for further improvement of the domain engineering methods.

Light-powered self-spinning of a button spinner

Self-oscillation can maintain own continuous motion by means of energy conversion from constant external stimuli to mechanical work, making them highly suitable for being applied in soft robotics, motors, military industry and so on. With the inspiration provided by the spinning of button spinner toy, we creatively develop a self-spinning button spinner, containing a button rotor and a pair of liquid crystal elastomer (LCE) fibers under steady illumination. Based on well-established twisting thread model and dynamic LCE model, a nonlinear dynamic model of self-spinning button spinner under steady illumination is proposed. Numerical calculation reveals that two motion regimes are involved for the button spinner on exposure to steady illumination, which are distinguished as the static regime and the self-spinning regime. The self-spinning of button spinner originates from the contraction of twisted segments of LCE fibers in illumination at winding state, and its continuous periodic motion is sustained through the interrelation between light energy and damping dissipation. In addition, the critical conditions necessary for triggering the self-spinning, as well as the vital system parameters affecting its frequency and amplitude, are investigated in detail. Different from the existing abundant self-oscillating systems, this self-spinning button spinner has superiority in simple structure, customizable size, and rapid speed, and it is anticipated to provide more diverse design ideas for soft robotics, energy harvesters, micromachines and so on.