Search Results (30)

The mechanisms by which rotation influences zonal flows (ZFs) in plasma are incompletely understood, presenting a significant challenge in the study of plasma dynamics. This research addresses this gap by investigating the role of non-inertial effects—specifically centrifugal and Coriolis forces—on Geodesic Acoustic Modes (GAMs) and ZFs in rotating tokamak plasmas. While previous studies have linked centrifugal convection to plasma toroidal rotation, they often overlook the Coriolis effects or inconsistently incorporate non-inertial terms into magneto-hydrodynamic (MHD) equations. In this work, we derive self-consistent drift-ordered two-fluid equations from the collisional Vlasov equation in a non-inertial frame, and we modify the Hermes cold ion code to simulate the impact of rotation on GAMs and ZFs. Our simulations reveal that toroidal rotation enhances ZF amplitude and GAM frequency, with Coriolis convection playing a critical role in GAM propagation and the global structure of ZFs. Analysis of simulation outcomes indicates that centrifugal drift drives parallel velocity growth, while Coriolis drift facilitates radial propagation of GAMs. This work may provide valuable insights into momentum transport and flow shear dynamics in tokamaks, with implications for turbulence suppression and confinement optimization. Full article

This work systematically addresses the dual challenges of non-inertial dynamic coupling and kinematic constraint redundancy encountered in dynamic modeling of serial–parallel–serial hybrid robotic mechanisms, and proposes an improved Newton–Euler modeling method with constraint compensation. Taking the Skiing Simulation Platform with 6-DOF as the research mechanism, the inverse kinematic model of the closed-chain mechanism is established through $G_F$ set theory, with explicit analytical expressions derived for the motion parameters of limb mass centers. Introducing a principal inertial coordinate system into the dynamics equations, a recursive algorithm incorporating force/moment coupling terms is developed. Numerical simulations reveal a 9.25% periodic deviation in joint moments using conventional methods. Through analysis of the mechanism’s intrinsic properties, it is identified that the lack of angular momentum conservation constraints on the end-effector in non-inertial frames leads to system controllability degradation. Accordingly, a constraint compensation strategy is proposed: establishing linearly independent differential algebraic equations supplemented with momentum/angular momentum balance equations for the end platform. Co-Simulation results demonstrate that the optimized model reduces the maximum relative error of actuator joint moments to 0.98%, and maintains numerical stability across the entire configuration space. The constraint compensation framework provides a universal solution for dynamics modeling of complex closed-chain mechanisms, validated through applications in flight simulators and automotive driving simulators. Full article

This work investigates the dynamics of a charged scalar boson in the Melvin universe by solving the Klein–Gordon equation with minimal coupling in both inertial and non-inertial frames. Non-inertial effects are introduced through a rotating reference frame, resulting in a modified spacetime geometry and the appearance of a critical radius that limits the radial domain of the field. Analytical solutions are obtained under appropriate approximations, and the corresponding energy spectra are derived. The results indicate that both the magnetic field and non-inertial effects modify the energy levels, with additional contributions depending on the coupling between the rotation parameter and the quantum numbers. A numerical analysis is also presented, illustrating the behavior of the solutions for two characteristic magnetic field scales: one that may be considered extreme, of the order of the ones proposed to be produced in heavy-ion collisions, and another near the Planck scale. Full article

This paper offers new insights into gravitational interactions within a general non-inertial reference frame. By utilizing symbolic tensor calculus, the study establishes a unified framework that connects time derivatives in non-inertial frames to those in inertial frames. The research introduces new first integrals of motion for a system of many particles in arbitrary non-inertial and barycentric rotating reference frames. These first integrals provide a kinematic and geometric visualization of motion in non-inertial frames. Additionally, a generalized potential energy function is presented for broader applicability. For the gravitational two-body problem, the paper delivers a closed-form, coordinate-free solution for the motion of each body relative to the original frame. Consequently, sufficient conditions for stability against collisions are established within the context of the two-body problem in a non-inertial reference frame. Furthermore, the paper examines the relative orbital motion of spacecraft, presenting a closed-form and coordinate-free solution in the local vertical local horizontal (LVLH) non-inertial frame, which is centered on the center of mass of the main spacecraft. Full article

This work describes a mathematical model for handwriting devices without a specific reference surface (SRS). The research was carried out on two hypotheses: the first considers possible circular segments that could be made during execution for the reconstruction of the trace, and the second is the combination of lines and circles. The proposed system has no flat reference surface, since the sensor is inside the pencil that describes the trace, not on the surface as in tablets or cell phones. An inertial sensor was used for the measurements, in this case, a commercial Micro-Electro Mechanical sensor of linear acceleration. The tracking device is an IMU sensor and a processing card that allows inertial measurements of the pen during on-the-fly tracing. It is essential to highlight that the system has a non-inertial reference frame. Comparing the two proposed models shows that it is possible to construct shapes from curved lines and that the patterns obtained are similar to what is recognized; this method provides an alternative to quaternion calculus for poorly specified orientation problems. Full article

The Oscillating Water Column (OWC) is the most promising self-rectifying device for power generation from ocean waves; over the past decade, its importance has been rekindled. The bidirectional airflow inside the OWC drives the Wells turbine connected to a generator to harness energy. This study evaluated the aerodynamic performance of two hybrid airfoil (NACA0015 and NACA0025) blade designs with variable chord distribution along the span of a Wells turbine. The present work examines the aerodynamic impact of the variable chord turbine and compares it with one with a constant chord. Ideally, Wells rotor blades with variable chords perform better since they have an even axial velocity distribution on their leading edge. The variable chord rotor blade configurations differ from hub to tip with taper ratios (Chord at Tip/Chord at Hub) of 1.58 and 0.63. The computation is performed in ANSYS™ CFX 2023 R2 by solving three-dimensional, steady-state, incompressible Reynolds Averaged Navier–Stokes (RANS) equations coupled with a k-ω Shear Stress Transport (SST) turbulence model in a non-inertial reference frame rotating with the turbine. The accuracy of the numerical results was achieved by performing a grid independence study. A refined mesh showed good agreement with the available experimental and numerical data in terms of efficiency, torque, and pressure drop at different flow coefficients. A variable chord Wells turbine with a taper ratio of 1.58 had a peak efficiency of 59.6%, as opposed to the one with a taper ratio of 0.63, which had a peak efficiency of 58.2%; the constant chord Wells turbine only had a peak efficiency of 58.5%. Furthermore, the variable chord rotor with the higher taper ratio had a larger operating range than others. There are significant improvements in the aerodynamic performance of the modified Wells turbine, compared to the conventional Wells turbine, which makes it suitable for wave energy harvesting. The flow field investigation around the turbine blades was conducted and analyzed. Full article

The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia using a unified Hamiltonian. For that purpose, we first re-derive, using the purely algebraic method, the energy spectrum of charged particles moving in a plane perpendicular to a constant and uniform magnetic field either (i) under the influence of a nonlinear gravitational potential or (ii) under the influence of a constant rotation. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained. The electrons mutual Coulomb interaction that gives rise to the familiar fractional quantum Hall effect is also discussed within such a combination. Full article

Multi-scale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems such as the solar and stellar winds. In this context, the Expanding Box Model (EBM) provides a valuable framework to mimic plasma expansion in a non-inertial reference frame, co-moving with the expansion but in a box with a fixed volume, which is especially useful for numerical simulations. Here, fundamentally based on the Vlasov equation for magnetized plasmas and the EBM formalism for coordinates transformations, for the first time, we develop a first principles description of radially expanding plasmas in the EB frame. From this approach, we aim to fill the gap between simulations and theory at microscopic scales to model plasma expansion at the kinetic level. Our results show that expansion introduces non-trivial changes in the Vlasov equation (in the EB frame), especially affecting its conservative form through non-inertial forces purely related to the expansion. In order to test the consistency of the equations, we also provide integral moments of the modified Vlasov equation, obtaining the related expanding moments (i.e., continuity, momentum, and energy equations). Comparing our results with the literature, we obtain the same fluids equations (ideal-MHD), but starting from a first principles approach. We also obtained the tensorial form of the energy/pressure equation in the EB frame. These results show the consistency between the kinetic and MHD descriptions. Thus, the expanding Vlasov kinetic theory provides a novel framework to explore plasma physics at both micro and macroscopic scales in complex astrophysical scenarios. Full article

The Sagnac effect and related twin paradox with a rotating disc are analyzed. It may seem that the special theory of relativity gives an easy and exhaustive treatment here. However, such consideration is deceptive since the principles of special relativity are originally established only for the inertial frames of reference, whereas the Sagnac experiment and the twin paradox exist in a noninertial one. We introduce an additional group of motions related to the rotation with uniform angular speed and show that these transformations leave the Minkowski metric invariant. Thus, we can give a firm mathematical ground to a usual easy consideration of the Sagnac effect. It should be noted that the presented result is true for a special case of motions; general coordinate transformations into accelerating frames of reference do not preserve the metric. Full article

This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided for the 6-DOF differential equation of motion in the arbitrary non-inertial reference frame. The problem of the 6-DOF relative motion of two spacecraft in the specific case of Keplerian confocal orbits is proposed. The result is an analytical method without secular terms and singularities. Tensors dual algebra and dual quaternions play a fundamental role, with the solution representation being the relative problem. Furthermore, the representation theorems for the rotation and translation parts of the 6-DOF relative orbital motion problems are obtained. Full article

We all have in mind Einstein’s famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Here, in addition to the qualitative aspect, the exact calculations are carried out, and the worldlines equations are given. A uniformly accelerated reference frame in rectilinear translation is considered, and it is shown that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the spacetime is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson–Morley interferometer is solved, and an experiment, where a new relativistic paradox appears—a particle of matter seems to go faster than light—is described. The differences, compared to the classical case, are important at a large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and an analogy with the black hole is made. Full article

According to the single-mode approximation applied to two different mo des, each associated with different uniformly accelerating reference frames, we present analytical expression of the Minkowski states for both the ground and first excited states. Applying such an approximation, we study the entanglement property of Bell and Greenberger–Horne–Zeilinger (GHZ) states formed by such states. The corresponding entanglement properties are described by studying negativity and von Neumann entropy. The degree of entanglement will be degraded when the acceleration parameters increase. We find that the greater the number of particles in the entangled system, the more stable the system that is studied by the von Neumann entropy. The present results will be reduced to those in the case of the uniformly accelerating reference frame. Full article

The Unruh effect can be considered a source of particle production. The idea has been widely employed in order to explain multiparticle production in hadronic and heavy-ion collisions at ultrarelativistic energies. The attractive feature of the application of the Unruh effect as a possible mechanism of the multiparticle production is the thermalized spectra of newly produced particles. In the present paper, the total entropy generated by the Unruh effect is calculated within the framework of information theory. In contrast to previous studies, here the calculations are conducted for the finite time of existence of the non-inertial reference frame. In this case, only a finite number of particles are produced. The dependence on the mass of the emitted particles is taken into account. Analytic expression for the entropy of radiated boson and fermion spectra is derived. We study also its asymptotics corresponding to low- and high-acceleration limiting cases. The obtained results can be further generalized to other intrinsic degrees of freedom of the emitted particles, such as spin and electric charge. Full article

We study both pentapartite GHZ and W-class states in the noninertial frame and explore their entanglement properties by carrying out the negativities including 1-4, 2-3, and 1-1 tangles, the whole entanglement measures such as algebraic and geometric averages ${\pi }_5$ and ${\mathrm{\Pi }}_5$, and von Neumann entropy. We illustrate graphically the difference between the pentapartite GHZ and W-class states. We find that all 1-4, 2-3 tangles and the whole entanglements, which are observer dependent, degrade more quickly as the number of accelerated qubits increases. The entanglements of these quantities still exist even at the infinite acceleration limit. We also notice that all 1-1 tangles of pentapartite GHZ state $N_{\alpha \beta }=N_{{\alpha }_I\beta }=N_{{\alpha }_I{\beta }_I}=0$ where $\alpha ,\beta \in (A,B,C,D,E)$, whereas all 1-1 tangles of the W-class state $N_{\alpha \beta },N_{{\alpha }_I\beta }$ and $N_{{\alpha }_I{\beta }_I}$ are unequal to zero, e.g., $N_{\alpha \beta }=0.12111$ but $N_{{\alpha }_I\beta }$ and $N_{{\alpha }_I{\beta }_I}$ disappear at $r>0.61548$ and $r>0.38671$, respectively. We notice that the entanglement of the pentapartite GHZ and W-class quantum systems decays faster as the number of accelerated particles increases. Moreover, we also illustrate the difference of von Neumann entropy between them and find that the entropy in the pentapartite W-class state is greater than that of GHZ state. The von Neumann entropy in the pentapartite case is more unstable than those of tripartite and tetrapartite subsystems in the noninertial frame. Full article

Legged robots are meant to autonomously navigate unstructured environments for applications like search and rescue, inspection, or maintenance. In autonomous navigation, a close relationship between locomotion and perception is crucial; the robot has to perceive the environment and detect any change in order to autonomously make decisions based on what it perceived. One main challenge in autonomous navigation for legged robots is locomotion over unstructured terrains. In particular, when the ground is slippery, common control techniques and state estimation algorithms may not be effective, because the ground is commonly assumed to be non-slippery. This paper addresses the problem of slip detection, a first fundamental step to implement appropriate control strategies and perform dynamic whole-body locomotion. We propose a slip detection approach, which is independent of the gait type and the estimation of the position and velocity of the robot in an inertial frame, that is usually prone to drift problems. To the best of our knowledge, this is the first approach of a quadruped robot slip detector that can detect more than one foot slippage at the same time, relying on the estimation of measurements expressed in a non-inertial frame. We validate the approach on the 90 kg Hydraulically actuated Quadruped robot (HyQ) from the Istituto Italiano di Tecnologia (IIT), and we compare it against a state-of-the-art slip detection algorithm. Full article