Arbitrary Motion Research Articles

Online facility location with mobile facilities

We examine the Online Facility Location problem in an extended version. Fotakis showed a lower bound of Ω(log⁡nlog⁡log⁡n) for the original Online Facility Location problem, where n is the number of clients. This bound holds even on the real line and for randomized algorithms against oblivious adversaries.We propose randomized online algorithms in the following setting: We consider the Euclidean space of arbitrary dimension and allow the facilities to either move arbitrarily or to move at most a constant distance m in each time step. The costs for moving a facility from a to b is D⋅d(a,b) where D≥1 is a constant. Clients are assigned to facilities instantly and irreversibly. The cost for serving the clients is either calculated as soon as a client arrives or at the end of the computation. The algorithms for these two cost models achieve the same competitiveness on the line, which, in contrast to the original Online Facility Location problem, is independent of n. In the case of arbitrary movement, it only depends on D. In the case of a limited movement distance m, it additionally depends on m and the opening costs of the facilities. We show that our results are asymptotically tight on the real line. For the Euclidean space of higher dimensions, we give an algorithm for the model where costs for clients are evaluated immediately. The competitive ratio of our algorithm depends on the above parameters and additionally on the number of optimal facilities.

О взаимоотношении движений динамических систем

In the earlier articles by the authors [A.P. Afanasiev, S.M. Dzyuba, “On new properties of recurrent motions and minimal sets of dynamical systems”, Russian Universities Reports. Mathematics, 26:133 (2021), 5–14] and [A.P. Afanasiev, S.M. Dzyuba, “New properties of recurrent motions and limit motions sets of dynamical systems”, Russian Universities Reports. Mathematics, 27:137 (2022), 5–15], there was actually established the interrelation of motions of dynamical systems in compact metric spaces. The goal of this paper is to extend these results to the case of dynamical systems in arbitrary metric spaces. Namely, let Σ, be an arbitrary metric space. In this article, first of all, a new important property is established that connects arbitrary and recurrent motions in such a space. Further, on the basis of this property, it is shown that if the positive (negative) semitrajectory of some motion f(t,p) located in Σ is relatively compact, then ω- (α-) limit set of the given motion is a compact minimal set. It follows, that in the space Σ, any nonrecurrent motion is either positively (negatively) outgoing or positively (negatively) asymptotic with respect to the corresponding minimal set.

Modeling the Dynamics of an American Football and the Stability Due to Spin

Abstract This paper develops a mathematical model describing the motion through the air of an American football. The model is based on established equations used to describe spinning projectiles. While the equations are applicable to general motions, the emphasis of the paper is on the spiral pass and punt. Separate sections introduce formulas for the forces and moments understood to act on spun projectiles. The discussion of each force and moment includes an assessment of how well available experimental data characterizes the force or moment for an American football. For each force or moment, there is a description of how it affects the motion and trajectory. While the equations are valid for arbitrary motions, the available aerodynamic data is not. In parallel with the derivation of the nonlinear mathematical model, a linearized dynamics model is developed. The linearized model is used to help explain the behavior of the nonlinear model and to provide insight into the underlying physics. The linearized model is also used to derive a relationship between linear and angular velocity that ensures that the gyroscopic motion of a football is stable. The paper provides physical insights into what causes the apparent “wobble” of a spiral pass and what the character of the wobble says about the quality of the pass. Among the physical insights provided are the reason some passes have a rapid wobble and some slow, why a pass exhibits a lateral swerve, and why the Magnus effect may be neglected. The results are applicable to rugby footballs.

General Solution for Unsteady MHD Natural Convection Flow with Arbitrary Motion of the Infinite Vertical Plate Embedded in Porous Medium

This article has concentrated on heat transfer analysis in the unsteady MHD natural convection flow of viscous fluid under radiation and uniform heat flux over an infinite vertical plate embedded in a porous medium. Overall solutions are found for temperature as well as velocity by the Laplace transform techniques. In the literature, the solutions that have been achieved are rare, meet with all the initial and boundary conditions imposed, and can make general solutions for any problem with motion with this form’s methodological relevance. Also, few different cases of engineering applications are discussed. Solutions are plotted graphically through the use of the Mathcad software to analyze how the variation is taking place in the physical behavior of the viscous fluid flow with respect to the change in a distinct physical parameter.

Evaluation of mechanical energy for human dynamics using posture estimation method

The purpose of this study is to realize a tailor-made exercise evaluation technology that can simultaneously perform highly accurate estimation of activity energy expenditure (AEE) and posture measurement during exercise in order to provide tailor-made training content, exercise intensity, and competition time according to the individual. To this end, we developed a measurement system that integrates three technologies: marker-less motion capture, human body dimension measurement, and activity energy expenditure estimation (AEE estimation) based on mechanical energy. Using the measurement system, AEE estimation was performed for two exercises (Arm Swings and Standing Jumps). The results showed that the proposed method is more individualized than the conventional method for the exercise in which a major part of the body moves. In addition, the AEE estimation of the proposed system can be applied to arbitrary movements because the calculation is based on the 3D posture estimation by FrankMocap and the change in mechanical energy.

Real-Time, Robot-Based, 3D Localization of RFID Tags, by Transforming Phase Measurements to a Linear Optimization Problem

In this paper, we propose a prototype method for fast and accurate 3D localization of RFID-tagged items by a mobile robot. The robot performs Simultaneous Localization of its own pose and Mapping of the surrounding environment (SLAM). It is equipped with RFID readers and antennas placed at different heights, collecting phase-measurements by all tags. Thanks to the self-localization property of the robot, a synthetic aperture is created for each tag. In this paper, we have manipulated the set of phase-measurements, combined with the known poses of the robot to craft an overdetermined system of linear equations which pinpoints the location of the tag. The linearity of the system preserves that localization is achieved rapidly. The problem is solved for any arbitrary movement of the robot and extended in three dimensions. The proposed method is experimentally compared against the state-of-the-art in SAR-based RFID localization. It is the fastest and the most accurate, when the robot moves along straight-paths. Its accuracy slightly worsens, when the robot moves along non-straight paths, while preserving its exceptionally small running-time. It can be applied in real-time 3D localization problems, demonstrating mean 3D accuracy below 20 cm.

Lubrication theory and boundary element hybrid method for calculating hydrodynamic forces between particles in near contact

Suspensions of small particles are ubiquitous; examples include aqueous dispersions of solid particles, vesicles, capsules, cells, swimming microorganisms and artificial microswimmers. The rheological and diffusion properties of small particle suspensions are strongly influenced by near-field interactions between particles. Lubrication theory (LT) is a classical analytical technique used to obtain asymptotic solutions of forces and torques acting in the lubrication region. The boundary element method (BEM), on the other hand, is a computational method for accurately calculating Stokes flow around particles. To dramatically improve the near-field accuracy of the BEM, a novel hybrid method combining LT and BEM (LT-BEM) is proposed in this study, in which the inner solution is obtained by LT, whereas the outer solution is obtained by BEM. The validity of the LT-BEM was confirmed based on the shearing, rotational, and squeezing motions of two spheres. The asymptotic nature of the forces and torques exerted on the two spheres were efficiently captured by the LT-BEM. Especially, the squeezing force of the BEM was improved dramatically by the LT-BEM, which is important to prevent particle overlap. The obtained results can be expanded to the arbitrary motions of many spheres without loss of generality. Moreover, the LT-BEM can accommodate particles with arbitrary shapes. The advantages of the LT-BEM are demonstrated for two kinds of applications; (i) dynamic interactions of pairwise microswimmers with surface velocities, and (ii) pairwise interactions of bacteria. The obtained knowledge should be useful for computing various suspensions of small particles in nature and industrial applications.

A Hybrid Self‐Powered Arbitrary Wave Motion Sensing System for Real‐Time Wireless Marine Environment Monitoring Application

AbstractSelf‐powered arbitrary wave monitoring is a hot research topic which aims to remove of the trouble associated with managing conventional power for continuous and real‐time acquisition of wave information from the marine environment. Herein, an effective approach is presented that simultaneously generates power from arbitrary motion waves and can sense and wirelessly transmit the wave information without requiring an external supply. The hybridized ellipsoidal device inspired from an elliptical trajectory of objects over shallow water waves, consists of six planar spiral coils arranged to cover the arbitrary direction of waves for power generation. Four magnetic force‐actuated triboelectric nanogenerators (TENGs) pairs along four sides as the arbitrary direction self‐powered wave motion sensors are integrated. Furthermore, all the required circuitry for signal processing and wireless transmission are integrally powered by the generated electricity to realize a self‐sustained wireless marine environment monitoring system. The generator can deliver peak power of 106 and 44.8 mW (at 3Hz) along with major and minor axis motion directions. The self‐powered sensors have excellent motion sensitivity thus the signals obtained from these sensors are utilized to acquire useful information related to the water waves which are very crucial parameters for real‐time monitoring of the marine environment.

State-Space Modeling of Viscous Unsteady Aerodynamic Loads

In this paper, we summarize our recently developed viscous unsteady theory, which couples potential flow with the triple-deck boundary-layer theory. This approach provides a viscous extension of potential-flow unsteady aerodynamics. As such, a Reynolds-number-dependent transfer function is determined for unsteady lift. We then use the Wiener–Hammerstein structure to develop a finite-dimensional approximation of such an infinite-dimensional theory, presenting it in a state-space model. This novel nonlinear state-space model of viscous unsteady aerodynamic loads is expected to serve aerodynamicists better than the classical Theodorsen’s model because it captures viscous effects (that is, Reynolds number dependence) as well as nonlinearity and additional lag in the lift dynamics; it also allows simulation of arbitrary time-varying airfoil motions (not necessarily harmonic). Moreover, being in a state-space form makes it quite convenient for simulation and coupling with structural dynamics to perform aeroelasticity, flight dynamics analysis, and control design. We then develop a linearization of such a model, which enables analytical results. Subsequently, we derive an analytical representation of the viscous lift frequency response function: an explicit function of both the frequency and Reynolds number. We also develop a state-space model of the linearized response. We finally simulate the nonlinear and linear models to a nonharmonic small-amplitude pitching maneuver at a Reynolds number of 100,000 and compare the resulting lift and pitching moment with those obtained from potential flow; this is in reference to relatively higher-fidelity computations of the unsteady Reynolds-averaged Navier–Stokes equations.

Adjustable carbon fiber reinforced plastic panel for a large-aperture telescope

Segmented mirrors are commonly used to construct large-aperture telescopes. We present a methodology for structural analysis and experimental results of an adjustment of a mm- to far-IR range (10 mm to 70 μm) segmented mirror panel to correct its deviation from an optimum paraboloid of rotation. The panel is made of high-modulus carbon fiber–reinforced plastic and has a shape of a 15-deg sector with a 1207 × 390 mm2 reflecting surface area. A system of mechanically operated adjusters for correcting large-scale surface deformations is described. We used our original method to correct fabrication errors and improved the surface shape accuracy from 23.8 to 4.5 μm (RMS values). The method is based on distance-to-target-surface minimization using vector influence functions and arbitrary movements. The results of the long-term panel shape stability monitoring and the effect of cooling the panel down to 77 K are also presented.

In-vitro validation of inertial-sensor-to-bone alignment

A major shortcoming in kinematic estimation using skin-attached inertial sensors is the alignment of sensor-embedded and segment-embedded coordinate systems. Only a correct alignment results in clinically relevant kinematics. Model-based inertial-sensor-to-bone alignment methods relate inertial sensor measurements with a model of the joint. Therefore, they do not rely on properly executed calibration movements or a correct sensor placement. However, it is unknown how accurate such model-based methods align the sensor axes and the underlying segment-embedded axes, as defined by clinical definitions. Also, validation of the alignment models is challenging, since an optical motion capture ground truth can be prone to disturbances from soft tissue movement, orientation estimation and manual palpation errors. We present an anatomical tibiofemoral ground truth on an unloaded cadaveric measurement set-up that intrinsically overcomes these disturbances. Additionally, we validate existing model-based alignment strategies. Modeling the degrees of freedom leads to the identification of rotation axes. However, there is no reason why these axes would align with the segment-embedded axes. Relative inertial-sensor orientation information and rich arbitrary movements showed to aid in identifying the underlying joint axes. The first dominant sagittal rotation axis aligned sufficiently well with the underlying segment-embedded reference. The estimated axes that relate to secondary kinematics tend to deviate from the underlying segment-embedded axes as much as their expected range of motion around the axes. In order to interpret the secondary kinematics, the alignment model should more closely match the biomechanics of the joint.

Viscous extension of vortex methods for unsteady aerodynamics

The Kutta condition has been extensively used to determine aerodynamic loads of steady and unsteady flows over airfoils. Nevertheless, the application of this condition to unsteady flows has been controversial for decades. A viscous correction to the Kutta condition was recently developed by matching the potential flow solution with a special boundary layer theory that resolves the flow field in the immediate vicinity of the trailing edge: the triple-deck boundary layer theory. In this work, we utilize this viscous condition to extend two common numerical methods for unsteady aerodynamics to capture viscous effects on the dynamics of unsteady lift and pitching moment—we develop viscous versions of the traditional discrete vortex method and unsteady vortex lattice/panel method. The resulting aerodynamic loads obtained from the proposed numerical models are compared against higher-fidelity simulations of unsteady Reynolds-averaged Navier–Stokes equations for an airfoil undergoing step, harmonic, and complex maneuvers. The obtained results are consistently in better agreement with the unsteady Reynolds-averaged Navier–Stokes simulations in comparison to their potential flow counterpart. In conclusion, the developed numerical methods are capable of capturing (i) unsteady effects; (ii) viscous effects (e.g., viscosity-induced lag) on the dynamics of lift and moment at high frequencies and low Reynolds numbers; and (iii) wake deformation, for arbitrary time-varying motion.

The use of kinesioplasty methods to optimize the motor activity of young players

The article presents a theoretical analysis and summarizes approaches to the use of kinesioplasty in the training of young football players to optimize motor activity and functional reserves of individual movements.
 The analysis of the literature showed that the anatomical-physiological and psychological features of the development of the body of young football players are most favorable for the development of most physical qualities of man.
 Based on the generalization of educational and methodological and scientific literature, it was found that the mechanisms of interaction of posture and arbitrary precise movements are closely interrelated and depend on the state of postural balance and the general center of gravity of the athlete's biomechanics.
 The expediency of expanding the range of means of the training process of young football players aimed at optimizing their motor activity has been studied.
 In the sports and training process of young football players found that it is extremely important to develop both cortical mechanisms of motor coordination and the manifestation of various forms of motor coordination in the distal parts of the body, and through muscular activity - changes in spatial, force, temporal characteristics of voluntary movement, biodynamic characteristics of the athlete's posture.
 It is proved that in order to obtain a positive effect of kinesioplasty methods on the optimization of coordination abilities of young players, it is necessary to restructure the pathological motor stereotype formed as a result of spontaneous development, which adapts the athlete to increase stress and energy expenditure during sports training. And the ability to regulate a variety of parameters of movements is determined by the accuracy of motor sensations and perceptions.
 The pedagogical experiment was carried out on the basis of FC "Kudrivka". The experiment was carried out by stretching the grass-sickle 2021 rock. It was attended by (n = 30 people) of which (n = 15 people) control group and (n = 15 people) experimental group). The age of the subjects was 8-11 years.

The Synthesis of an Adaptive Filter for Automatic Detection and Time Localization of Premotor EEG Patterns of the Human Brain

An adaptive low-pass filter has been synthesized for automatic patterns detection of arbitrary mental movements in records of multidimensional electroencephalograms (EEG). The filter is based on the multivariate singular spectrum analysis. The effective bandwidth of the filter corresponds to the spectrum of the sought patterns of mental activity on the observed EEG time interval. The use of the synthesized filter provided a reliable automatic search for patterns and the correct determination of their time boundaries. The correctness of the results has been confirmed in experiments with 24 volunteers.

Low-Reynolds Number Behavior of the Leading-Edge Suction Parameter at Low Pitch Rates

Small unmanned aerial vehicles (UAVs) are becoming increasingly popular as low-cost observation and research platforms. However, these aircraft operate low in the atmosphere, exposed to the turbulent wakes of man-made and natural roughness features. As such, it is important to estimate their unsteady aerodynamic performance. The leading-edge suction parameter (LESP) is one criterion used in vortex methods for predicting flow separation, which can arise in both steady and unsteady flows. The critical LESP represents the maximum suction supported in the leading-edge region, equivalent to the flat-plate behavior of thin airfoil theory. This parameter was investigated at low pitch rates for a NACA0012 airfoil at Reynolds numbers applicable to small UAVs, to examine the hypothesis of a constant critical value existing for an arbitrary motion. It is seen that the critical LESP shows a strong dependence on pitch rate, with a piecewise linear fit being obtained. A higher pitch rate induces a greater pressure-field lag, promoting a higher peak LESP for flow separation, and a lower value for reattachment. These peaks in the LESP agree well with the instances of separation and reattachment. Raising the Reynolds number also acts to raise the critical LESP for a given reduced pitch rate.

Free-surface disturbances due to the submersion of a cylindrical obstacle

We explore the initial perturbations that form on a liquid free surface as a result of the submersion of a circular cylinder beneath the surface, a scenario that arises in a number of diverse applications. The behaviour of the free surface is determined by transforming the equations of motion of the system via the Wehausen scheme, to variables for the free surface. A small-time series expansion is utilized to construct a recursive scheme that can be implemented numerically, and the time frame over which this approximation is valid is analysed. The resulting numerical model allows one to extend the results in the literature to study arbitrary cylinder sizes, including those where the cylinder is close to the free surface, and arbitrary cylinder motions. Of particular interest in this study was identifying the conditions under which strong jets would appear, and those were the free surface exhibited gravity waves. The formation of a central jet is found to be related to the growth of secondary, nonlinear waves, which rapidly merge as the obstacle is submerged. Classification maps are presented as a function of obstacle size and submersion speed, to identify the conditions which lead to jetting. Furthermore, the acceleration profile of the cylinder is shown to significantly affect the conditions under which jets form, which we argue is due to the rate at which energy is injected into the system.

Active speckle deflectometry based on 3D digital image correlation.

A method based on 3D digital image correlation (DIC) to measure the shape of specular surface is proposed. The proposed active speckle deflectometry (ASD) utilizes a stereo-camera system to monitor the liquid crystal display (LCD), which is deliberately moved during the measurement. Another testing camera (TC) is used to capture the single-shot speckle pattern displayed on the LCD screen after reflection by the test surface. With this proposal, the movement of the LCD screen can be arbitrary as long as the TC can capture the reflection of speckle pattern. The distance as well as the direction of the movement is not required to be known. The coordinates of the point source are determined by applying the 3D DIC technique with the monitoring stereo-cameras (MSC) before and after the movement of the LCD screen, then the slope and surface shape are obtained. The measurement accuracy of this method is evaluated by measuring a flat glass with a diameter of about 80 mm, compared with the measurement results of interferometer, the shape measurement difference is 0.278um in root mean square (RMS). The shape of two wafers is also measured, and the measurement results are compared to that of the traditional phase measuring deflectometry (PMD). ASD has the advantages of fast measurement, low cost, arbitrary LCD movement, tolerance for the out-of-plane shape of the LCD screen. It provides a new method for specular surface measurement.

CORRECTION OF THE THEORY OF RESEARCHING THE PROPERTIES OF CHARGED PARTICLES SOURCES

This work is devoted to the adjustment of the existing methods of research and design of charged particle sources, which are the most important components of most analytical electron-optical devices and ion-beam technological installations, widely used in various scientific and technical complexes and systems. Therefore, many scientific papers are devoted to the problems of the theory of cathode lenses. In these works, it is indicated that the development of the theory of cathode lenses is associated with noticeable difficulties of a mathematical nature, due to the specificity of the initial conditions of the differential equations to be solved. One of the most promising ways to overcome these difficulties was proposed in the works that used the method of analyzing arbitrary motion relative to the motion of the central particle. However, in these works there are inaccuracies associated with the inconsistent use of initial conditions in solving the equations of motion of charged particles. These inaccuracies did not allow in these works to achieve sufficient adequacy of the mathematical model to the physical process under study. In this paper, the inaccuracies of the existing theories of cathode lenses are eliminated and a theory for the study and design of cathode lenses with constant axisymmetric electric and magnetic fields is developed. The method proposed in this paper can be used to construct theories of charged particle sources with other types of focusing field symmetry.

Real-time deep dynamic characters

We propose a deep videorealistic 3D human character model displaying highly realistic shape, motion, and dynamic appearance learned in a new weakly supervised way from multi-view imagery. In contrast to previous work, our controllable 3D character displays dynamics, e.g., the swing of the skirt, dependent on skeletal body motion in an efficient data-driven way, without requiring complex physics simulation. Our character model also features a learned dynamic texture model that accounts for photo-realistic motion-dependent appearance details, as well as view-dependent lighting effects. During training, we do not need to resort to difficult dynamic 3D capture of the human; instead we can train our model entirely from multi-view video in a weakly supervised manner. To this end, we propose a parametric and differentiable character representation which allows us to model coarse and fine dynamic deformations, e.g., garment wrinkles, as explicit spacetime coherent mesh geometry that is augmented with high-quality dynamic textures dependent on motion and view point. As input to the model, only an arbitrary 3D skeleton motion is required, making it directly compatible with the established 3D animation pipeline. We use a novel graph convolutional network architecture to enable motion-dependent deformation learning of body and clothing, including dynamics, and a neural generative dynamic texture model creates corresponding dynamic texture maps. We show that by merely providing new skeletal motions, our model creates motion-dependent surface deformations, physically plausible dynamic clothing deformations, as well as video-realistic surface textures at a much higher level of detail than previous state of the art approaches, and even in real-time.

Dynamics of an unbalanced circular foil and point vortices in an ideal fluid

This paper addresses the problem of the motion of an unbalanced circular foil and point vortices in an ideal incompressible fluid. Using Bernoulli's theorem for unsteady potential flow, the force due to the pressure from the fluid on the foil is obtained for an arbitrary vortex motion. A detailed analysis is made of the case of free vortex motion in which a Hamiltonian reduction by symmetries is performed. For the resulting system, relative equilibria corresponding to the motion of an unbalanced foil and a vortex in a circle or in a straight line are found and their stability is investigated. New examples of stationary configurations of a vortex and a foil are given. Using a Poincaré map, it is also shown that in the general case of an unbalanced circular foil the reduced system exhibits chaotic trajectories.