Theory Of Motion Research Articles

Multilayered noise model for transport in complex environments.

Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.

Light-to-Heat Conversion of Optically Trapped Hot Brownian Particles.

Anisotropic hybrid nanostructures stand out as promising therapeutic agents in photothermal conversion-based treatments. Accordingly, understanding local heat generation mediated by light-to-heat conversion of absorbing multicomponent nanoparticles at the single-particle level has forthwith become a subject of broad and current interest. Nonetheless, evaluating reliable temperature profiles around a single trapped nanoparticle is challenging from all of the experimental, computational, and fundamental viewpoints. Committed to filling this gap, the heat generation of an anisotropic hybrid nanostructure is explored by means of two different experimental approaches from which the local temperature is measured in a direct or indirect way, all in the context of hot Brownian motion theory. The results were compared with analytical results supported by the numerical computation of the wavelength-dependent absorption efficiencies in the discrete dipole approximation for scattering calculations, which has been extended to inhomogeneous nanostructures. Overall, we provide a consistent and comprehensive view of the heat generation in optical traps of highly absorbing particles from the viewpoint of the hot Brownian motion theory.

Hardware–Software Embedded System for Real-Time Trajectory Planning of Multi-Axis Machine Using B-Spline Curve Interpolation Algorithm

This paper proposes a B-spline trajectory algorithm to realize multi-axis trajectory interpolation and analyzes the operating accuracy in an embedded system. However, the existing trajectory generation method needs to use computer-aided manufacturing (CAM) software to convert the interpolating trajectory into G code and download the code into the computer numerical control (CNC) system for processing. In this paper, the method of third-degree B-spline interpolation is proposed to generate a curved surface trajectory, and the trajectory generated by this algorithm can be run directly into a CNC system. The precision analysis of the ISO parameter segmentation interpolation algorithm and the theory of constant velocity motion is also presented. The significance of this project is that it designs a complete set of embedded systems, including hardware circuit design and software logic design, and uses low-cost STM32 architecture to realize a B-spline constant-speed interpolation algorithm, which is verified on CNC polishing equipment. A simulation conducted with the MATLAB software and the B-spline curve interpolation experiments performed on a multi-axis polishing machine tool demonstrate the effectiveness and accuracy of the optimized third-degree B-spline algorithm.

Theory of Heap Particle Motion in Vibration Cleaning of Potatoes

Abstract Theoretical research was conducted using the basic principles of higher mathematics and theoretical mechanics. Numerical calculations and graphical dependences are obtained using a PC based on developed and standard programs. The movement of the potato heap on the wing surface of the V-shaped heap distributor in the process of its distribution over the entire width of the separating conveyor was studied. An equivalent scheme of interaction of potato heap particle with the surface of the distributor wing is constructed, on the basis of which differential equations of its motion on the specified surface are made, taking into account the main constructive and kinematic parameters of the separating conveyor and V-shaped distributor. Based on the integration of the specified system of differential equations in quadratures, analytical expressions describing the laws of change of speed and movement of a particle of a potato heap in time at various values of constructive and kinematic parameters of the distributor and separating conveyor are received. Based on the obtained analytical expressions, calculations were performed and graphical dependences of heap velocity along the distributor wing on time at different values of the angle of distributor wings taking into account the oscillations of the separating conveyor blade were obtained. The allowable speed of movement of the heap along the wing of the distributor is determined from the condition of maintaining the equality of supply of the heap to the distributor and its ascent from the distributor. The specified speed is 1.62 m∙s−1. The analysis of graphical dependences shows that the speed of the heap along the wing of the distributor decreases with increasing angle of the wing. If the speed is reduced to less than the allowable value, the heap will be unloaded on the wings of the distributor, which will lead to a disturbance of the technological process of the potato harvester. With the allowable time of movement of the heap along the distributor wing, the maximum allowable values of the deflection of the distributor wing are within 40–45°.

Numerical investigation of cylinders’ motion trajectory and landing positions in regular waves

During the underwater motion of structures, random effect of waves and currents can lead to sudden changes in its hydrodynamic characteristics, the sudden changes in hydrodynamic characteristics and random effect of currents can further couple, seriously affecting its underwater motion mode affecting, so a targets' underwater motion situation model (TUMS) was proposed in this paper which can predict the targets' underwater motion trajectory envelope and the landing positions. Firstly, the influence of random factors such as wave, current, drag coefficient, and xt coefficient was considered based on the targets' three-dimensional (3-D) motion theory and a TUMS model was proposed. Secondly, the underwater motion trajectory of the cylinder is simulated using the TUMS model, and the numerical simulation results are compared with the experimental results which were in good agreement with experimental results. Thirdly, the effect of wave height and wave frequency on the cylinders' motion trajectory was discussed. Finally, the cylinders’ underwater motion trajectory envelope, landing position distribution, sinking bottom velocity distribution, and sinking bottom attitude distribution were calculated.

Colloquium 3 Commentary on Hayes

Abstract In his paper, Josh Hayes argues that inclination (ῥοπή) is the nature of each element. It is an active and passive principle that explains why the elements move to their proper places. Thus, according to Hayes, by introducing inclination in De Caelo IV 1, Aristotle posits a single explanatory factor that accounts for all elemental motions. By doing so, he answers the question, posed in Physics VIII 4, of what the cause of elemental motion is. In my comments, I will contest these claims. Aristotle’s theory of elemental motion does not rely on a single explanatory factor; yet, it is not, as Hayes claims, incoherent. Instead, the different strands merely reflect the special nature of the elements.

Physics-informed laboratory estimation of Sargassum windage

A recent Maxey–Riley theory for Sargassum raft motion, which models a raft as a network of elastically interacting finite size, buoyant particles, predicts the carrying flow velocity to be given by the weighted sum of the water and air velocities (1−α)v+αw. The theory provides a closed formula for parameter α, referred to as windage, depending on the water-to-particle-density ratio or buoyancy (δ). From a series of laboratory experiments in an air–water stream flume facility under controlled conditions, we estimate α ranging from 0.02% to 0.96%. On average, our windage estimates can be up to nine times smaller than that considered in conventional Sargassum raft transport modeling, wherein it is customary to add a fraction of w to v chosen in an ad hoc piecemeal manner. Using the formula provided by the Maxey–Riley theory, we estimate δ ranging from 1.00 to 1.49. This is consistent with direct δ measurements, ranging from 0.9 to 1.25, which provide support for our α estimation.

Thermal enhancement, thermophoretic diffusion, and Brownian motion impacts on MHD micropolar nanofluid over an inclined surface: Numerical simulation

The majority of liquids are undesirable for engineering due to their low heat conductivity. Scientists and researchers are developing nanofluids, which are made of nanoparticles (NPs) scattered in a base fluid, to boost the capacity for heat transfer in a variety of industries, including molten metals, pharmaceuticals, and computers. In this study, the magneto-hydrodynamics (MHD) flow of a micropolar nanofluid model with particle microstructure and inertial properties is investigated. A micropolar nanofluid’s flow is examined concerning the effects of a magnetic field. Aspects of heat and mass transfer are investigated using thermal radiation, thermophoresis, Brownian motion, and double diffusion theory toward an inclined surface. With the right level of similarity, the process converts partial differential equations emerging in nanofluidic systems into nonlinear differential equation systems. The FDM finite difference approach (FDM) (Lobatto IIIA) is used for the nonlinear nanofluid issue with the precision of order 4–5 and is implemented using a variety of collocation locations. The strength of Lobatto IIIA is its effectiveness in handling coupled differential equations that are extremely nonlinear. The higher-order differential equations are converted into a first-order method utilizing the boundary value dilemma (bvp4c) solver, which is part of the MATLAB software package, to computationally analyze the simplified mathematical model. The data obtained demonstrated a high degree of accuracy and symmetry when measured against previously published studies. Numerous variables’ effects on fluid flow are examined and graphically displayed with obtained numerical data. The results show that the temperature profile behaves in a way that is consistent with increasing thermophoresis and Brownian motion forces. This work provides insights into practical applications such as nanofluidic, energy conservation, friction reduction, and power generation. However, the work makes a significant point that the flow of a micropolar nanofluid including NPs can be regulated by appropriately modifying the thermophoresis parameter and Brownian motion parameter.

A Stochastic Price Duration Model for Estimating High-Frequency Volatility

Abstract We propose a stochastic price duration model to estimate high-frequency volatility. A price duration is directly linked to volatility from the passage time theory for Brownian motions, and it possesses several advantages over returns for estimating volatility. We employ price durations in a parametric model that directly specifies stochastic volatility dynamics. Our approach allows us to estimate intraday spot volatility and our empirical results suggest the presence of important intraday volatility dynamics. We conduct an extensive integrated variance forecast comparison, which demonstrates the superior performance of our proposed models compared with other duration-based or return-based estimators.

Advances in research on gas storage in sediment void of salt cavern in China

Salt cavern gas storage (SCGS) is a mature energy storage method that is applied around the world. Insoluble sediment particle (ISP) accumulated at the bottom of the salt cavern seriously affect the storage capacity of salt caverns. The ISP has greatly restricted large-scale underground energy in salt caverns in China. However, if the void in the ISP can be used for gas storage (SVGS), the gas storage capacity of salt caverns will be greatly improved. The sediment void is related to the grain size distribution, accumulation morphology, mechanical properties, and falling movement. Therefore, four models (grading model, accumulating model, mechanics and motion model, and simulation model) of the SVGS are constructed by the four theories (grading theory, accumulation theory, contact force chain and motion theories, and experiment and numerical theories) to analyze the feasibility of SVGS. Then, the practical application, model validation, and prospects of SVGS are also discussed. The models and practical application show that the SVGS is feasible, and it has wide application prospects. The research provides a favorable reference for the implementation of SVGS in China.

Comment on “Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field” [Phys. Plasmas 30, 042515 (2023)

A recent paper by L. Zheng [Phys. Plasmas 30, 042515 (2023)] presented a critical analysis of standard Lie-transform perturbation theory and suggested that its application to the problem of charged-particle motion in a magnetic field suffered from ordering inconsistencies. In the present Comment, we suggest that this criticism is unjustified and that standard Lie-transform perturbation theory does not need to be modified in its application to guiding-center theory.

Response to “Comment on ‘Modification of Lie's transform perturbation theory for charged particle motion in a magnetic field’” [Phys. Plasmas 30, 104701 (2023)

Dr. Brizard's comment on my work is based on a conceived procedure that does not come from my work. The defense of his claim that the modification of the so-called standard Lie's transform theory is unnecessary is also unsupported. This response reveals in detail the inconsistency issues in the so-called standard Lie's transform theory by analyzing both its results and root causes. The problem in the so-called standard Lie's transform theory is beyond the issue to take into account the ordering difference between the guiding center motion and gyromotion. The inconsistent commutation of derivative and limit causes another issue. In addition, the so-called standard Lie's transform formulation leads to an unnecessarily lengthy and tedious derivation process for a one or two page task under the singular (or renormalized) formalism described in my paper.

Adaptive Saturated Path Following Control of Underactuated AUV With Unmodeled Dynamics and Unknown Actuator Hysteresis

This article addresses the three-dimensional (3-D) path-following problem of underactuated autonomous underwater vehicles (AUVs) in the presence of multiple uncertainties and nonlinearities, including unmodeled dynamics, actuator hysteresis, input saturation, and oceanic disturbance. First, the AUV kinetic model is reconstructed as a second-order nonlinear system by coupling the smooth saturation function and hysteresis dynamics of actuators. Second, the 3-D tracking error is derived in a simplified manner based on the relative motion theory. Then the approach angle-based symmetrical hyperbolic-tangent line-of-sight (SHLOS) guidance and kinematic control scheme are designed to ensure the global asymptotic stability of the kinematic system. Third, two sets of kinetic control schemes are designed without prior knowledge of AUV dynamics and disturbance, where the Nussbaum gain technique is applied to deal with the unknown hysteresis parameter. The application of the reconstructed kinetic model avoids the degraded performance caused by actuator nonlinearities. The first scheme is improved by adaptively estimating the bound of the generalized disturbance-like term which lumps the unmodeled dynamics, external disturbance, and saturation approximation error. The improved scheme guarantees the global stability of the system and transient tracking performance. Finally, comparative simulation studies under dynamic oceanic environments prove the effectiveness and robustness of the proposed control schemes.

Comment on "Brownian motion with time-dependent friction and single-particle dynamics in liquids".

Recently, Lad, Patel, and Pratap [Phys. Rev. E 105, 064107 (2022)10.1103/PhysRevE.105.064107] revisited a microscopic theory of molecular motion in liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239]. They argued that the friction coefficient for a Brownian particle in a liquid should exponentially depend on time and derived an equation of motion for the particle's velocity autocorrelation function (VAF). The equation was solved numerically and fitted to the results of molecular dynamics simulations on different liquids. We show that this solution, obtained under the condition of zero derivative of the VAF at time t=0, is physically incorrect at long times. This is evidenced by our exact analytical solution for the VAF, not found by Lad etal., and numerically, by using the same method as in the commented work.

Reply to "Comment on 'Brownian motion with time-dependent friction and single-particle dynamics in liquids' ".

In this reply, we respond to the comments by Lisý and Tóthová (LT) on our recent work [Phys. Rev. E 105, 064107 (2022)10.1103/PhysRevE.105.064107], where we have extended the microscopic theory of molecular motion in atomic liquids that was originally proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)10.1103/PhysRev.176.239]. Contrary to our conclusion of nonavailability of a physically tractable analytical solution of the equation of motion involving dynamic friction, LT have attempted to obtain an analytical solution giving the velocity autocorrelation function in liquids. We show that the analytical solution of the equation of motion derived by LT is incomplete and not an appropriate solution for the description of atomic dynamics in liquids. It is demonstrated that the generalized statements made by LT regarding the equation of motion giving incorrect results are unjustified in the absence of substantial proofs. Also, until and unless proven otherwise, we do not find any reason for the reconsideration of the theory as suggested by LT.

Asymmetric Dynamic Buckling of Isotropic/ Anisotropic Spherical Caps

This paper deals with nonlinear asymmetric dynamic buckling of clamped isotropic/anisotropic spherical shells under suddenly applied pressure loads. The formulation is based on first-order shear deformation theory and Lagrange's equation of motion. The nonlinearity due to finite deformation of the shell considering von Karman's assumptions is included in the formulation. The buckling loads are obtained through dynamic response history using Newmark's numerical integration scheme coupled with a Newton-Raphson iteration technique. An axisymmetric curved shell element is used to investigate the dynamic characteristics of the spherical caps. The pressure value beyond which the maximum average displacement response shows significant growth rate in the time history of the shell structure is considered as critical dynamic load. Detailed numerical results are presented to highlight the influences of shell geometric parameter, orthotropicity, ply-angle, number of layers and asymmetric mode on the critical load of spherical caps.

Aristotle as an Astronomer? Sosigenes’ Account of Metaphysics Λ.8

Abstract I have argued elsewhere that the idea that Aristotle aspired to improve the theories of the planetary motions of Eudoxus and Callippus by adding the ‘counteracting’ spheres (ἀνελίττουσαι) first emerged with the Peripatetic exegete Sosigenes in the second century CE. This paper supplements that argument by contrasting two major lines of interpretation of the astronomical system set out in Metaphysics Λ.8: Adrastus of Aphrodisias’ widely ahistorical account, and Sosigenes’ attempt to save Aristotle against later developments of astronomical science.

OPTIMIZATION METHODS IN CALCULATIONS OF MECHANISMS OF VEHICLES OF TRANSPORT

Purpose. The optimal design of vehicle mechanisms is a detailed review and evaluation of the scientific and technical literature and individual publications on the methodology for optimizing the inherent calculations of these types of mechanical structures. The main purpose of this review material is to consider a number of directions for designing mechanisms of means of transport, especially highlighting the use of optimization methods. Research in the field of designing mechanisms is carried out in two directions: by the synthesis method according to given provisions and by the method of mathematical programming. Methods. Methods for the synthesis of hinged-lever mechanisms can be divided into two groups. In the first one, methods of approximation of functions are used, in the second one, optimization methods. The search for the optimal solution in the second group means the simultaneous search for the correct formulation of the problem, in which the parameters of the mechanisms should be sought under conditions of the best satisfaction of the requirements of the technological process. The problems of optimal design of mechanisms most often continue to be formulated as problems of the best approximation of functions. Optimization synthesis is a relatively new direction in the synthesis of lever mechanisms. Optimization synthesis is carried out on the basis of nonlinear optimization methods. At present, the complexity and complexity of the problems that arise and require solution in the process of designing mechanisms have significantly increased. A certain amount of research has been carried out within the framework of the classical theory of finite and infinitely small plane displacements. In these works, the theory of spatial motion of a general form is developed in detail and applied to the problems of kinematic synthesis. Results. Since the simplex method is quite effective in solving problems of linear programming, it became the founder of a number of methods of sequential linearization or methods of secant planes for solving nonlinear programming. Practical significance. With an extensive list of modern literature and scientific publications on the synthesis of mechanisms and mathematical programming, a complete chronological review of the achievements of the last decade would be quite loud. Therefore, individual trends in the synthesis of mechanisms were only noted, focusing on the desire to obtain a “better” design, taking into account practical requirements. The synthesis of mechanisms is an area in which the application of mathematical programming methods is quite promising due to their free formulation. The constraints and requirements of engineering practical problems can often be taken into account in forms consistent with the data of modern methods. The main purpose of this study is to make widely known the achievements in the two fields with the hope that currently existing optimization tools will be applied to these synthesis problems and that, conversely, the optimization tools will be further improved as a result of research on the design of vehicle mechanisms. This will contribute to a better understanding and accelerated development of both mechanisms calculation methods and optimization methodology.

ЕЛЕМЕНТИ ТЕОРІЇ ДИНАМІЧНО РОЗВИНУТОЇ ПІДВІСКИ ВІЙСЬКОВОГО АВТОМОБІЛЯ

In the authors' article, the elements of the theory of the dynamically developed suspension of the military vehicle are given by the constructive improvement of its suspension by connecting it to the wheel drive, the beam of which is attached to the frame of the car by springs. Also considered are the issues of researching the dynamically developed suspension of a military vehicle by creating an additional number of movements of the auxiliary system and the movement of the center of mass of this system. The conducted studies theoretically provided an improved technological scheme for loading the wheel drive when it moves the support, converting the energy supplied to the wheel drive and the quantitative movements kinematically distributed in the wheel drive into the controlled motion of the car relative to the wheel disk with the addition of the traction force of the car with the transferable forces of quantitative motion, which is an auxiliary factor to the innovative technology of its movement. For the first time, a technology was considered in which the law of change of mechanical energy is applied during the rotation of a wheel drive over an obstacle, i.e., the energy supplied to the wheel drive and quantitative movements kinematically distributed in the wheel drive in the controlled relative to the wheel disc movement of the car with the addition of the traction force of the car with the transferable forces of quantitative movement and this allows a more expedient approach to the consideration of the implementation of the torque on the wheel drive. The authors present the elements of the theory of quantitative motions kinematically dispersed in a wheel drive. When revealing the concept of "dynamically developed suspension", equations were used that mathematically confirm the connection with the quantitative movements kinematically distributed in the wheel drive in the controlled relative to the wheel disc movement of the car, which allows overcoming obstacles on the way and the supporting surface in certain conditions of the car’s operation. Keywords: physical-mathematical model, wheel force, obstacle, car.

Significance of chemically reactive magnetized Eyring-Powell nanofluid flow comprising gyrotactic moment of microorganism and radiative analysis

The emerging attention in nano-technology and thermal engineering has led to the concept of nanoparticles with improved theoretical mechanisms and accomplished influenced innovative usages in cooling and heating conveniences, air conditioning arrangements, heat carrying systems, bio-medical applications such as cancer cure, micromechanics, solar energy, artificial heart surgery etc. Currently, peristaltic movements joined with non-Newtonian fluids have enlarged innumerable devotion due to their enormous applications in physical, medical, engineering processes and medical. Eyring - Powell is unique type of non-Newtonian model consequential commencing the theory of motion of fluids. This research work inspects the 3D steady magnetohydrodynamic flow (MHD) containing microorganisms of a Powell-Eyring nanofluid with double stratification over a bidirectional stretched surface. Furthermore, the characteristics of the heat transfer phenomenon are prescribed out by means of thermal radiation. For changing nonlinear PDEs to nonlinear ODEs, we use the appropriate transformations and then numerically solve them with the help of bvp4c procedures. The possessions of several parameters modulating the heat and mass transfer properties are graphically depicted and illustrated in particular. It is interesting to perceived that the temperature field deteriorates for established estimates of the stretching parameter and the Prandtl number. The microorganism as well as concentration field improve for increasing estimates of magnetic parameter and the Biot number.