Theory Of Motion Research Articles

Robots and Dance: A Promising Young Alchemy

Research at the intersection of robots and dance promises to create vehicles for expression that enable new creative pursuits and allow robots to function better, especially in human-facing scenarios. Moving this research beyond fringe spectacle and establishing it as a serious, systematic field—a proper subdiscipline of both robotics and dance—will require answering a key question: How does dance advance the fundamentals of robotics, and vice versa? Focusing on the former, this article offers glimpses of this new field with examples of meaningful contributions to control, robotics, and autonomous systems, such as novel actuator designs, improved sensing systems, salient motion profiles for robots, reproducible experiment designs, and new theories of motion derived from the study of dance. It also poses two grand challenges for the emerging field of choreobotics: developing a robust symbolic system for representing bodily action and establishing rich, repeatable testing environments for human–robot interaction.

Electromagnetic frequency prediction pattern for electrical circuited shell based on FSTT theory using electromagnetic wave prediction method

This research focuses on electromagnetic analysis of electrical circuited shell to predict possible failure using wave prediction method. The equation is established considering axial and lateral hydrostatic pressure based on first order shear deformation theory of shell motion using the wave propagation approach and classic Flügge shell equations. For validation of accuracy of this research method, a comparison carried out with experimental data. With this method the effects of circuit parameters as well as different t power-law exponent on the frequencies are investigated. The results showed fantastic agreement between the present method and experimental ones.

Synthesis of Nanoparticles for Drug Delivery in Korea

Purpose: The aim of the study was to assess the synthesis of nanoparticles for drug delivery in Korea. Methodology: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries. Findings: The study indicated that the synthesis of nanoparticles for drug delivery has emerged as a promising strategy to enhance the efficacy and precision of therapeutic interventions. Nanoparticles offer several advantages, such as improved bioavailability, targeted delivery, and controlled release of drugs. Various methods are employed in their synthesis, including chemical reduction, sol-gel processes, and biological methods using natural organisms. These nanoparticles can be engineered to carry a wide range of drugs, including chemotherapeutics, antibiotics, and vaccines. Their small size allows them to navigate biological barriers and deliver drugs directly to specific tissues or cells, reducing side effects and improving treatment outcomes. However, challenges such as scalability, toxicity, and regulatory hurdles remain, necessitating further research to optimize their clinical applications. Implications to Theory, Practice and Policy: Brownian motion theory, nanoscale phenomena theory, thermodynamic theory of nanoparticle stability may be used to anchor future studies on the synthesis of nanoparticles for drug delivery in Korea. Practitioners in the field should prioritize the enhancement of synthesis techniques and the focus on biocompatibility and safety to improve the practical applications of nanoparticle drug delivery systems. To ensure the safe and effective use of nanoparticles in drug delivery, policymakers must establish clear guidelines and regulations governing their application.

Algorithmic Implementation of Visually Guided Interceptive Actions: Enhancing Motion Perception in Virtual and Augmented Reality Systems

This research introduces an innovative algorithmic framework designed to enhance motion perception and visually guided interceptive actions in virtual and augmented reality (VR/AR) environments. By applying harmonic ratios and stimulation invariants, the proposed algorithms enable real-time prediction of interception points and improve the responsiveness of VR/AR systems. This methodology translates complex theories of visual perception and motion into practical algorithmic solutions, providing dynamic prediction capabilities critical for applications such as online gaming, virtual simulations, and neurorehabilitation. Our findings underscore the potential of these algorithms to advance interactive systems, improving user experiences in immersive virtual environments through more precise and adaptive motion tracking and control. This approach is particularly relevant for enhancing the realism and efficiency of VR and AR applications in media, online gaming, and other collaborative digital environments.

An exactly solvable model for non-Fickian transport in dynamically heterogeneous media

Abstract Diffusion, observed in various condensed phases, finds its theoretical background in Einstein’s theory of Brownian motion, characterized by the linear time-dependence of mean square displacement (MSD) denoting Fickian behavior and the Gaussian distribution of particle displacement. Nevertheless, diverse systems exhibit either non-linear, non-Fickian time-dependence of the MSD or non-Gaussian displacement distribution. Montroll and Weiss’s continuous-time random walk (CTRW) model and the stochastic diffusivity (SD) model have provided insights into anomalous diffusion phenomena and Fickian-yet-non-Gaussian transport in dynamically heterogeneous environments, respectively. Building upon these approaches, Song et al developed a generalized transport equation with an environment-dependent diffusion kernel, providing a quantitative explanation for non-Fickian MSD and non-Gaussian displacement distribution. Based on the generalized transport equation, this study introduces an exactly solvable model for a non-Gaussian displacement distribution, accommodating arbitrary time profiles in its MSD, including both Fickian and non-Fickian behaviors. Our findings confirm the model’s capability in describing such transport processes. Furthermore, the proposed model unifies the CTRW model under fast environmental fluctuations and the SD model under Fickian time dependencies, making it suitable for understanding tracer particle motion within explicit solvent or complex media.

From Foucault pendulum to LHC on the rotating Earth

The Lagrange theory of particle motion in the noninertial systems is applied to the Foucault pendulum, isosceles triangle pendulum and the general triangle pendulum swinging on the rotating Earth. As an analogue, planet orbiting in the rotating galaxy is considered as the the giant galactic gyroscope. The Lorentz equation and the Bargmann-Michel-Telegdi equations are generalized for the rotation system. The knowledge of these equations is inevitable for the construction of LHC where each orbital proton "feels" the Coriolis force caused by the rotation of the Earth.

Scaling study of diffusion in dynamic crowded spaces

Abstract We formulate a scaling theory for the long-time diffusive motion
in a space occluded by a high density of moving obstacles in
dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in
time, before reaching a diffusive steady state with an effective diffusion
constant D eff, which depends on the obstacle diffusivity and density.
The scaling of D eff, above and below a critical regime,
is characterized by two independent critical
parameters: the conductivity exponent μ, also found in models with frozen
obstacles, and an exponent ψ, which quantifies the effect of obstacle
diffusivity.

Einstein–Perrin dilemma on the Brownian motion (Avogadro’s number) resolved?

The general recognition of the existence of atoms and molecules occurred only at the beginning of the twentieth century. Many researchers contributed to this, but the ultimate proof of the molecular nature of matter that convinced even the last sceptics was the confirmation of Albert Einstein’s statistical-fluctuation theory of Brownian motion, a part of his comprehension of interdisciplinary atomism, by Jean Perrin’s experiments on colloidal gamboge particles. Einstein noticed a difference between the values of Avogadro’s constant derived from Perrin’s experiments and Planck’s calculation from black-body radiation. Einstein assumed the incorrectly evaluated size of the gamboge spherules to be a culprit of the difference and asked Perrin to check the assumption with additional experiments and using the viscosity formula introduced in his own dissertation. The result was a discrepancy that neither Einstein nor Perrin settled any further. In this communication, based on the survey of developments in colloid and polymer science and their comparison with relevant experiments, an explanation of the dilemma is given that now, after more than a century, proves Einstein correct. The comparison was de facto possible during his lifetime.

Nonequilibrium microbial dynamics unveil a new macroecological pattern beyond Taylor's law.

We introduce a comprehensive analytical benchmark, relying on Fokker-Planck formalism, to study microbial dynamics in the presence of both biotic and abiotic forces. In equilibrium, we observe a balance between the two kinds of forces, leading to no correlations between species abundances. This implies that real microbiomes, where correlations have been observed, operate out of equilibrium. Therefore, we analyze nonequilibrium dynamics, presenting an ansatz for an approximate solution that embodies the complex interplay of forces in the system. This solution is consistent with Taylor's law as a coarse-grained approximation of the relation between species abundance and variance, but implies subtler effects, predicting unobserved structure beyond Taylor's law. Motivated by this theoretical prediction, we refine the analysis of existing metagenomic data, unveiling a novel universal macroecological pattern. Finally, we speculate on the physical origin of Taylor's law: building upon an analogy with Brownian motion theory, we propose that Taylor's law emerges as a fluctuation-growth relation resulting from equipartition of environmental resources among microbial species.

Determination of the density of dark matter in the Solar system

A method based on the Newtonian and relativistic theories of body motion is proposed for calculating the density of dark matter, which, like visible (baryonic) matter, creates a gravitational field. Experimental data obtained by the Pioneer 10 and Pioneer 11 spacecraft and a variety of astronomical observations are used to detect and establish the mass of dark matter in the solar system, which turned out to be approximately equal to the mass of the Sun. Using the equations of motion of test bodies in the Newtonian and post-Newtonian approximations of the general theory of relativity, calculation formulas are obtained for calculating the density of dark matter in three cases: 1) baryonic and dark matter are uniformly distributed in space (their density is constant); 2) they are distributed according to spherically symmetrical laws; 3) baryonic matter is distributed spherically symmetrically, while dark matter is uniformly distributed. In the volume of a sphere with radius of 45 a. u. with the center in the center of gravity of the Sun, on the basis of known experimental data, the average density of the gas-dust and relict matter located in it is calculated, equal to 1,26 · 10–16 g · cm–3. In the same volume, the density of dark matter in all three cases varies according to the derived calculation formulas in the range from 3,38 · 10–16 to 3,34 · 10–16 g · cm–3, which gives the superiority of dark matter over baryonic one from 2.68 to 2.72 times. The given numerical estimates may change when the experimental data used change. The paper also contains a brief discussion of other methods for calculating the density of dark matter in space and a comparison with our results.

Newton and the genesis of Leibniz’s theory of space

Abstract The paper in [1] provides a history of Gottfried Leibniz’s ideas about space. Contrary to standard readings, Leibniz did not develop a relational theory of space until 1688 when he read Isaac Newton’s Principia and realised that he had to respond to the theory of absolute space with a new, powerful and rich alternative theory. The paper details Leibniz’s theories of space prior to the relational theory and their philosophical sources. It discusses Leibniz’s theory in relation to his theories of time, motion and geometry. Finally, it shows the role of Newton in the genesis of Leibniz’s relational theory.

An elementary proof of the inequality $\chi\leq\chi^{*}$ for conditional free entropy

Through the study of large deviations theory for matrix Brownian motion, Biane, Capitaine, and Guionnet proved the inequality \chi(X)\leq\chi^{*}(X) that relates two analogs of entropy in free probability defined by Voiculescu. We give a new proof of \chi\leq\chi^{*} that is elementary in the sense that it does not rely on stochastic differential equations and large deviations theory. Moreover, we generalize the result to conditional microstates and non-microstates free entropy.

Numerical modeling of transient water table in shallow unconfined aquifers: A hyperbolic theory and well-balanced finite volume scheme

We present a new methodology capable of modeling transient motion of shallow phreatic surface of groundwater in unconfined aquifers. This methodology is founded on a new and comprehensive theory for water table motion and a corresponding efficient numerical scheme. In the theoretical aspect, we derived a new set of governing equations constituted by a depth-averaged continuity equation and momentum equations based on unsteady Darcy’s law. The derived governing equations are of the hyperbolic type and possess stiff terms in the momentum equations due to the inertia motion in a characteristic time scale that is relatively shorter than the time scale of seepage motion. To effectively solve the derived hyperbolic system with stiff terms, in the numerical aspect, we utilize f-wave propagation algorithm, an explicit finite volume method, that can ensure numerical convergence and well-balancing solutions when momentum is rapidly relaxing to an equilibrium of steady state. Verification is successfully performed by comparing the results with analytic solutions to the classic problem of multidimensional spreading of a groundwater mound. This study demonstrates that the proposed methodology can accurately and satisfactorily simulate the spatiotemporal distribution of shallow water table and its wetting front in unconfined aquifers.

Research on a new method for the degree of freedom analysis of parallel mechanism

At present, traditional analysis methods sometimes show incompatibility when analyzing the degree of freedom (DOF) of parallel mechanisms. In this research, a new DOF analysis method (MV-DOF method) based on primary-ancillary motion theory is developed. The 4PPRRR series-parallel mechanism is taken as an example, the analysis results by using the MV-DOF method are compared with those of traditional inverse helix theory and modified Grübler-Kutzbach formula, respectively. The comparison shows that this MV-DOF method can always analyze the DOF of the 4PPRRR series-parallel mechanism accurately, while the other two traditional methods show inapplicability sometimes. During the analysis, an important rule is also found that the ancillary motion is equivalent to local constraint helix motion, but it is not always true in turn. Based on this MV-DOF method, a DOF cutting analysis way is also suggested. Any output point on a complex mechanism can be taken as a cutting point, along which the mechanism can be cut into two independent sub-mechanisms. The output DOF of each sub-mechanism can be analyzed separately by using the MV-DOF method, then the intersection can be obtained as the DOF of the whole mechanism at this output point. This research provides a new and effective analytical way for DOF analysis of parallel mechanisms.

Single-Molecule Tracking in Live Cell without Immobilization or without Hydrodynamic Flow by Simulations: Thermodynamic Jitter

Experiments to measure a single molecule/particle, i.e., an individual molecule/particle, at room temperature or under physiological conditions without immobilization—for example, on a surface or without significant hydrodynamic flow—have so far failed. This failure has given impetus to the underlying theory of Brownian molecular motion towards its stochastics due to diffusion. Quantifying the thermodynamic jitter of molecules/particles inspires many and forms the theoretical basis of single-molecule/single-particle biophysics and biochemistry. For the first time, our simulation results for a live cell (cytoplasm) show that the tracks of individual single molecules are localized in Brownian motion, while there is fanning out in fractal diffusion (anomalous diffusion).

Diurnal and semi-diurnal effects of ocean tides on polar motion and UT1: An updated assessment

We revisit the computation of diurnal and semidiurnal effects of the ocean tide on Polar Motion (PM) and UT1 considering the principal waves of the Ocean Tidal Angular Momentum (OTAM) calculated from the FES 2014 ocean tide atlas. We take into account the recent development of polar motion theory, especially the frequency dependence of the transfer functions in (sub-) diurnal bands. The method of calculating the minor waves is also carefully studied and modified: instead of an interpolation based on neighboring waves, we propose a frequency dependent expression obtained by a linear fit to the admittances and phases of principal waves. Compared in time domain with polar motion (PM) and UT1 derived from Very Long Baseline Interferometry (VLBI) observations, our model performs as well as the recent Desai-Sibois model computed from TPXO8 tidal atlas. The impact of diurnal and semi-diurnal oscillations produced by the luni-solar tidal torque on the asymmetric mean mass distribution of the Earth are observed in the corresponding residuals, which is not the case for the older PM/UT1 model recommended in IERS Convention 2010. More generally, we conclude that tidal modelling of sub-daily terms and corresponding empirical developments are consistent to within 23 μas for PM and 3 μs for UT1. In parallel, the effects based on TPXO8 OTAM waves are recalculated according to our method, and present the best agreement with the observations. Our tables, calculated from FES 2014 or TPXO8 OTAM, can be truncated to the 48 or 50 terms with amplitudes above 1 μas for PM or 0.1 μs for UT1 to describe those Earth rotation Parameters in a way consistent with their current observation uncertainties.

Stability Analysis of the Secondary Motion of a Textured Piston

Piston–cylinder pairs are very common in industrial mechanisms. While a piston is primarily designed for axial reciprocating motion, the occurrence of secondary motions—lateral and rotational—due to the small clearance between the piston and the cylinder may lead to frictional contact, energy loss, wear and an increase in unwanted leakage. This study focuses on mitigating the secondary motion of a ringless piston. The influence of a Rayleigh step bearing and partial surface texturing with numerous micro-dimples on the dynamic stability of the secondary motion is studied. A linear model was used to obtain the trajectory of the secondary motion and Floquet theory was applied to analyze the stability and draw stability maps. The influence of various texturing and step parameters, including the dimple area density and aspect ratio for partial texturing, as well as the length and depth of treatment for both partial texturing and step profiles, on the stability of the secondary motion was examined. The normalization method is presented, enabling the expansion of the results for various operating conditions and geometries. Conclusions and guidelines regarding the optimal parameters, in terms of a wider stability range and higher decay rate, are formulated.

HEOM‐QUICK2: A general‐purpose simulator for fermionic many‐body open quantum systems—An update

AbstractMany‐body open quantum systems (OQSs) have a profound impact on various subdisciplines of physics, chemistry, and biology. Thus, the development of a computer program capable of accurately, efficiently, and versatilely simulating many‐body OQSs is highly desirable. In recent years, we have focused on the advancement of numerical algorithms based on the fermionic hierarchical equations of motion (HEOM) theory. Being in‐principle exact, this approach allows for the precise characterization of many‐body correlations, non‐Markovian memory, and non‐equilibrium thermodynamic conditions. These efforts now lead to the establishment of a new computer program, HEOM for QUantum Impurity with a Correlated Kernel, version 2 (HEOM‐QUICK2), which, to the best of our knowledge, is currently the only general‐purpose simulator for fermionic many‐body OQSs. Compared with version 1, the HEOM‐QUICK2 program features more efficient solvers for stationary states, more accurate treatment of non‐Markovian memory, and improved numerical stability for long‐time dissipative dynamics. Integrated with quantum chemistry software, HEOM‐QUICK2 has become a valuable theoretical tool for the precise simulation of realistic many‐body OQSs, particularly the single atomic or molecular junctions. Furthermore, the unprecedented precision achieved by HEOM‐QUICK2 enables accurate simulation of low‐energy spin excitations and coherent spin relaxation. The unique usefulness of HEOM‐QUICK2 is demonstrated through several examples of strongly correlated quantum impurity systems under non‐equilibrium conditions. Thus, the new HEOM‐QUICK2 program offers a powerful and comprehensive tool for studying many‐body OQSs with exotic quantum phenomena and exploring applications in various disciplines.This article is categorized under: Data Science > Computer Algorithms and Programming Software > Simulation Methods Theoretical and Physical Chemistry > Statistical Mechanics

Charge Motion in Solid Helium

We overview and discuss several advances in the understanding of the motion of ions through solid helium. Positive and negative ions in solid helium are microscopic complexes with internal structures embedded into the host crystal lattice. Their low-field mobilities normally decrease with cooling in both bcc and hcp crystals of either isotope of helium (3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He and 4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}He). Depending on the density of solid helium (as well as, in the case of positive ions in hcp 4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}He, on the crystal orientation), the corresponding activation energies for the mobility of the two species of ions may or may not coincide, and they are found to be typically either equal to or about twice the vacancy creation energy. In strong electric fields, the field dependence of the drift velocity of ions is often nonlinear but monotonic. However, for positive ions in hcp 4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^4$$\\end{document}He, non-monotonic anomalies in both temperature and field dependences of the drift velocity were observed. We discuss these features within the framework of the theory of ion motion via inelastic scattering of low-energy vacancions put forward by Alexander Andreev and co-workers.

To plasma electrons motion theory in high-frequency fields

The article is dedicated to the kinetic theory of plasma, where the problem of interaction of high-frequency electric fields with weakly non-uniform plasma is investigated using kinetic equations with binary collision integrals for plasma particles. A new methodology for determining the expression of the averaged highfrequency pressure force is proposed based on solving the kinetic equation and using the method of successive approximations (separation of slow motions and fast oscillations) under the limiting conditions. An expression for the averaged quasi-potential force is derived based on the kinetic equation for the electron distribution function in weakly inhomogeneous magnetoactive plasma, taking into account electrons collisions with fixed ions and the presence of a longitudinally inhomogeneous high-frequency electric field using wellknown methods of theoretical and mathematical physics, such as successive approximations, averaging over the effective field oscillation period, and integration over trajectories. The amplitude of the field is a slowly varying function in both time and space coordinates. The obtained expression allows us to estimate the influence of collisions of plasma particles on the Miller force, and under limiting conditions it coincides with the known expressions for the high-frequency pressure force derived from the equation of plasma electrons motion in high-frequency fields. In all calculations, the contribution of the magnetic component of the electromagnetic field is neglected, which is quite justified for the longitudinal electric field.