One-dimensional Motion Research Articles

One-Dimensional Motion Representation for Standing/Sitting and Their Transitions.

In everyday life, people often stand up and sit down. Unlike young, able-bodied individuals, older adults and those with disabilities usually stand up or sit down slowly, often pausing during the transition. It is crucial to design interfaces that accommodate these movements. Additionally, in public settings, protecting personal information is essential. Addressing these considerations, this paper presents a distance-based representation scheme for the motions of standing up and sitting down. This proposed scheme identifies both standing and sitting positions, as well as the transition process between these two states. Our scheme is based solely on the variations in distance between a sensor and the surfaces of the human body during these movements. Specifically, the proposed solution relies on distance as input, allowing for the use of a proximity sensor without the need for cameras or additional wearable sensor attachments. A single microcontroller is adequate for this purpose. Our contribution highlights that using a proximity sensor broadens the applicability of the approach while ensuring that personal information remains secure. Additionally, the scheme alleviates users' mental burden, particularly regarding privacy concerns. Extensive experiments were performed on 58 subjects, including 19 people over the age of 70, to verify the effectiveness of the proposed solution, and the results are described in detail.

Shock wave propagation in a real gas with or without gravitational field in the presence of magnetic field and monochromatic radiation via group invariance method

PurposeThis article aims to find the similarity solutions for the one-dimensional motion of spherical symmetric shock wave in non-ideal gas influenced by the azimuthal magnetic field and monochromatic radiation in the presence or absence of gravitational field. This paper also aims to study the effects of physical parameters on the strength of shock wave, and on the flow variables in the flow-field region behind the shock front.Design/methodology/approachThe Roche model is used to describe the gravitational field effects due to a massive nucleus at the point of symmetry. To derive the similarity solutions, the Lie group symmetry method has been used. Also, the numerical solutions to the present problem are obtained by using Rung–Kutta method of the fourth order with the use of Mathematica software. The effects of variation in the parameter of non-idealness of the gas, the gravitation parameter, the strength of the ambient magnetic field and the adiabatic index of the gas on the shock wave, and on the flow variables is discussed. A comparative study between with and without gravitational field is also, made.FindingsFor different choices of the arbitrary constants that appeared in the solution of infinitesimal generators, we have obtained seven distinct cases of similarity solutions. In the absence of the gravitational field, the similarity solution exists to the power and exponential law shock paths, but in the presence of gravitational field, the similarity solution exists to the power law shock path case only. In the absence of gravitational field, the shock strength is enhanced in the exponential law shock path case in comparison to the power law shock path case. It is found that the shock wave decays with an increase in the value of the adiabatic exponent, the strength of magnetic field, non-idealness of the gas or gravitational parameter.Research limitations/implicationsThe consideration of medium under the influence of gravitational field due to a heavy nucleus at the center and presence of magnetic field decrease the shock strength. This result may be helpful in designing space vehicle and jet engine.Practical implicationsThe result of the present study may be used in the analysis of data from the measurements by space craft in the solar wind and in neighborhood of the Earth’s magnetosphere.Social implicationsThe obtained results may be used for mankind.Originality/valueThe study of spherical shock wave propagation influenced by monochromatic radiation and azimuthal magnetic field in a non-ideal gas with or without gravitational field has yet to be discussed by any authors by using the Lie group symmetry method. In this article, we have discussed all possible cases of similarity solutions using the Lie group symmetry method, which is not studied by anyone as known to us.

Motility and pairwise interactions of chemically active droplets in one-dimensional confinement.

Self-propelled droplets serve as ideal model systems to delve deeper into understanding the motion of biological microswimmers by simulating their motility. Biological microorganisms are renowned for showcasing a diverse array of dynamic swimming behaviors when confronted with physical constraints. This study aims to elucidate the impact of physical constraints on swimming characteristics of biological microorganisms. To achieve this, we present observations on the individual and pairwise behavior of micellar solubilized self-propelled 4-cyano-4'-pentyl-biphenyl (5CB) oil droplets in a square capillary channel filled with a surfactant trimethyl ammonium bromide aqueous solution. To explore the effect of the underlying Péclet number of the swimming droplets, the study is also performed in the presence of additives such as high molecular weight polymer polyethylene oxide and molecular solute glycerol. The capillary confinement restricts droplet to predominantly one-dimensional motion, albeit with noticeable differences in their motion across the three scenarios. Through a characterization of the chemical and hydrodynamic flow fields surrounding the droplets, we illustrate that the modification of the droplets' chemical field due to confinement varies significantly based on the underlying differences in the Péclet number in these cases. This alteration in the chemical field distribution notably affects the individual droplets' motion. Moreover, these distinct chemical field interactions between the droplets also lead to variations in their pairwise motion, ranging from behaviors like chasing to scattering.

Anomalous scalings of fluctuations of the area swept by a Brownian particle trapped in a [formula omitted] potential

We study the fluctuations of the area A=∫0Tx(t)dt under a one-dimensional Brownian motion x(t) in a trapping potential ∼|x|, at long times T→∞. We find that typical fluctuations of A follow a Gaussian distribution with a variance that grows linearly in time (at large T), as do all higher cumulants of the distribution. However, large deviations of A are not described by the “usual” scaling (i.e., the large deviations principle), and are instead described by two different anomalous scaling behaviors: Moderately-large deviations of A, obey the anomalous scaling PA;T∼e−T1/3fA/T2/3 while very large deviations behave as PA;T∼e−TΨA/T2. We find the associated rate functions f and Ψ exactly. Each of the two functions contains a singularity, which we interpret as dynamical phase transitions of the first and third order, respectively. We uncover the origin of these striking behaviors by characterizing the most likely scenario(s) for the system to reach a given atypical value of A. We extend our analysis by studying the absolute area B=∫0T|x(t)|dt and also by generalizing to higher spatial dimension, focusing on the particular case of three dimensions.

Independent-oscillator model and the quantum Langevin equation for an oscillator: a review

This review provides a brief and quick introduction to the quantum Langevin equation for an oscillator, while focusing on the steady-state thermodynamic aspects. A derivation of the quantum Langevin equation is carefully outlined based on the microscopic model of the heat bath as a collection of a large number of independent quantum oscillators, the so-called independent-oscillator model. This is followed by a discussion on the relevant ‘weak-coupling’ limit. In the steady state, we analyze the quantum counterpart of energy equipartition theorem which has generated a considerable amount of interest in recent literature. The free energy, entropy, specific heat, and third law of thermodynamics are discussed for one-dimensional quantum Brownian motion in a harmonic well. Following this, we explore some aspects of dissipative diamagnetism in the context of quantum Brownian oscillators, emphasizing upon the role of confining potentials and also upon the environment-induced classical-quantum crossover. We discuss situations where the system-bath coupling is via the momentum variables by focusing on a gauge-invariant model of momentum-momentum coupling in the presence of a vector potential; for this problem, we derive the quantum Langevin equation and discuss quantum thermodynamic functions. Finally, the topic of fluctuation theorems is discussed (albeit, briefly) in the context of classical and quantum cyclotron motion of a particle coupled to a heat bath.

Memory effects in colloidal motion under confinement and driving

The transport of individual particles in inhomogeneous environments is complex and exhibits non-Markovian responses. The latter may be quantified by a memory function within the framework of the linear generalised Langevin equation (GLE). Here, we exemplify the implications of steady driving on the memory function of a colloidal model system for Brownian motion in a corrugated potential landscape, specifically, for one-dimensional motion in a sinusoidal potential. To this end, we consider the overdamped limit of the GLE, which is facilitated by separating the memory function into a singular (Markovian) and a regular (non-Markovian) part. Relying on exact solutions for the investigated model, we show that the random force entering the GLE must display a bias far from equilibrium, which corroborates a recent general prediction. Based on data for the mean-square displacement (MSD) obtained from Brownian dynamics simulations, we estimate the memory function for different driving strengths and show that already moderate driving accelerates the decay of the memory function by several orders of magnitude in time. We find that the memory may persist on much longer timescales than expected from the convergence of the MSD to its long-time asymptote. Furthermore, the functional form of the memory function changes from a monotonic decay to a non-monotonic, damped oscillatory behaviour, which can be understood from a competition of confined motion and depinning. Our analysis of the simulation data further reveals a pronounced non-Gaussianity, which questions the Gaussian approximation of the random force entering the GLE.

Wigner Analysis of Particle Dynamics and Decoherence in Wide Nonharmonic Potentials

We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting for both the classical dynamics of the centroid of the initial state and the rotation and squeezing about that trajectory. Subsequently, we employ two crucial approximations, namely the constant-angle and linearized-decoherence approximations, upon which our results rely. These approximations are effective in the regime of wide potentials and small fluctuations, namely potentials that enable spatial expansions orders of magnitude larger than the one of the initial state but that remain smaller compared to the relevant dynamical length scale (e.g., the distance between turning points). Our analytical result elucidates the interplay between classical and quantum physics and the impact of decoherence during nonlinear dynamics. This analytical result is instrumental to designing, optimizing, and understanding proposals using nonlinear dynamics to generate macroscopic quantum states of massive particles.

Estimating the Minimum Possible Deceleration of Cosmic Expansion Post-inflation

The inflationary epoch, occurring shortly after the Big Bang, initiated an extraordinarily rapid exponential expansion of the universe. Following this period, the rate of cosmic expansion decelerated for approximately 9.8 billion years, until observations indicated a transition to an accelerated expansion of space-time. This paper aims to estimate the minimum possible deceleration of cosmic expansion during the post-inflationary epoch, addressing an unresolved aspect of cosmological studies. The observable universe is modeled as a spherical region defined by the particle horizon in the FLRW metric. The model operates on the principle that the speed of light cannot exceed the speed of space-time expansion, given that photons are bound by space-time constraints. This paper hypothesizes that at the end of the 9.8 billion years of deceleration, the expansion speed was at its lowest, nearly equating to the speed of light. Subsequently, this speed has increased, correlating with the current accelerated expansion. Through a graphical representation assuming a uniform rate of change in expansion speed (for minimum possible values), we apply concepts of onedimensional motion to derive our estimates. This novel approach provides a foundational calculation of the minimum deceleration, significantly contributing to the understanding of the dynamics of cosmic expansion and offering a basis for future research and observational refinement.

Design and analysis of a new deployable articulated mast mechanism with two-dimensional deploying-folding motion

Abstract A traditional deployable articulated mast mechanism can only provide one-dimensional (1D) deploying-folding motion. This paper aims to investigate the design and analysis of a novel deployable articulated mast mechanism with two-dimensional (2D) deploying-folding motion. Firstly, the topological motion of deployable mast mechanisms can provide 2D deploying-folding motion is analyzed, and a potential rectangular prism linkage unit is presented to construct single degree-of-freedom (DOF) deployable mast mechanisms with 2D deploying-folding motion. Secondly, the kinematics of the new deployable mast mechanism is established based on its structural symmetry and modular features. Thirdly, the deploying dynamics of the new mechanism are built based on the Lagrange equation. Fourthly, the deployed/folded ratio, interference and singularity of the new mechanism are analyzed. Finally, a numerical example is used to illustrate the effectiveness of the theoretical analysis, and a physical prototype is developed to show the fabrication feasibility of the new deployable mechanism. Compared with the traditional counterparts with 1D deploying-folding motion, the new deployable mast mechanism has a larger deployed/folded ratio, which has a good application prospect in space missions to support solar arrays, magnetometers, cameras and antennas.

Dynamics and wave analysis in longitudinal motion of elastic bars or fluids

We look at the bifurcation analysis, chaotic behavior, multistability, and sensitivity analysis of the van der Waals equation, which is used in science and engineering to study the dynamics of various structures. The variant van der Waals equation covers one-dimensional longitudinal isothermal motion in elastic bars or fluids, which is the main focus of this research. The Galilean transformation transfers the given model into a planar dynamical system. The power series methodology produces exact wave solutions. In addition, after accounting for the perturbation component, sensitivity analysis for various initial value problems is used to investigate quasi-periodic, chaotic, and time series behavior. Numerical simulation results show that influencing viscosity and the coefficient of interfacial capillarity influence the dynamical factors of the examined model. We are observing what happens with viscosity and the interface coefficients to the wave solution. In some cases, for different parameter values, we present plots of both one-dimensional and two-dimensional graphical representations of individual solutions.

Assessing sand sedimentation in drilling slurry using particle methods for ground excavation management

In the construction of cast-in-place concrete piles, residual sand portions in the drilling slurry that are not completely removed can significantly influence the strength and characteristics of the concrete piles. Understanding the sedimentation behavior of these sand portions during concrete placement is crucial to ensure pile quality. However, directly observing this process in real-time at construction sites is challenging, making it difficult to accurately assess the impact of the sand portions. When predicting the sedimentation of sand particles in drilling slurry, the conventionally used Stokes' equation can only express one-dimensional motion of a single particle size, but to accurately capture the real phenomenon, three-dimensional behavior must be considered. In this study, a numerical simulation method based on the particle method (MPS method) was used to visually evaluate the sedimentation process of sand in the drilling slurry. By modeling the drilling slurry and sand particles using the MPS method, the complex three-dimensional settling behavior of sand particles in the drilling slurry at both laboratory and full scales was successfully represented, demonstrating the effectiveness of this modeling approach. The MPS method allows for the analytical visualization of the three-dimensional sedimentation behavior, enabling real-time observation and quantitative evaluation of the sand sedimentation process. Using this method, the temporal evolution of the settling process of sand components in the drilling slurry can be tracked, providing valuable insights into factors that influence the quality of concrete piles. The results of this study demonstrate the potential of the MPS method for visually evaluating the settling behavior of sand components in drilling slurry. This approach offers a more accurate and reliable method for assessing the impact of residual sand on the strength and characteristics of cast-in-place concrete piles. By enhancing the understanding of this process, more effective foundation techniques can be developed to improve the safety and stability of structures built on soft ground, particularly in earthquake-prone regions where fine particles such as clay and silt pose additional challenges to construction practices.

Quantitative in-situ investigation of dislocation loop motion in Fe9Cr1.5W ferritic/martensitic steel under the coupling effects of constant stress and irradiation

Dislocation loop motion plays an important role in irradiation creep but their dynamic evolution is hardly investigated. In this work, the one-dimensional motion of loops was investigated by in-situ TEM in Fe9Cr1.5W ferritic/martensitic steel under the combination of irradiation and constant compression stress and compared with the case of irradiation only to highlight the synergistic effect. Loops preferred to glide along one side that was close to the compression direction and the other side was retarded.. The proportion of large mobile loops was also increased. Jump frequency was doubled after the addition of compression, indicating the high sensitivity to stress.

Optimized raw data selection for artifact reduction of breathing controlled four-dimensional sequence scanning

Background and purposeEven with most breathing-controlled four-dimensional computed tomography (4DCT) algorithms image artifacts caused by single significant longer breathing still occur, resulting in negative consequences for radiotherapy. Our study presents first phantom examinations of a new optimized raw data selection and binning algorithm, aiming to improve image quality and geometric accuracy without additional dose exposure. Materials and methodsTo validate the new approach, phantom measurements were performed to assess geometric accuracy (volume fidelity, root mean square error, Dice coefficient of volume overlap) for one- and three-dimensional tumor motion trajectories with and without considering motion hysteresis effects. Scans without significantly longer breathing cycles served as references. ResultsMedian volume deviations between optimized approach and reference of at maximum 1% were obtained considering all movements. In comparison, standard reconstruction yielded median deviations of 9%, 21% and 12% for one-dimensional, three-dimensional, and hysteresis motion, respectively. Measurements in one- and three-dimensional directions reached a median Dice coefficient of 0.970 ± 0.013 and 0.975 ± 0.012, respectively, but only 0.918 ± 0.075 for hysteresis motions averaged over all measurements for the optimized selection. However, for the standard reconstruction median Dice coefficients were 0.845 ± 0.200, 0.868 ± 0.205 and 0.915 ± 0.075 for one- and three-dimensional as well as hysteresis motions, respectively. Median root mean square errors for the optimized algorithm were 30 ± 16HU2 and 120 ± 90HU2 for three-dimensional and hysteresis motions, compared to 212 ± 145HU2 and 130 ± 131HU2 for the standard reconstruction. ConclusionsThe algorithm was proven to reduce 4DCT-related artifacts due to missing projection data without further dose exposure. An improvement in radiotherapy treatment planning due to better image quality can be expected.

Asymptotic Behavior of the Solution to the Initial-boundary Value Problem for One-dimensional Motions of a Barotropic Compressible Viscous Multifluid

Asymptotic Behavior of the Solution to the Initial-boundary Value Problem for One-dimensional Motions of a Barotropic Compressible Viscous Multifluid

Self-propelled object that generates a boundary with amphiphiles at an air/aqueous interface

A benzoic acid (BA) disk was investigated as a novel self-propelled object whose driving force was the difference in surface tension. 4-Stearoyl amidobenzoic acid (SABA) was synthesized as an amphiphile to control the nature of motion based on intermolecular interactions between BA and SABA. The BA disk exhibited characteristic motion depending on the surface density of the SABA on the aqueous phase, that is, reciprocating motion as a one-dimensional motion and restricted and unrestricted motion as a two-dimensional motion. The trajectory of the reciprocating motion was determined by the initial direction of motion, and the boundary between an aqueous surface and the BA-SABA condensed molecular layer was used as the field’s boundary. The presented results indicate that the characteristic nature of motion can be designed at the molecular level based on the intermolecular interactions between an energy-source molecule and an amphiphile.

Graph plotting of 1-D motion in introductory physics education using scripts generated by ChatGPT 3.5

Introductory physics courses often necessitate students to graphically represent one-dimensional (1-D) motion and derive various physical parameters. Physical quantities are often solved by calculating either slope or the area under the graph. Instructors and students who do not have access to paid software must plot graphs by hand. This paper explores three introductory physics examples related to 1-D motion, and employs ChatGPT 3.5 to generate scripts that will produce graphs from raw data. It can generate scripts, based on accurate user inputs, in free programming languages like Python and/or GNU Octave to enable efficient graph plotting. Examples will be provided on calculating the slope of a distance–time graph and determining the area under a velocity–time graph. Given raw data, ChatGPT 3.5 may exhibit occasional inaccuracies when solving for physical parameters. However, user can communicate in English to modify the output. The author does not endorse the use of ChatGPT for academic misconducts such as assisting students to cheat in problem solving. Instead, ChatGPT is presented as a tool to enhance data visualisation for both instructors and students, which can potentially improve learning environments in introductory physics. This paper lays the groundwork for future initiatives, beyond the plotting of 1-D motion graphs, aiming to integrate artificial intelligence to assist more complex motion studies in physics learning environments.

Evaluation of weak discontinuity in rotating medium with magnetic field, characteristic shock and weak discontinuity interaction

Abstract In this article we investigated the characteristic shock and weak discontinuity wave in a rotating medium of perfect gas in the case of one-dimensional (1-D) adiabatic motion under an axial magnetic field governed by the system of PDEs (partial differential equations). We have obtained some classes of analytical solutions of the system of PDEs that demonstrates the time-space dependency. With change in the values of rotational parameter, adiabatic index and the ratio of initial magnetic pressure to dynamic pressure, effect on the acceleration wave’s amplitude and jump in the flow variables across the characteristic shock is analyzed in detail. We have obtained an expression for the jump in shock acceleration, the amplitudes of transmitted and reflected waves caused by the incident wave on the characteristic shock after the interaction of a weak discontinuity. It is investigated that the jump function across the characteristic shock decay effect, and goes to 0 as time t → ∞, whereas a weak discontinuity wave may culminate into a shock wave, depending on the initial amplitude value. It is also found that the shock formation time reduces due to the consideration of magnetic field or rotating medium.

The convergence rate of the equilibrium measure for the hybrid LQG Mean Field Game

In this work, we study the convergence rate of the N-player Linear-Quadratic-Gaussian (LQG) game with a Markov chain common noise towards its asymptotic Mean Field Game. By postulating a Markovian structure via two auxiliary processes for the first and second moments of the Mean Field Game equilibrium and applying the fixed point condition in Mean Field Game, we first provide the characterization of the equilibrium measure in Mean Field Game with a finite-dimensional Riccati system of ODEs. Additionally, with an explicit coupling of the optimal trajectory of the N-player game driven by N dimensional Brownian motion and Mean Field Game counterpart driven by one-dimensional Brownian motion, we obtain the convergence rate O(N−1/2) with respect to 2-Wasserstein distance.

Ergodic properties of Brownian motion under stochastic resetting.

We study the ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin- or fat-tailed distributions the normalized or non-normalized invariant density of this process. The former case corresponds to known results in the resetting literature and the latter to infinite ergodic theory. Two types of ergodic transitions are found in this system. The first is when the mean waiting time between resets diverges, when standard ergodic theory switches to infinite ergodic theory. The second is when the mean of the square root of time between resets diverges and the properties of the invariant density are drastically modified. We then find a fractional integral equationdescribing the density of particles. This finite time tool is particularly useful close to the ergodic transition where convergence to asymptotic limits is logarithmically slow. Our study implies rich ergodic behaviors for this nonequilibrium process which should hold far beyond the case of Brownian motion analyzed here.

Existence and Uniqueness Theorem of Fuzzy Stochastic Ordinary Differential Equations

A fuzzy valued diffusion term, which in a fuzzy stochastic differential equation refers to one-dimensional Brownian motion, is defined by the meaning of the stochastic integral of a fuzzy process. In this paper, the existence and uniqueness theorem of fuzzy stochastic ordinary differential equations, based on the mean square convergence of the mathematical induction approximations to the associated stochastic integral equation, are stated and demonstrated.