Trajectories In Space Research Articles

Towards Modelling Mechanical Shaking Using Potential Energy Surfaces: A Toy Model Analysis

In this work, we formalize the effect of mechanical shaking by using various forms of an externally exerted force, which may be constant or may be position-dependent, and we examine the changes in the potential energy surfaces that quantify the chemical reaction. We use a simple toy model to model the potential energy surfaces of a chemical reaction, and we study the effect of a constant or position-dependent externally exerted force for various forms of the force. As we demonstrate, the effect of the force can be quite dramatic on the potential energy surfaces, which acquire new stationary points and new Newton trajectories that are distinct from the original ones that were obtained in the absence of mechanochemical effects. We also introduce a new approach to mechanochemical interactions, using a dynamical systems approach for the Newton trajectories. As we show, the dynamical system attractor properties of the trajectories in the phase space are identical to the stationary points of the potential energy surfaces, but the phase space contains much more information regarding the possible evolution of the chemical reaction—information that is quantified by the existence of unstable or saddle fixed points in the phase space. We also discuss how an experimental method for a suitable symmetric liquid solution substance might formalize the effect of shaking via various forms of external force, even in the form of an extended coordinate-dependent force matrix. This approach may experimentally quantify the Epstein effect of shaking in chemical solutions via mechanochemistry methods.

Arbitrary engineering of spatial caustics with 3D-printed metasurfaces

Caustics occur in diverse physical systems, spanning the nano-scale in electron microscopy to astronomical-scale in gravitational lensing. As envelopes of rays, optical caustics result in sharp edges or extended networks. Caustics in structured light, characterized by complex-amplitude distributions, have innovated numerous applications including particle manipulation, high-resolution imaging techniques, and optical communication. However, these applications have encountered limitations due to a major challenge in engineering caustic fields with customizable propagation trajectories and in-plane intensity profiles. Here, we introduce the “compensation phase” via 3D-printed metasurfaces to shape caustic fields with curved trajectories in free space. The in-plane caustic patterns can be preserved or morphed from one structure to another during propagation. Large-scale fabrication of these metasurfaces is enabled by the fast-prototyping and cost-effective two-photon polymerization lithography. Our optical elements with the ultra-thin profile and sub-millimeter extension offer a compact solution to generating caustic structured light for beam shaping, high-resolution microscopy, and light-matter-interaction studies.

Experimental study on the disturbance of microbubble liquid jets

The presence of microbubble significantly influences the rheological properties of a jet, thereby considerably increasing the complexity of the jet instability problem. However, the instability of microbubble jets has been rarely studied, and their breakup mechanism remains obscure. The present study was focused on conducting a comprehensive analysis of bubble jet flows. A high-precision experimental system was constructed to extract the time-series signals of each cross-sectional profile along the axial direction of a jet. Glycerol solutions with three different bubble volume fractions were prepared, and the standard deviation, spectral relationship, and nonlinear dynamical behavior (i.e., autocorrelation, phase space trajectory, Poincaré section, and Lyapunov exponent) were studied. The detailed development process of small surface disturbances in space was assessed, and the influence of variations in the bubble volume fraction on the nonlinear dynamics of the jet was examined. The results demonstrate that microbubbles can significantly change the energy transfer relationship between various sections of a jet and enhance the periodicity of the signal.

Anisotropic dark energy from string compactifications

We explore the cosmological dynamics of a minimalistic yet generic string-inspired model for multifield dark energy. Adopting a supergravity four-dimensional viewpoint, we motivate the model’s structure arising from superstring compactifications involving a chiral superfield and a pure U(1) gauge sector. The chiral sector gives rise to a pair of scalar fields, such as the axio-dilaton, which are kinetically coupled. However, the scalar potential depends on only one of them, further entwined with the vector field through the gauge kinetic function. The model has two anisotropic attractor solutions that, despite a steep potential and thanks to multifield dynamics, could explain the current accelerated expansion of the Universe while satisfying observational constraints on the late-times cosmological anisotropy. Nevertheless, justifying the parameter space allowing for slow roll dynamics together with the correct cosmological parameters, would be challenging within the landscape of string theory. Intriguingly, we find that the vector field, particularly at one of the studied fixed points, plays a crucial role in enabling geodesic trajectories in the scalar field space while realizing slow-roll dynamics with a steep potential. This observation opens a new avenue for exploring multifield dark energy models within the superstring landscape.

Time-optimal coordinated detumbling and pose adjusting control of a non-cooperative target with model uncertainties

In this paper, a novel post-capture takeover control strategy of non-cooperative target with model uncertainties by the dual-arm space manipulator is proposed. Two mission objectives of target detumbling and pose adjusting are comprehensively considered. First, the motion trajectory of the target is parameterized with normalized time by a Bezier shape-based function. On this basis, by considering the resultant external force and moment constraint and the model uncertainties of the target, the mission duration is optimized to obtain the time optimal detumbling and pose adjusting the trajectory of the target. Furthermore, the desired trajectory in manipulator joint space is obtained by introducing the arm angle inverse kinematics method, and a joint trajectory tracking controller is designed based on the feedback linearization theory to track the desired joint trajectory. Simulation results show that detumbling and pose adjusting can be simultaneously achieved by one control action, which verifies the effectiveness of the proposed integrated control strategy.

Spatio‐temporal attention modules in orientation‐magnitude‐response guided multi‐stream CNNs for human action recognition

AbstractThis paper introduces a new descriptor called orientation‐magnitude response maps as a single 2D image to effectively explore motion patterns. Moreover, boosted multi‐stream CNN‐based model with various attention modules is designed for human action recognition. The model incorporates a convolutional self‐attention autoencoder to represent compressed and high‐level motion features. Sequential convolutional self‐attention modules are used to exploit the implicit relationships within motion patterns. Furthermore, 2D discrete wavelet transform is employed to decompose RGB frames into discriminative coefficients, providing supplementary spatial information related to the actors actions. A spatial attention block, implemented through the weighted inception module in a CNN‐based structure, is designed to weigh the multi‐scale neighbours of various image patches. Moreover, local and global body pose features are combined by extracting informative joints based on geometry features and joint trajectories in 3D space. To provide the importance of specific channels in pose descriptors, a multi‐scale channel attention module is proposed. For each data modality, a boosted CNN‐based model is designed, and the action predictions from different streams are seamlessly integrated. The effectiveness of the proposed model is evaluated across multiple datasets, including HMDB51, UTD‐MHAD, and MSR‐daily activity, showcasing its potential in the field of action recognition.

Target location method of intelligent deicing robot based on nonlinear auto disturbance rejection neural network

A visual navigation scheme for intermittent walking deicing robots was designed to address the issues of multiple iterations, long computation time, and poor real-time performance in the nonlinear optimization of the original SLAM system. A computer image acquisition unit, a computer image processing module, and a visual navigation parameter extraction algorithm were also designed. Implemented a visual navigation system for deicing robots based on image processing. It can meet the navigation requirements of the deicing robot. Simulation and experiments have shown that the method proposed in this paper can quickly and accurately identify abnormal point clouds. The visual servo control scheme constructed in this paper is aimed at robot task operations with unknown system calibration and target depth information. By calibrating the robot vision system, the conversion between camera pixel coordinates and robot base coordinates is achieved, with a transmission frame rate of 53.65 per second; The maximum error in positioning accuracy in space is 10.6 mm. The feature trajectory of visual space is smooth and stable within the camera's field of view, and the end movement of Cartesian space robots is stable without rebound, resulting in high grasping and positioning accuracy.

Constructing a non-degeneracy nD chaotic map model and counteracting dynamic degradation through adaptive impulsive perturbation

The characteristics of state point trajectory in phase space of a chaotic map, such as ergodicity, aperiodicity, broadband and noise-like, have been proved to be suitable for cryptography. However, some weaknesses, such as small key space, multiple bifurcations and dense windows that exist in some classic 1D and 2D chaotic maps, effect their practical application. To solve these problems, we constructed a non-degeneracy nD chaotic model, and instantiated it to obtain a 3D chaotic map (3D-NDCM), the dynamics analysis results demonstrated that the 3D-NDCM has a sufficiently large chaotic range, its state point trajectories has ergodicity in phase space. To counteract dynamic degradation and extend the aperiodic length of state time sequences, we further constructed a 6D-NDCM based on the model. Experimental analysis results demonstrated that, a state time sequence with longer aperiodicity can be obtained, through both dimension expansion and adaptive impulsive perturbation.

Unlocking Urban Accessibility: Proximity Analysis in Bangkok, Thailand’s Mega City

Accessibility serves as the fundamental link for mode shifts, enabling access to activity areas and facilitating connections to other forms of travel. However, navigating the transportation network in urban areas of Bangkok, Thailand, reveals persistent inconveniences, discomfort, and safety concerns, thereby failing to adequately meet the needs of users. This study aims to examine urban accessibility, focusing on multi-travel connections to amenities and public transport. It focuses on understanding how the level of engagement of road users in social activities contributes to well-being by addressing proximity access through a multidisciplinary approach aimed at enhancing accessibility and integrating the built environment. The comprehensive and inclusive Accessibility by Proximity Index (API) is proposed as a tool to evaluate the level of access to essential services and activities for residents. Additionally, this study acknowledges the impact of the physical and utilization characteristics of urban space and active trajectories by considering various travel needs and daily route patterns. Consequently, the API can inform the development of planning and urban design strategies aimed at enhancing walkability and cycling as non-motorization infrastructures, thereby improving accessibility through active modes of transportation. It was observed that areas with a higher concentration of urban amenities exhibit greater accessibility by walking, cycling, and public transport, particularly in inner-city areas. Thus, envisioning a more sustainable and inclusive city with adequate development of public transportation access is essential in urban areas, prompting policy-level initiatives to enhance the environment and elevate the overall commuting experience.

Dynamics of inspiraling dark energy

We investigate the dynamics of a multifield dark energy model, which arises from certain rapid-turning and inspiraling trajectories in field space. We find the speed of sound cs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s$$\\end{document} of the dark energy perturbations around the background and show that cs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_s$$\\end{document} is monotonically decreasing with time. Furthermore, it has a positive-definite lower bound that implies a certain clustering scale. We also extend the previously known background solution for dark energy to an exact solution that includes matter. This allows us to address the implications of our model for two cosmological tensions. More precisely, we argue that the σ8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _8$$\\end{document} tension can be alleviated generically, while reducing the Hubble tension requires certain constraints on the parameter space of the model. Notably, a necessary condition for alleviating the Hubble tension is that the transition from matter domination to the dark energy epoch begins earlier than in Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM.

A Formal Model of Affiliative Interpersonality

Capturing the complexity of interpersonal dynamics—emerging from approach and avoidance motives of two individuals in dyadic interplay—remains challenging. In line with calls for embracing complexity in psychological research using formal modeling, we employed evolutionary game theory to investigate the underlying mechanisms of affiliative interpersonality. We constructed a relational state space that represents the ways of relating available in the momentary state of an interpersonal relationship. Next, we modeled relationships as trajectories in that relational space. Qualitatively different interpersonal dynamics emerged: (a) global stability with only one relational attractor (e.g., pure reciprocal friendliness), (b) bistability with two mutually exclusive attractors (e.g., either pure friendliness or pure distance), and (c) cycles between friendliness and distance in the relational space. The bistable dynamics appear to resemble the phenomenon of interpersonal complementarity (e.g., friendliness invites friendliness). Furthermore, the model generates psychopathologically relevant dynamics (e.g., oscillating, unstable interpersonal relationships in borderline personality disorder).

Effective data-driven collective variables for free energy calculations from metadynamics of paths.

A variety of enhanced sampling (ES) methods predict multidimensional free energy landscapes associated with biological and other molecular processes as a function of a few selected collective variables (CVs). The accuracy of these methods is crucially dependent on the ability of the chosen CVs to capture the relevant slow degrees of freedom of the system. For complex processes, finding such CVs is the real challenge. Machine learning (ML) CVs offer, in principle, a solution to handle this problem. However, these methods rely on the availability of high-quality datasets-ideally incorporating information about physical pathways and transition states-which are difficult to access, therefore greatly limiting their domain of application. Here, we demonstrate how these datasets can be generated by means of ES simulations in trajectory space via the metadynamics of paths algorithm. The approach is expected to provide a general and efficient way to generate efficient ML-based CVs for the fast prediction of free energy landscapes in ES simulations. We demonstrate our approach with two numerical examples, a 2D model potential and the isomerization of alanine dipeptide, using deep targeted discriminant analysis as our ML-based CV of choice.

INVESTIGATION OF STABILITY OF NONLINEAR NORMAL MODES OF DISSIPATIVE SYSTEM OSCILLATIONS UNDER INFLUENCE OF MAGNETIC FIELD

In the paper the dynamics of the vibrating system consisting of two pendulums connected by elastic coupling and located in a magnetic field is studied. A case is considered when masses of the pendulums differ significantly. Under the influence of various external factors, such as magnetic forces and loads, which are present in engineering systems, the analysis of vibration regimes in non-linear systems becomes more complex. Here the nonlinear normal connected vibration mode in a system under consideration is analyzed. We have investigated the influence of changes in system parameters on the vibra- tion mode for both small and large initial angles of the pendulum deflection. Both the analytical method, namely, the method of many scales, and nu- merical simulations based on the fourth order Runge – Kutta method are used to analyze the vibration regimes. The initial conditions used to calculate this mode were determined analytically. The simulation includes construction of phase diagrams, trajectories in configuration space, and spectra, which allows us to evaluate the system dynamics, including both regular and complex regimes of vibrations. To study the stability of the vibration mode, a numerical-analytical method associated with the Lyapunov stability criterion is used. The stability of the mode is determined by assessing orthogonal deviations with respect to the corresponding modal trajectories in the configuration space. Regions of instability on planes and in the space of the system parameters are obtained.

A two-stage Duffing equation-based oscillator and stochastic resonance for mechanical fault diagnosis

Incipient fault-induced weak impulses will not be detected easily using the existing fault extraction methods. Stochastic resonance can flexibly use noises to enhance the signal-to-noise ratio, but it lacks the ability of anti-interference to obtain robustness and reliability fault detection performance. A two-stage method is presented to diagnose faults in mechanical components. The first is to judge the fault existence according to the characteristics of the phase space trajectory diagram of the Duffing oscillator. The second is to employ stochastic resonance method based on the Duffing equation to improve the signal-to-noise ratio of the raw signal, in which the two barrier parameters in the Duffing equation-based bistable system are carefully selected using the artificial bee colony algorithm. In the present two-stage method, the existence of faults and further the fault types in mechanical components are stepwise detected to make full usages of the advantages of Duffing oscillator and Duffing equation-based stochastic resonance method. Numerical simulations and two experimental cases verify the performance of the proposed method for mechanical components fault detection in a strong noise environment.

An alternative EMG normalization method: Heterogeneous recurrence quantification analysis of isometric maximum voluntary contraction movements

This study presents an alternative method of normalizing Surface Electromyography (EMG) signals, which provide valuable insights into the musculoskeletal properties of the human body. Traditional normalization through the peak maximum voluntary contraction (MVC) method may result in variable outcomes due to its dependence on pre-processing steps such as smoothing and window length. To address this issue, the study standardizes the EMG pre-processing steps by using non-linear techniques, namely recurrence quantification analysis (RQA) and heterogeneous RQA (HRQA). RQA, specifically HRQA, functions as EMG feature extractors to explore the nonlinear dynamical system and state space trajectories of chaotic EMG signals. Principal component analysis (PCA) and kernel PCA (KPCA) were further applied to the RQA and HRQA results to obtain data with more information. The results show that the first principal components (PC1 and KPC1) of HRQA have a very strong relationship with peak MVC (ρ > |0.90|, p < 0.001), indicating their potential compared to the traditional EMG normalization technique for lower limb muscle groups. Additionally, the study investigated the dynamic differences among isometric MVC movements in lower limb muscle groups and found that the RQA and HRQA methods indicated a greater separation for detecting these differences compared to peak MVC. This study offers a valuable method for assessing the musculoskeletal characteristics of individuals who may have difficulty with activities like walking or providing maximum force during EMG data collection, such as those suffering from Parkinson's disease or walking disabilities. This enhances our understanding of their musculoskeletal properties.

Enhanced Sampling of Configuration and Path Space in a Generalized Ensemble by Shooting Point Exchange.

The computer simulation of many molecular processes is complicated by long timescales caused by rare transitions between long-lived states. Here, we propose a new approach to simulate such rare events, which combines transition path sampling with enhanced exploration of configuration space. The method relies on exchange moves between configuration and trajectory space, carried out based on a generalized ensemble. This scheme substantially enhances the efficiency of the transition path sampling simulations, particularly for systems with multiple transition channels, and yields information on thermodynamics, kinetics and reaction coordinates of molecular processes without distorting their dynamics. The method is illustrated using the isomerization of proline in the KPTP tetrapeptide.

From the classical Frenet–Serret apparatus to the curvature and torsion of quantum-mechanical evolutions. Part II. Nonstationary Hamiltonians

In this paper, we present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying curvature and torsion coefficients play a key role. Specifically, we present a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced out by a parallel-transported pure quantum state evolving unitarily under a time-dependent Hamiltonian specifying the Schrödinger evolution equation. The time-varying curvature coefficient is specified by the magnitude squared of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text] and measures the bending of the quantum curve. The time-varying torsion coefficient, instead, is given by the magnitude squared of the projection of the covariant derivative of the tangent vector [Formula: see text] to the state vector [Formula: see text], orthogonal to [Formula: see text] and [Formula: see text] and, in addition, measures the twisting of the quantum curve. We find that the time-varying setting exhibits a richer structure from a statistical standpoint. For instance, unlike the time-independent configuration, we find that the notion of generalized variance enters nontrivially in the definition of the torsion of a curve traced out by a quantum state evolving under a nonstationary Hamiltonian. To physically illustrate the significance of our construct, we apply it to an exactly soluble time-dependent two-state Rabi problem specified by a sinusoidal oscillating time-dependent potential. In this context, we show that the analytical expressions for the curvature and torsion coefficients are completely described by only two real three-dimensional vectors, the Bloch vector that specifies the quantum system and the externally applied time-varying magnetic field. Although we show that the torsion is identically zero for an arbitrary time-dependent single-qubit Hamiltonian evolution, we study the temporal behavior of the curvature coefficient in different dynamical scenarios, including off-resonance and on-resonance regimes and, in addition, strong and weak driving configurations. While our formalism applies to pure quantum states in arbitrary dimensions, the analytic derivation of associated curvatures and orbit simulations can become quite involved as the dimension increases. Thus, finally we briefly comment on the possibility of applying our geometric formalism to higher-dimensional qudit systems that evolve unitarily under a general nonstationary Hamiltonian.

Analyzing the spatial motion of a rigid body subjected to constant body-fixed torques and gyrostatic moment

This paper aims to explore the rotatory spatial motion of an asymmetric rigid body (RB) under constant body-fixed torques and a nonzero first component gyrostatic moment vector (GM). Euler's equations of motion are used to derive a set of dimensionless equations of motion, which are then proposed for the stability analysis of equilibrium points. Specifically, this study develops 3D phase space trajectories for three distinct scenarios; two of them are applied constant torques that are directed on the minor and major axes, while the third one is the action of applied constant torque on the body’s middle axis. Novel analytical and simulation results for both scenarios of constant torque applied along the minor and middle axes are provided in the context of separatrix surfaces, equilibrium manifolds, periodic or non-periodic solutions, and periodic solutions’ extreme. Concerning the scenario of a directed torque on the major axis, a numerical solution for the problem is presented in addition to a simulation of the graphed results for the angular velocities' trajectories in various regions. Moreover, the influence of GM is examined for each case and a full modeling for the body's stability has been present. The exceptional impact of these results is evident in the development and assessment of systems involving asymmetric RBs, such as satellites and spacecraft. It may serve as a motivating factor to explore different angles within the GM in similar cases, thereby influencing various industries, including engineering and astrophysics applications.

Understanding scholar-trajectories across scientific periodicals

Despite the rapid growth in the number of scientific publications, our understanding of author publication trajectories remains limited. Here we propose an embedding-based framework for tracking author trajectories in a geometric space that leverages the information encoded in the publication sequences, namely the list of the consecutive publication venues for each scholar. Using the publication histories of approximately 30,000 social media researchers, we obtain a knowledge space that broadly captures essential information about periodicals as well as complex (inter-)disciplinary structures of science. Based on this space, we study academic success through the prism of movement across scientific periodicals. We use a measure from human mobility, the radius of gyration, to characterize individual scholars' trajectories. Results show that author mobility across periodicals negatively correlates with citations, suggesting that successful scholars tend to publish in a relatively proximal range of periodicals. Overall, our framework discovers intricate structures in large-scale sequential data and provides new ways to explore mobility and trajectory patterns.

An exact model for enhancing/suppressing primordial fluctuations

Abstract Enhancements of primordial curvature fluctuations in single field inflation often involve departures from attractor trajectories in the phase space. We study enhancement/suppression of primordial fluctuations in one of the simplest models with exact background solutions for arbitrary initial conditions: a single field inflationary model with a piecewise exponential potential. We then present close to exact analytical solutions for primordial fluctuations in a general transition between two slow-roll attractors, valid whether the first slow parameter increases or decreases. The main features in the primordial spectrum are determined by the ratio of exponents of the potential. We also discuss the imprint of such features in the induced GW spectrum. Lastly, we apply the δN formalism to discuss non-Gaussianities and the tail of the probability distribution. We find that while non-Gaussianities are at most 𝒪(1) in the case of enhancement, they can be very large in the case of suppression. Our work can be easily generalized to multiple piecewise exponential potentials.