Description Of Motion Research Articles

Dynamic modeling method for constrained system with singular mass matrices

The dynamic model is beneficial for system control design, especially when it is related to precise force adjustment. Traditional modeling methods make it difficult to address multi-body systems with singular mass matrices or are computationally expensive. In this paper, an approach termed the Extended Rosenberg Embedding Method for dynamic modeling is presented. By incorporating the constraints directly into the Fundamental Equation, the proposed approach enables the description of the system motion in two separate equations, which can reduce the computational cost of the constrained dynamic model. This method provides a new way to establish motion equations, regardless of whether the system is subject to holonomic or non-holonomic constraints. Moreover, as the method does not impose direct requirements on the rank of the mass matrix, it is capable of handling the modeling of multi-body systems with singular mass matrices. The validity of the proposed method is substantiated through rigorous mathematical derivation, while its accuracy and computational efficiency are corroborated through the examination of two numerical examples.

Crowd Density Estimation via Global Crowd Collectiveness Metric

Drone-captured crowd videos have become increasingly prevalent in various applications in recent years, including crowd density estimation via measuring crowd collectiveness. Traditional methods often measure local differences in motion directions among individuals and scarcely handle the challenge brought by the changing illumination of scenarios. They are limited in their generalization. The crowd density estimation needs both macroscopic and microscopic descriptions of collective motion. In this study, we introduce a Global Measuring Crowd Collectiveness (GMCC) metric that incorporates intra-crowd and inter-crowd collectiveness to assess the collective crowd motion. An energy spread process is introduced to explore the related crucial factors. This process measures the intra-crowd collectiveness of individuals within a crowded cluster by incorporating the collectiveness of motion direction and the velocity magnitude derived from the optical flow field. The global metric is adopted to keep the illumination-invariance of optical flow for intra-crowd motion. Then, we measure the motion consistency among various clusters to generate inter-crowd collectiveness, which constitutes the GMCC metric together with intra-collectiveness. Finally, the proposed energy spread process of GMCC is used to merge the inter-crowd collectiveness to estimate the global distribution of dense crowds. Experimental results validate that GMCC significantly improves the performance and efficiency of measuring crowd collectiveness and crowd density estimation on various crowd datasets, demonstrating a wide range of applications for real-time monitoring in public crowd management.

Particle Virtual Element Method (PVEM): an agglomeration technique for mesh optimization in explicit Lagrangian free-surface fluid modelling

Explicit solvers are commonly used for simulating fast dynamic and highly nonlinear engineering problems. However, these solvers are only conditionally stable, requiring very small time-step increments determined by the characteristic length of the smallest, and often most distorted, element in the mesh. In the Lagrangian description of fluid motion, the computational mesh quickly deteriorates. To circumvent this problem, the Particle Finite Element Method (PFEM) creates a new mesh (e.g., through a Delaunay tessellation, based on node positions) when the current one becomes overly distorted. A fast and efficient remeshing technique is therefore of pivotal importance for an effective PFEM implementation in explicit dynamics. Unfortunately, the 3D Delaunay tessellation does not guarantee well-shaped elements, often generating zero- or near-zero-volume elements (slivers), which drastically reduce the stable time-step size. Available mesh optimization techniques have limited applicability due to their high computational cost when runtime remeshing is required. An innovative possibility to overcome this problem is the use of the Virtual Element Method (VEM), a variant of the finite element method that can make use of polyhedral elements of arbitrary shapes and number of nodes. This paper presents the formulation of a 3D first-order Particle Virtual Element Method (PVEM) for weakly compressible flows. Starting from a tetrahedral mesh, poorly shaped elements, such as slivers, are agglomerated to form polyhedral Virtual Elements (VEs) with a controlled characteristic length. This approach ensures full control over the minimum time-step size in explicit dynamics simulations, maintaining stability throughout the entire analysis.

Automatic Inbetweening for Stroke‐Based Painterly Animation

AbstractPainterly 2D animation, like the paint‐on‐glass technique, is a tedious task performed by skilled artists, primarily using traditional manual methods. Although CG tools can simplify the creation process, previous works often focus on temporal coherence, which typically results in the loss of the handmade look and feel. In contrast to cartoon animation, where regions are typically filled with smooth gradients, stroke‐based stylized 2D animation requires careful consideration of how shapes are filled, as each stroke may be perceived individually. We propose a method to generate intermediate frames using example keyframes and a motion description. This method allows artists to create only one image for every five to 10 output images in the animation, while the automatically generated intermediate frames provide plausible inbetween frames.

Shear-induced migration of rigid spheres in a Couette flow

Concentration inhomogeneities occur in many flows of non-Brownian suspensions. Their modeling necessitates the description of the relative motion of the particle phase and of the fluid phase, as well as the accounting for their interaction, which is the object of the suspension balance model (SBM). We systematically investigate the dynamics and the steady state of shear-induced migration in a wide-gap Couette flow for a wide range of particle volume fraction, and we test the ability of the SBM to account for the observations. We use a model suspension for which macroscopic particle stresses are known. Surprisingly, the observed magnitude of migration is much lower than that predicted by the SBM when the particle stress in the SBM is equated to the macroscopic particle stress. Another noteworthy observation is the quasi-absence of migration for semidilute suspensions. From the steady-state volume fraction profiles, we derive the local particle normal stress responsible for shear-induced migration according to the SBM. However, the observed dynamics of migration is much faster than that predicted by the SBM when using this stress in the model. More generally, we show that it is not possible to build a local friction law consistent with both the magnitude and the dynamics of migration within the standard SBM framework. This suggests that there is a missing term in the usual macroscopic constitutive law for the particle normal stress driving migration. The SBM is indeed capable of accurately predicting both the magnitude and the dynamics of migration when a tentative phenomenological term involving a concentration gradient is added to the particle normal stresses determined in macroscopic experiments.

A general multi-scale description of metastable adaptive motion across fitness valleys

We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph G=(V,E)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$G=(V,E)$$\\end{document}. The evolution is driven by a linear birth rate, a density dependent logistic death rate and the possibility of mutations along the directed edges in E. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between Bovier et al. (Ann Appl Probab 29(6):3541–358, 2019) and Coquille et al. (Electron J Probab 26:1–37, 2021) we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales, corresponding to the widths of these fitness valleys. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between them. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scales, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.

State-restricted adaptive control of a multilevel rotating electromagnetic mechanical flexible device using electromagnetic actuators

This work presents the development of a multilevel electromagnetic actuation system that controls the shape of a flexible rotatory robotic structure. An array of electromagnets is used as the set of actuators that regulate the position of permanent magnets within the flexible device. The primary outcome of this study is the design and experimental validation of the multilevel rotating device. In addition, the theoretical description of the system motion under electromagnetic actuation is formulated using Euler–Lagrange and electromagnetic theories. Given the developed model, a theoretical study leads to designing an adaptive control that considers motion restrictions in the flexible device. The controller aims to modify the current applied to the electromagnets, which changes the interaction forces between the electromagnet and the permanent magnets in the robotic flexible structure. A set of numerical simulations confirms the proposed controller’s effectiveness compared to the traditional state feedback approach that does not consider the state restrictions, which is implemented in devices that also operate under an electromagnetic approach. Furthermore, an experimental version of the flexible device allows for testing of the developed controller. The experimental results show the suitability of the proposed control to generate non-oscillatory controlled motion during the regulation of the flexible mechanic device shape.

Assessing the Accuracy of Quantum Dynamics Performed in the Time-Dependent Basis Representation.

A full quantum-mechanical (QM) description of large amplitude nuclear motion, associated with chemical reactions or isomerization of high-dimensional molecular systems, is inherently challenging due to the exponential scaling of the QM complexity with system size. To ameliorate the scaling bottleneck in studies of realistic systems, typically modeled in the configuration space, the nuclear wave functions are represented in terms of time-dependent basis functions. Such bases are expected to give an accurate description with a modest number of basis functions employed, by adapting them to the wave function solving the time-dependent Schrödinger equation. It is not, however, straightforward to estimate the accuracy of the resulting solution: in QM the energy conservation, a convenient such measure for a classical trajectory evolving in a time-independent potential, is not a sufficient criterion of the dynamics' accuracy. In this work, we argue that the expectation value of the Hamiltonian's "variance", quantifying the basis completeness, is a suitable practical measure of the quantum dynamics' accuracy. Illustrations are given for several chemistry-relevant test systems, modeled employing time-independent as well as time-dependent bases, including the coupled and variational coherent states methods and the quantum-trajectory guided adaptable Gaussians (QTAG) as the latter basis type. A novel semilocal definition of the QTAG basis time-evolution for placing the basis functions "in the right place at the right time" is also presented.

Theory of particle beams transport over curved plasma-discharge capillaries

We present a new approach that demonstrates the deflection and guiding of relativistic electron beams over curved paths by means of the magnetic field generated in a plasma-discharge capillary. The active bending plasma (ABP) represents a promising solution that has been recently demonstrated with a proof of principle experiment. An ABP device consists of a curved capillary where large discharges (of the order of kA) are propagated in a plasma channel. Unlike conventional bending magnets, in which the field is constant over the bending plane, in the ABP, the azimuthal magnetic field generated by the discharge grows with the distance from the capillary axis. This features makes the device less affected by the beam chromatic dispersion so that it can be used to efficiently guide particle beams with non-negligible energy spreads. The study we present in the following aims to provide a theoretical basis of the main ABP features by presenting an analytical description of a single-particle motion and rms beam dynamics. The retrieved relationships are verified by means of numerical simulations and provide the theoretical matrix formalism needed to completely characterize such a new transport device. Published by the American Physical Society 2024

Description of phase separation motion in gas‒liquid two-phase flow

Understanding the physics of phase separation between gas and liquid phases as a mixture mass has long been a challenge. In this paper, a phase separation description criterion based on heterogeneous flow model is proposed. A mathematical method similar to Lagrangian coherent structure (LCS) is used to identify the two-phase separation process, which is called relative motion Lagrangian coherent structure (rLCS). The rLCS is able to describe the dynamic evolution of the phase separation process and flow pattern transition in multiphase flows, which is very common in gas‒liquid mixture transportation and industrial processes. The most striking finding of rLCS is that phase separation and phase distribution are not in the same spatial position, that is, the process and the result of separation may not be exactly corresponding as we thought. This new flow structure reflects the underlying dynamic behavior of the multiphase flow field. In addition, the phase separation process has obvious periodicity. This paper reveals the typical phase separation process in the simulation of gas‒liquid two-phase pipe flow and gas‒liquid multiphase pump. These are very important to improve the understanding of multiphase flow processes, and can also lay a solid foundation for future flow control based on multiphase flow characteristics, highlighting the application potential of the new method.

An Empirical Study of the Teachability and Learnability of L2 “Thinking for Speaking” Patterns

This study examines whether explicit pedagogical instructions of multimodal strategies based on typological contrastive analysis have any facilitative effect on the restructuring of “thinking for speaking” patterns, focusing on motion event construal which has been demonstrated to be notoriously difficult in second language acquisition (Hendriks and Hickmann 2011, Slobin 1996). Eighty adult Chinese intermediate-level EFL learners were recruited for a classroom-based quasi-experimental study with a pretest-posttest design. Teaching TFS instructions with awareness enhancement strategies as an independent variable divided the participants into two groups, the experimental group that received instructions and control group that followed a traditional teaching approach over a period of 4 weeks. Writing data were elicited by means of the <i>Frog Story</i> and was coded on specific measures of accuracy and complexity of the properties of lexicalization patterns: the description of Motion, Path and Ground. The results showed positive instructional effect on learners’ writing performance of motion event expression and confirmed the possibility of restructuring L1 thinking-for-speaking patterns in L2 through pedagogical instructions. The findings provide practical implications for teachers, typological contrastive awareness and explicit pedagogical instructions prove to be significant for learners’ development of L2 thinking for speaking patterns.

Modeling the skeleton-language uncertainty for 3D action recognition

Human 3D skeleton-based action recognition has received increasing interest in recent years. Inspired by the excellent ability of the multi-modal model, some pioneer attempts to employ diverse modalities, i.e., skeleton and language, to construct the skeleton-language model and have shown compelling results. Yet, these attempts model the data representation as deterministic point estimation, ignoring a key issue that descriptions of similar motions are uncertain and ambiguous, which brings about restricted comprehension of complex concept hierarchies and impoverished cross-modal alignment reliability. To tackle this challenge, this paper proposes a new Uncertain Skeleton-Language Learning Framework (USLLF) to capture the semantic ambiguity among diverse modalities in a probabilistic manner for the first time. USLLF consists of both inter- and intra-modal uncertainties. Specifically, first, we integrate the language (text) generated by ChatGPT with the generic skeleton-based network and develop a deterministic multi-modal baseline, which can be easily achieved via any off-the-shelf skeleton and text encoders. Then, based on this baseline, we explicitly model the intra-modal (skeleton/language) uncertainties as the Gaussian distributions using the new uncertainty networks capable of learning the distributional embeddings of modalities. Following this, these embeddings are aligned and formulated as inter-modal (skeleton-language) uncertainty using both the contrastive and negative log-likelihood objectives to alleviate the cross-modal alignment error. Experimental results on NTU RGB+D, NTU RGB+D 120, and NW-UCLA datasets show that our approach outperforms the proposed baseline and achieves comparable performance with a high inference efficiency compared to the state-of-the-art methods. Besides, we also deliver insightful analyses on how learned uncertainty reduces the impact of uncertain and ambiguous data on model performance.

Geometry of plastic deformation in metals as piecewise isometric transformations

Deformation mechanisms of crystalline solids has been the subject of research for more than two centuries. The theory of dislocations dominates modern views but still has significant gaps demanding the introduction of additional concepts for the coherent quantitative description of physical phenomena. In this work, we propose a coherent geometric description of motion and deformation in crystalline solids as piecewise isometric transformations (PWIT). The latter only includes operations that, similar to interatomic spacing in crystalline lattice, do not alter distances between reference points, i.e. translations, rotations and mirror reflections. The difference between solid-body translations and plastic deformations is that the isometric transformations have discontinuities that in real-life materials realise through dislocations (termination of shifts), disclinations (termination of rotations), and twins (mirror reflections). The conceptual description of plastic deformations as PWIT can be useful for the better description of physical phenomena, proposing new hypothesis, and for developing predictive analytical models. In this paper, the use of this conceptual description enables proposing new hypothesis about the nature of such interesting phenomena in severe plastic deformation as (i) stationary ‘solid state turbulence’ stage in high pressure torsion, and (ii) rate of mass transfer (mechanically assisted diffusion) in simple-shear deformation.

Photophoresis of a moderately large high-viscosity droplet in slip mode

Purpose of research. To obtain analytical expressions that allow calculating the strength and velocity of a moderately large, highly viscous droplet, taking into account the direct contribution of the evaporation coefficient, linear corrections by the Knudsen number and the reactive effect of a plane wave moving in the field of mono-chromatic radiationMethods. Methods of perturbation theory, gas kinetic methods, mathematical methods for solving linear partial differential equations with variable coefficients (the system of Stokes equations, Laplace and Poisson equations) were used.Results. In a quasi-stationary approximation, a theoretical description of the photophoretic motion of a moderately large evaporating highly viscous spherical droplet (there is no circulation of matter inside the droplet and interfacial surface tension forces) in a viscous binary gas mixture is carried out. A velocity-linearized system of Navi-Stokes equations and heat and mass transfer was solved. Expressions are obtained for the fields of mass velocity, pressure, temperature and the relative numerical concentration of the first component. The strength and speed of photophoresis of a highly viscous droplet was determined by integrating a stress tensor over the surface of the particle. Under boundary conditions on the surface of a highly viscous droplet, linear corrections in terms of the Knudsen number (isothermal, thermal and diffusion slips, temperature and concentration jumps, as well as sliding due to temperature inhomogeneity along the curved surface of the particle), the reactive effect and the contribution of the direct influence of the evaporation coefficient were taken into account. The contributions to the obtained formulas for the photophoresis of a moderately large highly viscous droplet are analyzed and the preliminary transitions to the results known in the literature (moderately large and large solid particles of spherical shape) are considered Conclusion. The obtained formulas based on the hydrodynamic method allow us to evaluate the effect of the direct contribution of the evaporation coefficient and linear corrections by the Knudsen number on the strength and speed of photophoresis of a moderately large evaporating highly viscous droplet in a binary gas mixture.

New operator realization of angular momentum for description of electron's motion in uniform magnetic field

New operator realization of angular momentum for description of electron's motion in uniform magnetic field

Linguistic-Driven Partial Semantic Relevance Learning for Skeleton-Based Action Recognition.

Skeleton-based action recognition, renowned for its computational efficiency and indifference to lighting variations, has become a focal point in the realm of motion analysis. However, most current methods typically only extract global skeleton features, overlooking the potential semantic relationships among various partial limb motions. For instance, the subtle differences between actions such as "brush teeth" and "brush hair" are mainly distinguished by specific elements. Although combining limb movements provides a more holistic representation of an action, relying solely on skeleton points proves inadequate for capturing these nuances. Therefore, integrating detailed linguistic descriptions into the learning process of skeleton features is essential. This motivates us to explore integrating fine-grained language descriptions into the learning process of skeleton features to capture more discriminative skeleton behavior representations. To this end, we introduce a new Linguistic-Driven Partial Semantic Relevance Learning framework (LPSR) in this work. While using state-of-the-art large language models to generate linguistic descriptions of local limb motions and further constrain the learning of local motions, we also aggregate global skeleton point representations and textual representations (which generated from an LLM) to obtain a more generalized cross-modal behavioral representation. On this basis, we propose a cyclic attentional interaction module to model the implicit correlations between partial limb motions. Numerous ablation experiments demonstrate the effectiveness of the method proposed in this paper, and our method also obtains state-of-the-art results.

Evaluation of the bilateral symmetry assumption in manual wheelchair propulsion: a systematic review of literature in daily-life and sports contexts.

This systematic review aimed to 1) verify bilateral symmetry assumption in manual wheelchair (MWC) propulsion in daily-life and sports, and its relationship with injury risk and sports performance; 2) evaluate methods for assessing bilateral symmetry. Scopus, Web-Of-Science, PubMed, and EBSCO databases were searched for articles published before January 2024 investigating bilateral symmetry in MWC users and/or healthy participants during MWC propulsion. Two independent reviewers screened, extracted data, and assessed methodological quality of retrieved papers. Twenty-five studies were included. In daily ground-level propulsion, minimal asymmetries were observed in kinematic, kinetic, and temporal parameters when averaging ≥3 push cycles. In the sports context, diverse findings emerged, ranging from up to 27% side-to-side differences in propulsion kinetics and kinematics during sprinting, to descriptions of both symmetrical and asymmetrical upper extremity motions. Limited evidence exists regarding the role of asymmetry in MWC propulsion as a risk factor for injury and pain, as well as the association between sprinting performance and symmetry. In conclusion, bilateral symmetry assumption in MWC propulsion is valid only under specific conditions (i.e., slow/moderate speed, averaging ≥3 push cycles, smooth level ground). The wheeling environment and inter-individual variability impact symmetry research outcome and require consideration in future studies.

Complex Fluid Models of Mixed Quantum–Classical Dynamics

Several methods in nonadiabatic molecular dynamics are based on Madelung’s hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential leads to severe computational challenges and one often seeks to neglect its contribution, thereby approximating nuclear motion as classical. The resulting model couples classical hydrodynamics for the nuclei to the quantum motion of the electronic component, leading to the structure of a complex fluid system. This type of mixed quantum–classical fluid models has also appeared in solvation dynamics to describe the coupling between liquid solvents and the quantum solute molecule. While these approaches represent a promising direction, their mathematical structure requires a certain care. In some cases, challenging higher-order gradients make these equations hardly tractable. In other cases, these models are based on phase-space formulations that suffer from well-known consistency issues. Here, we present a new complex fluid system that resolves these difficulties. Unlike common approaches, the current system is obtained by applying the fluid closure at the level of the action principle of the original phase-space model. As a result, the system inherits a Hamiltonian structure and retains energy/momentum balance. After discussing some of its structural properties and dynamical invariants, we illustrate the model in the case of pure-dephasing dynamics. We conclude by presenting some invariant planar models.

Killing versus branching: Unexplored facets of diffusive relaxation.

We analyze the relaxation dynamics of Feynman-Kac path integral kernel functions, in terms of branching diffusion processes with killing. This amounts to the killing versus branching approach to path integration, which seems to be a novelty in the pathwise description of conditioned Brownian motions and diffusion processes with absorbing boundaries. There, Feynman-Kac kernels appear as building blocks of inferred (Fokker-Planck) transition probability density functions. A consistent probabilistic meaning is hereby provided (killing versus branching time rate) to bounded from below Feynman-Kac potential functions, which instead of being positive-definite (a standard killing paradigm), may take negative values on bounded spatial subdomains (that inflicts trajectory branching).

The role of axial angular momentum in exact non-linear solutions of multipolar spherical and cylindrical vortices

The time-dependent acceleration of fluid particles in an arbitrary superposition of multipolar spherical and cylindrical vortices in presence of a background rotational rigid flow is the gradient of the difference between their kinetic energy and the product of their total axial angular momentum times the angular velocity of the background flow. If the potential energy is defined as the time-dependent field whose minus gradient equals the acceleration of the flow, then the total energy, defined as the sum of kinetic and potential energies, equals the total axial angular momentum times the angular velocity of the background flow. The total energy of a fluid particle has therefore a linear relationship with the azimuthal velocity field. The role of the axial angular momentum in these oscillating flows is explained also in the classical Lagrangian and Hamiltonian descriptions of motion. The linear relation between total energy and angular momentum makes possible that the free parameters of these flows may be obtained, in a way similar to that developed in the quantum mechanics description of motion, as the eigenvalues of linear operators acting on some components of the spherical modes. Beltrami flow solutions in prolate spheroidal geometry for axisymmetric flows are also discussed.