Motion Process Research Articles

On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes

On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes

Using space-filling curves and fractals to reveal spatial and temporal patterns in neuroimaging data

Objective. Magnetic resonance imaging (MRI), functional MRI (fMRI) and other neuroimaging techniques are routinely used in medical diagnosis, cognitive neuroscience or recently in brain decoding. They produce three- or four-dimensional scans reflecting the geometry of brain tissue or activity, which is highly correlated temporally and spatially. While there exist numerous theoretically guided methods for analyzing correlations in one-dimensional data, they often cannot be readily generalized to the multidimensional geometrically embedded setting.Approach. We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis. We conduct extensive feasibility studies on diverse, artificially generated data with known fractal characteristics: the fractional Brownian motion, Cantor sets, and Gaussian processes. We compare the suitability of dimensionality reduction via Hilbert SFC and a data-driven alternative. FSCA is then successfully applied to real-world MRI and fMRI scans.Main results. The method utilizing Hilbert curves is optimized for computational efficiency, proven robust against boundary effects typical in experimental data analysis, and resistant to data sub-sampling. It is able to correctly quantify and discern correlations in both stationary and dynamic two-dimensional images. In MRI Alzheimer's dataset, patients reveal a progression of the disease associated with a systematic decrease of the Hurst exponent. In fMRI recording of breath-holding task, the change in the exponent allows distinguishing different experimental phases.Significance. This study introduces a robust method for fractal characterization of spatial and temporal correlations in many types of multidimensional neuroimaging data. Very few assumptions allow it to be generalized to more dimensions than typical for neuroimaging and utilized in other scientific fields. The method can be particularly useful in analyzing fMRI experiments to compute markers of pathological conditions resulting from neurodegeneration. We also showcase its potential for providing insights into brain dynamics in task-related experiments.

Diverging evolutionary trajectories for palm seed sizes in mainland Africa and Madagascar.

Seed size is a trait which determines survival rates for individual plants and can vary as a result of numerous trade-offs. In the palm family (Arecaceae) today, there is great variation in seed sizes. Past studies attempting to establish drivers for palm seed evolution have sometimes yielded contradictory findings in part because modern seed size variations are complicated by long-term legacies, including biogeographic differences across lineages. Here, we examined palm seed size evolution in two adjacent regions (mainland Africa and Madagascar) utilizing single- and multi-regime Brownian Motion and Ornstein-Uhlenbeck processes. We explicitly take into account species' evolutionary histories to investigate whether there may be shared evolutionary pressures over regional scales. We found that regional selection pressures do exist for palm seed lengths, but these pressures are distinct in mainland Africa and Madagascar, despite the two regions' proximity. Our study indicates that evolutionary drivers may differ in these two regions, highlighting the importance of re-considering the widespread assumption to view mainland Africa and Madagascar as a single evolutionary region.

Investigation into the Motion Characteristics and Impact Loads of Buoy Water Entry Under the Influence of Combined Waves and Currents

As a crucial component in marine monitoring, meteorological observation, and navigation systems, studying the motion characteristics and impact loads of buoy water entry is vital for their long-term stability and reliability. When deployed, buoys undergo a complex motion process, including the impact of entering the water and a stable floating stage. During the water entry impact phase, the motion characteristics and impact loads involve interactions between the buoy and the water, the trajectory of motion, and dynamic water pressure, among other factors. In this paper, the VOF model is used to calculate the buoy’s water entry motion characteristics, and then the STAR-CCM+&ABAQUS bidirectional fluid–structure interaction (FSI) method is used to calculate the water entry impact load of the buoy under different water surface conditions and different initial throwing conditions, considering the influence of the flow field on the structure and the influence of the structure deformation on the flow field. The study finds that under the influence of wave and current impacts, changes in wave height significantly affect the buoy’s heave motions. Under different parametric conditions, due to the specific direction of wave and current impacts, the buoy’s pitch amplitude is relatively more intense compared to its roll amplitude, yet both pitch and roll motions exhibit periodic patterns. The buoy’s pitch motion is sensitive to changes in the entry angle; even small changes in this angle result in significant differences in pitch motion. Additionally, the entry angle significantly impacts the peak vertical overload on the buoy. Instantaneous stress increases sharply at the moment of water entry, particularly at the joints between the crossplate and the upper and lower panels, and where the mast connects to the upper panel, creating peak stress concentrations. In these concentrated stress areas, as the entry speed and angle increase, the maximum equivalent stress peak at the monitoring points rises significantly.

Rational engineering of DNA-nanoparticle motor with high speed and processivity comparable to motor proteins

DNA-nanoparticle motor is a burnt-bridge Brownian ratchet moving on RNA-modified surface driven by Ribonuclease H (RNase H), and one of the fastest nanoscale artificial motors. However, its speed is still much lower than those of motor proteins. Here we resolve elementary processes of motion and reveal long pauses caused by slow RNase H binding are the bottleneck. As RNase H concentration ([RNase H]) increases, pause lengths shorten from ~70 s to ~0.2 s, while step sizes (displacements between two consecutive pauses) are constant ( ~ 20 nm). At high [RNase H], speed reaches ~100 nm s−1, however, processivity (total number of steps before detachment), run-length, and unidirectionality largely decrease. A geometry-based kinetic simulation reveals switching of bottleneck from RNase H binding to DNA/RNA hybridization at high [RNase H], and trade-off mechanism between speed and other performances. An engineered motor with 3.8-times larger DNA/RNA hybridization rate simultaneously achieves 30 nm s−1 speed, 200 processivity, and 3 μm run-length comparable to motor proteins.

Analysis and Optimal Control of Propagation Model for Malware in Multi-Cloud Environments with Impact of Brownian Motion Process

Today, cloud computing is a widely used technology that provides a wide range of services to numerous sectors around the world. This technology depends on the interaction and cooperation of virtual machines (VMs) to complete various computing tasks, propagating malware attacks quickly due to the complexity of cloud computing environments and users’ interfaces. As a result of the rising demand for cloud computing from multiple perspectives for complete analysis and decision-making across a range of life disciplines, multi-cloud environments (MCEs) are established. Therefore, in this work, we discuss impacted mathematical modeling for the MCEs’ network dynamics using two deterministic and stochastic approaches. In both approaches, appropriate assumptions are considered. Then, the proposed networks’ VMs are classified to have six different possible states covering media, healthcare, finance, and educational servers. After that, the two developed modeling approaches’ solution existence, uniqueness, equilibrium, and stability are carefully investigated. Using an optimal control strategy, both proposed models are tested for sustaining a certain level of security of the VMs’ states and reducing the propagation of malware within the networks. Finally, we verify the theoretical results by employing numerical simulations to track the malware’s propagation immunization. Results showed how the implemented control methods maintained the essential objectives of managing malware infections.

Transient vibration reduction and energy dissipation characteristics of flexible vibration structure coupling with particle damping

In this paper, a fully time-domain coupling method of the discrete element method (DEM) combination with multi-flexible body dynamics (MFBD) was proposed to investigate the particle motion and vibration reduction as well as energy dissipation characteristics of flexible vibration structure coupling with particle damping under transient free vibration and random excitation conditions. The transient free vibration and random vibration reduction experiments of flexible vibration cantilever beam with particle damping were carried out. In addition, the influence of particle diameter and filling rate on the vibration reduction characteristics is further analyzed. Results show that the proposed DEM-MFBD coupling method is well verified by experiments. The particle motion process under free vibration condition can be manifested as three typical motion states, namely, the double-side particle–container collision, the single-side particle–container collision, and no collision. The vibration energy is mainly dissipated in the first state. Under random vibration excitation, the maximum energy dissipation of particle damping mainly occurs at the natural frequency, and the vibration reduction mechanism of particle damping is mainly attributed to the particle–particle energy dissipation.

SRCES: a simulation program for collective effects in electron storage rings

Collective effects are important in the physics design of electron storage rings, especially for the fourth-generation synchrotron light source, where the collective effects are more severe than before and limit maximum stored beam current. To estimate beam collective effects, besides theoretical analysis, numerical tracking methods are necessary for obtaining more accurate and comprehensive results. To systematically study the comprehensive influence of wakefields and various damping mechanisms, we developed a new code Storage Ring Collective Effects Simulator (SRCES), which is a tracking code based on macroparticle model in 6-dimensional phase space. Several models are employed to handle various processes of particle motion. The modified transfer matrix and high order Taylor transfer map are used to solve particle motion under external electro-magnetic fields. A simplified equivalent damping and excitation model is used to represent the effects of synchrotron radiation on particle motion. The kick model is used to represent the influence of wakefields and RF cavity. Furthermore, the wake function data can be input as numerical arrays directly or through specific impedance models. In this paper, we describe the basic theory foundation, functions and benchmarked results of the code SRCES. Then, SRCES is used to conduct preliminary research on the collective effects of the Hefei Advanced Light Facility storage ring.

Continuous motion and dissection process of Gampei landslide in Joetsu City, Niigata Prefecture, Japan

Continuous motion and dissection process of Gampei landslide in Joetsu City, Niigata Prefecture, Japan

Simulation Study of Motion Processes Based on Isometric Solenoidal Equation and Differential Evolutionary Algorithm

This paper mainly focuses on the position and speed changes during the traveling process of the bench dragon, collision detection, optimization of the turning path and the maximum traveling speed of the dragon head. Using the equidistant solenoidal equation and differential evolution algorithm, the key position coordinate model of each part of the bench dragon team is established and collision detection is carried out. Firstly, this paper deduces the movement path and speed of the dragon head through the solenoidal equation; secondly, based on the collision detection model, it analyzes the collision moments and conditions of the bench dragons in the marching; lastly, through the optimization of the turnaround path and the calculation of the speed, it determines the optimal turnaround path. The study shows that the model can effectively solve the optimization problem in the marching process of the complex dancing dragon team.

Complex Modal Synthesis Method for Viscoelastic Flexible Multibody Sys-tem described by ANCF

Abstract The viscoelastic dynamic model of flexible multibody coupled with large rotation and deformation can be described by the Absolute Nodal Co-ordinate Formulation (ANCF). However, with the increase of degrees of freedom, the computational cost of viscoelastic multibody systems will be very high. In addition, for non-proportionally viscoelastic flexible multibody systems, the orthogonality and superposition of complex modes only exist in the state space. In this investigation, a systematical procedure of model reduction method for viscoelastic flexible multibody systems de-scribed by ANCF is proposed based on the complex modal synthesis method. Firstly, the whole motion process of the system is divided into a se-ries of quasi-static equilibrium configurations. Then the dynamic equation is locally linearized based on the Talor expansion to obtain the constant tangent stiffness matrix and damping matrix. The initial modes and modal coordinates need to be updated for each subinterval. A modal selection criterion based on the energy judgment is proposed to ensure the energy conservation and accuracy by the minimum number of truncations. Finally, three numerical examples are carried out as verification. Simulation results indicate that the method proposed procedure reduces the system scale and improves the computational efficiency under the premise of ensuring the simulation accuracy.

Reflections about modeling processes: a case of translational motion in horizontal direction

Generally, motions are not included in basic education, and only a static view of isometries is studied. The main purpose of this paper is to present some results of research on the analysis of modeling processes of isometric translation motion, carried out by first-year high school students from a public school in Goiás-Brazil. Data were collected from the participant’s resolutions in face to face and on line workshops, but not to do compared. The analyses were conducted qualitatively, according to the claim-making/participatory conception, where participatory action is dialectic and focuses on producing changes in practices. This research is characterized as exploratory, descriptive, and explanatory. The data were categorized and we observed that the modeling processes involved: a graphic geometric approach; arithmetic approach; algebraic approach; written maternal language; and written mathematical language.

Investigation and optimization of parameters for bidirectional composite vibratory finishing of gears

ABSTRACT To meet the core requirements for uniform and efficient finishing of high-precision gears, a bidirectional composite vibratory finishing (BCVF) process was introduced. The influence of motion parameters (gear rotational speed n, vibration frequency f x and f z , vibration amplitude A x and A z , vibration phase difference ψ), process parameters (media loading height H, gear installation position h), gear parameters and container geometric parameters (cross-sectional shape, size L x × L y ) on the finishing effect was investigated by kinematic analysis and discrete element simulation (DEM). On this basis, the parameters with significant influence were selected and further optimized by gray relational analysis (GRA). Numerical simulations were carried out by orthogonal design, taking the cumulative contact energy and distribution uniformity on gear surface as evaluation indicators for multi-objective optimization. The results indicated that the affecting significance on comprehensive performance was ranked as f x > f z > A x > A z . Besides, the optimal parameter combination was obtained.

A refined prediction model for the initial disturbances of the projectile in the self-propelled gun

Abstract In the gun launch process, the continuous propellant combustion provides power and energy for the projectile. Due to the gap between the projectile and barrel, the high-speed motion of the former is generally accompanied by contact and collision with the latter. Meanwhile, the gun also recoils under the propellant gas. Notably, the above complex motion of the system causes the initial disturbances of the projectile and muzzle. Previous launch dynamic models usually neglect the influence of the gun recoil on the combustion and flow in the chamber. However, the gun recoil inevitably further increases the chamber’s free space, resulting in the calculation deviations of projectile and muzzle disturbances. The above deviations ultimately determine the firing accuracy and firing stability prediction. To study the in-bore projectile motion and subsequent external ballistic process more accurately, an improved coupled calculation method of launch dynamics is developed. This work combines the interior ballistic two-phase flow dynamics considering the gun recoil, in-bore projectile motion theory, multibody system dynamics, and necessary high-precision numerical schemes. The launch process of the 155 mm self-propelled gun is studied. As the results show, the calculated vibration characteristics, dynamic response, and interior ballistic performance indexes are consistent with measured ones, verifying the feasibility of the above method. In addition, the initial disturbances of the projectile with and without considering the recoil’s influence on the combustion and flow in the chamber is discussed. The work in this paper provides an accurate tool to predict the initial disturbances of the projectile.

Erosion and wear of barrel and its impact on projectile force

Abstract During gun firing, the inner surface of the barrel will undergo erosion and wear, leading to changes in the gap between the projectile and barrel. This cause the load environment in which the projectile moves inside the barrel to become more severe, and the cutting and wear of the rotating band increase. Therefore studying the erosion and wear of barrel and its impact on projectile force is of great significance for the lifespan and launch safety of the barrel. By testing the erosion and wear of the barrel with different firing numbers and analysing the anatomy of the end of life barrel, the damage and expansion patterns of the barrel were obtained. On this basis, a coupled dynamic model of projectile and barrel considering erosion and wear was established, and the influence of erosion and wear on the force acting on the motion process of the projectile inside the barrel was calculated. The results indicate that the erosion and wear value of the barrel follows a cubic polynomial along the axis, and the maximum value is located at the commencement of rifling. At the end of the barrel’s life, the engraving resistance of the rotating band is reduced by about 38.7%, the surface contact force between the rotating band and rifling land is reduced by 36.4%, and the impact force between the bourrelet and barrel is increased by about three times.

Changing sea level, changing shorelines: integration of remote-sensing observations at the Terschelling barrier island

Abstract. Sea level rise is associated with increased coastal erosion and inundation. However, the effects of sea level change on the shoreline can be enhanced or counteracted by vertical land motion and morphological processes. Therefore, knowledge about the individual contributions of sea level change, vertical land motion and morphodynamics on shoreline changes is necessary to make informed choices for climate change adaptation, such as applying coastal defence measures. Here, we assess the potential of remote-sensing techniques to detect a geometrical relationship between sea level rise and shoreline retreat for a case study at the Terschelling barrier island at the northern Dutch coast. First, we find that sea level observations from satellite radar altimetry retracked with ALES can represent sea level variations between 2002 and 2022 at the shoreline when the region to extract altimetry time series is chosen carefully. Second, results for cross-shore time series of satellite-derived shorelines extracted from optical remote-sensing images can change considerably, depending on choices made for tidal correction and parameter settings during the computation of time series. While absolute shoreline positions can differ on average by more than 200 m, the average trend differences are below 1 m yr−1. Third, by intersecting the 1992 land elevation with time-variable sea level, we find that inundation through sea level rise caused on average −0.3 m yr−1 of shoreline retreat between 1992 and 2022. The actual shoreline movement in this period was on average between −2.8 and −3.2 m yr−1, leading to the interpretation that the larger part of shoreline changes at Terschelling is driven by morphodynamics. We conclude that the combination of sea level from radar altimetry, satellite-derived shorelines and land elevation provides valuable information about the influence of sea level rise, vertical land motion and morphodynamics on shoreline movements.

Numerical simulation of cathode-spot crater and droplet formation with linear and circular motion process

Abstract In this paper, a three-dimensional cathode spot erosion model is proposed to study the development of cathode spot motion 
process on the surface of copper cathode. The formation and development process of cathode spots motion without external 
magnetic field is studied. In this model, energy flux density, pressure, and current value are considered as external parameters. 
The simulation results compared the cathode spot ablation trajectories and temperature distribution under different motion 
forms and motion velocities. The results indicated that during the spots expansion process, the flow of liquid metal will form a 
convex structure on the surface of the cathode and a hollow structure inside the cathode. Comparing different motion types, the 
annular motion significantly increased the roughness of the cathode surface. With the increase of the speed of spots movement, 
the interaction between the craters is significantly weakened, which will reduce the temperature and the roughness of the 
cathode surface. The simulation results are consistent with the experimental results.

Design of a Novel Macro-Micro Integrated Brain Surgery Robot Based on Modular Parallel Mechanisms

The advancement and development of medical surgical robots have provided new technological support for brain surgery and neurosurgical procedures, improving the reliability of highly complex and precise surgeries. In turn, this urges the design and development of novel surgical robots to possess higher precision, stability, and enhanced motion capabilities. In response to this practical demand, this paper introduces a macro-micro integrated medical brain surgery robot system based on the concept of modular PMs (parallel mechanisms), which have a total of 13 active DOFs (degrees of freedom). This system divides the motion process of brain surgery into a large-scale macro-motion space and a small-scale high-precision motion space for design and planning control. The introduction of the design concept that combines multiple modular parallel sub-mechanisms has brought a significant level of decoupling characteristics to the mechanism itself. A comprehensive introduction and analysis of the surgical robot are provided, covering aspects such as design, kinematics, motion planning, and performance indicators. To address the pose allocation and coordination of motion between the macro platform and the micro platform, a pose allocation algorithm based on the decoupling and non-decoupling characteristics in various dimensions of the macro-micro platform is proposed. The designed measurement experiments have demonstrated that the repeatability in positioning accuracy of the macro and micro platform reaches the level of micron and submicron respectively. Practical experiments of motion control and simulated brain electrode implantation validate the excellent performance and stability of the entire surgical robot system. This research contributes innovative insights to the development of medical surgical robot systems, particularly in the domain of mechanism design.

Application of LS-RAPID to simulate the motion of two contrasting landslides triggered by earthquakes

Abstract Earthquake-triggered landslides are one of the most significant hazards worldwide. These landslides, involving small or large volumes, can develop debris flows or avalanches with high mobility and long runout distances. The motion processes of this type of landslide are also quite complicated. This study reproduced the motion processes of two landslides using the LS-RAPID program. The Aso-Bridge landslide occurred on April 16, 2016, and it featured rapid movement and a long runout distance. The Kataragai landslide occurred on April 9, 2018, and it traveled with a flow-like behavior. This work presents the features and mechanical parameters of these two landslides by means of survey investigations and laboratory experiments. We established pre-failure models and reproduced motion processes of these two landslides using the LS-PAPID program. Two indicators, consisting of the sliding speed and traveling morphology at different intervals, were considered to describe the motion processes. Results indicated that the resultant maximum sliding speeds of these two landslides were approximately 297.1 and 43.6 m/s, respectively, and that post-failure morphologies were consistent with those observed in field investigations.

Trajectory Prediction Analysis of Basketball Players’ Movements Based on DSM Optimization Algorithm

In this paper, the action trajectory of basketball players is predicted and analyzed by the DSM optimization algorithm. Data on the movements of basketball players, including position, speed and acceleration are collected. The motion trajectory is predicted by the DSM optimization algorithm. At present, computer technology is more and more applied in sports training. Based on this, this paper studies the simulation of basketball players’ motion trajectory prediction. After describing the research background and significance, this paper constructs a human joint model and then proposes the motion process DSM algorithm to simulate the jump shot action of basketball players. In this paper, the algorithm and model are tested, and the experiment adopts the run-jump fatigue model to produce fatigue. The infrared high-speed motion capture system and three-dimensional force measuring table are used to collect the kinematics and dynamics data of the sudden stop jump shot before and after fatigue. The experimental results show that the trajectory prediction simulation proposed in this paper is feasible.