Elastic Collisions Research Articles

Elastic collisions on a simulated circular air track

Elastic collisions of gliders on linear air tracks are often used to explore conservation of energy and momentum. If one is interested in the glider behavior over a long time span, the analysis involves repeated collisions and is complicated by reflections from the track end stops. Here we analyze elastic collisions on a novel circular air track; since such a track lacks end stops, the mathematical analysis of repeated collisions is amenable to our students. Our analysis uncovers a variety of interesting behaviors which depend on the ratio of the glider masses. We examine periodic sequences where the gliders return to their initial conditions and progressions where (when plotted in polar coordinates) the collision positions take on the locus of a spiral. One set of initial conditions produces an “angle trap” where one glider remains within a certain angular range. We also explore making one glider's mass hypothetically negative, which results in a novel “chasing” motion. Our results were obtained using a 3D interactive simulation (created using C++ within the Unreal engine), which we make available as supplementary material.

Optimal Arrangements and Local Anisotropy of {100} Guinier-Preston (GP) Zones by Parametric Dislocation Dynamics (PDD) Simulations.

Stress-oriented precipitation and the resulting mechanical anisotropy have been widely studied over the decades. However, the local anisotropy of precipitates with specific orientations has been less thoroughly investigated. This study models the interaction between an edge dislocation source and {100} variants of Guinier-Preston (GP) zones in Al-Cu alloys using the parametric dislocation dynamics (PDD) method. Concentric geometrically necessary dislocation (GND) loops were employed to construct a line integral model for thin platelets. The simulations, conducted with our self-developed code based on Green's function method and Eshelby inclusion theory revealed distinct strengthening behavior along the strong and weak directions for 60° GP zones, demonstrating anisotropic strengthening from the perspective of elastic interactions. Furthermore, the optimal inclined arrangement of the GP zone array was determined through elastic energy calculations, and these results were corroborated by TEM observations.

Analysis of bolt load uniformity in raised flange connection

Aiming at the problem of uneven preload of raised flange, a model considering elastic interaction is established to study the uniformity of bolt load under raised flange connection. Firstly, the elastic interaction coefficient method of bolt flange connection structure is extended to multiple times, and the initial preload of all bolts at each tightening step is determined by analytical model; secondly, a three-dimensional finite element model of bolt flange connection structure is established, and the correctness of the finite element model is verified by comparing with the literature test, and the influence of tightening sequence and tightening steps on bolt preload is explored; finally, the results of raised flange under symmetrical tightening conditions with and without considering elastic interaction are compared and analyzed. The results show that when the tightening method is symmetrical tightening and the tightening steps are three steps, the elastic interaction of each bolt is the smallest, and the final preload uniformity is better; on this basis, the results of the model considering elastic interaction further improve the uniformity of the final preload and are closer to the target preload. The problem of bolt preload dispersion caused by elastic interaction is solved, and the research results can provide guidance for the safety and reliability design of bolt flange connection structure.

A Study on the Effect of Structural Compliance Placing in Soft Contact/Collision Properties of Multirotor Micro Aerial Vehicles

Adding compliance (softness) has been introduced as an effective way to improve the physical collision resilience characteristics of multirotor micro aerial vehicles (MAVs). This article answers the question “Where is the best place to apply compliance in a multirotor MAV to make it more collision‐resilient?” by analyzing the output data of more than 1200 drone collision tests through two sets of accelerated and nonaccelerated collision experiments for four main configurations of micro‐quadcopters each possessing a unique softness layout of physical frame. It is shown that while applying compliance to the protective propeller guards (bumpers) of a micro‐quadcopter provides a more elastic collision, it does not improve its energy‐dissipation (impact damping) characteristics. On the other hand, enhancing the inner frame of the micro‐quadcopter with a softer structure results in higher rates of impact energy damping during the collisions and an increase in the impact time, which results in lower impact accelerations the MAV experiences during the crush. A mathematical model is developed representing the contact/collision interactions as nonlinear viscoelastic forces. Comparing the results of the simulations to the experiments suggests that this model can effectively mimic the impact behavior of contacting/colliding MAVs with different structural stiffness and damping.

Charting the course of Sargassum: Incorporating nonlinear elastic interactions and life cycles in the Maxey-Riley model.

The surge of pelagic Sargassum in the Intra-America Seas, particularly the Caribbean Sea, since the early 2010s has raised significant ecological concerns. This study emphasizes the need for a mechanistic understanding of Sargassum dynamics to elucidate the ecological impacts and uncertainties associated with blooms. By introducing a novel transport model, physical components such as ocean currents and winds are integrated with biological aspects affecting the Sargassum life cycle, including reproduction, grounded in an enhanced Maxey-Riley theory for floating particles. Nonlinear elastic forces among the particles are included to simulate interactions within and among Sargassum rafts. This promotes aggregation, consistent with observations, within oceanic eddies, which facilitate their transport. This cannot be achieved by the so-called leeway approach to transport, which forms the basis of current Sargassum modeling. Using satellite-derived data, the model is validated, outperforming the leeway model. Publicly accessible codes are provided to support further research and ecosystem management efforts. This comprehensive approach is expected to improve predictive capabilities and management strategies regarding Sargassum dynamics in affected regions, thus contributing to a deeper understanding of marine ecosystem dynamics and resilience.

Drop Test Simulation of Packaging for Dangerous Goods: An Investigation of Appropriate Drop Height Adjustment in Case of Deviating Packaging Gross Mass

ABSTRACTIn the approval process of dangerous goods packagings, drop tests onto a flat, essentially unyielding surface are used to assess resistance against mechanical damage. International adopted regulations like ADR and RID define filling good dependent drop heights and filling degrees whilst the user needs to define the maximum gross mass to be tested and approved. Maximum packaging gross mass is defined conservatively and not reached in practice. To meet the defined gross mass in testing, using additives is permitted. However, in some cases, additives are not desirable due to packaging design or filling substance properties. This leads to deviations from the initial gross mass definition. Hence, a certain drop height adjustment is necessary to achieve the required impact loading. Laboratories frequently adjust drop height assuming a perfectly elastic collision that is inaccurate. Appropriate adjustment is not trivial due to energy conversion processes, for example, plastic deformation. In this work, a test stand is developed for measuring the change in kinetic energy of different packaging designs and filling substances in regulative drop tests. The experimental results are used to validate finite‐element (FE) models so that packaging properties can be varied in simulated drop test scenarios. The findings intend to describe the appropriate drop height adjustment of the respective packaging with same design but deviating gross mass to produce comparable mechanical response. The results are highly beneficial for testing laboratories, approval issuing authorities and packaging institutes confronted with the problem of testing packages with gross masses other than those to be approved.

Full non-LTE spectral line formation

In the present paper we consider the full nonlocal thermodynamic equilibrium (non-LTE) radiation transfer problem. This formalism allows us to account for deviation from equilibrium distribution of both the radiation field and the massive particles. In the present study, two-level atoms with broadened upper level represent the massive particles. In the absence of velocity-changing collisions, we demonstrate the analytic equivalence of the full non-LTE source function with the corresponding standard non-LTE partial frequency redistribution (PFR) model. We present an iterative method based on operator splitting techniques that can be used to numerically solve the problem at hand. We benchmark it against the standard non-LTE transfer problem for a two-level atom with PFR. We illustrate the deviation of the velocity distribution function of excited atoms from the equilibrium distribution. We also discuss the dependence of the emission profile and the velocity distribution function on elastic collisions and velocity-changing collisions.

Falling weight impact acceleration-time signals analysis for road modulus detection: theoretical and experimental investigations

Structural modulus detection is essential for construction and maintenance in road engineering. Falling weight impact loading method has significant strengths in large-scale, continuous, and rapid detection. To provide theoretical support for this, theoretical analysis and falling weight impact experiments were employed in this study to investigate the influence of road structure parameters and falling weight impact parameters on impact acceleration-time signals. First, the applicability of the Hertz model in road detection was analyzed, and theoretical formulas for peak acceleration amax and impact duration t2 were established, considering the perfectly elastic collision between falling weight and half-space. Second, the influence of layered structures’ properties on impact acceleration-time curves was studied through model box impact experiments. Third, field tests were conducted to study engineering applications. The results showed that the influence patterns were similar in both theoretical and experimental studies, with differences reflected in the time of compression and restitution phases due to the road materials’ viscosity and plasticity. Additionally, in indoor experiments, amax showed an excellent power function relationship with structural layer modulus, with R2 more than 0.95, and the contribution of each layer’s modulus to amax decreased from top to bottom. Finally, amax and resilient modulus of an old road also followed a good power function relationship, with R2 around 0.76. This study revealed that amax was recommended for road surface modulus detection based on solid theoretical and experimental support.

Using Schottky Arc-plasma for Modelling the Cathode Temperatures of Various Materials at High Pressure

Theoretical investigation for cathodes of different metals, including hafnium (Hf), niobium (Nb), tungsten (W), and molybdenum (Mo) were used. It was noticed that the plasma energy at the cathode (Hf) has a higher value than that at the cathode metal because the energy losses of electrons for (Hf) are less due to inelastic collisions. As for the energy of electrons, their value for the metal (Hf) is also higher than of the other metals, and the reason is that the energy is proportional to the temperature according to the equation: (E = 3/2 KT). It was also noted that the energy of ions for all metals is almost equal at temperature (Tw≅4000K) due to energy losses due to elastic and inelastic collisions, this leads to a state of saturation. There is a large decrease in the voltage barrier accompanied by an increase in the current density, differences occur in the values of the voltage barrier due to the difference in the work function which varies according to the metal.

Uncovering Intermolecular Interactions Driving the Liquid-Liquid Phase Separation of the TDP-43 Low-Complexity Domain via Atomistic Dimerization Simulations.

Liquid-liquid phase separation (LLPS) of transactive response DNA-binding protein of 43 kDa (TDP-43), which exerts multiple functions in the splicing, trafficking, and stabilization of RNA, mediates the formation of membraneless condensates with crucial physiological roles, while its aberrant LLPS is linked to multiple neurodegenerative diseases. However, due to the heterogeneous and dynamic nature of LLPS, major gaps remain in understanding the precise intermolecular interactions driving LLPS and how specific mutations alter LLPS dynamics. Here, we investigated the molecular mechanisms underlying the LLPS of the TDP-43 low-complexity domain (LCD) by simulating the dimerization process using all-atom discrete molecular dynamics with microsecond-long simulations. Our results showed that the TDP-43 LCD was intrinsically disordered, with helical structures consistent with prior nuclear magnetic resonance studies. Phase separation propensity was assessed by simulating the dimerization of the TDP-43 LCD and four mutants, showing that A321G, W334G, and M337V inhibited self-association, while G335D promoted it, fully consistent with experimental reports. During the dimerization process, two peptides experienced both elastic and nonelastic collisions, and the self-associated dimer featured both high- and low-contact states. These results suggested that the dimerization process of the TDP-43 LCD was accordingly dynamic and heterogeneous. Additionally, we identified crucial regions containing hydrophobic clusters and aromatic residues in the N-terminus, central region, and C-terminus that were essential for the self-association of the TDP-43 LCD. These residues with high binding affinities can act as stickers to form peptide networks in LLPS. Together, our simulation provides a comprehensive picture of the intermolecular interactions driving the phase separation of the TDP-43 LCD, offering insights into both physiological functions and pathological mechanisms.

Active Data-enabled Robot Learning of Elastic Workpiece Interactions

Abstract During manufacturing processes, such as clamping and drilling of elastic structures, it is essential to maintain tool-workpiece normality to minimize shear forces and torques, and thereby preventing damage to the tool or the workpiece. The challenge arises in making precise model-based predictions of the relatively large deformations that occur as the applied normal force (e.g., clamping force) is increased. However, precision deformation predictions are essential for selecting the optimal robot pose that maintains force normality. Therefore, recent works have employed force-displacement measurements at each work location to determine the robot pose for maintaining tool normality. Nevertheless, this approach, which relies on local measurements at each work location and at each gradual increment of the applied normal force, can be slow and consequently, time prohibitive. The main contributions of this work are to use: Gaussian Process methods to learn the robot-pose map for force normality at unmeasured workpiece locations; active learning to optimally select and minimize the number of measurement locations needed for accurate learning of the robot-pose map. Experimental results show that the number of data points needed with active learning is 77.8% less than the case with a benchmark linear positioning learning for the same level of model precision. Additionally, the learned robot-pose map enables a rapid increase of the normal force at unmeasured locations on the workpiece, reaching force-increment rates up to eight times faster than the original force-increment rate when the robot is learning the correct pose.

Site Disorder Drives Cyanide Dynamics and Fast Ion Transport in Li6PS5CN.

Halide argyrodite solid-state electrolytes of the general formula Li6PS5 X exhibit complex static and dynamic disorder that plays a crucial role in ion transport processes. Here, we unravel the rich interplay between site disorder and dynamics in the plastic crystal argyrodite Li6PS5CN and the impact on ion diffusion processes through a suite of experimental and computational methodologies, including temperature-dependent synchrotron powder X-ray diffraction, AC electrochemical impedance spectroscopy, 7Li solid-state NMR, and machine learning-assisted molecular dynamics simulations. Sulfide and (pseudo)halide site disorder between the two anion sublattices unilaterally improves long-range lithium diffusion irrespective of the (pseudo)halide identity, which demonstrates the importance of site disorder in dictating bulk ionic conductivity in the argyrodite family. Furthermore, we find that anion site disorder modulates the presence and time scales of cyanide rotational dynamics. Ordered configurations of anions enable fast, quasi-free rotations of cyanides that occur on time scales of 1011 Hz at T = 300 K. In contrast, we find that cyanide dynamics are slow or frozen in Li6PS5CN when site disorder between the cyanide and sulfide sublattices is present at T = 300 K. We rationalize the observed differences in cyanide dynamics in the context of elastic dipole interactions between neighboring cyanide anions and local strain induced by the configurations of site disorder that may impact the energetic landscape for cyanide rotational dynamics. Through this study, we find that anion disorder plays a decisive role in dictating the extent and time scales of both lithium ion and cyanide dynamics in Li6PS5CN.

Percolation versus depinning transition: The inherent role of damage hardening during quasibrittle failure.

The intermittent damage evolution preceding the failure of heterogeneous brittle solids is well described by scaling laws. In deciphering its origins, failure is routinely interpreted as a critical transition. However at odds with expectations of universality, a large scatter in the value of the scaling exponents is reported during acoustic emission experiments. Here we numerically examine the precursory damage activity to reconcile the experimental observations with critical phenomena framework. Along with the strength of disorder, we consider an additional parameter that describes the progressive damageability of material elements at mesoscopic scale. This hardening behavior encapsulates the microfracturing processes taking place at lower length scales. We find that damage hardening can not only delay the final failure but also affect the preceding damage accumulation. When hardening is low, the precursory activity is strongly influenced by the strength of the disorder and is reminiscent of damage percolation. On the contrary, for large hardening, long-range elastic interactions prevail over disorder, ensuring a rather homogeneous evolution of the damage field in the material. The power-law statistics of the damage bursts is robust to the strength of the disorder and is reminiscent of the collective avalanche dynamics of elastic interfaces near the depinning transition. The existence of these two distinct universality classes also manifests as different values of the scaling exponent characterizing the divergence of the precursor size on approaching failure. Our finding sheds new light on the connection between the level of quasibrittleness of materials and the statistical features of the failure precursors. Finally, it also provides a more complete description of the acoustic precursors and thus paves the way for quantitative techniques of damage monitoring of structures-in-service.

Theory and Measurement of Heat Transport in Solids: How Rigidity and Spectral Properties Govern Behavior.

Models of heat transport in solids, being based on idealized elastic collisions of gas molecules, are flawed because heat and mass diffuse independently in solids but together in gas. To better understand heat transfer, an analytical, theoretical approach is combined with data from laser flash analysis, which is the most accurate method available. Dimensional analysis of Fourier's heat equation shows that thermal diffusivity (D) depends on length-scale, which has been confirmed experimentally for metallic, semiconducting, and electrically insulating solids. A radiative diffusion model reproduces measured thermal conductivity (K = DρcP = D × density × specific heat) for thick solids from ~0 to >1200 K using idealized spectra represented by 2-4 parameters. Heat diffusion at laboratory temperatures (conduction) proceeds by absorption and re-emission of infrared light, which explains why heat flows into, through, and out of a material. Because heat added to matter performs work, thermal expansivity is proportional to ρcP/Young's modulus (i.e., rigidity or strength), which is confirmed experimentally over wide temperature ranges. Greater uptake of applied heat (e.g., cP generally increasing with T or at certain phase transitions) reduces the amount of heat that can flow through the solid, but because K = DρcP, the rate (D) must decrease to compensate. Laser flash analysis data confirm this proposal. Transport properties thus depend on heat uptake, which is controlled by the interaction of light with the material under the conditions of interest. This new finding supports a radiative diffusion mechanism for heat transport and explains behavior from ~0 K to above melting.

Three-dimensional phase field modeling, orientation prediction and stress field analyses of twin-twin, twin-grain boundary reactions mediated by disclinations in hexagonal close-packed metals

Crystalline defects, such as dislocations, disclinations, twins and grain boundaries, play critical roles in determining the mechanical properties of metals and alloys. In particular, with multiple competitive deformation modes activated, the mechanical behaviors of hexagonal close-packed metals are strongly influenced by the interactions and reactions of various types of defects. Despite extensive studies on the elastic interactions of defects, a theoretical framework capturing crystallographic reactions, especially reaction products and associated local stress concentration, is still unavailable. Here we suggest a disclination-based method to quantify defect reactions. By using a combination of crystallographic calculations and phase field modeling/simulations, twin-twin and twin-grain boundary reactions in hexagonal close-packed metals have been quantitatively analyzed. It has been found that partial disclinations, accompanied with other defects (e.g., {112¯6} and {112¯2} high-index twins), can be generated by defect reactions as typical byproducts. The orientation change and stress fields caused by disclination formation have been systematically calculated, which offers a rigorous mathematical foundation to explore twin-twin, twin-grain boundary reactions. By quantitatively determining defect reactions and local stress fields, our work provides new insights into the deformation mechanism and microstructure-property relationship in metallic materials.

Mechanism and improvement for tail vehicle swaying of power-centralized EMUs

The swing phenomenon of the tail vehicle will reduce the stability of the train operation, and even seriously deteriorate the ride comfort of passengers. In response to the relevant railway department, this paper reported the different dynamics performances in tail vehicle swaying when power-concentrated EMUs passed through a tunnel under push/pull operation. To analyze the characteristics and mechanism of the EMU tail swaying, field tests and numerical simulations were conducted. Firstly, through the on-track test, it was found that under push operation, the EMU tail continued to sway at a frequency of 1.3 Hz inside the tunnel, while under pull operation, only a swing of 1.7 Hz appeared at the tunnel entrance. Subsequently, through a simulation analysis, it was found that under push operation, the vortex-induced vibration of the tail carbody occurred inside the tunnel, leading to the sustained swing with a carbody hunting frequency of 1.3 Hz; under pull operation, due to the aerodynamic effect of the tunnel entrance, the secondary lateral stop had an abnormal elastic collision with the bogie frame, and the lateral impact on the bottom of the tail carbody caused a swing of 1.7 Hz, which was verified by the field test. Finally, for the motor vehicle of the EMU tail, two improvement measures of yaw damper optimization were proposed to alleviate the EMU tail swaying inside the tunnel. Furthermore, the research results can provide a reference for the aerodynamic swing problem of other trains, which has certain engineering significance.

Research on Influencing Factors of Cable Clamp Bolt Elastic Interaction in Cross-Ocean Suspension Bridges

Suspension bridges are the most common type of bridge used to cross the ocean. The cable clamps in suspension bridges clamp the main cables by bolt preload, but the elastic interaction of the bolts reduces the preload, which is detrimental to the force in suspension bridges. However, research on the factors influencing the elastic interaction of cable clamp bolts in suspension bridges is currently limited. This paper aims to explore the law of influence of external factors on the elastic interaction of bolts through a combined approach of theoretical analysis, full-scale experiment, and finite element simulation. The results indicate that the average preload loss was reduced by about 27% when the elastic modulus was increased by about 110%. The average preload loss was reduced by about 45% when the bolt center distance was increased by 75%. The number of bolts has a small effect on the elastic interaction, which can be ignored. When the preload of bolt installation was increased by 133%, the average preload loss was reduced by approximately 125%, which was almost a linear relationship. Tightening the bolt from the center bolt creates greater elastic interaction. The conclusions can provide suggestions for reducing the elastic interaction of bolts in the design and construction of suspension bridge cable clamps.

Study of the heavy quarks energy loss through medium polarization, elastic collision and radiative processes

Study of the heavy quarks energy loss through medium polarization, elastic collision and radiative processes

Elastic interactions compete with persistent cell motility to drive durotaxis

Many animal cells that crawl on extracellular substrates exhibit durotaxis, i.e., directed migration toward stiffer substrate regions. This has implications in several biological processes including tissue development and tumor progression. Here, we introduce a phenomenological model for single-cell durotaxis that incorporates both elastic deformation-mediated cell-substrate interactions and the stochasticity of cell migration. Our model is motivated by a key observation in an early demonstration of durotaxis: a single, contractile cell at a sharp interface between a softer and a stiffer region of an elastic substrate reorients and migrates toward the stiffer region. We model migrating cells as self-propelling, persistently motile agents that exert contractile traction forces on their elastic substrate. The resulting substrate deformations induce elastic interactions with mechanical boundaries, captured by an elastic potential. The dynamics is determined by two crucial parameters: the strength of the cellular traction-induced boundary elastic interaction (A), and the persistence of cell motility (Pe). Elastic forces and torques resulting from the potential orient cells perpendicular (parallel) to the boundary and accumulate (deplete) them at the clamped (free) boundary. Thus, a clamped boundary induces an attractive potential that drives durotaxis, while a free boundary induces a repulsive potential that prevents antidurotaxis. By quantifying the steady-state position and orientation probability densities, we show how the extent of accumulation (depletion) depends on the strength of the elastic potential and motility. We compare and contrast crawling cells with biological microswimmers and other synthetic active particles, where accumulation at confining boundaries is well known. We define metrics quantifying boundary accumulation and durotaxis, and present a phase diagram that identifies three possible regimes: durotaxis, and adurotaxis with and without motility-induced accumulation at the boundary. Overall, our model predicts how durotaxis depends on cell contractility and motility, successfully explains some previous observations, and provides testable predictions to guide future experiments.

Transport and clogging dynamics of flexible rods in pore constrictions.

The transport and clogging behavior of flexible particles in confined flows is a complex interplay between elastic and hydrodynamic forces and wall interactions. While the motion of non-spherical particles in unbounded flows is well understood, their behavior in confined spaces remains less explored. This study introduces a coupled computational fluid dynamics-discrete element method (CFD-DEM) approach to investigate the transport and clogging dynamics of flexible rod-shaped particles in confined pore constrictions. The spatio-temporal analysis reveals the influence of the rod's initial conditions and flexibility on its transport dynamics through a pore constriction. The simulation results demonstrate an increase in the lateral drift of the rod upon exiting the pore that can be scaled with channel height confinement. The clogging dynamics are explored based on hydrodynamic and mechanical forces, unveiling conditions for mechanical clogging through sieving. The developed method allows for the deconvolution of the forces that contribute to particle trajectories in confined flow, which is highly relevant in particle separation processes, fibrous-shaped virus filtration, biological flows, and related applications. The method is embedded into the open-source CFDEM framework, facilitating future extensions to explore multiple particle dynamics, intermolecular forces, external influences, and complex geometries.