Elastic Collisions Research Articles

Size and Surface Effects in the Ultrafast Dynamics of Strongly Cooperative Spin-Crossover Nanoparticles.

Cooperative photoinduced switching of molecular materials at the nanoscale is still in its infancy. Strongly cooperative spin-crossover nanomaterials are arguably the best prototypes of photomagnetic and volume-changing materials that can be manipulated by short pulses of light. Open questions remain regarding their non-equilibrium dynamics upon light excitation and the role of cooperative elastic interactions in nanoscale systems that are characterized by large surface/volume ratios. Femtosecond-resolved broadband spectroscopy is performed on nanorods of the strongly cooperative Fe-triazole, which undergoes a reversible low-spin to high-spin (HS) phase transition ≈360K. Supported by density functional theory and mechano-elastic Monte Carlo simulations, a marked difference is observed in the photoswitching dynamics at the surface of the nanoparticles compared with the core. Surprisingly, under low excitation (<2%) conditions, there occurs a transient increase in the HS population at the surface on the picosecond time scale, while the HS population in the core decays concomitantly. These results shed light onto the importance of surface properties and dynamical size limits of nanoscale photoresponsive nanomaterials that can be used in a broad range of applications.

Two types of interaction phenomena of the lump wave for nonlinear model of Rossby waves

In this paper, we show the interaction phenomena about the first-order lump wave and multiple solitons by four theorems. The interaction phenomena are divided into two types, one type is absorbing collision phenomenon and the other type is elastic collision phenomenon. Six sets of dynamic plots over time are showed the phenomenon of absorbing interactions with energy transfer process, the phenomenon of elastic interactions with restoration of the initial state after collision. We apply the four theorems to an equation which can characterize the Rossby waves’ amplitude, this equation can be used to describe the resonance phenomenon of Rossby waves. Different test functions with the same parameter values can present different wave-wave interaction properties. This study contributes to in-depth investigation of the mechanism of lump wave generation, evolution and interaction.

Solutions of a Neutron Transport Equation with a Partly Elastic Collision Operators

In this paper, we derive sufficient conditions that guarantee an description of long-time asymptotic behavior of the solution to the Cauchy problem governed by a linear neutron transport equation with a partially elastic collision operator under periodic boundary conditions. Our strategy involves showing that the strongly continuous semigroups et(T+Ke)t≥0 and et(T+Kc+Ke)t≥0, generated by the operators T+Ke and T+Kc+Ke, respectively, have the same essential type.According to Proposition , it is sufficient to show that remainder term in the Dyson–Philips expansion is compact. Our analysis focuses on the compactness properties of the second-order remainder term in the Dyson–Phillips expansion related to the problem. We first show that R2(t) is compact on L2(Ω×V,dxdv), and, using an interpolation argument (see Proposition ), we establish the compactness of R2(t) on Lp(Ω×V,dxdv)-spaces for 1&lt;p&lt;+∞. To the best of our knowledge, outside the one-dimensional case, this result is known only for vaccum boundary conditions in the multidimensional setting. However, our result, Theorem , is new for periodic boundary conditions.

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.

Langevin dynamics for a heavy particle immersed within a flow of light particles

A micro-hydrodynamics model based on elastic collisions of light point solvent particles with a heavy solute particle is investigated in the setting where the light particles have velocity distribution corresponding to a background flow. Considering a range of stationary background flows and distributions for the solvent particle velocities, the macroscopic Langevin-type description of the behaviour of the heavy particle is derived in the form of a generalized Ornstein–Uhlenbeck process. At leading order, the drift term in this process depends upon both the geometric structure of the background flow and the size of the heavy particle, while both drift and diffusion terms scale with moments of the light particle velocity distribution. Computational methods for simulating the micro-hydrodynamics model are then designed to confirm the theoretical results. To enable long-time calculations, simulations are performed in a frame co-moving with the heavy particle. Efficient methods for sampling the position and velocity distributions of incoming solvent particles at the boundaries of the co-moving frame are derived for a range of distributions of solvent particles. The simulations show good agreement with the theoretical results.

Defect dynamics modeling of mesoscale plasticity

The collective motion of defects and their interaction are the basic building blocks for plastic deformation and corresponding mechanical behaviors of crystalline metals. Especially, dislocations among various defects are the “carrier” of plastic deformation in many crystalline materials, particularly ductile materials. To get a fundamental understanding of plastic deformation mechanisms, it calls for an integrated computational platform to simultaneously capture detailed defects characteristics across several length scales together with corresponding macroscopic mechanical response. In this paper, we present a three-dimensional mesoscale defect dynamics model to directly couple the three dimensional discrete dislocation dynamics model with continuum finite element method, aiming at capturing both size dependent plasticity at micron-, and submicron scale and constitutive behaviors at larger scales where such size-dependence disappear. Using non-singular dislocation theories, our model could accurately consider both short- and long-range elastic interactions between multiple dislocation segments with even higher computational efficiency than traditional dislocation dynamics simulations, together with the careful consideration of crystal/material rotation in the coupled framework. In addition, our model could directly model dislocation nucleation from stress concentrators such as a void, crack and indentor tip, which could allow us to investigate various defects’ motion and their mutual interactions, predicting macroscopic mechanical response of complex structures. The developed concurrently coupled model could also consider multiphysical phenomena by solving coupled governing equations in finite element framework, which could shed light on complex defect behaviors under various physical environments.

Elastic and inelastic scattering of flat-top solitons

We investigate the interaction between two flat-top solitons within the cubic-quintic nonlinear Schrödinger equation framework. Our study results point towards a significant departure of flat-top solitons' collisional characteristics from the conventional behaviors exhibited in the scattering dynamics of two bright solitons. Our investigation outlines specific regimes corresponding to the dual flat-top solitons' elastic and inelastic collisions. We determine regimes in the parameter space where exchange in the widths of the interacting flat-top solitons is possible, even within the elastic collision domain. We find a periodic occurrence of completely elastic scattering of flat-top solitons in terms of the solitons' parameters. Investigating the internal energy transfers between the solitons and the emitted radiation reveals the origin of inelasticity in flat-top soliton collisions. We perform a variational calculation that accounts for the amount of radiation produced by the collision and hence provides further insight into the physics underlying the loss of elasticity of collisions. Published by the American Physical Society 2024

Mechanisms of separation of the elastic step and the thermal step

The elastic interaction causes a two‐step conversion from the low‐spin (LS) to the high‐spin state (HS) following a femtosecond laser pulse excitation. These steps occur on different timescales: a spin conversion (elastic step) in a short time due to pressure propagation and a late spin conversion (thermal step) resulting from heat diffusion. In this paper, we provide a brief review of models for spin crossover phenomena, emphasizing the role of the difference of degeneracy of the HS state and LS state and elastic interaction due to changes in local structures. We also review theoretical approaches to these effects. Additionally, to analyze the dynamical process of spin conversion after photo‐irradiation, it is necessary to consider mechanisms of heat transfer among spins. Recently, we proposed a two‐temperature model that incorporates both lattice and spin temperatures, which enables us to reproduce the two steps under an early uniformization of the lattice temperature, highlighting the importance of the timescales of these processes. Furthermore, we explore possible mechanisms to separate the two steps by examining the different timescales of processes of spin conversions by mechanical and entropic forces, and also by considering changes of local temperature due to spin conversion.

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.

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.

Soft-gluon exchange matters: Isotropic screening in QCD kinetic theory

QCD kinetic theory simulations are a prominent tool for studying the nonequilibrium initial stages in heavy-ion collisions. Despite their success, all implementations rely on approximations of the hard thermal loop (HTL) screened matrix elements in the collision terms. In this paper, we present our results for different isotropic screening prescriptions in the elastic collision term for gluons. In particular, we go beyond the simple Debye-like screening form that is used in all current implementations and apply the isotropic HTL matrix element instead. For isotropic systems, the evolution is nearly unchanged, but when studying the equilibration process in a Bjorken expanding plasma, we find qualitative and quantitative differences in a range of moments of the distribution function, such as a decrease in the maximum pressure anisotropy by up to 50%. In contrast, we find no significant qualitative impact on the jet quenching parameter or on the late-time hydrodynamization dynamics of anisotropic plasmas, but observe systematically smaller values of η/s by about 10% that coincide with perturbative calculations at small couplings. Our study reveals that the choice of the screening prescription can lead to large corrections at early times, but is less important close to equilibrium. Published by the American Physical Society 2024

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.

A mathematical model for pancreatic cancer during intraepithelial neoplasia.

Cancer is the result of complex interactions of intrinsic and extrinsic cell processes, which promote sustained proliferation, resistance to apoptosis, reprogramming and reorganization. The evolution of any type of cancer emerges from the role of the microenvironmental conditions and their impact of some molecular complexes on certain signalling pathways. The understanding of the early onset of cancer requires a multiscale analysis of the cellular microenvironment. In this paper, we analyse a qualitative multiscale model of pancreatic adenocarcinoma by modelling the cellular microenvironment through elastic cell interactions and their intercellular communication mechanisms, such as growth factors and cytokines. We focus on the low-grade dysplasia (PanIN 1) and moderate dysplasia (PanIN 2) stages of pancreatic adenocarcinoma. To this end, we propose a gene-regulatory network associated with the processes of proliferation and apoptosis of pancreatic cells and its kinetics in terms of delayed differential equations to mimic cell development. Likewise, we couple the cell cycle with the spatial distribution of cells and the transport of growth factors to show that the adenocarcinoma evolution is triggered by inflammatory processes. We show that the oncogene RAS may be an important target for developing anti-inflammatory strategies that limit the emergence of more aggressive adenocarcinomas.

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.