Bounce Trajectories Research Articles

Periodic bounce trajectories in moving domains

We study the existence of periodic trajectories in periodically moving domains. Our trajectories bounce at the boundary of moving domains in an elastic way. We prove the existence of infinitely many periodic bounce trajectories.

Task-evoked pupillary responses track precision-weighted prediction errors and learning rate during interceptive visuomotor actions

In this study, we examined the relationship between physiological encoding of surprise and the learning of anticipatory eye movements. Active inference portrays perception and action as interconnected inference processes, driven by the imperative to minimise the surprise of sensory observations. To examine this characterisation of oculomotor learning during a hand–eye coordination task, we tested whether anticipatory eye movements were updated in accordance with Bayesian principles and whether trial-by-trial learning rates tracked pupil dilation as a marker of ‘surprise’. Forty-four participants completed an interception task in immersive virtual reality that required them to hit bouncing balls that had either expected or unexpected bounce profiles. We recorded anticipatory eye movements known to index participants’ beliefs about likely ball bounce trajectories. By fitting a hierarchical Bayesian inference model to the trial-wise trajectories of these predictive eye movements, we were able to estimate each individual’s expectations about bounce trajectories, rates of belief updating, and precision-weighted prediction errors. We found that the task-evoked pupil response tracked prediction errors and learning rates but not beliefs about ball bounciness or environmental volatility. These findings are partially consistent with active inference accounts and shed light on how encoding of surprise may shape the control of action.

Interferometry and Simulation of the Thin Liquid Film between a Free-Rising Bubble and a Glass Substrate.

Because of their practical importance and complex underlying physics, the thin liquid films formed between colliding bubbles or droplets have long been the subject of experimental investigations and theoretical modeling. Here, we examine the possibility of accurately predicting the dynamics of the thin liquid film drainage using numerical simulations when compared to an experimental investigation of millimetric bubbles free-rising in pure water and colliding with a flat glass interface. A high-speed camera is used to track the bubble bounce trajectory, and a second high-speed camera together with a pulsed laser is used for interferometric determination of the shape and evolution of the thin liquid film profile during the bounce. The numerical simulations are conducted with the open source Gerris flow solver. The simulation reliability was first confirmed by comparison with the experimental bubble bounce trajectory and bubble shape evolution during the bounce. We further demonstrate that the simulation predicted time evolution for the shape of the thin liquid film profiles is in excellent agreement with the high-speed interferometry measured profiles for the entire experimentally accessible film size range. Finally, we discuss the implications of using numerical simulation together with theoretical modeling for resolving the complex processes of high velocity bubble and droplet collisions.

Influences of active control on attention allocation in MOT.

We investigated the influence of active involvement on the way visual attention is distributed during multiple-object tracking (MOT), specifically when objects bounce, using two experiments modeled after the videogame Pong. In both experiments, participants were either assigned to an active group or a passive group. The active groups were instructed to move a virtual paddle in order to bounce target objects as often as possible. Participants in the passive groups viewed recordings of trials from the active groups. In all conditions, participants were asked to track the target objects and to detect dot probes that briefly appeared on the screen. Using probe detection, we explored the distribution of attentional resources over the linear and bounce trajectories of tracked objects. We found that active involvement can enhance probe detection along the future post-bounce trajectory, but it depends on the difficulty of the task.

Object Permanence Through Audio-Visual Representations

As robots perform manipulation tasks and interact with objects, it is probable that they accidentally drop objects (e.g., due to an inadequate grasp of an unfamiliar object) that subsequently bounce out of their visual fields. To enable robots to recover from such errors, we draw upon the concept of object permanence-objects remain in existence even when they are not being sensed (e.g., seen) directly. In particular, we developed a multimodal neural network model-using a partial, observed bounce trajectory and the audio resulting from drop impact as its inputs-to predict the full bounce trajectory and the end location of a dropped object. We empirically show that: 1) our multimodal method predicted end locations close in proximity (i.e., within the visual field of the robot's wrist camera) to the actual locations and 2) the robot was able to retrieve dropped objects by applying minimal vision-based pick-up adjustments. Additionally, we show that our method outperformed five comparison baselines in retrieving dropped objects. Our results contribute to enabling object permanence for robots and error recovery from object drops.

Theoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane

AbstractTheoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane with arbitrary wave normal angle distributions is derived. Previous studies either assumed waves to cover the whole bounce trajectory or to have only one wave normal angle for a given frequency. In this work, we theoretically derive a new bounce resonance diffusion coefficient without these limitations. We demonstrate that the pitch angle diffusion from bounce resonance is significant for near‐equatorially mirroring particles using a published magnetosonic wave model. Our results suggest that the bounce resonance diffusion by magnetosonic waves could be an important mechanism for pitch angle scattering of near‐equatorially mirroring particles; therefore, it might be important to include bounce resonance with magnetosonic waves in global radiation belt modeling.

Scattering Dynamics, Survival, and Dispersal of Dimethyl Methylphosphonate Interacting with the Surface of Multilayer Graphene.

We explored the interaction of a molecular beam of dimethyl methylphosphonate with a multilayer graphene surface to better understand the fate of chemical warfare agents in the environment. The experiments were done at surface temperatures between 120 and 900 K and translational energies between 200 and 1500 meV. At the lowest temperatures, the dimethyl methylphosphonate is adsorbed, with the molecules next to the carbon surface held slightly more strongly than the bulk molecular film that grows with continued dosing. We measured the desorption energy for submonolayer coverage using modulated beam techniques and found a value of 290 meV (28 kJ/mol). At higher surface temperatures, where the residence times are very short, we measured the scattering of the dimethyl methylphosphonate as a function of angle and translational kinetic energy. For a surface temperature of 250 K, with translational kinetic energies between 200 and 1500 meV, much of the incident flux has nearly been accommodated by the surface temperature and has no memory of the incident momentum. The internal energy also seems to be at least partially accommodated. As the surface temperature increases, the scattering transitions to direct-inelastic reflection, where much of the incident translational energy is retained, and the intensity of the scattering peaks superspecularly toward glancing final angles. These results demonstrate the efficacy of using kinetic energy controlled molecular beams to probe the interactions of complex organic molecules with well-defined surfaces, extending our fundamental understanding of how the dynamics for such systems crossover from trapping-desorption to direct inelastic scattering. Moreover, these results indicate that simulations that model the dispersal of chemical warfare agents using common interfaces in the environment need to account for multiple bounce trajectories and survival of the impinging molecules.

Bounce resonance diffusion coefficients for spatially confined waves

AbstractTheoretical bounce resonance diffusion coefficients from interactions between electrons and spatially confined waves are derived and validated. Roberts and Schulz bounce resonance diffusion coefficients assume waves to be present on the whole bounce trajectory of particles; therefore, they are not directly applicable to waves that have a finite spatial extent. We theoretically derive and numerically validate a new set of bounce resonance diffusion coefficients for spatially confined waves. We apply our analysis to magnetosonic waves, which are confined to equatorial regions, using a previously published magnetosonic wave model. We find that the bounce resonance diffusion coefficients are comparable to the gyroresonance diffusion coefficients. We conclude that bounce resonance diffusion with magnetosonic waves might play an important role in relativistic electron dynamics.

Modelling bubble rise and interaction with a glass surface

A theoretical model has been developed to analyse bubble rise in water and subsequent impact and bounce against a horizontal glass plate. The multiscale nature of the problem, where the bubble size is on the millimetre range and the film drainage process happens on the micrometre to nanometre scale requires the combined use of different modelling techniques. On the macro scale we solve the full Navier–Stokes equations in cylindrical coordinates to model bubble rise whereas modelling film drainage on the micro scale is based on lubrication theory because the film Reynolds number becomes much smaller than unity. Quantitative predictions of this model are compared with experimental data obtained using synchronised high-speed cameras. Video recording of bubble rise and bounce trajectories are combined with interferometry data to deduce the position and time-dependent thickness of the thin water film trapped between the deformed bubble and the glass plate. Bubble rise velocity indicated that the boundary condition at the bubble surface was tangentially immobile. Quantitative comparisons are presented for bubbles of different size to quantify similarities and differences.

Whistler mode instability and pitch-angle diffusion near Ganymede

The present study is aimed at resolving the issue of pitch-angle diffusion by whistler mode waves near Ganymede and to understand the interaction of Ganymede with magnetosphere of Jupiter. A new electron distribution function, which is a combination of Maxwellian and kappa loss-cone distribution, is used to calculate whistler mode wave growth rates. The distribution function is fitted to observed distribution near Ganymede. Wave growth rates have been used to obtain bounce-averaged pitch-angle diffusion coefficients along the field line connecting Ganymede and Jupiter. Variations of electron density and magnetic field along the particle bounce trajectory and a non dipolar field have been taken into account. Pitch-angle variation of diffusion coefficients is parameterized in a simple form ~Dο(sinα)p. Do is diffusion coefficient (independent of pitch angle). The calculated energy dependence of diffusion coefficients (Do) is in good agreement with observed energy dependence of coefficient Do. Wave magnetic field ~16pT is required to match observed and calculated diffusion coefficients. The exponent p takes values from ~1 to 4 for electron energies 15keV to 1MeV, respectively. It is found that contribution of Ganymede interaction region to pitch-angle scattering is quite small (~4% to 20%). Further analysis of Galileo energetic particle detector (EPD) and plasma wave data or new particle and wave data near Ganymede from JUNO mission to Jupiter are necessary to confirm the findings of present work.

Pitch angle diffusion by whistler mode waves in the jovian magnetosphere and diffuse auroral precipitation

Bounce-averaged pitch angle diffusion rates of electrons due to whistler mode waves have been calculated in the Jupiter’s magnetosphere. Variations of electron density, magnetic field, wave intensity and upper cut-off frequency along the particle bounce trajectory have been taken into account. Field line tracing is performed to obtain the loss-cone size associated with the VIP 4 magnetic field model including the external field due to azimuthal current sheet. Numerical calculations have been carried out at L shells 10, 12, 15, 18, and 20. The longitudinal variations of electron energy precipitation into the atmosphere leading to diffuse aurora have been modelled. It is found that observed wave amplitudes at L⩽15 are insufficient to put electrons on strong pitch angle diffusion whereas at L=18 and 20 electrons of energies ⩽30keV can be put on strong diffusion. At L=10 electron energy precipitation supports auroral brightness of 25kR in the northern and 36kR in the southern hemisphere at west longitude ∼10–60°. At shells L=12 and 15 auroral brightness less than 10kR is obtained. This is in accord with Voyager observation of jovian UV aurora just beyond the Io torus (7–12RJ). At L=18 maximum auroral brightness 73kR in the northern hemisphere at west longitude of 163° and 30kR in the southern hemisphere for west longitudes ⩽50° are obtained. This is in agreement with the diffuse auroral brightness measured by Hubble Space Telescope (HST). Observations of longitudinal variation of diffuse auroral brightness are, however, required to ascertain the present findings.

Toward Detection of Electron-Hole Pair Excitation in H-atom Collisions with Au(111): Adiabatic Molecular Dynamics with a Semi-Empirical Full-Dimensional Potential Energy Surface

We report an analytic potential energy surface (PES) based on several hundred DFT energies for H interacting with a Au(111) surface. Effective medium theory is used to fit the DFT data, which were obtained for the Au atoms held at their equilibrium positions. This procedure also provides an adequate treatment of the PES for displacements of Au atoms that occur during scattering of H atoms. The fitted PES is compared to DFT energies obtained from ab initio molecular dynamics trajectories. We present molecular dynamics simulations of energy and angle resolved scattering probabilities at five incidence angles at an incidence energy, Ei = 5 eV, and at a surface temperature, TS = 10 K. Simple single bounce trajectories are important at all incidence conditions explored here. Double bounce events also make up a significant fraction of the scattering. A qualitative analysis of the double-bounce events reveals that most occur as collisions of an H-atom with two neighboring surface gold atoms. The energy losses observed are consistent with a simple binary collision model, transferring typically less than 150 meV to the solid per bounce.

Macroscopic quantum tunneling of Bose-Einstein condensates with long-range interaction

The ground state of Bose-Einstein condensates with attractive particle interactions is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory as a solution of the time-dependent Gross-Pitaevskii equation in imaginary time. For condensates with an electromagnetically induced gravity-like interaction, the bounce trajectory is computed with an extended variational approach using coupled Gaussian functions and is simulated numerically exact within the mean-field approach on a spacetime lattice. It is shown that the variational computations converge very rapidly to the numerically exact result with increasing number of Gaussians. The tunneling rate of the condensate is obtained from the classical action and additional parameters of the bounce trajectory. The converged variational and numerically exact results drastically improve by several orders of magnitude the decay rates obtained previously with a simple variational approach using a single Gaussian-type orbital for the condensate wave function.

Metodi topologici, disequazioni variazionali e traiettorie di rimbalzo elastico

The first part of this exposition briefly outlines the story of the encounter between two research streams active in Italy and particularly in Pisa in the second half of the twentieth century: Nonlinear Analysis led by Giovanni Prodi and Variational Inequalities led by Guido Stampacchia. This meeting was favoured by an independent proposal of Ennio De Giorgi. In the second part some recent outcomes concerning elastic bounce trajectories are reported.

The proton pressure tensor as a new proxy of the proton decoupling region in collisionless magnetic reconnection

Abstract. Cluster data is analyzed to test the proton pressure tensor variations as a proxy of the proton decoupling region in collisionless magnetic reconnection. The Hall electric potential well created in the proton decoupling region results in bounce trajectories of the protons which appears as a characteristic variation of one of the in-plane off-diagonal components of the proton pressure tensor in this region. The event studied in this paper is found to be consistent with classical Hall field signatures with a possible 20% guide field. Moreover, correlations between this pressure tensor component, magnetic field and bulk flow are proposed and validated, together with the expected counterstreaming proton distribution functions.

Asymptotically critical points and multiple elastic bounce trajectories

We study multiplicity of elastic bounce trajectories (e.b.t.'s) with fixed end points $A$ and $B$ on a nonconvex billiard table $\Omega$. As well known, in general, such trajectories might not exist at all. Assuming the existence of a ``bounce free'' trajectory $\gamma_0$ in $\Omega$ joining $A$ and $B$ we prove the existence of multiple families of e.b.t.'s $\gamma_{\lambda}$ bifurcating from $\gamma_0$ as a suitable parameter $\lambda$ varies. Here $\lambda$ appears in the dynamics equation as a multiplier of the potential term. We use a variational approach and look for solutions as the critical points of the standard Lagrange integrals on the space $X(A,B)$ of curves joining $A$ and $B$. Moreover, we adopt an approximation scheme to obtain the elastic response of the walls as the limit of a sequence of repulsive potentials fields which vanish inside $\Omega$ and get stronger and stronger outside. To overcome the inherent difficulty of distinct solutions for the approximating problems covering to a single solutions to the limit one, we use the notion of ``asymptotically critical points'' (a.c.p.'s) for a sequence of functional. Such a notion behaves much better than the simpler one of ``limit of critical points'' and allows to prove multliplicity theorems in a quite natural way. A remarkable feature of this framework is that, to obtain the e.b.t.'s as a.c.p.'s for the approximating Lagrange integrals, we are lead to consider the $L^2$ metric on $X(A,B)$. So we need to introduce a nonsmooth version of the definition of a.c.p. and prove nonsmooth versions of the multliplicity theorems, in particular of the ``$\nabla$-theorems'' used for the bifurcation result. To this aim we use several results from the theory of $\varphi$-convex functions.

Influence of nonlinear coupling on quantum decay rate of metastable dissipative systems

We develop the fast-Fourier-transformation path-integral approach to investigate the quantum decay of a nonlinear dissipative system. The action of the bounce trajectory, i.e. the exponential factor of decay rate, is obtained. In the case of the nonlinear coupling f(x)=tanh［λ(x-xb)］ between the system and its environment, we find that the nonlinear coupling suppresses the decay rate. In contrast to the usual linear coupling, the action will not abide by the law SB=a［1-b(T/Tc)2］ and the crossover temperature rebounds, which means that the system steps into the quantum tunneling region at a higher temperature.

Effects of some surfactants on foliar impaction and retention of monosize water droplets

The impaction and retention behavior of low-velocity (below 3 m s−1) monosize droplets (100–1000 μm diameter) containing either water or aqueous surfactant solutions was examined on wettable and water-repellant leaf surfaces using a high magnification video system. Mapping of bounce trajectories provided a history of droplet behaviour from first impact to final retention on, or escape from, a leaf, and yielded velocity thresholds for capture or bounce following impact of any droplet. Water droplets were captured on water-repellant leaves only when their pre-impact velocity fell below 0.25 m s−1, so that even small (120 μm) low-velocity (0.57 m s−1) droplets bounced between two and six times before finally being retained. Surfactant addition invariably reduced the number of bounces between first impact and retention, and increased the velocity threshold for capture following impact. The physical parameters of droplets, as expressed by Reynolds (Re) and Weber (We) numbers, are discussed and the trajectory data shown to generate two relationships between Re and We which define the transition from capture to bounce following impact. © 1999 Society of Chemical Industry

Morse Index of Approximating Periodic Solutions for the Billiard Problem. Application to Existence Results

AbstractThis paper deals with periodic solutions for the billiard problem in a bounded open set of ℝN which are limits of regular solutions of Lagrangian systems with a potential well. We give a precise link between the Morse index of approximate solutions (regarded as critical points of Lagrangian functionals) and the properties of the bounce trajectory to which they converge.

Transfer-energy-dependent escape rate of electrons influenced by dynamical flux fields.

A path-integral approach is used to study the dynamics of a tunneling electron coupled to a flux that is governed by a free field Lagrangian. The transfer-energy-dependent escape rate of electrons is obtained from an analytic bounce trajectory for a rectangular barrier. Results are compared with those previously obtained for the charge model.