Phase Space Research Articles

Cobalt-free spinel–layered structurally integrated Li0.8Mn0.64Ni0.183Fe0.091O2 cathodes for lithium-ion batteries

Cobalt-free, Li-rich layered-spinel structurally integrated positive electrode (cathode) materials for lithium-ion batteries (LIBs), with nominal composition 0.6(Li1.2Mn0.56Fe0.08Ni0.16O2) 0.4(LiFe0.2Mn1.4Ni0.4O4) which can otherwise be written as Li0.8Mn0.64Ni0.183Fe0.091O2 (FeSL) are synthesized via simple citric acid-assisted sol-gel route. Four different final annealing temperatures (550 °C, 650 °C, 750 °C, and 850 °C) were chosen to investigate their influence on electrochemical performance. The obtained composite materials contain spinel (space group Fd3¯m) as well as Li-rich layered phases (space group C2/m) as revealed by X-ray diffraction (XRD), HRTEM and cyclic voltammetry investigations. The excellent electrochemical performance of the composite material could be attributed to the structural stability achieved by the integration of spinel and layered components. Selected synthesized composite materials exhibit high discharge capacities close to 200 mAh g−1. The FeSL750 shows better capacity retention (92(3)% at the 50th cycle and 82(5)% at the 70th cycle) and rate capability than the FeSL550 and FeSL650 samples. However, the FeSL850 sample shows different charge-discharge behaviour. The charge capacity corresponding to FeSL850 is found to increase up to the 20th cycle, then stabilizes and displays a capacity retention of almost 100 % at the 50th cycle and 91(1)% at the 70th cycle. The electrochemical mechanism of FeSL750 was elucidated via in operando XAS investigations, which reveal electrochemical activity from all transition metals.

Nonseparable wave evolution equations in quantum kinetics

A nonseparable wave-like integro-differential equation for the time evolution of the Wigner distribution function in phase space is educed from the corresponding separable kinetic equation. By employing the quantum hydrodynamical description, a non-local evolution wave equation is also derived by synthesizing the Hamilton‐Jacobi equation with that of continuity, which predicts the generation of nonlocal and quadrupole quantum phenomena in the propagation of the spatial probability density.

Mechanisms of soil organic carbon and nitrogen stabilization in mineral-associated organic matter – insights from modeling in phase space

Abstract. Understanding the mechanisms of plant-derived carbon (C) and nitrogen (N) transformation and stabilization in soil is fundamental for predicting soil capacity to mitigate climate change and support other soil functions. The decomposition of plant residues and particulate organic matter (POM) contributes to the formation of mineral-associated (on average more stable) organic matter (MAOM) in soil. MAOM is formed from the binding of dissolved organic matter (ex vivo pathway) or microbial necromass and bioproducts (in vivo pathway) to minerals and metal colloids. Which of these two soil organic matter (SOM) stabilization pathways is more important and under which conditions remains an open question. To address this question, we propose a novel diagnostic model to describe C and N dynamics in MAOM as a function of the dynamics of residues and POM decomposition. Focusing on relations among soil compartments (i.e., modeling in phase space) rather than time trajectories allows isolating the fundamental processes underlying stabilization. Using this diagnostic model in combination with a database of 36 studies in which residue C and N were tracked into POM and MAOM, we found that MAOM is predominantly fueled by necromass produced by microbes decomposing residues and POM. The relevance of this in vivo pathway is higher in clayey soils but lower in C-rich soils and with N-poor added residues. Overall, our novel modeling in phase space proved to be a sound diagnostic tool for the mechanistic investigation of soil C dynamics and supported the current understanding of the critical role of both microbial transformation and mineral capacity for the stabilization of C in mineral soils.

On the search for the two poles of the Ξ(1820)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1820)$$\\end{document} in the ψ(3686)→Ξ¯+K¯0Σ∗-(π-Λ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3686) \\rightarrow \\bar{\\Xi }^+ \\bar{K}^0 \\Sigma ^{*-}(\\pi ^- \\Lambda )$$\\end{document} decay

We propose the reaction ψ(3686)→Ξ¯+K¯0Σ∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3686) \\rightarrow \\bar{\\Xi }^+ \\bar{K}^0 \\Sigma ^{*-}$$\\end{document}, with the Σ∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma ^{*-}$$\\end{document} decaying to π-Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi ^- \\Lambda $$\\end{document} in order to show evidence for the existence of two Ξ(1820)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1820)$$\\end{document} states, one around 1824 MeV and narrow, and another one around 1875 MeV and wide. The phase space for K¯0Σ∗-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{K}^0 \\Sigma ^{*-}$$\\end{document} production reduces the effect of the lower mass resonance, magnifying the effect of the higher mass resonance that shows clearly over the phase space. The estimated rate of the production is bigger than the one of the ψ(3686)→Ξ¯+K-Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi (3686) \\rightarrow \\bar{\\Xi }^+ K^- \\Lambda $$\\end{document} reaction, where a clear peak for Ξ(1820)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi (1820)$$\\end{document} was observed by the BESIII collaboration, what makes the Beijing facility ideal to carry out the reaction proposed.

Riemannian optimization of photonic quantum circuits in phase and Fock space

We propose a framework to design and optimize generic photonic quantum circuits composed of Gaussian objects (pure and mixed Gaussian states, Gaussian unitaries, Gaussian channels, Gaussian measurements) as well as non-Gaussian effects such as photon-number-resolving measurements. In this framework, we parametrize a phase space representation of Gaussian objects using elements of the symplectic group (or the unitary or orthogonal group in special cases), and then we transform it into the Fock representation using a single linear recurrence relation that computes the Fock amplitudes of any Gaussian object recursively. We also compute the gradient of the Fock amplitudes with respect to phase space parameters by differentiating through the recurrence relation. We can then use Riemannian optimization on the symplectic group to optimize MM-mode Gaussian objects, avoiding the need to commit to particular realizations in terms of fundamental gates. This allows us to “mod out” all the different gate-level implementations of the same circuit, which now can be chosen after the optimization has completed. This can be especially useful when looking to answer general questions, such as bounding the value of a property over a class of states or transformations, or when one would like to worry about hardware constraints separately from the circuit optimization step. Finally, we make our framework extendable to non-Gaussian objects that can be written as linear combinations of Gaussian ones, by explicitly computing the change in global phase when states undergo Gaussian transformations. We implemented all of these methods in the freely available open-source library MrMustard, which we use in three examples to optimize the 216-mode interferometer in Borealis, and 2- and 3-modes circuits (with Fock measurements) to produce cat states and cubic phase states.

Quantum instability and Ehrenfest time for inverted harmonic oscillator

Abstract We used out-of-time order correlators (OTOCs) to investigate the quantum instability and Ehrenfest time for the inverted harmonic oscillator (IHO). For the initial states located in the stable manifolds of IHO, we find that the corresponding OTOC exhibits identical evolutionary characteristics as the saddle point before the Ehrenfest time. For the initial states located in the unstable manifolds,
the OTOCs still grow exponentially but the time to maintain exponential growth is related to the center position of its wave packet in the phase space. Moreover, we use the Husimi Q function to visualize the quantum wave packets during the OTOC’s exponential growth. Our results show that the quantum instability exists at arbitrary orbits in the IHO system, and the Ehrenfest time in the IHO system depends not only on the initial system photon number, but also on the central positions of the initial states in the phase space.

On the convergence of phase space distributions to microcanonical equilibrium: dynamical isometry and generalized coarse-graining

Abstract This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining procedure that leads to convergence. We prove that the time evolution of phase space distributions is an isometry for a broad class of statistical distance metrics, implying that ensembles do not get any closer to (or farther from) equilibrium, according to these metrics. This extends the known result that strong convergence of phase space distributions to the microcanonical distribution does not occur. However, it has long been known that weak convergence can occur, such that coarse-grained distributions---defined by partitioning phase space into a finite number of cells---converge pointwise to the microcanonical distribution. We define a generalization of coarse-graining that removes the need for partitioning phase space into cells. We prove that our generalized coarse-grained distribution converges pointwise to the microcanonical distribution if the dynamics are strong mixing. As an example, we study an ensemble of triangular billiard systems.

Continuation of Bianchi spacetimes through the big bang

In this paper we present a framework in which the relational description of general relativity can be used to smoothly continue cosmological dynamical systems through the big bang without invoking quantum gravity effects. Cosmological spacetimes contain as a key dynamical variable a notion of scale through the volume factor ν. However, no cosmological observer is ever able to separate their measuring apparatus from the system they are measuring, in that sense every measurement is a relative one, and measurable dynamical variables are, in fact, dimensionless ratios. This is manifest in the identification of a scaling symmetry or “dynamical similarity” in the Einstein-Hilbert action associated with the volume factor. By quotienting out this scaling symmetry, we form a relational system defined on a contact manifold whose dynamical variables are decoupled from scale. When the phase space is reduced to shape space, we show that there exists unique solutions to the equations of motion that pass smoothly through the initial cosmological singularity in flat Friedmann-Lemaître-Robertson-Walker, Bianchi I, and Quiescent Bianchi IX cosmologies. Published by the American Physical Society 2024

Quantum Field Theory of Black Hole Perturbations with Backreaction: I General Framework

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers.

Heavy flavor production under a strong magnetic field

The magnetic field created in high energy nuclear collisions will affect the QCD dynamical processes, such as the heavy quark production which happens in the initial stage of the collisions. We calculate in a strong magnetic field the heavy quark production cross section of the process gg→QQ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ gg\ o Q\\overline{Q} $$\\end{document} at leading order and the corresponding transverse momentum distribution in nucleus-nucleus collisions. In comparison to the QED process, the heavy quark production is dominated by the unique QCD channel with gluon self-interaction. Due to the dimension reduction of quark phase space in a strong magnetic field, the production is concentrated in a very narrow energy region above the threshold. Since the rotational invariance is broken in a magnetic field, the production becomes anisotropic.

Kinematic study of the orion complex: Analysing the young stellar clusters from big and small structures

Abstract In this work, we analysed young stellar clusters with spatial and kinematic coherence in the Orion star-forming complex. For this study, we selected a sample of pre-main sequence candidates using parallaxes, proper motions and positions on the colour-magnitude diagram. After applying a hierarchical clustering algorithm in the 5D parameter space provided by Gaia DR3, we divided the recovered clusters into two regimes: Big Structures and Small Structures, defined by the number of detected stars per cluster. In the first regime, we found 13 stellar groups distributed along the declination axis in the regions where there is a high density of stars. In the second regime, we recovered 34 clusters classified into two types: 14 as small groups completely independent from the larger structures, including four candidates of new clusters, and 12 classified as sub-structures embedded within five larger clusters. Additionally, radial velocity data from APOGEE-2 and GALAH DR3 was included to study the phase space in some regions of the Orion complex. From the Big Structure regime, we found evidence of a general expansion in the Orion OB1 association over a common centre, giving a clue about the dynamical effects the region is undergoing. Likewise, in the Small Structure regime, the projected kinematics shows the ballistic expansion in the λ Orionis association and the detection of likely events of clusters’ close encounters in the OB1 association.

Observation of quantum entanglement with top quarks at the ATLAS detector

Entanglement is a key feature of quantum mechanics1–3, with applications in fields such as metrology, cryptography, quantum information and quantum computation4–8. It has been observed in a wide variety of systems and length scales, ranging from the microscopic9–13 to the macroscopic14–16. However, entanglement remains largely unexplored at the highest accessible energy scales. Here we report the highest-energy observation of entanglement, in top–antitop quark events produced at the Large Hadron Collider, using a proton–proton collision dataset with a centre-of-mass energy of √s = 13 TeV and an integrated luminosity of 140 inverse femtobarns (fb)−1 recorded with the ATLAS experiment. Spin entanglement is detected from the measurement of a single observable D, inferred from the angle between the charged leptons in their parent top- and antitop-quark rest frames. The observable is measured in a narrow interval around the top–antitop quark production threshold, at which the entanglement detection is expected to be significant. It is reported in a fiducial phase space defined with stable particles to minimize the uncertainties that stem from the limitations of the Monte Carlo event generators and the parton shower model in modelling top-quark pair production. The entanglement marker is measured to be D = −0.537 ± 0.002 (stat.) ± 0.019 (syst.) for 340GeV<mtt¯<380GeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$340\\,{\\rm{GeV}} < {m}_{t\\bar{t}} < 380\\,{\\rm{GeV}}$$\\end{document}. The observed result is more than five standard deviations from a scenario without entanglement and hence constitutes the first observation of entanglement in a pair of quarks and the highest-energy observation of entanglement so far.

Short-lived calcium carbonate precursors observed in situ via Bullet-dynamic nuclear polarization

The discovery of (meta)stable pre-nucleation species (PNS) challenges the established nucleation-and-growth paradigm. While stable PNS with long lifetimes are readily accessible experimentally, identifying and characterizing early-stage intermediates with short lifetimes remains challenging. We demonstrate that species with lifetimes ≪ 5 s can be characterized by nuclear magnetic resonance spectroscopy when boosted by ‘Bullet’ dynamic nuclear polarization (Bullet-DNP). We investigate the previously elusive early-stage prenucleation of calcium carbonates in the highly supersaturated concentration regime, characterizing species that form within milliseconds after the encounter of calcium and carbonate ions and show that ionic pre-nucleation species not only govern the solidification of calcium carbonates at weak oversaturation but also initiate rapid precipitation events at high concentrations. Such, we report a transient co-existence of two PNS with distinct molecular sizes and different compositions. This methodological advance may open new possibilities for studying and exploiting carbonate-based material formation in unexplored parts of the phase space.

LO, NLO, and NNLO parton distributions for LHC event generators

We present NNPDF4.0MC, a variant of the NNPDF4.0 set of parton distributions (PDFs) at LO, NLO and NNLO, with and without inclusion of the photon PDF, suitable for use with Monte Carlo (MC) event generators, which require PDFs to satisfy additional constraints in comparison to standard PDF sets. These requirements include PDF positivity down to a low scale Q ~ 1 GeV, smooth extrapolation in the very small and large x regions, and numerically stable results even in extreme regions of phase space for all PDFs. We compare the NNPDF4.0MC PDFs to their baseline NNPDF4.0 counterparts, and to the NNPDF2.3LO set entering the Monash tune of the Pythia8 event generator. We briefly assess the phenomenological impact of these PDFs on the cross-sections for hard and soft QCD processes at the LHC.

Comparison of monte carlo tally techniques for dosimetry in a transmission-type X-ray tube.

This study discussed comparing result accuracy and time cost under different tally methods using MCNP6 for a novel transmission X-ray tube which was designed for the Auger electron yield with specific material (eg. iodine). The assessment included photon spectrum, percent depth dose, mass-energy absorption coefficient corresponding to air and water, and figure of merit comparison. The mean energy of in-air phantom was from 41.8 keV (0 mm) to 40.9 keV (100 mm), and the mean energy of in-water phantom was from 41.41 keV (0 mm) to 45.2 keV (100 mm). The specific dose conversion factors based mass-energy absorption coefficient corresponding to different materials was established and the difference was less than 2% for the dose conversion of FMESH comparing to measurement data. FMESH had better figure of merit (FOM) than the F6 tally for the dose parameter assessment, which mean the dose calculation that focused on the superficial region could be assessed with more calculation efficiency by FMESH tally for this novel transmission X-ray tube. The results of this study could help develop treatment planning system (TPS) to quickly obtain the calculated data for phase space data establishment and heterogeneous correction under different physical condition settings.&#xD.

First results of a newly-built hard-X-ray/soft-Gamma spectrometer imaging system: on the aspect of plasma disruptions

Abstract A new Hard X-ray and soft gamma-ray spectrometer imaging System (HXS) has been built for the 2-Dimensional measurements of plasma emitted photons on the Experimental Advanced Superconducting Tokamak (EAST). The system uses a 2-D Cadmium Zinc Telluride (CZT) detector and an integrated electronics, which is as a whole shielded by a tungsten box with a pinhole and is tangential to the toroidal field. Three classes of typical energy spectra have been summarized in differently experimental scenarios over the past campaigns. After performing tomography calculations, the local emissivity contours have been obtained in different energy ranges which obviously show the asymmetry on the plasma cross section. The spatial perturbation structure is similar to the magnetohydrodynamics (MHD) modes with low mode numbers. In particular, the runaway island found by an infrared camera [R. Jaspers et al, Phys. Rev. Lett. 72, 4093 (1994)] is also measured by the HXS. There exists a reversal population on the energy spectra in both slide-away and strong neutral beam injection (NBI) shots. It is consistently observed that the count rate is increased in the low energy range before the plasma disruptions. Calculations in phase space indicate that the accelerated momentum flux can be deflected back to the low energy region by the large pitch-angle scattering. In the post-disruption phase the plasma current is not replaced by runaway electrons due to tearing modes or transiently bursting instabilities. This paper constructs the basics for the proper use of HXS for Hard X-ray and Soft Gamma-ray measurements in future investigations of plasma disruptions.

Thermodynamics of a rotating hadron resonance gas with van der Waals interaction

Studying the thermodynamics of the systems produced in ultra-relativistic heavy-ion collisions is crucial in understanding the QCD phase diagram. Recently, a new avenue has opened regarding the implications of large initial angular momentum and subsequent vorticity in the medium evolution in high-energy collisions. This adds a new type of chemical potential into the partonic and hadronic systems, called the rotational chemical potential. We study the thermodynamics of an interacting hadronic matter under rotation, formed in an ultra-relativistic collision. We introduce attractive and repulsive interactions through the van der Waals equation of state. Thermodynamic properties like the pressure (P), energy density (ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}), entropy density (s), trace anomaly ((ε-3P)/T4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\varepsilon - 3P)/T^{4}$$\\end{document}), specific heat (cv\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_\ extrm{v}$$\\end{document}) and squared speed of sound (cs2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_\ extrm{s}^{2}$$\\end{document}) are studied as functions of temperature (T) for zero and finite rotation chemical potential. The conserved charge fluctuations, which can be quantified by their respective susceptibilities, are also studied. The rotational (spin) density corresponding to the rotational chemical potential is explored. In addition, we explore the possible liquid–gas phase transition in the hadron gas with van der Waals interaction in the T – ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} phase space.

Investigating temporary capture in the Sun-Jupiter three-body system via Lagrangian coherent structures

Abstract The temporary capture (TC) of Jupiter-family objects has long been a pivotal focus in celestial mechanics research. This study investigates the temporary capture of objects near Jupiter within the context of the planar circular restricted three-body problem (PCRTBP), employing Lagrangian coherent structures (LCSs) and periapsis Poincaré maps. Initially, LCSs are identified via periapsis Poincaré maps and applied to segment the phase space. Parameter scanning enables a detailed analysis, classifying the orbital behaviors of objects in the proximity of Jupiter into three distinct categories: temporary capture, low-energy flyby, and collision, each designating specific regions in phase space. Subsequently, a novel method for screening potential TC objects within the Jupiter system is proposed and validated, informed by the dynamic characteristics of TC motions. The efficacy of this method is illustrated by the reidentification of six known TC comets and the prediction of a prospective TC asteroid, 2002 GV28. Within the framework of the PCRTBP, analogous TC trajectories for these comets and asteroids are identified, offering novel insights into the dynamics of temporary capture events.

A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves

We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a ‘trivial’ eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchgässner’s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (‘hydroelastic waves’). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.

Arbitrary sensitive transitions in recurrent neural networks

An Excitable Network Attractor (ENA) is a forward-invariant set in phase space that can be used to explain input-driven behaviour of Recurrent Neural Networks (RNNs) trained on tasks involving switching between a discrete set of states. An ENA is composed of two or more attractors and excitable connections that allow transitions from one attractor to another under some input perturbation. The smallest such perturbation that makes a connection between two attractors is called the excitability threshold associated with that connection. The excitability threshold provides a measure of sensitivity of the connection to input perturbations. Errors in performance of such trained RNNs can be related to errors in transitions around the associated ENA. Previous work has demonstrated that ENAs of arbitrary sensitivity and structure can be realised in a RNN by suitable choice of connection weights and nonlinear activation function. In this paper we show that ENAs of arbitrary sensitivity and structure can be realised even using a suitable fixed nonlinear activation function, i.e. by suitable choice of weights only. We show that there is a choice of weights such that the probability of erroneous transitions is very small.