Regions Of Phase Space Research Articles

The kinematic richness of star clusters – II. Stability of spherical anisotropic models with rotation

ABSTRACT We study the bar instability in collisionless, rotating, anisotropic, stellar systems, using N-body simulations and also the matrix technique for calculation of modes with the perturbed collisionless Boltzmann equation. These methods are applied to spherical systems with an initial Plummer density distribution, but modified kinematically in two ways: the velocity distribution is tangentially anisotropic, using results of Dejonghe, and the system is set in rotation by reversing the velocities of a fraction of stars in various regions of phase space, à la Lynden-Bell. The aim of the N-body simulations is first to survey the parameter space, and, using those results, to identify regions of phase space (by radius and orbital inclination) that have the most important influence on the bar instability. The matrix method is then used to identify the resonant interactions in the system that have the greatest effect on the growth rate of a bar. Complementary series of N-body simulations examine these processes in relation to the evolving frequency distribution and the pattern speed. Finally, the results are synthesized with an existing theoretical framework, and used to consider the old question of constructing a stability criterion.

Simulation of the loss of passing fast ions induced by magnetic islands in EAST tokamak plasmas

The loss of beam ions due to magnetic islands is investigated in a tokamak. The perturbed guiding-center drifts of passing particles including the effect of the finite orbit width are demonstrated. The widths of the drift islands under resonant conditions are studied theoretically and numerically. The ORBIT code is used to simulate the action of the neoclassical tearing mode with a toroidal mode number n = 1 and poloidal mode number m = 2 on passing fast ions generated by neutral beam injection in the Experimental Advanced Superconducting Tokamak. Two loss channels for passing fast ions are identified as the resonant interaction and the stochastic interaction. The lost fast ions in the loss detector zone (LDZ) to simulate the fast-ion loss detector assemble around two regions in phase space, namely, (i) a pitch angle of θ = 28° both with and without the mode and (ii) θ = 59° when the mode amplitude is large enough, where θ=arccosv∥/v. The number of these lost ions in the LDZ evolves in the period of the mode. The fraction of the total lost ions evolves in the period of the n = 1 oscillation in the toroidal direction. The fraction of lost beam ions has a linear relationship with the mode amplitude in first 10 µs and a quadratic one thereafter. The corresponding characteristics of the lost beam ions in phase space are also discussed.

Numerical simulation of synergistic effect of neoclassical tearing mode and toroidal field ripple on alpha particle loss in China Fusion Engineering Testing Reactor

Confinement of fusion born alpha particles in tokamak is the key issue to burning plasma. Apart from toroidal field ripple, instabilities can induce energetic particles to lose and be redistributed. Based on the parameters of China Fusion Engineering Testing Reactor (CFETT) hybrid scenario, alpha particle distribution and neoclassical tearing mode structure, the alpha particle loss induced under perturbation of ripple and neoclassical tearing mode (NTM) is calculated with the guiding center code ORBIT. The inputs have the initial distribution of alpha particles which is obtained with the TRANSP/NUBEAM code, the static NTM perturbation with different amplitudes which is obtained from TM1 code, and the ripple field from engineering design. The results show that the heat load on last closed flux surface is about 0.1 MW/m<sup>2</sup>, with ripple and collision included. The collisionless stochastic ripple diffusion is the main loss channel of initial alpha particle distribution in the CFETR, and the ripple perturbation has no influence on passing particles. The loss fraction does not increase with the NTM perturbation amplitude increasing, the synergistic effect is negligible. The scanning of ripple amplitude shows that the synergistic effect is slight. The monoenergetic initial distribution of alpha particles can give different types of orbits in the plane of (<inline-formula><tex-math id="M1">\begin{document}$ {P_\zeta },\mu $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20201972_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20201972_M1.png"/></alternatives></inline-formula>), such as the domains of trapped particle and passing particle, lost particle and confined particle. The trapped fraction of initial alpha particles is about 27%, ripple loss region in phase space is narrow and away from the main trapped particle distribution. The increasing of ripple perturbation in simulation does enlarge the ripple loss domain in the phase space (<inline-formula><tex-math id="M2">\begin{document}$ {P_\zeta },\mu $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20201972_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="11-20201972_M2.png"/></alternatives></inline-formula>), which is corresponding to a lager ripple loss fraction and has more trapped-passing boundaries. The NTM perturbation does enlarge the orbit excursions of trapped particles, and thus increasing the trapped passing transition near the boundary. The slight synergistic effect in calculation with larger ripple amplitude is explained by ripple loss region having more trapped-passing boundaries, not by the profile flattening of trapped particles. The NTM perturbation and finite collision can transit the passing particle to trapped particle near the boundary. With the help of kinetic Poincare plot, neither direct particle loss nor profile flattening of trapped particles is observed. The loss fraction enhancement can happen only when the profile flattening of trapped particles takes place within the ripple loss region, which is not the case in CFETR. The conclusion of this work contributes a lot to the design of CFETR and the study of alpha particle physics.

Reframing Jet Physics with New Computational Methods

We reframe common tasks in jet physics in probabilistic terms, including jet reconstruction, Monte Carlo tuning, matrix element – parton shower matching for large jet multiplicity, and efficient event generation of jets in complex, signal-like regions of phase space. We also introduce Ginkgo, a simplified, generative model for jets, that facilitates research into these tasks with techniques from statistics, machine learning, and combinatorial optimization. We also review some of the recent research in this direction that has been enabled with Ginkgo. We show how probabilistic programming can be used to efficiently sample the showering process, how a novel trellis algorithm can be used to efficiently marginalize over the enormous number of clustering histories for the same observed particles, and how the dynamic programming and reinforcement learning can be used to find the maximum likelihood clusterinng in this enormous search space. This work builds bridges with work in hierarchical clustering, statistics, combinatorial optmization, and reinforcement learning.

Mildly Hierarchical Triple Dynamics and Applications to the Outer Solar System

Abstract Three-body interactions are ubiquitous in astrophysics. For instance, Kozai–Lidov oscillations in hierarchical triple systems have been studied extensively and applied to a wide range of astrophysical systems. However, mildly hierarchical triples also play an important role, but they are less explored. In this work, we consider the secular dynamics of a test particle in a mildly hierarchical configuration. We find the limit within which the secular approximation is reliable when the outer perturber is in a circular orbit. In addition, we present resonances and chaotic regions using surface-of-section plots, and characterize regions of phase space that allow large eccentricity and inclination variations. Finally, we apply the secular results to the outer Solar System. We focus on the distribution of extreme trans-Neptunian objects (eTNOs) under the perturbation of a possible outer planet (Planet 9), and find that in addition to a low-inclination Planet 9, a polar or a counter-orbiting one could also produce pericenter clustering of eTNOs, while the polar one leads to a wider spread of eTNO inclinations.

Computationally Directed Discovery of MoBi2.

Incorporating bismuth, the heaviest element stable to radioactive decay, into new materials enables the creation of emergent properties such as permanent magnetism, superconductivity, and nontrivial topology. Understanding the factors that drive Bi reactivity is critical for the realization of these properties. Using pressure as a tunable synthetic vector, we can access unexplored regions of phase space to foster reactivity between elements that do not react under ambient conditions. Furthermore, combining computational and experimental methods for materials discovery at high-pressures provides broader insight into the thermodynamic landscape than can be achieved through experiment alone, informing our understanding of the dominant chemical factors governing structure formation. Herein, we report our combined computational and experimental exploration of the Mo-Bi system, for which no binary intermetallic structures were previously known. Using the ab initio random structure searching (AIRSS) approach, we identified multiple synthetic targets between 0-50 GPa. High-pressure in situ powder X-ray diffraction experiments performed in diamond anvil cells confirmed that Mo-Bi mixtures exhibit rich chemistry upon the application of pressure, including experimental realization of the computationally predicted CuAl2-type MoBi2 structure at 35.8(5) GPa. Electronic structure and phonon dispersion calculations on MoBi2 revealed a correlation between valence electron count and bonding in high-pressure transition metal-Bi structures as well as identified two dynamically stable ambient pressure polymorphs. Our study demonstrates the power of the combined computational-experimental approach in capturing high-pressure reactivity for efficient materials discovery.

A Surface of Heteroclinic Connections Between Two Saddle Slow Manifolds in the Olsen Model

The Olsen model for the biochemical peroxidase-oxidase reaction has a parameter regime where one of its four variables evolves much slower than the other three. It is characterized by the existence of periodic orbits along which a large oscillation is followed by many much smaller oscillations before the process repeats. We are concerned here with a crucial ingredient for such mixed-mode oscillations (MMOs) in the Olsen model: a surface of connecting orbits that is followed closely by the MMO periodic orbit during its global, large-amplitude transition back to another onset of small oscillations. Importantly, orbits on this surface connect two one-dimensional saddle slow manifolds, which exist near curves of equilibria of the limit where the slow variable is frozen and acts as a parameter of the so-called fast subsystem. We present a numerical method, based on formulating suitable boundary value problems, to compute such a surface of connecting orbits. It involves a number of steps to compute the slow manifolds, certain submanifolds of their stable and unstable manifolds and, finally, a first connecting orbit that is then used to sweep out the surface by continuation. If it exists, such a surface of connecting orbits between two one-dimensional saddle slow manifolds is robust under parameter variations. We compute and visualize it in the Olsen model and show how this surface organizes the global return mechanism of MMO periodic orbits from the end of small oscillations back to a region of phase space where they start again.

Nonperturbative signatures of nonlinear Compton scattering

The probabilities of various elementary laser - photon - electron/positron interactions display in selected phase space and parameter regions typical non-perturbative dependencies such as $\propto {\cal P} \exp\{- a E_{crit} /E\}$, where ${\cal P}$ is a pre-exponential factor, $E_{crit}$ denotes the critical Sauter-Schwinger field strength, and $E$ characterizes the (laser) field strength. While the Schwinger process with $a = a_S \equiv \pi$ and the non-linear Breit-Wheeler process in the tunneling regime with $a = a_{n \ell BW} \equiv 4 m / 3 \omega'$ (with $\omega'$ the probe photon energy and $m$ the electron/positron mass) are famous results, we point out here that also the non-linear Compton scattering exhibits a similar behavior when focusing on high harmonics. Using a suitable cut-off $c > 0$, the factor $a$ becomes $a = a_{n \ell C} \equiv \frac23 c m /(p_0 + \sqrt{p_0^2 -m^2)}$. This opens the avenue towards a new signature of the boiling point of the vacuum even for field strengths $E$ below $E_{crit}$ by employing a high electron beam-energy $p_0$ to counter balance the large ratio $E_{crit} / E$ by a small factor $a$ to achieve $E / a \to E_{crit}$. In the weak-field regime, the cut-off facilitates a threshold leading to multi-photon signatures showing up in the total cross section at sub-threshold energies.

A constructive approach to robust chaos using invariant manifolds and expanding cones

Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we provide formal results for robust chaos in the original parameter regime of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049-3052, 1998]. We first construct a trapping region in phase space to prove the existence of a topological attractor. We then construct an invariant expanding cone in tangent space to prove that tangent vectors expand and so no invariant set can have only negative Lyapunov exponents. Under additional assumptions we characterise an attractor as the closure of the unstable manifold of a fixed point and prove that it satisfies Devaney's definition of chaos.

Electron pairing induced by repulsive interactions in tunable one-dimensional platforms

We present a scheme comprised of a one-dimensional system with repulsive interactions, in which the formation of bound pairs can take place in an easily tunable fashion.By capacitively coupling a primary electronic quantum wire of interest to a secondary strongly-correlated fermionic system, the intrinsic electron-electron repulsion may be overcome, promoting the formation of bound electron pairs in the primary wire. The intrinsic repulsive interactions tend to favor the formation of charge density waves of these pairs, yet we find that superconducting correlations are dominant in a limited parameter regime. Our analysis show that the paired phase is stabilized in an intermediate region of phase space, encompassed by two additional phases: a decoupled phase, where the primary wire remains gapless, and a trion phase, where a primary electron pair binds a charge carrier from the secondary system. Tuning the strength of the primary-secondary interaction, as well as the chemical potential of the secondary system, one can control the different phase transitions. Our approach takes into account the interactions among the secondary degrees of freedom, and strongly relies on their highly correlated nature. Extension of our proposal to two dimensions is discussed, and the conditions for a long-range superconducting order from repulsion only are found. Our physical description, given by a simple model with a minimal amount of ingredients, may help to shed some light on pairing mechanism in various low-dimensional strongly correlated materials.

Anatomy of inclusive [formula omitted] production at hadron colliders

In LHC searches for new and rare phenomena the top-associated channel pp→tt‾W±+X is a challenging background that multilepton analyses must overcome. Motivated by sustained measurements of enhanced rates of same-sign and multi-lepton final states, we reexamine the importance of higher jet multiplicities in pp→tt‾W±+X that enter at O(αs3α) and O(αs4α), i.e., that contribute at NLO and NNLO in QCD in inclusive tt‾W± production. Using fixed-order computations, we estimate that a mixture of real and virtual corrections at O(αs4α) in well-defined regions of phase space can arguably increase the total tt‾W± rate at NLO by at least 10%−14%. However, by using non-unitary NLO multi-jet matching, we estimate that these same corrections are at most 10%−12%, and at the same time exhibit the enhanced jet multiplicities that are slightly favored by data. This seeming incongruity suggests a need for the full NNLO result. We comment on implications for the tt‾Z process.

Measurement of Bc(2S)+ and Bc*(2S)+ cross section ratios in proton-proton collisions at s=13 TeV

The ratios of the Bc(2S)+ to Bc+, Bc*(2S)+ to Bc+, and Bc*(2S)+ to Bc(2S)+ production cross sections are measured in proton-proton collisions at s=13 TeV, using a data sample collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 143 fb−1. The three measurements are made in the Bc+ meson phase space region defined by the transverse momentum pT>15 GeV and absolute rapidity |y|<2.4, with the excited Bc(*)(2S)+ states reconstructed through the Bc(*)+π+π−, followed by the Bc+→J/ψπ+ and J/ψ→μ+μ− decays. The Bc(2S)+ to Bc+, Bc*(2S)+ to Bc+, and Bc*(2S)+ to Bc(2S)+ cross section ratios, including the unknown Bc(*)(2S)+→Bc(*)+π+π− branching fractions, are (3.47±0.63(stat)±0.33(syst))%, (4.69±0.71(stat)±0.56(syst))%, and 1.35±0.32(stat)±0.09(syst), respectively. None of these ratios shows a significant dependence on the pT or |y| of the Bc+ meson. The normalized dipion invariant mass distributions from the decays Bc(*)(2S)+→Bc(*)+π+π− are also reported.Received 19 August 2020Accepted 29 September 2020DOI:https://doi.org/10.1103/PhysRevD.102.092007Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.© 2020 CERN, for the CMS CollaborationPhysics Subject Headings (PhySH)Research AreasBranching fractionPhysical SystemsBottom mesonsCharmed mesonsTechniquesHadron collidersParticles & Fields

Tailoring biocompatible Ti-Zr-Nb-Hf-Si metallic glasses based on high-entropy alloys design approach

Present work unveils novel magnetic resonance imaging (MRI) compatible glassy Ti-Zr-Nb-Hf-Si alloys designed based on a high entropy alloys approach, by exploring the central region of multi-component alloy phase space. Phase analysis has revealed the amorphous structure of developed alloys, with a higher thermal stability than the conventional metallic glasses. The alloys exhibit excellent corrosion properties in simulated body fluid. Most importantly, the weak paramagnetic nature (ultralow magnetic susceptibility) and superior radiopacity (high X-ray attenuation coefficients) offer compatibility with medical diagnostic imaging systems thereby opening unexplored realms for biomedical applications.

NLO QCD corrections to off-shell mathrm{t}overline{mathrm{t}}{mathrm{W}}^{pm } production at the LHC

We present results of a computation of NLO QCD corrections to the production of an off-shell top-antitop pair in association with an off-shell W+ boson in proton-proton collisions. As the calculation is based on the full matrix elements for the process mathrm{pp}to {mathrm{e}}^{+}{v}_{mathrm{e}}{mu}^{-}{overline{v}}_{mu }{tau}^{+}{v}_{tau}mathrm{b}overline{mathrm{b}} , all off-shell, spin-correlation, and interference effects are included. The NLO QCD corrections are about 20% for the integrated cross-section. Using a dynamical scale, the corrections to most distributions are at the same level, while some distributions show much larger K-factors in suppressed regions of phase space. We have performed a second calculation based on a double-pole approximation. While the corresponding results agree with the full calculation within few per cent for integrated cross-sections, the discrepancy can reach 10% and more in regions of phase space that are not dominated by top-antitop production. As a consequence, on-shell calculations should only be trusted to this level of accuracy.

Suitability of multiscale entropy for complexity quantification of cardiac rhythms in chronic pathological conditions: a similarity patterns based investigation

In this paper, based upon the appearance of patterns derived from a time series, we have investigated the suitability of multiscale entropy (MSE) technique for complexity quantification of cardiac rhythms in chronic pathological conditions. MSE analysis was developed to quantify the complexity of a wide variety of biomedical signals. Here, sample entropy (SampEn) technique was evaluated across multiple spatio-temporal scales. In SampEn, to find the appearance of repetitive patterns in multi-dimensional phase space, the threshold value ‘s’ is pre-fixed as 0.2. However, the cardiac rhythms of some pathologies are characterized with considerable erratic beat-to-beat fluctuations, and hence, in accordance with that, the patterns concealed in the pathologic cardiac rhythms spread across a wider region of multidimensional phase space. But, fixed threshold value ‘s’ assigns a fewer similarity pattern inside a circle of fixed dimensions, and hence, the higher entropy rate is associated with the chronic pathologic cardiac rhythms when compared to healthy cardiac rhythms. This flaw of SampEn is present in MSE, which leads to the wrong estimation of complexity associated with a time series. The outcome of this issue is clearly visible at low time scales, where period-to-period fluctuations in chronic pathologic cardiac rhythms and in randomized time series are significantly increased. In this present study, MSE analysis was performed over synthetic simulated database comprising of (white noise) WN and (power noise) PN signals. Further, MSE analysis was performed on the RR-interval series collected from (normal sinus rhythm) NSR group, and patients affected by (Atrial Fibrillation) AF. A fixed number of data samples ‘M’ of 10,000 were considered for each type of time series. Here, it is being observed that at some time scales, MSE assigns higher entropy to the WN and AF group, rather than PN and NSR group respectively, which is a wrong estimation of complexity. However, both the groups are discriminated efficiently by this algorithm. Further, it is concluded that MSE measure both the entropy and short term variations associated with a time series, but unable to investigate the real complexity (meaning full structural organization) present in a signal.

Using commensurabilities and orbit structure to understand barred galaxy evolution

ABSTRACTWe interpret simulations of secularly evolving disc galaxies through orbit morphology. Using a new algorithm that measures the volume of orbits in real space using a tessellation, we rapidly isolate commensurate (resonant) orbits. We identify phase-space regions occupied by different orbital families. Compared to spectral methods, the tessellation algorithm can identify resonant orbits within a few dynamical periods, crucial for understanding an evolving galaxy model. The flexible methodology accepts arbitrary potentials, enabling detailed descriptions of the orbital families. We apply the machinery to four different potential models, including two barred models, and fully characterize the orbital membership. We identify key differences in the content of orbit families, emphasizing the presence of orbit families indicative of the bar evolutionary state and the shape of the dark matter halo. We use the characterization of orbits to investigate the shortcomings of analytic and self-consistent studies, comparing our findings to the evolutionary epochs in self-consistent barred galaxy simulations. Using insight from our orbit analysis, we present a new observational metric that uses spatial and kinematic information from integral field spectrometers that may reveal signatures of commensurabilities and allow for a differentiation between models.

Vortex generation in the early Universe

Context. Accretion disks formed near primordial black holes can be sources of seed magnetic fields in the early Universe. In particular, the Biermann battery mechanism has been shown to generate primordial magnetic fields in an unmagnetized and turbulence-free accretion disk, but this depends on a delicate misalignment of density and pressure gradients in plasmas. Aims. We aim to reformulate the question of magnetogenesis in the context of plasma generalized vorticity and to search for a more robust mechanism of vorticity generation in the early Universe. Methods. We utilize the electro-vortical formalism in curved spacetime, which treats the plasma flow and electromagnetic field on an equal footing, and apply it to a thin accretion disk model near a rotating black hole. Results. We present a spacetime curvature-driven mechanism that persists even in the absence of the Biermann battery. We explore the vorticity and enstrophy generation rate dependencies on black hole masses and spin rates. Conclusions. Analysis indicates that the accretion disks around lower-mass, faster rotating black holes contribute the greatest amount to the enstrophy and vorticity generation rates from the spacetime curvature drive. The shorter turning radii at which the sign of the vorticity changes – corresponding with this region of phase space – may favor these length scales in vortical structure formation and subsequent evolution.

Development of Forward Tracker

The High Acceptence DiElectron Spectrometer has experienced many years of successful operation which revealed high capability of measuring resonance production in proton-proton and pion-proton reactions. Since many of the production channels that are crucial for the understanding of the resonance production are highly anisotropic, that a large part of the signal would be located in the most forward and backward phase space regions, a new opportunity to an upgrade to the detector for improving the phase-space acceptance in this region has been proposed. The Forward Tracker (FT) will cover the polar angle in the detector system between 0°and 6.5°, which significantly will increase the detection acceptance. The FT is in construction with the synergy with PANDA Central Tracker, and is realized by groups from Jagellionian University, FZ Jülich and LIP Coimbra. The development of the new and faster readout electronics (DAQ) to cope with higher data rates, track reconstruction and the results from the beam time at Forschungszentrum Jülich are discussed.

Higgs boson production cross-section measurements and their EFT interpretation in the 4ell decay channel at sqrt{s}=13\xa0TeV with the ATLAS detector

Higgs boson properties are studied in the four-lepton decay channel (where lepton = e, mu ) using 139 hbox {fb}^{-1} of proton–proton collision data recorded at sqrt{s}=13 TeV by the ATLAS experiment at the Large Hadron Collider. The inclusive cross-section times branching ratio for Hrightarrow ZZ^* decay is measured to be 1.34 pm 0.12 pb for a Higgs boson with absolute rapidity below 2.5, in good agreement with the Standard Model prediction of 1.33 pm 0.08 pb. Cross-sections times branching ratio are measured for the main Higgs boson production modes in several exclusive phase-space regions. The measurements are interpreted in terms of coupling modifiers and of the tensor structure of Higgs boson interactions using an effective field theory approach. Exclusion limits are set on the CP-even and CP-odd ‘beyond the Standard Model’ couplings of the Higgs boson to vector bosons, gluons and top quarks.

Hydrodynamic Attractors in Phase Space.

Hydrodynamic attractors have recently gained prominence in the context of early stages of ultrarelativistic heavy-ion collisions at the RHIC and LHC. We critically examine the existing ideas on this subject from a phase space point of view. In this picture the hydrodynamic attractor can be seen as a special case of the more general phenomenon of dynamical dimensionality reduction of phase space regions. We quantify this using principal component analysis. Furthermore, we adapt the well known slow-roll approximation to this setting. These techniques generalize easily to higher dimensional phase spaces, which we illustrate by a preliminary analysis of a dataset describing the evolution of a five-dimensional manifold of initial conditions immersed in a 16-dimensional representation of the phase space of the Boltzmann kinetic equation in the relaxation time approximation.