Specific Regions Of Phase Space Research Articles

Appearance of transient chaos and energy variability in Ueda oscillator driven by an amplitude‐modulated force

Transient chaos is a characteristic behavior observed in nonlinear systems, where trajectories within a specific region of phase space exhibit chaotic dynamics for a finite duration before transitioning to an external attractor. In many nonlinear systems, transient and chaotic behaviors are closely associated with variations in the system's energy. In this paper, we introduce the concept of an energy variable and establish its connection with the Melnikov integral. We explore the influence of energy variation in an amplitude‐modulated (AM) force‐driven Ueda oscillator through numerical simulations. Our investigation reveals the emergence of transient chaos, chaotic dynamics, and regular behaviors, underscoring the significant role played by the energy variable, denoted as , in the system. We employ various analytical tools, including phase diagrams, Poincaré maps, time series plots, and bifurcation diagrams, to characterize and visualize transient chaos, regular, and chaotic motions within the system.

Machine learning modeling of Wigner intracule functionals for two electrons in one-dimension.

In principle, many-electron correlation energy can be precisely computed from a reduced Wigner distribution function (W), thanks to a universal functional transformation (F), whose formal existence is akin to that of the exchange-correlation functional in density functional theory. While the exact dependence of F on W is unknown, a few approximate parametric models have been proposed in the past. Here, for a dataset of 923 one-dimensional external potentials with two interacting electrons, we apply machine learning to model F within the kernel Ansatz. We deal with over-fitting of the kernel to a specific region of phase-space by a one-step regularization not depending on any hyperparameters. Reference correlation energies have been computed by performing exact and Hartree-Fock calculations using discrete variable representation. The resulting models require W calculated at the Hartree-Fock level as input while yielding monotonous decay in the predicted correlation energies of new molecules reaching sub-chemical accuracy with training.

Measurements of Higgs boson properties in the diphoton decay channel with 36 fb−1 of pp collision data at s=13 TeV with the ATLAS detector

Properties of the Higgs boson are measured in the two-photon final state using 36.1 fb$^{-1}$ of proton-proton collision data recorded at $\sqrt{s} = 13$ TeV by the ATLAS experiment at the Large Hadron Collider. Cross-section measurements for the production of a Higgs boson through gluon-gluon fusion, vector-boson fusion, and in association with a vector bosonor a top-quark pair are reported. The signal strength, defined as the ratio of the observed to the expected signal yield, is measured for each of these production processes as well as inclusively. The global signal strength measurement of $0.99 \pm 0.14$ improves on the precision of the ATLAS measurement at $\sqrt{s} = 7$ and 8 TeV by a factor of two. Measurements of gluon-gluon fusion and vector-boson fusion productions yield signal strengths compatible with the Standard Model prediction. Measurements of simplified template cross sections, designed to quantify the different Higgs boson production processes in specific regions of phase space, are reported. The cross section for the production of the Higgs boson decaying to two isolated photons in a fiducial region closely matching the experimental selection of the photons is measured to be $55 \pm 10$ fb, which is in good agreement with the Standard Model prediction of $64 \pm 2$ fb. Furthermore, cross sections in fiducial regions enriched in Higgs boson production in vector-boson fusion or in association with large missing transverse momentum, leptons or top-quark pairs are reported. Differential and double-differential measurements are performed for several variables related to the diphoton kinematics as well as the kinematics and multiplicity of the jets produced in association with a Higgs boson. No significant deviations from a wide array of Standard Model predictions are observed.

Search for CP violation using triple product asymmetries in \u039bb0\u2009\u2192\u2009pK\u2212\u03c0+\u03c0\u2212, \u039bb0\u2009\u2192\u2009pK\u2212K+K\u2212 and \u039eb0\u2009\u2192\u2009pK\u2212K\u2212\u03c0+ decays

A search for CP and P violation using triple-product asymmetries is performed with Λb0 → pK−π+π−, Λb0 → pK−K+K− and Ξb0 → pK−K−π+ decays. The data sample corresponds to integrated luminosities of 1.0 fb−1 and 2.0 fb−1, recorded with the LHCb detector at centre-of-mass energies of 7 TeV and 8 TeV, respectively. The CP - and P - violating asymmetries are measured both integrating over all phase space and in specific phase-space regions. No significant deviation from CP or P symmetry is found. The first observation of Λb0 → pK−χc0(1P)(→π+π−, K+K−) decay is also reported.

Next-to-leading-order QCD and electroweak corrections to WWW production at proton-proton colliders

Triple-W-boson production in proton-proton collisions allows for a direct access to the triple and quartic gauge couplings and provides a window to the mechanism of electroweak symmetry breaking. It is an important process to test the Standard Model (SM) and might be background to physics beyond the SM. We present a calculation of the next-to-leading order (NLO) electroweak corrections to the production of WWW final states at proton-proton colliders with on-shell W bosons and combine the electroweak with the NLO QCD corrections. We study the impact of the corrections to the integrated cross sections and to kinematic distributions of the W bosons. The electroweak corrections are generically of the size of 5-10% for integrated cross sections and become more pronounced in specific phase-space regions. The real corrections induced by quark-photon scattering turn out to be as important as electroweak loops and photon bremsstrahlung corrections, but can be reduced by phase-space cuts. Considering that prior determinations of the photon parton distribution function (PDF) involve rather large uncertainties, we compare the results obtained with different photon PDFs and discuss the corresponding uncertainties in the NLO predictions. Moreover, we determine the scale and total PDF uncertainties at the LHC and a possible future 100 TeV pp collider.

Effective intermittency and cross correlations in the standard map.

We define auto- and cross-correlation functions capable of capturing dynamical characteristics induced by local phase-space structures in a general dynamical system. These correlation functions are calculated in the standard map for a range of values of the nonlinearity parameter k. Using a model of noninteracting particles, each evolving according to the same standard map dynamics and located initially at specific phase-space regions, we show that for 0.6<k≤1.2 long-range cross correlations emerge. They occur as an ensemble property of particle trajectories by an appropriate choice of the phase-space cells used in the statistical averaging. In this region of k values the single-particle phase space is either dominated by local chaos (k≤k(c) with k(c)≈0.97) or it is characterized by the transition from local to global chaos (k(c)<k≤1.2). Introducing suitable symbolic dynamics we demonstrate that the emergence of long-range cross correlations can be attributed to the existence of an effective intermittent dynamics in specific regions of the phase space. Our findings support the recently established relation of intermittent dynamics and cross correlations [F. K. Diakonos, A. K. Karlis, and P. Schmelcher, Europhys. Lett. 105, 26004 (2014)] in simple one-dimensional intermittent maps, suggesting its validity also for two-dimensional Hamiltonian maps.

Where the sidewalk ends: jets and missing energy search strategies for the 7 TeV LHC

This work explores the potential reach of the 7 TeV LHC to new colored states in the context of simplified models and addresses the issue of which search regions are necessary to cover an extensive set of event topologies and kinematic regimes. This article demonstrates that if searches are designed to focus on specific regions of phase space, then new physics may be missed if it lies in unexpected corners. Simple multiregion search strategies can be designed to cover all of kinematic possibilities. A set of benchmark models are created that cover the qualitatively different signatures and a benchmark multiregion search strategy is presented that covers these models.

Semiclassical scattering amplitude at the maximum of the potential

We study the scattering amplitude for Schrodinger operators at a critical energy level, which is a unique non- degenerate maximum of the potential. We do not assume that the maximum point is non-resonant and use results by Bony, Fujiie, Ramond and Zerzeri to analyze the contributions of the trapped trajectories. We prove a semiclassical expansion of the scattering amplitude and compute its leading term. We show that it has different orders of magnitude in specific regions of phase space. We also prove upper and lower bounds for the resolvent in this setting.

Absolute and Relative Orbit Analysis for Resonant Satellite Motion.

A concise, novel description of satellite motion for ideal tesseral resonance with a rotating primary is presented. A practical method is then given for determining the validity of the ideal resonance assumption in specific regions of phase space. Although less mathematically rigorous than previous analytical descriptions of such motion, the model compares favorably to the output of a symplectic numerical integrator lending itself to orbit propagation and determination applications, despite being sufficiently concise for use in limited computing environments such as exist on-board small satellites. Candidate resonances in the geopotential are identified, on the basis of strength, in which formations of satellites could exhibit relative resonant effects. The absolute resonant orbit descriptions are then used within a curvilinear relative orbit framework to characterize the effects of tesseral resonance on the relative motion of formations of satellites. The results show that the magnitudes of expected relative resonant motion can be equal to that due to short periodic J2 motion, or secular motion due to small inclination differences for low Earth orbit (LEO) satellite formations with separations up to the order of kilometers.

Coupling of Energy to Fusion Plasmas Through Distributed and Programmable Compact Energetic Neutral Beams

This paper presents a concept of coupling energy to fusion plasmas by spatially distributed and programmable compact energetic neutral beams. These energetic sources are pencil neutral beams with energy from 1 KeV up to 4 MeV. They are formed from the electron transfer between accelerated positive and negative ions in well-proven Radio Frequency Quadrupole (RFQ) structures. Symmetry in positive and negative ion plasmas favors the trapping of both species in adjacent potential wells of a travelling wave. Since this source does not require a large charge-exchange cell and high voltage sources, its compact size allows it to be positioned at multiple locations around the fusion device with various angles of injection.The motivation for this paper is to usher a new paradigm in the heating, fueling and diagnosis of fusion devices. Large fusion device of meter scale size will need energetic beams to penetrate to its center for heating, fueling and diagnostics. Kinetic instabilities might require ion injection in specific regions of phase space at particular times. Since the beam density scales favorably with decreasing size, we have utilized advances in computer and micro-fabrication and nanotechnology to design a multiple module beam injection system. This approach makes it possible to program each beam module such that beam injection is triggered by special events inside a dynamic fusion plasma.Current research devices will need inexpensive neutral beams to test their concepts at reasonably high ion energy. This proposed program is designed to demonstrate the versatility of such programmable compact beams in fusion research and ultimate reactor applications. The same principles used to produce these energetic neutral beams are equally applicable to produce neutralized beams that have potential applications in inertial fusion to prevent charge buildup at the target.1We will first describe our method of producing neutral beam sources based on the wave-acceleration process and the wave enhanced charge-transfer process. We will then describe how our beam sources can be tested in ECRH produced linear magnetized plasma equipped with ICRH and mirror confinement.The overall objective is to demonstrate the viability and versatility of these compact neutral beams for fusion. Physics issues connected with profile and instability control and the simulation of alpha particles are topics that can be investigated.

Isolated prompt photon production in hadronic final states of e+e- annihilation.

We provide complete analytic expressions for the isolated prompt photon production cross section in $e^+e^-$ annihilation reactions through one-loop order in quantum chromodynamics (QCD) perturbation theory. Functional dependences on the isolation cone size $\delta$ and isolation energy parameter $\epsilon$ are derived. The energy dependence as well as the full angular dependence of the cross section on $\theta_\gamma$ are displayed, where $\theta_\gamma$ specifies the direction of the photon with respect to the $e^+e^-$ collision axis. We point out that conventional perturbative QCD factorization breaks down for isolated photon production in $e^+e^-$ annihilation reactions in a specific region of phase space. We discuss the implications of this breakdown for the extraction of fragmentation functions from $e^+e^-$ annihilation data and for computations of prompt photon production in hadron-hadron reactions.

Inclusive prompt photon production in hadronic final states of e+e- annihilation.

We provide complete analytic expressions for the inclusive prompt photon production cross section in hadronic final states of ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ annihilation reactions through one-loop order in quantum chromodynamics perturbation theory. Computed explicitly are direct photon production through first order in the electromagnetic strength ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{em}}$ and the quark-to-photon and gluon-to-photon fragmentation contributions through first order in the strong coupling ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$. The full angular dependence of the cross sections is displayed, separated into transverse (1+${\mathrm{cos}}^{2}$${\mathrm{\ensuremath{\theta}}}_{\ensuremath{\gamma}}$) and longitudinal (${\mathrm{sin}}^{2}$${\mathrm{\ensuremath{\theta}}}_{\ensuremath{\gamma}}$) components, where ${\mathrm{\ensuremath{\theta}}}_{\ensuremath{\gamma}}$ specifies the direction of the photon with respect to the ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ collision axis. We discuss extraction of fragmentation functions from ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ data. \textcopyright{} 1996 The American Physical Society.

Some QCD estimates of the production of heavy quark flavours in hadron-hadron collisions

Quantum chromodynamic perturbation theory is used to investigate the hadronic production of heavy quark flavours. The theory is applied principally to the data on charmed meson production. Particular emphasis is placed on comparing data with this calculation in the specific region of phase space in which the data are taken. The general results of this approach are presented so that comparisons with data from future experiments on charm and heavier flavour production should be possible.