Phase Space Research Articles

Early Fault Diagnosis of Bearings Based on Symplectic Geometry Mode Decomposition Guided by Optimal Weight Spectrum Index

When the rotating machinery fails, the signal generated by the faulty component often no longer maintains the original symmetry, which makes the vibration signal with nonlinear and non-stationary characteristics, and is easily affected by background noise and other equipment excitation sources. In the early stage of fault occurrence, the fault signal is weak and difficult to extract. Traditional fault diagnosis methods are not able to easily diagnose fault information. To address this issue, this paper proposes an early fault diagnosis method for symplectic geometry mode decomposition (SGMD) based on the optimal weight spectrum index (OWSI). Firstly, using normal and fault signals, the optimal weight spectrum is derived through convex optimization. Secondly, SGMD is used to decompose the fault signal, obtaining a series of symplectic geometric modal components (SGCs) and calculating the optimal weight index of each component signal. Finally, using the principle of maximizing the OWSI, sensitive components reflecting fault characteristics are selected, and the signal is reconstructed based on this index. Then, envelope analysis is performed on the sensitive components to extract early fault characteristics of rolling bearings. OWSI can effectively distinguish the interference components in fault signals using normal signals, while SGMD has the characteristic of unchanged phase space structure, which can effectively ensure the integrity of internal features in data. Using actual fault data of rolling bearings for verification, the results show that the proposed method can effectively extract sensitive components that reflect fault characteristics. Compared with existing methods such as Variational Mode Decomposition (VMD), Feature Mode Decomposition (FMD), and Spectral Kurtosis (SK), this method has better performance.

On the reconstruction of unknown driving forces from low-mode observations in the 2D Navier–Stokes equations

This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is proposed for accomplishing this, which makes use of a nonlinear property of the equations of motions to asymptotically enslave small scales to large scales. In particular, an algorithm is introduced that systematically produces approximations of the flow field on the unobserved scales in order to generate an approximation to the unknown force; the process is then repeated to generate an improved approximation of the unobserved scales, and so on. A mathematical proof of convergence of this algorithm is established in the context of the two-dimensional Navier–Stokes equations with periodic boundary conditions under the assumption that the force belongs to the observational subspace of phase space; at each stage in the algorithm, it is shown that the model error, represented as the difference between the approximating and true force, asymptotically decreases to zero in a geometric fashion provided that sufficiently many scales are observed and certain parameters of the algorithm are appropriately tuned.

The credit card-augmented Divisia monetary aggregates: an analysis based on recurrence plots and visual boundary recurrence plots

In this paper, we compare the dynamics of the growth rates of the original Divisia monetary aggregates, the credit card-augmented Divisia monetary aggregates, and the credit card-augmented Divisia inside monetary aggregates. This analysis is based on the methods of recurrence plots, recurrence quantification analysis, and visual boundary recurrence plots which are phase space methods designed to depict the underlying dynamics of the system under study. We identify the events that affected Divisia money growth and point out the differences among the different Divisia monetary aggregates based on the recurrence and visual boundary recurrence plots. We argue that the broad Divisia monetary aggregates could be used for monetary policy and business cycle analysis as they are exhibiting less fluctuation compared to the narrow Divisia monetary aggregates. They could positively affect policy decisions regarding environmental choices and sustainability. We also point out the changes in the monetary dynamics locating the 2008 global financial crisis and the Covid-19 pandemic.

Phase Space Mixing of a Vlasov Gas in the Exterior of a Kerr Black Hole

Phase Space Mixing of a Vlasov Gas in the Exterior of a Kerr Black Hole

Revisiting the implications of Liouville's theorem to the anisotropy of cosmic rays

We present a solution to Liouville's equation for an ensemble of charged particles propagating in magnetic fields. The solution is presented using an expansion in spherical harmonics of the phase space density, allowing a direct interpretation of the distribution of arrival directions of cosmic rays. The results are found for chosen conditions of variability and source distributions. We show there are two conditions for an initially isotropic flux of particles to remain isotropic while traveling through a magnetic field: isotropy and homogeneity of the sources. In case isotropically-distributed sources inject particles continuously in time, a transient magnetic induced dipole will appear. This dipole will vanish if the system reaches a steady-state. The formalism is used to analyze the data measured by the Pierre Auger Observatory, contributing to the understanding of the dependence of the dipole amplitude with energy and predicting the energy in which the quadrupole signal should be measured.

Are the dynamics of wall turbulence in minimal channels and larger domain channels equivalent? A graph-theoretic approach

This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in a complex multilayer network. Network motif analysis, i.e., extracting dominant non-random elemental patterns within these networks, is used to identify the most dominant dynamical mechanisms. Both approaches, combined with network motif analysis, are used to answer whether the main dynamical mechanisms of a minimal flow unit (MFU) and a larger unconstrained channel flow, labeled a full channel (FC), at Reτ ≈ 180, are equivalent. The first approach tracks traditional coherent structures defined as low- and high-speed streaks, ejections, and sweeps. It is found that the roll-streak pairing, consistent with the current understanding of self-sustaining processes, is the most significant and simplest dynamical mechanism in both flows. However, the MFU has a timescale for this mechanism that is approximately 2.83 times slower than that of the FC. In the second approach, we use semi-Lagrangian wavepackets and define coherent structures from their energetic streak, roll, and small-scale phase space. This method also shows similar motifs for both the MFU and FC. It indicates that, on average, the most dominant phase-space motifs are similar between the two flows, with the significant events taking place approximately 2.21 times slower in the MFU than in the FC. This value is more consistent with the implied timescale ratio of only the slow speed streaks taking part in the roll-streak pairing extracted using the first multi-type spatiotemporal approach, which is approximately 2.17 slower in the MFU than the FC.

The Radial Orbits of Ram-pressure-stripped Galaxies in Clusters from the GASP Survey

We analyze a sample of 244 ram-pressure-stripped candidate galaxy members within the virial radius of 62 nearby clusters to determine their velocity anisotropy profile β(r). We use previously determined mass profiles for the 62 clusters to build an ensemble cluster by stacking the 62 cluster samples in projected phase space. We solve the Jeans equation for dynamical equilibrium by two methods, MAMPOSSt and the Jeans inversion technique, and determine β(r) both in parametric form and nonparametrically. The two methods consistently indicate that the orbits of the ram-pressure-stripped candidates are increasingly radial with distance from the cluster center, from almost isotropic (β ≃ 0) at the center, to very radial at the virial radius (β ≃ 0.7). The orbits of cluster galaxies undergoing ram pressure stripping are similar to those of spiral cluster galaxies but more radially elongated at large radii.

Characterization of Stream, Hyperconcentrated and Debris Flows from Seismic Signals: Insights into Sediment Transport Mechanisms and Flow Dynamics

AbstractSediments in steep channels can be mobilized to form stream flows, hyperconcentrated flows and debris flows, which can cause damage to downstream communities. However, the understanding of the sediment‐transport mechanisms that control these processes remains incomplete due to the lack of effective monitoring methods. In this study, we utilize seismic data captured during these sediment‐laden flows through field experiments and in situ monitoring to offer insights into flow mechanics and sediment transport mechanisms. Results show that sediment transport in stream flows and hyperconcentrated flows is primarily supported by viscous shear and turbulent stresses, whereas grain collisional stresses play a significant role in debris‐flow dynamics. By characterizing impact rates, basal impulses and flow discharge, seismic monitoring can reveal the internal flow dynamics and bulk flow characteristics as well as the characteristics of sediment transport. Increasing solid concentrations can elicit positive nonlinearities in the frequency‐based scaling relationships between seismic power and hydrographs, indicating transitions in the seismic signal from turbulence‐bedload‐dominated to bedload‐dominated, and grain collisional‐dominated regimes. By introducing the ratio of the real shear stress to the critical shear stress, we refined the phase space for sediment stability. Combining this criterion with the absolute seismic power enables us to establish ground‐motion thresholds for distinguishing different flow types. Our results highlight opportunities to use seismic data for the quantitative inversion of these fluvial processes and debris flows as well as early warning strategies.

Ultrafast oscillation in a field emission-driven miniaturized gaseous diode

We report an ultrafast oscillation (up to ∼104 GHz) in the early stage of field emission-driven microdischarges. Spatiotemporal behaviors of electron density, space charge density, and electric field, exhibiting high-frequency oscillations, are demonstrated based on first-principle particle-in-cell/Monte Carlo collision simulations. Intermittent electron emission fluxes are identified from the electron phase space distributions whereas the ions are rather non-oscillatory in the transient timescale. The mechanisms of oscillation with growing amplitude are found to be related to the rapid modification of the field emission current affected by the space charge electric field, which is also accompanied by the fast response of the electron transport and ionization in a dynamic double-layer sheath. Further, a transport equation for emission current is solved to estimate the oscillation frequency, which agrees well with the simulation results. This study provides a more precise understanding of the formation of the field emission-driven microdischarge, which informs the design and optimization of miniaturized gaseous electronic devices.

Peculiarities of charged particle kinetics in spherical plasma

We describe transient kinetic simulations of partially ionized weakly-collisional plasma around spherical bodies absorbing or emitting charged particles. Numerical solutions of kinetic equations for electrons and ions in 1D2V phase space are coupled to an electrostatic solver using the Poisson equation or quasineutrality condition for small Debye lengths. The formation of particle groups and their contributions to electric current flow and screening of charged bodies by plasma are discussed for applications to Langmuir probes and solar wind.

Optimizing dynamic aperture studies with active learning

Dynamic aperture is an important concept for the study of non-linear beam dynamics in circular accelerators. It describes the extent of the phase-space region where a particle's motion remains bounded over a given number of turns. Understanding the features of dynamic aperture is crucial for the design and operation of such accelerators, as it provides insights into nonlinear effects and the possibility of optimising beam lifetime. The standard approach to calculate the dynamic aperture requires numerical simulations of several initial conditions densely distributed in phase space for a sufficient number of turns to probe the time scale corresponding to machine operations. This process is very computationally intensive and practically outside the range of today's computers. In our study, we introduced a novel method to estimate dynamic aperture rapidly and accurately by utilising a Deep Neural Network model. This model was trained with simulated tracking data from the CERN Large Hadron Collider and takes into account variations in accelerator parameters such as betatron tune, chromaticity, and the strength of the Landau octupoles. To enhance its performance, we integrate the model into an innovative Active Learning framework. This framework not only enables retraining and updating of the computed model, but also facilitates efficient data generation through smart sampling. Since chaotic motion cannot be predicted, traditional tracking simulations are incorporated into the Active Learning framework to deal with the chaotic nature of some initial conditions. The results demonstrate that the use of the Active Learning framework allows faster scanning of the configuration parameters without compromising the accuracy of the dynamic aperture estimates.

Phase structures and critical behavior of rational non-linear electrodynamics Anti de Sitter black holes in Rastall gravity

This research paper presents a black hole solution with a rational nonlinear electrodynamics source within the Rastall gravity framework. The paper analyzes the thermodynamic properties of the solution in normal phase space and explores its critical behavior. The phase structure is examined using the extended first law of thermodynamics, with the cosmological constant Λ serving as pressure P. The isotherms exhibit van der Waals behavior at small values of horizon r +. The paper also investigates the Gibbs free energy behavior and finds two critical points with two pressures where the re-entrant phase transition occurs and disappears. We also explore the prevalent microstructure of black holes in Ruppeiner geometry, uncovering significant deviations in the nature of particle interactions from conventional practice. Moreover, the thermodynamic geometry is analyzed using the Ruppeiner formalism, with the normalized Ricci scalar indicating possible point-phase transitions of the heat capacity, and the normalized extrinsic curvature having the same sign as the normalized Ricci scalar. The three-phase transitions of the heat capacity are those that we find for the normalized Ruppeiner curvatures. Thus, there is an absolute correspondence.

Upper and lower bounds on phase-space rearrangements

Broad classes of plasma phenomena can be understood in terms of phase-space rearrangements. For example, the net effect of a wave–particle interaction may consist of moving populations of particles from one region of phase space to another. Different phenomena drive rearrangements that obey different rules. When those rules can be specified, it is possible to calculate bounds that limit the possible effects the rearrangement could have (such as limits on how much energy can be extracted from the particles). This leads to two problems. The first is to understand the mapping between the allowed class of rearrangements and the possible outcomes that these rearrangements can have on the overall distribution. The second is to understand which rules are appropriate for which physical systems. There has been recent progress on both fronts, but a variety of interesting questions remain unanswered.

Decoherence and entropy generation at one loop in the inflationary de Sitter spacetime for Yukawa interaction

Abstract The decoherence mechanism is believed to be possibly connected to the quantum to classical transition of the primordial cosmological perturbations in the early universe. In this paper, we extend our previous analysis on decoherence in a fermion and scalar quantum field theory coupled via the Yukawa interaction in the Minkowski spacetime, to the inflationary de Sitter background. We treat the scalar field as the system and the fermions as the environment, and both the fields are taken to be massless. We utilise a non-equilibrium effective field theory formalism, suitable for open quantum systems such as this. We assume that an observer measures only the Gaussian 2-point correlator for the scalar field, as the simplest realistic scenario. In order to compute the von Neumann entropy generated at late times as a measure of the decoherence, we construct the one loop renormalised Kadanoff-Baym equation, which is the equation of motion satisfied by the 2-point correlators in the closed time path Schwinger-Keldysh formalism. These equations account to the self energy corrections. Using this, we next construct the one loop corrected statistical propagator for the scalar, which is related to its phase space area, to compute the von Neumann entropy. We also compute the variation of the von Neumann entropy with respect to relevant parameters. We note the qualitative similarity between our findings and the scenario where both the system and the environment are scalars. Our result is also qualitatively similar to an earlier one found by using the influence functional technique for a massive Yukawa theory.

Thermodynamical analysis with extended phase transition of AdS hairy black hole in gravitational decoupling theory

This article explores various thermodynamical aspects and the extended phase space of the AdS hairy black hole within the context of gravitational decoupling. This study focused on thermodynamic properties such as geometrical mass, Hawking temperature, entropy, specific heat, Gibbs free energy (both locally and globally) and P-V criticality at the horizon radius. The thermodynamic stability of the AdS hairy black hole has been established based on its positive heat capacity. The analysis of Gibbs free energy is utilized to investigate the behavior of the first-order phase transition. Thermodynamic pressure, denoted by P, is related to the cosmological constant by the formula P=−Λ8π . In addition, a numerical investigation has been carried out to examine the equation of the state parameter and its critical values.

Recurrence analysis of meteorological data from climate zones in India.

We present a study on the spatiotemporal pattern underlying the climate dynamics in various locations spread over India, including the Himalayan region, coastal region, and central and northeastern parts of India. We try to capture the variations in the complexity of their dynamics derived from temperature and relative humidity data from 1948 to 2022. By estimating the recurrence-based measures from the reconstructed phase space dynamics using a sliding window analysis on the data sets, we study the climate variability in different spatial locations. The study brings out the variations in the complexity of the underlying dynamics as well as their heterogeneity across the locations in India. We find almost all locations indicate shifts to more irregular and stochastic dynamics for temperature data around 1972-79 and shifts back to more regular dynamics beyond 2000. These patterns correlate with reported shifts in the climate and Indian Summer Monsoon related to strong and moderate El Niño-Southern Oscillation events and confirm their associated regional variability.

On the motion stabilization of a three-link robotic manipulator with incomplete measurement

Abstract. This paper considers a mathematical model of a manipulator which consists of a vertical column, two links, connected to it in series, and a gripper with a load. The column resting on a fixed base can rotate around its vertical axis. The links are connected by cylindrical hinges allowing them to rotate in the same vertical plane. The column and the links are modeled as rigid bodies with the links having unequal principal moments of inertia. The position of the manipulator in space is determined by three rotation angles of the column and the links. The manipulator can have several types of steady-state program movements. When gravitational torques are compensated by control torques applied in the cylindrical hinges, the manipulator has a program equilibrium position. The manipulator can also have a program motion when the column rotates at a given constant angular velocity, and the links have given relative equilibrium positions in their plane. The stabilization problem of manipulator motion is investigated by means of control torques with feedback when only the rotation angles of the column and links are measured. The problem posed is solved in the form of a nonlinear proportional-integral controller taking into account the cylindrical phase space of the manipulator's mathematical model. The solution includes construction of a Lyapunov functional with a semi-definite derivative and application of the corresponding theorems on the asymptotic stability of non-autonomous functional differential retarded-type equations. The obtained conditions for the program motion stabilization are robust with respect to the mass-inertial parameters of the manipulator. The numerical simulation results demonstrate global attraction to its given position in cylindrical phase space.

Correction to: Generalization of Hamiltonian mechanics to a three-dimensional phase space

Abstract In a recent paper [N. Sato, Prog. Theor. Exp. Phys. 2021, 6, 063A01 (2021)] we introduced a generalization of Hamiltonian mechanics to three-dimensional phase spaces in terms of closed 3-forms. This correction addresses an error in the proof of theorem 3, which concerns the existence of a coordinate change transforming a closed 3-form into a constant form. Indeed, invertibility of a 3-form is not sufficient to ensure the existence of a solution Xt to eq. (77) when n > 3. The theorem can be corrected by restricting the class of 3-forms to those that are relevant to generalized Hamiltonian mechanics. Although the new theorem requires a stronger hypothesis, the formulation of dynamical systems with 2 invariants in terms of closed 3-forms, which is the key contribution of the paper, holds.

Symmetry-based study and dynamics of casual bulk viscous matter-dominated universe

The dynamics of cosmological expansion is studied for a spatially flat matter-dominated universe filled with barotropic casual bulk viscous fluid. The evolution equation for the Hubble parameter is derived using Friedmann equations and conservation law for the viscous fluid, in which the viscous pressure is modeled by truncated version of the full Israel-Stewart theory of bulk viscosity. We use a Lie symmetry-based approach to study the evolution of the expansion rate of the Universe. The model equation possesses eight-parameter Lie symmetry generators and gives two different analytic group invariant solutions for the Hubble parameter. Expressions for various important cosmological parameters are obtained and values are estimated analytically for the explanation of the evolution dynamics of the Universe. The interesting features of the obtained symmetry-based solutions are that, one satisfies the present acceleration of the Universe, while the other could not support present accelerating phase, rather represents a universe dominated by non-viscous stiff fluid. We make useful checks on the observational constraints on the model parameters from the latest released observational data. The accelerating phase of the current universe is investigated using observational bounds and compared the model under investigation with the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model. The evolutionary cosmic phases obtained from the analysis of the Lie symmetry-based solutions correspond to the association with the critical points in the equivalent phase space. These interesting features are investigated and analyzed using dynamical systems approach.

Research Photon Energy Spectrum of Medical Linear Accelerator by Monte Carlo Method

The distribution of the photon energy spectrum in isocenter plane of the medical linear accelerator and the influence of secondary collimator on the photon energy spectrum are studied. Methods Use the BEAMnrc program to simulate the transmission of the 6 MeV electrons and photons in 5 cm×5 cm,10 cm×10 cm,15 cm×15 cm and 20 cm×20 cm fields in treatment head of the medical linear accelerator, where a phase space file was set up at the isocenter plane to record the particle information passing through this plane. The BEAMdp program is used to analyze the phase space file, in order to obtain the distribution of the photon energy spectrum in isocenter plane and the influence of secondary collimator on the photon energy spectrum. By analyzing the photon energy spectrum of a medical linear accelerator with a nominal energy of 6 MV, it is found that the secondary collimator has little effect on the photon energy spectrum; different fields have different photon energy spectrum distributions; the photon energy spectrum in different central regions of the same field have the same normalized distribution. In the dose calculation of radiation therapy, the influence of photon energy spectrum should be carefully considered.