Phase Space Research Articles

Phase Space Graph Convolutional Network for Chaotic Time Series Learning

Phase Space Graph Convolutional Network for Chaotic Time Series Learning

Impact of Planetary Parameters on Water Clouds Microphysics

Potentially habitable exoplanets are targets of great interest for the James Webb Space Telescope and upcoming mission concepts such as the Habitable Worlds Observatory. Clouds strongly affect climate and habitability, but predicting their properties is difficult. In Global Climate Models (GCMs), especially those aiming at simulating Earth, cloud microphysics is often crudely approximated by assuming that all cloud particles have a single, constant size or a prescribed size distribution and that all clouds in a grid cell are identical. For exoplanets that range over a large phase space of planetary properties, this method could result in large errors. In this work, our goal is to determine how cloud microphysics on terrestrial exoplanets, whose condensable is mainly water vapor, depend on aerosol properties and planetary parameters such as surface pressure, surface gravity, and incident stellar radiation. We use the Community Aerosol and Radiation Model for Atmospheres as a 1D microphysical model to simulate the formation and evolution of clouds including the processes of nucleation, condensation, evaporation, coagulation, and vertical transfer. In these 1D idealized experiments, we find that the parameters that determine the macrophysical thermal structure of the atmospheres, including surface pressure and stellar flux, impact cloud radiative effect (CRE) most significantly. Parameters such as gravity and number density of aerosols working as cloud condensation nuclei affect the microphysical processes of cloud formation, including activation and vertical transfer. They also have a significant, though weaker effect on CRE. This work motivates the development of more accurate GCM cloud schemes and should aid in the interpretation of future observations.

Prompt extinction of bump-on-tail energy spectra for radiation belt electron phase space density

The bump-on-tail electron flux energy spectral distributions in the Earth's radiation belt are widely observed and have been proven to be generated by plasmaspheric hiss-led wave–particle interactions. Here, we report and discuss the prompt disappearance of them induced by the high solar wind dynamic pressure (Pdyn) combined with substorms on 12–13 March 2014. To remove the potential adiabatic influence, the electron fluxes are all converted to phase space density in the TS04 geomagnetic coordinate. Immediately after the Pdyn reached its maximum accompanied by the intensifying of substorms, the initial bump-on-tail spectra of the phase space density at L* (the third adiabatic invariant) from 3.8 to 4.4 were destroyed and rapidly smoothed to the exponential distributions, with a distinct ascent for lower energy electrons and a sharp decline for higher energy electrons. The balance line between the source and loss processes was located at μ = 50–200 MeV/G (μ is the first adiabatic invariant), which is sensitive to the spatial location. Further investigation of the temporal evolution of the phase space density along with L* and the plasma wave distributions provided evidence that the loss processes dominated at higher L* for electrons at μ ≳ 100 MeV/G, while the source processes became stronger at lower L* for electrons at μ ≲ 10 MeV/G. Our study provides new insight into the rapid change of the radiation belt electron spectral types in response to solar wind disturbances, which could be fully considered in further radiation belt particle modeling.

The Development of Pepper-Pot Emittance Monitor in Gunma University

The pepper-pot emittance monitor is a device that can measure the phase space distribution of the beam rapidly. We have introduced one at the ion source test stand of Gunma University. We confirmed that the phase space distribution can be measured accurately comparing to the existing wire-slit type emittance monitor.

Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics.

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton's equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton's equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton's and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton's, variational, and Schrödinger equations are described. Employing the Hénon-Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton's equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes.

EXPONENTIAL ATTRACTORS FOR THE VISCOUS CAHN-HILLIARD SYSTEM

In this article, we explore a viscous Cahn-Hilliard system, which has applications in biology. By imposing appropriate boundary and initial conditions, we examine the asymptotic behavior of its solutions. First, we show that the problem of initial and limit values generates by a continuous semigroup on an appropriate phase space, which has a global attractor denoted $\mathcal{A}$. Subsequently, we establish the existence of an exponential attractor $\mathcal{M}$. Therefore, the global attractor $\mathcal{A}$ has a finite fractal dimension.

Stationary coupled KdV systems and their Stäckel representations

AbstractIn this article, we investigate stationary coupled Korteweg–de Vries (cKdV) systems and prove that every ‐field stationary cKdV system can be written, after a careful reparameterization of jet variables, as a classical separable Stäckel system in different ways. For each of these parameterizations, we present an explicit map between the jet variables and the separation variables of the system. Finally, we show that each pair of Stäckel representations of the same stationary cKdV system, when considered in the phase space extended by Casimir variables, is connected by an appropriate finite‐dimensional Miura map, which leads to an ‐Hamiltonian formulation for the stationary cKdV system.

A method for calculating the technical readiness of aviation refuelling vehicles

In the paper a mathematical model of the process of operating aviation refuelling vehicles supplying fuel to aircraft before flight was developed. The present work is a continuation and supplement to the model contained in [52]. The phase space of the process under study was mapped by a 7-state directed graph of the operation process. To calculate the technical readiness index (K_gt) Markov chains and processes were used. Also, in Section 3, Results and discussions, optional methods for determining the technical readiness coefficient of a vehicle were provided k_gt) , based on the total time of the object in individual operating states. This is an alternative in a situation where the analysed process cannot reach a stable average state indefinitely. Two types of measures were used to determine the readiness, i.e. border probabilities and average times of the object in individual states. In both cases, the basis was statistical databases with operational vehicle data, which enabled the calculation of the readiness index and coefficient.

Interpreting Symplectic Linear Transformations in a Two-Qubit Phase Space

Interpreting Symplectic Linear Transformations in a Two-Qubit Phase Space

Axial friction coefficient of turbulent spiral Poiseuille flows

Direct numerical simulations of spiral Poiseuille flows in a narrow gap geometry are performed with the aim of identifying the mechanisms governing the dynamics of the axial friction coefficient. The investigation has explored a small portion of the Reynolds number–Taylor number phase space ( $600 \leq Re \leq 5766$ and $1500 \leq Ta \leq 5000$ ), for which reference experimental results are available. The study is focused on the mechanism leading to the enhancement of the axial friction coefficient with the Taylor number when the Reynolds number is kept constant. The analysis of the spatial distribution of the Reynolds stress tensor and of the turbulent energy budget has evidenced the key role of the pressure–strain correlation in the energy transfer from the azimuthal to the axial component. The latter eventually determines the increase of the axial friction coefficient through the enhanced radial mixing of axial momentum. Data have also shown that the flow dynamics is heavily dependent on the $Ta/Re$ ratio, and different regimes develop (ranging from laminar to turbulent), each with peculiar behaviours.

CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction

To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network, we propose a convolutional neural network (CNN)-long short-term memory (LSTM) prediction model based on the incremental attention mechanism. Firstly, a traversal search is conducted through the traversal layer for finite parameters in the phase space. Then, an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria (DWC). The phase space parameters that best meet DWC are selected and fed into the input layer. Finally, the constructed CNN-LSTM network extracts spatiotemporal features and provides the final prediction results. The model is verified using Logistic, Lorenz, and sunspot chaotic time series, and the performance is compared from the two dimensions of prediction accuracy and network phase space structure. Additionally, the CNN-LSTM network based on incremental attention is compared with LSTM, CNN, recurrent neural network (RNN), and support vector regression (SVR) for prediction accuracy. The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy. Also, the algorithm to estimate the phase space parameter is compared with the traditional CAO, false nearest neighbor, and C–C, three typical methods for determining the chaotic phase space parameters. The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks, including CNN-LSTM, LSTM, CNN, RNN, and SVR.

Reduced dimensional Monte Carlo method: Preliminary integrations.

A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least half of the integration variables prior to setting up the particular Monte Carlo calculation of interest, in some cases more. Proper accounting of invariant phase space structures shows that the system's dynamics is reducible into composite stable and unstable degrees of freedom. Stable degrees of freedom behave locally in the reduced dimensional phase space exactly as an analogous integrable system would. Classification of the unstable degrees of freedom is dependent upon the degree of chaos present in the dynamics. The techniques for deriving the requisite canonical coordinate transformations are developed and shown to block diagonalize the stability matrix into irreducible parts. In doing so, it is demonstrated how to reduce the amount of sampling directions necessary in a Monte Carlo simulation. The technique is illustrated by calculating return probabilities and expectation values for different dynamical regimes of a two-degrees-of-freedom coupled quartic oscillator within a classical Wigner method framework.

Towards a Reconciliation Between Simulational, Ludic, and Historiographical Practices in Research

Background Simulations, ludic or otherwise, have so far struggled to gain a foothold in mainstream historiography. Some authors suggest there may be fundamental incompatibilities between history and the language of simulations and scholarly games. Others believe that designing, employing, and validating historical simulations may be simply too costly and/or labor-intensive to justify their widespread adoption. Intervention This paper intends to identify points of friction between historiography and simulation-based research and suggest practical solutions to these issues. Methods My discussion is based on the description and analysis of a case study, the ThomondSim/ The Triumphs of Turlough research project. The initiative consisted of the development and application of an agent-based computational model (ABM) and a scholarly board game to investigate the possible associations between economic, environmental, and military hazards in 13th and 14th centuries Ireland. Results and Discussion Ensuring the simulations matched historical evidence to a standard deemed acceptable by the historiographical community limited their phase space, compromising their capacity to explore emergent phenomena. The intricacy of the underlying conceptual model suited the ABM better than the board game, which struggled to reconcile complexity with good game design practices. The board game, however, proved to be an effective validating tool for the ABM. Limitations and Suggestions for Further Research The project espoused an overt simulation- and game-centric approach, paying little attention to unguided play. Recent literature suggests that fostering, rather than hindering, playful exploration could address some of the pitfalls identified by this project. Conclusion Play could be a means of reconciliation between simulational, ludic, and historiographical practices. However, to ensure that projects adhere to epistemic standards, it is recommended that a methodology is developed to integrate it into research in ways that can be tested and evaluated.

Phase Space Spin-Entropy.

Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a quantum state are position and spin. We focus on the spin degree of freedom and elucidate the spin-entropy. Then, we present some of its properties and show how entanglement increases spin-entropy. A dynamic model for the time evolution of spin-entropy concludes the paper.

Chaotic characterization and chaotic prediction modelling of HFSWR ionospheric echoes excited by typhoon

ABSTRACT This research explores the intricate-coupling relationship between typhoons and the ionosphere by the high-frequency surface wave radar’s (HFSWR) over-the-horizon capabilities. This letter describes the gravity wave features in travelling ionospheric disturbances (TIDs) and ionospheric drift information. Further discussion is raised on the chaotic properties of gravity wave features using the Lyapunov exponents and chaotic attractors, particularly as they are influenced by typhoon. To predict these gravity wave features more accurately, a new model is developed by synergizing phase space reconstruction theory and statistical learning theory, a chaotic prediction model for gravity wave features constructed on a third-order Volterra filter. The experimental findings confirm that the gravity waves features detected via HFSWR present the hyperchaotic behaviour. More importantly, the innovative gravity wave prediction model based on chaotic attractor can capture the dynamics of the original chaotic system. Notably, the model’s prediction accuracy has been improved by 98.6% after the introduction of phase space reconstruction modelling.

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Beyond radial profiles: Using log-normal distributions to model the multiphase circumgalactic medium

Abstract Recent observations and simulations reveal that the circumgalactic medium (CGM) surrounding galaxies is multiphase, with the gas temperatures spanning a wide range at most radii, ∼104 K to the virial temperature (∼106 K for Milky Way). Traditional CGM models using simple density profiles are inadequate at reproducing observations that indicate a broad temperature range. Alternatively, a model based on probability distribution functions (PDFs) with parameters motivated by simulations can better match multi-wavelength observations. In this work, we use log-normal distributions, commonly seen in the simulations of the multiphase interstellar and circumgalactic media, to model the multiphase CGM. We generalize the isothermal background model by Faerman et al. 2017 to include more general CGM profiles. We extend the existing probabilistic models from 1D-PDFs in temperature to 2D-PDFs in density-temperature phase space and constrain its parameters using a Milky Way-like Illustris TNG50-1 halo. We generate various synthetic observables such as column densities of different ions, UV/X-ray spectra, and dispersion and emission measures. X-ray and radio (Fast Radio Burst) observations mainly constrain the hot gas properties. However, interpreting cold/warm phase diagnostics is not straightforward since these phases are patchy, with inherent variability in intercepting these clouds along arbitrary lines of sight. We provide a tabulated comparison of model predictions with observations and plan to expand this into a comprehensive compilation of models and data. Our modeling provides a simple analytic framework that is useful for describing important aspects of the multiphase CGM.

Gottesman-Kitaev-Preskill Encoding in Continuous Modal Variables of Single Photons.

GKP states, introduced by Gottesman, Kitaev, and Preskill, are continuous variable logical qubits that can be corrected for errors caused by phase space displacements. Their experimental realization is challenging, in particular, using propagating fields, where quantum information is encoded in the quadratures of the electromagnetic field. However, traveling photons are essential in many applications of GKP codes involving the long-distance transmission of quantum information. We introduce a new method for encoding GKP states in propagating fields using single photons, each occupying a distinct auxiliary mode given by the propagation direction. The GKP states are defined as highly correlated states described by collective continuous modes, as time and frequency. We analyze how the error detection and correction protocol scales with the total photon number and the spectral width. We show that the obtained code can be corrected for displacements in time-frequency phase space, which correspond to dephasing, or rotations, in the quadrature phase space and to photon losses. Most importantly, we show that generating two-photon GKP states is relatively simple, and that such states are currently produced and manipulated in several photonic platforms where frequency and time-bin biphoton entangled states can be engineered.

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. The ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

Phase stability and mechanical property trends for MAB phases by high-throughput ab initio calculations

MAB phases (MABs) are atomically-thin laminates of ceramic/metallic-like layers, having made a breakthrough in the development of 2D materials. Though offering a vast chemical and phase space, relatively few MABs have been synthesised. To guide experiments, we perform high-throughput ab initio screening of MABs that combine group 4–7 transition metals (M); Al, Si, Ga, Ge, or In (A); and boron (B) focusing on their phase stability trends and mechanical properties. Considering the 1:1:1, 2:1:1, 2:1:2, 3:1:2, 3:1:3, and 3:1:4 M:A:B ratios and 10 phase prototypes, synthesisability of a single-phase compound for each elemental combination is estimated through formation energy spectra of competing dynamically stable MABs. Based on the volumetric proximity of energetically-close phases, we identify systems in which volume-changing deformations may facilitate transformation toughening. Subsequently, chemistry- and phase-structure-related trends in the elastic stiffness and ductility are predicted using elastic-constants-based descriptors. The analysis of directional Cauchy pressures and Young's moduli allows comparing mechanical response parallel and normal to M–B/A layers. The suggested promising MABs include Nb3AlB4, Cr2SiB2, Mn2SiB2 or the already synthesised MoAlB.