Phase Space Research Articles

Cryptanalysis and construction of keyed strong S-Box based on random affine transformation matrix and 2D hyper chaotic map

As the only nonlinear module, S-Box (substitution box) is widely used in stream cipher, hash function, and so on. However, there exist some weaknesses in existing S-Boxes, such as fixed point, reverse fixed point and short iteration period rings. Furthermore, the S-Boxes in AES and SM4.0 were fixed, which makes them vulnerable to attack. To address these weaknesses, first, a non-degenerate 2D chaotic map (2D-NDCM) with ergodicity in phase space was constructed. Second, based on 2D-NDCM, the seed S-Boxes with high nonlinearity were constructed in batches by affine transformation and Boolean function, and then three possible weaknesses were eliminated to obtain strong keyed S-Boxes. Statistical analysis demonstrated the effectiveness and practicability of the proposed S-Box batch generating algorithm.

Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response.

Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator, which is characterized by linear dissipative gain and loss terms as well as three nonlinear dissipative terms. Since two of the nonlinear terms break the rotational phase space symmetry, the Wigner distribution of the quantum mechanical limit cycle state of the undriven system is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics of the driven system are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. We identify a large parameter space where the oscillators exhibit appreciable phase localization but only weak or no entrainment, indicating the absence of synchronization. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue; in some cases, the Arnold tongue is found to be asymmetric with respect to vanishing detuning between the external drive and the natural oscillator frequency.

Model reduction to spectral submanifolds in piecewise smooth dynamical systems

We develop a model reduction technique for piecewise smooth dynamical systems using spectral submanifolds. Specifically, we construct low-dimensional, sparse, nonlinear and piecewise smooth models on unions of slow and attracting spectral submanifolds (SSMs) for each smooth subregion of the phase space and then properly match them. We applied this methodology to both equation-driven and data-driven problems, with and without external forcing.

Simple analysis of complex system safety based on Finite State Machine Network and phase space theory

Safety analysis of complex systems, such as aero-engines, has always been a challenging problem. In particular, the risk propagation caused by system functional interactions has become increasingly prominent, leading to the difficulty of traditional safety analysis methods. Existing methods are mostly based on manual experience and deduction with difficulty to completely analyze the whole system safety regions. In this paper, a model-based framework is proposed by combining Finite State Machine Network (FSMN) and phase space theory to perform safety analysis of complex systems from function-logic perspective. We first construct the system model and system state-transition network based on FSMN. Then combining with phase space theory, we identify system safety regions of the entire operating space from macro perspective, and investigate the system risk propagation from micro perspective. An aero-engine system is taken as an example to illustrate the proposed method. Our results show that this method has the ability to effectively identify the potential risk factors and explore emergent unknown risks, which can provide guidance for safety testing.

The debris of the ‘last major merger’ is dynamically young

Abstract The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the ‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor collided with the MW proto-disk 8-11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the MW disk within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space, because the morphology of debris depends on how long it has had to phase mix. The recently-identified phase-space folds in Gaia DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago. We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data 1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’ did not collide with the MW proto-disk at early times, as is thought for the GSE, but instead collided with the MW disk within the last few Gyr, consistent with the body of work surrounding the VRM.

Magnon-mediated topological superconductivity in a quantum wire

Many emergent phases of matter stem from the intertwined dynamics of quasiparticles. Here we show that a topological superconducting phase emerges as the result of interactions between electrons and magnons in a quantum wire and a helical magnet. The magnon-mediated interaction favors triplet superconductivity over a large magnetic phase space region, and stabilizes topological superconductivity over an extended region of chemical potentials. The superconducting gap depends exponentially on the spin-electron coupling, allowing it to be enhanced through material engineering techniques. Published by the American Physical Society 2024

Unique ergodicity in stochastic electroconvection

We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions, we define the corresponding Markov semigroup, and we study its Feller properties. When the noise forces enough modes in phase space, we obtain the uniqueness of the smooth invariant measure for the Markov transition kernels associated with the model.

Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space.

Recent progress on the constraint coordinate-momentum phase space (CPS) formulation of finite-state quantum systems has revealed that the triangle window function approach is an isomorphic representation of the exact population-population correlation function of the two-state system. We use the triangle window (TW) function and the CPS mapping kernel element to formulate a novel useful representation of discrete electronic degrees of freedom (DOFs). When it is employed with nonadiabatic field (NaF) dynamics, a new variant of the NaF approach (i.e., NaF-TW) is proposed. The NaF-TW expression of the population of any adiabatic state is always positive semidefinite. Extensive benchmark tests of model systems in both the condensed phase and gas phase demonstrate that the NaF-TW approach is able to faithfully capture the dynamical interplay between electronic and nuclear DOFs in a broad region, including where the states remain coupled all the time, as well as where the bifurcation characteristic of nuclear motion is important.

M3D-K simulations of beam-driven instabilities in an energetic particle dominant KSTAR discharge

We perform a systematic simulation study of energetic passing particle-driven instabilities in KSTAR using the kinetic-MHD hybrid code M3D-K. Linear simulation results show that the observed n = 1 mode in the early phase of the discharge is the low-frequency fishbone driven by energetic passing beam ions. The mode frequency computed is in a good agreement with the experimental measurement. Nonlinear simulations show that the frequency of the n = 1 mode jumps up to a higher value corresponding to the β-induced Alfvén eigenmode (BAE). In the later phase of the discharge, the simulated n = 5 mode is identified as a BAE in its linear phase. In the nonlinear phase, the n = 5 mode exhibits a similar frequency jump to a higher value of an energetic particle (EP) mode after mode saturation. Analysis of perturbed beam ion distributions in phase space shows that these new modes in nonlinear stages are driven by new resonances due to nonlinearly evolved beam ion distributions. Further simulations of a beam beta scan for the n = 5 mode show that the frequency jump disappears for a sufficiently small beam beta or beam ion drive. This result may explain the non-existence of frequency jump in the experiment. Finally, the impact of toroidal rotation on mode characteristics is investigated, showing that it has a marginal influence on EP driven modes.

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Unlocking Predictive Capability and Enhancing Sensing Performances of Plasmonic Hydrogen Sensors via Phase Space Reconstruction and Convolutional Neural Networks.

This study innovates plasmonic hydrogen sensors (PHSs) by applying phase space reconstruction (PSR) and convolutional neural networks (CNNs), overcoming previous predictive and sensing limitations. Utilizing a low-cost and efficient colloidal lithography technique, palladium nanocap arrays are created and their spectral signals are transformed into images using PSR and then trained using CNNs for predicting the hydrogen level. The model achieves accurate predictions with average accuracies of 0.95 for pure hydrogen and 0.97 for mixed gases. Performance improvements observed are a reduction in response time by up to 3.7 times (average 2.1 times) across pressures, SNR increased by up to 9.3 times (average 3.9 times) across pressures, and LOD decreased from 16 Pa to an extrapolated 3 Pa, a 5.3-fold improvement. A practical application of remote hydrogen sensing without electronics in hydrogen environments is actualized and achieves a 0.98 average test accuracy. This methodology reimagines PHS capabilities, facilitating advancements in hydrogen monitoring technologies and intelligent spectrum-based sensing.

Black hole — wormhole transitions in two dimensional string theory

We study charged black hole and wormhole solutions of Type 0A/IIA string theory in two dimensions, by analysing their low energy equations of motion at leading order in α′. There is a competition between Euclidean wormholes and near extremal black holes in the thermodynamic ensemble. In a certain regime of phase space, the former can disassociate into the latter. Since such solutions are of string scale near the wormhole throat that takes an AdS2 form, there is a need for an exact worldsheet description. We discuss relevant WZW coset models which we argue will shed light on this problem. Finally, we present appropriate versions of the Type 0A/IIA matrix quantum mechanics models that are expected to describe these geometries.

Electron kinetic effects in back-stimulated Raman scattering bursts driven by broadband laser pulses

We examine electron kinetic effects in broadband-laser-driven back-stimulated Raman scattering (BSRS) bursts using particle-in-cell simulations. These bursts occur during the nonlinear stage, causing reflectivity spikes and generating large numbers of hot electrons. Long-duration simulations are performed to observe burst events, and a simplified model is developed to eliminate the interference of the broadband laser’s random intensity fluctuations. Using the simplified model, we isolate and characterize the spectrum of electron plasma waves. The spectrum changes from a sideband structure to a turbulence-like structure during the burst. A significant asymmetry in the spectrum is observed. This asymmetry is amplified and transferred to electron phase space by high-intensity broadband laser pulses, leading to violent vortex-merging and generation of hot electrons. The proportion of hot electrons increases from 6.76% to 14.7% during a single violent burst event. We demonstrate that kinetic effects profoundly influence the BSRS evolution driven by broadband lasers.

Расчеты сжатия сферической слоистой системы ударными волнами с учетом переноса тепла излучением в различных приближениях

Numerical modeling is one of the basic tools to investigate physical phenomena that occur in materials compressed by shock waves. A study of the behavior of shock waves using simplified models is helpful in the analysis of more complex systems, for instance, in the problems of inertial thermonuclear fusion on laser facilities. Mathematical simulation of the nonstationary radiative heat transfer in a spectral kinetic statement is rather complicated because the system of equations is nonlinear and large in size. Generally, the kinetic transport equation is solved in 7D phase space, which requires huge computational resources. The initial system is often approximated under certain assumptions but this immediately causes questions as to whether the simplified model is applicable to particular calculations. In this study, several economic radiative heat transfer models were implemented in a 2D hydrodynamic code. Based on these models, test calculations were performed to simulate the compression of a layered spherical system by shock waves, taking into account radiative heat transfer. When the shock wave reaches the center of the sphere, it is focused and reflected. In the neighborhood of the focal point of a converging wave, temperature gradients increase; therefore, thermal conduction and radiation become the main mechanisms of energy dissipation to be considered when taking into account heat transfer. Maximum densities and temperatures at the center of the sphere and their average values in its regions were calculated. In addition, the time when shock and heat waves cross the sphere center was determined, and their behavior before and after focusing at the sphere center was estimated. It is shown that solutions to such problems can be found much faster and with adequate accuracy when applying simplified models.

Do traffic flow states follow Markov properties? A high-order spatiotemporal traffic state reconstruction approach for traffic prediction and imputation

Assessing traffic states accurately is challenging due to the complex, high-dimensional, and nonlinear nature of traffic systems. This study introduces the innovative High-Order Spatiotemporal Traffic State Reconstruction (HOSTSR) algorithm, designed to track and predict traffic flow dynamics effectively. It combines phase space reconstruction with time delays and high-order neighborhood concepts from graph theory to improve traffic state assessments' accuracy. The algorithm's effectiveness is validated using chi-square tests and the Chapman-Kolmogorov equation to confirm the Markovian properties of traffic flows. A lean autoencoder, informed by prior Markov knowledge of traffic states, is developed for mapping traffic states to real traffic data, proving highly effective for traffic data imputation due to the Markov model's memoryless property. Experimental results from the PeMSD04 and PeMSD08 datasets show that HOSTSR outperforms traditional state reconstruction methods based on delayed coordinate embedding in predicting future traffic flow state based on four key metrics. The autoencoder framework, guided by prior Markov knowledge, shows significant advantages in addressing traffic data gaps in different cases over six baseline models. Gradient sensitivity analysis further evaluates the impact of prior knowledge on improving the autoencoder's interpretability for interpolation efforts.

Computational Spectroscopy of Aqueous Solutions: The Underlying Role of Conformational Sampling.

Fully atomistic multiscale polarizable quantum mechanics (QM)/molecular mechanics (MM) approaches, combined with techniques to sample the solute-solvent phase space, constitute the most accurate method to compute spectral signals in aqueous solution. Conventional sampling strategies, such as classical molecular dynamics (MD), may encounter drawbacks when the conformational space is particularly complex, and transition barriers between conformers are high. This can lead to inaccurate sampling, which can potentially impact the accuracy of spectral calculations. For this reason, in this work, we compare classical MD with enhanced sampling techniques, i.e., replica exchange MD and metadynamics. In particular, we show how the different sampling techniques affect computed UV, electronic circular dichroism, nuclear magnetic resonance shielding, and optical rotatory dispersion of N-acetylproline-amide in aqueous solution. Such a system is a model peptide characterized by complex conformational variability. Calculated values suggest that spectral properties are influenced by solute conformers, relative population, and solvent effects; therefore, particular care needs to be paid for when choosing the sampling technique.

Measurement of the Z boson invisible width at [formula omitted] TeV with the ATLAS detector

A measurement of the invisible width of the Z boson using events with jets and missing transverse momentum is presented using 37 fb−1 of 13 TeV proton–proton data collected by the ATLAS detector in 2015 and 2016. The ratio of Z→inv to Z→ℓℓ events, where inv refers to non-detected particles and ℓ is either an electron or a muon, is measured and corrected for detector effects. Events with at least one energetic central jet with pT≥110 GeV are selected for both the Z→inv and Z→ℓℓ final states to obtain a similar phase space in the ratio. The invisible width is measured to be 506±2(stat.)±12(syst.) MeV and is the single most precise recoil-based measurement. The result is in agreement with the most precise determination from LEP and the Standard Model prediction based on three neutrino generations.

2-in-1 Phase Space Sampling for Calculating the Absorption Spectrum of the Hydrated Electron.

The investigation of vibrational effects on absorption spectrum calculations often employs Wigner sampling or thermal sampling. While Wigner sampling incorporates zero-point energy, it may not be suitable for flexible systems. Thermal sampling is applicable to anharmonic systems yet treats nuclei classically. The application of generalized smoothed trajectory analysis (GSTA) as a postprocessing method allows for the incorporation of nuclear quantum effects (NQEs), combining the advantages of both sampling methods. We demonstrate this approach in computing the absorption spectrum of a hydrated electron. Theoretical exploration of the hydrated electron and its embryonic forms, such as water cluster anions, poses a significant challenge due to the diffusivity of the excess electron and the continuous motion of water molecules. In many previous studies, the wave nature of atomic nuclei is often neglected, despite the substantial impact of NQEs on thermodynamic and spectroscopic properties, particularly for hydrogen atoms. In our studies, we examine these NQEs for the excess electrons in various water systems. We obtained structures from mixed classical-quantum simulations for water cluster anions and the hydrated electron by incorporating the quantum effects of atomic nuclei with the filtration of the classical trajectories. Absorption spectra were determined at different theoretical levels. Our results indicate significant NQEs, red shift, and broadening of the spectra for hydrated electron systems. This study demonstrates the applicability of GSTA to complex systems, providing insights into NQEs on energetic and structural properties.

Measurement of the primary Lund jet plane density in proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\ extrm{s}} $$\\end{document} = 13 TeV

A measurement is presented of the primary Lund jet plane (LJP) density in inclusive jet production in proton-proton collisions. The analysis uses 138 fb−1 of data collected by the CMS experiment at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV. The LJP, a representation of the phase space of emissions inside jets, is constructed using iterative jet declustering. The transverse momentum kT and the splitting angle ∆R of an emission relative to its emitter are measured at each step of the jet declustering process. The average density of emissions as function of ln(kT/GeV) and ln(R/∆R) is measured for jets with distance parameters R = 0.4 or 0.8, transverse momentum pT> 700 GeV, and rapidity |y| < 1.7. The jet substructure is measured using the charged-particle tracks of the jet. The measured distributions, unfolded to the level of stable charged particles, are compared with theoretical predictions from simulations and with perturbative quantum chromodynamics calculations. Due to the ability of the LJP to factorize physical effects, these measurements can be used to improve different aspects of the physics modeling in event generators.

Semi-inclusive single-jet production in DIS at next-to-leading order in the Color Glass Condensate

Within the Color Glass Condensate (CGC) effective field theory, we derive the next-to-leading order (NLO) cross-section for the single-jet semi-inclusive cross-section in deep inelastic scattering (DIS) at small x, for both longitudinally and transversely polarized virtual photons. We provide analytic expressions, valid at finite Nc and suitable for numerical evaluation, for both the cross-section differential in rapidity and transverse momentum and the cross-section differential in rapidity only. Our NLO formulae demonstrate that the very forward rapidity regime is plagued by large double logarithmic corrections coming from phase space constraints on soft gluons close to the kinematic threshold for jet production. A joint resummation of small-x and threshold logarithms at single logarithmic accuracy is proposed to remedy the instability of the cross-section in this regime. By integrating over the single-jet phase space, we recover known results for the NLO DIS structure functions at small x, previously obtained using the optical theorem.