Entropy Modes Research Articles

Urban Land Expansion Simulation Considering the Diffusional and Aggregated Growth Simultaneously: A Case Study of Luoyang City

Restricted by urban development stages, natural conditions, urban form and structure, diffusional growth occupies a large proportion of area in many cities. Traditional cellular automata (CA) has been widely applied in urban growth studies because it can simulate complex system evolution with simple rules. However, due to the limitation of neighborhood conditions, it is insufficient for simulating urban diffusional growth process. A maximum entropy mode was used to estimate three layers of probability spaces: the probability layer of cell transformation from non-urban status to urban status (PLCT), the probability layer for aggregated growth (PLAP), and the probability layer for diffusional growth (PLOP). At the same time, a maxent category selected CA model (MaxEnt-CSCA) was designed to simulate aggregated and diffusional urban expansion processes simultaneously. Luoyang City, with a large proportion of diffusional urban expansion (65.29% in 2009–2018), was used to test the effectiveness of MaxEnt-CSCA. The results showed that: (1) MaxEnt-CSCA accurately simulated aggregated growth of 47.40% and diffusional growth of 37.13% in Luoyang from 2009 to 2018, and the overall Kappa coefficient was 0.78; (2) The prediction results for 2035 showed that future urban expansion will mainly take place in Luolong District and the counties around the main urban area, and the distribution pattern of Luolong District will change from the relative diffusion state to the aggregation stage. This paper also discusses the applicable areas of MaxEnt-CSCA and illustrates the importance of selecting an appropriate urban expansion model in a region with a large amount of diffusional growth.

Study of a Gas Disturbance Mode Content Based on the Measurement of Atmospheric Parameters at the Heights of the Mesosphere and Lower Thermosphere

The main result of this work is the estimation of the entropy mode accompanying a wave disturbance, observed at the atmosphere heights range of 90–120 km. The study is the direct continuation and development of recent results on diagnosis of the acoustic wave with the separation on direction of propagation. The estimation of the entropy mode contribution relies upon the measurements of the three dynamic variables (the temperature, density, and vertical velocity perturbations) of the neutral atmosphere measured by the method of the resonant scattering of radio waves on the artificial periodic irregularities of the ionospheric plasma. The measurement of the atmosphere dynamic parameters was carried out on the SURA heating facility. The mathematical foundation of the mode separation algorithm is based on the dynamic projection operators technique. The operators are constructed via the eigenvectors of the coordinate evolution operator of the transformed system of balance equations of the hydro-thermodynamics.

The description of non‐linear interactions of wave and non‐wave modes in a non‐adiabatic plasma flow

AbstractThe method of derivation of non‐linear equations for interacting modes is explained and applied to a plasma's flow affected by a magnetic field. It is based on the linear projecting of the total perturbation field into specific variations of variables in individual modes of a flow. The method may be applied in many examples of fluid flows with different mechanisms of non‐adiabaticity. It is of special importance in complex flows with large number of different modes. A flow of an ionized gas is one of the examples of such flows: it incorporates fast, slow magnetosonic modes, the Alfvén mode and the entropy mode. In the frames of this study, the wave vector may form an arbitrary angle with the straight equilibrium magnetic field. Thermal conduction, dynamic viscosity and a generic heating–cooling function, which is responsible for an energy inflow and radiative losses, are taken into account. Variable and plasma‐β, diversity of the wave modes and a balance of different mechanisms of non‐adiabaticity make the description of non‐linear interaction of modes special. The non‐linear excitation of the magnetosonic mode by the entropy mode is considered as an example.

Fault Diagnosis of the Gyratory Crusher Based on Fast Entropy Multilevel Variational Mode Decomposition

Gyratory crusher is a kind of commonly used mining machinery. Because of its heavy workload and complex working environment, it is prone to failure and low reliability. In order to solve this problem, this paper proposes a fault diagnosis method of the gyratory crusher based on fast entropy multistage VMD, which is used to quickly and accurately find the possible fault problems of the gyratory crusher. This method mainly extracts the vibration signal by combining fast entropy and variational mode decomposition, so as to analyze the components of the vibration signal. Among them, fast entropy is used to quickly determine the number of modes in the signal spectrum and the bandwidth occupied by the modes. The extracted parameters can be converted into the input parameters of VMD. VMD can accurately extract the modal components in the signal by inputting the number of modes and related parameters. Due to the differences between modes, using the same parameters to extract the modes often leads to inaccurate results. Therefore, the concept of multilevel VMD is proposed. The parameters of different modes are determined by fast entropy. The modes in the signals are separated and extracted with different parameters so that different signal modes can be accurately extracted. In order to verify the accuracy of the method, this paper uses the data collected from the rotary crusher to test, and the results show that the proposed FE method can quickly and effectively extract the fault components in the vibration signal.

Mixed Properties of Slow Magnetoacoustic and Entropy Waves in a Plasma with Heating/Cooling Misbalance

The processes of coronal plasma heating and cooling were previously shown to significantly affect the dynamics of slow magnetoacoustic (MA) waves, causing amplification or attenuation, and also dispersion. However, the entropy mode is also excited in such a thermodynamically active plasma and is affected by the heating/cooling misbalance too. This mode is usually associated with the phenomenon of coronal rain and formation of prominences. Unlike adiabatic plasmas, the properties and evolution of slow MA and entropy waves in continuously heated and cooling plasmas get mixed. Different regimes of the misbalance lead to a variety of scenarios for the initial perturbation to evolve. In order to describe properties and evolution of slow MA and entropy waves in various regimes of the misbalance, we obtained an exact analytical solution of the linear evolutionary equation. Using the characteristic timescales and the obtained exact solution, we identified regimes with qualitatively different behaviour of slow MA and entropy modes. For some of those regimes, the spatio-temporal evolution of the initial Gaussian pulse is shown. In particular, it is shown that slow MA modes may have a range of non-propagating harmonics. In this regime, perturbations caused by slow MA and entropy modes in a low- $\beta $ plasma would look identical in observations, as non-propagating disturbances of the plasma density (and temperature) either growing or decaying with time. We also showed that the partition of the initial energy between slow MA and entropy modes depends on the properties of the heating and cooling processes involved. The exact analytical solution obtained could be further applied to the interpretation of observations and results of numerical modelling of slow MA waves in the corona and the formation and evolution of coronal rain.

Multiphase AGN Winds from X-Ray-irradiated Disk Atmospheres

Abstract The mechanism of thermal driving for launching mass outflows is interconnected with classical thermal instability (TI). In a recent paper, we demonstrated that as a result of this interconnectedness, radial wind solutions of X-ray-heated flows are prone to becoming clumpy. In this paper, we first show that the Bernoulli function determines whether or not the entropy mode can grow due to TI in dynamical flows. Based on this finding, we identify a critical “unbound” radius beyond which TI should accompany thermal driving. Our numerical disk wind simulations support this result and reveal that clumpiness is a consequence of buoyancy disrupting the stratified structure of steady-state solutions. Namely, instead of a smooth transition layer separating the highly ionized disk wind from the cold phase atmosphere below, hot bubbles formed from TI rise up and fragment the atmosphere. These bubbles first appear within large-scale vortices that form below the transition layer, and they result in the episodic production of distinctive cold phase structures referred to as irradiated atmospheric fragments (IAFs). Upon interacting with the wind, IAFs advect outward and develop extended crests. The subsequent disintegration of the IAFs takes place within a turbulent wake that reaches high elevations above the disk. We show that this dynamics has the following observational implications: dips in the absorption measure distribution are no longer expected within TI zones, and there can be a less sudden desaturation of X-ray absorption lines such as O viii Lyα as well as multiple absorption troughs in Fe xxv Kα.

Flux Ropes, Turbulence, and Collisionless Perpendicular Shock Waves: High Plasma Beta Case

Abstract With the onset of solar maximum and the expected increased prevalence of interplanetary shock waves, Parker Solar Probe is likely to observe numerous shocks in the next few years. An outstanding question that has received surprisingly little attention has been how turbulence interacts with collisionless shock waves. Turbulence in the supersonic solar wind is described frequently as a superposition of a majority 2D and a minority slab component. We formulate a collisional perpendicular shock-turbulence transmission problem in a way that enables investigation of the interaction and transmission of quasi-perpendicular fluctuations such as magnetic flux ropes/islands and vortices as well as entropy and acoustic modes in the large plasma beta regime. We focus on the transmission of an upstream spectrum of these modes, finding that the downstream spectral amplitude is typically increased significantly (a factor of 10 or more), and that the upstream spectral index of the inertial range, and indeed the general spectral shape, is unchanged for the downstream magnetic variance, kinetic energy, and density variance. A comparison of the theoretically predicted downstream magnetic variance, kinetic energy, and density variance spectra with those observed at 1, 5, and 84 au by Wind, Ulysses, and Voyager 2 shows excellent agreement. The overall theoretically predicted characteristics of the transmission of turbulence across shocks observed in the solar wind appear to be largely consistent with recent observational studies by Pitňa et al. and Borovsky.

Spectrum of Cuscuton bounce

It has been recently shown that a cosmological bounce model based on Cuscuton gravity does not have any ghosts or curvature instabilities. We explore whether Cuscuton bounce can provide an alternative to inflation for generating near scale-invariant scalar perturbations. While a single field Cuscuton bounce generically produces a strongly blue power spectrum (for a variety of initial/boundary conditions), we demonstrate that scale-invariant entropy modes can be generated in a spectator field that starts in adiabatic vacuum, and is kinetically coupled to the primary field. Furthermore, our solution has no singularity, nor requires an ad hoc matching condition. We also study the generation of tensor modes (or gravitational waves) in Cuscuton bounce and show that while they are stable, similar to other bounce models, the produced spectrum is strongly blue and unobservable.

Hysteresis curves for some periodic and aperiodic perturbations in magnetosonic flow

A thermodynamic relation between perturbations of pressure and mass density in the magnetohydrodynamic flow is theoretically studied. Planar magnetohydrodynamic perturbations with the wave vector, which forms a constant angle with the equilibrium magnetic field, are under study. The theory considers thermal conduction of a plasma and the deviation from adiabaticity of a flow due to some kind of heating–cooling function. It also considers nonlinear distortion of a waveform and nonlinear excitation of the entropy mode in the field of intense magnetosonic perturbations. In some conditions, the total density of a plasma enlarges over a cycle of magnetosonic perturbations. These conditions depend on the type of magnetosonic waveform, heating–cooling function, thermal conduction, and equilibrium parameters of a plasma. They depend also on the angle between the wave vector and the magnetic field. The diagrams in the plane of total variation of pressure vs total variation of density indicate the nonlinear phenomena and irreversible processes in a flow. Harmonic perturbation and a bipolar impulse of pressure are considered as magnetosonic exciters of the entropy mode. Exemplary diagrams are plotted and discussed for these particular cases of exciters.

On the Diagnosis of Unidirectional Acoustic Waves as Applied to the Measurement of Atmospheric Parameters by the API Method in the SURA Experiment

The problem of wave identification is formulated as applied to the results of measurements of the temperature and the density of the neutral atmosphere in the range height 90–120 km by the artificial periodic irregularities (APIs) technique. The technique is based on the resonant scattering of radio waves by artificial periodic irregularities of the ionospheric plasma emerging in the field of a standing wave arising from the interference of the incident and reflected waves from the ionosphere. APIs were created using SURA heating facility (named as SURA experiment). The acoustic wave theory is reformulated on the base of data which can be observed in the given experimental setup. The basic system of equations is reduced so that it accounts only upward and downward directed waves, ignoring entropy mode. The algorithm of wave identification based on usage of dynamic projection operators for such a reduced case is proposed and explicit form of projection operators is derived. Its application to finite number dataset via Discrete Fourier Transform (DFT) is described and results of its application to the DFT-transformed set of experimental observation of the temperature and density perturbations are presented. The result yields hybrid amplitudes, that allow us to calculate energy of the directed waves that enter the observed superposition. The problem of entropy mode detection is discussed, the corresponding projecting operators for the full evolution system are built and a way to apply the method to quantification of it is proposed.

Two-dimensional time series sample entropy algorithm: Applications to rotor axis orbit feature identification

Traditional sample entropy algorithms are limited in their inability to analyze two-dimensional (2D) time series. Here, we describe a new feature algorithm for 2D time-series complexity and signal classification. This is a 2D sample entropy algorithm that includes the definitions of distance d and tolerance r in the 2D sample entropy algorithm on 2D signal scale and the difference between 2D and 1D sample entropies. The effectiveness of this algorithm in characterizing 2D signals was verified through simulated signal analysis. Then, by combining the 2D sample entropy algorithm with ensemble empirical mode decomposition (EEMD) and support vector machine (SVM) algorithms, we proposed a magnetically suspended rotor axis orbit feature identification and fault diagnosis method based on 2D sample entropy. This method was used to first perform EEMD of the 2D signals of a magnetically suspended rotor axis orbit to obtain several intrinsic mode functions (IMFs). We then calculated the 2D sample entropies of each IMF, and finally input the two-dimensional sample entropy as 2D feature vectors separately into the SVM, neural network, and logistic regression to identify the features of a rotor axis orbit. Finally, we compared the 1D sample entropy and variational mode decomposition (VMD) sample entropy. A comparison of experimental results showed that the 2D sample entropy algorithm can be used to characterize 2D signals, identify the features of the rotor axis orbit based on typical 2D signals, and identify and classify the rotor axis orbits under different fault conditions. The performance of this algorithm in feature identification is remarkably superior to that of 1D and VMD sample entropy algorithms. The availability of online diagnosis of this method was verified via speed testing.

Deforming charged black holes with dipolar differential rotation boundary

Motivated by the recent studies of the novel asymptotically global hbox {AdS}_4 black hole with deformed horizon, we consider the action of Einstein–Maxwell gravity in AdS spacetime and construct the charged deforming AdS black holes with differential boundary. In contrast to deforming black hole without charge, there exists at least one value of horizon for an arbitrary temperature. The extremum of temperature is determined by charge q and divides the range of temperature into several parts. Moreover, we use an isometric embedding in the three-dimensional space to investigate the horizon geometry. The entropy and quasinormal modes of deforming charged AdS black hole are also studied in this paper. Due to the existence of charge q, the phase diagram of entropy is more complicated. We consider two cases of solutions: (1) fixing the chemical potential mu ; (2) changing the value of mu according to the values of horizon radius and charge. In the first case, it is interesting to find there exist two families of black hole solutions with different horizon radii for a fixed temperature, but these two black holes have same horizon geometry and entropy. The second case ensures that deforming charged AdS black hole solutions can reduce to standard RN–AdS black holes.

Approximate Entropy and Empirical Mode Decomposition for Improved Speaker Recognition

When processing real-world recordings of speech, it is highly probable noise will be present at some instance in the signal. Compounding this problem is the situation when the noise occurs in short, impulsive bursts at random intervals. Traditional signal processing methods used to detect speech rely on the spectral energy of the incoming signal to make a determination whether or not a segment of the signal contains speech. However when noise is present, this simple energy detection is prone to falsely flagging noise as speech. This paper will demonstrate an alternative way of processing a noisy speech signal utilizing a combination of information theoretic and signal processing principles to differentiate speech segments from noise. The utilization of this preprocessing technique will allow a speaker recognition system to train statistical speaker model using noise-corrupted speech files, and construct models statistically similar to those constructed from noise-free data. This preprocessing method will be shown to outperform traditional spectrum-based methods for both low-entropy and high-entropy noise in low signal-to-noise ratio environments, with a reduction in the feature space distortion when measured using the Cauchy–Schwarz (CS) distance metric.

Measurements of freestream density fluctuations in a hypersonic wind tunnel

Density disturbances in the freestream of the University of Southern Queensland’s Mach 6 wind tunnel ( $$\rho _{\infty } \approx {34\, \hbox {gm}^{-3}}$$ ) have been measured using a focused laser differential interferometer (FLDI). The direct contribution of the turbulent shear layer from the Mach 6 nozzle to the FLDI signal was largely eliminated by mechanically shielding the FLDI beams from these effects. This improvement significantly enhanced the low wavenumber FLDI spectra which allowed a von Kármán spectrum fit and demonstrated a $$-5/3$$ roll-off in the inertial subrange and enabled the identification of the integral length scale (28–29 mm). The normalised root-mean-square density fluctuations were found to change over the flow duration (typically between 0.4 and $$0.6\%$$ ) for the 1–250 kHz frequency range which corresponds to the wavenumber range of 6– 1600 $${\mathrm{m}}^{-1}$$ in this Mach 6 flow. Previous disturbance measurements using intrusive methods have identified a narrowband 3–4 kHz disturbance that is first measured in the core flow about 65 ms after the flow begins and remains until the flow terminates. The onset of this narrowband disturbance was previously correlated with transition-to-turbulence in the subsonic test gas supply to the nozzle. This correlation was investigated further herein, and the 3–4 kHz feature was inferred to be entropy mode disturbances by showing the departure of the FLDI measurements from Pitot pressure measurements. Through the comparison of FLDI and Pitot pressure data, Pitot pressure probes were demonstrated to produce a poor estimate of the static pressure fluctuations when non-isentropic disturbances are non-negligible.

Interactions between turbulent flow and diffusion flame of composite propellant in a solid rocket motor with sidewall mass injection

The numerical procedure for a diffusion flame based on Ammonium Perchlorate/Hydroxyl-Terminated Polybutadiene (AP/HTPB) composite propellant in a solid rocket motor (SRM) is presented. This article accounts for the turbulence effects in a combustion chamber with sidewall mass injection and the propellant diffusion flames at various axial locations are studied. The mutual coupling between the vortical and entropy modes is discussed comprehensively, with the inclusion of the influence of the chamber pressure. The effects of the AP particle size and the combustion environment are also analyzed. The flow evolution in the SRM is clearly observed in the results: laminar, transitional, and turbulent. Compared with the laminar area, the flames fluctuate drastically in the turbulent flow, and the chemical kinetics processes are altered greatly. The diffusion and mixing processes of the reactants are enhanced due to the contribution of the turbulence, and the heat release of the flames is elevated. The high chamber pressure and smaller AP size could lead to more intensive fluctuations of the flame heat release. This may drive thermoacoustic instability in the SRM.

A study of longitudinal processes and interactions in compressible viscous flows

Fluid motion has two well-known fundamental processes: the vector transverse process characterized by vorticity, and the scalar longitudinal process consisting of a sound mode and an entropy mode, characterized by dilatation and thermodynamic variables. The existing theories for the sound mode involve the multi-variable issue and its associated difficulty of source identification. In this paper, we define the source of sound inside the fluid by the objective causality inherent in dynamic equations relevant to a longitudinal process, which naturally favours the material time-rate operator rather than the local time-rate operator , and describes the sound mode by inhomogeneous advective wave equations. The sources of sound physical production inside the fluid are then examined at two levels. For the conventional formulation in terms of thermodynamic variables at the first level, we show that the universal kinematic source can be condensed to a scalar invariant of the surface deformation tensor. Further, in the formulation in terms of dilatation at the second level, we find that the sound mode in viscous and heat-conducting flow has sources from rich nonlinear couplings of vorticity, entropy and surface deformation, which cannot be disclosed at the first level. Preliminary numerical demonstration of the theoretical findings is made for two typical compressible flows, i.e. the interaction of two corotating Gaussian vortices and the unsteady type IV shock/shock interaction. The results obtained in this study provide a new theoretical basis for, and physical insight into, understanding various nonlinear longitudinal processes and the interactions therein.

Entropy modes in multi-component plasmas confined by a dipole field

In this paper, the collisionless electrostatic instability of the entropy mode is investigated linearly in multi-component plasmas confined by a dipole magnetic field, which commonly exists in space environments, as well as laboratory plasmas, such as Collisionless Terrella eXperiment, Levitated Dipole eXperiment, and Dipole Research EXperiment. We focus on characteristics of the entropy mode driven by the plasma density or/and the temperature gradient at low plasma beta (=8πP0/B02). The theoretical analysis of this work agrees with the calculated results qualitatively. It is indicated that the peak growth rate of the instability is in the regime of k⊥ρi ∼ 1, and the entropy mode tends to be more stable as the percentage of the heavy ion increases. For multi-component plasmas, each component has the entropy mode feature of its own, instead of simply averaging all the components. While for the electron with an isotropic temperature, the use of weighted harmonic average can be a good approximation for simplification.

Linear gyrokinetics of electron–positron plasmas in closed field-line systems

Linear gyrokinetic simulations of magnetically confined electron–positron plasmas are performed for the first time in the geometry and parameter regimes likely to be relevant for upcoming laboratory experiments. In such plasmas, the density will be sufficiently small as to render the plasma effectively collisionless. The magnetic field will be very large, meaning that the Debye length will exceed the gyroradius by a few orders of magnitude. We show the results of linear simulations in flux tubes close to the current carrying ring and also in the bulk of the plasma, demonstrating the existence of entropy modes and interchange modes in pair plasmas. We study linear stability and show that in the relevant configurations, almost complete linear stability is attainable in large swathes of parameter space.

Algorithm for the Diagnostics of Waves and Entropy Mode in the Exponentially Stratified Atmosphere

The method of local diagnostics based on the three-mode problem in an exponentially stratified atmosphere is proposed. The Cauchy problem is reformulated as the cutoff mode propagation problem. Projection operators for all three modes are derived, including the entropy mode as a new element of the developed approach. The formula for calculating the mode energy for an arbitrary boundary condition in the frequency-domain representation is proposed. It is suggested to use this formula as a norm in the space of approximations of numerical calculations or geophysical observations.

Turbulent pinch in whole-plasma simulations of a dipole-confined plasma.

Whole-plasma simulations of turbulent transport and upgradient plasma pinch are presented in a dipole magnetic geometry relevant to the Levitated Dipole Experiment (LDX). The self-consistent evolution of an inward particle pinch and the establishment of centrally peaked plasma profiles in a dipole field are explored from whole-plasma simulations using a flux-tube averaged fluid model. The nonlinear evolution of global drift-interchange modes leads to the development of large-scale turbulent convection. Global convective cells are shown to play an important role in radial turbulent transport that causes centrally peaked profiles in a dipole magnetic field. The simulations show that the system self-consistently evolves towards a nonlinear saturated state in which the plasma pressure and density profiles are marginally stable to both drift-interchange and entropy modes.