Entropy Gradient Research Articles

Transient Phenomena of Inviscid Accretion Gasradiation Slim Disc in A Gravitational Potential after Adiabatic Perturbations of the Velocities

The formalisms for the analysis of the dynamics of slim inviscid accretion discs in a (also, non-Newtonian) gravitational potential are here developped; the role of the horizontal pressure and that of the entropy gradients are to be characterised. The adiabatic perturbations of the velocity are studied: the paradigms of the Lagrangian perturbations of the velocity are implemented. The perturbations of the slim disc is studied in the Lagrangean formalism of adiabatic perturbations of the velocities. The new conditions on the Eulerian variation of the gravitational potential are outlined. The equations of the transient phenomena are written.

3D Hydrodynamic Simulations of Massive Main-sequence Stars. III. The Effect of Radiation Pressure and Diffusion Leading to a 1D Equilibrium Model

We present 3D hydrodynamical simulations of core convection with a stably stratified envelope of a 25 M ⊙ star in the early phase of the main sequence. We use the explicit gas-dynamics code PPMstar, which tracks two fluids and includes radiation pressure and radiative diffusion. Multiple series of simulations with different luminosities and radiative thermal conductivities are presented. The entrainment rate at the convective boundary, internal gravity waves in and above the boundary region, and the approach to dynamical equilibrium shortly after a few convective turnovers are investigated. We perform very long simulations on 8963 grids accelerated by luminosity boost factors of 1000, 3162 and 10,000. In these simulations, the growing penetrative convection reduces the initially unrealistically large entrainment. This reduction is enabled by a spatial separation that develops between the entropy gradient and the composition gradient. The convective boundary moves outward much more slowly at the end of these simulations. Finally, we present a 1D method to predict the extent and character of penetrative convection beyond the Schwarzschild boundary. The 1D model is based on a spherically averaged reduced entropy equation that takes the turbulent dissipation as input from the 3D hydrodynamic simulation and takes buoyancy and all other energy sources and sinks into account. This 1D method is intended to be ultimately deployed in 1D stellar evolution calculations and is based on the properties of penetrative convection in our simulations carried forward through the local thermal timescale.

Full-field analysis of semi-transparent cenosphere-filled composites using backlight illumination

This study introduces a novel approach for measuring deformations in semi-transparent composites using digital image correlation (DIC). Unlike traditional approaches relying on artificial speckle patterns, this method uses backlighted cenosphere particles dispersed in a semi-transparent matrix as intrinsic speckle patterns, eliminating the need for surface painting. The effectiveness of the intrinsic pattern is evaluated by comparing global parameters, such as speckle size, distribution, coverage, Shannon entropy and Mean Intensity Gradient, with those of a conventional pattern. Results indicate a relationship between speckle characteristics and measurement accuracy. A factorial design is employed to optimize DIC analysis parameters, including facet size, grid spacing, and filtering, resulting in a significant reduction in noise. Rigid displacement and four-point bending tests confirm the pattern’s traceability, with results compared against a numerical model. This approach lays the groundwork for future investigations of transparent and semi-transparent materials using DIC, allowing comprehensive mechanical characterization without altering material transparency.

A Method for Fingerprint Edge Enhancement Based on Radial Hilbert Transform

Fingerprints play a significant role in various fields due to their uniqueness. In order to effectively utilize fingerprint information, it is necessary to enhance image quality. This paper introduces a method based on Radial Hilbert transform (RHLT), which simulates the vortex filter using the point spread function (PSF) of spiral phase plate (SPP) with a topological charge l=1, for fingerprint edge enhancement. The experimental results show that the processed fingerprint image has more distinct edges, with an increase in information entropy and average gradient. Unlike classical edge detection operators, the fingerprint edge image obtained by the RHLT method exhibits a lower mean square error (MSE) and a higher peak signal-to-noise ratio (PSNR). This indicates that the RHLT method provides more accurate edge detection and demonstrates higher noise-resistance capabilities. Due to its ability to highlight edge information while preserving more original features, this method has great application potential in fingerprint image processing.

DBMKA-Net:Dual branch multi-perception kernel adaptation for underwater image enhancement

In recent years, due to the dependence on wavelength-based light absorption and scattering, underwater photographs captured by devices often exhibit characteristics such as blurriness, faded color tones, and low contrast. To address these challenges, convolutional neural networks (CNNs) with their robust feature-capturing capabilities and adaptable structures have been employed for underwater image enhancement. However, most CNN-based studies on underwater image enhancement have not taken into account color space kernel convolution adaptability, which can significantly enhance the model’s expressive capacity. Building upon current academic research on adjusting the color space size for each perceptual field, this paper introduces a Double-Branch Multi-Perception Kernel Adaptive (DBMKA) model. A DBMKA module is constructed through two perceptual branches that adapt the kernels: channel features and local image entropy. Additionally, considering the pronounced attenuation of the red channel in underwater images, a Dependency-Capturing Feature Jump Connection module (DCFJC) has been designed to capture the red channel’s dependence on the blue and green channels for compensation. Its skip mechanism effectively preserves color contextual information. To better utilize the extracted features for enhancing underwater images, a Cross-Level Attention Feature Fusion (CLAFF) module has been designed. With the Double-Branch Multi-Perception Kernel Adaptive model, Dependency-Capturing Skip Connection module, and Cross-Level Adaptive Feature Fusion module, this network can effectively enhance various types of underwater images. Qualitative and quantitative evaluations were conducted on the UIEB and EUVP datasets. In the color correction comparison experiments, our method demonstrated a more uniform red channel distribution across all gray levels, maintaining color consistency and naturalness. Regarding image information entropy (IIE) and average gradient (AG), the data confirmed our method’s superiority in preserving image details. Furthermore, our proposed method showed performance improvements exceeding 10% on other metrics like MSE and UCIQE, further validating its effectiveness and accuracy.

Convective Overstability in Radially Global Protoplanetary Disks. I. Pure Gas Dynamics

Protoplanetary disks are prone to several hydrodynamic instabilities. One candidate, convective overstability (COS), can drive radial semiconvection that may influence dust dynamics and planetesimal formation. However, the COS has primarily been studied in local models. This paper investigates the COS near the midplane of radially global disk models. We first conduct a global linear stability analysis, which shows that linear COS modes exist only radially inward of their Lindblad resonance (LR). The fastest-growing modes have LRs near the inner radial domain boundary with effective radial wavelengths that can be a substantial fraction of the disk radius. We then perform axisymmetric global simulations and find that the COS’s nonlinear saturation is similar to previous incompressible shearing box simulations. In particular, we observe the onset of persistent zonal and elevator flows for sufficiently steep radial entropy gradients. In full 3D, nonaxisymmetric global simulations, we find the COS produces large-scale, long-lived vortices, which induce the outward radial transport of angular momentum via the excitation of spiral density waves. The corresponding α-viscosity values of order 10−3 agree well with those found in previous 3D compressible shearing box simulations. However, in global disks, significant modifications to their radial structure are found, including the formation of pressure bumps. Interestingly, the COS typically generates an outward radial mass transport, i.e., decretion. We briefly discuss the possible implications of our results for planetesimal formation and for interpreting dust rings and asymmetries observed in protoplanetary disks.

Rough solutions of the relativistic Euler equations

We prove that the time of classical existence of smooth solutions to the relativistic Euler equations can be bounded from below in terms of norms that measure the “(sound) wave-part” of the data in Sobolev space and “transport-part” in higher regularity Sobolev space and Hölder spaces. The solutions are allowed to have nontrivial vorticity and entropy. We use the geometric framework from [M. M. Disconzi and J. Speck, The relativistic Euler equations: Remarkable null structures and regularity properties, Ann. Henri Poincaré 20(7) (2019) 2173–2270], where the relativistic Euler flow is decomposed into a “wave-part”, that is, geometric wave equations for the velocity components, density and enthalpy, and a “transport-part”, that is, transport-div-curl systems for the vorticity and entropy gradient. Our main result is that the Sobolev norm [Formula: see text] of the variables in the “wave-part” and the Hölder norm [Formula: see text] of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption [Formula: see text] is the optimal result for the variables in the “wave-part”. Compared to low-regularity results for quasilinear wave equations and the three-dimensional (3D) non-relativistic compressible Euler equations, the main new challenge of the paper is that when controlling the acoustic geometry and bounding the wave equation energies, we must deal with the difficulty that the vorticity and entropy gradient are four-dimensional space-time vectors satisfying a space-time div-curl-transport system, where the space-time div-curl part is not elliptic. Due to lack of ellipticity, one cannot immediately rely on the approach taken in [M. M. Disconzi and J. Speck, The relativistic Euler equations: Remarkable null structures and regularity properties, Ann. Henri Poincaré 20(7) (2019) 2173–2270] to control these terms. To overcome this difficulty, we show that the space-time div-curl systems imply elliptic div-curl-transport systems on constant-time hypersurfaces plus error terms that involve favorable differentiations and contractions with respect to the four-velocity. By using these structures, we are able to adequately control the vorticity and entropy gradient with the help of energy estimates for transport equations, elliptic estimates, Schauder estimates and Littlewood–Paley theory.

Relative Entropy Gradient Sampler for Unnormalized Distribution

We propose a relative entropy gradient sampler (REGS) for sampling from unnormalized distributions. REGS is a particle method that seeks a sequence of simple nonlinear transforms iteratively pushing the initial samples from a reference distribution into the samples from an unnormalized target distribution. To determine the nonlinear transforms at each iteration, we consider the Wasserstein gradient flow of relative entropy. This gradient flow determines a path of probability distributions that interpolates the reference distribution and the target distribution. It is characterized by an ordinary differential equation (ODE) system with velocity fields depending on the density ratios of the density of evolving particles and the unnormalized target density. To sample with REGS, we need to estimate the density ratios and simulate the ODE system with particle evolution. We propose a novel nonparametric approach to estimating the logarithmic density ratio using neural networks. Extensive simulation studies on challenging multimodal 1D and 2D mixture distributions and Bayesian logistic regression on real datasets demonstrate that REGS has reasonable performance compared with popular samplers based on Wasserstein gradient flows. Supplementary materials for this article are available online.

Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.

Internally heated and fully compressible convection: Flow morphology and scaling laws

In stars and planets natural processes heat convective flows in the bulk of a convective region rather than at hard boundaries. By characterizing how convective dynamics are determined by the strength of an internal heating source we can gain insight into the processes driving astrophysical convection. Internally heated convection has been studied extensively in incompressible fluids, but the effects of stratification and compressibility have not been examined in detail. In this work, we study fully compressible convection driven by a spatially uniform heating source in two-dimensional (2D) and 3D Cartesian, hydrodynamic simulations. We use a fixed temperature upper boundary condition which results in a system that is internally heated in the bulk and cooled at the top. We find that the flow speed, as measured by the Mach number, and turbulence, as measured by the Reynolds number, can be independently controlled by separately varying the characteristic temperature gradient from internal heating and the diffusivities. Two-dimensional simulations at a fixed Mach number (flow speed) demonstrate consistent power at low wave number as diffusivities are decreased. We observe convection where the velocity distribution is skewed towards cold, fast downflows and that the flow speed is related to the length scale and entropy gradient of the upper boundary where the downflows are driven. We additionally find a heat transport scaling law which is consistent with prior incompressible work. Published by the American Physical Society 2024

Multi-Dimensional Fusion of Spectral and Polarimetric Images Followed by Pseudo-Color Algorithm Integration and Mapping in HSI Space

Spectral–polarization imaging technology plays a crucial role in remote sensing detection, enhancing target identification and tracking capabilities by capturing both spectral and polarization information reflected from object surfaces. However, the acquisition of multi-dimensional data often leads to extensive datasets that necessitate comprehensive analysis, thereby impeding the convenience and efficiency of remote sensing detection. To address this challenge, we propose a fusion algorithm based on spectral–polarization characteristics, incorporating principal component analysis (PCA) and energy weighting. This algorithm effectively consolidates multi-dimensional features within the scene into a single image, enhancing object details and enriching edge features. The robustness and universality of our proposed algorithm are demonstrated through experimentally obtained datasets and verified with publicly available datasets. Additionally, to meet the requirements of remote sensing tracking, we meticulously designed a pseudo-color mapping scheme consistent with human vision. This scheme maps polarization degree to color saturation, polarization angle to hue, and the fused image to intensity, resulting in a visual display aligned with human visual perception. We also discuss the application of this technique in processing data generated by the Channel-modulated static birefringent Fourier transform imaging spectropolarimeter (CSBFTIS). Experimental results demonstrate a significant enhancement in the information entropy and average gradient of the fused image compared to the optimal image before fusion, achieving maximum increases of 88% and 94%, respectively. This provides a solid foundation for target recognition and tracking in airborne remote sensing detection.

Assessing the Efficacy of Pixel-Level Fusion Techniques for Ultra-High-Resolution Imagery: A Case Study of BJ-3A.

Beijing Satellite 3 is a high-performance optical remote sensing satellite with a spatial resolution of 0.3-0.5 m. It can provide timely and independent ultra-high-resolution spatial big data and comprehensive spatial information application services. At present, there is no relevant research on the fusion method of BJ-3A satellite images. In many applications, high-resolution panchromatic images alone are insufficient. Therefore, it is necessary to fuse them with multispectral images that contain spectral color information. Currently, there is a lack of research on the fusion method of BJ-3A satellite images. This article explores six traditional pixel-level fusion methods (HPF, HCS, wavelet, modified-IHS, PC, and Brovey) for fusing the panchromatic image and multispectral image of the BJ-3A satellite. The fusion results were analyzed qualitatively from two aspects: spatial detail enhancement capability and spectral fidelity. Five indicators, namely mean, standard deviation, entropy, correlation coefficient, and average gradient, were used for quantitative analysis. Finally, the fusion results were comprehensively evaluated from three aspects: spectral curves of ground objects, absolute error figure, and object-oriented classification effects. The findings of the research suggest that the fusion method known as HPF is the optimum and appropriate technique for fusing panchromatic and multispectral images obtained from BJ-3A. These results can be utilized as a guide for the implementation of BJ-3A panchromatic and multispectral data fusion in real-world scenarios.

Research on the Theoretical Connotation and Practical Path of Aesthetics of Daily Human Life in the Background of Internet

Abstract As the living standard of the people in China has changed drastically, the aesthetic quality of daily life has been increasing day by day, and people’s desire for a better life is also increasing. This paper proposes a color harmony model based on hue statistical features, using maximum likelihood estimation to extract the main hue region and extract related features from the corresponding region. Based on the inconsistencies in feature dimensions, a model is created to evaluate color harmony using Gaussian mixture training and is employed for image aesthetics evaluation. Finally, regression is employed to analyze the factors that influence life aesthetics evaluation, and the model is tested and analyzed using linear diagnosis and residual analysis. The results show that the influence index affecting the evaluation of daily life aesthetics is judgment beauty, and its influence coefficient is 4.4323. The product of image entropy and image gradient is used as the connotation of judging the aesthetics of daily human life, which is consistent with the evaluation of human aesthetic judgment. The theoretical connotations of life aesthetics are clarified and enhanced in this paper, and it develops its thinking to construct the reality of the good life.

Ab-initio General-relativistic Neutrino-radiation Hydrodynamics Simulations of Long-lived Neutron Star Merger Remnants to Neutrino Cooling Timescales

We perform the first 3D ab-initio general-relativistic neutrino-radiation hydrodynamics of a long-lived neutron star merger remnant spanning a fraction of its cooling timescale. We find that neutrino cooling becomes the dominant energy loss mechanism after the gravitational-wave dominated phase (∼20 ms postmerger). Electron flavor antineutrino luminosity dominates over electron flavor neutrino luminosity at early times, resulting in a secular increase of the electron fraction in the outer layers of the remnant. However, the two luminosities become comparable ∼20–40 ms postmerger. A dense gas of electron antineutrinos is formed in the outer core of the remnant at densities ∼1014.5 g cm−3, corresponding to temperature hot spots. The neutrinos account for ∼10% of the lepton number in this region. Despite the negative radial temperature gradient, the radial entropy gradient remains positive, and the remnant is stably stratified according to the Ledoux criterion for convection. A massive accretion disk is formed from the material squeezed out of the collisional interface between the stars. The disk carries a large fraction of the angular momentum of the system, allowing the remnant massive neutron star to settle to a quasi-steady equilibrium within the region of possible, stable, rigidly rotating configurations. The remnant is differentially rotating, but it is stable against the magnetorotational instability. Other MHD mechanisms operating on longer timescales are likely responsible for the removal of the differential rotation. Our results indicate the remnant massive neutron star is thus qualitatively different from a protoneutron stars formed in core-collapse supernovae.

High entropy oxide coated BaTiO3 enabling high ionic transport

High entropy oxides (HEOs) have gained significant attention for their diverse applications in various fields, including energy-related research. However, their potential in solid oxide fuel cells (SOFCs) remains unexplored. This research presents a practical approach to creating a local gradient field by coating BaTiO3 (BTO) with HEO, enabling efficient and stable ionic transport for fuel cell applications. The coating of 10% HEO on BTO resulted in the HEO@BTO powders demonstrating a maximum power density of 640 mWcm−2 and suitable open circuit voltage (OCV) of 1.085 V at 520 °C. We propose that the local entropy gradient created by the HEO coating on the BTO surface establishes a core-shell structure and facilitates high ion transport through the induced built-in electric field. This work sheds light on the mechanisms underlying the enhanced performance of HEO-coated BTO and offers insights into the design of advanced materials for efficient ionic transport in fuel cell technologies.

The effect of tip clearance size on pre-stall flow features of a transonic axial compressor by using throttle model

This paper aims at the numerical analysis of the influence of tip clearance size on the pre-stall flow features of a transonic high-speed compressor by applying the throttle model at the exit of the compressor computational domain. Steady and unsteady calculations have been performed for design, double, and triple tip clearance sizes. The transition of the stall inception type when increasing the tip clearance size and the underlying flow physics has been analyzed in detail. The results show that the stall inception type transforms from spike to modal as the size of the tip clearance changes from design to triple tip clearance. The influence of the tip clearance size on the forward spillage of the tip leakage vortex near the stall limit, which is one of the two criteria for spike stall inception, is crucial for which type of stall inception would appear. For the design clearance case, a remarkable forward spillage of the tip leakage vortex occurs near the stall limit, leading to a typical strong spike stall inception. In the condition of double clearance, the intensity of tip leakage vortex spillage was weakened because the increase in the clearance size allows more low momentum tip leakage flow to go through the clearance instead of spilling from the leading edge. Thus, a weaker spike-type inception containing the content of modal disturbances was induced. Under the triple clearance condition, the high entropy gradient interface is located inside the blade passages all the time; thus, a typical modal-type stall inception appears.

Differential Rotation in Convecting Spherical Shells with Non-Uniform Viscosity and Entropy Diffusivity

Contemporary three-dimensional physics-based simulations of the solar convection zone disagree with observations. They feature differential rotation substantially different from the true rotation inferred by solar helioseismology and exhibit a conveyor belt of convective “Busse” columns not found in observations. To help unravel this so-called “convection conundrum”, we use a three-dimensional pseudospectral simulation code to investigate how radially non-uniform viscosity and entropy diffusivity affect differential rotation and convective flow patterns in density-stratified rotating spherical fluid shells. We find that radial non-uniformity in fluid properties enhances polar convection, which, in turn, induces non-negligible lateral entropy gradients that lead to large deviations from differential rotation geostrophy due to thermal wind balance. We report simulations wherein this mechanism maintains differential rotation patterns very similar to the true solar profile outside the tangent cylinder, although discrepancies remain at high latitudes. This is significant because differential rotation plays a key role in sustaining solar-like cyclic dipolar dynamos.

Specular highlight removal based on dichromatic reflection model and priority-based adaptive direction with light field camera

In this paper, an image restoration method with light field camera is proposed to effectively remove specular highlight, and it only needs single shot and has no special requirements for light source and environment. The x-means clustering method based on dichromatic reflection model is proposed to recover unsaturated highlight pixels, and a priority-based adaptive direction method is designed to eliminate saturated specular highlight pixels. After that, a method based on information entropy and mean gradient ratio, called EMGR, is established to quantitatively evaluate the image quality of specular highlight removal. The experimental results showed that our method can effectively utilized the multi-view advantage of the light field to remove the specular highlight of images in different scenes while completely preserving the images texture information, and has the advantages of low complexity and wide applicability.

Surrogate Modeling of the Relative Entropy for Inverse Design Using Smolyak Sparse Grids.

Relative entropy minimization, a statistical-mechanics approach for finding potential energy functions that produce target structural ensembles, has proven to be a powerful strategy for the inverse design of nanoparticle self-assembly. For a given target structure, the gradient of the relative entropy with respect to the adjustable parameters of the potential energy function is computed by performing a simulation, and then these parameters are updated using iterative gradient-based optimization. Small parameter updates per iteration and many iterations can be required for numerical stability, but this incurs considerable computational expense because a new simulation must be performed to reevaluate the gradient at each iteration. Here, we investigate the use of surrogate modeling to decouple the process of minimizing the relative entropy from the computationally demanding process of determining its gradient. We approximate the relative-entropy gradient using Chebyshev polynomial interpolation on Smolyak sparse grids. Our approach potentially increases the robustness and computational efficiency of using the relative entropy for inverse design, primarily for physically informed potential energy functions that have a small number of adjustable parameters.

Observed Power and Frequency Variations of Solar Rossby Waves with Solar Cycles

Several recent studies utilizing different helioseismic methods have confirmed the presence of large-scale vorticity waves known as solar Rossby waves within the Sun. Rossby waves are distinct from acoustic waves, typically with longer periods and lifetimes, and their general properties, even if only measured at the surface, may be used to infer properties of the deeper convection zone, such as the turbulent viscosity and entropy gradients that are otherwise difficult to observe. In this study, we utilize 12 yr of inverted subsurface velocity fields derived from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager’s time–distance and ring-diagram pipelines to investigate the properties of the solar equatorial Rossby waves. By covering the maximum and the decline phases of Solar Cycle 24, these data sets enable a systematic analysis of any potential cycle dependence of these waves. Our analysis provides evidence of a correlation between the average power of equatorial Rossby waves and the solar cycle, with stronger Rossby waves during the solar maximum and weaker waves during the minimum. Our result also shows that the frequency of the Rossby waves is lower during the magnetic active years, implying a larger retrograde drift relative to the solar rotation. Although the underlying mechanism that enhances the Rossby wave power and lowers its frequency during the cycle maximum is not immediately known, this observation has the potential to provide new insights into the interaction of large-scale flows with the solar cycle.