Entropy Gradient Research Articles

Dynamics of ITCZ Width: Ekman Processes, Non-Ekman Processes, and Links to Sea Surface Temperature

Abstract The dynamical processes controlling the width of the intertropical convergence zone (ITCZ) are investigated using idealized and CMIP5 simulations. ITCZ width is defined in terms of boundary layer vertical velocity. The tropical boundary layer is approximately in Ekman balance, suggesting that wind stress places a strong constraint on ITCZ width. A scaling based on Ekman balance predicts that ITCZ width is proportional to the wind stress and inversely proportional to its meridional gradient. A toy model of an Ekman boundary layer illustrates the effects of wind stress perturbations on ITCZ width. A westerly wind perturbation widens the ITCZ whereas an easterly perturbation narrows the ITCZ. Multiplying the wind stress by a constant factor does not shift the ITCZ edge, but ITCZ width is sensitive to the latitude of maximum wind stress. Scalings based on Ekman balance cannot fully capture the behavior of ITCZ width across simulations, suggesting that non-Ekman dynamical processes need to be accounted for. An alternative scaling based on the full momentum budget explains variations in ITCZ width and highlights the importance of horizontal and vertical momentum advection. Scalings are also introduced linking ITCZ width to surface temperature. An extension to Lindzen–Nigam theory predicts that ITCZ width scales with the latitude where the Laplacian of SST is zero. The supercriticality theory of Emanuel is also invoked to show that ITCZ width is dynamically linked to boundary layer moist entropy gradients. The results establish a dynamical understanding of ITCZ width that can be applied to interpret persistent ITCZ biases in climate models and the response of tropical precipitation to climate change.

Cosmic Snow Clouds: Self-gravitating Gas Spheres Manifesting Hydrogen Condensation

Abstract We present hydrostatic equilibrium models of spherical, self-gravitating clouds of helium and molecular hydrogen, focusing on the cold, high-density regime where solid- or liquid-hydrogen can form. The resulting structures have masses from 0.1 M ⊙ down to several ×10−8 M ⊙, and span a broad range of radii: 10−4 ≲ R(au) ≲ 107. Our models are fully convective, but all have a two-zone character with the majority of the mass in a small, condensate-free core, surrounded by a colder envelope where phase equilibrium obtains. Convection in the envelope is unusual in that it is driven by a mean-molecular-weight inversion, rather than by an entropy gradient. In fact, the entropy gradient is itself inverted, leading to the surprising result that envelope convection transports heat inward. In turn, that permits the outer layers to maintain steady-state temperatures below the cosmic microwave background. Among our hydrostatic equilibria we identify thermal equilibria appropriate to the Galaxy, in which radiative cooling from H2 is balanced by cosmic-ray heating. These equilibria are all thermally unstable, albeit with very long thermal timescales in some cases. The specific luminosities of all our models are very low, and they therefore describe a type of baryonic dark matter. Consequently such clouds are thermally fragile: when placed in a harsh radiation field, they will be unable to cool effectively and disruption will ensue as heat input drives a secular expansion. Disrupting clouds should leave trails of gas and H2 dust in their wake, which might make them easier to detect. Our models may be relevant to the cometary globules in the Helix Nebula and the G2 cloud orbiting Sgr A*.

Multiphase gas in the circumgalactic medium: relative role of tcool/tff and density fluctuations

ABSTRACT We perform a suite of simulations with realistic gravity and thermal balance in shells to quantify the role of the ratio of cooling time to the free-fall time (tcool/tff) and the amplitude of density perturbations (δρ/ρ) in the production of multiphase gas in the circumgalactic medium (CGM). Previous idealized simulations, focusing on small amplitude perturbations in the intracluster medium (ICM), found that cold gas can condense out of the hot ICM in global thermal balance when the background tcool/tff ≲ 10. Recent observations suggest the presence of cold gas even when the background profiles have somewhat large values of tcool/tff. This partly motivates a better understanding of additional factors such as large density perturbations that can enhance the propensity for cooling and condensation even when the background tcool/tff is high. Such large density contrasts can be seeded by galaxy wakes or dense cosmological filaments. From our simulations, we introduce a condensation curve in the (δρ/ρ) – min(tcool/tff) space, which defines the threshold for condensation of multiphase gas in the CGM. We show that this condensation curve corresponds to (tcool/tff)blob ≲ 10 applied to the overdense blob instead of the background for which tcool/tff can be higher. We also study the modification in the condensation curve by varying entropy stratification. Steeper (positive) entropy gradients shift the condensation curve to higher amplitudes of perturbations (i.e. make condensation difficult). A constant entropy core, applicable to the CGM in smaller haloes, shows condensation over a larger range of radii as compared to the steeper entropy profiles in the ICM.

Three-dimensional structure tensor based PET/CT fusion in gradient domain.

Gradient based image fusion can more effectively incorporate edge details using structure tensor, which is successfully used in 2D image fusion. In this study, we generalized and applied this gradient based image fusion method into 3D for non-small cell lung cancer PET/CT image fusion. According the characteristic of lung PET/CT images, we proposed a novel 3D structure tensor based feature, which can be used to construct a weighted structure tensor containing important local detail of both PET and CT images. The fusion gradient domain is deduced from a rank one tensor, which is the closest approximation of the weighted structure tensor in geometry. Based on the fusion gradient domain, final PET/CT fusion image is obtained by solving a Poisson equation. Comparing with the wavelet transform based fusion result, the average information entropy and average gradient measure of proposed fusion method increase 13.5% and 42.3%, respectively. The experimental results show that the proposed fusion method enables to effectively preserve lung vessel structure and sphere-like lesion detail while produces clear, stable and well consistent fusion images.

Quantifying Mass and Magnetic Flux Transport in Saturn's Magnetosphere

AbstractRadial transport is an important dynamical process in Saturn's internally driven magnetosphere. Radial transport is presumed to occur by a centrifugally driven interchange instability, determined by the gradient of flux tube content and flux tube entropy. Plasma produced in the inner magnetosphere must be transported radially outward. The outward motion of the plasma stretches the magnetic field lines, leading to magnetic reconnection. Reconnection allows the mass to be transported radially while allowing the flux to circulate back to the inner magnetosphere. Both radial transport of mass and magnetic flux in Saturn's magnetosphere have been estimated based on Cassani Plasma Spectrometer data provided by Wilson et al. (2017, https://doi.org/10.1002/2017JA024117) and suggesting the radial transport rate of plasma of around 55 kg/s. The net magnetic flux transport should be 0, but the data suggest a net outward magnetic flux transport indicating the existence of different possible transport mechanisms in Saturn's magnetodisc.

A novel image registration control system based on improved composite metric entropy function in color printing

The accuracy of overprint is one of the essential factors for the qualities of modern color printing technology. Using machine vision technology and image processing technology to detect overprint quality can steadily and accurately monitor overprint quality and avoid the disadvantages of human eyes detection. This paper firstly introduces the gradient entropy and direction constraint into sequential similarity detection algorithm (SSDA); then a novel joint function is proposed as similarity measure function; finally, Powell optimization algorithm is adopted to optimize the registration parameters. Simulation results, in both qualitative and quantitative, show that our proposed algorithm noticeably reduces the registration error compared with the traditional method. The obtained accurate registration parameter would make it possible for identifying the overprint qualities, sending signal when the misregister and deviation adjusting signal occur. In brief, our proposed algorithm can make the printing machine automatically adjust the plate location and correct the standard deviation in color printing system.

Fusion of Visible and Infrared Images Based on IHS Transformation and Regional Variance Matching Degree

It is usually necessary to identify and extract specific characteristics by deriving an informative fused image from multiple images. An effective fusion algorithm was proposed by combining the intensity-hue-saturation (IHS) transformation and the regional variance matching degree (RVMD) in our study. Visible and thermal infrared images of wheat were used as the original data sources. After finishing the IHS transformation, a fusion rule was designed to produce the new component I. More specifically, the high frequency fusion rule was generated by the RVMD with a threshold of 0.5 and a 3 × 3 moving window, and the weighted average was used as the low frequency fusion rule. Experimental results show that the proposed algorithm can avoid producing color distortion in comparison with the IHS transformation, and additionally, it can also enhance the edge contrast and produce more obvious texture resolution. In addition, three quantitative indicators including entropy, standard deviation and average gradient were used to validate the proposed algorithm. The analysis results show that the values of three indicators are respectively 7.82, 63.93, 10.06, which are better than the results derived from the IHS transformation and regional variance fusion.

A Model of Solar Equilibrium: The Hydrodynamic Limit

Abstract Helioseismology has revealed the internal density and rotation profiles of the Sun. Yet, knowledge of its magnetic fields and meridional circulation is confined much closer to the surface, and latitudinal entropy gradients are below detectable limits. While numerical simulations can offer insight into the interior dynamics and help identify which ingredients are necessary to reproduce particular observations, some features of the Sun can be understood analytically from an equilibrium perspective. Examples of such features include: the 1D density profile arising from steady-state energy transport from the core to the surface, and the tilting of isorotation contours in the convection zone (CZ) due to baroclinic forcing. To help answer the question of which features can be explained by equilibrium, we propose analyzing stationary axisymmetric ideal magnetohydrodynamic flows in the solar regime. By prescribing an appropriate entropy at the surface, we recover a rotation profile that reasonably matches observations in the bulk of the CZ. Additionally, by including the effects of poloidal flow, we reproduce a feature that is reminiscent of the near surface shear layer. However, no tachocline-like feature is seen in hydrodynamic equilibrium, suggesting the importance of either dynamics or magnetic fields in its description.

A Novel Inverse Synthetic Aperture Radar Imaging Method for Maneuvering Targets Based on Modified Chirp Fourier Transform

When inverse synthetic aperture radar (ISAR) imaging maneuvers targets, the azimuth echo of the target scattering point causes a Doppler frequency time-varying problem, which leads to the blurring and defocusing of the imaging results. Traditional imaging methods struggle to meet the imaging requirements for maneuvering targets due to a poor imaging effect or low efficiency. Given these challenges, a modified chirp Fourier transform (MCFT) imaging method is proposed in this paper, based on the specific relationship between the target rotation parameters and the radar echo signal parameters. Firstly, discrete chirp Fourier transform is used to quickly estimate the target’s coarse rotation ratio. Then, the minimum entropy function and gradient descent method are used to calculate the target’s accurate rotation ratio. Finally, the azimuth focusing image is accomplished by performing MCFT once on the azimuth echo signal using the accurate rotation ratio. This method avoids estimating and separating the sub-echo components one-by-one, considerably improves the imaging speed, and guarantees the best imaging quality by applying the global minimum entropy principle. The experimental results show that the proposed method effectively achieves the two-dimensional, high-quality, and fast imaging of maneuvering targets.

Penetrative Convection in Partly Stratified Rapidly Rotating Spherical Shells

Celestial objects host interfaces between convective and stable stratified interior regions. The interaction between both, e.g., the transfer of heat, mass, or angular momentum depends on whether and how flows penetrate into the stable layer. Powered from the unstable, convective regions, radial flows can pierce into the stable region depending on their inertia (overshooting). In rapidly rotating systems, the dynamics are strongly influenced by the Coriolis force and radial flows penetrate in stratified regions due to the geostrophic invariance of columnar convection even in the limit of vanishing inertia. Within this study, we numerically investigate both mechanisms and hence explore the nature of penetrative convection in rapidly rotating spherical shells. The study covers a broad range of system parameters, such as the strength of the stratification relative to the Coriolis force or the inertia. Guided by the application to Saturn, we model a sandwiched stable stratified layer (SSL) surrounded by two convective zones. A comprehensive analysis of the damping behavior of convective flows at the edges of the SSL showed that the mean penetration depth is controlled by the ratio of stratified and unstratified buoyancy gradients and is hence independent of rotation. A scaling law is derived and suggests that the penetration depth decreases with the square root of the ratio of unstabilizing and stabilizing entropy gradients. The influence of the Coriolis force, however, is evident by a modulation of the penetration depth along latitude, since convective columns are elongated vertically and hence pierce predominantly into the SSL around mid-latitudes and outside the tangent cylinder. Our result also show that the penetration depth decreases linearly with the flow length scale (low pass filter), confirming predictions from the linear theory of rotating partially stratified convection.

Characteristics of entropy layer for cones and cylinders in supersonic flows

An analytic method is presented to study the distribution of vorticity downstream the shock wave and the characteristics of the entropy layer for various cones and cylinders in supersonic flows. The relations of shock-shape, the distribution character of various parameters within the shock layer, and the entropy increment were combined to obtain the characteristics of vorticity and the entropy gradient. Numerical simulation are performed at the Mach number of 3, 5 and 10. The results indicate that the distribution of entropy and vorticity is connected with shock shape directly. Due to the differences of the shape of shock, the vorticity and the extreme value of entropy gradient for blunt-nosed cylinders are both larger than the cases for flat cylinders. As the shock-shape of flat-nosed cylinders is more liable to be affected than blunt-nosed cylinders with increasing Mach number, the position of the extreme value moves to the surface as the Mach number increases for flat-nosed cylinders, while it remains the identical value for blunt-nosed cylinders. The vorticity is regarded as the criterion of the edge of entropy layer in the normal direction, and two methods are proposed and discussed to estimate the edge.

Geometry and entanglement entropy of surfaces in loop quantum gravity

In loop quantum gravity, the area element of embedded spatial surfaces is given by a well-defined operator. We further characterize the quantized geometry of such surfaces by proposing definitions for operators quantizing scalar curvature and mean curvature. By investigating their properties, we shed light on the nature of the geometry of surfaces in loop quantum gravity. We also investigate the entanglement entropy across surfaces in the case where spin network edges are running within the surface. We observe that, on a certain class of states, the entropy gradient across a surface is proportional to the mean curvature. In particular, the entanglement entropy is constant for small deformations of a minimal surface in this case.

Effects of neutral buoyancy outer boundary condition in models of deep convection in giant planets

Cloud motions have revealed strong east–west jet streams on Jupiter and Saturn. Two different paradigms have emerged for the origin of these jets. In the shallow dynamics paradigm zonal flow is driven largely by solar radiation and weather dynamics in the troposphere. In the deep convection paradigm forcing is thought to originate primarily via heat flow from the deep interior. Most previous anelastic models that focus on the development of deep zonal flows implement a constant entropy difference from the inner to outer boundary with no internal heat sources. For models with strong density gradients these constant entropy boundary conditions yield strong convective forcing at the outer boundary. However, observations indicate that giant planet tropospheres are stably stratified or perhaps near neutrally buoyant. Based on these observations we present here a deep convection parameter study with a zero entropy gradient (neutral stability) outer boundary condition and a uniform internal heat sink. We find that near convective onset, a neutrally buoyant shallow layer modifies the flow strongly, pushing active convection to occur near the bottom boundary. Furthermore, deeply seated jets develop efficiently, even with relatively weak forcing. Thus, for near critical and weak forcing the zero entropy gradient top boundary condition yields flows that resemble Boussinesq results, even for strong density gradients. For strongly convecting flows, the jet structure is more similar to cases with constant entropy difference. However, with strong convective mixing, the zero entropy gradient outer boundary condition results in relatively extensive regions of dynamical stability (reversed entropy gradient). Under these conditions, surface flows can develop with larger scale non-zonal features and vorticity structures that have planetary characteristics.

Copy-move forgery detection based on compact color content descriptor and Delaunay triangle matching

Copy-move (region duplication) is one of the most common types of image forgeries, in which at least one part of an image is copied and pasted onto another area of the same image. The main aims of the copy-move forgery are to overemphasize a concept or conceal objects by duplicating some regions. Keypoint based copy-move forgery detection (CMFD) method extracts image feature points and employs local image features to identify duplicated regions, which exhibits remarkable detection performance with respect to memory requirement, computational cost, and robustness. However, they usually do not work well when the objects are hidden in smooth background areas. Also, the detection and localization accuracy always be lowered because of poor local image feature computation. In this paper, we present a novel approach for the detection and localization of copy-move forgeries, which is based on color invariance SIFER (Scale-invariant feature detector with error resilience) and FQRHFMs (Fast quaternion radial harmonic Fourier moments). Firstly, the original forgery image is segmented into nonoverlapping and nearly uniform superpixel blocks, and the stable keypoints are extracted adaptively from each superpixel block by incorporating the superpixel contents and color invariance SIFER. Secondly, a set of connected Delaunay triangles is constructed using the extracted image keypoints, and suitable local image feature for each Delaunay triangle is computed by using FQRHFMs and gradient entropy. Thirdly, the local image features and coherency sensitive hashing (CSH) are utilized to match quickly the Delaunay triangles. Finally, the falsely matched Delaunay triangles are removed by employing dense linear fitting (DLF), and the duplicated regions are localized using optimized zero mean normalized cross-correlation (ZNCC) measure. We conduct extensive experiments to evaluate the performance of the proposed copy-move forgery detection scheme, in which encouraging results validate the effectiveness of the proposed technique.

A hybrid approach for Medical Image Fusion Based on Wavelet Transform and Principal Component Analysis

This paper presents a hybrid approach for medical image fusion based on the Discrete Wavelet Transform (DWT) and Principal Component Analysis (PCA). The main idea of the approach is to select between two fusion methods; DWT and PCA based on the local variance estimated at each position in the fusion results. Simulation results on multi-modality images are presented in this paper. The two modalities adopted are Magnetic Resonance (MR) images and Computed Tomography (CT) images. Evaluation metrics such as entropy, edge intensity, contrast, and average gradient have been adopted for performance evaluation of the proposed method. The obtained results confirm that the proposed method is superior in performance to the DWT and PCA methods individually.

Breaking Taylor–Proudman Balance by Magnetic Fields in Stellar Convection Zones

Abstract We carry out high-resolution calculations for the stellar convection zone. The main purpose of this Letter is to investigate the effect of a small-scale dynamo on the differential rotation. The solar differential rotation deviates from the Taylor–Proudman state in which the angular velocity does not change along the rotational axis. To break the Taylor–Proudman state deep in the convection zone, it is thought that a latitudinal entropy gradient is required. In this Letter, we find that the small-scale dynamo has three roles in the deviation of the stellar differential rotation from the Taylor–Proudman state. 1) The shear of the angular velocity is suppressed. This leads to a situation where the latitudinal entropy gradient efficiently breaks the Taylor–Proudman state. 2) The perturbation of the entropy increases with the suppression of the turbulent velocity between upflows and downflows. 3) The convection velocity is reduced. This increases the effect of the rotation on the convection. The second and third factors increase the latitudinal entropy gradient and break the Taylor–Proudman state. We find that an efficient small-scale dynamo has a significant impact on the stellar differential rotation.

Edge and texture detection of metal image under high temperature and dynamic solidification condition

The zinc casting is a complicated process with high temperature, high dust content and dynamic solidification. To accurately detect the edge and texture of metal image under this condition, a sub-pixel detection based on gradient entropy and adaptive four-order cubic convolution interpolation (GEAF-CCI) algorithm is proposed. This method mainly involves three procedures. Firstly, the gradient image is generated from the grey images by using gradient operator. Then, a dynamic threshold based on the maximum local gradient entropy (DTMLGE) algorithm is applied to distinguishing the edge and texture pixels from gradient images. Finally, the adaptive four-order cubic convolution interpolation (AF-CCI) algorithm is proposed for interpolating calculation of the target edges and textures according to their variation differences in different directions. The experimental result shows that the proposed algorithm can remove the jag and blur of the edges and textures, improve the edge positioning precision and reduce the false or missing detection rate.

The primordial entropy of Jupiter

The formation history of giant planets determines their primordial structure and consequent evolution. We simulate various formation paths of Jupiter to determine its primordial entropy, and find that a common outcome is for proto-Jupiter to have non-convective regions in its interior. We use planet formation models to calculate how the entropy and post-formation luminosity depend on model properties such as the solid accretion rate and opacity, and show that the gas accretion rate and its time evolution play a key role in determining the entropy profile. The predicted luminosity of Jupiter shortly after formation varies by a factor of $2$--$3$ for different choices of model parameters. We find that entropy gradients inside Jupiter persist for $\sim 10\ {\rm Myr}$ after formation. We suggest that these gradients should be considered together with heavy-element composition gradients when modeling Jupiter's evolution and internal structure.

Deblurring traffic sign images based on exemplars.

Motion blur appearing in traffic sign images may lead to poor recognition results, and therefore it is of great significance to study how to deblur the images. In this paper, a novel method for deblurring traffic sign is proposed based on exemplars and several related approaches are also made. First, an exemplar dataset construction method is proposed based on multiple-size partition strategy to lower calculation cost of exemplar matching. Second, a matching criterion based on gradient information and entropy correlation coefficient is also proposed to enhance the matching accuracy. Third, L0.5-norm is introduced as the regularization item to maintain the sparsity of blur kernel. Experiments verify the superiority of the proposed approaches and extensive evaluations against state-of-the-art methods demonstrate the effectiveness of the proposed algorithm.

Spiral density waves and vertical circulation in protoplanetary discs

Spiral density waves dominate several facets of accretion disc dynamics --- planet-disc interactions and gravitational instability (GI) most prominently. Though they have been examined thoroughly in two-dimensional simulations, their vertical structures in the non-linear regime are somewhat unexplored. This neglect is unwarranted given that any strong vertical motions associated with these waves could profoundly impact dust dynamics, dust sedimentation, planet formation, and the emissivity of the disc surface. In this paper we combine linear calculations and shearing box simulations in order to investigate the vertical structure of spiral waves for various polytropic stratifications and wave amplitudes. For sub-adiabatic profiles we find that spiral waves develop a pair of counter-rotating poloidal rolls. Particularly strong in the nonlinear regime, these vortical structures issue from the baroclinicity supported by the background vertical entropy gradient. They are also intimately connected to the disk's g-modes which appear to interact nonlinearly with the density waves. Furthermore, we demonstrate that the poloidal rolls are ubiquitous in gravitoturbulence, emerging in the vicinity of GI spiral wakes, and potentially transporting grains off the disk midplane. Other than hindering sedimentation and planet formation, this phenomena may bear on observations of the disk's scattered infrared luminosity. The vortical features could also impact on the turbulent dynamo operating in young protoplanetary discs subject to GI, or possibly even galactic discs.