Entropy Gradient Research Articles

Vorticity and magnetic field production in relativistic ideal fluids

In the framework of relativistic ideal hydrodynamics, we study the production mechanism for vorticity and magnetic field in relativistic ideal fluids. It is demonstrated that in the uncharged fluids the thermal vorticity will always satisfy the Kelvin's theorem and the circulation must be conserved. However, in the charged fluids, the vorticity and magnetic field can be produced by the interaction between the entropy gradients and the fluid velocity gradients. Especially, in the multiple charged fluids, the vorticity and magnetic field can be produced by the interaction between the inhomogenous charge density ratio and the fluid velocity gradients even if the entropy distribution is homogeneous, which provides another mechanism for the production of vorticity and magnetic field in relativistic plasmas or in the early universe.

Image Fusion Algorithm Based on Contourlet Transform

Contourlet transform is a new multi-scale, multi-resolution analysis tool. This paper studied on the theory of Contourlet transform.,According to the practical application requirements of characteristics of data, much details in complex images it propose a novel image fusion method of remote sensing images based on contourlet Coefficients correlativity of directional region. Besides improving fused images spatial resolution, our method can better preserve original multi-spectral image’s color information.Extensive experimental results show that the proposed method is superior to conventional methods in terms of entropy, joint entropy, and average gradient. It can enhance the spatial resolution of target images. Meanwhile, it well preserves the color information of multi-spectral images.

Multi-Focus Image Fusion Based on Pyramid Decomposition

Image fusion algorithm is very important in image fusion process. Image fusion algorithm based on pyramid decomposition was reviewed in this paper. Pyramid decomposition algorithm mainly includes Contrast pyramid, Gradient Pyramid, Laplacian Pyramid and Ratio Pyramid. The fusion algorithms based on pyramid decomposition were respectively applied in multi-focus images, advantage and disadvantage were summarized and application was given. Fusion results were given by MATLAB simulation. Objective evaluation index including of mean, standard deviation, entropy and average gradient was calculated in this paper. Image fusion algorithm should be selected according to the information extracted and the aim of fusion.

Rotating protoneutron stars: Spin evolution, maximum mass, and I-Love-Q relations

Shortly after its birth in a gravitational collapse, a proto-neutron star enters in a phase of quasi-stationary evolution characterized by large gradients of the thermodynamical variables and intense neutrino emission. In few tens of seconds the gradients smooth out while the star contracts and cools down, until it becomes a neutron star. In this paper we study this phase of the proto-neutron star life including rotation, and employing finite temperature equations of state. We model the evolution of the rotation rate, and determine the relevant quantities characterizing the star. Our results show that an isolated neutron star cannot reach, at the end of the evolution, the maximum values of mass and rotation rate allowed by the zero-temperature equation of state. Moreover, a mature neutron star evolved in isolation cannot rotate too rapidly, even if it is born from a proto-neutron star rotating at the mass-shedding limit. We also show that the I-Love-Q relations are violated in the first second of life, but they are satisfied as soon as the entropy gradients smooth out.

Potential vorticity in magnetohydrodynamics

A version of Noether's second theorem using Lagrange multipliers is used to investigate fluid relabelling symmetries conservation laws in magnetohydrodynamics (MHD). We obtain a new generalized potential vorticity type conservation equation for MHD which takes into account entropy gradients and the J × B force on the plasma due to the current J and magnetic induction B. This new conservation law for MHD is derived by using Noether's second theorem in conjunction with a class of fluid relabelling symmetries in which the symmetry generator for the Lagrange label transformations is non-parallel to the magnetic field induction in Lagrange label space. This is associated with an Abelian Lie pseudo algebra and a foliated phase space in Lagrange label space. It contains as a special case Ertel's theorem in ideal fluid mechanics. An independent derivation shows that the new conservation law is also valid for more general physical situations.

An improved fractional-order differentiation model for image denoising

This paper investigates fractional order differentiation and its applications in digital image processing. We propose an improved model based on the Grünwald-Letnikov (G–L) fractional differential operator. Our improved denoising operator mask is based on G–L fractional order differentiation. The total coefficient of this mask is not equal to zero, which means that its response value is not zero in flat areas of the image. This nonlinear filter mask enhances and preserves detailed features while effectively denoising the image. Our experiments on texture-rich digital images demonstrated the capabilities of the filter. We used the information entropy and average gradient to quantitatively compare our method to existing techniques. Additionally, we have successfully used it to denoise three-dimensional magnetic resonance images.

Exploring embedding matrices and the entropy gradient for the segmentation of heart sounds in real noisy environments.

In this paper we explore a novel feature for the segmentation of heart sounds: the entropy gradient. We are motivated by the fact that auscultations in real environments are highly contaminated by noise and results reinforce our suspicions that the entropy gradient is not only robust to such noise but maintains a high sensitivity to the S1 and S2 components of the signal. Our whole approach consists of three stages, out of which the last two are novel contributions to this field. The first stage consists of typical pre-processing and wavelet reconstruction to obtain the Shannon energy envelogram. On the second stage we use an embedding matrix to track the dynamics of the system, which is formed by delay vectors with higher dimension than the corresponding attractor. On the third stage, we use the eigenvalues and eigenvectors of the embedding matrix to estimate the entropy of the envelogram. Finite differences are used to estimate entropy gradients, in which standard peak picking approaches are used for heart sound segmentation. Experiments are performed on a public dataset of pediatric auscultations obtained in real environments and results show the promising potential of this novel feature for such noisy scenarios.

Avoided crossings of modes of a finite target with adiabat shaping in inertial fusion implosions

In Inertial Confinement Fusion (ICF), a cold target material is accelerated by a hot low density plasma. In this work, the small amplitude disturbances in ablative Rayleigh-Taylor instability in the presence of entropy gradients is studied using a sharp boundary approximation, being the inverse entropy-gradient scale length the quantity Ko = ∝LnSo/∝y. For simplicity, the target considered here is a finite incompressible slab. Due to ablation, the phenomenon of the interactions of two types of modes (Rayleigh mode and entropic mode) is shown. This manifest itself in the occurrence of rapid shifts of rate growth (bumping, avoided crossings). The entire situation is strongly reminiscent of the well-know "avoided crossings" of modes of two coupled oscillators. The growth rate of one mode (Rayleigh mode) approaches that of another one (entropic mode) which is "bumped" to a quite different rate growth, while the "bumping" mode settles at roughly at the original rate growth of the bumped mode.

BAROCLINIC INSTABILITY IN THE SOLAR TACHOCLINE

The solar tachocline is likely to be close to a geostrophic 'thermal wind', for which the Coriolis force associated with differential rotation is closely balanced by a latitudinal pressure gradient, leading to a tight relation between the vertical gradient of rotation and the latitudinal entropy gradient. Using a hydrostatic but nongeostrophic spherical shell model, we examine baroclinic instability of the tachocline thermal wind. We find that both the overshoot and radiative parts of the tachocline should be baroclinicly unstable at most latitudes. Growth rates are roughly five times higher in middle and high latitudes compared to low latitudes, and much higher in the overshoot than in the radiative tachocline. They range in e-folding amplification from 10 days in the high latitude overshoot tachocline, down to 20 yr for the low latitude radiative tachocline. In the radiative tachocline only, longitudinal wavenumbers m = 1, 2 are unstable, while in the overshoot tachocline a much broader range of m are unstable. At all latitudes and with all stratifications, the longitudinal scale of the most unstable mode is comparable to the Rossby deformation radius, while the growth rate is set by the local latitudinal entropy gradient. Baroclinic instability in the tachocline competing withmore » instability of the latitude rotation gradient established in earlier studies should be important for the workings of the solar dynamo and should be expected to be found in most stars that contain an interface between radiative and convective domains.« less

Study on Adaptive and Fuzzy Weighted Image Fusion Based on Wavelet Transform in Trinocular Vision of Picking Robot

In order to improve the adaptive recognition abilities of picking robot in complex environment, a fusion approach of trinocular vision in wavelet domain based on fuzzy reasoning weight was proposed. Firstly, membership functions of fusion rules are determined by fuzzy reasoning of picking environmental features, and membership values of fusion types are calculated according to regional energy and match degree of origin images. Based on the maximum membership degree principle, fuzzy decision is carried on to determine the fusion types and fusion weight. Secondly, the mean weighted method and regional energy feature method are adopted respectively to carry on the low frequency as well as high frequency coefficients fusion among multi-source images by using two-level 2D wavelet, and the final fusion images are attained by inverse HIS transform based on inverse wavelet transform. Four groups of experiment show that in the complex picking environment like weak illumination and strong noise, the information entropy and average gradient of fused image that obtained by using the wavelet fusion method based on fuzzy reasoning weight are higher than that of traditional mean method, pyramid algorithm and wavelet packet method, which means that the fusion effect has been improved greatly.

SHEDDING LIGHT ON THE ECCENTRICITY VALLEY: GAP HEATING AND ECCENTRICITY EXCITATION OF GIANT PLANETS IN PROTOPLANETARY DISKS

We show that the first order (non co-orbital) corotation torques are significantly modified by entropy gradients in a non-barotropic protoplanetary disk. Such non-barotropic torques can dramatically alter the balance that, for barotropic cases, results in the net eccentricity damping for giant gap-clearing planets embedded in the disk. We demonstrate that stellar illumination can heat the gap enough for the planet's orbital eccentricity to instead be excited. We also discuss the "Eccentricity Valley" noted in the known exoplanet population, where low-metallicity stars have a deficit of eccentric planets between $\sim 0.1$ and $\sim 1$ AU compared to metal-rich systems (Dawson & Murray-Clay 2013). We show that this feature in the planet distribution may be due to the self-shadowing of the disk by a rim located at the dust sublimation radius $\sim 0.1$ AU, which is known to exist for several T Tauri systems. In the shadowed region between $\sim 0.1$ and $\sim 1$ AU lack of gap insolation allows disk interactions to damp eccentricity. Outside such shadowed regions stellar illumination can heat the planetary gaps and drive eccentricity growth for giant planets. We suggest that the self-shadowing does not arise at higher metallicity due to the increased optical depth of the gas interior to the dust sublimation radius.

LINEAR COROTATION TORQUES IN NON-BAROTROPIC DISKS

I derive a fully analytic expression for the linear corotation torque to first order in eccentricity for planets in non-barotropic protoplanetary disks, taking into account the effect of disk entropy gradients. This torque formula is applicable to both the co-orbital corotation torque and the non co-orbital corotation torques -- for planets in orbits with non-zero eccentricity -- in disks where the thermal diffusivity and viscosity are sufficient to maintain linearity of these interactions. While the co-orbital corotation torque is important for migration of planets in Type I migration, the non co-orbital corotation torque plays an important role in the eccentricity evolution of giant planets that have opened gaps in the disk. The presence of an entropy gradient in the disk can significantly modify the corotation torque in both these cases.

Image Fusion Algorithm Based on Contrast Pyramid and its Performance Evaluation

Contrast pyramid algorithm is put forward in this paper. The human visual system is sensitive to contrast information of image, so contrast pyramid algorithm would outstanding the contrast of image. The algorithm consists of creation process of Gauss Pyramid, the process of creating contrast Pyramid and reconstruction process of clear image. Simulation by MATLAB was completed in multi-focus image, multi-modality image and color image. Objective evaluation index such as mean, standard deviation, entropy and average gradient was calculated Simulation results and index show that the contrast pyramid algorithm has advantage of projecting the contrast of image, especially in color image fusion.

Gradient Entropy Estimate and Convergence of a Semi-Explicit Scheme for Diagonal Hyperbolic Systems

In this paper, we consider diagonal hyperbolic systems with monotone continuous initial data. We propose a natural semi-explicit and upwind first order scheme. Under a certain non-negativity condition on the Jacobian matrix of the velocities of the system, there is a gradient entropy estimate for the hyperbolic system. We show that our scheme enjoys a similar gradient entropy estimate at the discrete level. This property allows us to prove the convergence of the scheme.

DIFFERENTIAL ROTATION IN SOLAR-LIKE STARS FROM GLOBAL SIMULATIONS

To explore the physics of large-scale flows in solar-like stars, we perform 3D anelastic simulations of rotating convection for global models with stratification resembling the solar interior. The numerical method is based on an implicit large-eddy simulation approach designed to capture effects from non-resolved small scales. We obtain two regimes of differential rotation, with equatorial zonal flows accelerated either in the direction of rotation (solar-like) or in the opposite direction (anti-solar). While the models with the solar-like differential rotation tend to produce multiple cells of meridional circulation, the models with anti-solar differential rotation result in only one or two meridional cells. Our simulations indicate that the rotation and large-scale flow patterns critically depend on the ratio between buoyancy and Coriolis forces. By including a subadiabatic layer at the bottom of the domain, corresponding to the stratification of a radiative zone, we reproduce a layer of strong radial shear similar to the solar tachocline. Similarly, enhanced superadiabaticity at the top results in a near-surface shear layer located mainly at lower latitudes. The models reveal a latitudinal entropy gradient localized at the base of the convection zone and in the stable region, which however does not propagate across the convection zone. In consequence, baroclinicity effects remain small and the rotation iso-contours align in cylinders along the rotation axis. Our results confirm the alignment of large convective cells along the rotation axis in the deep convection zone, and suggest that such "banana-cell" pattern can be hidden beneath the supergranulation layer.

Universal steganalysis for RGB images based on color gradient matrix

A steganalysis algorithm for RGB images based on color gradient matrix was proposed in this paper.The algorithm was constructed with color gradient matrix of the RGB image,and 16-dimensional statistical features,including gradient asymmetry,gradient energy,gradient mean,gradient variance,gradient entropy and so on.Support Vector Machine(SVM) took the 16-dimensional statistical features to detect hidden message in RGB images.The experimental results indicate that the proposed algorithm realizes the reliable steganalysis of JSteg,F5,OutGuess,Steghide and MB1,which is suitable for universal steganalysis for RGB images.

SPOKE-LIKE DIFFERENTIAL ROTATION IN A CONVECTIVE DYNAMO WITH A CORONAL ENVELOPE

We report on the results of four convective dynamo simulations with an outer coronal layer. The magnetic field is self-consistently generated by the convective motions beneath the surface. Above the convection zone, we include a polytropic layer that extends to 1.6 solar radii. The temperature increases in this region to $\approx8$ times the value at the surface, corresponding to $\approx1.2$ times the value at the bottom of the spherical shell. We associate this region with the solar corona. We find solar-like differential rotation with radial contours of constant rotation rate, together with a near-surface shear layer. This non-cylindrical rotation profile is caused by a non-zero latitudinal entropy gradient that offsets the Taylor--Proudman balance through the baroclinic term. The meridional circulation is multi-cellular with a solar-like poleward flow near the surface at low latitudes. In most of the cases, the mean magnetic field is oscillatory with equatorward migration in two cases. In other cases, the equatorward migration is overlaid by stationary or even poleward migrating mean fields.

Linear stability analysis on supersonic streamwise vortices

In this study, the spatial growth rates of supersonic streamwise vortices were investigated by inviscid linear stability analysis. The freestream Mach numbers were 2.5, 5.0, and 7.5. In previous measurements taken to define the streamwise vortices, the stagnation temperature profile of supersonic flows is approximately uniform. This study found that the growth rate of vortices at the uniform stagnation temperature is smaller than that of isentropic vortices. The instability properties of the streamwise vortices can be explained by the ratio of the circulation to the axial velocity deficit, and also by the Mach number. Moreover, it is found that the compressibility effect, by which the instability reduces as the Mach number increases, is caused by the negative energy arising from the entropy gradient of supersonic vortices that accompanies the axial velocity deficit-like wake. From an energy perspective, the effect may reasonably be correlated with the large density perturbations in supersonic flows. This study also proposes a general convective Mach number for supersonic streamwise vortices. The normalized growth rates are shown to be a function of convective Mach number within the investigated range of ratio parameters.

Improving MR brain image segmentation using self-organising maps and entropy-gradient clustering

The primary brain image segmentation goal is to partition a given brain image into different regions representing anatomical structures. Magnetic resonance image (MRI) segmentation is especially interesting because the accurate representation of white matter, grey matter and cerebrospinal fluid provides a way to identify many brain disorders, such as dementia, schizophrenia or Alzheimer’s disease (AD). This paper presents a fully unsupervised method for MRI segmentation based on Self-Organising Maps (SOMs) and Genetic Algorithms (GAs). In particular, the proposed method is based on five stages consisting of image acquisition, feature extraction, feature selection using evolutionary computation, voxel classification using SOM, and sharp map clustering. Moreover, a novel SOM clustering mechanism is presented that defines cluster borders by considering the output space and the relationship with the input space. This clustering mechanism accommodates spatial relationships using an entropy-gradient (EG) function calculation to group the units on the output space (SOM). The complete procedure does not use any a priori knowledge regarding voxel class assignment, but reveals a fully unsupervised, automated method for MRI segmentation to directly identify different tissue classes. Our algorithm was tested using images from the Internet Brain Image Repository (IBSR), outperforming the CGMM method in WM and CSF delineation, and was found to be the most effective among other techniques. Furthermore, this method provided excellent results using high-resolution MR images provided by the Nuclear Medicine Service of the “Virgen de las Nieves” Hospital (Granada, Spain).

Enhancement of Medical Image Details via Wavelet Homomorphic Filtering Transform

AbstractA new medical image enhancement algorithm based on spatial frequency domain is presented in this article. The medical image is first divided into several sub-images based on dyadic wavelet scale analysis. At each level, different directional sub-band images can reflect the different characteristics of the image. A low-frequency sub-band image maintains the original image content information, and high-frequency sub-band images represent image details such as edges and regional boundaries. The corresponding sub-band images are then enhanced by different Butterworth homomorphic filtering functions, which can attenuate the low frequencies and amplify the high frequencies. A linear adjustment is carried out on the low frequency of the highest level. Then, the wavelet reconstruction course is used to obtain the final enhanced image. Experiments on magnetic resonance images of temporomandibular joint soft tissues have shown that the proposed method can effectively eliminate the non-uniform luminance distribution of medical images. Its performance is much better than traditional Butterworth homomorphic filtering algorithm whether in subjective vision quality or objective evaluations such as detailed information entropy and average gradient.