Sharp Regions Research Articles

Long-range Ising models: Contours, phase transitions and decaying fields

Inspired by Fröhlich–Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a definition of contour and a direct proof for the phase transition for ferromagnetic long-range Ising models on \mathbb{Z}^{d} , d\geq 2 . The argument, which is based on a multiscale analysis, works for the sharp region \alpha>d and improves previous results obtained by Park for \alpha>3d+1 , and by Ginibre, Grossmann and Ruelle for \alpha> d+1 , where \alpha is the power of the coupling constant. The key idea is to avoid a large number of small contours. As an application, we prove the persistence of the phase transition when we add a polynomially decaying magnetic field with power \delta>0 as h^{*}|x|^{-\delta} , where h^{*} >0 . For d<\alpha<d+1 , the phase transition occurs when \delta>\alpha-d , and when h^{*} is small enough over the critical line \delta=\alpha-d . For \alpha \geq d+1 , \delta>1 is enough to prove the phase transition, and for \delta=1 we have to ask h^{*} small. The natural conjecture is that this region is also sharp for the phase transition problem when we have a decaying field.

On the ground state of one-dimensional quantum droplets for large chemical potentials

Abstract In the present work we revisit the problem of the quantum droplet in atomic Bose–Einstein condensates with an eye towards describing its ground state in the large density, so-called Thomas–Fermi (TF) limit. We consider the problem as being separable into 3 distinct regions: an inner one, where the TF approximation is valid, a sharp transition region where the density abruptly drops towards the (vanishing) background value and an outer region which asymptotes to the background value. We analyze the spatial extent of each of these regions, and develop a systematic effective description of the rapid intermediate transition region. Accordingly, we derive a uniformly valid description of the ground state that is found to accurately match our numerical computations. As an additional application of our considerations, we show that this formulation allows for an analytical approximation of excited states such as the (trapped) dark soliton in the large density limit.

Foreground-background separation and deblurring super-resolution method

The limited depth of field (DOF) inherent in cameras often results in defocused and blurry backgrounds when capturing images in large aperture mode. This not only leads to the loss of crucial background information but also impedes the efficient reconstruction of the background regions. Usually, super-resolution (SR) techniques struggle to produce high-quality results for images captured with large apertures. To enhance the reconstruction quality of defocused regions in large aperture images, a foreground-background separation and deblurring super-resolution (FBSDSR) method was proposed in this paper. Based on the idea of foreground-background separation processing, we first divide the large aperture image into a sharp foreground region (If) and a blurry background region (Ib) based on depth information. The background region (Ib) is then deblurred using an end-to-end iterative filter adaptive network (IFAN). This deblurring process refocuses the background, ultimately restoring an image with sharp details throughout. Finally, the enhanced super-resolution generative adversarial networks (Real-ESRGAN) which specializes in images SR of realistic scenes was used to process the sharp all-in-focus image. This method results in high-quality reconstructions of both the foreground and background of large aperture images. The experimental results demonstrated that the proposed method achieved effective reconstruction of the entire large aperture images clearly, overcoming the limitations of existing methods that struggle to reconstruct defocused regions. This significantly enhances the quality and resolution of large aperture images. Specifically, when FBSDSR is integrated with Real-ESRGAN, the PSNR, LPIPS, NIQE, and hyperIQA metrics were improved by approximately 2.2 %, 45.1 %, 34.7 %, and 10.9 % respectively.

Solvent-vapor-triggered crystallization of a ZIF-90 membrane with versatile separation properties towards light hydrocarbons

Membrane separation has been well acknowledged as a forward-looking technology for hydrocarbon separation. Zeolitic imidazole framework-90 (ZIF-90) with effective pore size of 5.0 Å is a promising membrane material for hydrocarbon separation. Owing to the enormous challenges facing the fabrication process, the research on the ZIF-90 polycrystalline membrane is fairly underexplored. Herein we report a solvent-vapor-triggered crystallization strategy for the production of ZIF-90 membranes. The resultant ZIF-90 membrane had a typical polycrystalline membrane structure where the regular ZIF-90 grains propagated inside the whole porous support. Intriguingly, the membrane displayed two obvious sharp cut-off regions falling between the C3H6/C3H8 and n-C4H10/i-C4H10 gas pairs, respectively. The ZIF-90 membrane achieved ultrafast and selective permeation of C3H6 from the C3H6/C3H8 mixture. The C3H6 flux was about 3.4 kg·m−2·h−1 which was comparable to the commercial NaA zeolite membrane for organic solvent dehydration. Further, the distinctive gas transport kinetic nature enabled the ZIF-90 membranes to exclude i-C4H10 and thus harvest unprecedented n-/i-C4H10 separation ability in high-temperature regions. As the temperature elevated from 25 to 150 °C, the n-C4H10 permeance was enhanced from 3.0 × 10−9 to 12 × 10−9 mol·m−2·s−1·Pa−1 and the n-C4H10/i-C4H10 separation factors was improved from 63 to 95, respectively. The high permeance and permselectivity at industrially relevant high temperatures and pressures make ZIF-90 membrane attractive for industrial light hydrocarbon separation.

Impacts of spatial heterogeneity of anthropogenic aerosol emissions in a regionally refined global aerosol–climate model

Abstract. Emissions of anthropogenic aerosol and their precursors are often prescribed in global aerosol models. Most of these emissions are spatially heterogeneous at model grid scales. When remapped from low-resolution data, the spatial heterogeneity in emissions can be lost, leading to large errors in the simulation. It can also cause the conservation problem if non-conservative remapping is used. The default anthropogenic emission treatment in the Energy Exascale Earth System Model (E3SM) is subject to both problems. In this study, we introduce a revised emission treatment for the E3SM Atmosphere Model (EAM) that ensures conservation of mass fluxes and preserves the original emission heterogeneity at the model-resolved grid scale. We assess the error estimates associated with the default emission treatment and the impact of improved heterogeneity and mass conservation in both globally uniform standard-resolution (∼ 165 km) and regionally refined high-resolution (∼ 42 km) simulations. The default treatment incurs significant errors near the surface, particularly over sharp emission gradient zones. Much larger errors are observed in high-resolution simulations. It substantially underestimates the aerosol burden, surface concentration, and aerosol sources over highly polluted regions, while it overestimates these quantities over less-polluted adjacent areas. Large errors can persist at higher elevation for daily mean estimates, which can affect aerosol extinction profiles and aerosol optical depth (AOD). We find that the revised treatment significantly improves the accuracy of the aerosol emissions from surface and elevated sources near sharp spatial gradient regions, with significant improvement in the spatial heterogeneity and variability of simulated surface concentration in high-resolution simulations. In the next-generation E3SM running at convection-permitting scales where the resolved spatial heterogeneity is significantly increased, the revised emission treatment is expected to better represent the aerosol emissions as well as their lifecycle and impacts on climate.

Crosswise heat flux and temperature profiles over downstream surface of gas-fueled pool fires in relatively strong wind

This paper reveals the crosswise profiles of heat flux and temperature over the downstream surface (ground) of a pool fire in relative strong wind, which was not well addressed in the past. Two square gaseous burners (25 cm, 30 cm) are used with propane as the fuel producing different heat release rates to simulate pool fires. The wind speed ranges from 1.5 m/s to 4 m/s (with 0.5 m/s intervals for various cases), concerning relatively strong wind conditions (Fr > 0.87). The crosswise heat flux profile first shows to be nearly stable (fluctuation less than 20 %) in the continuous flame region, then a sharp decrease in the intermittent flame region and finally goes to near zero. The temperature profile shows a similar trend as heat flux. For the near stable region, the flame boundary layer goes into the counter-rotating streamwise vortex pairs to form the streak like flames. And the counter-rotating pair (CVP) on the flame makes the streaks on the sides of the burner to be even larger, as verified by the CFD simulation. The heat flux is different under the streaks and troughs of the flame (higher under trough than in streaks), which interprets the fluctuation in the nearly stable region. Then the sharp decrease happens in the intermittent flame region. The flame half-width is obtained, which sits at about the middle of the sharp decrease region. And finally, for the position further away in the crosswise direction, the profile turns to be nearly zero. The crosswise profiles can be well represented by a Boltzmann function. The obtained experimental results and the proposed functions on the crosswise profiles of heat flux and temperature provide an essential base to estimate the heat feedback to the downstream surface of a wind-driven fire.

Adaptive sampling physics-informed neural network method for high-order rogue waves and parameters discovery of the (2 + 1)-dimensional CHKP equation.

Rogue waves are important physical phenomena, which have wide applications in nonlinear optics, hydrodynamics, Bose-Einstein condensates, and oceanic and atmospheric dynamics. We find that when using the original PINNs to study rogue waves of high dimensional PDEs, the prediction performance will become very poor, especially for high-order rogue waves due to that the randomness of selection of sample points makes insufficient use of the physical information describing the local sharp regions of rogue waves. In this paper, we propose an adaptive sampling physics-informed neural network method (ASPINN), which renders the points in local sharp regions to be selected sufficiently by a new adaptive search algorithm to lead to a prefect prediction performance. To valid the performance of our method, the (2+1)-dimensional CHKP equation is taken as an illustrative example. Experimental results reveal that the original PINNs can hardly be able to predict dynamical behaviors of the high-order rogue waves for the CHKP equation, but the ASPINN method can not only predict dynamical behaviors of these high-order rogue waves, but also greatly improve the prediction efficiency and accuracy to four orders of magnitude. Then, the data-driven inverse problem for the CHKP equation with different levels of corrupted noise is studied to show that the ASPINN method has good robustness. Moreover, some main factors affecting the neural network performance are discussed in detail, including the size of training data, the number of layers of the neural network, and the number of neurons per layer.

Bessel-Gauss coherently combined beams.

The application of a conical wavefront in the near field of the tiled aperture coherent beam combination (CBC) produces a segmented, similar to Bessel-Gauss irradiance pattern (BG-CBC), in the far field. The properties of such a structured optical field were numerically investigated. In contrast to that for the classical CBC, the power diffracted beyond the 'zero' BG-CBC diffraction order is more smoothly and homogenously distributed, not evidencing sharp maxima and dark regions typical for CBC. The novelty of the BG-CBC with segmented conical wavefront is a simple way of caustics elongation and redistribution of power density for the same CBC architecture.

Comparisons on the thermal and entropic performance of helical tubes with varying cross-sections with constant wall temperature

This study investigates the thermal-hydraulic behavior of helical tubes with different cross-section types. The flow was considered to be in a turbulent flow regime, and the wall temperature of the tube was considered to be constant. Circle, horizontal oval, vertical oval, square, horizontal rectangle, vertical rectangle, equilateral triangle, and hexagons were eight cross-section types assessed in this study. Findings demonstrated that across the evaluated range of mass flow rates, cases with triangular cross-sections had the highest friction factor values. Also, it was observed that these cases have the largest and the most intense vorticity among all other cases. It was revealed that cases with sharp regions include vortices that increase the loss of kinetic energy. In circular cross-section and triangular cross-section examples, the Nu number was most varied. There is a 58% difference between maximum Nu values for circular and triangular cross-sections. The case with a circular cross-section and a mass flow rate of 2 kg/s exhibited the highest PEC factor value of approximately 1.001. Finally, it was determined that a circle cross-section is the best according to the first law of thermodynamics, but a triangular cross-section performed 52% better when compared to other cross-section forms according to the second law of thermodynamics.

Robust multi-scale weighting-based edge-smoothing filter for single image dehazing

The guided image filter (GIF) and weighted guided image filter (WGIF) are local linear model-based good edge-preserving filters. However, due to fixed regularization parameter, they suffer from halo artifacts (morphological artifacts) in the sharp regions. To overcome this issue, a robust multi-scale weighting-based edge-smoothing filter (RMWEF) for single image dehazing is proposed in this paper. It removes morphological artifacts and over-smoothness strongly and preserves edge information precisely in both flat and sharp regions. The proposed dehaze method has four-steps. First, initial transmission map and atmospheric map are estimated by using a novel dark channel prior (DCP) method. Then, the morphological artifacts of initial transmission map are reduced by using non-local haze line averaging (NL-HLA) method. In the third step, transmission map is refined by using the proposed RMWEF. Finally, the haze free image is restored. Theoretical and experimental analysis proves that the proposed algorithm produce effective dehaze results quicker than the existing methods.

Wrinkling and developable cones in centrally confined sheets.

Thin sheets respond to confinement by smoothly wrinkling or by focusing stress into small, sharp regions. From engineering to biology, geology, textiles, and art, thin sheets are packed and confined in a wide variety of ways, and yet fundamental questions remain about how stresses focus and patterns form in these structures. Using experiments and molecular dynamics simulations, we probe the confinement response of circular sheets, flattened in their central region and quasistatically drawn through a ring. Wrinkles develop in the outer, free region, then are replaced by a truncated cone, which forms in an abrupt transition to stress focusing. We explore how the force associated with this event, and the number of wrinkles, depend on geometry. Additional cones sequentially pattern the sheet until axisymmetry is recovered in most geometries. The cone size is sensitive to in-plane geometry. We uncover a coarse-grained description of this geometric dependence, which diverges depending on the proximity to the asymptotic d-cone limit, where the clamp size approaches zero. This paper contributes to the characterization of general confinement of thin sheets, while broadening the understanding of the d cone, a fundamental element of stress focusing, as it appears in realistic settings.

Dynamics near Couette flow for the β-plane equation

In this paper, we study stationary structures near the planar Couette flow in Sobolev spaces on a channel T×[−1,1], and asymptotic behavior of Couette flow in Gevrey spaces on T×R for the β-plane equation. Let T>0 be the horizontal period of the channel and α=2πT be the wave number. We obtain a sharp region O in the whole (α,β) half-plane such that non-shear traveling waves do not exist for (α,β)∈O and such traveling waves indeed exist for (α,β) in the remaining regions, near Couette flow for H≥5 velocity perturbation. The borderlines between the region O and its remaining are determined by two curves of the principal eigenvalues of singular Rayleigh-Kuo operators. Our results reveal that there exists β⁎>0 such that if |β|≤β⁎, then non-shear traveling waves do not exist for any T>0, while if |β|>β⁎, then there exists a critical period Tβ>0 so that such traveling waves exist for T∈[Tβ,∞) and do not exist for T∈(0,Tβ), near Couette flow for H≥5 velocity perturbation. This contrasting dynamics plays an important role in studying the long time dynamics near Couette flow with Coriolis effects. Moreover, for any β≠0 and T>0, we prove that there exist no non-shear traveling waves with traveling speeds converging in (−1,1) near Couette flow for H≥5 velocity perturbation, in contrast to this, we construct non-shear stationary solutions near Couette flow for H<52 velocity perturbation, which is a generalization of Theorem 1 in [22] but the construction is more difficult due to the Coriolis effects. Finally, we prove nonlinear inviscid damping for Couette flow in some Gevrey spaces by extending the method of [4] to the β-plane equation on T×R.

Symbiotic dynamics in living liquid crystals.

An amalgam of nematic liquid crystals and active matter, referred to as living liquid crystals, is a promising self-healing material with futuristic applications for targeted delivery of information and microcargo. We provide a phenomenological model to study the symbiotic pattern dynamics in this contemporary system using the Toner-Tu model for active matter (AM), the Landau-de Gennes free energy for liquid crystals (LCs), and an experimentally motivated coupling term that favours coalignment of the active and nematic components. Our extensive theoretical studies unfold two novel steady states, chimeras and solitons, with sharp regions of distinct orientational order that sweep through the coupled system in synchrony. The induced dynamics in the passive nematic is unprecedented. We show that the symbiotic dynamics of the AM and LC components can be exploited to induce and manipulate order in an otherwise disordered system.

Equivalence of Besov spaces on p.c.f. self-similar sets

AbstractOn post-critically finite self-similar sets, whose walk dimensions of diffusions are in general larger than 2, we find a sharp region where two classes of Besov spaces, the heat Besov spaces $B^{p,q}_\sigma (K)$ and the Lipschitz–Besov spaces $\Lambda ^{p,q}_\sigma (K)$ , are identical. In particular, we provide concrete examples that $B^{p,q}_\sigma (K)=\Lambda ^{p,q}_\sigma (K)$ with $\sigma&gt;1$ . Our method is purely analytical, and does not involve heat kernel estimate.

Efficient image blur detection via hierarchical edge guidance and region complementation

Blur detection is aimed to recognize the blurry pixels from a given image, which is increasingly valued in vision-centered applications. Albeit great improvement achieved by recent deep learning-based methods, the overweight model and rough boundary still pose challenges to blur detection. In this paper, we propose a Hierarchical Edge-guided Region-complemented Network (HER-Net) to tackle the above issues in quest of a favorable accuracy–complexity trade-off. First, we propose novel olive-shaped and pear-shaped inverted bottleneck structures based on large-kernel depth-wise convolutions to build a very concise architecture. Second, we provoke and exploit region-concerned and edge-concerned morphological priors to refine the boundary. To this end, we propose a reverse-region spatial attention to mine the complementary affinities between blurry and sharp regions so as to enrich the residual details around the boundary. In addition, we propose an edge spatial attention to guide the edge-concerned cues to emphasize the features related to the boundary. Both attentions are embedded into the model with hierarchical manners. Extensive experiments on three benchmark datasets demonstrate that the proposed method can achieve better detection performance using fewer parameters and lower floating-point operations compared to competitive methods. It proves the efficiency and effectiveness of our method in blur detection task.

Quantifying the role of higher order neoclassical corrections to gyrokinetics in tokamak plasmas

We implement the higher order gyrokinetic theory developed in Dudkovskaia et al (2023 Plasma Phys. Control. Fusion 65 045010), reduced to the limit of , where B 0 is the tokamak equilibrium magnetic field, and B ϑ is its poloidal component, in the local gyrokinetic turbulence code, GS2. The principal motivation for this extension is to quantify the importance of neoclassical flows in electromagnetic gyrokinetics, with a particular interest in sharp pressure gradient regions where the bootstrap current becomes dominant. To incorporate neoclassical equilibrium physics, GS2 is coupled to NEO, a multi-species drift kinetic solver. It is found that the regions where microinstabilities are most likely to be influenced by neoclassical equilibrium effects are in a pedestal plasma and a spherical tokamak core plasma.

Turbulent Anisotropy and Length Scale Variation Over Multiple Shaped Structure

AbstractThe turbulent flow characteristics over bed-mounted three different cubical shape bluff bodies are examined experimentally in the water channel facility. The steady and fluctuating flow fields are investigated to analyze the effect of corner radius and shapes of the bluff body on turbulent flow structure, particularly in the wake region. It is found that the sharp corner region significantly impacts the flow separation and alters the characteristics of the shear-layer flow. In particular, the relatively suitable change in geometry resulted in a remarkable variation of the mean flow in the wake is observed. The anisotropic nature of flow is analyzed using the turbulence triangle for the different cubical structures. The variation of the turbulent length scales is presented in the near- and far-wake regions of the submerged obstacles.

Energetic preference and topological constraint effects on the formation of DNA twisted toroidal bundles.

DNA toroids are compact torus-shaped bundles formed by one or multiple DNA molecules being condensed from the solution due to various condensing agents. It has been shown that the DNA toroidal bundles are twisted. However, the global conformations of DNA inside these bundles are still not well understood. In this study, we investigate this issue by solving different models for the toroidal bundles and performing replica-exchange molecular dynamics (REMD) simulations for self-attractive stiff polymers of various chain lengths. We find that a moderate degree of twisting is energetically favorable for toroidal bundles, yielding optimal configurations of lower energies than for other bundles corresponding to spool-like and constant radius of curvature arrangements. The REMD simulations show that the ground states of the stiff polymers are twisted toroidal bundles with the average twist degrees close to those predicted by the theoretical model. Constant-temperature simulations show that twisted toroidal bundles can be formed through successive processes of nucleation, growth, quick tightening, and slow tightening of the toroid, with the two last processes facilitating the polymer threading through the toroid's hole. A relatively long chain of 512 beads has an increased dynamical difficulty to access the twisted bundle states due to the polymer's topological constraint. Interestingly, we also observed significantly twisted toroidal bundles with a sharp U-shaped region in the polymer conformation. It is suggested that this U-shaped region makes the formation of twisted bundles easier by effectively reducing the polymer length. This effect can be equivalent to having multiple chains in the toroid.

Compressive failure analysis of in-situ Al-Mg2Si composites: Experiment and finite element modelling

Al-Mg2Si composites have been developed through gravity die-casting techniques. The influence of Mg2Si reinforcement concentration on strength, micromechanics and failure initiation of Al-Mg2Si composites subjected to compression has been studied. The compressive strength and brittle fracture of the Al-Mg2Si composite increase and strain decrease with an increase in Mg2Si concentration. The eutectic and primary Mg2Si phase sharp corners and narrow sections of Mg2Si are fracture initiation sites, and the Al phase nearby the eutectic and Mg2Si phase sharp corners and narrow Al phase regions between two Mg2Si islands are void initiation sites in the composites subjected to compression.

Robust watermarking based on blur‐guided JND model for macrophotography images

Macrophotography Images (MPIs) have recently emerged as an active topic due to the development of mobile phone camera technology. A large number of MPIs have been rapidly increasing in many rich visual services, such as smartphones or high-definition monitors. MPIs are often composed of sharp macroimage and blur background, which exhibit different perceptual properties that often lead to different just noticeable difference (JND) estimation. Inspired by this, we formulate the blur concealment (BC) as another factor to determine the total masking effect: the interaction is relatively straightforward with a limited masking effect in the sharp regions, and is complicated with a strong masking effect in the blur parts. Furthermore, texture and orientation adaption and color information weighting are separately incorporated into the contrast masking and color masking. Finally, considering both BC and masking effects, a novel robust watermarking framework based on the proposed blur-guided JND model for MPIs, targeting at further improving the MPIs copyright protection performance. Extensive experiments on MP2020 and Blur Detection data sets show that the applicability of the proposed JND model in the scenario of perceptually MPIs watermarking, and our proposed scheme can outperform the state-of-the-art watermarking schemes by providing better robustness performance at the uniform visual quality.