Uniform Domain Research Articles

Quasiconformal Mappings from Uniform Domains onto John Domains

AbstractWe establish nine equivalent conditions for a bounded domain which is quasiconformally equivalent to a bounded uniform domain with a connected boundary to be a John domain. These conditions connect the John property of the domain with other geometric properties, and with the quasisymmetry of quasiconformal mappings onto it. Our result is a generalization of the main result of Heinonen (Rev. Math. Iber. 5: 97–123, 1989), where a similar question was studied in the special case of the unit ball.

S&Reg v2: a probabilistically complete sampling-based planner to solve multi-goal path finding problem via multi-task learning networks

In this paper, we present a variant of our previous research on multi-goal path finding problem, focusing on finding a feasible and closed path to visit a sequence of goals in an environment with obstacles. The newly proposed method, Segmentation & Regression v2 (S&Reg v2), employs multi-task learning networks to generate regions and estimates of lengths of local paths between pairwise goals. Importantly, the estimates are performed as weights for a complete graph to compute the visiting sequence. Subsequently, the path-finding process is executed following the sequence, and the predicted region works as a sampling domain to enhance the search speed. A hybrid sampler is designed by combining a uniform domain with the region domain, ensuring successful samples, even if the region is disconnected. Besides, a selection rule is introduced to balance the sampling domain during different searching stages. A proof of probabilistic completeness of the S&Reg v2 method is given. Simulations verify the superior performance of the S&Reg v2 method, demonstrating a reduction in calculation time ranging from 3.9% to 13.0%. Furthermore, a practical scenario validates the reliability of S&Reg v2, achieving a 15.0% improvement in success rate and a 9.7% reduction in calculation time.

ScAlInN/GaN heterostructures grown by molecular beam epitaxy

Rare-earth (RE) elements doped III-nitride semiconductors have garnered attention for their potential in advanced high-frequency and high-power electronic applications. We report on the molecular beam epitaxy of quaternary alloy ScAlInN, which is an encouraging strategy to improve the heterointerface quality when grown at relatively low temperatures. Monocrystalline wurtzite phase and uniform domain structures are achieved in ScAlInN/GaN heterostructures, featuring atomically sharp interface. ScAlInN (the Sc content in the ScAlN fraction is 14%) films with lower In contents (less than 6%) are nearly lattice matched to GaN, exhibiting negligible in-plane strain, which are excellent barrier layer candidates for GaN high electron mobility transistors (HEMTs). Using a 15-nm-thick Sc0.13Al0.83In0.04N as a barrier layer in GaN HEMT, a two-dimensional electron gas density of 4.00 × 1013 cm−2 and a Hall mobility of 928 cm2/V s, with a corresponding sheet resistance of 169 Ω/□, have been achieved. This work underscores the potential of alloy engineering to adjust lattice parameters, bandgap, polarization, interfaces, and strain in emerging RE-III-nitrides, paving the way for their use in next-generation optoelectronic, electronic, acoustic, and ferroelectric applications.

Magnetic Structure-Dependent Spin Texture Lattice in Hexagonal MnFeCoGe Magnets.

Topological spin textures are of great significance in magnetic information storage and spintronics due to their high storage density and low drive current. In this work, the transformation of magnetic configuration from chaotic labyrinth domains to uniform stripe domains was observed in MnFe1-xCoxGe magnets. This change occurs due to the noncollinear magnetic structure switching to a uniaxial ferromagnetic structure with increasing Co content, as identified by neutron diffraction results and Lorentz transmission electron microscopy (L-TEM). Of utmost importance, a hexagonal lattice of high-density robust type-II magnetic bubble lattice was established for x = 0.8 through out-of-plane magnetic field stimulation and field-cooling. The dimensions of the type-II magnetic bubbles were found to be tuned by the sample thickness. Therefore, the stabilization of complex magnetic spin textures, associated with enhanced uniaxial ferromagnetic interaction and magnetic dipole-dipole interaction in MnFe1-xCoxGe through magnetic structure manipulation, as further confirmed by the micromagnetic simulations, will provide a convenient and efficient strategy for designing topological spin textures with potential applications in spintronic devices.

Layered seabed effects on buried pipeline response to ice gouging

In ice gouging analyses, the seabed is often simplified as a uniform material domain, over-looking the potential complexities inherent in layered seabed formations, which are wide-spread in numerous Arctic regions. This study investigates the pipeline response into the distinct seabed configurations, including layered soft over stiff clay, layered stiff over soft clay, and uniformly soft and uniformly stiff compositions, to ice gouging. This was achieved through comprehensive large deformation finite element (LDFE) analysis, employing a Coupled Eulerian Lagrangian (CEL) algorithm. Incorporation of the strain-rate dependency and strain-softening effects involved the development of a user-defined subroutine and incremental update of the undrained shear strength within the Abaqus software. The pipeline is explicitly incorporated into the model, allowing for a detailed investigation of its response to ice gouging phenomena within these layered seabed scenarios. This research demonstrates that simplifying a layered seabed into a uniform can be misleading. Such an approach can lead to significant errors, potentially overestimating or underestimating pipeline response to ice gouging. By incorporating these complexities, engineers can develop more optimized designs with enhanced safety margins in Arctic environments prone to ice gouging phenomena.

Weighted estimates for the Bergman projection on planar domains

We investigate weighted Lebesgue space estimates for the Bergman projection on a simply connected planar domain via the domain’s Riemann map. We extend the bounds which follow from a standard change-of-variable argument in two ways. First, we provide a regularity condition on the Riemann map, which turns out to be necessary in the case of uniform domains, in order to obtain the full range of weighted estimates for the Bergman projection for weights in a Békollè-Bonami-type class. Second, by slightly strengthening our condition on the Riemann map, we obtain the weighted weak-type (1,1) estimate as well. Our proofs draw on techniques from both conformal mapping and dyadic harmonic analysis.

Optimizing the Ferroelectric Performance of Hf0.5Zr0.5O2 Epitaxial Film by La0.67Sr0.33MnO3 Capping Layer

AbstractHafnium‐oxide‐based ferroelectrics have garnered considerable research interest, primarily for their robust ferroelectricity at the nanoscale and their high compatibility with complementary metal‐oxide‐semiconductors processes. However, the impact of electrodes on the ferroelectric properties of hafnium‐oxide layer, particularly that of top electrodes, is not yet fully understood even in the simplest capacitor geometry. In this study, the La0.67Sr0.33MnO3/Hf0.5Zr0.5O2 (LSMO/HZO) epitaxial heterostructure is utilized as a model system to conduct a systematic comparative study on ferroelectricity between the LSMO/HZO (H‐LS) bilayer and LSMO/HZO/LSMO (LS‐H‐LS) trilayer samples. In comparison to the H‐LS sample, the LS‐H‐LS sample exhibits a more uniform polar domain configuration and larger ferroelectric polarization. Moreover, the LS‐H‐LS sample exhibits significant improvements in leakage, endurance, and retention. These substantial enhancements in ferroelectricity are likely due to interfacial stress imposed by the LSMO capping layer and its capacity to accommodate extra oxygen vacancies. These results underscore the pivotal role of oxide‐based top electrodes in determining the ferroelectricity of hafnium‐oxide‐based heterostructures, providing crucial insights for optimizing the performance of innovative ferroelectric devices.

Poling induced changes in polarization domain structure of polymer ferroelectrics for application in organic thin film transistors

While electrical poling of organic ferroelectrics has been shown to improve device properties, there are challenges in visualizing accompanying structural changes. We observe poling induced changes in ferroelectric domains by applying differential phase contrast (DPC) imaging in the scanning transmission electron microscope, a method that has been used to observe spatial distributions of electromagnetic fields at the atomic scale. In this work, we obtain DPC images from unpoled and electrically poled polyvinylidene fluoride trifluorethylene films and compare their performance in polymer thin film transistors. The vertically poled films show uniform domains throughout the bulk compared to the unpoled film with a significantly higher magnitude of the overall polarization. Thin film transistors comprising a donor–acceptor copolymer as the active semiconductor layer show improved performance with the vertically poled ferroelectric dielectric film compared with the unpoled ferroelectric dielectric film. A poling field of 80–100 MV/m for the dielectric layer yields the best performing transistors; higher than 100 MV/m is seen to degrade the transistor performance. The results are consistent with a reduction in deleterious charge carrier scattering from ferroelectric domain boundaries or interfacial dipoles arising from electrical poling.

Obstacle Problems with Double Boundary Condition for Least Gradient Functions in Metric Measure Spaces

AbstractIn the setting of a metric space equipped with a doubling measure supporting a (1, 1)-Poincaré inequality, we study the problem of minimizing the BV-energy in a bounded domain $$\Omega $$ Ω of functions bounded between two obstacle functions inside $$\Omega $$ Ω , and whose trace lies between two prescribed functions on the boundary. If the class of candidate functions is nonempty, we show that solutions exist for continuous obstacles and continuous boundary data when $$\Omega $$ Ω is a uniform domain whose boundary is of positive mean curvature in the sense of Lahti, Malý, Shanmugalingam, and Speight (2019). While such solutions are not unique in general, we show the existence of unique minimal solutions. Since candidate functions need not agree outside of the domain, standard compactness arguments fail to provide existence of weak solutions as they are defined for the problem with single boundary condition. To overcome this, we introduce a class of $$ \varepsilon $$ ε -weak solutions as an intermediate step. Our existence results generalize those of Ziemer and Zumbrun (1999), who studied this problem in the Euclidean setting with a single obstacle and single boundary condition.

Gromov hyperbolicity and unbounded uniform domains

Gromov hyperbolicity and unbounded uniform domains

Heat kernel for reflected diffusion and extension property on uniform domains

Heat kernel for reflected diffusion and extension property on uniform domains

Trace Operator on von Koch’s Snowflake

AbstractWe study properties of the boundary trace operator on the Sobolev space $$W^1_1(\Omega )$$ W 1 1 ( Ω ) . Using the density result by Koskela and Zhang (Arch. Ration. Mech. Anal. 222(1), 1-14 2016), we define a surjective operator $$Tr: W^1_1(\Omega _K)\rightarrow X(\Omega _K)$$ T r : W 1 1 ( Ω K ) → X ( Ω K ) , where $$\Omega _K$$ Ω K is von Koch’s snowflake and $$X(\Omega _K)$$ X ( Ω K ) is a trace space with the quotient norm. Since $$\Omega _K$$ Ω K is a uniform domain whose boundary is Ahlfors-regular with an exponent strictly bigger than one, it was shown by L. Malý (2017) that there exists a right inverse to Tr, i.e. a linear operator $$S: X(\Omega _K) \rightarrow W^1_1(\Omega _K)$$ S : X ( Ω K ) → W 1 1 ( Ω K ) such that $$Tr \circ S= Id_{X(\Omega _K)}$$ T r ∘ S = I d X ( Ω K ) . In this paper we provide a different, purely combinatorial proof based on geometrical structure of von Koch’s snowflake. Moreover we identify the isomorphism class of the trace space as $$\ell _1$$ ℓ 1 . As an additional consequence of our approach we obtain a simple proof of the Peetre’s theorem (Special Issue 2, 277-282 1979) about non-existence of the right inverse for domain $$\Omega $$ Ω with regular boundary, which explains Banach space geometry cause for this phenomenon.

Weather-Domain Transfer-Based Attention YOLO for Multi-Domain Insulator Defect Detection and Classification in UAV Images.

Insulator defect detection of transmission line insulators is an important task for unmanned aerial vehicle (UAV) inspection, which is of immense importance in ensuring the stable operation of transmission lines. Transmission line insulators exist in complex weather scenarios, with small and inconsistent shapes. These insulators under various weather conditions could result in low-quality images captured, limited data numbers, and imbalanced sample problems. Traditional detection methods often struggle to accurately identify defect information, resulting in missed or false detections in real-world scenarios. In this paper, we propose a weather domain synthesis network for extracting cross-modality discriminative information on multi-domain insulator defect detection and classification tasks. Firstly, we design a novel weather domain synthesis (WDSt) module to convert various weather-conditioned insulator images to the uniform weather domain to decrease the existing domain gap. To further improve the detection performance, we leverage the attention mechanism to construct the Cross-modality Information Attention YOLO (CIA-YOLO) model to improve the detection capability for insulator defects. Here, we fuse both shallow and deep feature maps by adding the extra object detection layer, increasing the accuracy for detecting small targets. The experimental results prove the proposed Cross-modality Information Attention YOLO with the weather domain synthesis algorithm can achieve superior performance in multi-domain insulator datasets (MD-Insulator). Moreover, the proposed algorithm also gives a new perspective for decreasing the multi-domain insulator modality gap with weather-domain transfer, which can inspire more researchers to focus on the field.

A Graph Neural Network Approach with Improved Levenberg–Marquardt for Electrical Impedance Tomography

Electrical impedance tomography (EIT) is a non-invasive imaging method that allows for the acquisition of resistivity distribution information within an object without the use of radiation. EIT is widely used in various fields, such as medical imaging, industrial imaging, geological exploration, etc. Presently, most electrical impedance imaging methods are restricted to uniform domains, such as pixelated pictures. These algorithms rely on model learning-based image reconstruction techniques, which often necessitate interpolation and embedding if the fundamental imaging model is solved on a non-uniform grid. EIT technology still confronts several obstacles today, such as insufficient prior information, severe pathological conditions, numerous imaging artifacts, etc. In this paper, we propose a new electrical impedance tomography algorithm based on the graph convolutional neural network model. Our algorithm transforms the finite-element model (FEM) grid data from the ill-posed problem of EIT into a network graph within the graph convolutional neural network model. Subsequently, the parameters in the non-linear inverse problem of the EIT process are updated by using the improved Levenberg—Marquardt (ILM) method. This method generates an image that reflects the electrical impedance. The experimental results demonstrate the robust generalizability of our proposed algorithm, showcasing its effectiveness across different domain shapes, grids, and non-distributed data.

Investigation into the role of Co doping in the microstructure and magnetic characteristics of nanocrystalline Nd-Ce-La-Fe-B alloys

In this study, [Nd0.5(Ce0.5La0.5)0.5]17Fe78-xCoxB6 (x = 0 ∼ 1.5 at. %) ribbons are prepared via a direct melt-spun (wheel speed of 28 m/s). The impacts of Co doping on the crystal structure, Curie temperature Tc, magnetic parameters (Br, Hci and (BH)max) of [Nd0.5(Ce0.5La0.5)0.5]17Fe78-xCoxB6 alloys are systematically assessed. X-ray diffraction patterns and Rietveld refinement data demonstrate that the exclusive presence of a pure hard magnetic 2:14:1 phase without any secondary phases across all samples. Compared with Co-free sample (x = 0), the Br, Hci and (BH)max of Co-doped with x = 1 are increased by 15.0 %, 4.6 % and 42.9 %, respectively. The coercivity mechanism in the [Nd0.5(Ce0.5La0.5)0.5]17Fe78-xCoxB6 alloys arises from the integration of reversed domain nucleation and robust pinning of domain walls. The magnetic domain structure and quantitative analysis based on the microstructure and demagnetization behavior are conducted to investigate the exchange coupling interactions among the 2:14:1 grains. This exploration reveals that the enhanced magnetic properties stem from the refinement of the 2:14:1 phase's grains, leading to more uniform and smaller interaction domains.

Active carbon monoliths from soft brown coal: A systematic study of their preparation, pore structure modification and characterization

High surface area active carbons in a ‘honeycomb monolith’ (HM) configuration can be prepared directly from soft brown coal by a novel approach. Kneading the coal into a plasticine consistency enables it to be extruded in HM form, then dried, carbonized and activated, retaining its structural integrity throughout these steps. Unlike higher rank coals, soft brown coal, which inherently contains relatively high oxygen functional group concentrations and high moisture contents, develops a strong H-bonding network during kneading. This opens the way to a novel and simpler method of preparing activated carbons in a monolith configuration. A systematic study was therefore conducted to evaluate the potential of these monoliths for being converted into higher value activated carbons by a low-cost process. Carbon honeycomb monoliths HMs from brown coal were modified by carbon dioxide (CO2) activation with a uniform domain size over a wider range of activation conditions (1–3 h, 750–950 °C) and the products were characterized by N2 adsorption (surface area and porosity), SEM, TEM, Raman spectroscopy, XPS and elemental analysis. The optimum conditions for development of porosity, aromaticity and a graphitizing structure were activation at 900 °C for 3 h. Interestingly, higher temperatures did not yield additional benefits. These materials should be useful in applications requiring highly ordered carbon.

Microstructural evolution and enhanced magnetic properties of FeCoNiZrx medium entropy alloy films

Medium/High entropy alloys (M/HEAs) based on the FeCoNi system have gained significant attention due to their outstanding magnetic and electrical properties. In this study, the FeCoNiZrx (x = 0, 0.2, 0.4, 0.6, 0.8, 1) MEA films were prepared using the magnetron sputtering method. The effect of Zr on the structure and soft magnetic properties is studied. As the Zr content increases, the films transform from the face-centered cubic (FCC) phase to the amorphous phase. This study shows that FeCoNiZr0.4 film exhibits excellent combined properties, including a high magnetization saturation (Ms) of 1127.8 emu/cm3, a minimum coercivity (Hc) of 0.96 Oe, and a high resistivity of 147 μΩ·cm, which is superior to the Permalloy and soft magnetic materials reported in other articles. Combined structural analyses show that the FeCoNiZr0.4 film has the finest particle size, amorphous structure, and continuous and uniform magnetic domains, decreasing the pinning effect on magnetic domains. These results enhance the magnetic properties of FeCoNiZr0.4 film.

Triebel–Lizorkin regularity and bi-Lipschitz maps: Composition operator and inverse function regularity

We study the stability of Triebel–Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse function of a Triebel–Lizorkin bi-Lipschitz map in Lipschitz domains. To obtain the results we provide an equivalent norm for the Triebel–Lizorkin spaces with fractional smoothness in uniform domains in terms of the first-order difference of the last weak derivative available averaged on balls.

Tunable magnetic properties and magnetic domain structure of nanocomposite permanent materials via Ti addition into Nd-Fe-Co-B alloys

In this work, the effect of tunable Ti content on the microstructure, magnetic domain structure, and magnetic properties of as-spun and annealed Nd9.5Fe79-xCo5TixB6.5(x = 0,1,2,3,4) alloys at the quench speed of 18 m/s were investigated. For the as-spun alloy, augmenting the Ti content enhanced the initial crystallization temperature and the stability of the amorphous phase. Simultaneously, the incorporation of Ti led to augmentation in the quantity of nanocrystals within the amorphous matrix, thereby facilitating the formation of vortex-like magnetic domains with large size but reduced the saturation magnetization Ms. For the annealed alloy, the incorporation of Ti inhibited the precipitation of α-Fe phase, refined the grain, enhanced the exchange coupling between the soft and hard magnetic phase and facilitated the formation of smaller, more uniform vortex-like magnetic domains, These alterations were beneficial to improve the comprehensive magnetic properties. Furthermore, the addition of tunable Ti resulted in a remarkable impact on coercivity enhancement. The coercivity value exhibited a significant increase of 54.30%, surging from 374.24 kA/m to 577.51 kA/m. Upon a thorough analysis of the magnetic domains and coercive force mechanisms, it was ascertained that the introduction of Ti substantially augmented the creation of vortex-like domains. These domains effectively impede domain motion, consequently elevating the material's coercivity.

Solving a Dirichlet problem on unbounded domains via a conformal transformation

In this paper, we solve the p-Dirichlet problem for Besov boundary data on unbounded uniform domains with bounded boundaries when the domain is equipped with a doubling measure satisfying a Poincaré inequality. This is accomplished by studying a class of transformations that have been recently shown to render the domain bounded while maintaining uniformity. These transformations conformally deform the metric and measure in a way that depends on the distance to the boundary of the domain and, for the measure, a parameter p. We show that the transformed measure is doubling and the transformed domain supports a Poincaré inequality. This allows us to transfer known results for bounded uniform domains to unbounded ones, including trace results and Adams-type inequalities, culminating in a solution to the Dirichlet problem for boundary data in a Besov class.