Domain Shape Research Articles

Pattern formation on regular polygons and circles

We investigate the formation of Turing patterns on regular polygonal domains, as the number of edges grow, leading to the limiting case of the circle. Using linear and weakly nonlinear analysis, and evidence by simulations, we demonstrate how the domain shape can fundamentally change the expected bifurcation structure. Specifically, on the square domain we are able to derive pitchfork bifurcations for stripe and spot solutions, as well as show that both branches cannot bifurcate to produce stable patterns. This compares with the case of the equilateral triangle domain that causes the Turing bifurcation to be generically transcritical and, in some cases, none of the bifurcating branches are stable. Moreover, we find a monotonically increasing, but nonlinear relationship, between the minimal bifurcation area and the number of edges. Thus, patterns can occur on triangles with much smaller areas than circles. Overall, this work raises questions for researchers who are simulating applications on domains with simple shapes. Specifically, even small changes to domain geometry can have large impacts on the produced patterns; thus, domain perturbations should be considered in any sensitivity analyses.

Topological Polar Networks in Twisted Rhombohedral-Stacked Bilayer WSe2 Moiré Superlattices.

Sliding ferroelectricity enables materials with intrinsic centrosymmetric symmetry to generate spontaneous polarization via stacking engineering, extending the family of ferroelectric materials and enriching the field of low-dimensional ferroelectric physics. Vertical ferroelectric domains, where the polarization is perpendicular to atomic motion, have been discovered in twisted bilayers of inversion symmetry broken systems such as hexagonal boron nitride, graphene, and transition metal chalcogenides. In this study, we demonstrate that this symmetry breaking also induces lateral polar networks in twisted bilayer rhombohedral-stacked WSe2, as determined through symmetry considerations and vector piezoresponse force microscopy (V-PFM) results. Lateral polarization (LP) in saddle point (SP) regions forms head-to-tail triangular vortices, exhibiting elliptical domain shapes with widths up to 40 nm. The LP encloses the vertical polarization (VP), forming a network of Bloch-type merons and antimerons. Our work enhances the understanding of domain distribution and polarization orientation in moiré ferroelectrics.

Intertwined Flexoelectricity and Stacking Ferroelectricity in Marginally Twisted hBN Moiré Superlattice.

Moiré superlattices in twisted van der Waals homo/heterostructures present a fascinating interplay between electronic and atomic structures, with potential applications in electronic and optoelectronic devices. Flexoelectricity, an electromechanical coupling between electric polarization and strain gradient, is intrinsic to these superlattices because of the lattice misfit strain at the atomic scale. However, due to its weak magnitude, the effect of flexoelectricity on moiré ferroelectricity has remained underexplored. Here, the role of flexoelectricity in shaping and modulating the moiré ferroelectric patterns in twisted hBN homojunction is unveiled. Enhanced flexoelectric effects induce unique stacking ferroelectric domains with hollow triangular structures. Interlayer bubbles influence domain shape and periodicity through local electric field modulation, and tip-stress enables the reversible manipulation of domain area and polarization direction. These findings highlight the impact of flexoelectric effects on moiré ferroelectricity, offering a new tuning knob for its manipulation.

A one-time training machine learning method for general structural topology optimization

Machine learning (ML) methods have found some applications in structural topology optimization. In the existing methods, however, the ML models need to be retrained when the design domains and supporting conditions have been changed, posing a limitation to their wide applications. In this paper, we propose a one-time training ML (OTML) method for general topology optimization, where the self-attention convolutional long short-term memory (SaConvLSTM) model is introduced to update the design variables. An extension–division approach is used to enrich the training sets. By developing a splicing strategy, the training results of a small design space (i.e., a basic cell of either two- or three-dimensions) can be extended to tackling the optimization problem of a large design domain with arbitrary geometric shapes. Using the OTML method, the ML model needs to be trained for only one time, and the trained model can be used directly to solve various optimization problems with arbitrary shapes of design domains, loads, and boundary conditions. In the SaConvLSTM model, the material volume of the post-processed thresholded designs can be precisely controlled, though the control precision of the gray-scale designs might be slightly sacrificed. The effects of model parameters on the computational cost and the result quality are examined. Four examples are provided to demonstrate the high performance of this structural design method. For large-scale optimization problems, the present method can accelerate the structural form-finding process. This study holds a promise in the high-resolution structural form-finding and transdisciplinary computational morphogenesis.

The Creation of a Domain Structure Using Ultrashort Pulse NIR Laser Irradiation in the Bulk of MgO-Doped Lithium Tantalate

The fabrication of stable, tailored domain patterns in ferroelectric crystals has wide applications in optical and electronic industries. All-optical ferroelectric poling by pulse laser irradiation has been developed recently. In this work, we studied the creation of the domain structures in MgO-doped lithium tantalate by focused irradiation with a femtosecond near-infrared laser. Cherenkov-type second harmonic generation microscopy was used for domain imaging of the bulk. We have revealed the creation of enveloped domains around the induced microtracks under the action of the depolarization field. The domain growth is due to a pyroelectric field caused by a nonuniform temperature change. The domains in the bulk were revealed to have a three-ray star-shaped cross-section. It was shown that an increase in the field excess above the threshold leads to consequential changes in domain shape from a three-ray star to a triangular and a circular shape. The appearance of comb-like domains as a result of linear scanning was demonstrated. All effects were considered in terms of a kinetic approach, taking into account the domain wall motion by step generation and kink motion driven by excess of the local field over the threshold. The obtained knowledge is useful for the all-optical methods of domain engineering in ferroelectrics.

An in-depth analysis of the Radial Point Interpolation Method’s parameters in relation to the accuracy of fracture problem

The fracture problem has been modeled using Radial Point Interpolation Method (RPIM) to examine the effects of support domain size and shape parameter value on the calculation of Stress Intensity Factor (SIF). The study focuses on an edge crack problem subjected to normal load and shear loads, determining that the support domain size of ‘ α ≥ 3.5 and shape parameter value between ‘ n = 1.9 -2.1’ yield results of accuracy with error % ≤ 3 % . Additionally, research extended by varying the problem domain size and crack location to verify consistency. The findings indicate that selecting the optimal shape parameter value will ensure better accuracy over the enrichment techniques with lesser computational cost.

An improved sequential importance sampling method for structural reliability analysis of high dimensional problems

Reliability analysis for rare events has proven to be a significant challenge, particularly in non-linear and complex scenarios. Despite the effectiveness of Sequential Importance Sampling (SIS) and Subset Simulation (SUS) in addressing high-dimensional small failure probability problems, the computational burden associated with mechanical simulations for complex structures remains substantial. To address this issue, this paper introduces a novel approach referred to as SIS and Kriging Metamodel Integration (SISAK), designed for computing small failure probabilities in high dimensions. This method involves generating a small number of samples from the original distribution to construct an adaptive metamodel, which is then iteratively optimized using a series of intermediate distributions introduced by SIS. By substituting the function for intermediate distributions with a continuously optimized metamodel, the enhanced approach significantly reduces the computational load associated with mechanical model evaluations compared to the direct use of SIS. This approach does not depend on determining the most probable failure point and does not require consideration of the failure domain shape. Additionally, it inherits the advantages of SIS in addressing high-dimensional small failure probabilities, making it well-suited for structural reliability analysis of nonlinear systems, discontinuous failure domains, cascading functions, and high-dimensional problems.

Investigation of transverse exchange-springs in electrodeposited nano-heterostructured films through first-order reversal curve analysis

The prerequisite of efficient exchange-spring nano-heterostructures, i.e., tuning both hard and soft phases at a nanometer level, has posed significant preparation challenges to ensure effective exchange-coupling. Here, we present a novel approach to fabricate transverse exchange-spring nano-heterostructures using single starting material through an “in situ” electrodeposition technique at room temperature. Utilizing modified acidic bath chemistry and controlled hydrogen evolution, we successfully prepared stress-free, shiny, fine-grained amorphous, and nanocrystalline Co-rich cobalt phosphorus films. These nano-heterostructured films exhibit a unique non-collinear anisotropy-driven transverse exchange-spring behavior, investigated systematically under ambient conditions. The comprehensive functional analyses reveal that intricate interplay between in-plane (IP) anisotropy of amorphous phase and out-of-plane (OOP) anisotropy generating from a nanocrystalline structure compete with each other, while producing characteristic stripe domain structures to novel corrugated stripe domain shapes. The angle-dependent first-order reversal curve distributions demonstrate new insights into the magnetic reversal mechanisms, further confirming the non-exchange-spring and exchange-spring nature of the films depending on the prevalent interfacial exchange coupling. Formation of anisotropy-driven metastable-state due to competition between IP and OOP anisotropy at a particular OOP orientation has led the normal exchange-spring structures to a transverse exchange-spring structure. Micromagnetic simulations, in excellent agreement with experimental data, further elucidate the formation of characteristic stripe domain patterns and the influence of anisotropy on the magnetic properties. The innovative methodology and detailed functional analysis presented here offer significant understanding to the field of exchange-spring magnetic materials, including anisotropy-driven metastable states, demonstrating the potential for scalable and cost-effective fabrication of advanced nano-heterostructures with tailored magnetic properties.

Twice-topology optimized heat sinks for enhanced heat transfer performance: Numerical and experimental investigation

Since the heat dissipation problem is always confusing and hindering the computing power improvement of electronic chip, an effective thermal management strategy is critical to relieve these problems. In this work, a new twice topology optimization design method combining topology optimization and image processing to design heat sinks is presented, which extends topology optimization from 2Dimention (2D) to 3Dimention(3D). Firstly, on the horizontal design domain, the conventional topology optimization is conducted for the minimization of average temperature/standard deviation. Then the optimal shape of liquid domain is converted into 1D flow routine by thinning algorithm. After that, another topology optimization is performed on the flow channel cross-section plane to get the best cross-section shape of channels. The liquid domain of the final heat sink is then obtained by scanning the optimized flow channel cross-section along the 1 Dimension (1D) flow routine and solving the interference by introducing cylinder joints. Finally, two kinds of twice topology optimized heat sinks including TTOHS-1 with minimized temperature variation as optimal goal and TTOHS-2 with minimized average temperature as optimal goal are generated by combining the liquid domain and a cuboid using Boolean Operation. The performance of heat sinks is numerically investigated, and the results indicate that the thermal performance of TTOHS-1 and TTOHS-2 are much better than that of the traditional heat sink with straight channels (TSCHS). When Re = 689, the average temperature and the maximum temperature of the heat source surface of TTOHS-1 are decreased by 4.99 % and 6.29 % respectively, compared to the TSCHS. The Nusselt number is increased by 46.16 % while the thermal resistance is reduced by 33.13 %. At last, the thermal and flow performance of the TTOHS-1 is studied by conducting experiments, showing that the numerical results agree well with that of the experiment.

Two-dimensional conjugated metal–organic frameworks grown on a MoS2 surface

Molybdenum disulfide (MoS2) features an atomically flat surface without dangling bonds. Molecular self-assembly on this surface provides an effective route to constructing heterostructure devices. In this work, we show the successful synthesis of M3(1,4,5,8,9,12-hexaazatriphenylene, HAT)2 (M = Ni, Co) conjugated metal–organic frameworks (c-MOFs) on a MoS2 surface. In the frameworks, HAT molecules constitute a honeycomb lattice while the metal atoms constitute a Kagome lattice. The random orientations of the frameworks with respect to the substrate and irregular domain shapes indicate that the frameworks interact weakly with the MoS2. The successful synthesis of 2D c-MOFs on inert substrates opens a door for the construction of advanced 2D van der Waals heterojunctions.

Uniqueness, regularity, continuity, and stability of solutions of integral equations in irregular domains

This study explores the uniqueness, regularity, continuity, and stability of solutions to integral equations related to elliptical boundary value problems in irregular domains. Traditional methods usually consider soft boundaries, but this work extends these results to include domains with rough boundaries. By employing Sobolev spaces, especially fractional Sobolev spaces, we develop a comprehensive theoretical framework. Under appropriate conditions, the studied integral equation has a unique solution in fractional Sobolev spaces, maintaining the regularity properties of the input function. Two new theorems are introduced to strengthen the findings. The first theorem establishes that solutions are continuous with respect to perturbations in the input data. This means small changes in the input do not cause significant deviations in the solution, ensuring robustness in practical applications. The second theorem demonstrates the stability of the solutions when the domain geometry undergoes small changes. This stability is crucial for real-world scenarios where the exact shapes of domains may not be perfectly known or may vary slightly. These results significantly improve the mathematical understanding of boundary value problems in non-smooth domains. The proposed extended framework allows for more generalized applications, addressing challenges in various fields of physics and engineering. The ability to handle irregular domains with rough boundaries opens up new possibilities for modeling and solving complex problems where traditional soft boundary assumptions are not valid. This research provides a robust basis for future studies and applications, highlighting the importance of considering fractional Sobolev spaces in the analysis of integral equations.

Stress related magnetic imaging of iron-based metallic glass produced with laser beam powder bed fusion

Additive manufacturing makes the production of bulk metallic glasses possible in thicknesses exceeding the critical casting thickness. However, a crucial challenge is the build-up of thermally induced stress, often resulting in printed parts suffering from cracking. In this study, the process parameters are optimised for printing soft-magnetic metallic glass samples of an Fe-based alloy (Fe73.8P10.6Mo4.2B2.3Si2.3C6.7), using laser beam powder bed fusion. In addition, the structural and magnetic properties of as-received and heat-treated powder are investigated and compared to those of the printed samples. Kerr microscopy is used for imaging the magnetic domains on single track cross-sections produced on top of a polished printed sample. This reveals the shape of the melt pool of a single laser track, as well as the magnetic domains around it and in other regions of the printed sample. The shape and size of the magnetic domains reflect the residual stress in the sample through the effect of magneto-elastic coupling. This magnetic contrast could be used to get further insights into how to control the development of stress during the printing process.

Reconstructing the shape and material parameters of dissipative obstacles using an impedance model

In inverse scattering problems, a model that allows for the simultaneous recovery of both the domain shape and an impedance boundary condition covers a wide range of problems with impenetrable domains, including recovering the shape of sound-hard and sound-soft obstacles and obstacles with thin coatings. This work develops an optimization framework for recovering the shape and material parameters of a penetrable, dissipative obstacle in the multifrequency setting, using a constrained class of curvature-dependent impedance function models proposed by Antoine et al (2001 Asymptotic Anal. 26 257–83). We find that in certain regimes this constrained model improves the robustness of the recovery problem, compared to more general models, and provides meaningfully better obstacle recovery than simpler models. We explore the effectiveness of the model for varying levels of dissipation, for noise-corrupted data, and for limited aperture data in the numerical examples.

Integrated Framework to Model Microstructure Evolution and Decipher the Microstructure-Property Relationship in Polymeric Porous Materials.

Unraveling the microstructure-property relationship is crucial for improving material performance and advancing the design of next-generation structural and functional materials. However, this is inherently challenging because it requires both the comprehensive quantification of microstructural features and the accurate assessment of corresponding properties. To meet these requirements, we developed an efficient and comprehensive integrated modeling framework, using polymeric porous materials as a representative model system. Our framework generates microstructures using a physics-based phase-field model, characterizes them using various average and localized microstructural features, and evaluates microstructure-aware properties, such as effective diffusivity, using an efficient Fourier-based perturbation numerical scheme. Additionally, the framework incorporates machine learning methods to decipher the intricate microstructure-property relationships. Our findings indicate that the connectivity of phase channels is the most critical microstructural descriptor for determining effective diffusivity, followed by the domain shape represented by curvature distribution, while the domain size has a minor impact. This comprehensive approach offers a novel framework for assessing microstructure-property relationships in polymer-based porous materials, paving the way for the development of advanced materials for diverse applications.

Revealing the Biophysics of Lamina-Associated Domain Formation by Integrating Theoretical Modeling and High-Resolution Imaging.

The interactions between chromatin and the nuclear lamina orchestrate cell type-specific gene activity by forming lamina-associated domains (LADs) which preserve cellular characteristics through gene repression. However, unlike the interactions between chromatin segments, the strength of chromatin-lamina interactions and their dependence on cellular environment are not well understood. Here, we develop a theory to predict the size and shape of peripheral heterochromatin domains by considering the energetics of chromatin-chromatin interactions, the affinity between chromatin and the nuclear lamina and the kinetics of methylation and acetylation9in human mesenchymal stem cells (hMSCs). Through the analysis of super-resolution images of peripheral heterochromatin domains using this theoretical framework, we determine the nuclear lamina-wide distribution of chromatin-lamina affinities. We find that the extracted affinity is highly spatially heterogeneous and shows a bimodal distribution, indicating regions along the lamina with strong chromatin binding and those exhibiting vanishing chromatin affinity interspersed with some regions exhibiting a relatively diminished chromatin interactions, in line with the presence of structures such as nuclear pores. Exploring the role of environmental cues on peripheral chromatin, we find that LAD thickness increases when hMSCs are cultured on a softer substrate, in correlation with contractility-dependent translocation of histone deacetylase 3 (HDAC3) from the cytosol to the nucleus. In soft microenvironments, chromatin becomes sequestered at the nuclear lamina, likely due to the interactions of HDAC3 with the chromatin anchoring protein LAP2 β ,increasing chromatin-lamina affinity, as well as elevated levels of the intranuclear histone methylation. Our findings are further corroborated by pharmacological interventions that inhibit contractility, as well as by manipulating methylation levels using epigenetic drugs. Notably, in the context of tendinosis, a chronic condition characterized by collagen degeneration, we observed a similar increase in the thickness of peripheral chromatin akin to that of cells cultured on soft substrates consistent with theoretical predictions. Our findings underscore the pivotal role of the microenvironment in shaping genome organization and highlight its relevance in pathological conditions.

Sensitivity-matrix-independent electrical impedance tomography: Damage detection for composite materials

Carbon fiber reinforced polymer (CFRP) is widely utilized due to their superior properties. The structural health monitoring (SHM) for composite materials is crucial to prevent catastrophic failures. Electrical impedance tomography (EIT), which allows for the visualization of the conductivity distribution through the measurement of electrical parameters on the boundary, presents a potential solution for SHM. Existing studies applying EIT to CFRP concentrate on traditional linearization methods that rely on sensitivity matrix, which ignore challenges posed by non-uniform sensitivity. This paper introduces an EIT image reconstruction method that is independent of the sensitivity matrix, offering a novel way for rapid damage detection and real-time SHM. Furthermore, the domain shape transformation is achieved by conformal mapping. Simulations and experiments indicate that the sensitivity-matrix-independent EIT can avoid issues such as blurring in the central region and artifacts near the boundary caused by non-uniform distribution of the sensitivity in the CFRP damage detection.

MODELING THE DISTRIBUTION OF EMERGENCY RELEASE PRODUCTS AT A NUCLEAR POWER PLANT UNIT

Despite the fact that much attention is paid to the safe operation of nuclear power plants, there is a possibility of an accident with the release of radionuclides. This is especially true in Ukraine, where there is a threat of the damage to nuclear reactors as a result of military operations. It is impossible to research the distribution of products emergency releases radioactive substances in laboratory conditions. Therefore, the only tool for the development predicting of an accident is the modeling the spread of a radionuclides cloud. The purpose of the research is a modeling the distribution of emergency release products in a nuclear power plant unit, suitable for the operative assessment of a development an accident. Results of the research: The mathematical model of the distribution emission products of a nuclear power plant has been developed, which takes into account the value of the initial activity of emission products, the rate of the settling radioactive particles, the wind speed components, the intensity changes radionuclide emission over time. The technique for solving the boundary value problem of modeling in conditions of a complex shape of the computational domain, taking into account the presence of obstacles to the spread of emission products has been developed. The use of the velocity potential equation in evolutionary form allows us to speed up the calculation process. The chosen splitting scheme of an alternating-triangular method allows to find the speed potential according to the explicit form at each splitting step. This allowed software implementation of the CFD model. The visualized models of the emission cloud distribution allow to determine the radiation situation in any place of the emission product distribution zone. The developed model makes it possible to quickly predict the development of an accident in space and time, which makes it possible to take measures to protect people from exposure in the shortest possible time. Conclusions: The obtained emission cloud propagation models and their visualization make it possible to determine the state of environmental pollution under various initial conditions during the development of the accident.

A method of combined metamodel and subset simulation for reliability analysis of rare events

Reliability analysis of large, complex structures with high reliability has always been a challenging task. The Subset Simulation (SUS) has proven highly effective for high-dimensional and small failure probability problems. However, the computational demands of time-consuming numerical simulations in the field of mechanical engineering remain substantial. Metamodeling techniques provide an effective means to reduce simulation computational costs. This paper introduces a novel approach, termed SUSAK, which combines the Subset Simulation with Kriging metamodels to address the challenge of small failure probability calculations. By using the original distribution of input variables representing the structural system, the SUSAK method establishes an adaptive metamodel and iteratively optimizes it with intermediate failure domain samples corresponding to the intermediate events. By replacing the performance function in subsequent calculations of the probability associated with intermediate events with metamodels, the enhanced method significantly reduces the computational burden compared to using the SUS method. This approach does not rely on solving for the design point, is not constrained by the shape of the failure domain, and retains the advantages of the SUS method in high-dimensional small failure probability calculations. As a result, it is well-suited for calculating small failure probabilities in nonlinear, discontinuous failure domains, multiple failure domains, and high-dimensional problems.

The two upper critical dimensions of the Ising and Potts models

We derive the exact actions of the Q-state Potts model valid on any graph, first for the spin degrees of freedom, and second for the Fortuin-Kasteleyn clusters. In both cases the field is a traceless Q-component scalar field Φα. For the Ising model (Q = 2), the field theory for the spins has upper critical dimension \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{\ ext{c}}}^{{\ ext{spin}}}$$\\end{document} = 4, whereas for the clusters it has \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{\ ext{c}}}^{{\ ext{cluster}}}$$\\end{document} = 6. As a consequence, the probability for three points to be in the same cluster is not given by mean-field theory for d within 4 < d < 6. We estimate the associated universal structure constant as \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C=\\sqrt{6-d}+\\mathcal{O}{\\left(6-d\\right)}^{3/2}$$\\end{document}. This shows that some observables in the Ising model have an upper critical dimension of 4, while others have an upper critical dimension of 6. Combining perturbative results from the ϵ = 6 – d expansion with a non-perturbative treatment close to dimension d = 4 allows us to locate the shape of the critical domain of the Potts model in the whole (Q, d) plane.

Domain shape evolution under multiple IR laser irradiation in lithium niobate

In this work, we have studied the shape evolution of the isolated domains in domain array in congruent lithium niobate crystals under the action of pyroelectric fields arising during multiple irradiation by laser pulses. The loss of the circle shape with the pulse number was obtained in the arrays of isolated domains arising at the edges of the irradiated zone. The simulation of the domain growth under the action of the pyroelectric field allowed revealing two stages of domain shape evolution in the regular domain array. An important role of the neighboring domains was revealed.