Discontinuous Domain Research Articles

High temperature evolution of interfacial metal film bonding two 4H-SiC substrates

The high temperature behavior of thin metal films (tungsten and titanium) confined between two off-axis single crystal SiC substrates is investigated. Through the application of transmission and scanning transmission electron microscopy, scanning electron microscopy, and X-ray scattering techniques, we examine the phase and morphology changes induced by high temperature annealing in thin layers consisting of these materials, as well as at their interfaces with SiC. Upon high-temperature annealing, a uniform and continuous W film formed by low-temperature deposition undergoes a transition to an array of discontinuous domains surrounded by a direct SiC/SiC interface. In contrast, a Ti film remains continuous with a strong thickness alteration. In parallel to step-bunching process of the internal SiC surfaces, both materials transform into new crystalline phases which contain Si and/or C atoms and achieve an epitaxial relationship with the SiC structures. The experimental findings are discussed in terms of dewetting phenomena and analyzed in light of potential chemical and structural reactions that may occur during interface reconstructions.

Random Walk Modeling of Conductive Heat Transport in Discontinuous Media

AbstractWe consider heat transport within a discontinuous domain by relying on the modeling approach proposed by Baioni et al. Such approach has been specifically designed to address diffusive processes in media with discontinuous physical properties and generalized boundary conditions at the discontinuities. Three algorithms are here applied to estimate the conductive heat transport in a bimaterial medium. The algorithms undergo testing using two test cases that share the same computational domain but differ in terms of their initial conditions. According to the numerical results all the algorithms ensure the conservation of thermal energy and preserve thermal equilibrium under steady state conditions. The Generalized Uffink Method (GUM) and Generalized HYMLA demonstrate sensitivity to the choice of the time step, whereas the Generalized Skew Brownian Motion appears to be unaffected by the value of $$\Delta t$$ Δ t . The GUM algorithm presents an optimal trade-off between accuracy and computational time.

Projective structures with (Quasi‐)Hitchin holonomy

AbstractIn this paper, we investigate the properties of the real and complex projective structures associated to Hitchin and quasi‐Hitchin representations that were originally constructed using Guichard–Wienhard's theory of domains of discontinuity. We determine the topology of the underlying manifolds and we prove that some of these geometric structures are fibered in a special standard way. In order to prove these results, we give two new ways to construct these geometric structures: we construct them using gauge theory, flat bundles, and Higgs bundles, and we also give a new geometric way to construct them.

Permafrost Hydrogeology of Taylor Valley, Antarctica: Insights From Deep Electrical Resistivity Tomography

AbstractGlobal warming has prompted globally widespread permafrost thawing, resulting in enhanced greenhouse gas release into the atmosphere. Studies conducted in the Northern Hemisphere reveal an alarming increase in permafrost thawing. However, similar data from Antarctica are scarce. We conducted a 2‐D Deep Electrical Resistivity Tomography (DERT) survey in Taylor Valley, Antarctica, to image the distribution of permafrost, its thicknesses, lower boundaries, and hydrogeology. Results show resistive, discontinuous domains that we suggest represent permafrost units. We also find highly conductive layers (5–10 Ω·m), between 300–350 m and 600–650 m below ground level and a shallower (∼50–100 m depth) conductive layer. The combined data set reveals a broad brine system in Taylor Valley, implying multi‐tiered groundwater circulation: a shallow, localized system linked with surface water bodies and a separate deeper, regional circulation system. The arrangement of these brines across different levels, coupled with the uneven permafrost distribution, underscores potential interplay between the two systems.

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.

Domains of discontinuity of Lorentzian affine group actions

We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations of Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb R}^n$$\\end{document}.

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.

Tribo-dynamic modeling method and application to three-dimensional flexible PRL system

Research on the tribo-dynamics of the piston-cylinder liner (PCL) and piston ring-cylinder liner (PRCL) is vital due to their role in generating over 50 % of total engine friction loss and the impact on carbon emissions. Traditional studies, hindered by the structural and functional differences between pistons and rings, required separate simulation models, often overlooking crucial coupling characteristics. A unified tribo-dynamics modeling method for the piston-ring-liner (PRL) system is proposed in this paper, integrating the ring pack and piston into one multi-body system. This article models with global coordinates, unifying the form of governing, film thickness, and load equations of discontinuous lubrication domains for more efficient dynamics-lubrication coupling. The described method is applied to a marine engine, and the new tribology characteristics discovered after calculations are exhibited. It shows how piston deformation impacts ring tribology, indicating that increased profile height reduces the squeezing effect by allowing more ring movement. Additionally, ring assembly position significantly affects tribology parameters' circumferential distribution. Installing the ring with the end gap facing the piston pin side should be avoided, as it maximizes the negative impact of elastic force and secondary motion, deteriorating lubrication.

DP2Net: A discontinuous physical property-constrained single-source domain generalization network for tool wear state recognition

Cross-conditions tool wear monitoring has a wide application prospect in manufacturing. However, the data distribution discrepancies caused by the inconsistency of process elements restrict the generalization of models under cross-conditions or even similar conditions. The existing methods based on diversity enhancement make it difficult to effectively establish the correlation between the source domain and target domains, which limits the improvement of model generalization. Therefore, this paper details the cause of data distribution discrepancies and proposes a discontinuous physical property-constrained single-source domain generalization network for milling tool wear monitoring. Firstly, a spatial attention mechanism is introduced to weight key signal segments adaptively. Secondly, the generation module is constrained by a standard sample and is used to generate diverse samples with physical properties. Thirdly, extensive recognition experiments on an open dataset and machining experiments with three distribution discrepancy levels were conducted to verify the effectiveness of the proposed method. Finally, feature visualizations provide consistency and interpretability.

Meta-model based sequential importance sampling method for structural reliability analysis under high dimensional small failure probability

Reliability analysis poses a significant challenge for complex structures with stringent reliability requirements. While Sequential Importance Sampling (SIS) and Subset Simulation (SUS) have proven highly effective in addressing high-dimensional problems with small failure probabilities, the computational burden of mechanical simulations remains substantial due to the time-consuming nature of numerical simulation processes. Consequently, this paper introduces a novel approach, denoted as AK-SIS, which combines SIS with Kriging metamodeling specifically designed to address computational challenges associated with small failure probabilities. The fundamental principle of this approach involves utilizing AK-MCS technology (Echard et al., 2011) [1] as a precursor to the SIS approach to initially generate metamodels. These metamodels are then employed in lieu of performance functions in subsequent steps, significantly reducing the number of function calls required to simulate complex engineering problems when applying SIS techniques directly. By inheriting the advantages of SIS, AK-SIS has demonstrated its suitability for reliability analysis in scenarios involving high-dimensional spaces and small fault probabilities. Furthermore, AK-SIS is not limited by the shape of the failure domain, eliminates the need to solve the design point, and is particularly well-suited for analyzing reliability in cases of discontinuous failure domains, multiple failure domains, as well as complex failure domains and rare events. The efficacy of AK-SIS is substantiated through rigorous evaluation encompassing nonlinear, high-dimensional examples, and an engineering application. These empirical validations collectively contribute to a robust methodological framework for reliability analysis of intricate structures characterized by stringent reliability requirements.

A Mixed Discretization Scheme for Discontinuous Galerkin Domain Decomposition Method Applied to Surface Integral Equations

A Mixed Discretization Scheme for Discontinuous Galerkin Domain Decomposition Method Applied to Surface Integral Equations

Balanced ideals and domains of discontinuity of Anosov representations

Balanced ideals and domains of discontinuity of Anosov representations

An Efficient and Effective Preconditioner for the Discontinuous Galerkin Domain Decomposition Method of Surface Integral Equation

This paper proposes a new preconditioning technique based on a restricted additive Schwarz (RAS) approach to improve the efficiency of the discontinuous Galerkin surface integral equation method. The RAS preconditioning is implemented efficiently using an oct-tree structure derived from the multilevel fast multipole algorithm (MLFMA) and is constructed using near-field matrices associated with boxes at the finest level. Compared to existing domain decomposition preconditioning methods based on subdomain block matrices, the proposed RAS preconditioning significantly reduces computation time and memory requirements, while providing scalable convergence for iterative solutions. Numerical experiments are presented to demonstrate the performance of the proposed cost-effective preconditioning technique.

Structural and biochemical characterisation of the N-carbamoyl-β-alanine amidohydrolase from Rhizobium radiobacter MDC 8606.

N-carbamoyl-β-alanine amidohydrolase (CβAA) constitutes one of the most important groups of industrially relevant enzymes used in the production of optically pure amino acids and derivatives. In this study, a CβAA-encoding gene from Rhizobium radiobacter strain MDC 8606 was cloned and overexpressed in Escherichia coli. The purified recombinant enzyme (RrCβAA) showed a specific activity of 14 U·mg-1 using N-carbamoyl-β-alanine as a substrate with an optimum activity at 55 °C and pH 8.0. In this work, we report also the first prokaryotic CβAA structure at a resolution of 2.0 Å. A discontinuous catalytic domain and a dimerisation domain attached through a flexible hinge region at the domain interface have been revealed. We identify key ligand binding residues, including a conserved glutamic acid (Glu131), histidine (H385) and arginine (Arg291). Our results allowed us to explain the preference of the enzyme for linear carbamoyl substrates, as large and branched carbamoyl substrates cannot fit in the active site of the enzyme. This work envisages the use of RrCβAA from R. radiobacter MDC 8606 for the industrial production of L-α-, L-β- and L-γ-amino acids. The structural analysis provides new insights on enzyme-substrate interaction, which shed light on engineering of CβAAs for high catalytic activity and broad substrate specificity.

As predicted and more: modulated channel occupation in YZn5+x.

Like many complex intermetallic phases, the crystal structures of REZn5+x compounds (RE = lanthanide or Group 3 element) based on the EuMg5 type have gradually unfolded. The original reports described a complex hexagonal structure with an unusual combination of tetrahedrally close-packed regions and open spaces, as well as observations of superstructure reflections. More recently, we reinvestigated the structure of YZn5, reclassifying it as the EuMg5+x-type compound YZn5+x (x ≃ 0.2), in which disordered channels run along c through the spaces formerly considered open. In addition, DFT-chemical pressure (DFT-CP) analysis of ordered models of YZn5+x highlighted paths for communication between neighboring channels setting the stage for superstructure formation. Herein, the experimental elucidation of this effect is presented with the synthesis and structure determination of a modulated form of YZn5+x. By slow-cooling samples of YZn5+x from the annealing temperature, crystals were obtained that exhibit satellite reflections with the modulation wavevector q = {1\over 3}a* + {1\over 3}b* + 0.3041c*. Structure solution and refinement using a (3+1)D model in superspace group P31c({1\over 3}\,\!{1\over 3}σ3)00s reveals incommensurate order in the structure's channels. Here, two Zn sites associated with the channels are present, each with discontinuous atomic domains that are slanted in the x3x4 plane. Their slanting corresponds to adjustments along the c axis for the presence or absence of close neighbors along that axis, while the occupation patterns of neighboring channels are shifted by {1\over 3} of the modulation period. These features follow earlier predictions from CP analysis, highlighting how this approach can be used predictively in search of new phenomena.

Grain boundary construction and properties enhancement for hot deformed (Ce,La,Y)-Fe-B magnet by a two-step diffusion process

The rare earth-iron-boron magnets based on high abundance rare earths (REs) show potential for cost-effective permanent magnets but their hard magnetic properties have to be greatly improved. The grain boundary diffusion process (GBDP) is known as an effective way to improve the coercivity of Nd-Fe-B magnets, however, the conventional diffusion method faces a challenge for Ce-based magnets since there is no enough continuous GB layer as the diffusion channel. Here, a two-step (Nd-Cu doping followed by Nd-Cu diffusion) GBDP was introduced for hot deformed (Ce,La,Y)-Fe-B magnet, and the excellent magnetic properties of μ0Hc=0.63 T, μ0Mr=0.68 T, and (BH)max=72.4 kJ/m3 were achieved. The Nd-Cu doping helps the formation of RE-rich GB layer, and then it acts as the diffusion channel for increasing the efficiency of the subsequent Nd-Cu diffusion and results in the increased volume fraction of continuously distributed GB phase, whose paramagnetism was verified by 57Fe Mössbauer spectrometry. Those paramagnetic GB phases help to form the discontinuous domain walls, as observed by Lorentz transmission electron microscopy, and break the magnetic exchange coupling of RE2Fe14B grains. It thus contributes to the coercivity enhancement of the hot deformed magnet with two-step diffusion, which is further proved by micromagnetic simulation. This study proposes a potential technique to prepare anisotropic hot deformed (Ce,La,Y)-Fe-B magnet with high cost-performance.

Chimeric deletion mutation of rpoC2 underlies the leaf-patterning of Clivia miniata var. variegata.

The deletion mutated rpoC2 leads to yellow stripes of Clivia miniata var. variegata by down regulating the transcription of 28 chloroplast genes and disturbing chloroplast biogenesis and thylakoid membrane development. Clivia miniata var. variegata (Cmvv) is a common mutant of Clivia miniata but its genetic basis is unclear. Here, we found that a 425bp deletion mutation of chloroplast rpoC2 underlies the yellow stripes (YSs) of Cmvv. Both RNA polymerase PEP and NEP coexist in seed-plant chloroplasts and the β″ subunit of PEP is encoded by rpoC2. The rpoC2 mutation changed the discontinuous cleft domain required to form the PEP central cleft for DNA binding from 1103 to 59aa. RNA-Seq revealed that 28 chloroplast genes (cpDEGs) were all down-regulated in YSs, of which, four involved in chloroplast protein translation and 21 of photosynthesis system (PS)I, PSII, cytochrome b6/f complex and ATP synthase are crucial for chloroplast biogenesis/development. The accuracy and reliability of RNA-Seq was verified by qRT-PCR. Moreover, the chlorophyll (Chl) a/b content, ratio of Chla/Chlb and photosynthetic rate (Pn) of YS decreased significantly. Meanwhile, chloroplasts of the YS mesophyll cells were smaller, irregular in shape, contain almost no thylakoid membrane, and even proplastid was found in YS. These findings indicate that the rpoC2 mutation down-regulated expression of the 28 cpDEGs, which disturb chloroplast biogenesis and its thylakoid membrane development. Thus, there are not enough PSI and II components to bind Chl, so that the corresponding areas of the leaf are yellow and show a low Pn. In this study, the molecular mechanism of three phenotypes of F1 (Cmvv ♀ × C. miniata ♂) was revealed, which lays a foundation for the breeding of variegated plants.

Affine deformations of quasi‐divisible convex cones

AbstractWe study subgroups of obtained by adding a translation part to the holonomy of a finite‐volume convex projective surface. Under a natural condition on the translations added to the peripheral parabolic elements, we show that the affine action of the group on has convex domains of discontinuity which are regular, generalizing a result of Mess for globally hyperbolic flat spacetimes. We then classify all such domains arising from a fixed group and show that the quotient of each of them is an affine manifold foliated by convex surfaces with constant affine Gaussian curvature (CAGC). The proof is based on the analysis of CAGC surfaces developed in a previous work, along with a correspondence between the geometry of an affine space endowed with a convex cone and the geometry of a convex tube domain. We also show that the moduli space of such groups is a vector bundle over the moduli space of finite‐volume convex projective structures, with rank equal to the dimension of the Teichmüller space.

Thermodynamic and kinetic analysis of the LAO binding protein and its isolated domains reveal non-additivity in stability, folding and function.

Substrate-binding proteins (SBPs) are used by organisms from the three domains of life for transport and signalling. SBPs are composed of two domains that collectively trap ligands with high affinity and selectivity. To explore the role of the domains and the integrity of the hinge region between them in the function and conformation of SBPs, here, we describe the ligand binding, conformational stability and folding kinetics of the Lysine Arginine Ornithine (LAO) binding protein from Salmonella thiphimurium and constructs corresponding to its two independent domains. LAO is a class II SBP formed by a continuous and a discontinuous domain. Contrary to the expected behaviour based on their connectivity, the discontinuous domain shows a stable native-like structure that binds l-arginine with moderate affinity, whereas the continuous domain is barely stable and shows no detectable ligand binding. Regarding folding kinetics, studies of the entire protein revealed the presence of at least two intermediates. While the unfolding and refolding of the continuous domain exhibited only a single intermediate and simpler and faster kinetics than LAO, the folding mechanism of the discontinuous domain was complex and involved multiple intermediates. These findings suggest that in the complete protein the continuous domain nucleates folding and that its presence funnels the folding of the discontinuous domain avoiding nonproductive interactions. The strong dependence of the function, stability and folding pathway of the lobes on their covalent association is most likely the result of the coevolution of both domains as a single unit.

A hybrid implicit-explicit discontinuous Galerkin spectral element time domain (DG-SETD) method for computational elastodynamics

SUMMARY A hybrid implicit-explicit (IMEX) discontinuous Galerkin spectral element time domain (DG-SETD) algorithm is proposed to simulate 3D elastic wave propagation in inhomogeneous media. In this method, the original problem can be divided into a number of well designed subdomains, and the mesh generation of different subdomains is completely independent, thus allowing flexible spatial discretization of complex geometry. The neighboring subdomains are connected by a Riemann transmission condition (RTC), and spectral elements with different interpolation orders can be used in different subdomains to maximize the computational efficiency of multiscale problems to facilitate parallel computing for different subdomains. In particular, the explicit or implicit time iteration scheme can be appropriately selected for a subdomain according to the size of its mesh elements to increase the global time step increment, thus giving higher computational efficiency: For subdomains with coarse meshes, the explicit time integration scheme is used and the time step increment is limited by the Courant−Friedrichs−Lewy (CFL) stability condition; for subdomain with fine structures and thus fine meshes, an implicit time integration scheme is used so that a large time step increment can be used without affecting the stability. In addition, a jump condition of displacement and velocity is introduced to accurately simulating fractures and faults, including lossless and viscous fractures with plane, curve or cross structures. This avoids the volume modeling of the extremely thin fracture structures, and effectively reduces the number of degrees of freedoms (DoFs) in the discretized system without the loss of accuracy. The accuracy, robustness and efficiency of the DG-SETD algorithm are demonstrated by quantitative comparisons of the waveforms with the commercial finite element software COMSOL.