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We consider a spectral problem for convolution-type operators in environments with locally periodic microstructure and study the asymptotic behavior of the bottom of the spectrum. We show that the bottom point of the spectrum converges as the microstructure period tends to zero, and identify the limit in terms of an additive eigenvalue problem for effective Hamilton–Jacobi equation. In the periodic case, we establish a more accurate two-term asymptotic formula. [ABSTRACT FROM AUTHOR]

Aim: The species that compose local communities possess unique sets of functional and ecological traits that can be used as indicators of biotic and abiotic variation across space and time. Body size is a particularly relevant trait because species with different body sizes typically have different life history strategies and occupy distinct niches. Here we used the body sizes of non‐volant (i.e., non‐flying) terrestrial mammals to quantify and compare the body size disparity of mammal communities across the globe. Location: Global. Time Period: Present. Major Taxa Studied: Non‐volant terrestrial mammals. Methods: We used IUCN range maps of 3982 terrestrial mammals to identify 1876 communities. We then combined diet data with data on climate, elevation and anthropogenic pressures to evaluate these variables' relative importance on the observed body size dispersion of these communities and its deviation from a null model. Results: Dispersion for these communities is significantly greater than expected in 54% of communities and significantly less than expected in 30% of communities. The number of very large species, continent, range sizes, diet disparity and annual temperature collectively explain > 50% of the variation in observed dispersion, whereas continent, the number of very large species, and precipitation collectively explain > 30% of the deviation from the null model. Main Conclusions: Climate and elevation have minimal predictive power, suggesting that biotic factors may be more important for explaining community body size distributions. However, continent is consistently a strong predictor of dispersion, likely due to it capturing the combined effects of climate, size‐selective human‐induced extinctions and more. Overall, our results are consistent with several plausible explanations, including, but not limited to, competitive exclusion, unequal distribution of resources, within‐community environmental heterogeneity, habitat filtering and ecosystem engineering. Further work focusing on other confounding variables, at finer spatial scales and/or within more causal frameworks is required to better understand the driver(s) of these patterns. [ABSTRACT FROM AUTHOR]

Titan aluminium alloys belong to the group of α – β -alloys, which are used for many applications in industry due to their advantageous mechanical properties, e.g. for laser powder bed fusion (PBF-LB) processes. However, the composition of the crystal structure and the respective magnitude of the solid fraction highly influences the material properties of titan aluminium alloys. Specifically, the thermal history, i.e. the cooling rate, determines the phase composition and microstructure for example during heat treatment and PBF-LB processes. For that reason, the present work introduces a phase transformation framework based, amongst others, on energy densities and thermodynamically consistent evolution equations, which is able to capture the different material compositions resulting from cooling and heating rates. The evolution of the underlying phases is governed by a specifically designed dissipation function, the coefficients of which are determined by a parameter identification process based on available continuous cooling temperature (CCT) diagrams. In order to calibrate the model and its preparation for further applications such as the simulation of additive manufacturing processes, these CCT diagrams are computationally reconstructed. In contrast to empirical formulations, the developed thermodynamically consistent and physically sound model can straightforwardly be extended to further phase fractions and different materials. With this formulation, it is possible to predict not only the microstructure evolution during processes with high temperature gradients, as occurring in e.g. PBF-LB processes, but also the evolving strains during and at the end of the process. [ABSTRACT FROM AUTHOR]

For the KPZ equation on a torus with a 1 + 1 spacetime white noise, it was shown in Dunlap et al. (Commun Pure Appl Math, 2023, https://doi.org/10.1002/cpa.22110) and Gu and Komorowski (Ann Inst H Poincare Prob Stat, 2021, arXiv:2104.13540v2) that the height function satisfies a central limit theorem, and the variance can be written as the expectation of an exponential functional of Brownian bridges. In this paper, we consider another physically relevant quantity, the winding number of the directed polymer on a cylinder, or equivalently, the displacement of the directed polymer endpoint in a spatially periodic random environment. It was shown in Gu and Komorowski (SIAM J Math Anal, arXiv:2207.14091) that the polymer endpoint satisfies a central limit theorem on diffusive scales. The main result of this paper is an explicit expression of the effective diffusivity, in terms of the expectation of another exponential functional of Brownian bridges. Our argument is based on a combination of tools from Malliavin calculus, homogenization, and diffusion in distribution-valued random environments. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel homogenization method for piezoelectric composites with periodic microstructures. In the proposed homogenization method, one can find the analytical expressions for the material properties of the composites in the representative volume element (RVE) via diffused material interface method. The availability of analytical expressions for the material properties in the entire domain of the RVE enables one to determine the effective homogenized material properties with the standard finite element method. As the proposed homogenization method regularizes the discontinuity in material properties across the interfaces, there is no need to explicitly track the material interfaces while implementing the finite element method for determining the effective material properties. Hence, one can implement the proposed homogenized method for any piezoelectric composites with complicated material interfaces and determine the effective material properties. In this study, we have considered the piezoelectric composites to be comprised of periodic microstructures where the RVE constitutes a matrix with an inclusion of a specific shape. We have carried out a study on the effect of the shape of inclusion viz. square-shaped, I-shaped, T-shaped, and plus-shaped, and the size of inclusion on the effective piezoelectric material properties. We have also studied the influence of shape and size of inclusion on the electro-mechanical response of a homogenized piezoelectric continuum. To implement the proposed homogenization method, we have used Gridap, an open-source finite element toolbox in Julia that provides very compact codes freely available to all the researchers and makes a third-party verification of the proposed method straightforward. [ABSTRACT FROM AUTHOR]

In the era of big data, online updating problems have attracted extensive attention. In practice, the covariates set of the models may change according to the conditions of data streams. In this paper, we propose a two-stage online debiased lasso estimation and inference method for high-dimensional heterogenous linear regression models with new variables added midway. At the first stage, the homogenization strategy is conducted to represent the heterogenous models by defining the pseudo covariates and responses. At the second stage, we conduct the online debiased lasso estimation procedure to obtain the final estimator. Theoretically, the asymptotic normality of the heterogenous online debiased lasso estimator (HODL) is established. The finite-sample performance of the proposed estimators is studied through simulation studies and a real data example. [ABSTRACT FROM AUTHOR]

We consider a boundary value problem for the p-Laplacian, posed in the exterior of small cavities that all have the same p-capacity and are anchored to the unit sphere in R d , where 1 < p < d. We assume that the distance between anchoring points is at least ε and the characteristic diameter of cavities is α ε , where α = α (ε) tends to 0 with ε . We also assume that anchoring points are asymptotically uniformly distributed as ε ↓ 0 , and their number is asymptotic to a positive constant times ε 1 - d . The solution u = u ε is required to be 1 on all cavities and decay to 0 at infinity. Our goal is to describe the behavior of solutions for small ε > 0 . We show that the problem possesses a critical window characterized by τ : = lim ε ↓ 0 α / α c ∈ (0 , ∞) , where α c = ε 1 / γ and γ = d - p p - 1. We prove that outside the unit sphere, as ε ↓ 0 , the solution converges to A ∗ U for some constant A ∗ , where U (x) = min { 1 , | x | - γ } is the radial p-harmonic function outside the unit ball. Here the constant A ∗ equals 0 if τ = 0 , while A ∗ = 1 if τ = ∞ . In the critical window where τ is positive and finite, A ∗ ∈ (0 , 1) is explicitly computed in terms of the parameters of the problem. We also evaluate the limiting p-capacity in all three cases mentioned above. Our key new tool is the construction of an explicit ansatz function u A ∗ ε that approximates the solution u ε in L ∞ (R d) and satisfies ‖ ∇ u ε - ∇ u A ∗ ε ‖ L p (R d) → 0 as ε ↓ 0 . [ABSTRACT FROM AUTHOR]

This paper presents volumetric homogenization, a spatially varying homogenization scheme for knitwear simulation. We are motivated by the observation that macro-scale fabric dynamics is strongly correlated with its underlying knitting patterns. Therefore, homogenization towards a single material is less effective when the knitting is complex and non-repetitive. Our method tackles this challenge by homogenizing the yarn-level material locally at volumetric elements. Assigning a virtual volume of a knitting structure enables us to model bending and twisting effects via a simple volume-preserving penalty and thus effectively alleviates the material nonlinearity. We employ an adjoint Gauss-Newton formulation[Zehnder et al. 2021] to battle the dimensionality challenge of such per-element material optimization. This intuitive material model makes the forward simulation GPU-friendly. To this end, our pipeline also equips a novel domain-decomposed subspace solver crafted for GPU projective dynamics, which makes our simulator hundreds of times faster than the yarn-level simulator. Experiments validate the capability and effectiveness of volumetric homogenization. Our method produces realistic animations of knitwear matching the quality of full-scale yarn-level simulations. It is also orders of magnitude faster than existing homogenization techniques in both the training and simulation stages. [ABSTRACT FROM AUTHOR]

Mechanical shock is a common occurrence in various settings, there are two different scenarios for shock protection: catastrophic protection (e.g. car collisions and falls) and routine protection (e.g. shoe soles and mattresses). The former protects against one-time events, the latter against periodic shocks and loads. Common shock absorbers based on plasticity and fracturing materials are suitable for the former, while our focus is on the latter, where elastic structures are useful. Further, we optimize the effective elastic material properties which control the critical shock parameter, maximal stress, with energy dissipation by viscous forces assumed adequate. Improved elastic materials protecting against shock can be used in applications such as automotive suspension, furniture like sofas and mattresses, landing gear systems, etc. Materials offering optimal protection against shock have a highly non-linear elastic response: their reaction force needs to be as close as possible to constant with respect to deformation. In this paper, we use shape optimization and topology search to design 2D families of microstructures approximating the ideal behavior across a range of deformations, leading to superior shock protection. We present an algorithmic pipeline for the optimal design of such families combining differentiable nonlinear homogenization with self-contact and an optimization algorithm. We validate the effectiveness of our advanced 2D designs by extruding and fabricating them with 3D printing technologies and performing material and drop testing. [ABSTRACT FROM AUTHOR]

In this paper, we highlight a set of ad hoc test functions to study the homogenization of viscous compressible fluids in domains with very tiny holes. This set of functions allows to improve previous results in dimensions two and three. As an application, we show that the presence of a small obstacle does not influence the dynamics of a viscous compressible fluid in dimension two. [ABSTRACT FROM AUTHOR]

The complex mechanical and damage mechanisms of rocks are intricately tied to their diverse mineral compositions and the formation of pores and cracks under external loads. Numerous rock tests reveal a complex interplay between the closure of porous defects and the propagation of induced cracks, presenting challenges in accurately representing their mechanical properties, especially under true triaxial stress conditions. This paper proposes a conceptualization of rock at the mesoscopic level as a two-phase composite, consisting of a bonded medium matrix and frictional medium inclusions. The bonded medium is characterized as a mesoscopic elastic material, encompassing various minerals surrounding porous defects. Its mechanical properties are determined using the mixed multi-inclusion method. Transformation of the bonded medium into the frictional medium occurs through crack extension, with its elastoplastic properties defined by the Drucker–Prager yield criterion, accounting for hardening, softening, and extension. Mori–Tanaka and Eshelby’s equivalent inclusion methods are applied to the bonded and frictional media, respectively. The macroscopic mechanical properties of the rock are derived from these mesoscopic media. Consequently, a True Triaxial Macro-Mesoscopic (TTMM) constitutive model is developed. This model effectively captures the competitive effect and accurately describes the stress-deformation characteristics of granite. Utilizing the TTMM model, the strains resulting from porous defect closure and induced crack extension are differentiated, enabling quantitative determination of the associated damage evolution.

The effects of homogenization temperature at 465 °C and different homogenization times (6h/12h/24h/36/h/48h) on the microstructure and mechanical properties of as-cast 7075 aluminum alloy were studied using optical microscopy (OM), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), X-ray diffraction (XRD), transmission electron microscopy (TEM), hardness testing, and tensile testing. The results show that during the initial stage of homogenization, the continuous bright white network of σ-Mg (Zn, Cu, Al)2 phase transforms into a white broken flocculent S–Al2CuMg phase with the dissolution of Zn. In the middle stage, the S–Al2CuMg phase dissolves and Cu diffuses into primary Al7Cu2Fe, accompanied by precipitation of a large amount of dispersed nanoscale MgZn2 phase. With the homogenization time, the Al7Cu2Fe and MgZn2 phase are coarsened. The strength and plasticity of the alloy show a trend of first increase and then decrease. When the homogenization time is 24 h, the ultimate tensile strength (UTS), yield strength (YS), and elongation reach the peak values of 231.1 MPa, 134.2 MPa, and 4.0%, respectively. The phase transformation and dissolution mechanism during the homogenization process of 7075 aluminum alloy provides a scientific theoretical basis for improving the mechanical properties of the alloy.

The control of MnS inclusions is crucial in developing high‐quality nonquenched and tempered steel. Single‐pass compression experiments are conducted on F40MnVS steel using a Gleeble‐3800 thermomechanical simulation testing machine, and the hot deformation behaviors of MnS inclusions at temperatures of 950–1150 °C and strain rates of 0.01 s−1 are investigated. Based on the experimental results of hot deformation, the steel is isothermally homogenized after forging to study the effect of holding time on the morphology and characteristics of MnS. Results indicate that at a lower deformation temperature of 950 °C and increased deformation, the relative plasticity of MnS diminishes, reducing the aspect ratio from 3.38 to 1.44 and primarily causing MnS fragmentation. At 1150 °C, as deformation increases, the relative plasticity of MnS also increases, with the aspect ratio rising from 1.46 to 2.01, leading to the growth of MnS. Under either low temperature and high deformation conditions or high temperature and low deformation, MnS fragmentation is more pronounced, resulting in more spherical MnS. With extended homogenization time, elongated MnS fractures, progressively transforming into spheroidal or ellipsoidal shapes before enlarging. The diffusion of S primarily controls the fracture and growth of MnS during isothermal heating. [ABSTRACT FROM AUTHOR]

The dynamical problem of linear thermoelasticity for a body with incorporated thin rectilinear inclusions is studied. It is assumed that the inclusions (i.e. filaments and threads) are parallel to each other and the problem contains a small parameter ϵ>0 , which characterizes the distance between two neighbouring inclusions. Using the two-scale convergence approach, we find the limiting problem as ϵ→0. As a result, we get a well-posed homogenized model of an anisotropic inhomogeneous body with effective characteristics inheriting thermomechanical properties of inclusions. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

This paper investigates the mechanical properties of carbon‐based nanostructures, in particular graphene, using the FE2${\mathrm{FE}}^{2}$ method. The local boundary value problem is calculated using molecular mechanics and is therefore, in contrast to continuum mechanics, discrete. In the case of graphene as a microstructure, atomistic interactions occur with a range of up to three or more atoms. For the local boundary value problem, a representative volume element is developed that is compatible with the atomistic interactions. Boundary effects resulting from the molecular mechanical consideration are eliminated. Boundary conditions compatible with the Hill–Mandel condition are formulated for the local boundary value problem. The results are verified with fully atomistic simulations. [ABSTRACT FROM AUTHOR]

The conversion of urban montane forest resources into urban parks requires careful assessment to understand its impacts on plant diversity over time. This study aims to enhance urban biodiversity conservation strategies by analyzing how habitat type and park age affect woody plant diversity. We surveyed woody plant species in 60 sample plots across two different habitats (remnant forest vs. artificial green space) within three mountain parks in Guiyang, China, established at different times. The alpha diversity of saplings/seedlings was significantly higher in remnant forests than in artificial green spaces. Artificial green spaces exhibited more homogenous woody plant composition compared with remnant forests. Newer parks showed greater variation in plant composition between the two habitats than older parks. Indicative species in remnant forests were predominantly native, whereas those in artificial green spaces were mainly ornamental species. The transformation of karst mountainous forests into urban parks leads to the homogenization of woody plant composition and impedes the regeneration of saplings/seedlings. Therefore, it is crucial to manage these conversions carefully and strive to preserve as many native species as possible to support urban plant diversity conservation. [ABSTRACT FROM AUTHOR]

Antarctica terrestrial ecosystems are facing the most threats from global climate change, which is altering plant composition greatly. These transformations may cause major reshuffling of soil community composition, including functional traits and diversity, and therefore affect ecosystem processes in Antarctica. We used high‐throughput sequencing analysis to investigate soil nematodes under 3 dominant plant functional groups (lichens, mosses, and vascular plants) and bare ground in the Antarctic region. We calculated functional diversity of nematodes based on their diet, life histories, and body mass with kernel density n‐dimensional hypervolumes. We also calculated taxonomic and functional beta diversity of the nematode communities based on Jaccard dissimilarity. The presence of plants had no significant effect on the taxonomic richness of nematodes but significantly increased nematode functional richness. The presence of plants also significantly decreased taxonomic beta diversity (homogenization). Only mosses and vascular plants decreased nematode functional beta diversity, which was mostly due to a decreased effect of the richness difference component. The presence of plants also increased the effect of deterministic processes potentially because environmental filtering created conditions favorable to nematodes at low trophic levels with short life histories and small body size. Increasing plant cover in the Antarctic due to climate change may lead to increased diversity of nematode species that can use the scarce resources and nematode taxonomic and functional homogenization. In a future under climate change, community restructuring in the region is possible. [ABSTRACT FROM AUTHOR]

The list of standard abbreviations for JDS is available at adsa.org/jds-abbreviations-24. Nonstandard abbreviations are available in the Notes. Milk and dairy products are excellent sources of mineral elements, including Ca, P, Mg, Na, K, and Zn. The purpose of this study was to determine the effect of nonthermal (homogenization) and thermal (heat treatment) treatments on the distribution of mineral elements in 4 milk fractions: fat, casein, whey protein, and aqueous phase. The study results revealed that the distribution of mineral elements (such as Mg and Fe) in fat fractions is extremely low, whereas significant mineral elements such as Ca, Zn, Fe, and Cu are mostly dispersed in casein fractions. For nontreated goat milk, Mo is the only element identified in the whey protein fraction, whereas K and Na are mostly found in the aqueous phase. Mineral element concentrations in fat (K, Zn, and so on) and casein fractions (Fe, Mo, and so on) increased dramatically after homogenization. Homogenization greatly decreased the concentration of mineral elements in the whey protein fraction (Ca, Na, and so on) and aqueous phase (Fe, Cu, and so on). After heat treatment, the element content in the fat fraction and casein fraction increased greatly when compared with raw milk, such as Cu and Mg in the fat fraction, Na and Cu in the whey protein fraction, the concentration of components such as Mg and Na in casein fraction increased considerably. In contrast, after homogenization, Zn in the aqueous phase decreased substantially, whereas Fe increased significantly. Therefore, both homogenization and heat treatment have an effect on the mineral element distribution in goat milk fractions. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the homogenization and dimension reduction for a nonlinear elasticity problem of a textile structure. The structure is represented as a squared piece of cloth and modeled as a woven canvas made of long and thin fibers, crossing each other in a periodic pattern. The squared domain is partially clamped on the left and bottom. The fibers are assumed to be glued, a condition that allows to extend the woven structure to a non-perforate plate. The nonlinear elasticity problem is stated via minimization over the energy functional. The homogenization is made via the periodic unfolding method, with an additional dimension reduction. Since the existence of a minimum of the limit energy functional is not ensured, sufficient conditions for the existence are given by assuming that the material is homogeneous and isotropic. [ABSTRACT FROM AUTHOR]

The aim of the present study is to design a solid material with specific and tailored mechanical properties through a suitably defined design framework and to evaluate the effectiveness of different microstructure geometries in an engineering perspective. To these ends, topology optimization algorithms are applied on a 2D homogenized equivalent model of a periodic structure. The design framework, developed in a previous work for 2D lattices made of regular hexagons, is here expanded and validated also in the cases of circular and square unit cells. The proposed approach involves optimizing porosity distribution of a homogenized equivalent solid, obtained through a Bloch–Floquet-based analysis, within a 2D lattice of regular unit cells forming the core element of a sandwich panel. Finite-element analyses on homogenized and fine structural models are carried out in order to validate the procedure, beyond the particular choice of the unit cell geometry and to detect its effectiveness and limits. [ABSTRACT FROM AUTHOR]

We extend the applicability of the embedded unit cell (EUC) method to three-dimensional (3D) fracture problems, which are modeled by the extended finite element method (XFEM). The EUC method is a concurrent multiscale method based on the computational homogenization theory for nonperiodic domains. Herein, we show that this method can accurately estimate fracture parameters and, in particular, stress intensity factors using the J-integral method. Additionally, the method is shown to capture crack propagation within the microscale domain, as well as cracks initiating at the microscale and propagating outwards onto the macroscale through the internal subdomain boundaries. To demonstrate the accuracy, robustness, and computational efficiency of the proposed method, several 3D numerical benchmark examples, including planar cracks with single and mixed-mode fractures, are considered. In particular, we analyze horizontal, inclined, square, and penny-shaped cracks embedded in a homogeneous material. The results are verified against full FEM models and known analytical solutions if available. Practical Applications: The insights of this research offer practical application for engineers and scientists in designing more resilient and durable structures. By extending the EUC method to 3D fracture problems, the study addresses the ability to forecast and access fracture phenomena in materials. This method is shown to be an effective approach for exploring the interaction between local microscopic discontinuities and cross-scale crack propagation, crucial for evaluating the durability of engineering structures. The EUC approach, integrated with XFEM, provides a comprehensive methodology for analyzing different fracture scenarios, including stationary mixed-mode cracks and crack-propagation examples. Its ability to accurately transition from microscale to macroscale analysis without remeshing introduces a valuable computational advantage, making it a more cost-efficient solution in fracture analysis. This research's application offers tangible benefits in industrial context, especially in aerospace, automotive, and construction industries, where precise evaluation of structure and material failure can lead to more cost-efficient and safer designs by reducing the maintenance costs and failure risks. [ABSTRACT FROM AUTHOR]

This study evaluated two fundamental assumptions about the geometry of the wood cell wall to develop a mechanistic characterization of wood behavior at the scale of wood structural components. This paper used a three-step homogenization scheme implemented through homogenization techniques and finite-element analyses to evaluate a multilayered cell wall and a simplified single-layer method. Both earlywood and latewood geometries were considered. A three-part sensitivity analysis assessed the influence of wood constituent proportions, microfibril angle, and cellulose crystallinity on cell wall stiffness. Sensitivity to constituent ratios was evaluated through a Monte Carlo simulation of 1,000 sampled points and correlation analysis. Sensitivity to microfibril angle and cellulose crystallinity was evaluated through parametric characterization. The investigation found that both methods provided an accurate assessment of wood stiffness when compared with experimentally determined values. Care should be taken when modeling higher densities of wood, and use of either method in higher order models should be determined by the resolution of input data and computational needs. [ABSTRACT FROM AUTHOR]

We investigated the mechanism and kinetics of the formation of metastable BiGe solid phases during the amorphous-to-crystalline transformation of Ge films in contact with Bi. Ge/Bi/Ge sandwich films with a Bi film between amorphous Ge films, which were fabricated by sequential deposition of the components in a vacuum, were used in this study. The total thickness and composition of the sandwich films varied in the range from 30 to 400 nm and from 22 to 48 wt% Bi, respectively. Electron diffraction, high-resolution (S)TEM imaging, EDX, and EEL spectroscopy were used for in situ and ex situ characterization of the morphology, composition, and structure of Ge/Bi/Ge films in the temperature range of 20–271 °C. We proved the formation of polycrystalline Ge films containing up to 28 wt% Bi during low-temperature treatment. The interaction process was activated at ≈150 °C, resulting in the crystallization of Ge with the simultaneous formation of a quasi-homogeneous supersaturated solid solution throughout the entire volume of the film at ≈210 °C. We showed that the formation of crystalline Ge films with an extended solid solubility of Bi depended mostly on the overall composition of the tri-layer film. The role of metal-induced crystallization of the amorphous germanium in the formation of the supersaturated solid phases is discussed. [ABSTRACT FROM AUTHOR]

The electron beam cold hearth melting (EBCHM) process is one of the key processes for titanium alloy production. However, EBCHM is prone to cause elemental volatilization and segregation during the melting of aluminum-containing titanium alloys such as Ti-6wt%Al-4wt%V. To gain deeper insights into the physical and chemical phenomena occurring during the EBCHM process, this paper establishes melting process models for the Ti-6wt%Al-4wt%V titanium alloy in a crystallizer with multiple overflow inlets. It examines the evolution of melt pool morphology, flow dynamics, heat transfer, and mass transfer during the casting process. The results indicate that the design of multi-overflow inlets can effectively suppress the longitudinal development of impact pits within the melt pool, thereby preventing the formation of solidification defects such as leaks in the melt. Concurrently, the diversion effect of multi-overflow inlets significantly enhances the elemental homogeneity within the melt pool. At a casting speed of 20 mm/min and a casting temperature of 2273 K, compared to a single overflow inlet, the design with three overflow inlets can reduce the depth of thermal impact pits within the crystallizer by 132 mm and decrease the maximum concentration difference in the Al element within the crystallizer by 0.933 wt.%. The aforementioned simulation results provide a theoretical basis for the control of metallurgical and solidification defects in large-scale titanium alloy ingots. [ABSTRACT FROM AUTHOR]

The optimization of two-scale structures can adapt to the different needs of materials in various regions by reasonably arranging different microstructures at the macro scale, thereby considerably improving structural performance. Here, a multiple variable cutting (M-VCUT) level set-based data-driven model of microstructures is presented, and a method based on this model is proposed for the optimal design of two-scale structures. The geometry of the microstructure is described using the M-VCUT level set method, and the effective mechanical properties of microstructures are computed by the homogenization method. Then, a database of microstructures containing their geometric and mechanical parameters is constructed. The two sets of parameters are adopted as input and output datasets, and a mapping relationship between the two datasets is established to build the data-driven model of microstructures. During the optimization of two-scale structures, the data-driven model is used for macroscale finite element and sensitivity analyses. The efficiency of the analysis and optimization of two-scale structures is improved because the computational costs of invoking such a data-driven model are much smaller than those of homogenization. [ABSTRACT FROM AUTHOR]

This study investigated the effect of milk homogenization/fat globule size on the plasticization of fresh and frozen stored cheese curd and its respective oiling-off behavior. The cheese was frozen either slowly in a freezing chamber or quickly with liquid nitrogen to study the influence of freezing, frozen storage, and thawing. For non-frozen cheese curd, a one-stage homogenization at 2 MPa before renneting still leads to plasticization, while relative oiling off is reduced from 2.6 to 1.9%. This was explained by reduced fat globule size and an increased surface area covered by whey proteins and casein, which is denser and more stable than the native fat globule membrane. For homogenization pressures above 4 MPa, no plasticization was observed. However, freezing and thawing counteract mild homogenization, so minor oiling off occurs, and flowability is enhanced. Extending frozen storage time up to 3 months did not result in more oiling off or higher tan δ values. Moreover, there was no significant effect between the two freezing methods. In conclusion, freezing and frozen storage for up to 3 months is a valid method to preserve cheese curd as techno-functional properties are regained after thawing. [ABSTRACT FROM AUTHOR]

An experimental investigation has been conducted with respect to the element segregation and microstructure evolution of a Mn–Cr–Mo alloyed oil casing steel from different solidification cooling rates (0.5 °C/s, 3 °C/s and 10 °C/s) and subsequent defined homogenization treatment using the confocal scanning laser microscope (CSLM). A quantitative relation between the secondary dendrite arm spacing and cooling rates is achieved through regression analysis. The experimental results shown that the micro-segregation area of Mn, Cr and Mo elements decreased significantly, but its concentration increased in the finer inter-dendritic region with the increase of solidification cooling rate. The distribution of the experimental elements determined by the grid point measurements (obtained with EPMA-WDS) processed by the weighted interval rank sort method is consistent with the modified V–B segregation model considering the proper partition coefficient by the mass balance analysis method. Moreover, the residual element segregation index apparently decreased and the element micro-segregation was effectively eliminated during the subsequent homogenization treatment especially for the sample prepared by a higher cooling rate in the as-cast period. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the limit behavior of a family of solutions of the Laplace operator with homogeneous Neumann boundary conditions, set in a two‐dimensional thin domain that presents weak oscillations on both boundaries and with terms concentrated in a narrow oscillating neighborhood of the top boundary. The aim of this problem is to study the behavior of the solutions as the thin domain presents oscillatory behaviors beyond the classical periodic assumptions,including scenarios such as quasi‐periodic or almost‐periodic oscillations. We then prove that the family of solutions converges to the solution of a one‐dimensional limit equation capturing the geometry and oscillatory behavior of boundary of the domain and the narrow strip where the concentration terms take place. In addition, we include a series of numerical experiments illustrating the theoretical results obtained in the quasi‐periodic context. [ABSTRACT FROM AUTHOR]

The characterization of the flexural performances of short glass fiber reinforced polyether‐ether‐ketone (SGFR‐PEEK) composites fabricated by injection molding is a crucial and challenging task due to the process‐induced fiber orientation at different locations, resulting layered shell‐core‐shell microstructures and exhibiting large variations in mechanical performances. This article proposes a method for predicting the bending performance of SGFR‐PEEK and indicates the influence of fiber orientation on its bending behavior. This article reports a new scheme that combines multiscale homogenization with periodic microstructures and presents an experimental investigation of the flexural properties of SGFR‐PEEK composites. The distributions of fiber orientation through the thickness extracted from the micro‐computed tomography (μCT) were analyzed and reproduced with a layered skin‐shell‐core structure along the thickness at meso‐scale finite element model within representative volume elements (RVEs) of the macroscopic composites. Then, the effective properties of the RVEs were predicted using the homogenization method with the periodic boundary condition. The elastic modulus of skin‐shell‐core layers in the direction of flow are 4260.51, 4541.27, 4628.52, and 4630.84 MPa, respectively. The classical laminate theory (CLT) and the second homogenization implementation were then utilized in conjunction with the obtained mechanical properties of RVEs to predict the effective macrostructural behavior. The flexural modulus of the composite material was determined to be 5448.7 MPa through a three‐point bending test. The results obtained through lamination plate reinforcement theory and finite element simulation were 5887.4 and 5785.9 MPa, respectively, showing good agreement with the experimental findings. It is shown that the proposed multiscale scheme yields satisfactory agreement with experimental measurements. In addition, the effect of layered skin‐shell‐core microstructures on the flexural behavior was discussed. Highlights: RVEs of layered shell‐core‐shell microstructures were generated with specified fiber orientations.The homogenization scheme with the periodic boundary condition was adopted to accurately predict each layer mechanical properties.The proposed multiscale scheme was compared with experimental results and yielded satisfactory predictions.The effect of layered skin‐shell‐core microstructures on the flexural behavior was thoroughly studied by the multiscale analytical approach. [ABSTRACT FROM AUTHOR]

Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to solve due to prohibitively small mesh and time step sizes limited by the scaling parameter and CFL condition. Another challenge in scientific computing could come from curse-of-dimensionality. In this paper, we aim to provide a quantum algorithm, based on either direct approximations of the original PDEs or their homogenized models, for prototypical multiscale problems in PDEs, including elliptic, parabolic, and hyperbolic PDEs. To achieve this, we will lift these problems to higher dimensions and leverage the recently developed Schrödingerization based quantum simulation algorithms to efficiently reduce the computational cost of the resulting high-dimensional and multiscale problems. We will examine the error contributions arising from discretization, homogenization, and relaxation, and analyze and compare the complexities of these algorithms in order to identify the best algorithms in terms of complexities for different equations in different regimes. [ABSTRACT FROM AUTHOR]

In this work, we derive a homogenized mathematical model for a porous intercalation electrode with a phase separating active material. We start from a microscopic model consisting of transport equations for lithium ions in an electrolyte phase and intercalated lithium in a solid active phase. Both are coupled through a Neumann–boundary condition modeling the lithium intercalation reaction Li+ + e- ⇌ Li. . The active material phase is considered to be phase separating upon lithium intercalation. We assume that the porous material is a given periodic microstructure and perform analytical homogenization. Effectively, the microscopic model consists of a diffusion and a Cahn–Hilliard equation, whereas the limit model consists of a diffusion and an Allen–Cahn equation. Thus, we observe a Cahn–Hilliard to Allen–Cahn transition during the upscaling process. In the sense of gradient flows, the transition coincides with a change in the underlying metric structure of the PDE system. [ABSTRACT FROM AUTHOR]

Multiscale partial differential equations (PDEs) arise in various applications, and several schemes have been developed to solve them efficiently. Homogenization theory is a powerful methodology that eliminates the small-scale dependence, resulting in simplified equations that are computationally tractable while accurately predicting the macroscopic response. In the field of continuum mechanics, homogenization is crucial for deriving constitutive laws that incorporate microscale physics in order to formulate balance laws for the macroscopic quantities of interest. However, obtaining homogenized constitutive laws is often challenging as they do not in general have an analytic form and can exhibit phenomena not present on the microscale. In response, data-driven learning of the constitutive law has been proposed as appropriate for this task. However, a major challenge in data-driven learning approaches for this problem has remained unexplored: the impact of discontinuities and corner interfaces in the underlying material. These discontinuities in the coefficients affect the smoothness of the solutions of the underlying equations. Given the prevalence of discontinuous materials in continuum mechanics applications, it is important to address the challenge of learning in this context, in particular, to develop underpinning theory that establishes the reliability of data-driven methods in this scientific domain. The paper addresses this unexplored challenge by investigating the learnability of homogenized constitutive laws for elliptic operators in the presence of such complexities. Approximation theory is presented, and numerical experiments are performed which validate the theory in the context of learning the solution operator defined by the cell problem arising in homogenization for elliptic PDEs. [ABSTRACT FROM AUTHOR]

We consider a singularly perturbed system of stochastic differential equations proposed by Chaudhari et al. (Res. Math. Sci. 2018) to approximate the entropic gradient descent in the optimization of deep neural networks via homogenization. We embed it in a much larger class of two-scale stochastic control problems and rely on convergence results for Hamilton--Jacobi--Bellman equations with unbounded data proved recently by ourselves (ESAIM Control Optim. Calc. Var. 2023). We show that the limit of the value functions is itself the value function of an effective control problem with extended controls and that the trajectories of the perturbed system converge in a suitable sense to the trajectories of the limiting effective control system. These rigorous results improve the understanding of the convergence of the algorithms used by Chaudhari et al., as well as of their possible extensions where some tuning parameters are modeled as dynamic controls. [ABSTRACT FROM AUTHOR]

Composite metal foams (CMFs) are a new class of closed-cell porous materials that can be produced by distributing metallic spheres in a metallic matrix. CMFs could offer better mechanical performance in comparison to the conventional metal foams due to the uniform shape and even distribution of voids. To evaluate elastic properties of CMFs, the conventional theoretical approaches for periodic models are not good candidates due to the random distribution of voids in these materials. Thus, in this research, first, a three-dimensional model is developed based on the Lubachevsky and Stillinger (LS) approach, which is then used for the FE analysis. Using homogenization technique, the elastic properties of the CMFs are evaluated focusing here on elastic modulus and Poisson's ratio. Comparing results against experimental results shows a very good agreement. In this paper, for the first time, effects of geometrical and material parameters such as thickness of the spheres, microporosity in the wall of spheres and matrix, matrix materials, and diameter of the spheres on the elastic properties of CMFs are examined. It is observed that the microporosity in the matrix has higher effect on the elastic modulus of the CMFs than the microporosity in the wall of the spherical particles. [ABSTRACT FROM AUTHOR]

This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic perforated plate made of stiff material with holes filled by a soft matrix material. The structure is clamped on a cylindrical part. Two cases of asymptotic analysis are considered: one without pre-strain and the other with matrix pre-strain. In both cases, the total elastic energy is in the von-Kármán (vK) regime ( ε 5 ). A new splitting of the displacements is introduced to analyze the asymptotic behavior. The displacements are decomposed using the Kirchhoff–Love (KL) plate displacement decomposition. The use of a re-scaling unfolding operator allows for deriving the asymptotic behavior of the Green St. Venant's strain tensor in terms of displacements. The limit homogenized energy is shown to be of vK type with linear elastic cell problems, established using the Γ-convergence. Additionally, it is shown that for isotropic homogenized material, our limit vK plate is orthotropic. The derived results have practical applications in the design and analysis of composite structures. [ABSTRACT FROM AUTHOR]

The as‐cast microstructure, microsegregation of alloying elements, and microstructure evolution during homogenization of the newly designed 15Cr–30Ni–Fe heat‐resistant alloy are studied. Ti, Nb, Si, and Mo segregate at the interdendritic region. The brittle eutectic Laves phase contains Fe, Ti, Ni, Nb, Si, and Mo, which is identified as the Fe2Ti Laves phase. The activation energy for the Fe2Ti Laves phase dissolution is close to the activation energy for Ti diffusion in the γ matrix based on the Johnson–Mehl–Avrami–Kolmogorov analysis. The back‐diffusion of Ti to the γ matrix is the limiting step for the dissolution of Fe2Ti Laves phase. The kinetic equation of homogenization considering lattice parameters and pre‐exponential factor correction is established. After the double‐stage homogenization at 980 °C/10 h + 1140 °C/4 h, the volume fraction of the Laves phase decreases from 5.11% to 0.26%, and the large eutectic Laves phase is completely dissolved. The reduction in the standard deviation of microhardness at different soaking times effectively reflects the gradual decrease in the degree of microsegregation of alloying elements. The average grain size of the alloy after homogenization is 410 ± 63.1 μm, which is beneficial to control the further refinement of grain during the subsequent hot working. [ABSTRACT FROM AUTHOR]

In this study, 6201 Al–Mg–Si cast ingots were investigated to determine the influence of total iron and silicon contents and homogenization on their microstructure and performance, including electrical and creep resistance. The tests included scanning electron microscopy, electron back scatter diffraction, and X-ray diffraction. The results showed that an increase in the total Fe and Si contents refined the microstructure, increased the weight of the ∑3 twin boundaries, and decreased the texture index FCGB in the initial Al–Mg–Si cast ingots. With increasing homogenization treatment time, the electrical conductivity (EC) in all three groups of homogenized ingots first decreased significantly (within 4 h) and then remained relatively stable. The increase in the total Fe and Si contents resulted in a decrease in the EC and an increase in the hardness of the as-homogenized cast ingot samples. The improvement in the EC of the initial and as-homogenized cast ingots was due to the high content of low-angle grain boundaries and strong Cube texture. The room-temperature creep resistance of the as-homogenized cast ingots was improved by high Fe and Si contents. The texture index FCGB and orientation streamline approach were determined to be powerful indicators for distinguishing and describing texture evolution during the homogenization of cast ingots with various chemical compositions. [ABSTRACT FROM AUTHOR]

In this study, we applied the penalized maximum F test (PMF) method in the Relative Homogenization test V4 (RHtestV4) package without reference series to improve the reliability of monthly mean long-term sea surface salinity (SSS) data. The data were obtained from six coastal hydrological stations along the coast of the northern SCS, spanning from January 1960 to December 2018. Based on the detailed metadata, taking the influence of regional climate change factors into full account, the inhomogeneity of these SSS data was detected and adjusted. The findings indicate that all six coastal hydrological stations exhibited breakpoints, and among them, 22 breakpoints were identified in total, which were the causes of inhomogeneity in the monthly SSS time series. The primary factors contributing to these breakpoints were human-related and, specifically, related to changes in instruments. The average adjustment of monthly quantile matching (QM) of the salinity series ranged from around −4.25 to 3.33‰. The quality of the adjusted annual mean SSS time series was greatly improved. Notably, the annual mean SSS of the NZU and ZPO coastal hydrological stations in Guangdong Province exhibited a significant downward trend, indicating a trend of seawater freshening. Conversely, the WZU, BHI, HKO and QLN coastal hydrological stations in the Guangxi and Hainan coastal areas displayed an upward trend in SSS. This study fills the gap in current research on inhomogeneity detection and adjustment of SSS along the coast of the northern SCS. It also provides reliable and accurate first-hand information for research on climate change and marine science along the coast of the northern SCS. [ABSTRACT FROM AUTHOR]

This paper studies the upscaling of an elliptic problem with a highly oscillating quasilinear matrix coefficient, a quasilinear term, and a semilinear term in domains periodically perforated with holes of critical size. A Signorini boundary condition is imposed on the boundary of the holes, while a Dirichlet boundary condition is prescribed on the exterior boundary. Using the periodic unfolding method, we obtain an obstacle problem with a nonnegativity spreading effect. [ABSTRACT FROM AUTHOR]

Surface-based inflatables are composed of two thin layers of nearly inextensible sheet material joined together along carefully selected fusing curves. During inflation, pressure forces separate the two sheets to maximize the enclosed volume. The fusing curves restrict this expansion, leading to a spatially varying in-plane contraction and hence metric frustration. The inflated structure settles into a 3D equilibrium that balances pressure forces with the internal elastic forces of the sheets. We present a computational framework for analyzing and designing surface-based inflatable structures with arbitrary fusing patterns. Our approach employs numerical homogenization to characterize the behavior of parametric families of periodic inflatable patch geometries, which can then be combined to tessellate the sheet with smoothly varying patterns. We propose a novel parametrization of the underlying deformation space that allows accurate, efficient, and systematical analysis of the stretching and bending behavior of inflated patches with potentially open boundaries. We apply our homogenization algorithm to create a database of geometrically diverse fusing patterns spanning a wide range of material properties and deformation characteristics. This database is employed in an inverse design algorithm that solves for fusing curves to best approximate a given input target surface. Local patches are selected and blended to form a global network of curves based on a geometric flattening algorithm. These fusing curves are then further optimized to minimize the distance of the deployed structure to target surface. We show that this approach offers greater flexibility to approximate given target geometries compared to previous work while significantly improving structural performance. [ABSTRACT FROM AUTHOR]

We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore scale is modeled using a diffuse interface approach in the form of a coupled Allen–Cahn Navier–Stokes system with an additional momentum flux due to surface tension forces. Using periodic homogenization and formal asymptotic expansions, a two-scale model with cell problems for phase evolution and velocity contributions is derived. We investigate the computed effective parameters and their relation to the saturation for different fluid distributions, in comparison to commonly used relative permeability saturation curves. The two-scale model yields non-monotone relations for relative permeability and saturation. The strong dependence on local fluid distribution and effects captured by the cell problems highlights the importance of incorporating pore-scale information into the macro-scale equations. [ABSTRACT FROM AUTHOR]

We derive, through the deterministic homogenization theory in thin domains, a new model consisting of Hele–Shaw equation with memory coupled with the convective Cahn–Hilliard equation. The obtained system, which models in particular tumor growth, is then analyzed and we prove its well-posedness in dimension 2. To achieve our goal, we develop and use the new concept of sigma-convergence in thin heterogeneous media, and we prove some regularity results for the upscaled model. [ABSTRACT FROM AUTHOR]

The present study concerns the interface mode II fracture of hydroxyl functionalized multi‐walled carbon nanotubes (MWCNTs) reinforced carbon fiber epoxy composites. The well‐known cohesive zone model (CZM) is employed for investigating crack propagation. The major difficulty in applying the CZM is the parameter identification. In this work, the CZM's strength and energy parameters are determined reliably from the Short beam shear (SBS) and End‐notched flexure (ENF) tests, respectively, for pristine and three MWCNTs variations—0.1 wt.%, 0.2 wt.%, and 0.3 wt.%. The derived CZM parameters from the tests are imputed to a bilinear cohesive law to simulate the global load vs. displacement responses, which correlate well with the experimental findings. It is observed that the addition of 0.2 wt.% of MWCNTs increases the cohesive strength and fracture energy up to 14.14% and 17.78%, respectively, when compared to the pristine composites. Finally, the field emission scanning electron microscopy (FESEM) analysis is carried out to investigate the fracture mechanisms. Highlights: Cohesive properties under mode II are estimated using standard fracture tests.The homogenization technique is used to calculate the effective properties of CFRP.The maximum % error among the experimental and the numerical peak load is 3.01%.A higher density of hackles with an increase of MWCNTs up to 0.2 wt.%. [ABSTRACT FROM AUTHOR]

Permeability is a fundamental property of porous media. It quantifies the ease with which a fluid can flow under the effect of a pressure gradient in a network of connected pores. Porous materials can be natural, such as soil and rocks, or synthetic, such as a densified network of fibres or open-cell foams. The measurement of permeability is difficult and time-consuming in heterogeneous and anisotropic porous media; thus, a numerical approach based on the calculation of the tensor components on a 3D image of the material can be very advantageous. For this type of microstructure, it is important to perform calculations on large samples using boundary conditions that do not suppress the transverse flows that occur when flow is forced out of the principal directions. Since these are not necessarily known in complex media, the permeability determination method must not introduce bias by generating non-physical flows. A new finite element-based method proposed in this study allows us to solve very high-dimensional flow problems while limiting the biases associated with boundary conditions and the small size of the numerical samples addressed. This method includes a new boundary condition, full permeability tensor identification based on the multiscale homogenization approach, and an optimized solver to handle flow problems with a large number of degrees of freedom. The method is first validated against academic test cases and against the results of a recent permeability benchmark exercise. The results underline the suitability of the proposed approach for heterogeneous and anisotropic microstructures. [ABSTRACT FROM AUTHOR]

AbstractEducational frameworks emphasize to students the importance of gaining differentiated worldviews and being open-minded toward other cultures. As a primary medium in class, textbooks should accurately represent diversity to help students develop intercultural awareness and critical thinking. This study aims to analyze geography textbooks’ of Hesse (Germany) on their representation of diversity dimensions across different countries and continents using a multidimensional approach to superdiversity. For the analysis, a qualitative content analysis is initially conducted. Then, the representation of the continents is compared using network analysis. Our findings reveal a biased portrayal across all continents, leading to homogenization within the teaching material. This inconsistency contradicts the curricular requirements of Hessian geography and suggests that the textbook approval process is not sufficiently rigorous in ensuring that the standards are met. [ABSTRACT FROM AUTHOR]

The conditions of resonant (almost complete) tunneling of photons (plane monochromatic electromagnetic waves) through layered dielectric and metal-dielectric structures are considered. Resonant tunneling occurs at frequencies at which the resonance conditions for the corresponding structures of open resonators are met. For metal-dielectric structures, the possibility of tunneling in the optical range with a strong barrier in the IR range is shown, which can be used to control the transmission of window panes. [ABSTRACT FROM AUTHOR]

Studying convection–diffusion problems of delayed type in physics helps us to understand transport phenomena and has practical applications in various fields. The mathematical analysis of this model has practical applications in various fields, such as flow dynamics, material science, and environmental modeling. In this paper, the theory of reproducing kernel spaces (RKS) is utilized to solve singularly perturbed 2D parabolic convection–diffusion problems of delayed type. To this end, a series form for the solution is first constructed in reproducing kernel Hilbert space, and then, the approximate solution is given as an N -term summation. The main contribution of the present research is that, for the first time, a novel formula is found for the homogenization of 2D initial-boundary-value problems. Furthermore, a semi-analytical RKS method is employed without employing the Gram–Schmidt orthogonalization algorithm. We derive theorems to reveal stability and convergence properties which are examined by numerical experiments. The technique is especially suited for problems having boundary-layer behavior. Numerical results are provided to demonstrate the efficiency, stability, and superiority of the proposed technique. [ABSTRACT FROM AUTHOR]

We study the asymptotic behaviour of a linear optimal control problem posed on a locally periodic rapidly oscillating domain. We consider an $ L^2 $ L 2 -cost functional constrained by a Poisson problem having a mixed boundary condition: we assume a homogeneous Neumann condition on the oscillating part of the boundary and a homogeneous Dirichlet condition on the remaining part. [ABSTRACT FROM AUTHOR]

This paper presents a multiscale progressive fatigue damage model to predict the fatigue life of composite laminates. The multi-level damage model was employed considering the interfacial debonding effect, and effective material properties were calculated through homogenization. Damage variables and damage slopes were defined at the constituent level, and fatigue damage parameters were obtained using the residual stiffness data with the chaotic firefly algorithm. The model was implemented into ABAQUS, then validated with flat-bar and pin-loaded specimens of AS4/3501-6 composite. The numerical results corresponded well with the experimental data and showed the ability to capture the failure propagation of composite laminates. [ABSTRACT FROM AUTHOR]

The electron beam cold hearth melting (EBCHM) process is one of the key processes for titanium alloy production. The unique characteristic of this pyrometallurgy process is the application of the cold hearth, which is responsible for controlling the Low-Density Inclusions (LDIs) and High-Density Inclusions (HDIs) in the melt. As a key process of inclusion removal, the information such as melt residence time in the cold hearth is directly related to the control of metallurgical defects in the ingot, and may also affect the composition distribution of the ingot. In this paper, the details for the physical phenomena, namely the evolution of the pool, the evolution of the flow, and the evolution of the component in the cold hearth during EBCHM are investigated using a modified multi-physical numerical model. The effects of melting temperature and melting speed on these phenomena were investigated. The purpose is to provide more fundamental knowledge and to further enhance the applications of EBCHM for more titanium alloys. [ABSTRACT FROM AUTHOR]