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At least 235 records · Page 13

Crafting pixels in wood: understanding the interplay of technologies and visual perception in wooden photo engraving

This paper delves into the realm of laser engraving of photographs on wooden surfaces and explores the diferences between mathematical and human perception. A comprehensive quality study was conducted to explore the results achieved by 27 diferent realizations. The evaluation process involves both objective analyses and subjective assessments from hundreds of ratings of 60 evaluators, with the aim of unravelling the intricate interplay between technology and visual perception. The study also poses the intriguing question of whether the image most accurately transferred onto a wooden surface is also the most favourably perceived by potential customers and what are their preferences for laser engraved products.

Jurek, Martin [Ostrava, Tech. U.]↗

Exact Ground State of Interacting Electrons in Magic Angle Graphene

One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi-θ$${\theta }$$ and Weierstrass-℘$${\wp }$$ functions.

Becker, Simon↗

A rheological model for loose sands with insights from DEM

A rheological model for loose granular media is developed to capture both solid-like and fluid-like responses during shearing. The proposed model is built by following the mathematical structure of an extended Kelvin–Voigt model, where an elastic spring and plastic slider act in parallel to a viscous damper. This arrangement requires the partition of the total stress into rate-independent and rate-dependent stress components. To model the solid-like behavior, a simple frictional plasticity model is adopted without modifications, thus contributing to the rate-independent stress. Instead, the fluid-like or rate-dependent stress is further decomposed into deviatoric and volumetric parts, by proposing a new formulation based on a combination of the μ(I) relation, originally developed under pressure-controlled shear, with a pressure-shear rate relation derived under volume-controlled shear. The proposed formulation allows the model to capture both the increase in the friction coefficient and the enhanced dilation at high shear rates. High-fidelity simulation data, obtained from discrete element method and multiscale modelling, are used to evaluate the performance of the proposed constitutive model. The model provides accurate results under both drained and undrained simple shear paths across a wide range of shear rates. Furthermore, it successfully reproduces at much lower computational cost the flowslide mobility computed through multiscale simulations, which is primarily regulated by the shear rate dependence of the material properties during the dynamic runout stage.

Elasticity↗

Methodologies and strategies for detecting fiber orientation in polymeric fiber-reinforced composites

In this review paper different methods and techniques for representing fiber orientation in advanced polymer matrix composites are presented. A description of the effect of fiber orientation on processing, fabrication and mechanical properties of a composite material is presented. The paper discusses the mathematical modeling and modeling techniques for fiber structure representation in polymeric composites, with an emphasis on fiber orientation in a composite part. The paper is divided into two sections; namely—destructive techniques and non-destructive techniques. The capabilities and limitations of each technique with respect to fiber orientation detection and measurements are discussed.

composites↗

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

Autoencoders↗

A cluster of results on amplituhedron tiles

Abstract The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in $$\mathcal {N}=4$$ N = 4 super Yang–Mills theory. It generalizes cyclic polytopes and the positive Grassmannian and has a very rich combinatorics with connections to cluster algebras. In this article, we provide a series of results about tiles and tilings of the $$m=4$$ m = 4 amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for $$\text{ Gr}_{4,n}$$ Gr 4 , n . Secondly, we exhibit a tiling of the $$m=4$$ m = 4 amplituhedron which involves a tile which does not come from the BCFW recurrence—the spurion tile, which also satisfies all cluster properties. Finally, strengthening the connection with cluster algebras, we show that each standard BCFW tile is the positive part of a cluster variety, which allows us to compute the canonical form of each such tile explicitly in terms of cluster variables for $$\text{ Gr}_{4,n}$$ Gr 4 , n . This paper is a companion to our previous paper “Cluster algebras and tilings for the $$m=4$$ m = 4 amplituhedron.”

Physics↗

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions

Many imaging techniques for biological systems—like fixation of cells coupled with fluorescence microscopy—provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. In this study, these snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

59 BASIC BIOLOGICAL SCIENCES↗

Enhancing occupant behavior representation for interoperability between building information modeling and building energy modeling

Building Performance Simulation (BPS) has been adopted as an essential tool for designing, operating, and retrofitting buildings to optimize energy efficiency throughout the building life cycle. The Green Building XML (gbXML) schema facilitates seamless data exchange between Building Information Modeling (BIM) and Building Energy Modeling (BEM) software tools. However, limited occupant behavior (OB) representation in BIM often leads to inconsistent and inaccurate energy simulation in BEM software. This paper presents 154 systematic enhancements to the existing occupant behavior XML (obXML) schema v1.3.4, initially developed for standardizing OB representation for BEM, to address existing limitations and improve interoperability with BIM models. The enhancements encompass improved integration with BIM models through extended building representations and system operations, expanded support for advanced OB models with additional environmental parameters and mathematical capabilities, and implementation of a standardized model documentation framework. To facilitate seamless data transformation between gbXML and obXML schemas, we developed a publicly available gb-obXML Schema Converter. Three case studies demonstrate the enhanced schema’s capabilities: representation of building information using a two-story office building model, documentation of a window operation behavior model, and validation of the schema converter’s functionality. The enhanced obXML schema v1.4 enables sophisticated modeling of occupant-building interactions while maintaining consistency with industry-standard BIM schemas. The standardized documentation framework facilitates reproducibility and knowledge sharing in the OB research community, while the schema converter automates the integration of building information into OB simulation workflows. These enhancements establish a foundation for more accurate building performance simulation by supporting sophisticated representation of occupant behavior within the BIM-to-BEM simulation workflows.

Chung, Jihoon↗

Comparative studies of cross-phase dynamics in turbulent momentum flux and particle flux at the tokamak edge

Turbulent transport events, including turbulent transport flux of momentum (i.e., turbulent momentum flux or Reynolds stress) and turbulent transport flux of particle (i.e., turbulent particle flux), have important effects on the confinement performance of magnetic confinement fusion devices. Poloidal Reynolds stress is the ensemble average of the product of radial velocity fluctuations and poloidal velocity fluctuations, i.e., $\langle {\widetilde{v}}_{r}{\widetilde{v}}_{\theta }\rangle$. Turbulent particle flux is the ensemble average of the product of radial velocity fluctuations and density fluctuations, i.e., $\langle \widetilde{n}{\widetilde{v}}_{r}\rangle$. Changes in either amplitude of fluctuations or cross phase between fluctuations can cause changes in turbulent transport. In this paper, cross-phase dynamics in the Reynolds stress and turbulent particle flux at the tokamak edge are studied in detail. Reynolds stress and turbulent particle flux are, respectively, written as the product of fluctuation amplitudes and an average cross-phase factor. The mathematical expressions of the average cross-phase factors are derived. The average cross-phase factors and the power spectra of cross phase are obtained using experimental measurement data. It is found that the cross-phase dynamics in Reynolds stress and particle flux are very different. Reynolds stress is found to be more sensitive to cross phase than particle flux is. In the strong $E\times B$ shear layer, spatial slips of cross phase lead to the obvious radial gradient of Reynolds stress. In the no/weak $E\times B$ shear region, the cross phase in Reynolds stress tends to lock. Here, phase locking refers to that the power spectra of phase tend to distribute around a fixed phase which does not change with radial position, while phase slip means that the power spectra of cross phase tend to distribute around a phase that varies with radial position. Phase slip or locking mainly describes the central phase weighted by the power spectra, while the phase scattering mainly describes the dispersion of the power spectrum distribution of the phase. The increased scattering of cross phase, which indicates the power spectra distribution of the phase is more dispersed, contributes to the decreased Reynolds stress for higher collisionality. The cross phase in particle flux tends to lock in both strong and no/weak shear regions. The degree of scattering of cross phase in the particle flux does not change obviously as collisionality increases. For higher collisionality, it is the increased density fluctuation amplitude rather than cross-phase dynamics that leads to the increased particle flux. The underlying physical mechanism that causes Reynolds stress and particle flux to exhibit different phase dynamics is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗

Elucidating grain boundary energy minimization mechanisms in textured Ca-doped alumina with inclination-dependent Monte Carlo Potts simulations

The grain growth behavior of textured Ca-doped alumina is compared to Monte Carlo Potts (MCP) simulations to investigate the effect of anisotropic grain boundary (GB) properties on local boundary migration. Experimentally, the growth of textured Ca-doped alumina results in highly elongated grains. The relative GB energy distribution is measured using the thermal groove method before and after heat treating at 1600°C, finding that high energy GBs are eliminated during grain growth. No significant difference in the GB energy distributions is found between the long and short axes of the elongated grains, suggesting that anisotropic mobility may be responsible for the grain shape. However, MCP simulations with anisotropic mobility as a function of plane inclination do not result in grains with distinct morphologies, regardless of the degree of anisotropy introduced. The final grain shape after grain growth of textured Ca-doped alumina resembles that of the MCP simulations using an anisotropic GB energy as a cosine function of plane inclination. Several energy functions are tested and only those that mathematically impose a torque (second derivative of energy with respect to the plane inclination angle) result in elongated grains. Although area reduction is the dominant energy minimization mechanism, these results suggest that local GB migration is affected by anisotropic GB energy and torque and alternative mechanisms like GB replacement and reorientation.

36 MATERIALS SCIENCE↗

Localized material compression to correct distortion in wire arc additive manufacturing

Wire Arc Additive Manufacturing (WAAM) is an advanced manufacturing technology which utilizes welding systems to generate three dimensional geometries in a layer-by-layer fashion. Distortion or warping of a print substrate and WAAM components due to thermally induced residual stresses is an ongoing challenge limiting the widespread adoption of WAAM technologies for producing components. In this manuscript, a novel approach is described to address thermal distortion in deposited components by applying lateral compressions along the length of the deposited material. To demonstrate this method, a series of single-track walls were printed and compressed at evenly spaced intervals using a modified hydraulic cutter tool. The jaws of the tool were modified to compress material rather than to shear it. A mathematical model was developed to relate the curvature of the deposited material to the volume of compression required to eliminate this distortion. Validation of this model was performed using 3D scan data to compare the change in wall curvature induced by compression to the volume of the applied compressions. Substrate deflection was also compared against a control wall, and implementation of wall compression reduced maximum deflections by 93% across a series of four depositions and subsequent compressions. Wall cross sections were also analyzed to determine the impact of compression on material hardness and grain structure. The results demonstrate that successively placed lateral compressions can effectively control and potentially eliminate bending distortion in printed parts. This methodology can be further developed to form a robust model for correction of thermally-induced distortion in WAAM components.

Additive manufacturing↗

A dynamic volumetric heat source model for laser additive manufacturing

Melt pool scale models of laser powder bed fusion (LPBF) offer insights into the process-structure-property relationships in additive manufacturing (AM). These models often neglect physical phenomena such as vapor cavity formation and fluid mechanics to reduce computational demands. Instead, volumetric heat source models are used to represent the effects that these phenomena have on the predicted melt pool dimensions. Generally, the dimensions and effective absorption of the volumetric heat source are calibrated to reproduce melt pool dimensions observed in metallographic cross sections taken from single-track experiments on bare plate. However, the transient nature of LPBF often deviates the melt pool dimensions from the assumed steady-state conditions of single-track experiments, motivating the need for a volumetric heat source model that more generally considers the dynamic relationship between melt pool shape and laser-material interactions. Here, we introduce a two-parameter volumetric heat source model that integrates several existing models into a generalized mathematical expression, providing independent control over the radial heat distribution via the parameter k and the volumetric shape of the heat source via the parameter m. This parameterization enables the calibration of melt pool shape predictions through simultaneous adjustment of these parameters, while keeping the radial heat source dimensions consistent with the experimental spot size (D4σ) and constraining the heat source depth and absorption to physically derived expressions for cavities. Consequently, the proposed volumetric heat source model adapts to changes in the local melt pool conditions due to scanning strategy and part geometry by dynamically adjusting the heat source depth and absorption. We demonstrate the capabilities of the proposed model through comparisons with a collection of experiments from the Additive Manufacturing Benchmark (AMBench).

36 MATERIALS SCIENCE↗

Catalytic hydrogenation of HMF to BHMF over copper catalysts

2,5-Bis(hydroxymethyl)furan (BHMF) is a bio-derived building block for polyester production, obtained via the hydrogenation of 5-hydroxymethylfurfural (HMF). First-principles thermodynamic equilibrium calculations indicate that this reaction is not thermodynamically limited under relevant conditions (e.g., 100 °C and high H 2 partial pressure). In this work, crude HMF was employed as the feedstock for BHMF synthesis. Initially, acidic impurities and humins were removed from unrefined HMF through filtration using a packed bed of γ-alumina. A comprehensive study of the filtration process is presented, including filtration kinetics, breakthrough curve analysis, and mathematical modeling. The purified HMF was subsequently hydrogenated over a 10 wt% CuZrO 2 catalyst, using ethanol as the reaction solvent. Batch reactions were first performed for collection of kinetic data to guide the transition to continuous flow operation. Kinetic data was collected in a fixed bed reactor at varying contact time, time on stream, temperature, and HMF concentration. This data was used to develop a kinetic model for HMF hydrogenation. Maximum BHMF production rates were achieved at 130 °C, accompanied by minor formation of byproducts from BHMF ring-opening reactions. The BHMF selectivity was 100 % at 100 °C although with lower reaction rates. Furthermore, catalyst stability tests revealed a loss of up to 50 % in catalytic activity within the first 24 h, likely due to the adsorption of HMF-derived oligomers that are not easily removed by filtration.

Crude HMF filtration↗

CFD modeling of turbulent air flow in self-heated gyroid TPMS structures: Thermal-hydraulic performance and validation

The application of mathematically derived geometries, such as triply periodic minimal surface (TPMS) lattices, has garnered significant interest across various fields, including the nuclear sector, due to their superior thermal-hydraulic characteristics for heat transfer compared to traditional plain or finned tubes. Here, this study validates a computational fluid dynamics (CFD) model, evaluates different turbulence models and CFD model settings, and performs uncertainty quantification to provide a comprehensive analysis. Despite extensive research on CFD modeling of TPMS lattices, such as gyroid and diamond geometries, there is a notable lack of publicly available literature providing comprehensive details on numerical analysis aspects, including convergence and methodological best practices. This study embarks on a benchmark analysis of a gyroid geometry to evaluate its thermal-hydraulic performance under turbulent flow conditions and scrutinize various CFD model configurations. The main contributions of this work include validating the CFD model, assessing and comparing different turbulence models, and enhancing pressure drop and temperature prediction capabilities. The results aim to support the development of methodologies needed to benchmark and enhance numerical analysis techniques for TPMS lattices. This work seeks to complement the existing body of knowledge, support the development of TPMS reactor concepts, and improve best practices for CFD modeling of TPMS lattices, ultimately advancing methodologies to support future applications in this domain.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.

Approximate domain boundaries↗

Degrees of rate control and AutoDiff-driven direct sensitivity analysis in heterogeneous catalysis

Despite the wide application and benefits of the degree of rate control (DRC) analysis, several details remain argued, particularly about the conservation of DRCs at transient (TR) and steady-state (SS) conditions, especially for complex reaction networks. This work argues that previous proofs about the conservation properties of DRCs have been incomplete, and we provide new mathematical proofs at TR and SS conditions. In addition, we use both analytical (automatic differentiation) and numerical (finite difference) approaches to compute DRCs for the case study of ethane hydrogenolysis (EH) over Pt(111). This work confirms that at both TR and SS conditions, the sum of all DRCs, i.e., sum of the degrees of kinetic (DKRC) and thermodynamic rate control (DTRC), is conserved at zero. At SS conditions, the sum of DKRC is conserved at 1 while the sum of DTRC is conserved at −1. In corroboration of previous works, we show that the DTRC for any adsorbate at SS is equal to the product of the species coverage and a constant. In contrast, at TR conditions, the individual sums of both DTRC and DKRC are not conserved and can be any real number, with potential implications for the novel field of dynamic catalysis. Finally, we show that the conventional finite difference (FD) approach, only useful at SS, is prone to inaccuracy and very sensitive to the value of the differential change applied. The optimal differential value also varies significantly with system and rate definition. Consequently, we describe and illustrate in this work the application of the automatic differentiation (AD) approach for the more accurate determination of DRCs at both TR and SS conditions.

Automatic differentiation↗

Implementation and evaluation of multi-dual mode counter-current chromatography in the CUP Modeler software

Counter-current chromatography (CCC) is a separation technique that utilizes immiscible solvent pairs as stationary and mobile phases, which imparts numerous benefits compared to solid-liquid chromatography including the ability to treat either the more-dense or less-dense solvent layer as the mobile phase. Multi-dual mode (MDM) is a CCC elution mode capable of improving the separation of closely eluting compounds by alternating upper- and lower-layer solvent flows in opposing directions within the same separation. While some effort has been made to model MDM, implementation of these models in experimental design has yet to be widely adopted. Accordingly, we further developed our previously published cell utilized partitioning (CUP) model to include MDM predictions with CCC and packaged the full suite of CUP modeling capabilities into a user-friendly, open-source tool called the CUP Modeler. The mathematical model for MDM CCC was derived and validated with experimental separation of ethyl guaiacol (EG) and ethyl phenol (EP), two compounds that co-elute in our previously demonstrated reductive catalytic fractionation (RCF) lignin monomer isolation method. The developed MDM model provided insights into the effect of multiple operating parameters - including stationary phase retention, flow rate, column efficiency, feed concentration ratio, selectivity factor, and solute distribution ratios - on the separation yields, productivity, and purities. Our model agreed with prevailing understanding of MDM but also revealed new insights including that the ideal distribution ratios for co-eluting solutes to be separated by MDM is between 1.1 and 1.5, with the lower value ideally close to 1.25. Overall, this work provides fundamental insights for MDM process design and enables broader adoption of general liquid-liquid chromatography with a new, open-source user-friendly interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗