3D Domain Research Articles

Limit stationary statistical solutions of stochastic Navier–Stokes–Voigt equation in a 3D thin domain

Limit stationary statistical solutions of stochastic Navier–Stokes–Voigt equation in a 3D thin domain

A meshless local Galerkin method for solving a class of nonlinear time-dependent mixed integral equations on non-rectangular 2D domains

A meshless local Galerkin method for solving a class of nonlinear time-dependent mixed integral equations on non-rectangular 2D domains

Whole Organ Volumetric Sensing Ultrasound Localization Microscopy for Characterization of Kidney Structure.

Glomeruli are the filtration units of the kidney and their function relies heavily on their microcirculation. Despite its obvious diagnostic importance, an accurate estimation of blood flow in the capillary bundle within glomeruli defies the resolution of conventional imaging modalities. Ultrasound Localization Microscopy (ULM) has demonstrated its ability to image in-vivo deep organs in the body. Recently, the concept of sensing ULM or sULM was introduced to classify individual microbubble behavior based on the expected physiological conditions at the micrometric scale. In the kidney of both rats and humans, it revealed glomerular structures in 2D but was severely limited by planar projection. In this work, we aim to extend sULM in 3D to image the whole organ and in order to perform an accurate characterization of the entire kidney structure. The extension of sULM into the 3D domain allows better localization and more robust tracking. The 3D metrics of velocity and pathway angular shift made glomerular mask possible. This approach facilitated the quantification of glomerular physiological parameter such as an interior traveled distance of approximately 7.5 ±0.6 microns within the glomerulus. This study introduces a technique that characterize the kidney physiology which can serve as a method to facilite pathology assessment. Furthermore, its potential for clinical relevance could serve as a bridge between research and practical application, leading to innovative diagnostics and improved patient care.

On interpolation spaces of piecewise polynomials on mixed meshes

We consider fractional Sobolev spaces Hθ, θ ∈ (0,1), on 2D domains and H1-conforming discretizations by globally continuous piecewise polynomials on a mesh consisting of shaperegular triangles and quadrilaterals. We prove that the norm obtained from interpolating between the discrete space equipped with the L2-norm on the one hand and the H1-norm on the other hand is equivalent to the corresponding continuous interpolation Sobolev norm, and the norm-equivalence constants are independent of meshsize and polynomial degree. This characterization of the Sobolev norm is then used to show an inverse inequality between H1 and Hθ.

Superior Piezoelectric Performance in Textured CaBi2Nb2O9 Ferroelectric Ceramics through Rare-Earth Gadolinium Doping and Spark Plasma Sintering.

High-performance piezoelectric ceramics with excellent thermal stability are crucial for high-temperature piezoelectric sensor applications. However, conventional fabrication processes offer limited enhancements in piezoelectric performance. In this study, we achieved a significant breakthrough in the piezoelectric performance of highly textured CaBi2Nb2O9 (CBN) ceramics by incorporating rare-earth gadolinium doping and utilizing spark plasma sintering. The resulting Ca0.97Gd0.03Bi2Nb2O9 (CBN-3Gd) ceramics exhibited superior piezoelectric properties, with a high piezoelectric constant d33 of 26 pC/N and a high Curie temperature TC of 946 °C. We employed piezoresponse force microscopy (PFM) to observe the morphology and dimensions of the ferroelectric domains, revealing a rod-shaped 3D domain configuration. This configuration facilitated polarization rotation in the textured ceramics, as analyzed using X-ray photoelectron spectroscopy (XPS) and polarization-electric field (P-E) hysteresis loops. Furthermore, the textured CBN-3Gd ceramics demonstrated exceptional thermal stability and reliability. The piezoelectric constant d33 decreased by only 11.8% over a temperature range of room temperature to 500 °C, and the DC electrical resistivity remained at 6.7 × 105 Ω cm at 600 °C. This work not only highlights the great potential of textured CBN-based ceramics for high-temperature piezoelectric sensors but also provides a viable strategy for enhancing the performance of piezoelectric materials with large aspect ratio micromorphology.

Shape effects on wave propagation in a 2D domain using the finite element method

Shape effects on wave propagation in a 2D domain using the finite element method

Integrating an urban fire model into an operational wildland fire model to simulate one dimensional wildland–urban interface fires: a parametric study

Background Wildland fires that occur near communities, in the wildland–urban interface (WUI), can inflict significant damage to urban structures. Although computational models are vital in wildfires, they often focus solely on wildland landscapes. Aim We conducted a computational study to investigate WUI fire spread, encompassing both urban and wildland landscapes. Methods We developed a 1D landscape-scale semi-physical model by integrating a semi-physical urban fire spread model into an Eulerian level set model of wildfire. The model includes ignition and spread through radiation, direct flame contact and ember deposition. Key results Through a parametric study, we compare the relative change of spread rate from various structural properties and landscape layouts represented by model parameters, highlighting the significant impact of fire-resistant structure materials over surface treatments. Layout configurations play a pivotal role in fire spread, with isolated islands of combustibles effective in reducing spread rate, aligning with existing mitigation strategies. Conclusion Despite using a 1D domain and limitations on spatial and temporal variability, our model provides insights into underlying phenomena observed in WUI fires and their mitigation. It offers early-stage development of strategies for managing structure materials and landscape layouts. Implications Our model and findings provide insights into WUI fire dynamics, paving the way for advanced mitigation strategies.

Accuracy of the Pore Morphology Method in Modeling Fluid Saturation in 3D Fibrous Domains

Accuracy of the Pore Morphology Method in Modeling Fluid Saturation in 3D Fibrous Domains

Design of a switchable triple-waveguide-based TE-converted polarization beam splitter based on lithium niobate

The lithium-niobate-on-insulator (LNOI) platform has been the new force to drive the developments of integrated photonics, where efficient polarization management and mode conversion are the fundamental issues to be solved. In this work, we proposed a switchable TE-converted polarization beam splitter (PBS) based on optical phase change material (PCM) and a triple-waveguide in simulation. To optimize and analyze the proposed design, the 3D finite difference time domain (3D-FDTD) method is applied in this work. The simulated results indicate that when PCM is in the amorphous state, the device can effectively separate the TM and TE modes, achieving a low insertion loss (<0.5dB) for both modes at 1550 nm. While the PCM is in the crystalline state, the proposed device can realize the efficient conversion from the input TE0 mode to output TE1 mode, which obtains a mode conversion efficiency of 99.5%, crosstalk of −26dB, and insertion loss of 0.5 dB at 1550 nm. We hope such a device can make compact integration and capacity improvement for the integrated photonics in LNOI.

Characterization and property prediction of fibre structures within discontinuous-fibre reinforced polymer matrix composites using 3D fibre cells assisted by contrastive learning

Fibre-cell-based fibre structure characterization approach was proposed recently to characterize the fibre distribution within discontinuous-fibre reinforced polymer matrix composites (DFR PMCs) over a 2D domain. This approach determines the distribution state of each fibre based on the relative size and topological features of its fibre cell. In this study, the fibre-cell-based approach is extended for 3D fibre domains. A convolutional neural network (CNN) encoder is trained through contrastive learning to quantitatively represent topological features of 3D fibre cells. Subsequently, the feature–property correlations are established using an artificial neural network (ANN). For practical application, the ANN is integrated with an image analysis software to provide in situ predictions of local elastic modulus of a DFR PMC based on its fibre structures observed from micro-CT images. The predictions are also compared with the experimental measurements acquired through microindentation testing, and it shows a good agreement.

Quantifying the frequency modulation in electrograms during simulated atrial fibrillation in 2D domains

Atrial fibrillation (AF) affects millions of people in the world, causing increased morbidity and mortality. Treatment involves antiarrhythmic drugs and catheter ablation, showing high success for paroxysmal AF but challenges for persistent AF. Experimental evidence suggests reentrant waves and rotors contribute to AF substrates. Ablation procedures rely on electroanatomical maps and electrogram (EGM) signals; however, current methods used in clinical practice lack consideration for time–frequency varying EGM components. The fractional Fourier transform (FrFT) can be adopted to capture time-varying frequency components, thereby enhancing the comprehension of arrhythmogenic substrates during AF for improved ablation strategies. To this end, a FrFT-based algorithm is developed to characterize non-stationary components in EGM signals from simulated AF episodes. The proposed algorithm comprises a pre-processing step to enhance the coarser features of the EGM waveform, a windowing process for dynamic assessment of the EGM, and a FrFT order optimization stage that seeks compact signal representations in fractional Fourier domains. The resulting order is related to the rate of frequency change in the signal, making it a useful indicator for frequency-modulated components. The FrFT-based algorithm is implemented on EGM signals from AF simulations in 2D domains representing a region of the atrial tissue. Consequently, the computed optimum FrFT orders are used to build maps that are spatially correlated to the underlying propagation dynamics of the simulated AF episode. The results evince that the extreme values in the optimum orders map pinpoint the localization of fibrillatory mechanisms, generating EGM activation waveforms with varying frequency content over time.

Full-wave simulations on helicon and parasitic excitation of slow waves near the edge plasma

Helicon waves are thought to be promising in various tokamaks, such as DIII-D, because they can penetrate reactor-grade high-density cores and drive the off-axis current with higher efficiency. In the frequency regime ∼ 476 MHz, both slow electrostatic and fast electromagnetic helicon waves can coexist in DIII-D. If the antenna parasitically excites the slow mode, these waves can propagate along the magnetic field line into the scrape-off layer (SOL). Although the importance of the misalignment of the Faraday screen and the electron density in the SOL on the excitation and propagation of slow modes is well known, the conditions for minimizing slow mode excitation have yet to be optimized. Using the Petra-M simulation code in the 2D domain, we analyze the effects of the misalignment of the antenna in the poloidal direction, the misalignment of the Faraday screen in the toroidal direction, and the density in front of the antenna on slow mode generation. Our results suggest that the misalignment of the Faraday screen is a critical factor in reducing the slow mode and that the misalignment angle should be below ∼ 5° to minimize the slow wave excitation. When the electron density is higher than 3.5×1018 m−3 in the SOL, the generation of the slow mode from the antenna is minimized and unaffected by the misalignment of the Faraday screen.

A Coupled Spatial-Network Model: A Mathematical Framework for Applications in Epidemiology.

There is extensive evidence that network structure (e.g., air transport, rivers, or roads) may significantly enhance the spread of epidemics into the surrounding geographical area. A new compartmental modeling framework is proposed which couples well-mixed (ODE in time) population centers at the vertices, 1D travel routes on the graph's edges, and a 2D continuum containing the rest of the population to simulate how an infection spreads through a population. The edge equations are coupled to the vertex ODEs through junction conditions, while the domain equations are coupled to the edges through boundary conditions. A numerical method based on spatial finite differences for the edges and finite elements in the 2D domain is described to approximate the model, and numerical verification of the method is provided. The model is illustrated on two simple and one complex example geometries, and a parameter study example is performed. The observed solutions exhibit exponential decay after a certain time has passed, and the cumulative infected population over the vertices, edges, and domain tends to a constant in time but varying in space, i.e., a steady state solution.

Numerical Investigation of the Fuel Tank Sloshing Condition of a Commercial Vehicle

This study investigates the impact of baffles on fuel sloshing behavior within truck fuel tanks using numerical simulations. The volume of the fluid multiphase model is employed to analyze the flow dynamics of 25% diesel fuel in a 250 L tank, modeled in a 3D domain. Two configurations were compared: a tank with baffles and one without. The primary focus is to analyze fuel distribution within the intake port region during vehicle acceleration and deceleration maneuvers. The simulated scenario mimics a realistic driving situation. The vehicle accelerates from 0 km/h to 60 km/h over 10 s, followed by a 3-s braking period to reach a complete stop (0 km/h) at the 13-s mark. The simulation then observes the fuel behavior within the tank for an addi-tional 7 s while the vehicle remains stationary. Results reveal significant differences in fuel behavior between baffled and unbaffled tanks. In the absence of baffles, the sloshing motion is substantial, leading to a complete depletion of fuel in the intake port region for a duration of 3 s during both the acceleration and deceleration phases (between 10 and 13 s). Compared to a standard tank, the presence of baffles significantly reduced the sloshing amplitude by approximately 70%. Furthermore, baffles led to a 50% decrease in pressure variations on the tank walls. Temporary fuel starvation can negatively impact engine performance and combustion efficiency. Conversely, the presence of baffles within the tank effectively mitigates sloshing and ensures continuous fuel presence at the intake port the entire simulation. This suggests that baffles play a crucial role in maintaining a stable and consistent fuel supply to the engine, even during dynamic vehicle maneuvers.

Why is Dimeric 3D Domain Swapping in Antibody Light Chains Missing from the Solution? Atomistic Insights Mechanisms.

Misfolding of antibody light chains can lead to systemic light chain amyloidosis, which is associated with misfolding and aggregation. The antibody light chain may engage in 3D domain swapping within the variable region (#4VL) through hydrogen bonding (HB) interactions, potentially forming the tetramer, as revealed in solution and crystal structures. However, the 3D-domain swapping (3D-DS) dimers could not be detected experimentally. This study investigates the absence of 3D-DS using computational approaches, focusing on structural dynamics, solvation effects, and stability relevant to the loss of 3D-DS. Microscale molecular dynamics simulations of #4VL and 3D-DS confirm that native HB interactions are essential to maintain β-sheet structures in both #4VL and 3D-DS. A flickering native HB interaction in the 3D-DS system, caused by repulsive interaction with water molecules in the hydrophobic region, leads to intramolecular breathing motions and oligomerization in another 3D-DS. Structural dynamics of the 3D-DS dimer in long-run simulations were analyzed using the newly developed integrated solvation-based principal component analysis (3D-RISM/PCA) and density-based spatial clustering of applications with noise, confirm that if the 3D-DS cannot form the tetramer within the breathing motion process, the 3D-DS will collapse. This finding provides insights into why the 3D-DS dimer is missing from the solution and can be used to design and develop 3D-DS in other antibodies.

Intrinsic Ferroelectric Switching in Two-Dimensional α-In2Se3.

Two-dimensional (2D) ferroelectric semiconductors present opportunities for integrating ferroelectrics into high-density ultrathin nanoelectronics. Among the few synthesized 2D ferroelectrics, α-In2Se3, known for its electrically addressable vertical polarization, has attracted significant interest. However, the understanding of many fundamental characteristics of this material, such as the existence of spontaneous in-plane polarization and switching mechanisms, remains controversial, marked by conflicting experimental and theoretical results. Here, our combined experimental characterizations with piezoresponse force microscope and symmetry analysis conclusively dismiss previous claims of in-plane ferroelectricity in single-domain α-In2Se3. The processes of vertical polarization switching in monolayer α-In2Se3 are explored with deep-learning-assisted large-scale molecular dynamics simulations, revealing atomistic mechanisms fundamentally different from those of bulk ferroelectrics. Despite lacking in-plane effective polarization, 1D domain walls can be moved by both out-of-plane and in-plane fields, exhibiting avalanche dynamics characterized by abrupt, intermittent moving patterns. The propagating velocity at various temperatures, field orientations, and strengths can be statistically described with a universal creep equation, featuring a dynamical exponent of 2 that is distinct from all known values for elastic interfaces moving in disordered media. This work rectifies a long-held misunderstanding regarding the in-plane ferroelectricity of α-In2Se3, and the quantitative characterizations of domain wall velocity will hold broad implications for both the fundamental understanding and technological applications of 2D ferroelectrics.

2D Embeddings of Multi-dimensional Partitionings.

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models, where each segment of the partitioning represents a region of similar model behavior. Having computed a partitioning, one is commonly interested in understanding how large the segments are and which segments lie next to each other. While visual representations of 2D domain partitionings that reveal sizes and neighborhoods are straightforward, this is no longer the case when considering multi-dimensional domains of three or more dimensions. We propose an algorithm for computing 2D embeddings of multi-dimensional partitionings. The embedding shall have the following properties: It shall maintain the topology of the partitioning and optimize the area sizes and joint boundary lengths of the embedded segments to match the respective sizes and lengths in the multi-dimensional domain. We demonstrate the effectiveness of our approach by applying it to different use cases, including the visual exploration of 3D spatial domain segmentations and multi-dimensional parameter space partitionings of simulation ensembles. We numerically evaluate our algorithm with respect to how well sizes and lengths are preserved depending on the dimensionality of the domain and the number of segments.

Research and Proposal of 3D Domain Processing Techniques in Woodblock Model Restoration

Research and Proposal of 3D Domain Processing Techniques in Woodblock Model Restoration

Three-Dimensional Spectral Element Method Implementation for Evaluating Rooted Soil Behavior in Slope Stability Analysis

Bioengineering techniques are being increasingly adopted as a sustainable solution to soil slope instability. Despite their recognized benefits, however, the mechanistic contribution of vegetation to slope stability remains inadequately understood due to the intricate nature of soil–root interactions and the complexity of root architectures. Most existing research predominantly offers qualitative assessments of vegetation effectiveness. This study aims to numerically substantiate the role of vegetation as a bioengineering technique for soil slope stabilization. Various plant species used commonly for soil stabilization were identified, and undisturbed soil samples were collected to quantify the shear strength parameters of the soils from both barren and vegetated slopes, along with root tensile strengths. A comprehensive topographic survey was conducted to capture the precise topography of the study area. Utilizing these primary data, in this work we develop 3D models for five representative plants within each species category and employ the Spectral Element Method (SEM), an advanced higher-order formulation of the finite element method (FEM), within the 3D domain to evaluate the factor of safety for the soil slopes. The SEM offers superior accuracy and stability in numerical computations. The results obtained through the SEM were corroborated through the FEM modeling and were found to be consistent with other established methodologies. This innovative approach of 3D SEM aims to quantitatively assess the impact of vegetation on soil slope stability and provide a more rigorous understanding of bioengineering applications in geotechnical engineering.

GPU-enabled extreme-scale turbulence simulations: Fourier pseudo-spectral algorithms at the exascale using OpenMP offloading

Fourier pseudo-spectral methods for nonlinear partial differential equations are of wide interest in many areas of advanced computational science, including direct numerical simulation of three-dimensional (3-D) turbulence governed by the Navier-Stokes equations in fluid dynamics. This paper presents a new capability for simulating turbulence at a new record resolution up to 35 trillion grid points, on the world's first exascale computer, Frontier, comprising AMD MI250x GPUs with HPE's Slingshot interconnect and operated by the US Department of Energy's Oak Ridge Leadership Computing Facility (OLCF). Key programming strategies designed to take maximum advantage of the machine architecture involve performing almost all computations on the GPU which has the same memory capacity as the CPU, performing all-to-all communication among sets of parallel processes directly on the GPU, and targeting GPUs efficiently using OpenMP offloading for intensive number-crunching including 1-D Fast Fourier Transforms (FFT) performed using AMD ROCm library calls. With 99% of computing power on Frontier being on the GPU, leaving the CPU idle leads to a net performance gain via avoiding the overhead of data movement between host and device except when needed for some I/O purposes. Memory footprint including the size of communication buffers for MPI_ALLTOALL is managed carefully to maximize the largest problem size possible for a given node count.Detailed performance data including separate contributions from different categories of operations to the elapsed wall time per step are reported for five grid resolutions, from 20483 on a single node to 327683 on 4096 or 8192 nodes out of 9408 on the system. Both 1D and 2D domain decompositions which divide a 3D periodic domain into slabs and pencils respectively are implemented. The present code suite (labeled by the acronym GESTS, GPUs for Extreme Scale Turbulence Simulations) achieves a figure of merit (in grid points per second) exceeding goals set in the Center for Accelerated Application Readiness (CAAR) program for Frontier. The performance attained is highly favorable in both weak scaling and strong scaling, with notable departures only for 20483 where communication is entirely intra-node, and for 327683, where a challenge due to small message sizes does arise. Communication performance is addressed further using a lightweight test code that performs all-to-all communication in a manner matching the full turbulence simulation code. Performance at large problem sizes is affected by both small message size due to high node counts as well as dragonfly network topology features on the machine, but is consistent with official expectations of sustained performance on Frontier. Overall, although not perfect, the scalability achieved at the extreme problem size of 327683 (and up to 8192 nodes — which corresponds to hardware rated at just under 1 exaflop/sec of theoretical peak computational performance) is arguably better than the scalability observed using prior state-of-the-art algorithms on Frontier's predecessor machine (Summit) at OLCF. New science results for the study of intermittency in turbulence enabled by this code and its extensions are to be reported separately in the near future.