3D Problems Research Articles

A new approach for spatio-temporal interface treatment in fluid–solid interaction using artificial neural networks employing coupled partitioned fluid–solid solvers

Partitioned fluid–solid interaction (FSI) problems involving non-conforming grids pose formidable challenge in interface treatment, especially for information exchange, interface tracking, and field variable interpolation between solvers in both space and time. These demand special considerations for accurate and efficient simulations. This paper presents an application of artificial neural networks (ANN) for the interface treatment in a coupled FSI problem employing partitioned solvers. A shallow time-series ANN (nonlinear auto-regressive model with exogenous inputs, NARX) scheme is proposed to handle the exchange of Neumann/Dirichlet information at the coupling interface. This scheme involves two interface treatment models that were developed and analysed. The proposed models interpolate and transfer loads from the fluid to the solid domains, and conversely, displacements from the solid to the fluid domains between non-collocated grids. To validate this approach, we tested it on a 3D FSI problem, which involved damped oscillations of a flexible flap submerged in a fluid cavity. Adequately trained NARX interface models demonstrate reliable input–output mapping and accurate prediction of transient behaviour at the interface. Additionally, we explored the concept of reduced-order modelling (ROM) in the time domain. This allowed us to reduce the model’s complexity by half. Different training algorithms were evaluated to enhance the efficiency and performance of the proposed scheme. The study demonstrates that NARX networks trained with Bayesian Regularization (BR) and Levenberg–Marquardt (LM) algorithms exhibit the best accuracy, while the scaled conjugate gradient (SCG)-based training method provides better computational efficiency with acceptable accuracy. Overall, the NARX interface models provide precise performance and offer a viable potential for applications in FSI problems requiring accurate and faster computations.

Resilience enhancement of cyber-physical distribution systems via mobile power sources and unmanned aerial vehicles

Mobile power sources (MPS) and unmanned aerial vehicles (UAV) are critical and flexible resources to enhance the resilience of cyber–physical distribution systems. However, they are usually independently planned and dispatched. In this paper, considering the cyber–physical interdependence, topology reconfiguration and planned distribution generator islanding, an allocation and dispatch strategy of MPSs and UAVs is proposed. Before an event, a two-stage stochastic optimization based allocation model is built to pre-position MPSs and UAVs considering the uncertainty of events. After the event, a dispatch model is proposed to identify routings of MPSs and UAVs to restore electricity services. Note that both the models are mixed-integer nonlinear three-dimensional (3D) problems. As the optimal service radius and height of a UAV are independent with other variables, these two models are decomposed into two parts, i.e., one part to calculate the optimal service radius and height, and the other to identify resilience enhancement strategy. Then the two models are transformed into a mixed-integer convex programming solved by Progressive Hedging algorithm and a mixed-integer second-order cone programming, respectively. The effectiveness is verified on the modified IEEE 33-node and 123-node test systems. Numerical results highlight the necessity of co-optimizing MPSs and UAVs on cyber–physical distribution systems.

A least-squares Fourier frame method for nonlocal diffusion models on arbitrary domains

We introduce a least-squares Fourier frame method for solving nonlocal diffusion models with Dirichlet volume constraint on arbitrary domains. The mathematical structure of a frame rather than a basis allows using a discrete least-squares approximation on irregular domains and imposing non-periodic boundary conditions. The method has inherited the one-dimensional integral expression of Fourier symbols of the nonlocal diffusion operator from Fourier spectral methods for any d spatial dimensions. High precision of its solution can be achieved via a direct solver such as pivoted QR decomposition even though the corresponding system is extremely ill-conditioned, due to the redundancy in the frame. The extension of AZ algorithm improves the complexity of solving the rectangular linear system to O(Nlog2⁡N) for 1d problems and O(N2log2⁡N) for 2d problems, compared with O(N3) of the direct solvers, where N is the number of degrees of freedom. We present ample numerical experiments to show the flexibility, fast convergence and asymptotical compatibility of the proposed method.

A 3D multiobjective multi-item eco-routing problem for refrigerated fresh products delivery using NSGA-II with hybrid chromosome

In a developing countries, say India, about 40 percent fresh foods are wasted during transportation and $14 billion of post harvest products are lost due to inefficiency of cold supply chain such as using non-refrigerated vehicle during last mile transport. Hence, temperature control through refrigerated transportation is very essential. But, the by-product of this process i.e., carbon emission (CE) due to transportation and refrigeration is detrimental for the world. Only logistic transportation contributes about 25 percent of global CE. Due to the world wide infrastructural development, there are several available routes for the road transportation among different cities. For the maintenance of these routes, there are some toll plazas for collection of money. Some routes also cross the rail lines. For maximum profit, a supplier distributes the products at the earliest as the retailers fix the product’s price with respect to its freshness. Again, this process generates more CE. With these realities, a 3D multiobjective multi-item eco-routing problems for refrigerated fresh products (3DMOMIERPsfRFPs) are developed, where a refrigerated vehicle starts from a depot (refrigerated) and comes back after distributing the fresh products to retailers as per their demands. The optimal routing plan, vehicle’s velocity and preservation rate are determined so that total profit and CE are respectively maximized and minimized simultaneously. For solution, an NSGA-II with different modified operators (NSGA-IIwDOs) is developed with hybrid chromosomes having discrete and continuous variables together, probabilistic selection, problem-specific crossover and generation-dependent mutation. Some performance metrics are presented through NSGA-IIwDOs on the standard TSPLIB problems. Results of 3DMOMIERPsfRFPs without and with specific delivery time slots, road-dependent vehicle velocity and time constraints are evaluated. Pareto front for multiobjective are depicted. As a particular case, results of a previous investigation are obtained. Some of the managerial decisions are observed.

Bridging electronic and classical density-functional theory using universal machine-learned functional approximations.

The accuracy of density-functional theory (DFT) calculations is ultimately determined by the quality of the underlying approximate functionals, namely the exchange-correlation functional in electronic DFT and the excess functional in the classical DFT formalism of fluids. For both electrons and fluids, the exact functional is highly nonlocal, yet most calculations employ approximate functionals that are semi-local or nonlocal in a limited weighted-density form. Machine-learned (ML) nonlocal density-functional approximations show promise in advancing applications of both electronic and classical DFTs, but so far these two distinct research areas have implemented disparate approaches with limited generality. Here, we formulate a universal ML framework and training protocol to learn nonlocal functionals that combine features of equivariant convolutional neural networks and the weighted-density approximation. We prototype this new approach for several 1D and quasi-1D problems and demonstrate that functionals with exactly the same hyperparameters achieve excellent accuracy for a diverse set of systems, including the hard-rod fluid, the inhomogeneous Ising model, the exact exchange energy of electrons, the electron kinetic energy for orbital-free DFT, as well as for liquid water with 1D inhomogeneities. These results lay the foundation for a universal ML approach to approximate exact 3D functionals spanning electronic and classical DFTs.

Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization

Understanding the orientation of geologic structures is crucial for analyzing the complexity of the earths’ subsurface. For instance, information about geologic structure orientation can be incorporated into local anisotropic regularization methods as a valuable tool to stabilize the solution of inverse problems and produce geologically plausible solutions. We introduce a new variational method that uses the alternating direction method of multipliers within an alternating minimization scheme to jointly estimate orientation and model parameters in 2D and 3D inverse problems. Specifically, our approach adaptively integrates recovered information about structural orientation, enhancing the effectiveness of anisotropic Tikhonov regularization in recovering geophysical parameters. The paper also discusses the automatic tuning of algorithmic parameters to maximize the new method’s performance. Our algorithm is tested across diverse 2D and 3D examples, including structure-oriented denoising and trace interpolation. The results indicate that the algorithm is robust in solving the considered large and challenging problems, alongside efficiently estimating the associated tilt field in 2D cases and the dip, strike, and tilt fields in 3D cases. Synthetic and field examples show that our anisotropic regularization method produces a model with enhanced resolution and provides a more accurate representation of the true structures.

Integrating angular and domain decomposition with space-angle discontinuous Galerkin methods in 2D radiative transfer

A space-angle discontinuous Galerkin (saDG) method is used to solve the steady-state radiative transfer equation (RTE) for 2D problems involving absorption, emission, and scattering for a semitransparent medium. This approach discretizes both spatial and angular domains. Parallel computing is based on angular decomposition (AD), and domain decomposition (DD) techniques. The DD technique directly solves the entire domain using the MUMPS library, whereas the AD technique results in an iterative approach for scattering media. This study proposes a novel hybrid AD-DD method, combining the best aspects of both techniques. Numerical results investigate the scalability, performance, and efficiency of AD and DD techniques. It is shown that a hybrid AD-DD technique is superior to these individual techniques by taking advantage of their strengths. Numerical methods demonstrate the applicability of the method of the best combination of hybrid AD-DD to 2D scattering gray media with complex geometries or enclosures with circular and square obstacles.

SLIDING FRICTION IN CONTACTS WITH ONE- AND TWO-DIMENSIONAL VISCOELASTIC FOUNDATIONS AND VISCOELASTIC HALF-SPACE

Solid viscoelasticity is one of the essential origins of sliding friction, as every solid exhibits energy dissipation due to it during deformation processes. In this paper, we first show theoretical solutions for one-dimensional (1D) problems of viscoelastic friction with a 1D viscoelastic foundation. Then, we extend the 1D model to a two-dimensional (2D) model to find theoretical solutions for 2D problems of viscoelastic friction. Finally, we apply the Method of Dimensionality Reduction (MDR) to the theoretical solutions for the 1D problems to discuss three-dimensional (3D) problems of viscoelastic friction.

Parametric indoor 3D reconstruction based on binary image feature point extraction

Abstract In recent years, with the rapid advancement of laser scanning technology, indoor 3D modeling technology has significantly developed, becoming a research hotspot in the field of 3D reconstruction. Addressing the issues of high complexity in decoding point cloud surfaces in traditional indoor reconstruction, this paper proposes an indoor 3D reconstruction method based on binary image feature point extraction. The method utilizes point cloud data for semantic segmentation of the indoor environment to accurately extract the ceiling area, which is then projected onto the XOY plane and converted into a binary image, thereby transforming the 3D problem into a 2D problem. Subsequently, key feature points are identified through feature point detection technology, and systematic model construction is carried out based on the sequence of these feature points and their associated parameters. This method effectively simplifies the complexity of traditional 3D modeling, achieving accurate and parametric indoor 3D reconstruction.

A new higher-order super compact finite difference scheme to study three-dimensional non-Newtonian flows

This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the first ever developed higher-order compact finite difference scheme to solve 3D non-Newtonian flow problems. The proposed scheme is fourth-order accurate in space and second-order accurate in time, utilizing only seven adjacent grid points at the (n+1)th time level for the finite difference discretization. A time-marching methodology is employed with pressure calculated via a pressure-correction strategy based on the modified artificial compressibility method. Using the power-law viscosity model, we tackle the benchmark problem of a 3D lid-driven cavity, systematically analyzing the varied rheological behavior of shear-thinning (n = 0.5), shear-thickening (n = 1.5), and Newtonian (n = 1.0) fluids across different Reynolds numbers (Re=1,50,100,200). Both Newtonian and non-Newtonian results are carefully investigated in terms of streamlines, velocity variation, pressure distributions, and viscosity contours, and the computed results are validated with the existing benchmark results. The findings demonstrate excellent agreement with the existing results. It is found that for shear-thinning fluid (n = 0.5), u velocity is higher near the top moving wall than the case of Newtonian (n = 1.0) and shear-thickening fluid (n = 1.5) for all Re values. This extensive analysis, using the new HOSC scheme, not only increases our understanding of non-Newtonian fluid behavior but also provides a robust foundation for future research and practical applications.

A frequency domain analysis method for the dynamic response of a submerged floating tunnel under wave action

To investigate the dynamic response of a submerged floating tunnel (SFT) under the action of waves, a modal superposition method in the frequency domain was established, and the amplitudes of the modals were determined using the generalized wave loads and hydrodynamic coefficients of the structural modals. In this model, the SFT was simplified as a constant-cross-section Euler–Bernoulli beam with multiple anchor cables, and its structural modals were resolved using the finite element method (FEM). The generalized wave loads and generalized hydrodynamic coefficients were obtained using the Fourier expansion strategy of the modal function, by which the hydrodynamic problem can be converted into 2D problems with the modified Helmholtz controlling equation and solved using the matched higher-order boundary element method (HOBEM) and eigenfunction expansion. The effects of the diameter of the anchor cables and length of the SFT on the stiffness of the structure and the dynamic response of an SFT with anchor cables under wave action were investigated. Furthermore, the effects of different added mass calculation methods on the structural response were studied. In addition, the wave exciting forces were calculated using potential flow theory or linearized Morison equations according to the wave scale. Finally, the effects of the incident wave frequencies and incident angles were investigated in detail to reveal the combined resonance mechanism.

The Alpha Angle.

➢ The alpha angle was originally defined on magnetic resonance imaging (MRI) scans, using a plane, parallel to the axis of the femoral neck. However, much of the literature on the alpha angle has used radiographs or other imaging modalities to quantify the alpha angle.➢ The measurement of the alpha angle can be unreliable, particularly on radiographs and ultrasound.➢ If radiographs are used to measure the alpha angle, the circle of best-fit method should be used on multiple different views to capture various locations of the cam lesion, and "eyeballing" or estimating the alpha angle should be avoided.➢ The cam lesion is a dynamic and 3-dimensional (3D) problem and is unlikely to be adequately defined or captured by a single angle.➢ Modern technology, including readily available 3D imaging modalities, as well as intraoperative and dynamic imaging options, provides novel, and potentially more clinically relevant, ways to quantify the alpha angle.

Heat Conduction Control Using Deep Q-Learning Approach with Physics-Informed Neural Networks

As modern systems become more complex, their control strategy no longer relies only on measurement data from probes; it also requires information from mathematical models for non-measurable places. On the other hand, those mathematical models can lead to unbearable computation times due to their own complexity, making the control process non-viable. To overcome this problem, it is possible to implement any kind of surrogate model that enables the computation of such estimates within an acceptable time frame, which allows for making decisions. Using a Physics-Informed Neural Network as a surrogate model, it is possible to compute the temperature distribution at each time step, replacing the need for running direct numerical simulations. This approach enables the use of a Deep Reinforcement Learning algorithm to train a control strategy. On this work, we considered a one-dimensional heat conduction problem, in which temperature distribution feeds a control system. Such control system has the objective of reacing and maintaining constant temperature value at a specific location of the 1D problem by activating a heat source; the desired location somehow cannot be directly measured so, the PINN approach allows to estimate its temperature with a minimum computational workload. With this approach, the control training becomes much faster without the need of performing numerical simulations or laboratory measurements.

Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations

In this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference formula is considered for temporal discretization. The convergence behavior of the methods is analyzed, and the error bounds are provided. The main objective of this paper is to propose the error bounds for 2D problems by using the Sinc-Galerkin method. The proposed method in terms of convergence is studied by using the characteristics of the Sinc function in detail with optimal rates of exponential convergence for 2D problems. Some numerical experiments validate the theoretical results and present the efficiency of the proposed schemes.

Multi-Dimensional Medical Image Fusion With Complex Sparse Representation.

In the field of medical imaging, the fusion of data from diverse modalities plays a pivotal role in advancing our understanding of pathological conditions. Sparse representation (SR), a robust signal modeling technique, has demonstrated noteworthy success in multi-dimensional (MD) medical image fusion. However, a fundamental limitation appearing in existing SR models is their lack of directionality, restricting their efficacy in extracting anatomical details from different imaging modalities. To tackle this issue, we propose a novel directional SR model, termed complex sparse representation (ComSR), specifically designed for medical image fusion. ComSR independently represents MD signals over directional dictionaries along specific directions, allowing precise analysis of intricate details of MD signals. Besides, current studies in medical image fusion mostly concentrate on addressing either 2D or 3D fusion problems. This work bridges this gap by proposing a MD medical image fusion method based on ComSR, presenting a unified framework for both 2D and 3D fusion tasks. Experimental results across six multi-modal medical image fusion tasks, involving 93 pairs of 2D source images and 20 pairs of 3D source images, substantiate the superiority of our proposed method over 11 state-of-the-art 2D fusion methods and 4 representative 3D fusion methods, in terms of both visual quality and objective evaluation. The source code of our fusion method is available at https://github.com/Imagefusions/imagefusions/tree/main.

A hybrid interpolating element-free Galerkin method for 3D steady-state convection diffusion problems

This study investigates a hybrid interpolating element-free Galerkin (HIEFG) method for solving 3D convection diffusion problems. The HIEFG approach divides a 3D solution domain into a sequence of interconnected 2D sub-domains, and in these 2D sub-domains, the interpolating element-free Galerkin (IEFG) method is applied to form the discretized equations. The improved interpolating moving least-squares (IMLS) method is used to obtain the shape function of the IEFG method for 2D problems. The finite difference method is employed to combine the discretized equations in 2D sub-domains in the splitting direction. Then, the HIEFG method's formulas are derived for steady-state convection diffusion problems in 3D solution domain. Three numerical examples are used to discuss the impacts of the number of nodes, the number of split layers, and the scaling parameters of the influence domain on the computational precision and CPU time of the HIEFG technique. Imposing boundary conditions directly and the dimension splitting technique in this method significantly improves the computational speed greatly.

Determining the aerodynamic performance of a high-speed unmanned marine wig craft

The study object of this paper is the aerodynamic processes during the movement of an unmanned aerial vehicle flying low over the underlying surface. The ground effect is known to enhance the aerodynamic performance of low-flying aircraft, particularly larger ones. However, this effect is most noticeable for large objects. Unmanned vehicles are typically characterized by their relatively compact geometry. This study explores the aerodynamic processes involved in the flight of a small-sized vehicle using the principle of dynamic support over a surface. The particular prototype of the unmanned aerial vehicle suggested by the authors has been examined herein. The aim of the study is to evaluate the aerodynamic forces affecting a small-sized unmanned high-speed vehicle that employs the dynamic principle of support over the surface (WIG craft) by using CFD modeling. In contrast to most available studies on the ground effect, a 3D problem statement was used in this work. Computational experiments have visualized the physical fields surrounding an aircraft in flight over the ground. This study determines how the distance from the surface affects the aerodynamic properties of a small-sized aircraft, as well as the height of the effective zone where ground effect influences the small-sized WIG craft within . It has been shown that approaching the surface leads to a shift in the center of pressure of the vehicle, which leads to a change in aerodynamic momentum. This phenomenon must be taken into account when designing a control system to provide a stable flight. The study's findings are directly relevant for the development of a type of unmanned vehicles that use the dynamic principle of support over the surface.

Dimensionality reduction simplifies synaptic partner matching in an olfactory circuit.

The distribution of postsynaptic partners in three-dimensional (3D) space presents complex choices for a navigating axon. Here, we discovered a dimensionality reduction principle in establishing the 3D glomerular map in the fly antennal lobe. Olfactory receptor neuron (ORN) axons first contact partner projection neuron (PN) dendrites at the 2D spherical surface of the antennal lobe during development, regardless of whether the adult glomeruli are at the surface or interior of the antennal lobe. Along the antennal lobe surface, axons of each ORN type take a specific 1D arc-shaped trajectory that precisely intersects with their partner PN dendrites. Altering axon trajectories compromises synaptic partner matching. Thus, a 3D search problem is reduced to 1D, which simplifies synaptic partner matching and may generalize to the wiring process of more complex brains.

An explicit fourth‐order hybrid‐variable method for Euler equations with a residual‐consistent viscosity

AbstractIn this article, we present a formally fourth‐order accurate hybrid‐variable (HV) method for the Euler equations in the context of method of lines. The HV method seeks numerical approximations to both cell averages and nodal solutions and evolves them in time simultaneously; and it is proved in previous work that these methods are supraconvergent, that is, the order of the method is higher than that of the local truncation error. Taking advantage of the supraconvergence, the method is built on a third‐order discrete differential operator, which approximates the first spatial derivative at each grid point using only the information in the two neighboring cells. Analyses of stability, accuracy, and pointwise convergence are conducted in the one‐dimensional case for the linear advection equation; whereas extension to nonlinear systems including the Euler equations is achieved using characteristic decomposition and the incorporation of a residual‐consistent viscosity to capture strong discontinuities. Extensive numerical tests are presented to assess the numerical performance of the method for both 1D and 2D problems.

Timestep-dependent element interpolation functions in the method of matched sections on the example of heat conduction problem

The paper is devoted to further elaboration of the method of matched sections as a new technique within the finite element method. Like FEM it supposes that: a) the complex domain is represented as a mesh of nonintersecting simple elements; b) algebraic relations between the main parameters of an element are established from the governing differential equations; c) all relationships from all elements are assembled into one global matrix. On the other hand, it has two distinct features. The first one is that relations between kinematic and inner force parameters (called Connection equations) are derived from the approximate analytical solution of the governing equations rather than by the application of minimization techniques. The second one consists in that the conjugation between elements is provided between the adjacent sides (sections) rather than in the nodes of the elements. In application to the transient 2D heat conduction, it is assumed that for each small rectangular element, the 2D problem can be considered as the combination of two 1D problems – one is x-dependent, and another is y-dependent. Each problem is characterized by two functions – the temperature, T, and heat flux Q. In practical realization for rectangular finite elements, the method is reduced to the determination of eight unknowns for each element – two unknowns on each side, which are related by the connection equations, and the requirement of the temperature continuity at the center of the element. Another salient feature of the paper is an implementation of the original implicit time integration scheme, where the time step becomes the parameter of the element interpolation function within the element, i.e. it determines the behavior of the connection equations. This method was initially proposed by the first author for several 1D problems, and here for the first time, it is applied to 2D problems. The number of tests for rectangular plates exhibits the remarkable properties of the proposed time integration scheme concerning stability, accuracy, and absence of any restrictions as to increasing the time step.