Arbitrary Complex Research Articles

Three-dimensional quasi-complete information numerical simulation of gravity anomalies and parallel computing on CPU-GPU

Abstract In order to improve the efficiency and accuracy of numerical simulation of gravity anomalies in large-scale complex models, this paper proposes a method for three-dimensional numerical simulation of gravity anomalies under arbitrary terrain, and implements its CPU-GPU parallel acceleration scheme. By performing a two-dimensional Fourier transform along the horizontal direction, three-dimensional partial differential satisfied by gravitational potential are transformed into one-dimensional ordinary differential equations in different wavenumbers, reducing computational and storage requirements. Moreover, the ordinary differential equations in different wavenumbers are independent of each other and have good parallelism. By retaining the vertical direction as the spatial domain and introducing traveling wave decomposition, the effects caused by upper and lower boundaries are eliminated. The vertical grid is arbitrary. A two-dimensional quasi-complete information Fourier transform is utilized to enhance both the accuracy and efficiency of the Fourier transform process, allowing both uniform and non-uniform flexible sampling. Based on the high parallelism, one-dimensional ordinary differential equations are solved in parallel using CPU, and quasi-complete information Fourier transform are computed in parallel using GPU. An abnormal sphere is designed to analyze the wavenumber spectral distribution characteristics of the anomalous potential and summarize the wavenumber sampling rules. The logarithmic uniform sampling in the wavenumber domain has high accuracy. Compared with Gauss-FFT, the quasi-complete information Fourier transform selects fewer wavenumbers and exhibits higher accuracy. The computational efficiency is greatly enhanced through the use of single-precision CPU-GPU parallel scheme, and a model with tens of millions of nodes only takes a few seconds. Two terrain models are designed to verify the algorithm’s adaptability to arbitrary complex terrains. This is significant for achieving fine inversion imaging and interpretation of gravity anomalies under large-scale complex conditions.

A new property of arbitrary complex polynomials

A new property of an arbitrary complex polynomial P ( z ) related to its derivative is established. It turns out that for arbitrary three values a 1 , a 2 and a 3 , there are lower bounds for | P ( z ) | when z belongs to the set of a 1 , a 2 , a 3 points of P ( z ) .

Dynamic Modeling and Vibration Characteristic Analysis of Fiber Woven Composite Shaft–Disk Rotor with Weight-Reducing Holes

In order to achieve the goal of a lightweight shaft–disk rotor, this paper applies the fiber woven composite material to the disk structure, and at the same time considers the design of the weight-reducing holes on the porous disk. It introduces the domain decomposition and coordinate mapping technology for this, and then establishes the dynamics model of the fiber woven composite material shaft–disk rotor. The model is based on the differential quadrature finite element method, which is suitable for fiber woven composite rotors with arbitrary complex hole patterns. The validity of the model is verified by comparing the results with the literature, finite element simulation, and experiments, and the mechanism of the influence of the material parameters and pore parameters on the vibration characteristics of the system is investigated, which provides the data support and theoretical basis for the analysis of the dynamics of the fiber woven composite rotor.

Generalized field inversion strategies for data-driven turbulence closure modeling

Most data-driven turbulence closures are based on the general structure of nonlinear eddy viscosity models. Although this structure can be embedded into the machine learning algorithm and the Reynolds stress tensor itself can be fit as a function of scalar- and tensor-valued inputs, there exists an alternative two-step approach. First, the spatial distributions of the optimal closure coefficients are computed by solving an inverse problem. Subsequently, these are expressed as functions of solely scalar-valued invariants of the flow field by virtue of an arbitrary regression algorithm. In this paper, we present two general inversion strategies that overcome the limitation of being applicable only when all closure tensors are linearly independent. We propose to either cast the inversion into a constrained and regularized optimization problem or project the anisotropy tensor onto a set of previously orthogonalized closure tensors. Using the two-step approach together with either of these strategies then enables us to quantify the model-form error associated with the closure structure independent of a particular regression algorithm. Eventually, this allows for the selection of the a priori optimal set of closure tensors for a given, arbitrary complex test case.

An Efficient and Automatic Simplification Method for Arbitrary Complex Networks in Mine Ventilation

An Efficient and Automatic Simplification Method for Arbitrary Complex Networks in Mine Ventilation

Building-block-flow computational model for large-eddy simulation of external aerodynamic applications

Computational fluid dynamics is an essential tool for accelerating the discovery and adoption of transformative designs across multiple engineering disciplines. Despite its many successes, no single approach consistently achieves high accuracy for all flow phenomena of interest, primarily due to limitations in the modeling assumptions. Here, we introduce a closure model for wall-modeled large-eddy simulation to address this challenge. The model, referred to as the Building-block Flow Model (BFM), rests on the premise that a finite collection of simple flows encapsulates the essential missing physics necessary to predict more complex scenarios. The BFM is designed to: (1) predict multiple flow regimes, (2) unify the closure model at solid boundaries and the rest of the flow, (3) ensure consistency with numerical schemes and gridding strategies by accounting for numerical errors, (4) be directly applicable to arbitrary complex geometries, and (5) be scalable to model additional flow physics in the future. The BFM is utilized to predict key quantities in five cases, including an aircraft in landing configuration, demonstrating similar or superior capabilities compared to previous state-of-the-art models. The design of BFM opens up new opportunities for developing closure models that can accurately represent various flow physics across different scenarios.

Learning arbitrary complex matrices by interlacing amplitude and phase masks with fixed unitary operations

Learning arbitrary complex matrices by interlacing amplitude and phase masks with fixed unitary operations

Segmentation of stroke lesions using transformers-augmented MRI analysis.

Accurate segmentation of chronic stroke lesions from mono-spectral magnetic resonance imaging scans (e.g., T1-weighted images) is a difficult task due to the arbitrary shape, complex texture, variable size and intensities, and varied locations of the lesions. Due to this inherent spatial heterogeneity, existing machine learning methods have shown moderate performance for chronic lesion delineation. In this study, we introduced: (1) a method that integrates transformers' deformable feature attention mechanism with convolutional deep learning architecture to improve the accuracy and generalizability of stroke lesion segmentation, and (2) an ecological data augmentation technique based on inserting real lesions into intact brain regions. Our combination of these two approaches resulted in a significant increase in segmentation performance, with a Dice index of 0.82 (±0.39), outperforming the existing methods trained and tested on the same Anatomical Tracings of Lesions After Stroke (ATLAS) 2022 dataset. Our method performed relatively well even for cases with small stroke lesions. We validated the robustness of our method through an ablation study and by testing it on new unseen brain scans from the Ischemic Stroke Lesion Segmentation (ISLES) 2015 dataset. Overall, our proposed approach of transformers with ecological data augmentation offers a robust way to delineate chronic stroke lesions with clinically relevant accuracy. Our method can be extended to other challenging tasks that require automated detection and segmentation of diverse brain abnormalities from clinical scans.

Deep learning-based general beam synthesis for atmospheric propagation

Optimizing the transmit light beams unlocks the full potential of free-space optical systems. However, designing application-specific light beams remains a challenge, especially for those traversing random media. In this study, we address this gap by proposing a deep learning-based method to generate optimal beams for propagation through atmospheric turbulence. The key mechanism is approximating the receiver statistics through batch-wise computation during the training of a convolutional neural network (CNN). On that basis, statistical performance metrics including average received power, scintillation index, and mean signal-to-noise ratio (SNR) are considered for optimization. Pseudo-modes of the beam are synthesized by weighted superposition of Hermite-Gaussian eigenmodes, enabling the creation of arbitrary complex amplitude profiles, i.e., general beams. An end-to-end implementation framework is designed to facilitate self-supervised learning and eliminate the need for pre-calculated datasets. Effectiveness of the synthesized beam is validated by wave optics simulation and experiments. In particular, comparison with Gaussian Schell-model beams demonstrates that the synthesized beam can achieve lower scintillation and greater intensity at the same time, leading to markedly enhanced receiver SNR. This advantage persists in a wider range of link configurations, extending the application range of stochastic beams.

A comprehensive investigation of the bending and vibration behavior of size-dependent functionally graded nanoplates via an enhanced nonlocal finite element shear model

This research paper conducts a comprehensive investigation into the linear bending and free vibration of size-dependent functionally graded (FG) nanoplates using an improved first-order shear deformation theory (IFSDT). The present IFSDT offers an enhanced representation and precise computation of normal and shear stresses across the thickness of the nanoplates. Notably, it not only ensures compliance with free conditions on both the upper and lower surfaces but also eliminates the need for a conventional correction factor commonly employed in the first-order shear deformation theory (FSDT). To transcend the assumptions of classical continuum mechanics and address the impacts of small-scale effects in discrete nanoplates, Eringen’s nonlocal elasticity theory is applied. The formulation of the governing equation for the bending and free vibration analyses of the FG nanoplates is achieved through the application of Hamilton’s principle. The proposed IFSDT is implemented with an efficient C0-continuous quadrilateral element which is suitable for analysis of structures with arbitrary shapes and complex forces. The model’s performance is showcased through a comparative evaluation against literature predictions, highlighting its high accuracy and rapid convergence. Additionally, the research scrutinizes the effects of various parameters, such as plate thickness, boundary conditions, aspect ratio, nonlocal parameter, different material compositions, and power-law index on the deflections, stresses, and naturel frequencies of the FG nanoplates. The results underscore the significant impact of size-dependent effects on the linear bending and vibration behaviors of the nanoplates.

The analytical model of time-harmonic electric field and impedance spectrum in the multilayered interdigital electrode structure

Accurately determining the time-harmonic electric field and impedance spectrum in the multilayered interdigital electrode (IDE) transducers with lossy dielectrics is essential for the design of the structure, the property estimation of the dielectric, and performance optimization. This paper presents an analytical model of the electric field and impedance within a multilayered interdigitated electrode (IDE) when subjected to alternating excitation through the method of separation of variables (MSV). The equivalent circuit of IDE is established, where the impedance is the parallel of capacitive coupling and resistive coupling between electrodes. The general solutions for the electric field and impedance involving arbitrary numbers and complex permittivities of the dielectric layers are analytically derived. However, due to the approximation of boundary conditions, these physical quantities cannot be accurately obtained by the conventional analytical method using conformal mapping technique (CMT) and partial capacitance technique (PCT). The proposed model exhibits proficiency in generating precise electric field images and impedance values that closely correspond with simulated data, even when accounting for the frequency-dependent characteristics of permittivity and conductivity in lossy dielectrics. Moreover, the approaches to improve the sensitivity of a traditional three-layered IDE-based sensor are demonstrated. For a three-layered IDE-based capacitive sensor, improving the sensitivity can be accomplished through the incorporation of a ground plane at the substrate's bottom and increasing the metallization rate. Conversely, it is recommended to reduce the metallization rate, increase substrate thickness, and remove the ground plane in order to enhance the sensitivity of the IDE-based impedance sensor. The experimental results demonstrate that the proposed model generates outstanding impedance spectra (involving capacitance spectra and resistance spectra) results for various metallization ratios and top layers. This exemplifies the model's potential for predicting, designing, and enhancing a complex multilayered IDE-based transducer to achieve precise and sensitive detection.

A physics knowledge-based neural network method for three-dimensional fracture mechanics of attachment lugs

The lug type joint serves as a critical connecting structure in aerospace vehicles, allowing for convenient assembly and disassembly, and transfer the load during service. However, cracks often initiate at the stress concentration location near the lugs hole, posing a significant threat to the safety of the aircraft structure. Therefore, evaluating the stress intensity factors for complex lug structures is of great significance. In this study, a physics knowledge-based neural network method of calculating the stress intensity factors of attachment lugs is proposed. Three types of cracked lug structures are analyzed: through-thickness crack in straight lug, quarter elliptical corner crack in straight lug and quarter elliptical corner crack in tapered lug. Various complex influencing factors in actual situations are also considered, such as the impact of the interference fit between the pin and the lug, as well as different loading directions and crack positions of tapered lugs. The stress intensity factor dataset generated by 3D finite element method, and then the neural network with its powerful learning ability and prior physical knowledge are used to achieve accurate fitting of the data. The results demonstrate that incorporating physical knowledge features significantly improves the model performance of the neural network. This method can be extended to analyze crack in structures with arbitrary geometry and complex loading conditions.

Semi-analytic modeling and experimental verification of arbitrary aero-engine complex spatial pipeline

In-depth research is imperative for complex spatial pipelines with fluid-structure interaction. A comprehensive and universal three-dimensional semi-analytical modeling method is first established for complex fluid-conveying spatial pipelines under the base excitation with arbitrary connections and configurations under different boundary conditions. The virtual spring technology is used to connect the straight and curved pipeline segments with spatial angles and simulate boundary conditions. For a thorough analysis, the actual stiffness of the bracket-clamp system is experimentally measured for the first time. The multi-level coupling dynamic model of part, component, and system levels under actual boundary conditions is established. An efficient method for solving the fluid-structure coupling pipeline system dynamics considering the base excitation is proposed based on energy method. The mid-plane displacement function of the Fourier series is introduced and solved using the principle of modal superposition. Hammer impact modal experiments, ANSYS software and vibration response experiments are performed on spatial pipelines supported by flexible bracket-clamps; the numerical and experimental results support the semi-analytical results. The degenerate model is verified with the simple plane pipelines in other references, and the errors are less than 5 %. The proposed method exhibits broad applicability and generalizability, making it suitable for various configurations and boundary conditions.

The Stieltjes–Fekete Problem and Degenerate Orthogonal Polynomials

Abstract A result of Stieltjes famously relates the zeroes of the classical orthogonal polynomials with the configurations of points on the line that minimize a suitable energy with logarithmic interactions under an external field. The optimal configuration satisfies an algebraic set of equations: we call this set of algebraic equations the Stieltjes–Fekete problem. In this work we consider the Stieltjes-Fekete problem when the derivative of the external field is an arbitrary rational complex function. We show that, under assumption of genericity, its solutions are in one-to-one correspondence with the zeroes of certain non-hermitian orthogonal polynomials that satisfy an excess of orthogonality conditions and are thus termed “degenerate”. When the differential of the external field on the Riemann sphere is of degree $3$ our result reproduces Stieltjes’ original result and provides its direct generalization for higher degree after more than a century since the original result.

Adjoint-based shape optimization for radiative transfer in porous structure for volumetric solar receiver

Due to their large surface areas, porous structures are often used for volumetric solar receivers for efficient utilization of the solar energy. However, the precise simulation and optimization of radiative heat transfer inside porous structures are still challenging due to their complex geometries. In the present study, an adjoint-based shape optimization framework for radiative transfer in porous structures is first proposed. Specifically, an arbitrary complex geometry of a porous structure is represented by a level-set function embedded in a Cartesian grid system. The volume penalization method combined with the discrete ordinate method is employed to simulate a forward radiative transfer problem in a porous structure. Then, a cost functional for an adjoint analysis is defined by the volume average of the divergence of the radiative heat flux, which corresponds to the total heat absorbed by the porous structure with a negative sign. The adjoint equations for minimizing the cost functional, and the corresponding shape update formula are derived and implemented in an open-source software, OpenFOAM. The developed adjoint-based shape optimization framework is applied to three types of initial porous structures, i.e., SC Kelvin, BCC Kelvin, and square honeycomb models. For all the initial porous models, the front surface commonly extends towards the direction of the incident radiation, and consequently notable improvements of the absorption efficiency can be achieved through the optimization. In addition, a systematic parametric survey for the initial shape of the SC Kelvin model is conducted to reveal the impacts of the number of unit cells, the solid emissivity, and the solid temperature on the optimal shapes and the resulting absorption efficiencies.

A unifying Rayleigh-Plesset-type equation for bubbles in viscoelastic media.

Understanding the ultrasound pressure-driven dynamics of microbubbles confined in viscoelastic materials is relevant for multiple biomedical applications, ranging from contrast-enhanced ultrasound imaging to ultrasound-assisted drug delivery. The volumetric oscillations of spherical bubbles are analyzed using the Rayleigh-Plesset equation, which describes the conservation of mass and momentum in the surrounding medium. Several studies have considered an extension of the Rayleigh-Plesset equation for bubbles embedded into viscoelastic media, but these are restricted to a particular choice of constitutive model and/or to small deformations. Here, we derive a unifying equation applicable to bubbles in viscoelastic media with arbitrary complex moduli and that can account for large bubble deformations. To derive this equation, we borrow concepts from finite-strain theory. We validate our approach by comparing the result of our model to previously published results and extend it to show how microbubbles behave in arbitrary viscoelastic materials. In particular, we use our viscoelastic Rayleigh-Plesset model to compute the bubble dynamics in benchmarked viscoelastic liquids and solids.

A GPU accelerated three-dimensional ghost cell method with an improved implicit surface representation for complex rigid or flexible boundary flows

This paper presents an efficient and reliable three-dimensional (3D) ghost cell method for complex rigid or flexible boundary flows. An improved implicit interface representation method is developed to treat the arbitrary complex interfaces including the thin or sharp boundaries. This method is robust and avoids the solving of a large dense matrix, and thus the computational efficiency is greatly enhanced. The ghost cell method with a unified eight-node interpolation scheme is adopted to enforce the no-slip boundary conditions on complex boundaries. To perform 3D high-resolution simulation on a desktop computer, a GPU parallel framework in CUDA environment is developed to significantly accelerate the computational efficiency of the present solver. The horizontal oscillations of a two-dimensional (2D) cylinder and a 3D sphere in the rest fluid are simulated to validate the accuracy and computational performance of the present model. Spatial accuracy of near second-order on the boundary treatment and good grid convergence are confirmed. Also, the present solver can achieve hundreds of acceleration ratios for 2D grids and thousands of acceleration ratios for 3D grids. Then, uniform flows around a 3D arbitrary rigid or flexible object such as a stationary cylindrical cylinder, a stationary square cylinder, an oscillating airfoil, and a swimming carangiform are simulated. The accuracy and capability of the present model for 3D complex geometries with large-amplitude movement or deformation is satisfactorily validated. Moreover, typical 3D wake structures are well captured.

Efficient Rollout of a Dynamic Optimization Algorithm

A successful deployment process of a complex software solution, such as optimization algorithms in a dynamic production environment is an extremely complicated and time-consuming task. Over this, the acceptance by those employees where the software solution is to be used later should not be underestimated; it is essential to involve them in the entire development process, as they can be game changers. This paper summarizes some best practices and lessons learned about the full integration of an optimization algorithm in the dynamic steelmaking environment of voestalpine Stahl GmbH. The focus is on the development of a practical test strategy and ultimately a generally valid rollout concept for an arbitrary complex software system for every conceivable industry. Over that, emerging gaps between theory and practice are highlighted, an attempt is made to justify their cause, and, as a result, possible solutions to tackle those challenges are presented.

Multi-Mode Vector Light Field Generation Using Modified Off-Axis Interferometric Holography and Liquid Crystal Spatial Light Modulators

The increasing enhancement in the modulation accuracy of spatial light modulators has garnered significant attention towards real-time control technology for light fields based on these modulators. It has been demonstrated that this technology possesses a remarkable capability to generate vector beams with arbitrary complex amplitude distributions. Nevertheless, past studies indicate that the generation of only one vector beam at a time has been observed. The simultaneous generation of numerous vector light fields can give rise to several challenges, including compromised picture quality, limited single-mode operation, and intricate optical path configurations. In pursuit of this objective, we present a novel methodology that integrates the coding methodology of modified off-axis interferometric holography with the idea of optical superposition. This technique facilitates the concurrent generation of several vector beams. In this study, we present a demonstration of the simultaneous creation of twelve vector beams using a single spatial light modulator (SLM) as a proof of concept. Significantly, this technology has the ability to generate an unlimited quantity of vector light fields concurrently under the assumption that the resolution of the SLM does not impose any limitations. The findings indicate that the imaging quality achieved by this technology is of a high standard. Furthermore, it is possible to separately control the beam waist radius, topological charge, polarization order, and extra phase of each beam.

Deformation features of trunk pipelines with composite linings under static loads

This paper considers the deformation process of a typical section of a steel trunk pipeline with a defective zone, strengthened with a carbon fiber composite lining, under the influence of stationary internal pressure. Defects in the form of thinning of the pipe thickness and cracks were investigated. The stressed-strained state of the structure at critical pressure was analyzed. The thickness of the composite lining was determined, at which the bandage compensates for the effect of internal pressure on the damaged section of the pipeline. Research was carried out numerically based on finite element modeling in the ANSYS software package. When studying the stressed-strained state of a pipe with a defect of an arbitrary complex shape under the influence of critical pressure, a compensating value was obtained. The result showed that a carbon fiber lining with a thickness of 17 % of the rated thickness of the pipe could completely compensate for the effects of internal pressure in the defect area. In this case, the stresses in the carbon fiber lining were close to minimal. When studying the stressed-strained state of a pipe with a large crack of arbitrary shape at critical pressure, a compensating value was also obtained. It has been established that to compensate for the concentration of internal pressure in the crack zone, the thickness of the composite lining should be at the level of 34 % of the rated thickness of the pipe. In this case, the deformation of the steel pipe in the area of the crack occurs in the elastic region. The exception is the crack tips, where plastic deformations are observed, and stresses arise up to 93 % of the ultimate strength of the pipe steel. At the same time, the stresses in the carbon fiber lining remain close to minimal. Thus, it is recommended to use carbon fiber linings with a thickness of 17 % or more of the rated pipe thickness to bandage damage constituting up to 75 % of the thickness of a steel pipe. To bandage cracks, it is recommended to use carbon fiber linings with a thickness of at least 34 % of the rated pipe thickness