Function Matrix Research Articles

A lightweight, conservation-moment-based implicit gas kinetic Lax–Wendroff scheme for all Knudsen number isothermal gas flows

This work presents an efficient implicit gas kinetic Lax–Wendroff scheme for steady isothermal gas flows in all Knudsen number (Kn) regimes. In the scheme, the discrete velocity Bhatnagar–Gross–Krook model equations (DVE) and the associated conservation moment equations (CME) are coupled and solved by matrix-free implicit schemes. Thanks to obtaining the fluxes of the CME by multiplying the fluxes of the DVE with a projection matrix and utilizing the equilibrium distribution functions at the new time predicted by the CME, both the complicated macro fluxes reconstruction of the CME and the calculation of the Jacobian matrix of the equilibrium distribution functions are not needed in the scheme, which makes the scheme lightweight. Moreover, to enhance the accuracy of the predicted equilibrium distribution functions at the new time to improve the convergence, a symmetric Gauss–Seidel scheme with inner iterations is used to solve the CME system. Due to the coupling between the DVE and the CME, the highly efficient implicit scheme for the CME drives the DVE system to converge quickly for the continuum and near-continuum flows. Furthermore, to verify the accuracy and high efficiency of the proposed implicit scheme, comparison studies of several two-dimensional isothermal rarefied gas flow cases simulated by the present implicit scheme and the explicit gas kinetic Lax–Wendroff scheme are also provided. The numerical results show that the present implicit scheme can be as accurate as its explicit counterpart with one to two orders times speed-up in all Kn number flow regimes.

Synthesis of realistic non-homogeneous non-Gaussian turbulent wind fields

This paper presents a sequential method for generating synthetic non-homogeneous non-Gaussian turbulent wind fields with a prescribed time-space covariance structure. The proposed methodology is based on the optimisation of restricted multivariate autoregressive (VAR) models, and the quantile-to-quantile transform between statistical distributions. The considered case study is a non-homogeneous non-Gaussian turbulent wind field over the roof of a high rise building simulated with LES. Results show a notably good matching in terms of the reproduced wind statistical distributions, Covariance Matrix Function (CMF) and Cross Power Spectral Density Matrix (CPSDM). In addition, the synthetic wind field reproduced accurately the recirculation bubble close to the roof. The main advantages of the proposed method are that, once the VAR model is computed, the synthesis of several realisations is computationally very cheap, which is useful for performing several aeroelastic simulations of the same analysis case, as suggested by the standards. The critical point is that, to characterise the statistical features for a specific case study (such as wind turbine wakes or turbulence due to obstacles), an LES simulation of the wind field is required as input. The software employed in this work is open source and it is available on GitHub.

Pregnancy-Related Disorders and Intrauterine Impaired Lung Development

Various pregnancy-related disorders are known to affect fetal lung development negatively. During pregnancy, chronic nutrition and/or oxygen limitation is known to impede lung maturation and induce airway and lung abnormalities. Structural abnormalities and reduced lung function may be evident immediately after birth, persist, or develop with age. The expansion of the fetal lung, fetal breath movements, fetal lung growth, alveolarization, blood-air barrier, extracellular matrix (ECM), airways, surfactant system, and lung immune function are all affected by nutritional limitations during pregnancy. Gestational hypoxia disrupts fetal lung development, which manifests as morphological and functional pulmonary abnormalities. Additionally, intrauterine growth restriction (IUGR), preeclampsia (PE), exposure to air pollution, and smoking are known to interfere with embryonic lung development. Birth defects, such as bronchopulmonary dysplasia, as well as chronic obstructive pulmonary disease (COPD), can be caused by abnormalities in pregnancy. Adequate nutrition, avoidance of smoking, and watchful monitoring and intervention during pregnancy should be promoted to prevent chronic lung disease of the newborn, child, and adult.

Exploring the Extended Beta-Logarithmic Function: Matrix Arguments and Properties

The beta-logarithmic function substantially generalizes the standard beta function, which is widely recognized for its significance in many applications. This article is devoted to the study of a generalization of the classical beta-logarithmic function in a matrix setting called the extended beta-logarithmic matrix function. The proofs of some essential properties of this extension, such as convergence, partial derivative formulas, functional relations, integral representations, inequalities, and finite and infinite sums, are established. Moreover, an application of the extended beta-logarithmic function in matrix arguments is proposed in probability theory. Further, numerical examples and graphical presentations of the new generalization are obtained.

A novel apoferritin nanocage with ECM promoting, ferroptosis suppressing and inflammation targeting property for osteoarthritis therapy

Osteoarthritis (OA) currently affects over 15% of the global population. However, OA management primarily focuses on symptom relief, with a lack of targeted and effective therapeutic strategies. SM04690 (Adavivint, Lorecivivint) represents a small molecule with promising potential as a novel agent for cartilage regeneration and pain relief in OA treatment, Phase III clinical trials are currently underway. This study explores its previously unexamined effects on regulating chondrocyte extracellular matrix (ECM) function. However, its targeted delivery to the inflammatory cells remains a challenge; also, ideal therapeutic agent for OA requires to be multi-functional, e.g. suppressing ferroptosis in chondrocytes. In the current study, we designed an ApoFerritin nanocage loaded with SM04690 (SM04690@ApoFn) for OA therapy. In vitro study showed that SM04690 may have chondro-regenerative effect similar to kartogenin (KGN) but works at much lower concentrations. SM04690@ApoFn demonstrated good biocompatibility both in vitro and in vivo. The following studies revealed that SM04690@ApoFn may effectively promote ECM metabolism in chondrocytes, it may also suppress ferroptosis; meanwhile, it may have the ability to targeting the inflammatory chondrocytes through binding to transferrin receptor (TfR). In vivo study demonstrated that SM04690@ApoFn may alleviate the progression of OA in mice. In conclusion, the multifunctional SM04690@ApoFn nanocage shows great potential for OA therapy by promoting ECM metabolism, suppressing ferroptosis and targeting inflammatory chondrocytes.

Dimension-Reduction Representation of Multivariate Mainshock-Aftershock Ground Motions Based on Measured Records

ABSTRACT This study proposes an integrated dimension-reduction representation strategy for simulating multivariate mainshock-aftershock stochastic ground motions based on measured motion records. The strategy includes a parameter identification method for modeling evolutionary power spectrum density (EPSD) of mainshock-aftershocks, a coherence function describing the spectrum correlation between mainshock and aftershock, and the EPSD function matrix establishment for mainshock-aftershock field combining with complex spatial coherence function. Furthermore, the dimension-reduction representation for simulating the ground motions considering the sequence and spatial variability simultaneously is presented with merely two elementary random variables. Numerical results effectively demonstrate the accuracy, efficiency, and engineering applicability of the proposed method.

An efficient and universal parallel algorithm for high-dimensional quantum dynamics in poly-atomic reactions.

This study presents a parallel algorithm for high-dimensional quantum dynamics simulations in poly atomic reactions, integrating distributed- and shared-memory models. The distributions of the wave function and potential energy matrix across message passing interface processes are based on bundled radial and angular dimensions, with implementations featuring either two- or one-sided communication schemes. Using realistic parameters for the H + NH3 reaction, performance assessment reveals linear scalability, exceeding 90% efficiency with up to 600 processors. In addition, owing to the universal and concise structure, the algorithm demonstrates remarkable extensibility to diverse reaction systems, as demonstrated by successes with six-atom and four-atom reactions. This work establishes a robust foundation for high-dimensional dynamics studies, showcasing the algorithm's efficiency, scalability, and adaptability. The algorithm's potential as a valuable tool for unraveling quantum dynamics complexities is underscored, paving the way for future advancements in the field.

Time-Varying Function Matrix Projection Synchronization of Caputo Fractional-Order Uncertain Memristive Neural Networks with Multiple Delays via Mixed Open Loop Feedback Control and Impulsive Control

This paper shows solicitude for the generalized projective synchronization of Caputo fractional-order uncertain memristive neural networks (FOUMNNs) with multiple delays. By extending the constant scale factor to the time-varying function matrix, we establish an extraordinary synchronization mode called time-varying function matrix projection synchronization (TFMPS), which is a generalized version of traditional matrix projection synchronization, modified projection synchronization, complete synchronization, and anti-synchronization. To achieve the goal of TFMPS, we design a novel mixed controller including the open loop feedback control and impulsive control, which employs the state information in the time-delayed interval and the sampling information at the impulse instants. It has a prominent advantage that impulse intervals are not restricted by time delays. To establish the connection between the error system and the auxiliary system, a generalized fractional-order comparison theorem with time-varying coefficients and impulses is established. Applying the stability theory, the comparison theorem, and the Laplace transform, new synchronization criteria of FOUMNNs are acquired under the mixed impulsive control schemes, and the derived synchronization theorem and corollary can effectively expand the correlative synchronization achievements of fractional-order systems.

A probabilistic framework to evaluate seismic resilience of substations based on three-stage uncertainty

Electrical substation systems exhibit vulnerability after an earthquake. It results in significant economic losses because of the uncertainty of the functional state and recovery process. To quantitatively assess the uncertainty of substations, this paper proposes a probability-based seismic resilience assessment framework. This framework considers uncertainty in three stages: functional state, functional recovery, and resource constraints. Based on the functional characteristics of substation systems, a directed acyclic graph was constructed, and the Monte Carlo algorithm was used to obtain the functional state matrix, thereby establishing a probability-based functional state model. Moreover, a dynamic post-earthquake functional recovery analysis framework was built based on recovery efficiency metrics, and functional recovery paths were obtained through iterative simulations. A stepped functional recovery curve was developed based on resource constraints. Three-stage uncertainty parameters were transformed into resilience features for quantitative assessment. By analysing seismic resilience of a typical 220 kV step-down substation, probability distributions of functional recovery curves and confidence intervals for seismic resilience metrics were obtained. Notably, mutual constraint relationships among resource conditions were identified.

A study of Horn matrix functions and Horn confluent matrix functions

Abstract In this paper, we give the matrix version of Horn’s hypergeometric function and their confluent cases. We also discuss the regions of convergence, system of matrix differential equations of bilateral type, differential formulae and infinite summation formulae satisfied by these hypergeometric matrix functions. With the study of these 23 matrix functions, matrix generalization of Horn’s list of 34 hypergeometric series will be completed.

Role of Hypoxia and Rac1 Inhibition in the Metastatic Cascade.

The hypoxic condition has a pivotal role in solid tumors and was shown to correlate with the poor outcome of anticancer treatments. Hypoxia contributes to tumor progression and leads to therapy resistance. Two forms of a hypoxic environment might have relevance in tumor mass formation: chronic and cyclic hypoxia. The main regulators of hypoxia are hypoxia-inducible factors, which regulate the cell survival, proliferation, motility, metabolism, pH, extracellular matrix function, inflammatory cells recruitment and angiogenesis. The metastatic process consists of different steps in which hypoxia-inducible factors can play an important role. Rac1, belonging to small G-proteins, is involved in the metastasis process as one of the key molecules of migration, especially in a hypoxic environment. The effect of hypoxia on the tumor phenotype and the signaling pathways which may interfere with tumor progression are already quite well known. Although the role of Rac1, one of the small G-proteins, in hypoxia remains unclear, predominantly, in vitro studies performed so far confirm that Rac1 inhibition may represent a viable direction for tumor therapy.

Effects of mechanical loading on matrix homeostasis and differentiation potential of periodontal ligament cells: A scoping review.

Various mechanical loadings, including mechanical stress, orthodontics forces, and masticatory force, affect the functions of periodontal ligament cells. Regulation of periodontal tissue destruction, formation, and differentiation functions are crucial processes for periodontal regeneration therapy. Numerous studies have reported that different types of mechanical loading play a role in maintaining periodontal tissue matrix homeostasis, and osteogenic differentiation of the periodontal ligament cells. This scoping review aims to evaluate the studies regarding the effects of various mechanical loadings on the secretion of extracellular matrix (ECM) components, regulation of the balance between formation and destruction of periodontal tissue matrix, osteogenic differentiation, and multiple differentiation functions of the periodontal ligament. An electronic search for this review has been conducted on two databases; MEDLINE via PubMed and SCOPUS. Study selection criteria included original research written in English that reported the effects of different mechanical loadings on matrix homeostasis and differentiation potential of periodontal ligament cells. The final 204 articles were mainly included in the present scoping review. Mechanical forces of the appropriate magnitude, duration, and pattern have a positive influence on the secretion of ECM components such as collagen, as well as regulate the secretion of matrix metalloproteinases and tissue inhibitors of matrix metalloproteinases. Additionally, these forces regulate a balance between osteoblastic and osteoclast differentiation. Conversely, incorrect mechanical loadings can lead to abnormal formation and destruction of both soft and hard tissue. This review provides additional insight into how mechanical loadings impact ECM homeostasis and multiple differentiation functions of periodontal ligament cells (PDLCs), thus making it valuable for regenerative periodontal treatment. In combination with advancing technologies, the utilization of ECM components, application of different aspects of mechanical force, and differentiation potential of PDLCs could bring potential benefits to future periodontal regeneration therapy.

Adaptive fast nonlinear blind deconvolution based on nonuniform particle swarm optimization for the rolling bearing fault diagnosis

Although superior fault extraction performance is possessed by fast nonlinear blind deconvolution (FNBD) through the introduction of penalty terms and nonlinear features, its wide application is limited by the complexity and diversity of parameter selection. The fault extraction performance of FNBD is impacted by the contingency of parameter selection. To reduce the prior experience dependence of FNBD and improve the performance of fault extraction, an end-to-end adaptive fast nonlinear blind deconvolution (AFNBD) is proposed. First, the proposed nonuniform particle swarm optimization (NPSO) is employed to assign parameters to be optimized for each particle to construct its Hankel matrix, nonlinear features and objective functions. Secondly, Gaussian fitting is applied to modify the filters. Then, NPSO is utilized to update relevant parameters and the corresponding filter of each particle to explore the optimum filter. Finally, simulations and experiments verify the effectiveness of AFNBD and the results indicate that AFNBD is a powerful tool for incipient fault feature extraction.

Investigations of cardiac fibrosis rheology by in vitro cardiac tissue modeling with 3D cellular spheroids

Cardiac fibrosis refers to the abnormal accumulation of extracellular matrix within the cardiac muscle, leading to increased stiffness and impaired heart function. From a rheological standpoint, knowledge about myocardial behavior is still lacking, partially due to a lack of appropriate techniques to investigate the rheology of in vitro cardiac tissue models. 3D multicellular cardiac spheroids are powerful and versatile platforms for modeling healthy and fibrotic cardiac tissue in vitro and studying how their mechanical properties are modulated. In this study, cardiac spheroids were created by co-culturing neonatal rat ventricular cardiomyocytes and fibroblasts in definite ratios using the hanging-drop method. The rheological characterization of such models was performed by Atomic Force Microscopy-based stress-relaxation measurements on the whole spheroid. After strain application, a viscoelastic bi-exponential relaxation was observed, characterized by a fast relaxation time (τ1) followed by a slower one (τ2). In particular, spheroids with higher fibroblasts density showed reduction for both relaxation times comparing to control, with a more pronounced decrement of τ1 with respect to τ2. Such response was found compatible with the increased production of extracellular matrix within these spheroids, which recapitulates the main feature of the fibrosis pathophysiology. These results demonstrate how the rheological characteristics of cardiac tissue vary as a function of cellular composition and extracellular matrix, confirming the suitability of such system as an in vitro preclinical model of cardiac fibrosis.

Simulating non-stationary and non-Gaussian cross-correlated fields using multivariate Karhunen–Loève expansion and L-moments-based Hermite polynomial model

In practical engineering, cross-correlated random fields are often used to model structural materials or random loads containing multiple correlations. Effective and accurate simulation of these cross-correlation fields is an important prerequisite for subsequent reliability analysis and uncertainty quantification of complex systems. Therefore, this paper proposes a new simulation method for non-stationary non-Gaussian cross-correlated random fields to satisfy realistic engineering requirements. In this new method, L-moments-based Hermite polynomials model (LHPM) is extended to non-stationary non-Gaussian cross-correlated fields. Then, a transformation model from non-stationary non-Gaussian correlation matrix function (CMF) to the underlying Gaussian CMF is explicitly given. Multivariate K-L expansion is further used to approximate the underlying Gaussian cross-correlated fields, where the eigenvalue and eigenfunctions are estimated via the Nyström method with uniform weights. The approximation permits the application of few random variables to characterize the entire Gaussian cross-correlated fields. Ultimately, the simulated underlying Gaussian cross-correlated fields are mapped back to the target non-stationary non-Gaussian cross-correlated fields based on LHPM. Three typical examples, including exponential kernel, Wiener process kernel and spatially varying non-Gaussian and nonstationary seismic ground motions, are used to validate the effectiveness of the proposed method. The source code is readily available at: https://github.com/zhaozhao23/Simulation-of-non-stationary-and-non-Gaussian-cross-correlated-fields.

Integrating intrinsic and configural superiority into advanced impact-resistant organohydrogels via cryo-assisted direct ink writing

The growing safety consciousness towards life and engineering poses demand for efficient anti-impact materials. Decent advances have been made in material development and structure design, whereas the superiority synergism of materials and structures remains challenging. This work develops an advanced impact-resistant shear stiffening gel-polyvinyl alcohol-chitosan (SSG-PVA-CS) organohydrogel by integrating 3D printed customized architectures with strain rate enhanced matrix materials. Following rheological optimization of components, the precursor ink presents shear thinning and yield stress fluid behaviors enabling the direct ink writing (DIW) printing techinique. The printability is systemically explored through finite element modeling assisted flow dynamics analysis and experimental validating, and a quantitative phase diagram is constructed which determines the dependence of parameters on the printing mode and quality. The organohydrogel presents favorable mechanical strength, cyclic durability and rate enhancement effect, which imparts basis of impact resistance to the matrix. The rational structure design effectively reduces the volume density within 0.60 to 0.71 g/cm3 while maintaining considerable attenuation ratios of 73.09 % to 83.55 %, with structure-dependent dynamic mechanical behaviors clarified via finite element analysis. This study provides a reliable approach to fabricate impact-resistance materials with tailored architectures and mechanically functional matrix materials, unlocking paths to break through the performance bottleneck.

Intent inferring based human-machine game control strategy for spacecraft rendezvous

In this paper, we propose a game control method for a machine-controlled spacecraft to cooperate with a human-controlled spacecraft in near-circular orbit for a rendezvous mission. Inspired by the cooperative game theory, the two-spacecraft rendezvous process is formulated as a cooperative differential game (DG) with a common cost function. A challenging problem is that the intent of the human-controlled spacecraft represented by the weighting matrix in the cost function is not available to the machine-controlled spacecraft. To complete the rendezvous mission optimally, an intent inferring based game control algorithm is developed for the machine-controlled spacecraft. Specifically, an adaptive approach is proposed for the machine-controlled spacecraft to identify the feedback gain matrix of the human-controlled spacecraft online based on the system state alone with the concurrent learning (CL) technique; furthermore, the unknown weighting matrix representing the intent of the human-controlled spacecraft in the cost function is retrieved by an inverse differential game (IDG) method. Accordingly, the control law of the machine-controlled spacecraft is updated in real-time. The control strategies of the spacecraft converge to near the Nash equilibrium. Finally, the simulation result is presented to illustrate the effectiveness of the approach.

Enhancing Battery Capacity Estimation Accuracy through the Neural Network Algorithm

Accurate estimation of battery metrics, such as state of health (SOH), is crucial for effective battery management systems (BMS) due to capacity degradation over time. This paper proposes a methodology to enhance battery capacity estimation accuracy by addressing uncertainties related to state of charge (SOC) estimation and measurement. The methodology employs the Neural Network Algorithm (NNA), an optimization algorithm inspired by artificial neural networks (ANNs). The NNA generates an initial population of pattern solutions and iteratively updates them using a weight matrix, bias operator, and transfer function operator. By combining the advantages of ANNs and optimization techniques, the NNA aims to find an optimal solution considering interdependent variables and incorporating global and local feedbacks. Leveraging the capabilities of the NNA, our objective is to identify the candidate that minimizes a specified cost function, ensuring up-to-date cell capacity through a memory forgetting factor. The algorithm's precision was validated using NASA's Prognostic Data, demonstrating outstanding performance by surpassing two aggressive algorithms in terms of accuracy. In the most severe case scenario, the algorithm achieved a peak error of less than 0.4%. Furthermore, the algorithm consistently demonstrated predictive performance measures that were superior to those of the compared algorithms.

Iterative algorithm to the generalized coupled Sylvester‐transpose matrix equations with application in robust and minimum norm observer design of linear systems

AbstractThis article consider a class of generalized coupled Sylvester‐transpose matrix equations which play an important role in control and systems theory. Based on the Jacobi iterative algorithm, the full‐row rank accelerated Jacobi gradient based iterative (RRAJGI) algorithm and the full‐column rank accelerated Jacobi gradient based iterative (CRAJGI) algorithm are proposed. By using the Frobenius norm of matrix and the trace function of matrix, the convergence of the algorithms are proved. The results show that the new algorithms are convergent for arbitrary initial matrices under the convergence number satisfies appropriate conditions. Numerical examples show that RRAJGI algorithm and CRAJGI algorithm have the advantages of faster convergence speed and higher convergence accuracy than other existing algorithms. Finally, an application example for robust and minimum norm observer design of linear systems is given.

Multidirectional cascade of square MIMO LTI subsystems: Transfer function representation

This paper considers continuous transfer function representation for a cascade composed of N mutually interconnected square multiple-input multiple-output (MIMO) linear time-invariant (LTI) subsystems with general multidirectional input–output configurations. Such cascaded structure can arise, e.g., from the spatial discretization of one-dimensional distributed parameter systems (DPSs) described by partial differential equations (PDEs) with boundary conditions representing different configurations of boundary input signals. As shown in the paper, the transfer function matrix of the resulting cascade can be calculated using the Redheffer star product of the subsystems’ transfer function matrices, which simplifies into the usual matrix product for the unidirectional cascade. For the particular case of 2 × 2 cascade composed of rational transfer function subsystems, the recursive formulas for its boundary and distributed transfer functions have been derived for both uni- and multidirectional configurations. The well-posedness and the stability criteria are also analyzed, proving to be more restrictive for the multidirectional cascade than for the unidirectional one due to the internal positive feedback in the first case. As shown in the attached example, the presented results can be used to approximate one-dimensional distributed parameter systems using rational transfer function subsystems representing the spatial sections of the original DPS.