Differential Matrix Research Articles

Nonlinear bending analysis of hyperelastic Mindlin plates: a numerical approach

In this paper, a numerical solution strategy is proposed for studying the large deformations of rectangular plates made of hyperelastic materials in the compressible and nearly incompressible regimes. The plate is considered to be Mindlin-type, and material nonlinearities are captured based on the Neo-Hookean model. Based on the Euler–Lagrange description, the governing equations are derived using the minimum total potential energy principle. The tensor form of equations is replaced by a novel matrix–vector format for the computational aims. In the solution strategy, based on the variational differential quadrature technique, a new numerical approach is proposed by which the discretized governing equations are directly obtained through introducing differential and integral matrix operators. Fast convergence rate, computational efficiency and simple implementation are advantages of this approach. The results are first validated with available data in the literature. Selected numerical results are then presented to investigate the nonlinear bending behavior of hyperelastic plates under various types of boundary conditions in the compressible and nearly incompressible regimes. The results reveal that the developed approach has a good performance to address the large deformation problem of hyperelastic plates in both regimes.

Numerical Method with Shifted Chebyshev Polynomials for a Set of Variable Order Fractional Partial Differential Equations

In this paper, a high-efficiency numerical algorithm based on shifted Chebyshev polynomials is given to solve a set of variable-order fractional partial differential equations. First, we structure the differential operator matrix of the shifted Chebyshev polynomials. Then, we transform the problem into solving a set of linear algebraic equations to obtain the numerical solution. Moreover, a step of error correction is given. Finally, numerical examples are given to show the effectiveness and practicability of the proposed method.

Sampled-data control of Lur’e systems

The main purpose of this paper is to fill a gap in the literature concerning the problem of designing a sampled-data control law for continuous-time Lur’e systems. The goal is to design a state feedback sampled-data control for this class of nonlinear systems preserving global asymptotic stability and minimizing a guaranteed quadratic cost. The main challenge towards the solution of the proposed problem is to handle this class of nonlinear system in order to propose less conservative design conditions expressed through differential linear matrix inequalities - (DLMIs). Bellman’s Principle of Optimality applied together with the Popov–Lyapunov function that emerges from the celebrated Popov Stability Criterion is the key issue to obtain the reported results. Two examples are solved for illustration.

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

A new methodology to evaluate housing comfort: defining a differential diagnosis matrix

This paper focuses on comfort optimization methods in contemporary housing in Lisbon, Portugal. Faced with the notorious lack of comfort in buildings from different construction periods, rehabilitation appears as an opportunity to change this reality, by improving the residents’ quality of life, allowing users to control their own variables. In present times, the technological developments have simplified the diffusion of information, allowing each person to easily comprehend more complex technical contents and increasing awareness for more effective and conscious interventions. The design of a differential diagnosis matrix aims to identify and categorize problems associated with the lack of housing comfort, by relating specific constraints through rules of correspondence and by establishing a logical relationship of flow charts of interdependent and specific variables for each case. A more effective and simplified method is proposed, that will work as a tool to make the process of improving the comfort in the houses more accessible, even for the non-specialist user. Through the increase of adequate and conscious micro interventions, it is possible to create sustainable and better practices in this sector.

Finite-Time Control of Continuous-Time Networked Dynamical Systems

Finite-time stability (FTS) analysis and control problems are investigated in this paper for continuous-time networked dynamical systems constituted by many subsystems. Interactions among these subsystems are arbitrary and time-varying, and every subsystem has different and time-varying dynamics. Several differential linear matrix inequality (LMI) formed methods are presented for the FTS analysis and control, which avoid the inverse computation of matrices with large dimensions and efficiently utilize the block diagonal characteristic of system parameters and the sparseness of the subsystem connection matrix. Sufficient conditions only depending on the parameters of each individual subsystem are then derived. Furthermore, LMI-based conditions are also provided for the FTS analysis and control of linear time-invariant networked systems. Numerical simulations show that they are computationally effective to analyze and synthesize a large-scale networked dynamical systems.

Extended precise integration solution to layered transversely isotropic unsaturated poroelastic media under harmonically dynamic loads

A fully coupled dynamic model is presented in this paper by considering the effect of matric suction, varying parameters in connection with saturation, stratification and transverse isotropy. This model can describe separate flows of two immiscible fluids in layered transversely isotropic unsaturated poroelastic media subjected to harmonically dynamic loads. The ordinary differential matrix equations of this model are derived based on Hankel integral transform and a series of algebraic manipulations. Then the final solution is obtained by conducting the extended precise integration method, and further verified against the existing solution. Numerical examples are carried out to demonstrate the effects of saturation, transversely isotropic parameters, angular frequency and soil thickness on dynamic behavior of unsaturated porous media.

In Vivo 3D Determination of Peripapillary Scleral and Retinal Layer Architecture Using Polarization-Sensitive Optical Coherence Tomography.

PurposeThe purpose of this paper was to determine the architecture of the collagen fibers of the peripapillary sclera, the retinal nerve fiber layer (RNFL), and Henle's fiber layer in vivo in 3D using polarization-sensitive optical coherence tomography (PS-OCT).MethodsSeven healthy volunteers were imaged with our in-house built PS-OCT system. PS-OCT imaging included intensity, local phase retardation, relative optic axis, and optic axis uniformity (OAxU). Differential Mueller matrix calculus was used for the first time in ocular tissues to visualize local orientations that varied with depth, incorporating a correction method for the fiber orientation in preceding layers.ResultsScleral collagen fiber orientation images clearly showed an inner layer with an orientation parallel to the RNFL orientation, and a deeper layer where the collagen was circularly oriented. RNFL orientation images visualized the nerve fibers leaving the optic nerve head (ONH) in a radial pattern. The phase retardation and orientation of Henle's fiber layer were visualized locally for the first time.ConclusionsPS-OCT successfully showed the orientation of the retinal nerve fibers, sclera, and Henle's fiber layer, and is to the extent of our knowledge the only technique able to do so in 3D in vivo.Translational RelevanceIn vivo 3D imaging of scleral collagen architecture and the retinal neural fibrous structures can improve our understanding of retinal biomechanics and structural alterations in different disease stages of myopia and glaucoma.

Lie algebras of matrix difference differential operators and special matrix functions

We discuss certain models of irreducible representations of Lie algebra sl(2,C) from the special matrix functions point of view. These models are constructed in terms of matrix differential operators and matrix difference differential operators and are connected through a matrix integral transformation. In the process, we find new matrix function identities involving one and two variable special matrix functions.

Brain connectivity alteration detection via matrix-variate differential network model.

Brain functional connectivity reveals the synchronization of brain systems through correlations in neurophysiological measures of brain activities. Growing evidence now suggests that the brain connectivity network experiences alterations with the presence of numerous neurological disorders, thus differential brain network analysis may provide new insights into disease pathologies. The data from neurophysiological measurement are often multidimensional and in a matrix form, posing a challenge in brain connectivity analysis. Existing graphical model estimation methods either assume a vector normal distribution that in essence requires the columns of the matrix data to be independent or fail to address the estimation of differential networks across different populations. To tackle these issues, we propose an innovative matrix-variate differential network (MVDN) model. We exploit the D-trace loss function and a Lasso-type penalty to directly estimate the spatial differential partial correlation matrix and use an alternating direction method of multipliers algorithm for the optimization problem. Theoretical and simulation studies demonstrate that MVDN significantly outperforms other state-of-the-art methods in dynamic differential network analysis. We illustrate with a functional connectivity analysis of an attention deficit hyperactivity disorder dataset. The hub nodes and differential interaction patterns identified are consistent with existing experimentalstudies.

Comparative Study of Heuristic Algorithms for Electrical Impedance Tomography

Based on electrical measurements from electrodes placed around the boundary of a body, electrical impedance tomography (EIT) is an imaging procedure that recovers the spatial distribution of the conductivities in the interior of a body. Recent studies have shown promising results in reconstructing EIT images using heuristic algorithms. This work presents a study of the applicability of six heuristic algorithms – firefly algorithm (FA), novel bat algorithm (NBA), genetic algorithm with new multi-parent crossover (GA-MPC), success history-based adaptive differential evolution with linear population size reduction with semiparameter adaptation hybrid with covariance matrix adaptation evolutionary strategy (LSHADE-SPACMA), ensemble sinusoidal differential covariance matrix adaptation (LSHADE-cnEpSin), and effective butterfly optimizer with covariance matrix adapted retreat phase (EBOwithCMAR) – for the EIT image reconstruction problem. These algorithms have never been employed to solve the EIT inverse problem. Series of numerical tests were carried out to compare the performance of the selected algorithms.

Modified Douglas splitting method for differential matrix equations

In this paper, we consider a modified Douglas splitting method for a class of differential matrix equations, including differential Lyapunov and differential Riccati equations. The method we consider is based on a natural three-term splitting of the equations. The implementation of the algorithm requires only the solution of a linear algebraic system with multiple right-hand sides in each time step. It is proved that the method is convergent of order two and it preserves the symmetry and positive semidefiniteness of solutions of differential Lyapunov equations. Moreover, we show how the method can be handled in a low-rank setting for large-scale computations. We also provide a theoretical a priori error analysis for the low-rank algorithms. Numerical results are presented to verify the theoretical analysis.

Abstract 3962: Differential extracellular matrix remodeling induced by VEGF-A and TGF-β activated fibroblasts

Abstract Introduction: Tumor progression is modulated by the presence within the tumor microenvironment of activated fibroblasts called cancer-associated fibroblasts (CAFs). CAFs exhibit an increase in the production of collagen (COL), tenascin C (TNC) and fibronectin (FN), resulting in a remodeling of the extracellular matrix (ECM) within the tumor mass. CAFs-derived ECM guides the cancer cells to migrate directionally increasing metastasis. TGF-β and VEGF-A are highly express in tumors and promote progression, however, their role in ECM remodeling is poorly understood. This study seeks to analyze the ECM protein remodeling mediated by TGF- β o VEGF-A activated fibroblasts. Materials and methods: In vitro and in vivo ECM protein remodeling mediated by TGF- β o VEGF-A activated fibroblasts was analyzed through expression of TNC, FN and COL using immunofluorescence and second harmonic generation (SHG); alignment and thickness of the fibers; Organoleptic invasion and 2D migration assay were conducted to study the effect of the stiffness of collagen gels generated by VEGF-A and TGF-β activated fibroblasts in the migration/invasion of tumor cells. Results and discussion: ECM derived from VEGF-A and TGF-β activated fibroblasts have differential ECM remodeling patterns, including differences in the secretion of TNC, FN, and COL; alignment and thickness of the fibers, and migration/invasion rate. These changes results in a differential stiffness of the ECM, which would alter the directional migration of cancer cells within tumor microenvironment. Citation Format: Muriel A. Nuñez, Javier Cerda-Infante, Francisco Nualart, Gustavo Cerda, Isabel M. Yussef, Viviana P. Montecinos. Differential extracellular matrix remodeling induced by VEGF-A and TGF-β activated fibroblasts [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 3962.

Revealing Shared and Distinct Genes Responding to JA and SA Signaling in Arabidopsis by Meta-Analysis.

Plant resistance against biotrophic and necrotrophic pathogens is mediated by mutually synergistic and antagonistic effects of salicylic acid (SA) and jasmonic acid (JA) signals. However, the unique and shared genes responding to the defense mediated by JA/SA signals were largely unclear. To reveal discrete, synergistic and antagonistic JA/SA responsive genes in Arabidopsis thaliana, Meta-Analysis was employed with 257 publicly available Arabidopsis thaliana RNA-Seq gene expression profiles following treatment of mock, JA or SA analogs. JA/SA signalings were found to co-induce broad-spectrum disease-response genes, co-repress the genes related to photosynthesis, auxin, and gibberellin, and reallocate resources of growth toward defense. JA might attenuate SA induced immune response by inhibiting the expression of resistance genes and receptor-like proteins/kinases. Strikingly, co-expression network analysis revealed that JA/SA uniquely regulated genes showing highly coordinated co-expression only in their respective treatment. Using principal component analysis, and hierarchical cluster analysis, JA/SA analogs were segregated into separate entities based on the global differential expression matrix rather than the expression matrix. To accurately classify JA/SA analogs with as few genes as possible, 87 genes, including the SA receptor NPR4, and JA biosynthesis gene AOC1 and JA response biomarkers VSP1/2, were identified by three feature selection algorithms as JA/SA markers. The results were confirmed by independent datasets and provided valuable resources for further functional analyses in JA- or SA- mediated plant defense. These methods would provide cues to build a promising approach for probing the mode of action of potential elicitors.

Combination of surface plasmon resonance and differential Mueller matrix formalism for noninvasive glucose sensing

A novel technique is proposed for circular birefringence (CB) sensing using a surface plasmon resonance (SPR) prism coupler and differential Mueller matrix polarimetry. In the proposed system, the SPR prism coupler is placed in front of the sample in order to generate a weak-scattering medium model and enhance the sensitivity of the measurement process. The CB properties of the sample are then extracted using a dynamic Stokes-Mueller matrix polarimetry measurement system in the reflectance mode. The practical feasibility of the system is demonstrated by measuring the CB properties of aqueous glucose solutions and glucose phantom solutions containing 2% lipofundin. The oral glucose tolerance tests pilot study was performed on four healthy human volunteers aged between 20 and 25 years old. The experimental results show that the proposed method has a resolution of just 10 mg/dL. In general, the results confirm that the proposed polarimetry-SPR system provides a fastand reliable approach for CB detection and has significant potential for noninvasive glucose monitoring device (NIGMD) applications.

Numerical Analysis of Eddy Current Induced by z-Gradient Coil in a Superconducting MRI Magnet

In magnetic resonance imaging (MRI), pulsed magnetic gradient fields induce eddy currents in surrounding conducting components of the MRI scanner. These eddy currents distort MRI image and introduce thermal load in cryostat. Ohmic heating of superconducting magnet due to eddy currents changes the operating temperature of magnet, which can lead to system quench. Numerical simulation of these eddy current is important to compensate/control their adverse effects. In this paper, a coupled circuit network method is outlined to model eddy currents in a superconducting magnet that induced by z-gradient coil. According to the axial symmetry, the cylindrical cryostat vessels are divided into several concentric slices with a finite thickness. Each slice is modeled as a series circuit composed of a resistor and an inductor, and inductively coupled with other slices and gradient coil. To improve the calculation efficiency, the Eigen matrix technique is used to simplify the coupled differential matrix equation. The undesired eddy current effects including time-varying secondary magnetic field and power losses are analyzed. In addition, the eddy current behavior due to mechanical errors of gradient coil is discussed. Compared with the simulation results of ideal gradient coil design, the misalignment between primary and secondary layer of z-gradient coil can cause asymmetric secondary magnetic field along z-axis and further introduce $B_{0}$ -shift in imaging area.

Quantization of Some Generalized Jaynes-Cummings Models in a Kerr-Like Medium

Based on fundamental principles of quantum mechanics, we present a method for a rigorous analytic construction of the spectra of the one- and two-photon Jaynes-Cummings models in a Kerr medium. To obtain an idea of the method, we consider a first generalized Jaynes-Cummings model with a real, linear superpotential using techniques of supersymmetric quantum mechanics. The Hamiltonian of this model is written as a combination of operators generating the underlying superalgebra whose elements are defined as differential matrix operators. Based on the formalism of supersymmetric quantum mechanics and the properties of sets of common observables, we derive solutions of the one- and two-photon models expressed in terms of confluent hypergeometric functions. Finally, using numerical analysis, we study the influence of the Kerr effect on the energy spectra of the physical system.

Image Watermarking in Curvelet Domain Using Edge Surface Blocks

Digital image watermarking aims to protect the information in an image without significantly affecting visual quality. In this paper, a new image watermarking technique has been proposed that uses Gaussian filters and first-order partial differential matrix to extort the edge surface of a host image. This paper influence on the edge surface curvelet coefficients as human eyes are not equally sensitive to a smooth and an edged surface. To preserve the quality of the artwork and to increase the resistance against attacks, the author utilizes the edge surface area of an image, coarse levels of curvelet transform, and strength parameters. The selection of host coefficients are conforming to the human visual system (HVS) is the uniqueness of the research. The exploitation of the Gaussian filters and first-order partial differential coarse curvelet coefficients and the watermark strength parameter offers robustness against image processing attacks. The standard visual quality perception of HVS evaluation metrics are used to measure the superiority of the presented work.

Numerical Methods for Solving Optimization Problems with Differential Linear Matrix Inequalities

Numerical Methods for Solving Optimization Problems with Differential Linear Matrix Inequalities

Reggeized model for γp → ρ− Δ++(1232) photoproduction

A model for the reaction is presented with the t-channel π + ρ exchanges reggeized to describe the reaction up to high energies. Gauge invariance of ρ exchange is discussed in connection with the convergence of the reaction cross section at high energies. The roles of electromagnetic (EM) multipole moments of Δ++ baryon and ρ−meson are analyzed in total and differential cross sections and spin density matrix elements. Photon polarization asymmetry Σ is predicted for the measurement of electromagnetic moments of ρ−and Δ++.