System Matrix Research Articles

Asymptotic and Probabilistic Perturbation Analysis of Controllable Subspaces

In this paper, we consider the sensitivity of the controllable subspaces of single-input linear control systems to small perturbations of the system matrices. The analysis is based on the strict component-wise asymptotic bounds for the matrix of the orthogonal transformation to canonical form derived by the method of the splitting operators. The asymptotic bounds are used to obtain probabilistic bounds on the angles between perturbed and unperturbed controllable subspaces implementing the Markoff inequality. It is demonstrated that the probability bounds allow us to obtain sensitivity estimates, which are much tighter than the usual deterministic bounds. The analysis is illustrated by a high-order example.

Stochastic Entropy Production Associated with Quantum Measurement in a Framework of Markovian Quantum State Diffusion

The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given reduced version. Without a specification of relevant details of the environment, the time evolution of a reduced density matrix is therefore typically unpredictable, even if the dynamics of the full density matrix are deterministic. With this in mind, we investigate a two-level open quantum system using a framework of quantum state diffusion. We consider the pseudorandom evolution of its reduced density matrix when subjected to an environment-driven process that performs a continuous quantum measurement of a system observable, invoking dynamics that asymptotically send the system to one of the relevant eigenstates. The unpredictability is characterised by a stochastic entropy production, the average of which corresponds to an increase in the subjective uncertainty of the quantum state adopted by the system and environment, given the underspecified dynamics. This differs from a change in von Neumann entropy, and can continue indefinitely as the system is guided towards an eigenstate. As one would expect, the simultaneous measurement of two non-commuting observables within the same framework does not send the system to an eigenstate. Instead, the probability density function describing the reduced density matrix of the system becomes stationary over a continuum of pure states, a situation characterised by zero further stochastic entropy production. Transitions between such stationary states, brought about by changes in the relative strengths of the two measurement processes, give rise to finite positive mean stochastic entropy production. The framework investigated can offer useful perspectives on both the dynamics and irreversible thermodynamics of measurement in quantum systems.

A novel flexible infinite element for transient acoustic simulations

This article addresses the efficient solution of exterior acoustic transient problems using the Finite Element Method (FEM) in combination with infinite elements. Infinite elements are a popular technique to enforce non-reflecting boundary conditions. The Astley–Leis formulation presents several advantages in terms of ease of implementation, and results in frequency-independent system matrices, that can be used for transient simulations of wave propagation phenomena. However, for time-domain simulations, the geometrical flexibility of Astley–Leis infinite elements is limited by time-stability requirements. In this article, we present a novel infinite element formulation, called flexible infinite element, for which the accuracy does not depend on the positioning of the virtual sources. From a software implementation perspective, the element proposed can be seen as a specialized FEM element and can be easily integrated into a high-order FEM code. The effectiveness of the flexible formulation is demonstrated with frequency and time-domain examples; for both cases, we show how the flexible infinite elements can be attached to arbitrarily-shaped convex FE boundaries. In particular, we show how the proposed technique can be used in combination with existing model order reduction strategies to run fast and accurate transient simulations.

Transdermal Patches: Design and Current Approaches Using Natural Polymers

One method of controlled drug delivery is the transdermal drug delivery system (TDDS), which aims to distribute the drug through the skin at a predetermined and regulated rate. It provides a number of benefits, including a longer therapeutic impact, fewer side effects, increased bioavailability, better patient compliance, and simple medication therapy discontinuation. For most compounds, the stratum corneum is thought to be the rate limiting barrier in transdermal penetration. The appendageal, transcellular, and intercellular pathways are the three main ways that drugs can enter the body. When giving medication by this route, it is important to take into account the following aspects: skin age, condition, physicochemical characteristics, and environmental conditions. Polymer matrix, membrane, drug, penetration enhancers, pressure-sensitive adhesives, backing laminates, release liner, etc. are some of the fundamental parts of TDDS. Transdermal patches are used to deliver active chemicals to the circulatory system through the skin. These patches can be classified into a variety of systems, such as reservoir, matrix, and micro-reservoir systems. Consistent methodologies are used to assess the adhesion qualities, physicochemical properties, in vitro drug release studies, in vitro skin penetration studies, skin irritation studies, and stability studies once transdermal patches have been prepared. Different medications are marketed as transdermal patches, depending on the length of the therapy. Natural polymers can be used as the means of achieving predetermined rates of drug delivery. Natural polymers are basically polysaccharides so they are biocompatible and without any side effects. Gums, mucilages, resins and plant extracts are widely used natural materials for conventional and novel dosage forms. The present article highlights the available information on natural polymers and their versatile use.

Can storage-discharge characteristics of karst matrix system quantified through recession analysis be reliable?

Storage and subsequent release of water in matrix system is a key function of karst catchments that controlling baseflow variation. Hydrograph recession analysis is currently the economic way to assess storage-discharge characteristics broadly at the catchment scale. However, there is large uncertainty in the related quantification due to recession data extraction. This study, by combining recursive digital filters with different automatic extraction methods, slow flow recession segments were extracted for hydrograph recession analysis and the further dynamic matrix storage (DMS) and related recession time (RT) assessment. The diversity and consistence among DMS and RT derived from different recession extraction methods (REMs) were analyzed, using hydrometric data in 20 catchments in the Wujiang river Basin in southwest China. Results indicate that the estimates of DMS and RT remarkedly varied between different REMs, however the order in which they ranked was mostly consistent. Moreover, the relationships between the derived DMS and RT with catchment physical features that potentially control storage and release processes are mostly consistent. Larger DMS are strongly associated with catchments featured as lower soil saturated hydraulic conductivity and smoother hydrographs. Longer RT are mostly related with drier catchments characterized as less variation of elevation and lower soil saturated hydraulic conductivity. This study highlights not only the uncertainty in quantifying storage and accompanied release characteristics, but also the reliability of storage-discharge characteristics quantified through recession analysis in terms of catchment comparison. Considering the diversity among catchments, ensemble of multi-method estimates of DMS and RT can enhance our understanding of the storage-discharge processes in the karst matrix system.

BO-KM: A comprehensive solver for dispersion relation of obliquely propagating waves in magnetized multi-species plasma with anisotropic drift kappa-Maxwellian distribution

The observation of superthermal plasma distributions in space reveals a multitude of distributions with high-energy tails, and the kappa-Maxwellian distribution is a type of non-Maxwellian distribution that exhibits this characteristic. However, accurately determining the multiple roots of the dispersion relation for superthermal plasma waves propagating obliquely presents a challenge. To tackle this issue, we have developed a comprehensive solver, BO-KM, utilizing an innovative numerical algorithm that eliminates the need for initial value iteration. The solver offers an efficient approach to simultaneously compute the roots of the kinetic dispersion equation for oblique propagation in magnetized plasmas. It can be applied to magnetized superthermal plasma with multi-species, characterized by anisotropic drifting kappa-Maxwellian, bi-Maxwellian distributions, or a combination of the two. The rational and J-pole Padé expansions of the dispersion relation are equivalent to solving a linear system's matrix eigenvalue problem. This study presents the numerical findings for kappa-Maxwellian plasmas, bi-Maxwellian plasmas, and their combination, demonstrating the solver's outstanding performance through benchmark analyses. Program summaryProgram Title: BO-KMCPC Library link to program files:https://doi.org/10.17632/pr9cvjrvfv.1Licensing provisions: BSD 3-clauseProgramming language: MatlabNature of problem: To efficiently solve for multiple roots of the kinetic dispersion relation in superthermal plasma distributions with high-energy tails observed in space, we have developed BO-KM, a novel and comprehensive solver that employs a unified framework for computing uprathermal (or thermal) waves and instabilities. This solver is applicable to magnetized multi-species collisionless plasmas with anisotropic drift kappa-Maxwellian, bi-Maxwellian distributions, or a combination of both. Furthermore, BO-KM incorporates a submodule dedicated to the perpendicular propagation dispersion relation of bi-Kappa plasmas, thereby significantly improving computational efficiency at high κ values.Solution method: The method converts the kinetic plasma dispersion relation based on rational expansion (for the kappa-Maxwellian model) and J-pole Padé expansion (for the bi-Maxwellian model) into an equivalent linear eigenvalue system. This transformation effectively turns the root-finding task into an eigenvalue problem, enabling the simultaneous determination of roots using standard eigenvalue libraries.Additional comments including restrictions and unusual features: Kinetic relativistic effects are not included in the present version yet.

Efficient Acceleration Framework for Complex‐Valued Linear Systems: Alternating Anderson Accelerating Preconditioned Richardson Approach

ABSTRACTInspired by the efficiency of Anderson acceleration (AA) and the fact that its un‐truncated version is essentially equivalent to the generalized minimal residual method (GMRES) for solving linear systems, in this study, the preconditioned alternating Anderson acceleration Richardson (PA3R) approach is proposed as an acceleration framework, and its relationship to AA and GMRES is examined from a spectrum perspective. Next, the convergence condition of the PA3R approach is demonstrated to be (where is the splitting of system matrix ) for a general system matrix, which always holds for the mature splitting iteration methods. This new approach is applied to four well‐established splitting methods to solve complex symmetric linear systems. Furthermore, the optimal relaxation parameters are investigated, showing that the eigenvalue distribution region of the iteration matrices of the resulting methods are approximately half of that of the original methods. The numerical results indicate that for examples with dimensions exceeding 4 million, the use of the PA3R approach results in a significant efficiency improvement especially in terms of CPU time compared with the non‐PA3R version.

Inertial and elastic properties of general composite beams

Slender composite structures can be modeled using engineering beam models with properties computed using a cross-sectional analysis program, such as VABS. These properties are given in terms of the mass matrix, stiffness matrix, and compliance matrix in a general coordinate system. The invariance of strain energy and kinetic energy is employed to rigorously transform sectional properties into different coordinate systems with parallel shifts and rotations. Additionally, the computation of commonly used inertial properties (mass center, principal inertial axes, and mass moments of inertia) from the mass matrix, and commonly used elastic properties (extension stiffness, bending stiffness, torsion stiffness, tension center, shear center, principal bending axes, principal shear axes, etc.) from the compliance matrix, is elucidated. The elastic properties are given for both the Timoshenko model and the Euler–Bernoulli model. The definitions for shear center and twist center are clarified and consistently generalized for composite beams. Isotropic homogeneous beams are used to illustrate how to relate commonly used engineering beam properties with the compliance matrix and the stiffness matrix for composite beams. Finally, engineering beam properties necessary for general-purpose aeromechanical analysis programs such as CAMRAD II are derived from the properties computed by VABS.

A transient source-function-based embedded discrete fracture model for simulation of multiscale-fractured reservoir: Application in coalbed methane extraction

The classic embedded discrete fracture model (EDFM) may cause certain errors when simulating the transient flow process within the multi-scale fractured system. In this study, the transient transmissibility was derived by using the point (matrix-fracture) and line (fracture-fracture) source functions. The transient source-function-based EDFM (tSEDFM) is established via this method. Then, based on the dual criteria that dNNC is less than a certain distance and its projection point is within the corresponding fracture domain, a 3D fracture meshing method for arbitrary fracture geometry and orientation is established. The finite volume method is used to discrete the fluid flow equations for matrix and fracture systems, considering the multi-deformation-induced permeability evolution. Consequently, the numerical simulation framework of FVM-tSEDFM is proposed to investigate the transient mass transfer characteristics. Compared with the current pEDFM, the pressure drop near fractures of the proposed model is higher and the gap narrows as pressure wave further spreads. Compared with AEDFM, the Tmf of tSEDFM is almost the same, but AEDFM's Tff is substantially higher in the initial stage and the attenuation rate is slower, resulting in an error of nearly 15% at the hydraulic fracture location. As fracture density increases, more transient flow makes AEDFM- and EDFM-calculated BHP values deviate from tSEDFM. History matching using the tSEDFM with only 10000 meshes shows better results where the mismatching rate is larger than 90%. Simulation of CBM extraction indicate that sharp pressure decline occurs near the fractures, resulting in gas desorption enhancement and rapid productivity increment. The tSEDFM demonstrates good practicality in calculating the production and long-term permeability evolution. Results also show that the tSEDFM can correct the underestimation of mass exchange in the early stage and overestimation since the pseudo-steady stage, and can be better applied to the numerical simulation of multi-scale fractured reservoirs. As the dominant factor for gas extraction, sensitivity analyses of fracture properties are also documented.

Toward robust linear implicit schemes for steady state hypersonic flows

Implicit time discretization in computational fluid dynamics dedicated to compute steady state solution of hypersonic flows was an intense field of research in the 70's-80's. It is suitable for computational efficiency to use implicit schemes that do not suffer from time step restriction to guarantee stability, unlike explicit ones. Unfortunately time step restriction is still required in practice, especially for stiff numerical test cases such as high Mach number flows around objects. A method introduced by Yee et al. (1985) [34] is commonly used to simulate computational fluid dynamics problems in an implicit fashion. However this method has no formal theoretical basis for systems of conservation laws. Consequently the practical time step is driven by a ad-hoc user-given profile. The purpose of this work is first to study the mathematical properties of such linearized implicit finite volume schemes to enlighten their weaknesses and exhibit more adequate linearization processes. We rely on the hyperbolicity of the Euler equations to establish a general framework to design implicit schemes. Secondly, we propose a correction of the system matrix to adapt to any given finite volume scheme. The obtained linearized implicit finite volume methods are more robust and less constrained with regards to ad-hoc user-given profile. Numerical results in 1D and 2D will provide evidences to confirm the analysis on relevant and challenging hypersonic test cases.

Stability and l∞ Performance Analysis for Nabla Discrete Fractional Linear Positive System with Time-Varying Delays

In this paper, the stability and l∞-gain problem are investigated for the Nabla discrete fractional linear positive systems with bounded time-varying delays. First, a sufficient condition and a necessary condition are presented to ensure the system’s positivity. Then, based on the system’s positivity property, an asymptotically stable condition is established. Furthermore, it is demonstrated that the l∞-gain of such systems is determined by the system matrices and is independent of the magnitude of delays. Finally, numerical examples are provided to demonstrate the validity of the obtained results.

Emerging Spatiotemporal Dynamics in Multiterminal Neuromorphic Nanowire Networks Through Conductance Matrices and Voltage Maps

AbstractSelf‐organizing memristive nanowire (NW) networks are promising candidates for neuromorphic‐type data processing in a physical reservoir computing framework because of their collective emergent behavior, which enables spatiotemporal signal processing. However, understanding emergent dynamics in multiterminal networks remains challenging. Here experimental spatiotemporal characterization of memristive NW networks dynamics in multiterminal configuration is reported, analyzing the activation and relaxation of network's global and local conductance, as well as the inherent spatial nonlinear transformation capabilities. Emergent effects are analyzed i) during activation, by investigating the spatiotemporal dynamics of the electric field distribution across the network through voltage mapping; ii) during relaxation, by monitoring the evolution of the conductance matrix of the multiterminal system. The multiterminal approach also allowed monitoring the spatial distribution of nonlinear activity, demonstrating the impact of different network areas on the system's information processing capabilities. Nonlinear transformation tasks are experimentally performed by driving the network into different conductive states, demonstrating the importance of selecting proper operating conditions for efficient information processing. This work allows a better understanding of the local nonlinear dynamics in NW networks and their impact on the information processing capabilities, providing new insights for a rational design of self‐organizing neuromorphic systems.

New error estimates for the conjugate gradient method

The conjugate gradient method is the default iterative method for the solution of linear systems of equations with a large symmetric positive definite matrix A. The development of techniques for estimating the norm of the error in iterates computed by this method has received considerable attention. Available methods for bracketing the A-norm of the error evaluate pairs of Gauss and Gauss–Radau quadrature rules to determine lower and upper bounds. The latter rule requires a user to allocate a node (the Radau node) between the origin and the smallest eigenvalue of the system matrix. The determination of such a node generally demands further computations to estimate the location of the smallest eigenvalue; see, e.g., Golub and Meurant (1997), Golub and Meurant (2010), Golub and Strakoš (1994), Meurant (1997), Meurant (1999). An approach that avoids the need to know a lower bound for the smallest eigenvalue is to replace the Gauss–Radau quadrature rule by an anti-Gauss rule as described by Calvetti et al. (2000). However, this approach may sometimes yield inaccurate error norm estimates. This paper proposes the use of pairs of Gauss and associated optimal averaged Gauss quadrature rules to estimate the A-norm of the error in iterates determined by the conjugate gradient method.

Kinetic and Mechanistic Release Studies on Hyaluronan Hydrogels for Their Potential Use as a pH-Responsive Drug Delivery Device.

Hyaluronic acid, a biocompatible polymer, holds significant potential for drug delivery applications. Its variable degree of protonation, which entails tunable physical properties, makes it an ideal candidate for developing pH-sensitive hydrogels. Like other smart drug delivery systems, pH-responsive hydrogels can enhance medical treatment and expedite the healing process. However, the inherent complexity of hydrogels poses challenges in identifying suitable matrix systems. This study evaluates the potential of thiolated hyaluronic acid hydrogels, physically cross-linked with deacetylated disaccharide units of the polymer, for use in drug delivery. Using low-molecular-weight dextrans as model drugs, we investigated the system's response to different pH environments in terms of swelling as well as the kinetic and mechanistic release of the encapsulated compound. The data suggest tunable release properties of the gel regarding drug size and pH value. Our results demonstrate the gel system's potential for smart drug delivery. We anticipate that this system is a promising candidate for use in transdermal wound healing applications and strongly encourage further investigations using other sorts of (model) drugs to gain a more detailed insight into its pH-responsive transport qualities.

3D-Printed Gelatin-Based Scaffold Crosslinked by Genipin: Evaluation of Mechanical Properties and Biological Effect.

In this study, scaffolds based on natural polymer gelatin A, blended with polyvinylpyrrolidone were crosslinked by genipin (0.5 and 1 wt%), in order to investigate their mechanical performance and potential for biomedical application. Semi-solid extrusion (SSE) 3D printing technique was used, enabling insitu crosslinking of the blend during processing. Swelling test showed that the swelling ratio reduces with higher concentration of genipin due to an increased crosslinking. The FTIR analysis confirmed the crosslinking of scaffolds by genipin. DSC analysis and mechanical testing have shown improved thermal and mechanical properties. Morphological analysis of scaffolds by FESEM showed increased toughening of the material with the crosslinking. Tensile strength and microhardness showed a significant rise in scaffolds with the increase in genipin content, which was up to 93.8% and 125.3%, respectively. These findings were in accordance with morphological features present in samples. The biological effect of the scaffold matrix system was evaluated by qualitative and quantitative cytotoxicity assessment invitro, demonstrating the absence of cytotoxicity in tested preparations in a direct test. The cytotoxicity index based on the metabolic activity of cells in an indirect test showed up to 20% reduction of viability compared with the control, confirming the absence of cytotoxicity, which was additionally verified by propidium iodine staining of the cells exposed to scaffolds. The presented gelatin-based crosslinked scaffolds obtained by 3D printing represent good candidates for biomedical application and future research that includes further invitro and invivo analysis.

A displacement formulation for coupled elastoacoustic problems that preserves flow irrotationality

Two-way fluid–structure interaction (FSI) problems, in the sense that a flow induces the motion of a solid, which in turn modifies the flow boundary conditions, have been approached with very different strategies, the most common of which is probably the finite element method (FEM). In the case of elastoacoustics, the flow consists of an acoustic field interacting with a vibrating structure. When the problem is discretized with the FEM, an algebraic block matrix system is obtained and the coupling between the acoustic field and the structure takes place through a coupling matrix with off-diagonal terms. Usually the structure is characterized by its displacement field, while for the acoustics several options are available, ranging from pressure to acoustic displacement or velocity/displacement acoustic potentials. Depending on the formulation, symmetric or asymmetric systems are obtained and different types of numerical stability problems have to be faced. In this work, a monolithic strategy based on the Rayleigh–Ritz method is proposed. The displacement is used as the primary variable for both the structure and the acoustic field and is expanded in terms of Gaussians as basis functions. This provides an algebraic block matrix system for the global uncoupled problem. However, instead of resorting to a coupling matrix, the essential continuity conditions at the acoustic-structure interface are imposed by the nullspace method (NSM). That is, the solution of the uncoupled system is expanded in terms of a basis of the nullspace generated by the essential conditions of the problem, including the displacement continuity constraints at the interface, thus giving the solution of the coupled problem. As for natural conditions, they are imposed in a weak sense. For ease of explanation, a one-dimensional (1D) case is first introduced, followed by the coupling of a 2D acoustic cavity with a beam and a 3D one with a plate. The proposed method is validated with FEM simulations on fine meshes and the advantage of using Gaussian basis functions over trigonometric ones is also demonstrated.

Claudin2 is involved in the interaction between Megalocytivirus-induced virus-mock basement membrane (VMBM) and lymphatic endothelial cells

The genus Megalocytivirus, belonging to the family Iridoviridae, is one of the most detrimental virus groups to fish aquaculture. Megalocytivirus creates a virus-mock basement membrane (VMBM) on the surface of infected cells. This membrane provides attachment sites for lymphatic endothelial cells (LECs), disrupting fish's endothelial cell-extracellular matrix system. This disruption triggers injury to the vascular system and can result in death. Exploring the VMBM-cell interaction mechanism is crucial for uncovering the pathogenesis of Megalocytivirus and identifying therapeutic targets. Claudins, a class of tetra transmembrane proteins, play a key role in creating tight junctions between endothelial or epithelial cells. In this study, we demonstrated that the expression of Claudin2, a member of the Claudin family in fish, was significantly up-regulated by Megalocytivirus infection. Claudin2 was found in LECs attached to the surface of infected cells. It interacted with the VMBM viral components VP23R, VP08R, and VP33L at multiple binding sites through its two extracellular loops. However, it did not interact with the host basement membrane’s nidogen. Therefore, Claudin2 is involved in the interaction of LEC with VMBM and plays a role in the disturbed distribution of extracellular matrix and endothelial cells in Megalocytivirus-infected fish tissues. This study aims to uncover the molecular mechanisms by which Megalocytivirus infection leads to pathological changes in the vascular system.

Quantification and Sensitivity Analysis of the Model Uncertainty in the Projectile-Barrel Coupled Artillery Dynamics System Based on Random Matrix Theory

Simplifications in the engineering of artillery firing dynamics modeling introduce model uncertainty, which seriously affects the model’s predictive performance. To this end, a typical variable-section hollow cylindrical cantilever beam structure in artillery firing dynamics is investigated in this paper. The statistical approximation methods quantify parameter and model uncertainty separately, and their respective confidence intervals were calculated and compared. The results show that the traditional parameter uncertainty approach overestimates the parameter uncertainty ranges, and introducing the model uncertainty approach dramatically improves the model prediction performance. Additionally, a projectile-barrel coupled artillery dynamics model considering model uncertainty is established, and its effectiveness is validated through the actual launch experiments. The sensitivity of the dynamic responses to the system matrix, namely model uncertainty, is further analyzed. This paper provides theoretical references for the study of uncertainty in artillery launch dynamics and proposes effective methods to enhance the predictability of computational models for complex structural systems.

Sequential Scan-Based Single-Dimension Multi-Voxel System Matrix Calibration for Open-Sided Magnetic Particle Imaging.

Open-sided magnetic particle imaging (OS-MPI) has garnered significant interest due to its potential for interventional applications. However, the system matrix calibration in OS-MPI using sequential scans is a time-consuming task and susceptible to the low signal-to-noise ratio (SNR) resulting from the small calibration sample size. These challenges have hindered the practical implementation of system matrix-based reconstruction for sequentially scanned OS-MPI. To address these issues, we propose a novel calibration method, named sequen- tial scan-based single-dimension multi-voxel calibration (SS-SDMVC), to efficiently obtain a high-SNR system matrix. This method was implemented in a cylindrical field of view (FOV), where a bar calibration sample parallel to the field-free line (FFL) was shifted along a fixed radial direction. A standard image reconstruction process was also introduced to verify the feasibility of SS-SDMVC. Through simulations, we analyzed the effects of noise levels and scanner imperfections on the SS-SDMVC-based reconstruction and demonstrated its robustness. In experiments, we compared the imaging performance of SS-SDMVC and the sequential scan-based traditional cubic-FOV SMC. The results showed that SS-SDMVC reduced the number of measurements by a factor of 210.94 and achieved higher reconstruction quality. Therefore, SS-SDMVC is expected to improve the reconstruction quality of human- scale or high-gradient FFL MPI scanners.

Descriptor continuousand discrete-time linear systems with zero transfer matrices

In this paper, necessary and sufficient conditions for zeroing of the transfer matrices of descriptor continuous-time and discrete-time linear systems are established. The conditions are illustrated by simple numerical examples of the descriptor continuous-time and discrete-time linear systems. Also some remarks on the systems with delays on control are given.