Stability Matrices Research Articles

Solvothermal Synthesis of Cu3(BTC)2 Metal Organic Framework

For the last two decades the research with Metal Organic Framework (MOF) is proving to be most fruitful, due to their crystalline-inorganic hybrid material with uniform porous structure, high environmental stability and tuneable matrices. With these unique properties of MOFs material have vast applications in storage, chemical separation, catalysis, drug delivery. In present investigation we have reported the chemical synthesis of copper benzenetricarboxylate. In Teflon-lined stainless-steel autoclave at 80oC for 20hr. The resulting Copper benzenetricarboxylate (Cu-BTC) is further characterised by Fourier Transform Infrared Spectroscopy and X-ray diffraction (XRD)

Mechanistic insight into the mode of inhibition of dietary flavonoids; targeting macrophage migration inhibitory factor.

Introduction: The Macrophage Migration Inhibitory Factor (MIF), a key pro-inflammatory mediator, is responsible for modulating immune responses. An array of inflammatory and autoimmune diseases has been linked to the dysregulated activity of MIF. The significance in physiological as well as pathophysiological phenomena underscores the potential of MIF as an attractive target with pharmacological relevance. Extensive research in past has uncovered a number of inhibitors, while the ISO-1, or (S, R)-3-(4-hydroxyphenyl)-4,5-dihydro-5-isoxazole acetic acid methyl ester being recognized as a benchmark standard so far. Recent work by Yang and coworkers identified five promising dietary flavonoids, with superior activity compared to the standard ISO-1. Nevertheless, the exact atomic-level inhibitory mechanism is still elusive. Methods: To improve the dynamic research, and rigorously characterize, and compare molecular signatures of MIF complexes with ISO-1 and flavonoids, principal component analysis (PCA) was linked with molecular dynamics (MD) simulations and binding free energy calculations. Results: The results suggest that by blocking the tautomerase site these small molecule inhibitors could modify the MIF activity by disrupting the intrinsic dynamics in particular functional areas. The stability matrices revealed the average deviation values ranging from 0.27-0.32nm while the residue level fluctuations indicated that binding of the selected flavonoids confer enhanced stability relative to the ISO-1. Furthermore, the gyration values extracted from the simulated trajectories were found in the range of 1.80-1.83nm. Discussion: Although all the tested flavonoids demonstrated remarkable results, the one obtained for the potent inhibitors, particularly Morin and Amentoflavone exhibited a good correlation with biological activity. The PCA results featured relatively less variance and constricted conformational landscape than others. The stable ensembles and reduced variation in turns might be the possible reasons for their outstanding performance documented previously. The results from the present exploration provide a comprehensive understanding of the molecular complexes formed by flavonoids and MIF, shedding light on their potential roles and impacts. Future studies on MIF inhibitors may benefit from the knowledge gathered from this investigation.

An Integrated Approach for Yaw Stability of Linear Time Varying Bicycle Model Utilizing Adaptive Model Predictive Control

Accidents during critical maneuvering on roads while overtaking or changing lanes are mainly due to the insufficient generation of the stability matrices of vehicles, including yaw rate. The parameters responsible for stable operation of the vehicle during these driving scenarios may vary, causing improper steering angle input actuation to the vehicle, due to which the desired yaw rate is not generated. To overcome this problem, corrective yaw moments are applied to the yaw dynamics to generate the desired yaw rate and operate the vehicle within the defined stability limit. Therefore - in this paper - to improve the yaw stability of the vehicle, a novel yaw rate gradient-based control approach is proposed for a linear time-varying (LTV) bicycle model. A 2 degrees of freedom bicycle model with the linear approximation for low slip angles in the magic formula tire model is utilized to develop the LTV model. The longitudinal velocity and friction coefficient are chosen as the parameters of interest to be varied during model simulation. Two different critical driving scenarios, including a sine maneuver and a double lane change, are chosen as input actuation with and without corrective yaw moments. The obtained simulation results unveil that, by the application of steering angle with a corrective yaw moment, the yaw stability has effectively been improved by obtaining a feasible adaptive model predictive control solution. Additionally, the root mean square error (RMSE) is calculated to evaluate the performance of the proposed methodology. A RMSE of 0.0768 and 0.0395 for steering without corrective yaw moment (CYM) is decreased to 0.0234 and 0.0214 for sine and double lane change steering input with CYM, respectively. Moreover, the proposed methodology is compared with previous methods and found to have better yaw stability.

Advanced controller design for uncertain linear systems with time‐varying delays via augmented zero equality approach

This paper deals with the stability analysis and controller design for linear systems with time‐varying delays and parameter uncertainties. By choosing appropriate augmented Lyapunov–Krasovskii functionals, a set of linear matrix inequalities is derived to get advanced feasible region of stability and controller gain matrices that guarantee the asymptotic stability of the concerned systems within maximum bound of time delays and its time derivative. To further reduce the conservatism of stabilization criterion, a recently developed mathematical technique that constructed a new augmented zero equality is applied. Finally, two numerical examples are utilized to show the validity and superiority of the proposed methods.

Examining the significance of the ignition characteristics of hydrogen and liquefied-petroleum-gas on the reactivity controlled compression ignition and its interspersed profiles induced in an existing diesel engine: A comparative perspective

The present study highlights the comparative analysis of diesel-hydrogen and diesel- Liquefied-petroleum-gas bi-fuel operation. It investigates the ignition delay criterion and its effects on performance, emission, and stability characteristics under varying injection and reactivity phasings in an existing single-cylinder diesel engine. The experimental analysis-based statistical modelling approach for simultaneous identification of relative optimum parametric combination to improve the performance, emission, and stability has been incorporated in this study through response surface methodology. It is evident from the results that the different parametric combinations of input variables for both Liquefied-petroleum-gas and hydrogen-enriched diesel operation influenced the combustion parameter (ignition delay), performance, and emission significantly. Subsequently, the ignition delay corresponding to the maximum hydrogen enrichment scenario is 41.2% more than the corresponding Liquefied-petroleum-gas operational mode. Similarly, the exergetic efficiency attained with maximum hydrogen substitution is 9.54% higher than the exergetic efficiency of the corresponding Liquefied-petroleum-gas enriched operation. On the other hand, the minimum footprints of soot, total unburnt hydrocarbon, Carbon monoxide, and Carbon dioxide registered with hydrogen enrichment were 15.77%, 72.45%, 38.48%, and 2.37% lower than the corresponding Liquefied-petroleum-gas enriched operation. In contrast, the lowest recorded value of oxides of nitrogen with Liquefied-petroleum-gas enriched diesel operation was 77.93% lower than the corresponding hydrogen-enriched operation. Thus, the study presents itself as a first-of-a-kind strategy for the comparative analysis of the effect of ignition delay on the performance, emission, and stability matrices of existing infrastructure with diesel- Liquefied-petroleum-gas and diesel-hydrogen operation.

Self-Excitation Thresholds in RF Structures

A theory and general method for calculating self-excitation thresholds for a large class of standing and traveling-wave structures used in amplifiers, klystrons, traveling-wave tubes, and other vacuum electronic devices (VED) is presented. One determines the circuit parameters of RF structures that are changed due to the presence of electron beam and analyze the stability of the obtained matrices. New determinant equations defined by such stability matrices are derived in a general form applicable to any RF structure and as an important special case for RF structures with electron beams. The theory and computational methods described here are essential for stability analysis of RF structures and VED.

A Separation Principle for Linear Event-Triggered Output Feedback Systems

The purpose of this article is to revisit the well-known separation principle of classical control for systems implemented in an event-triggered fashion. We consider a scenario consistent of two independent digital channels for communications between a sensor and a controller, and a controller and an actuator, and propose a methodology to separately design controller and observer gains as well as the event conditions. Under the proposed design, we address the problem of restoring the classical separation principle for the event-based design. We show that fast enough sampling at the sensor-to-observer channel suffices to ensure a separation principle. In contrast, under fast sampling at the controller-to-actuator channel, a separation principle can be obtained provided that an additional mild assumption is imposed on the stability matrices. A numerical example is provided to support the theoretical findings.

Power boundedness in the maximum norm of stability matrices for ADI methods

Power boundedness in the maximum norm of stability matrices for ADI methods

Model selection for inferential models with high dimensional data: synthesis and graphical representation of multiple techniques

Inferential research commonly involves identification of causal factors from within high dimensional data but selection of the ‘correct’ variables can be problematic. One specific problem is that results vary depending on statistical method employed and it has been argued that triangulation of multiple methods is advantageous to safely identify the correct, important variables. To date, no formal method of triangulation has been reported that incorporates both model stability and coefficient estimates; in this paper we develop an adaptable, straightforward method to achieve this. Six methods of variable selection were evaluated using simulated datasets of different dimensions with known underlying relationships. We used a bootstrap methodology to combine stability matrices across methods and estimate aggregated coefficient distributions. Novel graphical approaches provided a transparent route to visualise and compare results between methods. The proposed aggregated method provides a flexible route to formally triangulate results across any chosen number of variable selection methods and provides a combined result that incorporates uncertainty arising from between-method variability. In these simulated datasets, the combined method generally performed as well or better than the individual methods, with low error rates and clearer demarcation of the true causal variables than for the individual methods.

Identification of Aircraft Models

State space identification of aircraft flight models is carried out in this work. The identification results in estimation of derivatives of stability and control matrices and also biases of sensors. The identification procedure is based on likelihood function minimization based on Kalman filter and stochastic approximation. The least square method determines initial values for unknown parameter of state space models which are important for identification of models. The results obtained for models are presented. The decoupled longitudinal and lateral models of a small six seat aircraft are utilized in this work.

On the Event-Triggered Controller Design

The majority of event-triggered control (ETC) literature concentrates on designing triggering rule while assuming control input to emulate an analog design. In this article, however, both state and output feedback laws are jointly synthesized with the triggering law for nonlinear Lipschitz systems. In the proposed method, the dominant eigenvalues of the linear stability matrices are assigned according to desired performance and triggering specifications. The results serve as a local framework for stability of general nonlinear ETC systems. The efficiency of design is validated through compelling examples.

Nonlinear time varying perturbation stability analysis of a double diabetes system

Background and objective:The stability problem in double delay differential diabetes system is affected by delay term and meal perturbation. This paper is addressed to assess the stability of such double diabetes system with unknown nonlinear perturbation and bounded time varying delay. Method:The stability of a double diabetes system following a meal function as an unknown nonlinear perturbation function has been analyzed by using a Lyapunov–Krasovskii function. The stability matrices according to linear matrix inequality (LMI) were constructed and solved using YALMIP. Results:The solution of the stability theorem gives semi definite matrices which fulfilled the stability criteria. Simulations observed such oscillation in the early meal intake. Conclusion:Thus, it shows that for given values (30–51 min delay and unknown time varying perturbation) the double diabetes system is stable.

Stability conditions and local minima in multicomponent Hartree-Fock and density functional theory

Multicomponent quantum chemistry allows the quantum mechanical treatment of electrons and specified protons on the same level. Typically the goal is to identify a self-consistent-field (SCF) solution that is the global minimum associated with the molecular orbital coefficients of the underlying Hartree-Fock (HF) or density functional theory (DFT) calculation. To determine whether the solution is a minimum or a saddle point, herein we derive the stability conditions for multicomponent HF and DFT in the nuclear-electronic orbital (NEO) framework. The gradient is always zero for an SCF solution, whereas the Hessian must be positive semi-definite for the solution to be a minimum rather than a saddle point. The stability matrices for NEO-HF and NEO-DFT have the same matrix structures, which are identical to the working matrices of their corresponding linear response time-dependent theories (NEO-TDHF and NEO-TDDFT) but with a different metric. A negative eigenvalue of the stability matrix is a necessary but not sufficient condition for the corresponding NEO-TDHF or NEO-TDDFT working equation to have an imaginary eigenvalue solution. Electron-proton systems could potentially exhibit three types of instabilities: electronic, protonic, and electron-proton vibronic instabilities. The internal and external stabilities for theories with different constraints on the spin and spatial orbitals can be analyzed. This stability analysis is a useful tool for characterizing SCF solutions and is helpful when searching for lower-energy solutions. Initial applications to HCN, HNC, and 2-cyanomalonaldehyde, in conjunction with NEO ∆SCF calculations, highlight possible connections between stationary points in nuclear coordinate space for conventional electronic structure calculations and stationary points in orbital space for NEO calculations.

Asymptotic mean-square stability of weak second-order balanced stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential systems

In this paper, the linear asymptotic mean-square stability of the weak second-order stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential equations due to Rößler (2009) and Tang and Xiao (2017) are obtained. Further, we have developed the stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential equations to the balanced stochastic Runge–Kutta methods by using the control functions. We carry out a linear stability analysis of the class of stochastic Runge–Kutta methods for the linear test equations with multiplicative noise thereby providing an explicit structure of stability matrices. Some comparisons and illustrations shows that there is an improvement in the stability and error analysis of these new balanced stochastic Runge–Kutta methods comparatively to stochastic Runge–Kutta methods and thus conforming the obtained theoretical results.

Numerical instabilities of vector‐invariant momentum equations on rectangular C‐grids

The linear stability of two well‐known energy‐ and enstrophy‐conserving schemes for the vector‐invariant hydrostatic primitive equations is examined. The problem is analyzed for a stably stratified Boussinesq fluid on an f‐plane with a constant velocity field, in height and isopycnal coordinates, by separation of variables into vertical normal modes and a linearized form of the shallow‐water equations (SWEs). As found by Hollingsworth et al. the schemes are linearly unstable in height coordinate models, due to non‐cancellation of terms in the momentum equations. The schemes with the modified formulations of kinetic energy proposed by Hollingsworth et al. are shown to have Hermitian stability matrices and hence to be stable to all perturbations. All perturbations in isopycnal models are also shown to be neutrally stable, even with the original formulations for kinetic energy. Analytical expressions are derived for the smallest equivalent depths obtained using Charney–Phillips and Lorenz vertical grids, which show that the Lorenz grid has larger growth rates for unstable schemes than the Charney–Phillips grid. Test cases are proposed for assessing the stability of new numerical schemes using the SWEs.

Linear mean-square stability properties of semi-implicit weak order 2.0 Taylor schemes for systems of stochastic differential equations

We consider the two-parameter family of semi-implicit weak second order Taylor schemes introduced by Milstein to investigate mean-square stability (MS-stability) properties of these schemes for systems of stochastic differential equations (SDEs). We obtain stability matrices and other conditions for the schemes to be MS-stable for normal and non-normal test systems. It is shown that for normal test systems the MS-stability conditions are similar to those of linear scalar test, reported by other authors, while for non-normal test systems this property is not necessarily valid any more. Some figures are included to illustrate the MS-stability properties of the schemes.

Nonlocal buckling and vibration analysis of thick rectangular nanoplates using finite strip method based on refined plate theory

The buckling and vibration of thick rectangular nanoplates is analyzed in this article. A graphene sheet is theoretically assumed and modeled as a nanoplate in this study. The two-variable refined plate theory (RPT) is applied to obtain the differential equations of the nanoplate. The theory accounts for parabolic variation of transverse shear stress through the thickness of the plate without using a shear correction factor. Besides, the analysis is based on the nonlocal theory of elasticity to take the small-scale effects into account. For the first time, the finite strip method (FSM) based on RPT is employed to study the vibration and buckling behavior of nanoplates and graphene sheets. Hamilton’s principle is employed to obtain the differential equations of the nanoplate. The stiffness, stability and mass matrices of the nanoplate are formed using the FSM. The displacement functions of the strips are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. A matrix eigenvalue problem is solved to find the free vibration frequency and buckling load of the nanoplates subjected to different types of in-plane loadings including the uniform and nonuniform uni-axial and biaxial compression. Comparison studies are presented to verify the validity and accuracy of the proposed nonlocal refined finite strip method. Furthermore, a number of examples are presented to investigate the effects of various parameters (e.g., boundary conditions, nonlocal parameter, aspect ratio, type of loading) on the results.

Split-step Milstein methods for multi-channel stiff stochastic differential systems

We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability properties for different noise and drift structures. The stability matrices are established in a form convenient for analyzing their impact arising from different deterministic drift integrators. Numerical examples are provided to illustrate the effectiveness and reliability of these methods.

Hyperchaos in SC-CNN based modified canonical Chua’s circuit

In this paper, a state-controlled cellular neural network (SC-CNN)-based hyperchaotic circuit is implemented for classical modified canonical Chua’s circuit. The proposed system is modeled by using a suitable connection of four state-controlled generalized CNN cells, while the stability of the circuit is studied by determining the eigenvalues of the stability matrices, the system parameter is varied, and the dynamics as well as the onset of chaos and hyperchaos followed by a period-three doubling bifurcation has been studied through numerical analysis of the generalized SC-CNN equations and real-time experiments. We further validate our findings, the chaotic and hyperchaotic dynamics, characterized by two positive Lyapunov exponents and Lyapunov dimension, is described by a set of four coupled first-order generalized SC-CNN equations. This has been investigated extensively not only analyzing by computer simulation but also demonstrating by laboratory experiments. The experimental results such as phase portraits, Poincare surface sections and power spectra are in good agreement with those of numerical computations.

Longitudinal Control System Design Using Gradient Method for a Suborbital Launcher

The aim of this paper is to present a design method for the guidance navigation and control system (GNC) of a suborbital launcher. In order to achieve a symmetric evolution in the vertical plane we start with the decoupled form of the equation of motion. Afterwards these equations are linearized and the extended stability and command matrices are constructed by adding some auxiliary equations. The linear control law is obtained and the control matrix containing the unknown coefficients is presented. The design of the control system is based on a modified gradient method. To illustrate the proposed method the synthesis of the control system in the specific case of the SLT ("Suborbital Launcher for Testing - SLT" financed thru „Programme for Research-Development-Innovation on Space Technology and Advanced Research – STAR”) is presented.