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This study is concerned with the problem of the functional observer‐based sliding mode control (SMC) design for parametric uncertain discrete‐time delayed stochastic systems includes mismatched parameter uncertainty in the state matrix and in the delayed state matrix. Stability analysis of sliding function is presented in the time delayed stochastic system with a linear matrix inequality approach. Moreover, it is shown that the state trajectories can be driven onto the specified sliding surface despite the presence of state delay, unmatched parameter uncertainty and stochastic noise in the system. The research is motivated by the fact that the system states are not always accessible for the state feedback. Therefore, SMC is estimated using the functional observer technique. To mitigate the side effect of the parameter uncertainty on the estimation error, a sufficient condition of stability is proposed based on Gershgorin disc theorem. The claims made are validated through numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, we discuss modified three level implicit difference methods of order two in time and four in space for the numerical solution of two‐ and three‐dimensional telegraphic equation with Robin boundary conditions. Ghost points are introduced to obtain fourth‐order approximations for boundary conditions. Matrix stability analysis is carried out to prove stability of the method for telegraphic equations in two and three dimensions with Neumann boundary conditions. Numerical experiments are carried out and the results are found to be better when compared with the results obtained by other existing methods. [ABSTRACT FROM AUTHOR]

A systematic procedure is presented to derive stability conditions for leap-frog-type finite-difference schemes for the multidimensional constant-coefficient convective-diffusion equation. The treatise includes von Neumann stability analysis for pure initial-value problems and matrix stability analysis for Dirichlet boundary-value problems. Discrepancies on time-step restriction between von Neumann stability analysis and matrix stability analysis are observed. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the attitude tracking control problem of rigid spacecraft with inertia parameter identification. Based on the relative attitude and angular velocity error dynamics, a basic adaptive backstepping based attitude tracking control scheme is firstly designed such that asymptotic attitude tracking can be achieved. However, the parameter identification error cannot decay to zero if the persistent excitation (PE) condition is not satisfied. To solve this issue, a filtering‐based concurrent learning adaptive backstepping control scheme is then proposed, by incorporating torque filtering technique with concurrent learning technique. A more mild rank condition, which consists of some collectable historical data, is provided to guarantee the convergence of parameter identification error. In addition, a valid data collection algorithm is given. It should be mentioned that a distinctive feature of the proposed filtering‐based concurrent learning adaptive control scheme is that the convergence rate of attitude tracking errors can be improved from asymptotical to exponential. Finally, simulation results are provided to illustrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

In this paper, the problem of attack detection for actuator attacks and power balance on cyber physical power systems (CPPSs) is investigated. An economic optimization strategy based on observer data is proposed to enable optimal power balance of the attacked system. System states and cyber attacks are estimated by a sliding mode observer satisfying the H∞$H_{\infty }$ performance index. Then, the system power is redistributed according to the optimal economic dispatch. Finally, several simulation cases are presented to illustrate the effectiveness of attack detection and economic optimization strategy. [ABSTRACT FROM AUTHOR]

Studies on the unphysical increase of turbulent quantities for RANS simulation induced by shock waves in hypersonic flows are carried out. Numerical experiments on the hypersonic flow over a blunt body reveal that the phenomenon of unphysical increase of turbulent quantities across the detached shock wave is induced by the strain‐rate‐based production terms of the k‐ω$$ \omega $$ and k‐ω$$ \omega $$ SST turbulence models, which leads to the over‐prediction of aerothermal prediction. While this phenomenon does not occur for Spalart–Allmaras (S–A) turbulence model because of its vorticity‐based production term. In order to eliminate this unphysical phenomenon, and to maintain the accuracy of the original models for boundary layer and separation flows, a new correction method for the k‐ω$$ \omega $$ and k‐ω$$ \omega $$ SST models is proposed: by comparing the orders of magnitude between the strain‐rate‐based and vorticity‐based production terms, the vorticity‐based production term is used near the shock waves, while the original strain‐rate‐based production term is still used in other regions. Finally, the correction method is applied to turbulence and transition flows over blunt bodies, and the numerical results show that the correction method effectively eliminates the unphysical increase of turbulent quantities across shock waves and improves the accuracy of aerothermal and transition onset location prediction. [ABSTRACT FROM AUTHOR]

We investigate the numerical artifact known as a carbuncle, in the solution of the shallow water equations. We propose a new Riemann solver that is based on a local measure of the entropy residual and aims to avoid carbuncles while maintaining high accuracy. We propose a new challenging test problem for shallow water codes, consisting of a steady circular hydraulic jump that can be physically unstable. We show that numerical methods are prone to either suppress the instability completely or form carbuncles. We test existing cures for the carbuncle. In our experiments, only the proposed method is able to avoid unphysical carbuncles without suppressing the physical instability. [ABSTRACT FROM AUTHOR]

There is a consistent demand for reliable, efficient, small‐sized, and light weight power supply for electronics devices. To meet the aforesaid requirements, Quasi Resonant converters are being used due to low switching losses, high efficiency, small size and weight. With these motivations, in this paper, two different methodologies of passivity‐based controllers namely (EL‐PBC and PCH‐PBC) are proposed for Zero Voltage Switching Quasi Resonant (ZVS‐QR) boost converter to regulate the output voltage. First, the Euler‐Lagrange (EL) formulation is used to derive state‐space equations for ZVS‐QR boost converter under different operating modes and then, average state‐space model is developed using generalized state space average (GSSA) technique. In order to improve the dynamic performance of the ZVS‐QR boost converter, the aforesaid passivity‐based controllers are designed and its stability analysis is carried out. The entire system is developed with Sim Power System toolbox of MATLAB software and validated through OP‐5142 real time simulator. Steady state and dynamic performances are examined under several operating conditions. It is observed that the passivity‐based controllers of the paper achieve robustness against the uncertainties at the input and the load side. It is compared with benchmark PI controller as well. [ABSTRACT FROM AUTHOR]

In this work, we study the numerical simulation of the one‐dimensional reaction‐diffusion system known as the Gray‐Scott model. This model is responsible for the spatial pattern formation, which we often meet in nature as the result of some chemical reactions. We have used the trigonometric quartic B‐spline (T4B) functions for space discretization with the Crank‐Nicolson method for time integration to integrate the nonlinear reaction‐diffusion equation into a system of algebraic equations. The solutions of the Gray‐Scott model are presented with different wave simulations. Test problems are chosen from the literature to illustrate the stationary waves, pulse‐splitting waves, and self‐replicating waves. [ABSTRACT FROM AUTHOR]

Summary: The HLLEM scheme is a popular contact and shear preserving approximate Riemann solver that is known to be plagued by various forms of numerical shock instability. In this paper, we clarify that the shock instability exhibited by this scheme is primarily triggered by the spurious activation of the antidiffusive terms present in the first and third Riemann flux components on the transverse interfaces adjoining the shock front due to numerical perturbations. These erroneously activated terms are shown to counteract the favorable damping mechanism provided by its inherent HLL‐type diffusive terms, causing an unphysical variation of the conserved quantity ρu both along and across the numerical shock. To prevent this, two distinct strategies are proposed termed as Selective Wave Modification and Anti Diffusion Control. The former focuses on enhancing the quantity of the favorable HLL‐type dissipation available on these critical flux components by carefully increasing the magnitudes of certain nonlinear wave speed estimates, while the latter focuses on directly controlling the magnitude of these critical antidiffusive terms. A linear perturbation analysis is performed to gauge the effectiveness of these cures and to estimate a von Neumann–type stability bounds on the CFL number associated with their use. Results from a variety of classic shock instability test cases show that the proposed strategies are able to provide excellent shock stable solutions even on grids that are highly elongated across the shock front without compromising the accuracy on inviscid contact or shear dominated viscous flows. Numerical shock instability in the HLLEM scheme is found to be triggered by the erroneous activation of certain antidiffusive terms, within the numerical shock region, which counteract the stabilizing action of the inherent HLL‐type diffusive terms. Two distinct strategies named 'Selective Wave Modification' and 'Anti Diffusion Control' are proposed to avert the instability. The schemes resulting from these, are found to be robust on a wide variety of problems involving a wide range of grid aspect ratios. [ABSTRACT FROM AUTHOR]

Summary: A simple, robust, and accurate HLLC‐type Riemann solver for the compressible Euler equations at various Mach numbers is built. To cure shock instability of the HLLC solver at strong shocks, a pressure‐control technique, which plays a role in limiting the propagation of erroneous pressure perturbation, is proposed. With an all Mach correction method for the compressible Euler system, the proposed method is further extended to compute flow problems at low Mach numbers. The proposed all Mach HLLC‐type scheme has been implemented and used to compute a variety of flow problems ranging from hypersonic compressible to low Mach incompressible flow regimes. Various numerical results demonstrate that the obtained all Mach HLLC‐type scheme is both accurate and stable for all speed ranges. A simple, robust and accurate HLLC‐type Riemann solver for the compressible Euler equations at various Mach numbers is built. The proposed solver is endowed with a high level of robustness against shock instability while preserves sharp capturing of different kinds of discontinuities. With an all Mach correction, it is able to maintain solution accuracy and efficiency for computations of flow at all speeds [ABSTRACT FROM AUTHOR]

Abstract: The aim of this study was to investigate the interplay between structural connectivity and cortical demyelination in early multiple sclerosis. About 27 multiple sclerosis patients and 18 age‐matched controls underwent two MRI scanning sessions. The first was done at 7T and involved acquiring quantitative T1 and T2* high‐resolution maps to estimate cortical myelination. The second was done on a Connectom scanner and consisted of acquiring high angular resolution diffusion‐weighted images to compute white matter structural connectivity metrics: strength, clustering and local efficiency. To further investigate the interplay between structural connectivity and cortical demyelination, patients were divided into four groups according to disease‐duration: 0–1 year, 1–2 years, 2–3 years, and >3 years. ANOVA and Spearman's correlations were used to highlight relations between metrics. ANOVA detected a significant effect between disease duration and both cortical myelin (p = 2 × 10−8) and connectivity metrics (p < 10−4). We observed significant cortical myelin loss in the shorter disease‐duration cohorts (0–1 year, p = .0015), and an increase in connectivity in the longer disease‐duration cohort (2–3 years, strength: p = .01, local efficiency: p = .002, clustering: p = .001). Moreover, significant covariations between myelin estimation and white matter connectivity metrics were observed: Spearman's Rho correlation coefficients of 0.52 (p = .0003), 0.55 (p = .0001), and 0.53 (p = .0001) for strength, local efficiency, and clustering, respectively. An association between cortical myelin loss and changes in white matter connectivity in early multiple sclerosis was detected. These changes in network organization might be the result of compensatory mechanisms in response to the ongoing cortical diffuse damage in the early stages of multiple sclerosis. [ABSTRACT FROM AUTHOR]

The simple low-dissipation advection upwind splitting method (SLAU) scheme is a parameter-free, low-dissipation upwind scheme that has been applied in a wide range of aerodynamic numerical simulations. In spite of its successful applications, the SLAU scheme could be showing shock instabilities on unstructured grids, as many other contact resolved upwind schemes. Therefore, a hybrid upwind flux scheme is devised for improving the shock stability of SLAU scheme, without compromising on accuracy and low Mach number performance. Numerical flux function of the hybrid scheme is written in a general form, in which only the scalar dissipation term is different from that of the SLAU scheme. The hybrid dissipation term is defined by using a differentiable multidimensional-shock-detection pressure weight function, and the dissipation term of SLAU scheme is combined with that of the Van Leer scheme. Furthermore, the hybrid dissipation term is only applied for the solution of momentum fluxes in numerical flux function. Based on the numerical test results, the hybrid scheme is deemed to be a successful improvement on the shock stability of SLAU scheme, without compromising on the efficiency and accuracy. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this article, the meshless local radial point interpolation method is applied to analyze three space dimensional wave equations of the form utt + α ut + βu = uxx + uyy + uzz + ƒ(x, y, z, t), xT = (x, y, z) ∈ Ω ⊆ ℝd, (d = 2, 3), t > 0 subject to given initial and Dirichlet boundary conditions. The main difficulty of the great number of methods in full 3-D problems is the large computational costs. In meshless local radial point interpolation method, it does not require any background integration cells, so that all integrations are carried out locally over small quadrature domains of regular shapes such as circles or squares in two dimensions and spheres or cubes in three dimensions. The point interpolation method with the help of radial basis functions is proposed to construct shape functions that have Kronecker delta function property. A weak formulation with the Heaviside step function converts the set of governing equations into local integral equations on local subdomains. A two-step time discretization method is employed to evaluate the time derivatives. This suggests Crank-Nicolson technique to be applied on the right hand side of the equation. The convergence analysis and stability of the method are fully discussed. Three illustrative examples are presented, and satisfactory agreements are achieved. It is shown theoretically that the proposed method is unconditionally stable for the second example whereas it is not for the first and third ones. [ABSTRACT FROM AUTHOR]

The AUFS scheme by Sun and Takayama is a flux splitting scheme without breakdown of discrete shock profiles, usually called carbuncle, but still with a good resolution of entropy waves. Unfortunately, numerical tests with this scheme yield that the viscosity on entropy waves is too small while the viscosity on shear waves is too large. In this paper, we prove that both deficiencies are inherent to the construction of the scheme and provide fixes to overcome them. [ABSTRACT FROM AUTHOR]

Natural communities commonly contain many different species and functional groups, and multiple types of species interactions act simultaneously, such as competition, predation, commensalism or mutualism. However, experimental and theoretical investigations have generally been limited by focusing on one type of interaction at a time or by a lack of a common methodological and conceptual approach to measure species interactions., We compared four methods to measure and express species interactions. These approaches are, with increasing degree of model complexity, an extinction-based model, a relative yield model and two generalized Lotka-Volterra (LV) models. All four approaches have been individually applied in different fields of community ecology, but rarely integrated. We provide an overview of the definitions, assumptions and data needed for the specific methods and apply them to empirical data by experimentally deriving the interaction matrices among 11 protist and rotifer species, belonging to three functional groups. Furthermore, we compare their advantages and limitations to predict multispecies community dynamics and ecosystem functioning., The relative yield method is, in terms of final biomass production, the best method in predicting the 11-species community dynamics from the pairwise competition experiments. The LV model, which is considering equilibrium among the species, suffers from experimental constraints given the strict equilibrium assumption, and this may be rarely satisfied in ecological communities., We show how simulations of a LV stochastic community model, derived from an empirical interaction matrix, can be used to predict multispecies community dynamics across multiple functional groups., Our work unites available tools to measure species interactions under one framework. This improves our ability to make management-oriented predictions of species coexistence/extinction and to compare ecosystem processes across study systems. [ABSTRACT FROM AUTHOR]

Computational structural dynamics plays an essential role in the simulation of linear and nonlinear systems. Indeed, the characteristics of the time integration procedure have a critical impact on the feasibility of the calculation. In order to go beyond the classical approach (a unique time integrator and a unique timescale), the pioneer approach of Belytschko and co-workers consisted in developing mixed implicit-explicit time integrators for structural dynamics. In a first step, the implementation and stability analyses of partitioned integrators with one time step have been achieved for a large class of time integrators. In a second step, the implementation and stability analyses of partitioned integrators with different time steps were studied in detail for particular cases. However, stability results involving different time steps and different time integrators in different parts of the mesh is still an open question in the general case for structural dynamics. The aim of this paper is to propose a state-of-the art of heterogeneous (different time schemes) asynchronous (different time steps) time integrators (HATI) for computational structural dynamics. Finally, an alternative approach based on energy considerations (with velocity continuity at the interface) is proposed in order to develop a general class of HATI for structural dynamics. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A classic problem in gas dynamics simulation is the occurrence of the carbuncle phenomenon, a breakdown of discrete shock profiles. We show that for high Froude number, this also occurs in shallow water simulations. Numerical evidence is given that commonly accepted cures developed for the numerics of gas dynamics should also work for shallow water flows. [ABSTRACT FROM AUTHOR]

This study presents new sufficient conditions for Hurwitz and Schur stability of interval matrices. Tight bounds for the spectrum of interval matrices are estimated using computationally simple optimisation problems. The conservativeness is reduced further by application of ordinary similarity transformation. A necessary and sufficient vertex based criterion for the stability of a subclass of interval systems in continuous and discrete-time cases is also proposed. This enables the spectra for this class of interval systems to be determined exactly. A selection of various examples adopted from existing literature is used to demonstrate the utility of the proposed criteria. [ABSTRACT FROM AUTHOR]

SUMMARY Stability is achieved in most approximate Riemann solvers through 'flux upwinding', where the flux at the interface is arrived at by adding a dissipative term to the average of the left and right flux. Motivated by the existence of a collapsed interface state in the gas-kinetic Bhatnagar-Gross-Krook (BGK) method, an alternative approach to upwinding is attempted here; an interface state is arrived at by taking an upwinded average of left and right states, and then the flux is calculated as a function of this 'collapsed' interface state. This so called 'state-upwinding' approach gives rise to a new scheme called the linearized Riemann solver for the Euler and Navier-Stokes equations. The scheme is shown to be closely associated with the Roe scheme. It is, however, computationally less expensive and gives qualitatively comparable results over a wide range of problems. Most importantly, this scheme is found to preserve stationary contacts while not exhibiting the carbuncle phenomenon which plagues the Roe and other contact-preserving schemes. The scheme is therefore motivated as a new starting point to analyze the origin of the carbuncle phenomenon. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The solution of the Crank-Nicolson (CN) method may present spurious modes, which mostly happens in systems with an initial singularity. In this work, we analyze the onset of spurious oscillations for the CN method for large time steps. This analysis is performed on the general one-dimensional linear advection-diffusion-reaction transport equation with initial singularity that models a broad range of mass transfer phenomena in natural and engineering sciences. The discrete problem is obtained using a stable finite element method in space and the generalized trapezoidal family of methods in time. Depending on the range of parameters, either the Galerkin or the streamline upwind Petrov-Galerkin methods are used to guarantee stability in space. We derive a stability analysis of the fully discrete method and investigate the techniques proposed in the literature to damp oscillations. We propose a new threshold of time oscillations to overcome the spurious modes, which is also extended to deal with nonlinear problems. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We have developed a new fully anisotropic 3D FDTD Maxwell solver for arbitrary electrically and magnetically anisotropic media for piecewise constant electric and magnetic materials that are co‐located over the primary computational cells. Two numerical methods were developed that are called nonaveraged and averaged methods, respectively. The nonaveraged method is first‐order accurate, while the averaged method is second‐order accurate for smoothly‐varying materials and reduces to first order for discontinuous material distributions. For the standard FDTD field locations with the co‐location of the electric and magnetic materials at the primary computational cells, the averaged method required development of the different inversion algorithms of the constitutive relations for the electric and magnetic fields. We provide a mathematically rigorous stability proof followed by extensive numerical testing that includes long‐time integration, eigenvalue analysis, tests with extreme, randomly placed material parameters, and various boundary conditions. For accuracy evaluation, we have constructed a test case with an explicit analytic solution. Using transformation optics, we have constructed complex, spatially inhomogeneous geometrical object with fully‐anisotropic materials and a large dynamic range of ε_ and μ_, such that a plane wave incident on the object is perfectly reconstructed downstream. [ABSTRACT FROM AUTHOR]