Nonhomogeneous System Research Articles

Dynamic analysis and experiment of chaotic circuit of non-homogeneous fractional memristor with bias voltage source

A physical memristor has an asymmetric tight hysteresis loop. In order to simulate the asymmetric tight hysteresis curve of the physical memristor more conveniently, a fractional-order diode bridge memristor model with a bias voltage source is proposed in this paper, which can continuously regulate the hysteresis loop. Firstly, based on fractional calculus theory, a fractional order model of a diode bridge memristor with a bias voltage source is established, and its electrical characteristics are analyzed. Secondly, by integrating it with the Jerk chaotic circuit, a non-homogeneous fractional order memristor chaotic circuit model with a bias voltage source is established, and the influence of bias voltage on its system dynamic behavior is studied. Once again, a fractional-order equivalent circuit model is built in PSpice and validated through circuit simulation. The experimental results are basically consistent with the numerical simulation results. Finally, the experiments on the circuit are completed in LabVIEW to validate the correctness and feasibility of the theoretical analysis. The results indicate that the fractional order memristor with bias voltage source can continuously obtain asymmetric tight hysteresis loop by adjusting the voltage of the bias voltage source. As the bias power supply voltage changes, the non-homogeneous fractional order memristor chaotic system exhibits that the period doubling bifurcation turns into chaos due to the symmetry breaking.

Free vibrations of a nonhomogeneous rod-cylindrical shell-fluid system

Free vibrations of a nonhomogeneous rod-cylindrical shell-fluid system

Free Vibrations of Multi-Degree Structures: Solving Quadratic Eigenvalue Problems with an Excitation and Fast Iterative Detection Method

For the free vibrations of multi-degree mechanical structures appeared in structural dynamics, we solve the quadratic eigenvalue problem either by linearizing it to a generalized eigenvalue problem or directly treating it by developing the iterative detection methods for the real and complex eigenvalues. To solve the generalized eigenvalue problem, we impose a nonzero exciting vector into the eigen-equation, and solve a nonhomogeneous linear system to obtain a response curve, which consists of the magnitudes of the n-vectors with respect to the eigen-parameters in a range. The n-dimensional eigenvector is supposed to be a superposition of a constant exciting vector and an m-vector, which can be obtained in terms of eigen-parameter by solving the projected eigen-equation. In doing so, we can save computational cost because the response curve is generated from the data acquired in a lower dimensional subspace. We develop a fast iterative detection method by maximizing the magnitude to locate the eigenvalue, which appears as a peak in the response curve. Through zoom-in sequentially, very accurate eigenvalue can be obtained. We reduce the number of eigen-equation to n−1 to find the eigen-mode with its certain component being normalized to the unit. The real and complex eigenvalues and eigen-modes can be determined simultaneously, quickly and accurately by the proposed methods.

System dynamics modelling for calculation of carbon footprint on a non-homogeneous production system: A case in a ceramic studio

The production system of a typical ceramic studio is simple but non-homogeneous. Production stages are batch, and some are accumulative (unit by unit). This inhomogeneity leads to a non-smooth product flow along the production line. Energy for processing comes from three sources: fuel oil, electricity, and liquified petroleum gas (LPG), so it has the potential to generate relatively large carbon emissions. This paper discusses how the inhomogeneity of the production system can be analysed by system dynamics modelling when mathematical modelling is impossible because of its states' complexity, or discrete-events simulation modelling is not efficient enough to use. Scenario analysis can be done using the system dynamics model created. Existing conditions provide a carbon footprint of 19.57 kg. If an additional set of trays is provided, obtaining a firing timing configuration in both kilns is possible. The number of carbon emissions can be reduced by up to 22.8%, or save about US$ 16,350 per year. This value means a lot for a micro, small and medium enterprise (MSME).

Estimating bulk and edge topological indices in finite open chiral chains

We develop a formalism to estimate, simultaneously, the usual bulk and edge indices from topological insulators in the case of a finite sample with open boundary conditions and provide a physical interpretation of these quantities. We then show that they converge exponentially fast to an integer value when we increase the system size and also show that bulk and edge index estimates coincide at finite size. The theorem applies to any non-homogeneous system, such as disordered or defect configurations. We focus on one-dimensional chains with chiral symmetry, such as the Su–Schrieffer–Heeger model, but the proof actually only requires the Hamiltonian to be of short range and with a spectral gap in the bulk. The definition of bulk and edge index estimates relies on a finite-size version of the switch-function formalism where the Fermi projector is smoothed in energy using a carefully chosen regularization parameter.

Advancing contact of a 2D elastic curved beam indented by a rigid pin with clearance

A two-dimensional analytical solution is presented for stresses and displacements in an elastic curved beam forming an incomplete ring in frictionless and unbonded contact with a rigid pin loaded by a point force and in the presence of clearance. The circular beam is modeled as an incomplete elastic thick ring, constrained at both ends and in a plane stress state. The stress and displacement fields within the beam are derived from a biharmonic Airy stress function, according to the Michell solution in polar coordinates. The mixed boundary value problem is reduced to a set of dual series equations and then to a non-homogeneous linear system of infinite equations, which is then solved by truncation. The non-linear relations between the applied load and the contact angle or the pressure distribution are obtained by using an inverse method. The analytical results are compared with finite element predictions for a pin-lug connection and a reasonable agreement is observed for several typical geometries. The peaks of contact pressure and von Mises equivalent stress and their location within the curved beam are evidenced.

Blood Flow through an Elliptical Stenosed Artery with the Heat Source and Chemical Reaction

The research article scrutinized blood circulation in the arteries in abnormal (elliptical) form. In the evaluation, the mathematical model originated as coupled partial differential equations solved employing the parameter variation method through the boundary conditions by solving the non-homogeneous linear system of matrices in the Bessel function. To understand the influence of blood flow characterized by velocity, temperature, wall shear stress, concentration, frequency rate and volumetric flow rate for different values of dimensionless parameters, the current investigation is helpful in the biomedical field for treating various cardiovascular diseases.

Singularity for the one-dimensional rotating Euler equations of Chaplygin gases

This paper is focused on the singularity formation of smooth solutions for the one-dimensional rotating Euler equations of Chaplygin gases, which is a nonhomogeneous quasilinear hyperbolic system with linearly degenerate characteristic fields. We overcome the influence of the rotation terms and show that the density itself of the smooth solution tends to infinity in finite time for a kind of initial data.

Riemann problems for the nonhomogeneous Aw-Rascle model

In this paper the celebrated second order Aw-Rascle nonhomogeneous system describing traffic flows is considered. Within the framework of the method of differential constraints, a suitable reduction procedure is developed for solving a class of Riemann problems which are of interest in traffic flows theory. In particular, for a given source term, we find the general solution of the Riemann problem in terms of shock waves, contact discontinuities and generalized rarefaction waves. The interaction between a shock wave and a generalized rarefaction wave is also studied and a related generalized Riemann problem is solved. Numerical results are in agreement with the exact analytical solution.

MOFFeCo/B-CN composites achieve efficient degradation of antibiotics in a non-homogeneous concurrent photocatalytic-persulfate activation system

We synthesized an MFeCoB0.4CNx% (MOF-Fe/Co nanosheets/boron-doped g-C3N4) composite catalyst for enhancing the concurrent photocatalytic-persulfate activation (CPPA) system and achieved efficient degradation of antibiotics. The role of MOF-Fe/Co is to activate persulfate, while boron-doped g-C3N4 can generate photogenerated electrons for the reduction of Co3+/Fe3+ to enhance the regeneration of the active center. The rate constant for Tetracycline degradation by the CPPA system was 4.74 and 7.54 times higher than the photocatalytic and persulfate-activated systems, respectively. This composite was shown to be practical and economically viable for antibiotic degradation. The degradation behavior was explored based on experiments, and molecular orbitals and Fukui functions were obtained by density functional theory calculations. Mechanisms were investigated using reactive oxygen species trapping studies and electron spin resonance, and the process was explained in terms of the charge population and electron density difference of MOF-Fe/Co nanosheets. The CPPA system is an ecologically benign technology for removing antibiotic-related risks to the environment and human health.

The Riemann problem for one-dimensional dusty gas dynamics with external forces

This article concerns the study of the Riemann Problem (RP) for a non-homogeneous system governing the one-dimensional compressible flow of dusty gas, where the external forces are assumed to be continuous function of time. The elementary wave solutions such as rarefaction wave, shock wave, and contact discontinuity are rigorously determined. The effect of dust particles on the density and flow velocity and shock speed is examined, and their consequences on the solution of the Riemann Problem are discussed. Moreover, we discussed the condition for the existence of vacuum appears in the solution of the Riemann Problem.

Controllability and observability for fractal linear dynamical systems

In the present paper, we investigate the controllability, and observability of a non-homogeneous continuous-time fractal dynamical system (NC-TFDS). We show that the controllability is equivalent to a controllability matrix that has a full rank. We also show a relationship between controllability and fractal differential Lyapunov equation (F-DLE). We give some theorems for the observability of a NC-TFDS. Finally, we offer two examples are provided to illustrate the effectiveness of our results and compare it with the two papers Al-Zhour (2022) and (Sadek et al., 2022).

On the Preservation with Respect to Nonlinear Perturbations of the Stability Property for Nonautonomous Linear Neutral Fractional Systems with Distributed Delays

In the present paper, sufficient conditions are obtained under which the Cauchy problem for a nonlinearly perturbed nonautonomous neutral fractional system with distributed delays and Caputo type derivatives has a unique solution in the case of initial functions with first-kind discontinuities. For this system, by applying a formula for the integral presentation of the solution of the nonhomogeneous linear neutral fractional system, we found some additional natural conditions to ensure that from the global asymptotically stability of the zero solution of the linear part of the nonlinearly perturbed system, global asymptotic stability of the zero solution of the whole nonlinearly perturbed system follows.

Hopf Bifurcation Analysis in a Gierer–Meinhardt Activator–Inhibitor Model

In this paper, we study the Hopf bifurcation in a Gierer–Meinhardt model of the activator–inhibitor type with different sources. In the absence of diffusion, we determine the dynamics of the corresponding kinetic equations. Then, we investigate the impact of the diffusion rates on the stability of the homogeneous steady state. By choosing a proper bifurcation parameter, we prove that, under some suitable conditions of the parameters, a Hopf bifurcation occurs in the nonhomogeneous system. We compute the normal form of this bifurcation up to the third order. Next, we specify the direction of the Hopf bifurcation by the normal form theory. Moreover, we provide numerical simulations to illustrate our analytical results.

On time-decay rates of strong solutions for the 3D magnetohydrodynamics equations with nonlinear damping

In this paper we investigate the existence and time-decay rates of strong solutions with small perturbation to the systems of equations of a compressible magnetohydrodynamic fluid with nonlinear damping. First we reformulate the system into a perturbation form. Then we establish a priori estimates of solutions, and prove the existence of the global-in-time based on the local existence of unique solutions. Finally we will establish the optimal time-decay rates of the non-homogeneous system by constructing some decay estimates of the linearized system based on the decomposition technique of both the low and high frequencies of solutions as in [40].

Integral representation formulas for higher order Dirac equations

The aim of this paper is to establish a representation formula for the null solutions of some higher order Dirac operator, which particularly will be recognized as an iterated Lamé-Navier system of linear elasticity theory. We will show how to express the inverse of such a higher order partial differential operator, and this leads to a particular solution of the non-homogeneous system.

Optimal time-decay rates of the Keller–Segel system coupled to compressible Navier–Stokes equation in three dimensions

Recently, Hattori–Lagha established the global existence and asymptotic behavior of the solutions for a three-dimensional compressible chemotaxis system with chemoattractant and repellent (Hattori and Lagha in Discrete Contin. Dyn. Syst. 41(11):5141–5164, 2021). Motivated by Hattori–Lagha’s work, we further investigated the optimal time-decay rates of strong solutions with small perturbation to the three-dimensional Keller–Segel system coupled to the compressible Navier–Stokes equations, which models for the motion of swimming bacteria in a compressible viscous fluid. First, we reformulate the system into a perturbation form. Then we establish a prior estimates of solutions and prove the existence of the global-in-time solutions based on the local existence of unique solutions. Finally, we will establish the optimal time-decay rates of the nonhomogeneous system by the decomposition technique of both low and high frequencies of solutions as in (Wang and Wen in Sci. China Math., 2020, https://doi.org/10.1007/s11425-020-1779-7). Moreover, the decay rate is optimal since it agrees with the solutions of the linearized system.

Incident indicators for freeway traffic flow models

Developed in this paper is a traffic flow model parametrised to describe abnormal traffic behaviour. In large traffic networks, the immediate detection and categorisation of traffic incidents/accidents is of capital importance to avoid breakdowns, further accidents. First, this claims for traffic flow models capable to capture abnormal traffic condition like accidents. Second, by means of proper real-time estimation technique, observing accident related parameters, one may even categorize the severity of accidents. Hence, in this paper, we suggest to modify the nominal Aw-Rascle (AR) traffic model by a proper incident related parametrisation. The proposed Incident Traffic Flow (ITF) model is defined by introducing the incident parameters modifying the anticipation and the dynamic speed relaxation terms in the speed equation of the AR model. These modifications are proven to have physical meaning. Furthermore, the characteristic properties of the ITF model is discussed in the paper. A multi stage numerical scheme is suggested to discretise in space and time the resulting non-homogeneous system of PDEs. The resulting systems of ODE is then combined with receding horizon estimation methods to reconstruct the incident parameters. Finally, the viability of the suggested incident parametrisation is validated in a simulation environment.

Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time

The stochastic process non-homogeneous Markov system in a stochastic environment in continuous time (S-NHMSC) is introduced in the present paper. The ordinary non-homogeneous Markov process is a very special case of an S-NHMSC. I studied the expected population structure of the S-NHMSC, the first central classical problem of finding the conditions under which the asymptotic behavior of the expected population structure exists and the second central problem of finding which expected relative population structures are possible limiting ones, provided that the limiting vector of input probabilities into the population is controlled. Finally, the rate of convergence was studied.

Regularity and Energy Conservation of the Nonhomogeneous Incompressible Ideal Magnetohydrodynamics Equations

In this paper, we study the regularity and local energy equation of the weak solutions for nonhomogeneous incompressible ideal magnetohydrodynamics system. The conditions given on the regularity of solutions guarantee the energy to be conserved. The main method we have employed relies on the commutator estimates.