Dimensional Subsystems Research Articles

THEORETICAL AND EXPERIMENTAL MODELING OF THE PROCESS OF MELTING COMPLEX ALLOYED STEELS (Fe-Si-Al-Mn)

In the practice of complex theoretical research of multicomponent systems, the so-called thermodynamic-diagram method of analysis is known, which significantly simplifies the study of phase transformations in multicomponent systems by dividing them into thermodynamically stable elementary partial subsystems of equal dimensionality as the main ones. Thermodynamic-diagram analysis combines the thermodynamic assessment of chemical interactions between components in the studied system with a geometric diagram. Such a combination, as studies of the physicochemical principles of refractories and ferroalloys production have shown, proves to be productive in interpreting chemical interactions in complex systems.

Leader‐following distributed control of networked linear multi‐input systems: A prescribed‐time framework

AbstractThis paper concentrates on the leader‐following distributed control problem for linear multi‐input systems while guaranteeing prescribed finite‐time performance. Compared with the current state of the arts, novel nonsingular coordinate transformations are proposed by using the block decomposition technique and smooth time‐varying scaling functions, such that a prescribed‐time control framework dealing with distinct subsystem dimensions featured by multi‐input systems is acquired. The prescribed‐time boundedness of the closed‐loop system and the control input is proven by introducing nonsingular inverse coordinate transformations. Moreover, the settling time can relax the initial conditions and any other control parameters. Numerical examples are provided to confirm the efficacy of the proposed method.

Numerical and experimental investigation on autoparametric resonance of multi-system structures

The analysis of dynamic stability in frame structures has always been a critical issue in engineering and mechanical design. Autoparametric resonance instability problems present a more complex dynamic instability mechanism than general parametric resonance, and determining the unstable regions of frame structures with multiple subsystems requires consideration of the coupled vibration of each subsystem. Unfortunately, existing approximate formulas are inadequate to analyze the stable boundary of autoparametric resonance in frame structures. To address this issue, this paper proposes a novel method called the dynamic axial force transfer coefficient (DTC) method to investigate the spatial dynamic instability characteristics of complex frame structures under parametric excitation due to autoparametric resonance. The proposed method, in conjunction with the harmonic balance method and the finite element method (FEM), established the global finite element equation of the frame and derived the stable boundary equation of autoparametric resonance for general frame structures. A complex spatial frame model is built to verify the effectiveness of the DTC method, and a comprehensive parametric analysis is conducted to investigate the dynamic instability mechanism of autoparametric resonance, including structural damping, static load coefficient, connection and boundary conditions of subsystems, and cross-sectional dimensions of subsystems. The results show that autoparametric resonance stability analysis of frame structures should consider the design parameters of each subsystem independently. In addition, strong coupling interaction between subsystems may induce autoparametric internal resonance of structure subjected to dynamic load. An autoparametric resonance test of a Γ-shaped frame is presented to further verify the proposed method. The test reveals the mechanism of the strong coupling effect, which may lead to a high risk of structural failure. More importantly, the DTC method can accurately determine the unstable boundary of multi-system frame structures, which is consistent with conventional methods (EGE) and experimental results, and predict the strong coupling effect of practical structures. The proposed method is simpler and more convenient than the existing methods for stability analysis of the autoparametric resonance of general frame structures, and can provide more effective guidance for structural design.

Reliability Analysis of the Cactus-Based Networks Based on Subsystem

Abstract Multiprocessor systems play a significant role in big data era. As the probability of presence of processor failures in a multiprocessor system raises with the increase of the system scale, the effect of processor failure is worthy of quantifying. The subsystem reliability of a multiprocessor system is the probability that a fault-free subsystem of certain size still operate with the rise of individual faults. In this work, we employ the probabilistic fault model and the Principle of Inclusion-Exclusion (PIE) to establish the approximation and upper bound on the subsystem reliability of the cactus-based networks through decomposition into $(n-1)$-dimensional subsystems by fixing one position-pair. Numerical simulations show that the upper bound derived in this way is close to the approximation of the accurate subsystem reliability.

Modelling Silicosis: Dynamics of a Model with Piecewise Constant Rate Coefficients

We study the dynamics about equilibria of an infinite dimensional system of ordinary differential equations of coagulation–fragmentation–death type that was introduced recently by da Costa et al. (Eur J Appl Math 31(6):950–967, 2020) as a model for the silicosis disease mechanism. For a class of piecewise constant rate coefficients an appropriate change of variables allows for the appearance of a closed finite dimensional subsystem of the infinite-dimensional system and the analysis of the eigenvalues of the linearizations of this finite dimensional subsystem about the equilibria is then used to obtain the results on the stability of the equilibria in the original infinite dimensional model.

Stability of multi-dimensional switched systems with an application to open multi-agent systems

A multi-dimensional switched system or multi-mode multi-dimensional (M3D) system extends the classic switched system by allowing different subsystem dimensions. The stability problem of the M3D system, whose state transitions at switching instants can be discontinuous due to the dimension-varying feature, is studied. The discontinuous state transition is formulated by an affine map that captures both the dimension variations and the state impulses, with no extra constraint imposed. In the presence of unstable subsystems, the general criteria featuring a series of Lyapunov-like conditions for the practical and asymptotic stability properties of the M3D system are provided under the proposed slow/fast transition-dependent average dwell time framework. Then, by considering linear subsystems, we propose a class of parametric multiple Lyapunov functions to verify the obtained Lyapunov-like stability conditions and explicitly reveal a connection between the practical/asymptotic stability property and the non-vanishing/vanishing property of the impulsive effects in the state transition process. Further, the obtained stability results for the M3D system are applied to the consensus problem of the open multi-agent system (MAS), whose network topology can be switching and size-varying due to the migrations of agents. It shows that through a proper transformation, the seeking of the (practical) consensus performance of the open MAS with disconnected digraphs boils down to that of the (practical) stability property of an M3D system with unstable subsystems.

Non-fragile consensus control for nonlinear singular multi-agent systems: An event-triggered sampling scheme

This paper is devoted to the problem of non-fragile consensus control for a class of nonlinear singular multi-agent systems based on an event-triggered control strategy. To reduce the resource occupancy, a decentralized event-triggered sampling consensus control protocol for each agent is proposed, which does not require continuous communication among agents. Analysis of non-fragile consensus problem in the multi-agent systems is transformed into asymptotical stability issues of some lower dimensional subsystems via nonsingular transformation. Using the Lyapunov theory, sufficient conditions are obtained such that for all possible norm-bounded parameter variations in the protocol gains, the designed protocol can bring all agents’ states to a point of agreement. Furthermore, the corresponding protocol design method is also given. Numerical examples are included to illustrate the effectiveness of the derived results.

Industrial Internet Platform (IIP) enabled Smart Product Lifecycle-Service System (SPLSS) for manufacturing model transformation: From an industrial practice survey

Nowadays, the focus of enterprises is gradually expanding from product manufacturing system to Product service system (PSS). In the existing research, scholars mainly focus on the in-depth study of a certain method or technology, and the research on traditional PSS is relatively mature. In addition, it is a tendency that transform towards SPLSS with the characteristics of industrial internet platform (IIP) and sustainable operation theory. Based on this, this paper explores the research path from traditional product service system (PSS) to smart product service system (SPSS), and then to smart product lifecycle service system (SPLSS), which can endow the products with intelligent perception, intelligent analysis and intelligent decision-making capabilities based on Industrial Internet Platform (IIP). A reference model of IIP enabled SPLSS for industrial services based on system engineering method and theory from a very detailed practical investigation is proposed. Moreover, on the basis of this model, its three dimensional subsystems are expanded, including: supporting environment subsystem, evolution path subsystem, and added value subsystem. The study can provide a reference for the enterprise's manufacturing strategy and manufacturing path. It will promote the transformation and upgrading of enterprise manufacturing model to improve service efficiency and reduce operating costs, and then realize the value-added of products and services.

Second-order statistics of fermionic Gaussian states

We study the statistical behavior of entanglement in quantum bipartite systems over fermionic Gaussian states as measured by von Neumann entropy and entanglement capacity. The focus is on the variance of von Neumann entropy and the mean entanglement capacity that belong to the so-defined second-order statistics. The main results are the exact yet explicit formulas of the two considered second-order statistics for fixed subsystem dimension differences. We also conjecture the exact variance of von Neumann entropy valid for arbitrary subsystem dimensions. Based on the obtained results, we analytically study the numerically observed phenomena of Gaussianity of von Neumann entropy and linear growth of average capacity.

About switched affine system interconnected with fast LTI dynamics

We study an interconnection between a slow switched affine system and a fast LTI system. The lower dimensional slow and fast subsystems are computed via the singular perturbation approach. We consider the classical stabilization method based on the existence of a stable convex combination (while ignoring the fast dynamics) and we provide an LMI condition for checking ultimate boundedness when the fast dynamics is taken into account. Numerical example illustrates the main result.

Non-isothermal diffusion in interconnected discrete-distributed systems: a variational approach

Motivated by compartmental analysis in engineering and biophysical systems, we present a variational framework for the nonequilibrium thermodynamics of systems involving both distributed and discrete (finite dimensional) subsystems by specifically using the ideas of interconnected systems. We focus on the process of non-isothermal diffusion and show how the resulting form of the entropy equation naturally yields phenomenological expressions for the diffusion and entropy fluxes between two compartments, which results in generalized forms of Robin type interface conditions.

Geometric quantification of multiparty entanglement through orthogonality of vectors

The wedge product of vectors has been shown to yield the generalised entanglement measure I-concurrence, wherein the separability of the multiparty qubit system arises from the parallelism of vectors in the underlying Hilbert space of the subsystems. Here, we demonstrate the geometrical conditions of the post-measurement vectors which maximize the entanglement corresponding to the bi-partitions and can yield non-identical set of maximally entangled states. The Bell states for the two qubit case, GHZ and GHZ like states with superposition of four constituents for three qubits, naturally arise as the maximally entangled states. The geometric conditions for maximally entangled two qudit systems are derived, leading to the generalised Bell states, where the reduced density matrices are maximally mixed. We further show that the reduced density matrix for an arbitrary finite dimensional subsystem of a general qudit state can be constructed from the overlap of the post-measurement vectors. Using this approach, we discuss the trade-off between the local properties namely predictability and coherence with the global property, entanglement for the non-maximally entangled two qubit state.

Moments of quantum purity and biorthogonal polynomial recurrence

The Bures–Hall ensemble is a unique measure of density matrices that satisfies various distinguished properties in quantum information processing. In this work, we study the statistical behavior of entanglement over the Bures–Hall ensemble as measured by the simplest form of an entanglement measure—the quantum purity. The main results of this work are the exact second and third moment expressions of quantum purity valid for any subsystem dimensions, where the corresponding results in the literature are limited to the scenario of equal subsystem dimensions. In obtaining the results, we have derived recurrence relations of the underlying integrals over the Cauchy–Laguerre biorthogonal polynomials that may be of independent interest.

Differential Entropy of Induced Random State Ensemble

In this paper, we will consider the exact calculation of differential entropy of induced random state ensemble by partial tracing a subsystem over larger dimensional subsystem of a Haar-distributed pure bipartite state.

On the effects of the Chern-Simons term in an Abelian gauged Skyrme model in d = 4 + 1 dimensions

We study an Abelian gauged O(5) Skyrme model in 4+1 dimensions, featuring the F4 Maxwell and the Chern-Simons terms. Our aim is to expose the mechanism, discovered in the analogous Abelian gauged O(3) Skyrme model in 2+1 dimensions, which leads to the unusual relation of the mass-energy E to the electric charge Qe and angular momentum J, and, to the change in the value of the “baryon number” q due to the influence of the Abelian field on the Skyrmion. Chern-Simons dynamics together with the dynamics of the gauged Skyrme scalar, allows for solutions with varying asymptotic values of the magnetic field, resulting in these unusual properties listed. Numerical work is carried out on an effective one dimensional subsystem resulting from imposition of an enhanced radial symmetry on R4.

Firing patterns of the CA1 pyramidal neuron with geometric singular perturbation: a model study

An investigation of CA1 pyramidal model is an important issue for applications, which is intimately related to the composition of ions in the extracellular environment and external stimulation. In this paper, it is demonstrated that the effects of different electrophysiological parameters such as muscarinic-sensitive potassium current activation variable and sustained sodium current inactivation variable on the firing sequence of model by numerical simulations. Furthermore, the paper also discusses that the temperature affects the firing of the CA1 model from direct current (DC) and alternating current (AC) stimuli. It is found that the model exhibits excellent spiking and bursting patterns, even chaotic patterns occur. Meanwhile, generalized mixed oscillations emerge in the model. Additionally, the firing modes are depicted by providing the response curve (RC), inter-spike interval curve (ISI), phase diagram curve (PDC) and the number of spikes per burst curve (NC). Mathematically, the paper elaborates the results which are presented to obtain two lower dimensional subsystems, which govern the fast and slow dynamics for giving insight into the dynamic behaviors of the full 5D system based on the geometric singular perturbation theory (GSPT). Particularly, we analyse the phase diagrams of the CA1 model to understand the properties better. The present results may contribute to further understand the information processing of the CA1 pyramidal neurons.

Stability and stabilisation of heterogeneous switched systems with arbitrary switching constraints

Heterogeneous switched systems are a class of special hybrid systems containing different dimensional subsystems. To research the stability and stabilisation of heterogeneous switched systems, a novel approach is presented to design static output feedback controllers for asymptotically stabilising heterogeneous continuous-time and discrete-time switched systems under arbitrary switching rules. This approach, which has less computation complexity, includes a main diagonal square block common Lyapunov function for stability analysis of heterogeneous switched systems and a main diagonal square block common homogeneous polynomial Lyapunov function for stabilisation of heterogeneous switched systems. In the study of stabilisation of heterogeneous switched systems, a two-step iterative method including two convex optimisation functions is established by sums of squares to express existing properties condition and solvable properties condition for determining block controller. At last, a practical example and two numerical examples are presented to show the feasibility of the proposed results.

Wave-Particle-Entanglement-Ignorance Complementarity for General Bipartite Systems.

Wave–particle duality as the defining characteristic of quantum objects is a typical example of the principle of complementarity. The wave–particle–entanglement (WPE) complementarity, initially developed for two-qubit systems, is an extended form of complementarity that combines wave–particle duality with a previously missing ingredient, quantum entanglement. For two-qubit systems in mixed states, the WPE complementarity was further completed by adding yet another piece that characterizes ignorance, forming the wave–particle–entanglement–ignorance (WPEI) complementarity. A general formulation of the WPEI complementarity can not only shed new light on fundamental problems in quantum mechanics, but can also have a wide range of experimental and practical applications in quantum-mechanical settings. The purpose of this study is to establish the WPEI complementarity for general multi-dimensional bipartite systems in pure or mixed states, and extend its range of applications to incorporate hierarchical and infinite-dimensional bipartite systems. The general formulation is facilitated by well-motivated generalizations of the relevant quantities. When faced with different directions of extensions to take, our guiding principle is that the formulated complementarity should be as simple and powerful as possible. We find that the generalized form of the WPEI complementarity contains unequal-weight averages reflecting the difference in the subsystem dimensions, and that the tangle, instead of the squared concurrence, serves as a more suitable entanglement measure in the general scenario. Two examples, a finite-dimensional bipartite system in mixed states and an infinite-dimensional bipartite system in pure states, are studied in detail to illustrate the general formalism. We also discuss our results in connection with some previous work. The WPEI complementarity for general finite-dimensional bipartite systems may be tested in multi-beam interference experiments, while the second example we studied may facilitate future experimental investigations on complementarity in infinite-dimensional bipartite systems.

SO(2) gauged Skyrmions in 4+1 dimensions

We study the simplest $SO(2)$ gauged $O(5)$ Skyrme models in $4+1$ (flat) dimensions. In the gauge decoupled limit, the model supports topologically stable solitons (Skyrmions) and after gauging, the static energy of the solutions is bounded from below by a "baryon number". The studied model features both Maxwell and Maxwell--Chern-Simons dynamics. The considered configurations are subject to bi-azimuthal symmetry in the ${\mathbb R}^4$ subspace resulting in a two dimensional subsystem, as well as subject to an enhanced symmetry relating the two planes in the ${\mathbb R}^4$ subspace, which results in a one dimensional subsystem. Numerical solutions are constructed in both cases. In the purely magnetic case, fully bi-azimuthal solutions were given, while electrically charged and spinning solutions were constructed only in the radial (enhanced symmetric) case, both in the presence of a Chern-Simons term, and in its absence. We find that, in contrast with the analogous models in $2+1$ dimensions, the presence of the Chern-Simons term in the model under study here results only in quantitative effects.

Multistep and Runge–Kutta convolution quadrature methods for coupled dynamical systems

We consider the efficient numerical solution of coupled dynamical systems, consisting of a low dimensional nonlinear part and a high dimensional linear time invariant part, e.g., stemming from spatial discretization of an underlying partial differential equation. The linear subsystem can be eliminated in frequency domain and for the numerical solution of the resulting integro-differential algebraic equations, we propose a combination of Runge–Kutta or multistep time stepping methods with appropriate convolution quadrature to handle the integral terms. The resulting methods are shown to be algebraically equivalent to a Runge–Kutta or multistep solution of the coupled system and thus automatically inherit the corresponding stability and accuracy properties. After a computationally expensive pre-processing step, the online simulation can, however, be performed at essentially the same cost as solving only the low dimensional nonlinear subsystem. The proposed method is, therefore, particularly attractive, if repeated simulation of the coupled dynamical system is required.