General Coupling Matrix Research Articles

On the Reconfiguration of Coupling Matrix

In this article, a general coupling matrix reconfiguration approach is proposed considering arbitrary topology, frequency-dependent couplings (FDCs), and nonresonating nodes (NRNs). The principle is developed in two steps: 1) a systematic procedure is introduced to reconfigure an arbitrary coupling matrix into the transversal topology using the similarity transformation and the eigen decomposition of the coupling matrix; an analytical solution with excellent accuracy is achieved in this process and 2) a framework of coupling matrix reconfiguration is constructed as a much simpler inverse problem, which can be optimized with low computational cost. Both local and global optimization approaches are exploited for this problem. The proposed framework is general and applicable to various scenarios. To verify the proposed algorithm, three traditional coupling matrix examples, two FDCs-incorporated coupling matrix examples, an NRNs-incorporated coupling matrix example, and a five-pole waveguide filter implementation are presented, respectively.

Synchronisation of multiple neural networks via event‐triggered time‐varying delay hybrid impulsive control

This article discusses the exponential synchronisation problem for multiple neural networks with time-varying delay and a more general non-Laplacian coupling matrix is considered. To reduce the redundant communication, two event-based time-varying delay hybrid impulsive control schemes are proposed with static event-triggered condition and dynamic event-triggered condition. These novel control schemes neatly combine the event-triggered coupling strategy with the time-varying delay hybrid impulsive control, where the impulsive instant is only determined by the specified event-triggered condition. Moreover, a delay impulsive differential inequality is established to discuss the synchronisation problem for controlled multiple neural networks. By using Stolz's theorem and introducing the average event-triggered delay impulsive gain, some less conservative sufficient conditions are derived to assure the stability of the time-varying delay multiple neural networks. Furthermore, the Zeno behaviour can be eliminated effectively and the consumption of the computing resources can be reduced. Finally, some examples are given to verify the superiority of the results. First, a static event-triggered time-varying delay hybrid impulsive control scheme was proposed to lessen the communication burden. Then, a time-varying delay impulsive differential inequality was established to guarantee the synchronisation of multiple neural networks. Moreover, the authors also discussed the issue that continuously triggering and sampling can be excluded.

A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations

In this paper, we mainly focus on the development and study of a new global GCRO-DR method that allows both the flexible preconditioning and the subspace recycling for sequences of shifted linear systems. The novel method presented here has two main advantages: firstly, it does not require the right-hand sides to be related, and, secondly, it can also be compatible with the general preconditioning. Meanwhile, we apply the new algorithm to solve the general coupled matrix equations. Moreover, by performing an error analysis, we deduce that a much looser tolerance can be applied to save computation by limiting the flexible preconditioned work without sacrificing the closeness of the computed and the true residuals. Finally, numerical experiments demonstrate that the proposed method illustrated can be more competitive than some other global GMRES-type methods.

Synchronous patterns of oscillatory power network with general coupling matrix

The electrical power grid is a fundamental infrastructure in the modern society. Theoretically, the Kuramoto-type model with inertia can be modeled with the generators and consumers working for a power network. The purpose of this work is to investigate the emergence of synchronous patterns of power network with the general coupling strategy, which is the most general setting for an oscillatory network. Here, we analyze the dynamics of the simplest non-trivial network that exhibits synchronous state. Furthermore, we find a counterintuitive range of coupling strength values where the synchronization stability suddenly decreases as the coupling strength increases, based on a number of simple topology structures. Furthermore, it is found that nontrivial behaviors of the coupling scheme in the small-size oscillatory power network potentially vary with the synchronous patterns. Therefore, our simulation results suggest that adjusting coupling scheme is vital to prevent the unexpected catastrophic instability in building blocks of power network.

Modeling the Resonance Shifts Due to Coupling Between HTS Coils in NMR Probes

Nuclear magnetic resonance (NMR) probes using thin-film HTS coils offer high sensitivity and are particularly suitable for small-sample applications. Typically, HTS probes are optimized for the detection of multiple nuclei and require several coils to be located within a small volume near the sample. Coupling between the coils shifts coil resonances and complicates coil trimming when tuning HTS probes. We have modeled the magnetic coupling between the coils of a 1.5-mm all-HTS NMR probe with 13C, 1H, and 2H channels. By measuring the magnetic coupling coefficients between individual coils, we solve the general coupling matrix given by KVL for six coupled resonators. Our results indicate that required trims can be accurately predicted by applying single coil trimming simulations to this magnetic coupling model. Use of the magnetic coupling model significantly improves the efficiency of tuning HTS probes.

Direct Synthesis and Design of Dispersive Waveguide Bandpass Filters

In this article, a direct synthesis and dimensional design method for narrowband waveguide bandpass filters with a general dispersive coupling element is proposed. Comparing with the dispersion-less filter synthesis approaches, the general dispersive coupling matrix (DCM) that incorporates unique dispersive characteristics of a physical realization is introduced to provide an accurate description of the filter to be designed. Moreover, the DCM can describe not only strong dispersive coupling elements for realizing transmission zeros (TZs), but also dispersive resonators. A DCM consists of a frequency-invariant part and a dispersive part. For a given dispersive part, by iteratively remedying the characteristic polynomials, the frequency-invariant part for an equal-ripple response can be directly obtained. Consequently, according to the synthesized frequency-invariant coupling matrix, the filter dimensions can be designed only by electromagnetic (EM) simulation of each individual coupling element at the center frequency. Two design examples are presented, including a four-pole filter with two TZs and an eight-pole filter with four TZs. The examples are validated either by hardware prototyping or by EM simulation, demonstrating the effectiveness, accuracy, and generality of the proposed synthesis and design framework.

A General Coupling Matrix Synthesis Method for All-Resonator Diplexers and Multiplexers

Coupling matrix (CM) synthesis methods for all-resonator diplexers and multiplexers are far from mature. For complex coupling topologies, the existing methods are often not able to find the appropriate CMs that satisfy the S-parameter specifications. To address this challenge, a new synthesis method, which hybridizes analytical and optimization techniques, called general all-resonator diplexer/multiplexer CM synthesis (GACMS) method, is proposed in this article. The two main innovations of GACMS are: 1) an optimization framework incorporating filter design knowledge, which effectively reduces the search space for CM synthesis and 2) a new memetic algorithm-based optimizer, which tackles the challenges from the complex landscape (function characteristics) of CM synthesis problems. GACMS is tested by six complex practical problems and CMs are successfully obtained for all of them. Comparisons with the existing methods demonstrate the advantages of GACMS in terms of solution quality and robustness.

Coupling Matrix Synthesis and Impedance-Matching Optimization Method for Magnetic Resonance Coupling Systems

The general coupling matrix representation of bandpass filter (BPF) circuits is a widely used technique that has simplified the analysis and optimization of complex microwave filters. In this paper, we demonstrate a novel application of the general coupling matrix for modeling wireless power-transfer (WPT) systems based on the BPF model of magnetically coupled resonators. Compared to other methods of WPT analysis, our model simplifies accommodation of complex loads and provides direct expressions for impedance matching (IM) in WPT systems. Using this tool, we achieve optimal IM for two resonator systems with a complex load, thus achieving the greatest possible power-transfer efficiency (PTE). Furthermore, our model reveals additional design constraints for optimizing PTE in coupled resonator systems exhibiting low quality factor and small interresonator coupling. Overall, this paper introduces a new, versatile framework for the analysis and optimization of coupled resonator WPT systems. Experimental results are presented, verifying the optimal IM design process.

Phase models and clustering in networks of oscillators with delayed coupling

We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to determine model independent existence and stability results for symmetric cluster solutions. Our results extend previous work to systems with time delay and a more general coupling matrix. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.

Locking of length scales in two-band superconductors

A model of a clean two-band s-wave superconductor with cylindrical Fermi surfaces, different Fermi velocities v_{1,2}, and a general 2x2 coupling matrix V_{alpha beta} is used to study the order parameter distribution in vortex lattices. The Eilenberger weak coupling formalism is used to calculate numerically the spatial distributions of the pairing amplitudes Delta_1_ and Delta_2_ of the two bands for vortices parallel to the Fermi cylinders. For generic values of the interband coupling V_{12}, it is shown that, independently of the couplings V_{alpha beta}, of the ratio v_1 /v_2, of the temperature, and the applied field, the length scales of spatial variation of Delta_1 and of Delta_2 are the same within the accuracy of our calculations. The only exception from this single length-scale behavior is found for V_{12} --> 0, i.e., for nearly decoupled bands.

Beyond minimal lepton-flavored Dark Matter

We consider a class of flavored dark matter (DM) theories where dark matter interacts with the Standard Model lepton fields at the renormalizable level. We allow for a general coupling matrix between the dark matter and leptons whose structure is beyond the one permitted by the minimal flavor violation (MFV) assumption. It is assumed that this is the only new source of flavor violation in addition to the Standard Model (SM) Yukawa interactions. The setup can be described by augmenting the SM flavor symmetry by an additional $\mathrm{SU}(3)_{\chi}$, under which the dark matter $\chi$ transforms. This framework is especially phenomenologically rich, due to possible novel flavor-changing interactions which are not present within the more restrictive MFV framework. As a representative case study of this setting, which we call "beyond MFV" (BMFV), we consider Dirac fermion dark matter which transforms as a singlet under the SM gauge group and a triplet under $\mathrm{SU}(3)_{\chi}$. The DM fermion couples to the SM lepton sector through a scalar mediator $\phi$. Unlike the case of quark-flavored DM, we show that there is no $\mathbb{Z}_3$ symmetry within either the MFV or BMFV settings which automatically stabilizes the lepton-flavored DM. We discuss constraints on this setup from flavor-changing processes, DM relic abundance as well as direct and indirect detections. We find that relatively large flavor-changing couplings are possible, while the dark matter mass is still within the phenomenologically interesting region below the TeV scale. Collider signatures which can be potentially searched for at the lepton and hadron colliders are discussed. Finally, we discuss the implications for decaying dark matter, which can appear if an additional stabilizing symmetry is not imposed.

LSMR Iterative Method for General Coupled Matrix Equations

By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations∑k=1qAikXkBik=Ci,i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups(X1,X2,…,Xq), such as symmetric, generalized bisymmetric, and(R,S)-symmetric matrix groups. By this iterative method, for any initial matrix group(X1(0),X2(0),…,Xq(0)), a solution group(X1*,X2*,…,Xq*)can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group(X¯1,X¯2,…,X¯q)in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method.

Efficient Iterative Solutions to General Coupled Matrix Equations

Linear matrix equations are encountered in many systems and control applications. In this paper, we consider the general coupled matrix equations (including the generalized coupled Sylvester matrix equations as a special case) #### over the generalized reflexive matrix group (Y1, Y2, ?, Yi). We derive an efficient gradient-iterative (GI) algorithm for finding the generalized reflexive solution group of the general coupled matrix equations. Convergence analysis indicates that the algorithm always converges to the generalized reflexive solution group for any initial generalized reflexive matrix group (Y1(1), Y2(1), ?, Yl(1)). Finally, numerical results are presented to test and illustrate the performance of the algorithm in terms of convergence, accuracy as well as the efficiency.

An Iterative Algorithm for the Reflexive Solution of the General Coupled Matrix Equations

The general coupled matrix equations (including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations over reflexive matrix solution. When the general coupled matrix equations are consistent over reflexive matrices, the reflexive solution can be determined automatically by the iterative algorithm within finite iterative steps in the absence of round-off errors. The least Frobenius norm reflexive solution of the general coupled matrix equations can be derived when an appropriate initial matrix is chosen. Furthermore, the unique optimal approximation reflexive solution to a given matrix group in Frobenius norm can be derived by finding the least-norm reflexive solution of the corresponding general coupled matrix equations. A numerical example is given to illustrate the effectiveness of the proposed iterative algorithm.

Fermionic Chern-Simons theory of SU(4) fractional quantum Hall effect

We develop a Fermionic Chern-Simons (CS) theory for the fractional quantum Hall effect in monolayer graphene with SU(4) symmetry. We construct a general CS coupling matrix such that an even number of spin- and valley-dependent flux quanta is attached to all electrons and that any electron sees an integer number of flux attached to other electrons with different spin and valley quantum numbers. Using this matrix, we obtain a list of possible fractional quantum Hall states (FQHS) in graphene and propose wave functions for them. Our analysis unifies previously studied FQHS with different symmetries, predicts several states whose presence may be tested experimentally, and also applies to FQHS of bilayer spin polarized graphene and conventional bilayer quantum Hall systems. We thus provide a systematic way of charting FQHS in these systems and also reproduce earlier results as special cases.

Bandpass–Bandstop Filter Cascade Performance Over Wide Frequency Tuning Ranges

A tunable, substrate integrated, high Q bandpass-bandstop filter cascade is demonstrated that is capable of providing up to 100 dB of isolation between two dynamically selectable frequencies of interest. Evanescent-mode cavity filters are used in the cascade to allow high quality factors and wide tuning ranges. It is shown that it is theoretically possible to tune the cascade circuit's passband and transmission nulls independently over more than an octave in frequency while displaying good performance. General coupling matrix theory, ABCD matrix theory, and measurements are shown that describe the behavior of the filter cascade over the entire frequency tuning range. The high, dynamic isolation provided by cascade circuits has potential to be useful in concurrent transmit-receive systems, shared aperture systems, and spectral environments with strong co-site interference.

Synchronization and Bifurcation of General ComplexDynamical Networks

In the present paper, synchronization and bifurcationof general complex dynamical networks are investigated. We mainly focuson networks with a somewhat general coupling matrix, i.e., the sum ofeach row equals a nonzero constant u. We derive a result that thenetworks can reach a new synchronous state, which is not the asymptoticlimit set determined by the node equation. At the synchronous state, thenetworks appear bifurcation if we regard the constant u as abifurcation parameter. Numerical examples are given to illustrateour derived conclusions.

Synthesis of canonical topology microwave filters using Householder's transformations

The general even-mode coupling matrix, which contains all possible couplings of a microwave filter can be synthesised with well established filter synthesis technique. Presented is a simple but efficient method to annihilate unwanted couplings to realise canonical topology microwave filters using Householder's transformations. Furthermore, this method can be easily adopted into filter design software to synthesise canonical topology microwave filters.

General Coupling Matrix Synthesis Method for Microwave Resonator Filters with Arbitrary Topology

This letter presents a new approach to synthesize the resonator filters of an arbitrary topology. This method employs an optimization method based on the relation between the polynomial coefficients of the transfer function and those of the S 21 from the coupling matrix. Therefore, this new method can also be applied to self-equalized filters that were not considered in the conventional optimization methods. Two microwave filters, a symmetric 4-pole filter with four transmission zeros (TZs) and an asymmetric 8-pole filter with seven TZs, are synthesized using the present method for validation. Excellent agreement between the response of the transfer junction and that of the synthesized S 21 from the coupling matrix is shown.

Master–slave chaos synchronization criteria for the horizontal platform systems via linear state error feedback control

Global chaos synchronization of two identical non-autonomous horizontal platform systems coupled by linear state error feedback controller is investigated. The sufficient criteria for global chaos synchronization are deduced based on the stability theory of linear time-varied systems and Lyapunov's direct method, of which, the criteria related to general coupling matrix are first proved and applied to derive the ones related to some special coupling matrices. In the examples, the coupling strengths are designed by the obtained criteria and the appearances of chaos synchronization are verified. It is analytically and numerically examined that the synchronization criteria based on Lyapunov's direct method are sharper than the criteria based on the stability theory of linear time-varied systems.