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Circuits with diverse electrical behavior are often placed in close physical proximity in order to achieve high-levels of on-chip integration. The activity of certain types of circuits can generate harmful interference, and degrade the performance of the system through electromagnetic coupling. Considerable effort in system-on-a-chip implementations is in fact related to technology and architectural considerations for minimizing this interference. This is especially the case in systems that have exacting requirements on the dynamic range such as those for wireless applications.

In this paper, we will discuss the evolution of techniques for modeling and analyzing these sources of noise generation and interference. We will provide a physical description of the problem. Techniques for extraction of electrical models to represent the media that support these noise sources will be covered. Macromodeling techniques will be discussed. Finally we will introduce the concept of functional modeling of circuit functions and present such a model for an integrated flash analog-to-digital converter.

Graphics processing unit (GPU) is becoming a powerful computational tool in scientific and engineering fields. In this paper, for the purpose of the full employment of computing capability, a novel mode for parallel molecular dynamics (MD) simulation is presented and implemented on basis of multiple GPUs and hybrids with central processing units (CPUs). Taking into account the interactions between CPUs, GPUs, and the threads on GPU in a multi-scale and multilevel computational architecture, several cases, such as polycrystalline silicon and heat transfer on the surface of silicon crystals, are provided and taken as model systems to verify the feasibility and validity of the mode. Furthermore, the mode can be extended to MD simulation of other areas such as biology, chemistry and so forth.

This paper describes three models arising from the theory of excitable media, whose primary visual feature are expanding rings of excitation. Rigorous mathematical results and experimental/computational issues are both addressed. We start with the much-studied Greenberg–Hastings model (GHM) in which the rings are very short-lived, but they do have a transient percolation property. By contrast, in the model we call annihilating nested rings (ANR), excitation centers only gradually lose strength, i.e., each time they become inactive (and then stay so forever) with a fixed probability; we show how the long-term global connectivity properties of the set of excited sites undergo a phase transition. Second part of the paper is devoted to digital boiling (DB) in which new rings spontaneously appear at rested sites with a positive probability. We focus on such (related) issues as convergence to equilibrium, equilibrium excitation level and success of the basic coupling.

The frozen QCD coupling is a parameter often used as an effective fixed coupling. It is supposed to mimic both the running coupling effects and the lack of knowledge of α_s in the infrared region. Usually the value of the frozen coupling is fixed from the analysis of the experimental data. A novel way to define such coupling(s) independently of the experiments is presented. We argue that there are different frozen couplings which are used in the double-logarithmic (DL) and single-logarithmic (SL) approximations. They also differ for space- and time-like arguments. Our estimates are in a good agreement with the results available in the literature.

Unification ideas motivate the formulation of field equations on an extended matrix-spin space. Demanding that the Poincaré symmetry be maintained, one derives scalar symmetries that are associated with flavor and gauge groups. Boson and fermion solutions are obtained with a fixed representation. A field theory can be equivalently written and interpreted in terms of elements of such a space and is similarly constrained. At 5+1 dimensions, one obtains isospin and hypercharge SU(2)_L×U(1) symmetries, their vector carriers, two-flavor charged and chargeless leptons, and scalar particles. Mass terms produce breaking of the symmetry to an electromagnetic U(1), a Weinberg's angle with sin²(θ_W)=0.25, and additional information on the respective coupling constants. The particles' underlying spin symmetry gives information on their masses; one reproduces the Standard Model ratio M_Z/M_W, and predicts possible Higgs masses of M_H≈114 and M_H≈161 GeV, at tree level.

A prototype of a cylindrical ERF coupling was fabricated, and its transmission capability in steady and unsteady running conditions was investigated. The torque transmitted by the coupling with viscous force in wide ranges of driving speed and field strength was measured. The relationship between the transmission torque, the zero field viscosity of ERF and the shear yield stress of ERF under field was obtained, and was compared with theoretical prediction. Moreover, by modulating the strength of the applied DC field, under a fixed load and input speed, the output speed of the coupling was controlled in the range of transmission ratio from 0 to 1. This provides a means to construct transmission systems in which the output speed can be conveniently adjusted and controlled. Further, square wave electric pulses were applied on the ERF coupling, with a fixed external load added on the output shaft, a uniform stepping rotation of the output shaft has been realized. Experiments showed that under certain conditions the rotation angle of the output axle can be precisely controlled.

Occurring in many natural and engineered systems, the collective synchronization of oscillators has attracted much research attention to understand its behavior. Following the well-known similarity of the synchronization to a condensation phase transition, we present a new approach on how a distribution kinetics model for cluster growth can be adapted to describe synchronization dynamics. We find that oscillators which synchronize, or cluster, according to a reversible association-dissociation mechanism demonstrate behavior like the conventional stability analysis. Oscillators proceed through exponential time dependence before taking on the power law behavior at intermediate times, as reported for model computations. The power varies for synchronization and depends on the rate coefficient, but is constant for desynchronization. In this analysis, the rate coefficient for cluster growth replaces the coupling constant in the conventional linear analysis. In terms of the coupling constant K and its critical value K_c, the coherence increases as (1-K_c/K), the expression that has been found to hold in the absence of noise.

Weighted and unweighted networks composed of coupled bistable oscillators with small-world topology are investigated under the co-presence of a weak signal and multiplicative Gaussian white noise. As the noise intensity is adjusted to one or two optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of stochastic resonance (SR) or stochastic bi-resonance (SBR). The resonance behavior is strongly-dependent on the coupling strength in both networks. At a weak coupling, SR more likely takes place; whereas at a strong coupling, SBR is prone to occur. Compared with unweighted networks, the span of coupling strength for SBR is narrower in weighted networks. In addition, the weak signal cannot be amplified so effectively in the weighted networks as in the unweighted networks, attributing to the weakening effect of the link weight on the coupling between oscillators and the heterogeneity of the whole network connectivity caused by the weight distribution.

We present the study on the interlayer and intergranular exchange and dipolar coupling in [Fe₉₇Si₃/SiO₂]₅ discontinuous multilayers by means of ferromagnetic resonance. Due to strong ferromagnetic exchange coupling (J~-3 erg/cm²) the precessional motions of magnetic moments of granules are coupled and results in an acoustic and optical mode. Moreover there is notable line splitting in optical mode under external field normal to the layer, which is explained by an interlayer dipolar coupling, only possible for discontinuous layer. Some aspects of the damping processes in discontinuous multilayers are discussed as well.

In this paper, the n-th root of a matrix is defined, and the explicit form of n-th root of an Hermitian matrix is given. A new method for diagonalizing quadratic Hamiltonians is proposed. Also, a class of quantum operators is induced by the linear transformation in configuration space, and its unitary properties and transformation behavior are studied. Our new method based on n-th root of matrices can develop the mathematical methods of quantum mechanics and quantum optics, and can also be applied to engineering, quantum optics and quantum fields states with squeezing properties, as well as the binomial field states.

Highly efficient coupling outer electromagnetic (EM) waves into photonic crystal (PhC) waveguides (PhCWs) is critical to the applications of PhCs in photonic integrated circuits. We investigate and simulate an efficient way of coupling EM waves into PhCWs of air holes array by using surface dielectric margin based on all-PhCs structure. Good matching of modal field profiles on both sides of the interface is obtained by adjusting the surface dielectric margin along the propagation direction. The coupling efficiency can be highly enhanced by suppressing the surface field propagating along the transverse margin at the interface. The numerical results using finite-difference time-domain simulations show that the bandwidth for coupling efficiency larger than 90% can be as broad as about 100nm.

The mechanism of formation and transformation of white-eye square patterns in dielectric barrier discharge system is investigated numerically, using the two-layer Lengyel–Epstein model with asymmetric and symmetric coupling. When the scale of the simulation system $N$ is two to three times of pattern wavelength $\lambda$, it is found that an obvious intermediate state with square distribution appears by adjusting the ratio of diffusion coefficients $D_v$/$D_u$. When it is coupled with a suitable short-wavelength Turing mode in the range of $\lambda /6$ to $\lambda /5$, a new spatial resonance structure can be formed in the short-wavelength mode subsystem, and the pattern evolves from a simple square pattern to a white-eye square pattern. Although the two coupling methods achieve the same results, the duration time of the white-eye square pattern in the symmetric coupling method is significantly longer than that in the asymmetric coupling method. Because the quadratic coefficient of the amplitude equation in the reaction–diffusion system is not zero, the simple square pattern of the long wavelength mode subsystem gradually transits into a stable hexagon pattern gradually. As a result, the white-eye pattern transits from a square to a hexagon.

In power line communication (PLC), coupling transformers are usually required for coupling, band-pass filtering and impedance matching. However, coupling transformer design involves so many parameters that it is typically an imprecise and experimental procedure. In addition, the cost and size of transformers prevent them from being an economic and compact solution for PLC couplers. This paper first analyzes a simplified, distributed parameter model of the power line, which can be used to calculate power line impedance easily and accurately. Next, a low-cost, band-pass matching coupler with compact architecture is designed to replace the coupling transformer for direct current PLC (DC-PLC), which ensures impedance matching on the basis of an accurate power line impedance instead of using an average value. Finally, simulations as well as laboratory tests are conducted under 95–125kHz (CENELEC B-band), which confirm the new coupler’s excellent band-pass filtering and impedance matching performance.

In many signal processing applications, especially in the analysis of complex physiological systems, an important problem is to detect and quantify the interdependencies between signals (or time series). In this paper, we focus on asymmetrical relations between two time series with the aim of quantification of the directional influences between them in the sense of "who drives whom and how strongly". To meet this aim, we modify the mixed state analysis, which was proposed by Wiesenfeldt et al. [2001] to detect primarily the nature of the coupling (unidirectional or bidirectional), for the quantification of the strength of coupling in each direction. We introduce the predictability improvement of one time series by additional consideration of another time series. The newly developed measure is an analogue of the information theoretic concept of transfer entropy and is applicable to short time series. We demonstrate the application of this approach to coupled deterministic systems and to EEG data.

Bonhöffer–van der Pol(BVP) oscillator is a classic model exhibiting typical nonlinear phenomena in the planar autonomous system. This paper gives an analysis of equilibria, periodic solutions, strange attractors of two BVP oscillators coupled by a resister. When an oscillator is fixed its parameter values in nonoscillatory region and the others in oscillatory region, create the double scroll attractor due to the coupling. Bifurcation diagrams are obtained numerically from the mathematical model and chaotic parameter regions are clarified. We also confirm the existence of period-doubling cascades and chaotic attractors in the experimental laboratory.

In this paper we study the relationships between local and global properties in networks of dynamical systems by focusing on two global properties, synchronization and peak-to-peak dynamics, and on two local properties, coherence of the components of the network and coupling strength. The analysis is restricted to networks of low-dimensional chaotic oscillators, i.e. oscillators which have peak-to-peak dynamics when they work in isolation. The results are obtained through simulation, first by considering pairs of coupled Lorenz, Rössler and Chua systems, and then by studying the behavior of spatially extended tritrophic food chains described by the Rosenzweig–MacArthur model. The conclusion is that synchronization and peak-to-peak dynamics are different aspects of the same collective behavior, which is easily obtained by enhancing local coupling and coherence. The importance of these findings is briefly discussed within the context of ecological modeling.

Traditional Boolean networks consist of nodes within a single network, each updating synchronously, although asynchronous versions have also been presented. In this paper the dynamics of two, mutually coupled traditional networks are investigated. In particular, the effects of varying the degree and type of intra-network connectivity are explored. The effects from different inter-network evolution rates are then considered, i.e. asynchronousity at the network level is examined. Finally, state memory is included within the nodes of coupled networks and shown to alter the dynamics of the networks under certain circumstances.

We discuss the synchronization of coupled neurons which are modeled as FitzHugh–Nagumo systems. As smallest entity in a larger network, we focus on two diffusively coupled subsystems, which can be interpreted as two mutually interacting neural populations. Each system is prepared in the excitable regime and subject to independent random fluctuations. In order to modify their cooperative dynamics, we apply a local external stimulus in the form of an extended time-delayed feedback loop that involves multiple delays weighted by a memory parameter and investigate if the local control applied to a subsystem can allow one to steer the global cooperative dynamics. Depending on the choice of this new control parameter, we investigate different measures to quantify the influence on synchronization: ratio of interspike intervals, power spectrum, interspike interval distribution and phase synchronization intervals. We show that the control method is more robust for increasing memory parameter.

We briefly present lag sequential analysis for behavioral streams, a commonly used method in psychology for quantifying the relationships between two nominal time series. Cross recurrence quantification analysis (CRQA) is shown as an extension of this technique, and we exemplify this nominal application of CRQA to eye-movement data in human interaction. In addition, we demonstrate nominal CRQA in a simple coupled logistic map simulation used in previous communication research, permitting the investigation of properties of nonlinear systems such as bifurcation and onset to chaos, even in the streams obtained by coarse-graining a coupled nonlinear model. We end with a summary of the importance of CRQA for exploring the relationship between two behavioral streams, and review a recent theoretical trend in the cognitive sciences that would be usefully informed by this and similar nonlinear methods. We hope this work will encourage scientists interested in general properties of complex, nonlinear dynamical systems to apply emerging methods to coarse-grained, nominal units of measure, as there is an immediate need for their application in the psychological domain.

A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.