Uncoupled System Research Articles

Relation between initial conditions and entanglement sudden death for two-qubit extended Werner-like states

In this paper, the dynamical behavior of entanglement of an uncoupled two-qubit system, which interacts with independent identical amplitude damping environments and is initially prepared in the extended Werner-like (EWL) states, is investigated. The results show that whether entanglement sudden death (ESD) of an EWL state will occur or not depends on initial purity and concurrence. The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different. Furthermore, some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.

Evaluation of lateral‐torsional coupling in earthquake response of asymmetric multistory buildings

SUMMARYThis paper presents a practical method for evaluating lateral‐torsional coupling in the elastic earthquake response of asymmetric multistory buildings. A transformation technique is first developed to shift the floor centers of mass of an asymmetric building to new reference positions where the sum of the squares of all floor rotations of the building due to lateral inertia loads is a minimum. By setting the locus of the floor centers of mass of the building at the new reference positions, a representative eccentricity and an effectively uncoupled system for the building can be established on the basis which an equivalent eccentric single mass system can be developed. The additional lateral translations caused by seismic torsional effects in the building can be analytically determined and expressed in terms of the representative building eccentricity and the uncoupled periods evaluated using the effectively uncoupled system. The effectiveness and practicality of the proposed method are illustrated with two 30‐story practical buildings. Copyright © 2013 John Wiley & Sons, Ltd.

Spherical functions associated with the three-dimensional sphere

In this paper, we determine all irreducible spherical functions \Phi of any K -type associated to the pair (G,K)=(\SO(4),\SO(3)). This is accomplished by associating to \Phi a vector valued function H=H(u) of a real variable u, which is analytic at u=0 and whose components are solutions of two coupled systems of ordinary differential equations. By an appropriate conjugation involving Hahn polynomials we uncouple one of the systems. Then this is taken to an uncoupled system of hypergeometric equations, leading to a vector valued solution P=P(u) whose entries are Gegenbauer's polynomials. Afterward, we identify those simultaneous solutions and use the representation theory of \SO(4) to characterize all irreducible spherical functions. The functions P=P(u) corresponding to the irreducible spherical functions of a fixed K-type \pi_\ell are appropriately packaged into a sequence of matrix valued polynomials (P_w)_{w\ge0} of size (\ell+1)\times(\ell+1). Finally we proved that \widetilde P_w={P_0}^{-1}P_w is a sequence of matrix orthogonal polynomials with respect to a weight matrix W. Moreover we showed that W admits a second order symmetric hypergeometric operator \widetilde D and a first order symmetric differential operator \widetilde E.

Amplitude death phenomena in delay-coupled Hamiltonian systems

Hamiltonian systems, when coupled via time-delayed interactions, do not remain conservative. In the uncoupled system, the motion can typically be periodic, quasiperiodic, or chaotic. This changes drastically when delay coupling is introduced since now attractors can be created in the phase space. In particular, for sufficiently strong coupling there can be amplitude death (AD), namely, the stabilization of point attractors and the cessation of oscillatory motion. The approach to the state of AD or oscillation death is also accompanied by a phase flip in the transient dynamics. A discussion and analysis of the phenomenology is made through an application to the specific cases of harmonic as well as anharmonic coupled oscillators, in particular the Hénon-Heiles system.

PT-symmetric lattices with a local degree of freedom

Recently, open systems with balanced, spatially separated loss and gain have been realized and studied using non-Hermitian Hamiltonians that are invariant under the combined parity and time-reversal ($\mathcal{PT}$) operations. Here, we model and investigate the effects of a local, two-state, quantum degree of freedom, called a pseudospin, on a one-dimensional tight-binding lattice with position-dependent tunneling amplitudes and a single pair of non-Hermitian, $\mathcal{PT}$-symmetric impurities. We show that if the resulting Hamiltonian is invariant under exchange of two pseudospin labels, the system can be decomposed into two uncoupled systems with tunable threshold for $\mathcal{PT}$ symmetry breaking. We discuss implications of our results to systems with specific tunneling profiles, and open or periodic boundary conditions.

The complete synchronization of Morris–Lecar neurons influenced by noise

The influence of noise on the complete synchronization in a Morris–Lecar (ML) model neuronal system is studied in this work. Two individual ML neurons with different initial conditions can discharge completely synchronously when the noise intensity is large enough, and for a smaller reversal potential (VCa), the uncoupled neuronal system could be induced to a complete synchronization state under smaller noise intensity. Two coupled ML neurons could be synchronized under very small noise intensity even in the case of weak coupling, the synchronization characteristics of the two coupled neurons are discussed by analyzing the Similarity Function (S(0)) of their membrane potentials, which proves that noise can promote the complete synchronization. The critical noise intensity (Dj) to induce complete synchronization in coupled ML neurons will decrease with the increase of VCa. This result is helpful to study the synchronization and the code of a neural system.

Optimal value functions for weakly coupled systems: a posteriori estimates

AbstractWe consider weakly coupled LQ optimal control problems and derive estimates on the sensitivity of the optimal value function in dependence of the coupling strength. In order to improve these sensitivity estimates a “coupling adapted” norm is proposed. Our main result is that if a weak coupling suffices to destabilize the closed loop system with the optimal feedback of the uncoupled system then the value function might change drastically with the coupling. As a consequence, it is not reasonable to expect that a weakly coupled system possesses a weakly coupled optimal value function. Also, for a known result on the connection of the separation operator and the stability radius a new and simpler proof is given.

Common noise induced synchronous circadian oscillations in uncoupled non-identical systems

The effect of common noise on the collective behavior of circadian oscillation systems was studied in an elementary circadian clock model. It is shown that common noise could induce synchronous oscillations in two uncoupled non-identical systems in the deterministic stable steady state region. The synchronicity of common noise induced oscillations is suppressed by the internal noise, but is not remarkably decreased within a wide range of internal noise intensity. This demonstrates that the common noise induced synchronous oscillations are rather robust to internal fluctuations.

Practical and Robust Synchronization of Systems with Additive Linear Uncertainties

Abstract We investigate the synchronization of systems with additive uncertainties. In doing so, we establish a setup of diffusively coupled nonlinear systems that are perturbed by unknown linear functions, each. By assuming bounded solutions of the nominal uncoupled systems, we derive sufficient conditions for boundedness of the solutions of the coupled systems with uncertainties. Next, using the QUAD condition, we derive conditions for the synchronization error to remain bounded. Subsequently, we investigate the impact of the coupling strength on this bound and find that the bound can be made arbitrarily small for sufficiently large gains, thus establishing criteria for practical synchronization. Finally, we consider classes of uncertainties which consist of matrices whose maximal singular value is smaller than a specific value and show practical synchronization for all uncertainties belonging to that class. Therefore, we establish conditions for robust synchronization with respect to such a class. Our theoretical results are validated with a numerical example composed of perturbed Van der Pol oscillators.

Accurate quantum dynamics calculations using symmetrized Gaussians on a doubly dense Von Neumann lattice

In a series of earlier articles [B. Poirier, J. Theor. Comput. Chem. 2, 65 (2003); B. Poirier and A. Salam, J. Chem. Phys. 121, 1690 (2004); and ibid. 121, 1704 (2004)], a new method was introduced for performing exact quantum dynamics calculations. The method uses a "weylet" basis set (orthogonalized Weyl-Heisenberg wavelets) combined with phase space truncation, to defeat the exponential scaling of CPU effort with system dimensionality--the first method ever able to achieve this long-standing goal. Here, we develop another such method, which uses a much more convenient basis of momentum-symmetrized Gaussians. Despite being non-orthogonal, symmetrized Gaussians are collectively local, allowing for effective phase space truncation. A dimension-independent code for computing energy eigenstates of both coupled and uncoupled systems has been created, exploiting massively parallel algorithms. Results are presented for model isotropic uncoupled harmonic oscillators and coupled anharmonic oscillators up to 27 dimensions. These are compared with the previous weylet calculations (uncoupled harmonic oscillators up to 15 dimensions), and found to be essentially just as efficient. Coupled system results are also compared to corresponding exact results obtained using a harmonic oscillator basis, and also to approximate results obtained using first-order perturbation theory up to the maximum dimensionality for which the latter may be feasibly obtained (four dimensions).

Transport characteristics of a Glaser magnet for an axisymmetric and non-axisymmetric space charge dominated beam

This paper describes the dynamics of space charge dominated beam through a Glaser magnet which is often used to focus charged particle beams in the low energy section of accelerators and in many other devices. Various beam optical properties of the magnet and emittance evolution that results from the coupling between the two transverse planes are studied. We have derived ten independent first order differential equations for the beam sigma matrix elements assuming the linear space-charge force consistent with the assumption of the canonically transformed KV like distribution. In addition, the feasibility of using a Glaser magnet doublet in a low energy beam injection line to match an initial non-axisymmetric high intensity beam with net angular momentum to an axisymmetric system to suppress effective emittance growth after transition back to an uncoupled system, has also been studied.

Adaptable dual control systems. a comparative parametric analysis

Structural control through energy dissipation systems has been increasingly implemented internationally in the last years and has proven to be a most promising strategy for earthquake safety of the structures. The control concept is based on the integration of passive damping devices within the structure for the necessary energy dissipation and the elastic response of the primary system. Adaptable dual control systems (ADCS) presented in this paper, consist of tension-only bracing members with closed circuit and a hysteretic damper of steel plates. The implementation of ADCS in frame structures enables a dual function of the component members, leading to two practically uncoupled systems, i.e. the primary frame, responsible for the static vertical and horizontal forces and the bracing-damper mechanism, for the earthquake forces and the necessary energy dissipation. ADCS are investigated and compared in their energy dissipation behavior for three differing configurations of the bracing-damper mechanism. In all cases the hysteretic damper utilizes effectively the relative displacements between its connection joints, i.e. a bracing and a primary frame's member, through its own yielding deformations for the necessary energy dissipation. In the present paper parametric dynamic analyses of the SDOF system's responses have been performed, based on three representative international earthquake motions of differing frequency contents. A nonlinear link parameter, defined as the ratio of the stiffness to the yield force of the hysteretic damper, DR, characterizes the behavior of the controlled systems in each configuration. Optimum DR values are proposed for each system configuration in achieving high energy dissipation capacity, while preventing possible increase of the maximum base shear and relative displacements. Keywords Adaptable Systems, Earthquake Resistance, Frame Structures, Passive Control. Language: en

Uncoupled multi-core fiber enhancing signal-to-noise ratio

We designed and fabricated a low-crosstalk seven-core fiber with transmission losses of 0.17 dB/km or lower, effective areas larger than 120 μm(2), and a total mean crosstalk to the center core of -53 dB after 6.99-km propagation (equivalent to -42.5 dB after 80 km), at 1550 nm. We also investigated the signal-to-noise ratio (SNR) achievable in uncoupled multi-core transmission systems by regarding the crosstalk as a virtual additive white Gaussian noise. The SNR under existence of crosstalk in the fabricated multi-core fiber (MCF) was estimated to be 2.4 dB higher than that in a standard single-mode fiber (SSMF) in the case of 80-km span, and 2.9 dB higher in the case of 100-km span; which are the best values among MCFs ever reported, to the best of our knowledge. The SNR penalties from crosstalk in this MCF were calculated to be 0.4 dB for 80-km span and 0.2 dB for 100-km span. We also investigated SNR penalty from crosstalk in the more ordinary case of an MCF with SSMF cores, and found that the total mean crosstalk to the worst core after one 80-km span should be less than about -47 dB for 0.1-dB penalty, about -40 dB for 0.5-dB penalty, and about -36 dB for 1-dB penalty.

Structural-Acoustic Vibration Problems in the Presence of Strong Coupling

Free vibrations of fluid–solid structures are governed by unsymmetric eigenvalue problems. A common approach which works fine for weakly coupled systems is to project the problem to a space spanned by modes of the uncoupled system. For strongly coupled systems, however, the approximation properties are not satisfactory. This paper reports on a framework for taking advantage of the structure of the unsymmetric eigenvalue problem allowing for a variational characterization of its eigenvalues and structure preserving iterative projection methods. We further cover an adjusted automated multilevel substructuring (AMLS) method for huge fluid–solid structures. The reliability and efficiency of the method are demonstrated by the free vibrations of a structure completely filled with water.

Effect of a particular coupling on the dynamic behavior of nonlinear systems

SUMMARY In this paper, the dynamics of particular nonlinear dynamic systems of order six, characterized by two positive Lyapunov exponents, is analyzed. Transformation techniques are applied to the study of these systems; in particular, the analysis of the transverse and tangent systems showed that they are equivalent to two uncoupled identical chaotic systems of order three. Examples of polynomial and piecewise linear systems are proposed. Both numerical simulation and circuit implementation have been performed. Moreover, a systematic method to project these systems is presented. Copyright © 2012 John Wiley & Sons, Ltd.

Numerical verification of a dual system's seismic response

Structural control through integration of passive damping devices within the building structure has been increasingly implemented internationally in the last years and has proven to be a most promising strategy for earthquake safety. In the present paper an alternative configuration of an innovative energy dissipation mechanism that consists of slender tension only bracing members with closed loop and a hysteretic damper is investigated in its dynamic behavior. The implementation of the adaptable dual control system, ADCS, in frame structures enables a dual function of the component members, leading to two practically uncoupled systems, i.e., the primary frame, responsible for the normal vertical and horizontal forces and the closed bracing-damper mechanism, for the earthquake forces and the necessary energy dissipation. Three representative international earthquake motions of differing frequency contents, duration and peak ground acceleration have been considered for the numerical verification of the effectiveness and properties of the SDOF systems with the proposed ADCS-configuration. The control mechanism may result in significant energy dissipation, when the geometrical and mechanical properties, i.e., stiffness and yield force of the integrated damper, are predefined. An optimum damper ratio, DR, defined as the ratio of the stiffness to the yield force of the hysteretic damper, is proposed to be used along with the stiffness factor of the damper's- to the primary frame's stiffness, in order for the control mechanism to achieve high energy dissipation and at the same time to prevent any increase of the system's maximum base shear and relative displacements. The results are summarized in a preliminary design methodology for ADCS.

Dynamics and synchronization analysis of coupled fractional-order nonlinear electromechanical systems

A fractional-order (FO) nonlinear model is used to describe an electromechanical system. We make capital out of the fact that for realistic modeling, the electric characteristics of a capacitor include a fractional-order time derivative. The dynamics and synchronization of coupled fractional-order nonlinear electromechanical systems are analyzed. Detailed attention is granted to the bifurcations that can occur in the dynamics of a single uncoupled electromechanical system as the fractional-order varies. For example, the fractional-order counterparts of the chaotic 4-order system are periodic at orders less than 3.985. The effect of the fractional-order on the condition of occurrence of synchronization phenomena in the network of many mutually coupled fractional-order nonlinear electromechanical systems is analyzed, especially when they are chaotic. An insight on the overall dynamics of the network is provided. It is shown that the dynamics of both the uncoupled system and the network are very sensitive to changes in the order of the fractional derivative.

An equilibrated method of fundamental solutions to choose the best source points for the Laplace equation

For the method of fundamental solutions (MFS), a trial solution is expressed as a linear combination of fundamental solutions. However, the accuracy of MFS is heavily dependent on the distribution of source points. Two distributions of source points are frequently adopted: one on a circle with a radius R, and another along an offset D to the boundary, where R and D are problem dependent constants. In the present paper, we propose a new method to choose the best source points, by using the MFS with multiple lengths Rk for the distribution of source points, which are solved from an uncoupled system of nonlinear algebraic equations. Based on the concept of equilibrated matrix, the multiple-length Rk is fully determined by the collocated points and a parameter R or D, such that the condition number of the multiple-length MFS (MLMFS) can be reduced smaller than that of the original MFS. This new technique significantly improves the accuracy of the numerical solution in several orders than the MFS with the distribution of source points using R or D. Some numerical tests for the Laplace equation confirm that the MLMFS has a good efficiency and accuracy, and the computational cost is rather cheap.

WRF-CMAQ two-way coupled system with aerosol feedback: software development and preliminary results

Abstract. Air quality models such as the EPA Community Multiscale Air Quality (CMAQ) require meteorological data as part of the input to drive the chemistry and transport simulation. The Meteorology-Chemistry Interface Processor (MCIP) is used to convert meteorological data into CMAQ-ready input. Key shortcoming of such one-way coupling include: excessive temporal interpolation of coarsely saved meteorological input and lack of feedback of atmospheric pollutant loading on simulated dynamics. We have developed a two-way coupled system to address these issues. A single source code principle was used to construct this two-way coupling system so that CMAQ can be consistently executed as a stand-alone model or part of the coupled system without any code changes; this approach eliminates maintenance of separate code versions for the coupled and uncoupled systems. The design also provides the flexibility to permit users: (1) to adjust the call frequency of WRF and CMAQ to balance the accuracy of the simulation versus computational intensity of the system, and (2) to execute the two-way coupling system with feedbacks to study the effect of gases and aerosols on short wave radiation and subsequent simulated dynamics. Details on the development and implementation of this two-way coupled system are provided. When the coupled system is executed without radiative feedback, computational time is virtually identical when using the Community Atmospheric Model (CAM) radiation option and a slightly increased (~8.5%) when using the Rapid Radiative Transfer Model for GCMs (RRTMG) radiation option in the coupled system compared to the offline WRF-CMAQ system. Once the feedback mechanism is turned on, the execution time increases only slightly with CAM but increases about 60% with RRTMG due to the use of a more detailed Mie calculation in this implementation of feedback mechanism. This two-way model with radiative feedback shows noticeably reduced bias in simulated surface shortwave radiation and 2-m temperatures as well improved correlation of simulated ambient ozone and PM2.5 relative to observed values for a test case with significant tropospheric aerosol loading from California wildfires.

Stationary states of weakly coupled lattice dynamical systems arising in strong competition models

In this work, we consider a weakly coupled lattice dynamical system arising in a strong competition system with bistable nonlinearity. By employing the continuation method developed by MacKay and Sepulchre (1995) [13] , we derive estimations of the bounds of the diffusive values d 1 and d 2 below which the existence of infinite stationary states is proved. These stationary states are continuations from the uncoupled lattice dynamical system.