Computational method for radar absorbing composite lattice grids

Composite lattice grids reinforced by glass fibers (GFRC) and carbon fibers (CFRC) filled with spongy materials can be designed as lightweight radar absorbing structures (RAS). In the present paper, a computational approach based on periodic moment method (PMM) has been developed to calculate reflection coefficients of radar absorbing composite lattice grids. Total reflection backing (TRB) is considered directly in our PMM program by treating it as a dielectric material with large imaginary part of permittivity. Two different mechanisms of reflection reduction for radar absorbing lattice grids are revealed. At low frequency, reflection coefficients increase with the volume fraction of the grid cell wall. At high frequency, several grating lobes propagate away from the doubly periodic plane, and reflection coefficients depend on both the cell wall volume fraction and interelement distance.     

Two-dimensional scattering from a multilayered periodic structure of arbitrary shapes

A numerical approach is presented to analyze the two-dimensional scattering properties from a multilayered periodic dielectric structure of an arbitrary number of arbitrarily shaped unit cells. The approach is enhanced by the periodic moment method, the lattice sums technique, and the Poisson summation formula. The matrix element's evaluation accounts for the overall coupling between layers. The choosing of lattice parameters allows designs for a wide range of applications, including the electromagnetic bandgap filtering of an E-polarized wave, which is simulated and reported here.     

Dynamical properties and synchronization of complex non-linear equations for detuned lasers

We study the dynamics and synchronization properties of a system of complex non-linear equations describing detuned lasers. These equations possess a whole circle of fixed points, while the corresponding real variable equations have only isolated fixed points. We examine the stability of their equilibrium points and determine conditions under which the complex equations have positive, negative or zero Lyapunov exponents and chaotic, quasiperiodic or periodic attractors for a wide range of parameter values. We investigate the synchronization of chaotic solutions of our detuned laser system, using as a drive a similar set of equations and applying the method of global synchronization. We find attractors whose three-dimensional projection is not at all similar to the well-known shape of the (real) Lorenz attractor. Finally, we apply complex periodic driving to the electric field equation and show that the model can exhibit a transition from chaotic to quasiperiodic oscillations. This leads us to the discovery of an exact periodic solution, whose amplitude and frequency depend on the parameters of the system. Since this solution is stable for a wide range of parameter values, it may be used to control the system by entraining it with the applied periodic forcing.     

Phase synchronization of switchings in stochastic and chaotic bistable systems

We study synchronization of switching processes in stochastic and chaotic bistable systems driven by a periodic signal in terms of phase synchronization. By introduction of instantaneous phases of transitions between metastable states and of the periodic forcing we show explicitly the effect of phase locking. The dynamics of phase difference appears to be qualitatively equivalent to that of a synchronized classical self-sustained oscillator. We have found that the degree of phase coherence between the input signal and the response estimated employing the effective diffusion constant is maximal at an optimal noise level in a stochastic bistable system or at an optimal value of a control parameter in a purely deterministic case. We also consider the effect of mutual synchronization of the switching processes in coupled stochastic and chaotic bistable systems.     

An Effective Interaction Approach to Anisotropic Superconductors Beyond the Weak Coupling Theory—An Origin of the d-wave Symmetry in High-T c Cuprate

We propose an effective interaction approach to superconducting systems which is adapted to periodic systems and intermediate net coupling between charge carriers by phonon mediated and Coulomb repulsive interactions. A coupling function of effective interaction is given for homogeneous field beyond the weak coupling approximation by using a generalized intermediate coupling method. Adequate kernel for the periodic systems is also reduced to that coupling function in homogeneous field and the Fourier coefficients relevant to the Bloch function. Within the present approach we discuss the symmetry of the superconducting gap in cuprate under the assumption that a nonbonding band filled by 2p_σ electrons exists in an undoped system and that doped holes occupy orbitals in this band. Those orbitals are represented by linear combinations of p _x and p _y functions. It is argued, in the tetragonal limit, that the symmetry of the gap function is d-wave-like on account of the products of orbital functions in combination of singlet spin-pair in the kernel.     

Chiral Surface Lattice Resonances

Collective excitation of periodic arrays of metallic nanoparticles by coupling localized surface plasmon resonances to grazing diffraction orders leads to surface lattice resonances with narrow line width. These resonances may find numerous applications in optical sensing and information processing. Here, a new degree of freedom of surface lattice resonances is experimentally investigated by demonstrating handedness-dependent excitation of surface lattice resonances in arrays of chiral plasmonic crescents. The self-assembly of particles used as mask and modified colloidal lithography is applied to produce arrays of planar and 3D gold crescents over large areas. The excitation of surface lattice resonances as a function of the interparticle distance and the degree of order within the arrays is investigated. The chirality of the individual 3D crescents leads to the formation of chiral lattice modes, that is, surface lattice resonances that exhibit optical activity.     

Generation of chaotic dissipative solitons in active ring resonator with one-dimensional periodic ferromagnetic miscrostructure

Generation of chaotic dissipative solitons has been observed in an active ring resonator with one-dimensional periodic ferromagnetic microstructure comprising a single-crystalline film of yttrium iron garnet (YIG) with a lattice of grooves oriented perpendicular to the direction of propagation of a magnetostatic surface wave (MSSW). A quasi-periodic train of chaotic dissipative solitons was generated in this system under the conditions of three-magnon processes of MSSW decay due to the passive synchronization (PS) of spin wave self-modulation in a frequency band corresponding to the first bandgap. The PS onset was caused by the saturable absorption of microwave signals within the bandgap of the MSSW transmission line.     

Emergence of polar order and cooperativity in hydrodynamically coupled model cilia

As a model of ciliary beat, we use two-state oscillators that have a defined direction of oscillation and have strong synchronization properties. By allowing the direction of oscillation to vary according to the interaction with the fluid, with a timescale longer than the timescale of synchronization, we show in simulations that several oscillators can align in a direction set by the geometrical configuration of the system. In this system, the alignment depends on the state of synchronization of the system, and is therefore linked to the beat pattern of the model cilia. By testing various configurations from two to 64 oscillators, we deduce empirically that, when the synchronization state of neighbouring oscillators is in phase, the angles of the oscillators align in a configuration of high hydrodynamic coupling. In arrays of oscillators that break the planar symmetry, a global direction of alignment emerges reflecting this polarity. In symmetric configurations, where several directions are geometrically equivalent, the array still displays strong internal cooperative behaviour. It also appears that the shape of the array is more important than the lattice type and orientation in determining the preferred direction.     

Synchronization of coupled bistable chaotic systems: experimental study

We carried out an experimental study of the synchronization of two unidirectionally coupled R?ssler-like electronic circuits with two coexisting chaotic attractors. Different stages of synchronization are identified on the route from asynchronous motion to complete synchronization, as the coupling parameter is increased: intermittent asynchronous jumps between coexisting attractors; intermittent anticipating phase synchronization; and generalized synchronization in the form of subharmonic entrainment terminated by complete synchronization. All these regimes are analysed with time-series, power spectra and phase-space plots of the drive and response oscillators. The experimental study implicitly confirms the results of numerical simulations.     

Time shift between unstable periodic orbits of coupled chaotic oscillators

The shift Δt between unstable periodic orbits of coupled oscillators occurring in the chaotic synchronization regime has been studied. It is shown that this time shift is the same for all equiphase orbits with various topological parameters and depends on the coupling parameter ε. This dependence obeys the universal power law Δt ∼ εⁿ with an exponent of n = −1.     

关于Riccati方程的周期解

本文给出Riccati方程周期解存在与不存在的若干新准则。     

Dynamics of a map lattice with threshold coupling

An analysis is made of the dynamics of a logistic map lattice with threshold coupling and it is shown that, depending on the values of the control parameters, various types of spatial structures are formed in these lattices. For these structures there is a set of numerical values characterizing the type of structure which depends on the values of the control parameters. It is shown that in the spatially steady-state structures formed in a coupled-map lattice, there are small regions of nonstationary processes in which periodic oscillations occur. Pis’ma Zh. Tekh. Fiz. 25, 28–34 (February 26, 1999)     

Superfluid-Insulator Transition of a Bose–Einstein Condensation in a Periodic Potential and Its Interference Pattern

Recent experiments have succeeded in observing the superfluid-Mott insulator quantum phase transition of an alkali atomic Bose–Einstein condensate in an optical lattice potential. Motivated by this work, we studied the two-dimensional Bose gas in a periodic potential by analyzing the Gross–Pitaevskii equation. We found evidence of a superfluid-insulator transition that occurs as the potential depth of the lattice is increased. For the periodic potential, the phase of the macroscopic wave function in the ground state is localized in each potential minimum. Also, according to the resugts using the Hartree–Fock–Bogoliubov equation, an energy gap appears in the lowest excitation state. We then added a parabolic trapping potential to the periodic potential and studied how the dynamics of the wave function and its interference pattern depend on the initial ground state. For the initial ground state localized by the deep periodic potential, the wave function oscillates in the central potential minimum after removing only the trapping potential. After turning off both the trapping and periodic potentials, the wave packets with periodicity escape from the condensate.     

On the dynamics of uncertain coupled structures through a wave based method in mid- and high-frequency ranges

This paper focuses on guided wave propagation in elastic random structures. A numerical tool, referred to as the ’stochastic wave finite element method’ (SWFE) describing uncertain spectral parameters in periodic structures is presented. This approach represents an extension of the wave finite element for homogenous randomness media. The statistics of the kinematic diffusion matrix for two semi-infinite waveguides connected through an uncertain coupling element is offered. The diffusion relationships presented evaluate the statistics of reflection and transmission coefficients for semi-infinite connected waveguides subject to structural and geometrical variabilities on a coupling element. Finally, the effects of the uncertainties on kinematic and energetic parameters are investigated for two finite coupled structures based on the stochastic spectral approach. Numerical experiments show the effectiveness of the proposed formulation to predict the dynamics of periodic systems in mid- and high-frequency ranges with low CPU consumption.     

Effects of unwanted feedback on synchronized chaotic optical communications

The effects of unwanted external optical feedback on synchronized chaotic optical communication systems are studied numerically. We consider an open-loop configuration consisting of a transmitter laser with double external optical feedbacks and a receiver laser with optical injection from the transmitter laser. First, including the effects of unwanted optical feedback, the synchronization performances of both the complete synchronization and the generalized synchronization are examined. Then the encoding and decoding performances of the generalized synchronization and the effects of the introduced feedback are investigated, respectively. Finally, we study the control of the unwanted feedback on the dynamics of the transmitter laser and briefly discuss the system security when the transmitter laser is driven to operate in a steady state or periodic oscillation state by the additional feedback.     

Coarse-Grained Finite-Temperature Theory for the Bose Condensate in Optical Lattices

In this paper, we derive a coarse-grained finite-temperature theory for a Bose condensate in a one-dimensional optical lattice, in addition to a confining harmonic trap potential. We start with a two-particle irreducible (2PI) effective action on the Schwinger-Keldysh closed-time contour path. In principle, this action involves all information of equilibrium and non-equilibrium properties of the condensate and noncondensate atoms. In constructing a theory for the condensate and noncondensate in a periodic lattice potential, a difficulty arises from the rapid spatial variation due to a lattice potential, compared to the length scale of the harmonic potential. We employ a coarse-graining procedure to eliminate this rapid variation. By introducing a variational ansatz for the condensate order parameter in an effective action, we derive a coarse-grained effective action, which describes the dynamics on the length scale much longer than a lattice constant. Using the variational principle, coarse-grained equations of motion for condensate variables are obtained. These equations include a dissipative term due to collisions between condensate and noncondensate atoms, as well as noncondensate mean-field. As a result of a coarse-graining procedure, the effects of a lattice potential are incorporated into equations of motion for the condensate by an effective mass, a renormalized coupling constant, and an umklapp scattering process. To illustrate the usefulness of our formalism, we discuss a Landau instability of the condensate moving in optical lattices by using the coarse-grained generalized Gross-Pitaevskii hydrodynamics. We find that the collisional damping rate due to collisions between the condensate and noncondensate atoms changes its sign when the condensate velocity exceeds a renormalized sound velocity, leading to a Landau instability consistent with the Landau criterion. Our results in this work give an insight into the microscopic origin of the Landau instability.      

Controlling gradient phase distributions in a model of active antenna array with locally coupled elements

The regime of synchronization with a certain gradient phase distribution and the possibility of controlling such distribution in a linear array of oscillators coupled by phase-locked loops (PLLs) have been theoretically studied. It is shown that a constant phase progression can be controlled by manipulating collective dynamics, with oscillator eigenfrequencies and coupling coefficients being the control parameters. The proposed principle of control, based on the nonlinear dynamics of PLL-coupled oscillators, can be used in solving the problems of phasing and controlled beam scanning in antenna arrays operating in different frequency bands.     

Effective Superelastic Domains of Schwarz Primitive Shape Memory Alloy Lattices Subjected to Cyclic Loading

This work investigates the evolution of effective phase transformation thresholds in superelastic shape memory alloy (SMA) lattice architectures subjected to cyclic loading. The investigation is carried out by means of finite element analysis and numerical homogenization methods, considering Schwarz primitive triply periodic minimal surface (TPMS) SMA unit cells subjected to periodic boundary conditions. The results are reported for relative densities between 10% and 50%. It is shown that, in all the cases considered, the loading surfaces governing both forward and reverse phase transformations have an ellipsoidal shape that can be reasonably well represented using an extended Hill's criterion that accounts for the influence of hydrostatic pressure. Moreover, by considering polynomial expressions of the coefficients of Hill's criterion in terms of martensite volume fraction and cumulated fraction, the evolution of the loading surfaces as a consequence of functional fatigue is reasonably well approximated. The results suggest that an extended Hill's criterion with variable coefficients can well be used to simulate effective phase transformation and functional fatigue in architected TPMS SMAs.     

Summation of perturbation solutions to nonlinear oscillations

Summary By coupling the Lindstedt-Poincaré perturbation technique with a rational approximation, we propose a method for summing up the perturbation solutions of the nonlinear oscillation of a conservative single-degree-of-freedom system. The equation of motion contains a parameter. This method can represent the singularities of the period at certain values of the oscillation amplitude and extend the range of validity of the perturbation solution. For constructing the summation, all is needed are the coefficients of the pertubation expansion of the periodic solution. Approximate formulas for the period and the corresponding periodic solution of the nonlinear oscillation are established. Two examples are used to illustrate the effectiveness of the method.