Resonance in Defect Turbulence under Periodic External Force

The periodically forced spatially extended Brusselator is investigated in the chaotic regime. We explore resonant or non-resonant patterns generated under various forcing frequencies and forcing amplitudes. Resonant spatially uniform oscillation and irregular structures are found. Furthermore two types of regular spatial patterns are generated under appropriate parameters. Our results of numerical simulations demonstrate that periodic force can give rise to resonant patterns in forced systems of spatiotemporal chaos similar to the situation of forced systems of regular oscillations.     

Homoclinic snaking of localized patterns in a spatially forced system

Dissipative localized structures exhibit intricate bifurcation diagrams. An adequate theory has been developed in one space dimension; however, discrepancies arise with the experiments. Based on an optical feedback with spatially modulated input beam, we set up a 1D forced configuration in a nematic liquid crystal layer. We characterize experimentally and theoretically the homoclinic snaking diagram of localized patterns, providing a reconciliation between theory and experiments.     

Resonantly forced inhomogeneous reaction-diffusion systems

The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex Ginzburg-Landau equation in the 3:1 resonance regime. Front roughening and spontaneous nucleation of target patterns are observed and characterized. Time dependent spatially varying forcing fields are studied in the 3:1 forced FitzHugh-Nagumo system. The periodic variation of the spatially random forcing amplitude breaks the symmetry among the three quasi-homogeneous states of the system, making the three types of fronts separating phases inequivalent. The resulting inequality in the front velocities leads to the formation of "compound fronts" with velocities lying between those of the individual component fronts, and "pulses" which are analogous structures arising from the combination of three fronts. Spiral wave dynamics is studied in systems with compound fronts. (c) 2000 American Institute of Physics.     

Forcing and control of localized states in optical single feedback systems

Under feedback extended nonlinear optical systems spontaneously show a variety of periodic patterns and structures. Control gives new insight into these phenomena and it can open the way for potential application of nonlinear optical structures. We briefly review methods to control localized states in single feedback experiments. Application of a Fourier control method allows to modify interaction behavior of the localized states. As a further approach we study a forcing method, using externally created light fields as additional input to the system. Recent experiments show that the forcing method enables to favor addressing positions for localized structures. We demonstrate static addressing and favoring of addressing positions. We extend the forcing method to a dynamic forcing scheme, which allows to move and reposition localized states. Additionally forcing is used to balance experimental imperfections. PACS 05.45.Gg; 42.60.Jf; 42.65.Tg     

Shape-optimal design of graded index sonic crystal formations using natural cubic splines

Noise reduction through upward refraction can be achieved by artificial means, using a graded index sonic crystal. In addition to upward refraction, it will be shown that these periodically spaced cylinder formations can simultaneously benefit from band-gap phenomena. The aim of this paper is to present a method to optimise the broadband noise reducing performance of graded index sonic crystals, in a frequency range from well below to well above the lowest band-gap frequency. A design technique based on the creation of complex cylinder formations has been explored, in which the effective propagation speed is spatially varied using natural cubic splines. Sets of complex barrier shapes are compactly described by re-locating a number of control points in a two-dimensional cartesian plane and connecting the control points by (curved) line segments. In addition to the cluster shape, a complex graded index sonic crystal structure was formed by varying the lattice constant and the cylinder radius, where the cylinder radius was varied as a function of height. All these parameters were optimised with a multi-objective genetic algorithm, for structures based on horizontally oriented acoustically hard cylinders, located above a perfectly reflecting ground plane. A four-lane outdoor situation, with a traffic scenario consisting of 95% light and 5% heavy duty vehicles driving at 70 km/h has been studied in a two-dimensional domain. For such a configuration we obtained a spatially averaged mean reduction of 4.2–5.3 dBA, with structures covering an effective cross-sectional area of 1 m². It was found that the insertion loss among the studied traffic lanes was reasonably constant. In addition, it was found that the low-frequency performance of the studied structures is enhanced by incrementing the barrier-height while increasing the number of scatterers as a function of height.     

Texture transitions in the liquid crystalline alkyloxybenzoic acid 6OBAC

The 4,n-alkyloxybenzoic acid 6OBAC has a very rich variety of crystalline structures and two nematic sub-phases, characterised by different textures. It is a material belonging to a family of liquid crystals formed by hydrogen bonded molecules, the 4,n-alkyloxybenzoic acids (n indicates the homologue number). The homologues with 7?≤?n?≤?13 display both smectic C and N phases. In spite of the absence of a smectic phase, 6OBAC exhibits two sub-phases with different textures, as it happens in other materials of the homologue series which possess the smectic phase. This is the first material that exhibits a texture transition in a nematic phase directly originating from a crystal phase. Here we present the results of an image processing assisted optical investigation to characterise the textures and the transitions between textures. This processing is necessary to discriminate between crystal modifications and nematic sub-phases.     

Forced snaking: Localized structures in the real Ginzburg-Landau equation with spatially periodic parametric forcing

We study spatial localization in the real subcritical Ginzburg-Landau equation u _t = m ₀ u + Q(x)u + u _xx + d|u|² u ?|u|⁴ u with spatially periodic forcing Q(x). When d>0 and Q ≡ 0 this equation exhibits bistability between the trivial state u = 0 and a homogeneous nontrivial state u = u ₀ with stationary localized structures which accumulate at the Maxwell point m ₀ = ?3d ²/16. When spatial forcing is included its wavelength is imprinted on u ₀ creating conditions favorable to front pinning and hence spatial localization. We use numerical continuation to show that under appropriate conditions such forcing generates a sequence of localized states organized within a snakes-and-ladders structure centered on the Maxwell point, and refer to this phenomenon as forced snaking. We determine the stability properties of these states and show that longer lengthscale forcing leads to stationary trains consisting of a finite number of strongly localized, weakly interacting pulses exhibiting foliated snaking.     

Pattern formation in forced reaction diffusion systems with nearly degenerate bifurcations

The existence and stability of stable standing-wave patterns in an assembly of spatially distributed generic oscillators governed by a couple of complex Ginzburg-Landau equations, subjected to parametric forcing, are reported. The mechanism of a dispersion-induced pattern in dissipative oscillators parametrically forced near the degenerate Turing-Hopf bifurcation is also illustrated. We show that, when excitation occurs just after the Turing bifurcation and before the Hopf instability, the system exhibits a new type of stable standing-wave structures, namely the mixed-mode solutions. The Brussellator-model, parametrically forced below the threshold of oscillations, is analyzed as an example of calculation.     

Photonic network laser

We demonstrated lasing in two-dimensional trivalent network structures with short-range order. Despite the lack of translational and rotational symmetries, such structures possess a large isotropic photonic bandgap. Different from those of a photonic crystal, the band-edge modes are spatially localized and have high quality factor.     

Determining Modes for Continuous Data Assimilation in 2D Turbulence

We study the number of determining modes necessary for continuous data assimilation in the two-dimensional incompressible Navier–Stokes equations. Our focus is on how the spatial structure of the body forcing affects the rate of continuous data assimilation and the number of determining modes. We treat this problem analytically by proving a convergence result depending on the H ^–1 norm of f and computationally by considering a family of forcing functions with identical Grashof numbers that are supported on different annuli in Fourier space. The rate of continuous data assimilation and the number of determining modes is shown to depend strongly on the length scales present in the forcing.     

Delocalizing transition of Bose-Einstein condensates in optical lattices

A Bose-Einstein condensate trapped in a two-dimensional optical lattice exhibits an abrupt transition manifested by the macroscopic wave function changing character from spatially localized to extended. Resulting from a bifurcation, this irreversible transition takes place as the interwell potential barrier is adiabatically decreased below a critical value. This is in sharp contrast to the corresponding one-dimensional case where such a bifurcation is absent and the extent of a localized mode is continuously tunable. We demonstrate how these phenomena can be experimentally explored.     

Tunable lightwave propagation in two-dimensional hole-type photonic crystals infiltrated with nematic liquid crystal

Photonic crystals have many potential applications because of their ability to control lightwave propagation. We have investigated the tunability of lightwave propagation in two-dimensional hole-type photonic crystal structures. The linear waveguides can be obtained by the infiltration of liquid crystals into air holes in hole-type photonic crystal with square lattices. The refractive indices of liquid crystals can be changed by rotating the directors of liquid crystals. Therefore, we can control the lightwave propagation in two-dimensional hole-type photonic crystal structures. Such a mechanism of lightwave adjustment should open up a new application for designing components in photonic integrated circuits.     

Controlled mixing enhancement in turbulent rectangular jets responding to periodically forced inflow conditions

We present numerical studies of active flow control applied to jet flow. We focus on rectangular jets, which are more unstable than their circular counterparts. The higher level of instability is expressed mainly by an increased intensity of mixing of the main flow with its surroundings. We analyse jets with aspect ratio A_r = 1, A_r = 2 and A_r = 3 at Re = 10,000. It is shown that the application of control with a suitable excitation (forcing) at the jet nozzle can amplify the mixing and qualitatively alter the character of the flow. This can result in an increased spreading rate of the jet or even splitting into nearly separate streams. The excitations studied are obtained from a superposition of axial and flapping forcing terms. We consider the effect of varying parameters such as the frequency of the excitations and phase shift between forcing components. The amplitude of the forcing is 10% of the inlet centreline jet velocity and the forcing frequencies correspond to Strouhal numbers in a range St = 0.3–0.7. It is shown that qualitatively different flow regimes and a rich variety of possible flow behaviours can be achieved simply by changing aspect ratio and forcing parameters. The numerical results are obtained applying large eddy simulation in combination with a high-order compact difference code for incompressible flows. The solutions are validated based on experimental data from literature for non-excited jets for A_r = 1 at Re = 1.84 × 10⁵ and A_r = 2 at Re = 1.28 × 10⁵. Both the mean velocities as well as their fluctuations are predicted with good accuracy.     

Visualization of low Reynolds boundary-driven cavity flows in thin liquid shells

Abstract  

Classic examples of low-Reynolds recirculating cavity flows are typically generated from lid-driven boundary motion at a solid–fluid interface, or alternatively may result from shear flow over cavity openings. Here, we are interested in an original family of boundary-driven cavity flows occurring, in contrast to classic setups, at fluid–fluid interfaces. Particle image velocimetry (PIV) is used to investigate the structure of internal convective flows observed in thin liquid shells. Under the specific configuration investigated, the soap bubble’s liquid shell is in fact in motion and exhibits sporadic local “bursts”. These bursts induce transient flow motion within the cavity of order Re ∼ O(1). The combination of PIV and proper orthogonal decomposition (POD) is used to extract dominant flow structures present within bubble cavities. Next, we show that thermally induced Marangoni flows in the liquid shell can lead to forced, (quasi) steady-state, internal recirculating flows. The present findings illustrate a novel example of low-Reynolds boundary-driven cavity flows.     

一种具有大带隙的各向异性二维光子晶体结构

提出一种新型各向异性材料(碲)二维光子晶体结构,应用有限时域差分法,对该结构特性进行数值分析,结果表明:通过优化结构参量,该结构具有较大的绝对光子禁带,禁带宽度为0.064ω_e(ω_e=2πc/a,a为晶格常量,c为光速),且该光子晶体的带隙具有很好的稳定性.     

Resonant and nonresonant patterns in forced oscillators

Uniform oscillations in spatially extended systems resonate with temporal periodic forcing within the Arnold tongues of single forced oscillators. The Arnold tongues are wedge-like domains in the parameter space spanned by the forcing amplitude and frequency, within which the oscillator's frequency is locked to a fraction of the forcing frequency. Spatial patterning can modify these domains. We describe here two pattern formation mechanisms affecting frequency locking at half the forcing frequency. The mechanisms are associated with phase-front instabilities and a Turing-like instability of the rest state. Our studies combine experiments on the ruthenium catalyzed light-sensitive Belousov-Zhabotinsky reaction forced by periodic illumination, and numerical and analytical studies of two model systems, the FitzHugh-Nagumo model and the complex Ginzburg-Landau equation, with additional terms describing periodic forcing.     

Forced Synchronization of Electroconvective Roll Oscillations in Nematic Liquid Crystals

The forced phase locking in a system of the oscillating electroconvective rolls that form in a nematic liquid crystal layer in a dc electric field is studied. As a result of the action of an additive ac electric field with a small amplitude, the system of oscillators is found to be divided into clusters, where oscillations are fully phase locked. The electroconvective rolls in neighboring clusters oscillate in antiphase and the clusters are separated by Ising walls. The phase locking is shown to be maximal at the forcing frequency that is close to the double frequency of the natural oscillations of rolls. A model is proposed to describe spatially distributed phase oscillators, and it takes into account the symmetries of a system of electroconvective rolls and external forcing. The results of numerical simulations agree well with the experimental data.     

二维函数光子晶体

光子晶体是由两种或两种以上不同介电常数材料所构成的周期性光学纳米结构.光子晶体结构可分为一维、二维和三维,其中二维光子晶体已成为研究的热点.可调带隙的二维光子晶体可以设计出新型的光学器件,因此,对它的研究具有重要的理论意义和应用价值.本文提出的二维新型函数光子晶体可以实现光子晶体带隙的可调性.所谓二维函数光子晶体,即组成它的介质柱的介电常数是空间坐标的函数,它不同于介电常数为常数的二维常规光子晶体.二维函数光子晶体是通过光折变非线性光学效应或电光效应使介质柱的介电常数成为空间坐标的函数.运用平面波展开法给出了TE和TM波的本征方程,由傅里叶变换得到二维函数光子晶体介电常数ε(r)的傅里叶变换ε(G),其傅里叶变换比常规二维光子晶体的复杂.计算发现当介质柱介电常数为常数时,其傅里叶变换与常规二维光子晶体的相同,因此二维常规光子晶体是二维函数光子晶体的特例.在此基础上具体研究了二维函数光子晶体TE波和TM波的带隙结构,其介质柱介电常数函数形式取为ε(r)=k·r+b,其中k,b为可调的参数.并与二维常规光子晶体TE波和TM波的带隙结构进行了比较,发现二维函数光子晶体与二维常规光子晶体TE波和TM波的带隙结构有明显的区别,二维函数光子晶体的带隙数目、位置以及宽度随参数k的变化而发生改变.从而实现了二维函数光子晶体带隙结构的可调性,为基于二维光子晶体的光学器件的设计提供了新的设计方法和重要的理论依据.     

Narrowband optical filter design for DWDM communication applications based on Generalized Aperiodic Thue-Morse structures

We present here a novel proposal for multichannel narrowband DWDM filter design, based on Generalized Aperiodic Thue-Morse (GATM) multilayer structures. Transmission spectra of light propagation through these structures are studied in this article. Numerical simulations in this research show an ultra high efficiency and a very low crosstalk for this filter so that the total transmission of filter output channels is up to 100% and the range of output wavelength is 1550 nm which is suitable for DWDM communication systems. By studying the effects of parameters of GATM structure, we realized that by varying parameters such as number of layers, distance between layers, refractive index of layers, etc., a suitable DWDM filter can be accomplished, which is in accordance with the communication ITU-T standard. This narrowband DWDM filter has capability of changing the number of channels and the bandwidth of each channel, at the special wavelength. By changing the thickness of each layer, the transmittance wavelength of the filter will change. The main advantage of the Thue-Morse structure is the numbers of selective layers, which in our designed structure, we choose GATM(3,2) where m = 3 and n = 2 in B^mAⁿ, and for the first time we change both m and n simultaneously in the proposed structure to control optical properties of the introduced filter.     

Defect-mediated snaking: A new growth mechanism for localized structures

Stationary spatially localized patterns in parametrically driven systems are studied, focusing on the 2:1 and 1:1 resonance tongues as described by the forced complex Ginzburg-Landau equation. Homoclinic snaking is identified in both cases and the nature of the growth of the localized structures along the snaking branches is described. The structures grow from a central defect that inserts new rolls on either side, while pushing existing rolls outwards. This growth mechanism differs fundamentally from that found in other systems exhibiting homoclinic snaking in which new rolls are added at the fronts that connect the structure to the background homogeneous state.