Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates

We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom s-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schrodinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.

Are there non-linearities in short-term interest rates?

The present paper investigates the characteristics of short-term interest rates in several countries. We examine the importance of nonlinearities in the mean reversion and volatility of short-term interest rates. We examine various models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate.We find that different markets require different models. In particular, we find evidence of nonlinear mean reversion in some of the countries that we examine, linear mean reversion in others and no mean reversion in some countries. For all countries we examine, there is strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the short-term interest rate. Out-of-sample forecasting performance of one-factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data.

Bright tripartite entanglement in triply concurrent parametric oscillation

We show that an optical parametric oscillator based on three concurrent chi((2)) nonlinearities can produce, above threshold, bright output beams of macroscopic intensities which exhibit strong tripartite continuous-variable entanglement. We also show that there are two ways that the system can exhibit a three-mode form of the Einstein-Podolsky-Rosen paradox, and calculate the extracavity fluctuation spectra that may be measured to verify our predictions.

Identification of MIMO Hammerstein systems using cardinal spline functions

A new approach to identify multivariable Hammerstein systems is proposed in this paper. By using cardinal cubic spline functions to model the static nonlinearities, the proposed method is effective in modelling processes with hard and/or coupled nonlinearities. With an appropriate transformation, the nonlinear models are parameterized such that the nonlinear identification problem is converted into a linear one. The persistently exciting condition for the transformed input is derived to ensure the estimates are consistent with the true system. A simulation study is performed to demonstrate the effectiveness of the proposed method compared with the existing approaches based on polynomials. (C) 2006 Elsevier Ltd. All rights reserved.

Greenberger-Horne-Zeilinger-type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting

We study Greenberger-Horne-Zeilinger-type (GHZ-type) and W-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the W-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

Nonlinear dynamics of cilia and flagella

Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.

A comparison of linear forecasting models and neural networks:an application to Euro inflation and Euro Divisia

Linear models reach their limitations in applications with nonlinearities in the data. In this paper new empirical evidence is provided on the relative Euro inflation forecasting performance of linear and non-linear models. The well established and widely used univariate ARIMA and multivariate VAR models are used as linear forecasting models whereas neural networks (NN) are used as non-linear forecasting models. It is endeavoured to keep the level of subjectivity in the NN building process to a minimum in an attempt to exploit the full potentials of the NN. It is also investigated whether the historically poor performance of the theoretically superior measure of the monetary services flow, Divisia, relative to the traditional Simple Sum measure could be attributed to a certain extent to the evaluation of these indices within a linear framework. Results obtained suggest that non-linear models provide better within-sample and out-of-sample forecasts and linear models are simply a subset of them. The Divisia index also outperforms the Simple Sum index when evaluated in a non-linear framework. © 2005 Taylor & Francis Group Ltd.

Recent developments in all-optical nonlinear data processing

Photonic technologies for data processing in the optical domain are expected to play a major role in future high-speed communications. Nonlinear effects in optical fibres have many attractive features and great, but not yet fully explored potential for optical signal processing. Here we provide an overview of our recent advances in developing novel techniques and approaches to all-optical processing based on fibre nonlinearities.

Suppression and summation in contrast gain control for human vision

Over the last ten years our understanding of early spatial vision has improved enormously. The long-standing model of probability summation amongst multiple independent mechanisms with static output nonlinearities responsible for masking is obsolete. It has been replaced by a much more complex network of additive, suppressive, and facilitatory interactions and nonlinearities across eyes, area, spatial frequency, and orientation that extend well beyond the classical recep-tive field (CRF). A review of a substantial body of psychophysical work performed by ourselves (20 papers), and others, leads us to the following tentative account of the processing path for signal contrast. The first suppression stage is monocular, isotropic, non-adaptable, accelerates with RMS contrast, most potent for low spatial and high temporal frequencies, and extends slightly beyond the CRF. Second and third stages of suppression are difficult to disentangle but are possibly pre- and post-binocular summation, and involve components that are scale invariant, isotropic, anisotropic, chromatic, achromatic, adaptable, interocular, substantially larger than the CRF, and saturated by contrast. The monocular excitatory pathways begin with half-wave rectification, followed by a preliminary stage of half-binocular summation, a square-law transducer, full binocular summation, pooling over phase, cross-mechanism facilitatory interactions, additive noise, linear summation over area, and a slightly uncertain decision-maker. The purpose of each of these interactions is far from clear, but the system benefits from area and binocular summation of weak contrast signals as well as area and ocularity invariances above threshold (a herd of zebras doesn't change its contrast when it increases in number or when you close one eye). One of many remaining challenges is to determine the stage or stages of spatial tuning in the excitatory pathway.

Identification of nonlinear systems by correlation using pseudorandom signals

This thesis is concerned with the measurement of the characteristics of nonlinear systems by crosscorrelation, using pseudorandom input signals based on m sequences. The systems are characterised by Volterra series, and analytical expressions relating the rth order Volterra kernel to r-dimensional crosscorrelation measurements are derived. It is shown that the two-dimensional crosscorrelation measurements are related to the corresponding second order kernel values by a set of equations which may be structured into a number of independent subsets. The m sequence properties determine how the maximum order of the subsets for off-diagonal values is related to the upper bound of the arguments for nonzero kernel values. The upper bound of the arguments is used as a performance index, and the performance of antisymmetric pseudorandom binary, ternary and quinary signals is investigated. The performance indices obtained above are small in relation to the periods of the corresponding signals. To achieve higher performance with ternary signals, a method is proposed for combining the estimates of the second order kernel values so that the effects of some of the undesirable nonzero values in the fourth order autocorrelation function of the input signal are removed. The identification of the dynamics of two-input, single-output systems with multiplicative nonlinearity is investigated. It is shown that the characteristics of such a system may be determined by crosscorrelation experiments using phase-shifted versions of a common signal as inputs. The effects of nonlinearities on the estimates of system weighting functions obtained by crosscorrelation are also investigated. Results obtained by correlation testing of an industrial process are presented, and the differences between theoretical and experimental results discussed for this case;

Neuronal convergence in early contrast vision: binocular summation is followed by response nonlinearity and area summation

We assessed summation of contrast across eyes and area at detection threshold ( C t). Stimuli were sine-wave gratings (2.5 c/deg) spatially modulated by cosine- and anticosine-phase raised plaids (0.5 c/deg components oriented at ±45°). When presented dichoptically the signal regions were interdigitated across eyes but produced a smooth continuous grating following their linear binocular sum. The average summation ratio ( C t1/([ C t1+2]) for this stimulus pair was 1.64 (4.3 dB). This was only slightly less than the binocular summation found for the same patch type presented to both eyes, and the area summation found for the two different patch types presented to the same eye. We considered 192 model architectures containing each of the following four elements in all possible orders: (i) linear summation or a MAX operator across eyes, (ii) linear summation or a MAX operator across area, (iii) linear or accelerating contrast transduction, and (iv) additive Gaussian, stochastic noise. Formal equivalences reduced this to 62 different models. The most successful four-element model was: linear summation across eyes followed by nonlinear contrast transduction, linear summation across area, and late noise. Model performance was enhanced when additional nonlinearities were placed before binocular summation and after area summation. The implications for models of probability summation and uncertainty are discussed.

Photorefractive subharmonics - a beam-coupling effect?

Using the so-called ac field technique, we investigate experimentally the influence of optical beam coupling on the generation of subharmonic gratings in a photorefractive sillenite crystal. By the use of two different recording configurations, we are able to distinguish between effects caused by material nonlinearities and effects caused by optical beam coupling.

Photorefractive subharmonics - a beam-coupling effect?

Using the so-called ac field technique, we investigate experimentally the influence of optical beam coupling on the generation of subharmonic gratings in a photorefractive sillenite crystal. By the use of two different recording configurations, we are able to distinguish between effects caused by material nonlinearities and effects caused by optical beam coupling.

Novel approaches in nonlinear optical fibre-based signal processing

All-optical data processing is expected to play a major role in future optical communications. Nonlinear effects in optical fibres have many attractive features and a great, not yet fully explored potential in optical signal processing. Here, we overview our recent advances in developing novel techniques and approaches to all-optical processing based on optical fibre nonlinearities.