Violations of Bell's inequality for Gaussian states with homodyne detection and nonlinear interactions

We show that homodyne measurements can be used to demonstrate violations of Bell's inequality with Gaussian states, when the local rotations used for these types of tests are implemented using nonlinear unitary operations. We reveal that the local structure of the Gaussian state under scrutiny is crucial in the performance of the test. The effects of finite detection efficiency are thoroughly studied and shown to only mildly affect the revelation of Bell violations. We speculate that our approach may be extended to other applications such as entanglement distillation where local operations are necessary elements besides quantum entanglement.

Nonlinear frequency coupling in dual radio-frequency driven atmospheric pressure plasmas

Plasma ionization, and associated mode transitions, in dual radio-frequency driven atmospheric pressure plasmas are governed through nonlinear frequency coupling in the dynamics of the plasma boundary sheath. Ionization in low-power mode is determined by the nonlinear coupling of electron heating and the momentary local plasma density. Ionization in high-power mode is driven by electron avalanches during phases of transient high electric fields within the boundary sheath. The transition between these distinctly different modes is controlled by the total voltage of both frequency components.

Two-stage mixed discrete-continuous identification of radial basis function (RBF) neural models for nonlinear systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous; identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.

Moving window kernel PCA for adaptive monitoring of nonlinear processes

This paper discusses the monitoring of complex nonlinear and time-varying processes. Kernel principal component analysis (KPCA) has gained significant attention as a monitoring tool for nonlinear systems in recent years but relies on a fixed model that cannot be employed for time-varying systems. The contribution of this article is the development of a numerically efficient and memory saving moving window KPCA (MWKPCA) monitoring approach. The proposed technique incorporates an up- and downdating procedure to adapt (i) the data mean and covariance matrix in the feature space and (ii) approximates the eigenvalues and eigenvectors of the Gram matrix. The article shows that the proposed MWKPCA algorithm has a computation complexity of O(N2), whilst batch techniques, e.g. the Lanczos method, are of O(N3). Including the adaptation of the number of retained components and an l-step ahead application of the MWKPCA monitoring model, the paper finally demonstrates the utility of the proposed technique using a simulated nonlinear time-varying system and recorded data from an industrial distillation column.

On the treatment of singularities of the Watson Hamiltonian for nonlinear molecules

The applicability of the Watson Hamiltonian for the description of nonlinear molecules—especially triatomic ones—has always been questioned, as the Jacobian of the transformation that leads to the Watson Hamiltonian, vanishes at the linear configuration. This results in singular behavior of the Watson Hamiltonian, giving rise to serious numerical problems in the computation of vibrational spectra, with unphysical, spurious vibrational states appearing among the physical vibrations, especially in the region of highly excited states. In this work, we analyze the problem and propose a simple way to confine the nuclear wavefunction in such a way that the spurious solutions are eliminated. We study the water molecule and observe an improvement compared with previous results. We also apply the method to the van der Walls molecule XeHe2.

FMRFamide-like peptides (FLPs) enhance voltage-gated calcium currents to elicit muscle contraction in the human parasite Schistosoma mansoni.

Schistosomes are amongst the most important and neglected pathogens in the world, and schistosomiasis control relies almost exclusively on a single drug. The neuromuscular system of schistosomes is fertile ground for therapeutic intervention, yet the details of physiological events involved in neuromuscular function remain largely unknown. Short amidated neuropeptides, FMRFamide-like peptides (FLPs), are distributed abundantly throughout the nervous system of every flatworm examined and they produce potent myoexcitation. Our goal here was to determine the mechanism by which FLPs elicit contractions of schistosome muscle fibers. Contraction studies showed that the FLP Tyr-Ile-Arg-Phe-amide (YIRFamide) contracts the muscle fibers through a mechanism that requires Ca2+ influx through sarcolemmal voltage operated Ca2+ channels (VOCCs), as the contractions are inhibited by classical VOCC blockers nicardipine, verapamil and methoxyverapamil. Whole-cell patch-clamp experiments revealed that inward currents through VOCCs are significantly and reversibly enhanced by the application of 1 µM YIRFamide; the sustained inward currents were increased to 190% of controls and the peak currents were increased to 180%. In order to examine the biochemical link between the FLP receptor and the VOCCs, PKC inhibitors calphostin C, RO 31–8220 and chelerythrine were tested and all produced concentration dependent block of the contractions elicited by 1 µM YIRFamide. Taken together, the data show that FLPs elicit contractions by enhancing Ca2+ influx through VOCC currents using a PKC-dependent pathway.

Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes (approximate to hydrodynamic modes) of the underlying physical system, much more than quasi-one- (1D) and two-dimensional (2D) patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the pattern dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for 3D pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a 2D one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given. [S1063-651X(00)09512-X].