Structural changes in quasi-one-dimensional many-electron systems: From linear to zigzag and beyond

Many-electron systems confined to a quasi-one-dimensional geometry by a cylindrical distribution of positive charge have been investigated by density functional computations in the unrestricted local spin density approximation. Our investigations have been focused on the low-density regime, in which electrons are localized. The results reveal a wide variety of different charge and spin configurations, including linear and zig-zag chains, single-and double-strand helices, and twisted chains of dimers. The spin-spin coupling turns from weakly antiferromagnetic at relatively high density, to weakly ferromagnetic at the lowest densities considered in our computations. The stability of linear chains of localized charge has been investigated by analyzing the radial dependence of the self-consistent potential and by computing the dispersion relation of low-energy harmonic excitations.

Real-valued fixed-complexity sphere decoder for high dimensional QAM-MIMO systems

The development of high performance, low computational complexity detection algorithms is a key challenge for real-time Multiple-Input Multiple-Output (MIMO) communication system design. The Fixed-Complexity Sphere Decoder (FSD) algorithm is one of the most promising approaches, enabling quasi-ML decoding accuracy and high performance implementation due to its deterministic, highly parallel structure. However, it suffers from exponential growth in computational complexity as the number of MIMO transmit antennas increases, critically limiting its scalability to larger MIMO system topologies. In this paper, we present a solution to this problem by applying a novel cutting protocol to the decoding tree of a real-valued FSD algorithm. The new Real-valued Fixed-Complexity Sphere Decoder (RFSD) algorithm derived achieves similar quasi-ML decoding performance as FSD, but with an average 70% reduction in computational complexity, as we demonstrate from both theoretical and implementation perspectives for Quadrature Amplitude Modulation (QAM)-MIMO systems.

Existence of multibreathers in one-dimensional Debye crystals

The existence of highly localized multisite oscillatory structures (discrete multibreathers) in a nonlinear Klein-Gordon chain which is characterized by an inverse dispersion law is proven and their linear stability is investigated. The results are applied in the description of vertical (transverse, off-plane) dust grain motion in dusty plasma crystals, by taking into account the lattice discreteness and the sheath electric and/or magnetic field nonlinearity. Explicit values from experimental plasma discharge experiments are considered. The possibility for the occurrence of multibreathers associated with vertical charged dust grain motion in strongly coupled dusty plasmas (dust crystals) is thus established. From a fundamental point of view, this study aims at providing a rigorous investigation of the existence of intrinsic localized modes in Debye crystals and/or dusty plasma crystals and, in fact, suggesting those lattices as model systems for the study of fundamental crystal properties.

One-dimensional particle simulation of the filamentation instability: Electrostatic field driven by the magnetic pressure gradient force

Two counterpropagating cool and equally dense electron beams are modeled with particle-in-cell simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasiplanar filament boundary. It is confirmed that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.

Boson pairs in a one-dimensional split trap

We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonic trapping potential with a tunable zero-ranged barrier at the trap center. The full characterization of the ground state is done by calculating the reduced single-particle density, the momentum distribution, and the two-particle entanglement. We derive several analytical expressions in the limit of infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle interactions by numerical solution. As pair interactions in double wells form a fundamental building block for many-body systems in periodic potentials, our results have implications for a wide range of problems.

B-spline methods in R-matrix theory for scattering in two-electron systems

The use of B-spline basis sets in R-matrix theory for scattering processes has been investigated. In the present approach a B-spline basis is used for the description of the inner region, which is matched to the physical outgoing wavefunctions by the R-matrix. Using B-splines, continuum basis functions can be determined easily, while pseudostates can be included naturally. The accuracy for low-energy scattering processes is demonstrated by calculating inelastic scattering cross sections for e colliding on H. Very good agreement with other calculations has been obtained. Further extensions of the codes to quasi two-electron systems and general atoms are discussed as well as the application to (multi) photoionization.

Recoil-induced electronic excitation and ionization in one-and two-electron ions

The electronic redistribution of an ion or atom induced by a sudden recoil of the nucleus occurring during the emission or capture of a neutral particle is theoretically investigated. For one-electron systems, analytical expressions are derived for the electronic transition probabilities to bound and continuum states. The quality of a B-spline basis set approach is evaluated from a detailed comparison with the analytical results. This numerical approach is then used Io study the dynamics of two-electron systems (neutral He and Ne ) using correlated wavefunctions for both the target and daughter ions. The total transition probabilities to discrete states, autoionizing states and direct single- and double-ionization probabilities are calculated from the pseudospectra. Sum rules for transition probabilities involving an initial bound state and a complete final series are discussed.

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

Analysis procedure for calculation of electron energy distribution functions from incoherent Thomson scattering spectra

Incoherent Thomson scattering (ITS) provides a nonintrusive diagnostic for the determination of one-dimensional (1D) electron velocity distribution in plasmas. When the ITS spectrum is Gaussian its interpretation as a three-dimensional (3D) Maxwellian velocity distribution is straightforward. For more complex ITS line shapes derivation of the corresponding 3D velocity distribution and electron energy probability distribution function is more difficult. This article reviews current techniques and proposes an approach to making the transformation between a 1D velocity distribution and the corresponding 3D energy distribution. Previous approaches have either transformed the ITS spectra directly from a 1D distribution to a 3D or fitted two Gaussians assuming a Maxwellian or bi-Maxwellian distribution. Here, the measured ITS spectrum transformed into a 1D velocity distribution and the probability of finding a particle with speed within 0 and given value v is calculated. The differentiation of this probability function is shown to be the normalized electron velocity distribution function. (C) 2003 American Institute of Physics.

Modelling the mechanical response of the Reed-mouthpiece-lip system of a clarinet. Part I. A one-dimensional distributed model

The motion of a clarinet reed that is clamped to a mouthpiece and supported by a lip is simulated in the time-domain using finite difference methods. The reed is modelled as a bar with non-uniform cross section, and is described using a one-dimensional, fourth-order partial differential equation. The interactions with the mouthpiece Jay and the player's lip are taken into account by incorporating conditional contact forces in the bar equation. The model is completed by clamped-free boundary conditions for the reed. An implicit finite difference method is used for discretising the system, and values for the physical parameters are chosen both from laboratory measurements and by accurate tuning of the numerical simulations. The accuracy of the numerical system is assessed through analysis of frequency warping effects and of resonance estimation. Finally, the mechanical properties of the system are studied by analysing its response to external driving forces. In particular, the effects of reed curling are investigated.

Phase diagram of spin-1 bosons on one-dimensional lattices

Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S=1 Heisenberg model with biquadratic interaction.

One Dimensional Modeling of a Turbogenerating Spark Ignition Engine Operating on Biogas

Turbocompounding is generally regarded as the process of recovering a proportion of the exhaust gas energy from a reciprocating engine and applying it to the output power of the crankshaft. In conventional turbocompounding, the power turbine has been mechanically connected to the crankshaft but now a new method has emerged. Recent advances in high speed electrical machines have enabled the power turbine to be coupled to an electric generator. Decoupling the power turbine from the crankshaft and coupling it to a generator allows the power electronics to control the turbine speed independently in order to optimize the turbine efficiency for different engine operating conditions.