Ion dynamics in a supersonic jet: Experiments and simulations.

The authors suggest a model to simulate the dynamics of ions in a supersonic plasma jet. The model relies on experimental argon ion, Ar(+), energy distribution functions measured by a quadrupole mass spectrometer at different positions along the central axis of a supersonic argon plasma jet. The latter is generated by the pressure difference between two vacuum chambers connected through a converging nozzle: a high-pressure chamber (P ≃ 3.20 Pa), where an inductively coupled argon plasma discharge is maintained, and a lower-pressure one (P ≃ 0.11 Pa), where the plasma jet expands. The model is based on the integration of the equations of motion of a single Ar(+), moving along the supersonic jet in a reference system in which neutral species are at rest. Ar(+)-Ar induced dipole interactions are treated using a 12-4 Lennard-Jones potential. The resulting collisions are considered to be purely elastic, and in addition to them, we allow for charge transfer processes. The energy and position of 1000 Ar(+) were calculated, using an integration time step of 10 ps for ion trajectories ranging from 5 mm to 20 mm from the nozzle, well inside the spatial extension of the supersonic jet. The numerically obtained ion energy distribution functions agree remarkably well with the experimental measurements. From our calculations we can draw conclusions about the energy loss and the mean free paths along the jet. In particular, we can distinguish between processes with and without charge transfer, allowing us to determine the effect of charge exchange phenomena in which the ion changes its nature. The calculated mean free paths were used to evaluate the effective cross sections for momentum transfer and charge transfer collisions, valid for ion energies in the range (0.5-10) eV, in very good agreement with those reported in the literature.

Two-dimensional signal reconstruction: the correlation sampling method.

An accurate approach for reconstructing a time-dependent two-dimensional signal from non-synchronized time series recorded at points located on a grid is discussed. The method, denoted as correlation sampling, improves the standard conditional sampling approach commonly employed in the study of turbulence in magnetoplasma devices. Its implementation is illustrated in the case of an artificial time-dependent signal constructed using a fractal algorithm that simulates a fluctuating surface. A statistical method is also discussed for distinguishing coherent (i.e., collective) from purely random (noisy) behavior for such two-dimensional fluctuating phenomena.

Modeling cross correlations within a many-assets market.

A simple model for simulating cross correlations of a many-assets market is discussed. Correlations between assets are initially considered within the context of the well-known one-factor model, in which a driving term common to all stocks is present. The results are compared to those of real market data corresponding to a set of 445 stocks taken from the Standard and Poors 500 index. The model is further extended by introducing a stochastic volatility within each time series using an autoregressive scheme. This artificial market reproduces the empirically observed fat tails in the distribution function of logarithmic price variations and, more important, leads to additional cross correlations between the time series, in better agreement with the real market behavior.

Statistical analysis of correlations and intermittency of a turbulent rotating column in a magnetoplasma device.

A statistical analysis of density fluctuations in a cylindrical non-fusion device is performed. The experimental setup is implemented in order to reach a turbulent behavior of the linear plasma column. Two different turbulent regimes are obtained corresponding to two selected sets of values for the discharge parameters. The first regime displays a rotating column characterized by the presence of a shear layer separating the plasma bulk from the tenuous plasma in the shadow of the limiter, the latter showing a strong intermittent behavior and superdiffusion. The second regime corresponds to a weakly rotating column in which coherence is lost in the plasma bulk and a standard diffusive process takes place in the shadow region. These findings are supported by the calculation of the Hurst's exponent using wavelet-analysis techniques. Furthermore the intermittent behavior is characterized and related to the diffusive process. Finally the shape of the probability distribution function of density fluctuations seems to be well described by an analytical form suggested on the basis of Tsallis generalized statistics.

Self-generated power-law tails in probability distributions.

We consider random processes characterized by the presence of correlations in their variance, or more generally in some of their moments. Typical examples are constituted by autoregressive conditional heteroskedasticity (ARCH) processes which are known to display power-law tails in the associated probability distributions. Here, we determine the corresponding exponents exactly and extend these results to relaxation phenomena which can be expected to play a role in natural sciences.

Multifractal behavior of linear polymers in disordered media.

The scaling behavior of linear polymers in disordered media modeled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p(c) is studied. All possible SAW configurations of N steps on a single backbone configuration are enumerated exactly. We find that the moments of order q of the total number of SAWs obtained by averaging over many backbone configurations display multifractal behavior; i.e., different moments are dominated by different subsets of the backbone. This leads to generalized coordination numbers mu(q) and enhancement exponents gamma(q), which depend on q. Our numerical results suggest that the relation mu(1)=p(c)mu between the first moment mu(1) and its regular lattice counterpart mu is valid.

Neutral evolution of model proteins: diffusion in sequence space and overdispersion.

We stimulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves (1) the structure of the ground state, (2) its thermodynamic stability and (3) its kinetic accessibility. All other mutations are considered lethal and are rejected. We adopt a lattice model, amenable to a reliable solution of the protein folding problem. We prove the existence of extended neutral networks in sequence space-sequences can evolve until their similarity with the starting point is almost the same as for random sequences. Furthermore, we find that the rate of neutral mutations has a broad distribution in sequence space. Due to this fact, the substitution process is overdispersed (the ratio between variance and mean is larger than 1). This result is in contrast with the simplest model of neutral evolution, which assumes a Poisson process for substitutions, and in qualitative agreement with the biological data.

Folding and aggregation of designed proteins.

Protein aggregation is studied by following the simultaneous folding of two designed identical 20-letter amino acid chains within the framework of a lattice model and using Monte Carlo simulations. It is found that protein aggregation is determined by elementary structures (partially folded intermediates) controlled by local contacts among some of the most strongly interacting amino acids and formed at an early stage in the folding process.