Complex Time Evolution Research Articles

Particle densities of the pulsed dielectric barrier discharges in nitrogen at atmospheric pressure

Pulsed dielectric barrier discharges (DBDs) have become a promising solution to generate atmospheric-pressure non-equilibrium plasmas. In this work, a one-dimensional fluid model is carried out to research particle densities of the pulsed nitrogen DBDs at atmospheric pressure. Averaged particle densities, time evolutions of axial distributions of particle densities and influences of discharge gap distance dg on the particle densities are systematically illustrated and discussed. The calculation results show that averaged electron densities are lower than averaged N2+ densities, but higher than other averaged ion densities. Time evolutions of axial distributions of electron, N+ and N2+ densities show two peaks during rising and falling phases of applied voltage when dg is 0.2 cm but present gradual increases during pulse width when dg is 0.6 cm, which are similar to those of N2(a′) and N2(B). Maximums of N3+ densities are close to the momentary cathode under dg of 0.2 cm but locate near the grounded electrode under dg of 0.6 cm, which are alike to those of N2(A) and N2(C). Besides, N4+ densities nearby the momentary anode are higher than those nearby the momentary cathode when dg is 0.2 cm. N(2D) has low averaged particle densities and complex time evolutions compared to N.

On Complexified Analytic Hamiltonian Flows and Geodesics on the Space of Kähler Metrics

In the case of a compact real analytic symplectic manifold M we describe an approach to the complexification of Hamiltonian flows [Se, Do1, Th1] and corresponding geodesics on the space of Kahler metrics. In this approach, motivated by recent work on quantization, the complexified Hamiltonian flows act, through the Grobner theory of Lie series, on the sheaf of complex valued real analytic functions, changing the sheaves of holomorphic functions. This defines an action on the space of (equivalent) complex structures on M and also a direct action on M. This description is related to the approach of [BLU] where one has an action on a complexification M_C of M followed by projection to M. Our approach allows for the study of some Hamiltonian functions which are not real analytic. It also leads naturally to the consideration of continuous degenerations of diffeomorphisms and of Kahler structures of M. Hence, one can link continuously (geometric quantization) real, and more general non-Kahler, polarizations with Kahler polarizations. This corresponds to the extension of the geodesics to the boundary of the space of Kahler metrics. Three illustrative examples are considered. We find an explicit formula for the complex time evolution of the Kahler potential under the flow. For integral symplectic forms, this formula corresponds to the complexification of the prequantization of Hamiltonian symplectomorphisms. We verify that certain families of Kahler structures, which have been studied in geometric quantization, are geodesic families.

Computer-controlled Two-Roll Mill flow cell for the experimental study of particle and drop dynamics

In this paper, we present for the deformation of a drop under flow, using an experimental device based on the Two-Roll Mill geometry. To study the drop deformation for extended periods of time, the use of this device requires implementation of a non-linear control scheme that has not previously been used. The device and control scheme generate well characterized flow fields, which present a richness of behavior of the drop dynamics that smoothly varies from that observed in simple shear flows, where the vorticity dominates, to those observed in purely Hyperbolic flows. The Two-Roll Mill flow cell allows detailed studies such as the critical capillary number versus the critical viscosities ratio for elongational flows with significant vorticity. As well, the experimental device is able to track the time evolution of the drop shape permitting to study its complex time evolutions. Experiments were performed for sub-millimeter size drops with the determination of the surface tension with high accuracy.

Approximating Time-Dependent Quantum Statistical Properties

Computing quantum dynamics in condensed matter systems is an open challenge due to the exponential scaling of exact algorithms with the number of degrees of freedom. Current methods try to reduce the cost of the calculation using classical dynamics as the key ingredient of approximations of the quantum time evolution. Two main approaches exist, quantum classical and semi-classical, but they suffer from various difficulties, in particular when trying to go beyond the classical approximation. It may then be useful to reconsider the problem focusing on statistical time-dependent averages rather than directly on the dynamics. In this paper, we discuss a recently developed scheme for calculating symmetrized correlation functions. In this scheme, the full (complex time) evolution is broken into segments alternating thermal and real-time propagation, and the latter is reduced to classical dynamics via a linearization approximation. Increasing the number of segments systematically improves the result with respect to full classical dynamics, but at a cost which is still prohibitive. If only one segment is considered, a cumulant expansion can be used to obtain a computationally efficient algorithm, which has proven accurate for condensed phase systems in moderately quantum regimes. This scheme is summarized in the second part of the paper. We conclude by outlining how the cumulant expansion formally provides a way to improve convergence also for more than one segment. Future work will focus on testing the numerical performance of this extension and, more importantly, on investigating the limit for the number of segments that goes to infinity of the approximate expression for the symmetrized correlation function to assess formally its convergence to the exact result.

Determination of Ionization and Tunneling Times in High-Order Harmonic Generation

From the numerical solution of the time-dependent Schrödinger equation, we obtain the times of ionization and return of the laser-driven electron in high-order harmonic generation by probing the dynamics with a second harmonic field polarized orthogonal to the fundamental field and observing the harmonic emission in dependence on the two-color delay. Our retrieval method using complex-time evolution gives ionization and return times in excellent agreement with the quantum-orbit model, while a retrieval based on real-time classical dynamics can introduce substantial errors. Because of the imaginary parts, the harmonic signal polarized along the probe field is nonzero for any two-color delay. The tunneling time can be retrieved under an assumption for the return time.

Complex time evolution in geometric quantization and generalized coherent state transforms

For the cotangent bundle T⁎K of a compact Lie group K, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space L2(K) under an infinite-dimensional family of Hamiltonian flows. For each such flow, we construct a generalized coherent state transform (CST), which is a unitary isomorphism between L2(K) and a certain weighted L2-space of holomorphic functions. For a particular set of choices, we show that this isomorphism is naturally decomposed as a product of a Heisenberg-type evolution (for complex time −τ) within L2(K), followed by a polarization-changing geometric-quantization evolution (for complex time +τ). In this case, our construction yields the usual generalized Segal–Bargmann transform of Hall. We show that the infinite-dimensional family of Hamiltonian flows can also be understood in terms of Thiemannʼs “complexifier” method (which generalizes the construction of adapted complex structures).

Discovery of Metastable Helium Absorption Lines in V1280 Scorpii

Abstract We report on the discovery of blue-shifted metastable He I* absorption lines at 3188 Å and 3889 Å with multiple components on high-resolution spectra ($ R$$ \sim$ 60000) of V1280 Scorpii. Similar multiple absorption lines associated with the Na I D doublet as well as Ca II H and K were observed. Na I D doublet absorption lines have been observed since 2009, while the metastable He I* absorption lines were absent in 2009, but were detected in 2011 (four years after the burst). We have found different time variations in the depths and velocities of blue-shifted absorption components among He I*, Na I, and Ca II. The complex time evolutions of these lines can be explained by assuming changes in the density and recombination/ionization rate when the ejecta expands and the photosphere contracts to become hotter. The multiple absorption lines originate in ejected materials consisting of clumpy components, which obscure a significant part of the continuum emitting region. We estimate the total mass of the ejected material to be on the order of $ \sim$ 10$ ^{-4}$$ M_{\odot}$ , using metastable He I*$ \lambda\lambda$ 3188 and 3889 absorption lines.

Radiation from accelerated particles in relativistic jets with shocks, shear-flow, and reconnection

We have investigated particle acceleration and shock structure associated with an unmagnetized relativistic jet propagating into an unmagnetized plasma for electron-positron and electron-ion plasmas. Strong magnetic fields generated in the trailing jet shock lead to transverse deflection and acceleration of the electrons. We have self-consistently calculated the radiation from the electrons accelerated in the turbulent magnetic fields for different jet Lorentz factors. We find that the synthetic spectra depend on the bulk Lorentz factor of the jet, the jet temperature, and the strength of the magnetic fields generated in the shock. We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic (core) jet and an unmagnetized sheath plasma. We discuss particle acceleration in collimation shocks for AGN jets formed by relativistic MHD simulations. Our calculated spectra should lead to a better understanding of the complex time evolution and/or spectral structure from gamma-ray bursts, relativistic jets, and supernova remnants.

Radiation from accelerated particles in relativistic jets with shocks, shear-flow, and reconnection

We have investigated particle acceleration and shock structure associated with an unmagnetized relativistic jet propagating into an unmagnetized plasma. Strong magnetic fields generated in the trailing jet shock lead to transverse deflection and acceleration of the electrons. We have self-consistently calculated the radiation from the electrons accelerated in the turbulent magnetic fields. We find that the synthetic spectra depend on the bulk Lorentz factor of the jet, the jet temperature, and the strength of the magnetic fields generated in the shock. We have also begun study of electron acceleration in the strong magnetic fields generated by kinetic shear (Kelvin-Helmholtz) instabilities. Our calculated spectra should lead to a better understanding of the complex time evolution and/or spectral structure from gamma-ray bursts, relativistic jets, and supernova remnants.

Ions Transport and Adsorption Mechanisms in Porous Electrodes During Capacitive-Mixing Double Layer Expansion (CDLE).

A model of the electro-diffusion of ions in porous electrodes is applied to analyze the dynamics of capacitive-mixing extraction of energy from salinity gradients with carbon porous electrodes. The complex time-evolution of the cell voltage observed in experiments is satisfactorily described. The asymmetry on the duration of the solution-change steps performed in open circuit is found to be due to the nonlinear voltage–concentration relationship of the electric double layers and to a current that redistributes the counterions along the depth of the electrode leading to nonuniform charge and salt adsorption. The validated model is an essential tool for the design and optimization of renewable energy extraction by this technique.

SIMULATION OF RELATIVISTIC JETS AND ASSOCIATED SELF-CONSISTENT RADIATION

Plasma instabilities are responsible not only for the onset and mediation of collisionless shocks but also for the associated acceleration of particles. We have investigated particle acceleration and shock structure associated with an unmagnetized relativistic electron-positron jet propagating into an unmagnetized electron-positron plasma. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic-like shock structure. In the leading shock, electron density increases by a factor of about 3.5 in the simulation frame. Strong electromagnetic fields are generated in the trailing shock and provide an emission site. These magnetic fields contribute to the electrons transverse deflection and, more generally, relativistic acceleration behind the shock. We have calculated, self-consistently, the radiation from electrons accelerated in the turbulent magnetic fields. We found that the synthetic spectra depend on the Lorentz factor of the jet, its thermal temperature and strength of the generated magnetic fields. The properties of the radiation may be important for understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets in general, and supernova remnants.

Modal versus nonmodal linear stability analysis of river dunes

When a free surface turbulent shear flow interacts with a deformable cohesionless sediment bottom, dune patterns can arise and perform a complex time evolution. These bed forms are very widespread in fluvial environments and have catalyzed an intense research activity of both an applicative and theoretical nature. This work investigates the non-normality of the linearized mathematical operator which rules the initial value problem, in order to detect possible transient growths and make a comparison with the picture described by the outcome of the eigenvalue problem. The dune dynamics have resulted to be heavily non-normal in large regions of the parameter space and to be able to develop important transient growths, even for asymptotically stable wavenumbers. The effects on progressive wavelength elongation that has been observed in some experiments are discussed, and an explanation, based on purely linearly mechanisms, is proposed and compared with some experimental data. A discussion about the saturation length concept in the sediment transport modeling is also proposed.

Radiation from accelerated particles in shocks

AbstractRecent PIC simulations of relativistic electron-positron (electron-ion) jets injected into a stationary medium show that particle acceleration occurs in the shocked regions. Simulations show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields and for particle acceleration. These magnetic fields contribute to the electron's transverse deflection behind the shock. The “jitter” radiation from deflected electrons in turbulent magnetic fields has properties different from synchrotron radiation calculated in a uniform magnetic field. This jitter radiation may be important for understanding the complex time evolution and/or spectral structure of gamma-ray bursts, relativistic jets in general, and supernova remnants. In order to calculate radiation from first principles and go beyond the standard synchrotron model, we have used PIC simulations. We present synthetic spectra to compare with the spectra obtained from Fermi observations.

Simulation of relativistic shocks and associated radiation from turbulent magnetic fields

AbstractRecent PIC simulations of relativistic electron-positron (electron-ion) jets injected into a stationary medium show that particle acceleration occurs in the shocked regions. Simulations show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields and for particle acceleration. These magnetic fields contribute to the electron's transverse deflection behind the shock. The “jitter” radiation from deflected electrons in turbulent magnetic fields has different properties from synchrotron radiation calculated in a uniform magnetic field. This jitter radiation may be important for understanding the complex time evolution and/or spectral structure of gamma-ray bursts, relativistic jets in general, and supernova remnants. In order to calculate radiation from first principles and go beyond the standard synchrotron model, we have used PIC simulations. We will present detailed spectra for conditions relevant to various astrophysical sites of collisionless shock formation. In particular we will discuss application to GRBs and SNRs.

Acclimation to Heat Interpreted from the Analysis of Heart-Rate Variability by the Multipole Method

The Multipole Method is a recently developed method to describe time series with highly complex time evolution, such as cardiac rhythm. We hypothesized that applying this method in the analysis of heart rate variability (HRV) could provide valuable physiological information that usually cannot be extracted from the commonly used time and frequency domains analyses. The hypothesis was tested during a 12-day heat acclimation process on four young healthy, male subjects. On the first and the last day of acclimation, HRV was investigated by two different measures: the conventional Standard Deviation of Normal to Normal R-R intervals (SDNN), and the Multipole Method. The analyses revealed that stress on the cardiovascular system was still evident after the 12th day of acclimation, but both methods showed that stress was diminished. Using the Multipole analysis, following acclimation to heat, the autonomic nervous system shows a more effective response. We conclude that the Multipole Method is a very valuable tool for investigating the series of R-R intervals, which are a non-stationary and non-linear complex time series, reflecting a complex regulatory physiological mechanism. Specifically, we showed that stress on the cardiovascular system diminishes following the course of acclimation, but not to its complete relief, which indicates that acclimation to heat is a much longer process than can be judged from the early phenotypic picture.

Meteorological complexity in the Amazonian area of Ecuador: An approach based on dynamical system theory

Meteorological rhythms and trends are important components for ecosystem functioning. The complex time evolution of meteorology is often difficult to capture using linear methods. The objective of this work was to use basic concepts of dynamical system theory for assessing time evolution of daily records from six local meteorological variables collected at the Amazonian basin. We analysed rainfall, relative humidity, evaporation, minimum temperature, relative sunshine duration and evaporation/precipitation ratio. Data were collected from Puyo meteorological station, Pastaza Province, Ecuador. Data sets covered 4 years (from 1st January 2001 to 1st January 2005) (a total of 1460 data points). The TISEAN Software Package (public domain software available at http://www.mpipks-dresdren.mpg.de/∼tisean) was used for deriving nonlinear parameters from each time series. We found interesting evidence of chaotic behaviour as maximal Lyapunov exponents were positive for all time series considered. These results were consistent with those computed from corresponding surrogate time series. Positive Lyapunov exponents allow an estimation of the lead time of correlation for making reliable predictions.

Experimental properties of an efficient stress-dependent magnetostriction model

In this paper a generalization of a stress-dependent magnetostriction phenomenological model is presented. The model makes use of a classical Preisach operator and of a memoryless bivariate function and includes a pure elastic contribution. It is shown that, even if the structure of the model is simple, the operator state is still influenced by the applied stress. This property is important because the model is able to catch real magnetostrictive behavior in the presence of complex time evolutions of both the variables, current and stress. Experimental and numerical results confirm the effectiveness of the proposed approach.

Three‐dimensional MHD Simulation of the 2003 October 28 Coronal Mass Ejection: Comparison with LASCO Coronagraph Observations

We numerically model the coronal mass ejection (CME) event of 2003 October 28 that erupted from AR 10486 and propagated to Earth in less than 20 hr, causing severe geomagnetic storms. The magnetohydrodynamic (MHD) model is formulated by first arriving at a steady state corona and solar wind employing synoptic magnetograms. We initiate two CMEs from the same active region, one approximately a day earlier that preconditions the solar wind for the much faster CME on the 28th. This second CME travels through the corona at a rate of over 2500 km s−1, driving a strong forward shock. We clearly identify this shock in an image produced by the Large Angle Spectrometric Coronagraph (LASCO) C3 and reproduce the shock and its appearance in synthetic white-light images from the simulation. We find excellent agreement with both the general morphology and the quantitative brightness of the model CME with LASCO observations. These results demonstrate that the CME shape is largely determined by its interaction with the ambient solar wind and may not be sensitive to the initiation process. We then show how the CME would appear as observed by wide-angle coronagraphs on board the Solar Terrestrial Relations Observatory (STEREO) spacecraft. We find complex time evolution of the white-light images as a result of the way in which the density structures pass through the Thomson sphere. The simulation is performed with the Space Weather Modeling Framework (SWMF).

PARTICLE ACCELERATION, MAGNETIC FIELD GENERATION, AND ASSOCIATED EMISSION IN COLLISIONLESS RELATIVISTIC JETS

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., active galactic nuclei (AGNs), gamma-ray bursts (GRBs), and galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations using injected relativistic electron-ion (electron-positron) jets show that acceleration occurs within the downstream jet. Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, other two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electrons' transverse deflection behind the jet head. The "jitter" radiation from deflected electrons has different properties to synchrotron radiation which assumes a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.

Comment on “Regularizing capacity of metabolic networks”

In a recent paper, Marr, Müller-Linow, and Hütt [Phys. Rev. E 75, 041917 (2007)] investigate an artificial dynamic system on metabolic networks. They find a less complex time evolution of this dynamic system in real networks, compared to networks of null models. The authors argue that this suggests that metabolic network structure is a major factor behind the stability of biochemical steady states. We reanalyze the same kind of data using a dynamic system modeling actual reaction kinetics. The conclusions about stability, from our analysis, are inconsistent with those of Marr We argue that this issue calls for a more detailed type of modeling.