Generalized correlation functions for conductance fluctuations and the mesoscopic spin Hall effect

We study the spin Hall conductance fluctuations in ballistic mesoscopic systems. We obtain universal expressions for the spin and charge current fluctuations, cast in terms of current-current autocorrelation functions. We show that the latter are conveniently parametrized as deformed Lorentzian shape lines, functions of an external applied magnetic field and the Fermi energy. We find that the charge current fluctuations show quite unique statistical features at the symplectic-unitary crossover regime. Our findings are based on an evaluation of the generalized transmission coefficients correlation functions within the stub model and are amenable to experimental test. DOI: 10.1103/PhysRevB.86.235112

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

Percolation transition and the onset of nonexponential relaxation in fully frustrated models

We numerically study the dynamical properties of fully frustrated models in two and three dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the large scale effects of frustration, present below the percolation threshold. Moreover, these results are consistent with the picture suggested by Campbell et al. [J. Phys. C 20, L47 (1987)] in the space of configurations.

Dynamic properties of Lennard Jones fluids and liquid metals

The dependence of the dynamic properties of liquid metals and Lennard-Jones fluids on the characteristics of the interaction potentials is analyzed. Molecular-dynamics simulations of liquids in analogous conditions but assuming that their particles interact either through a Lennard-Jones or a liquid-metal potential were carried out. The Lennard-Jones potentials were chosen so that both the effective size of the particles and the depth of the potential well were very close to those of the liquid-metal potentials. In order to investigate the extent to which the dynamic properties of liquids depend on the short-range attractive interactions as well as on the softness of the potential cores, molecular-dynamics simulations of the same systems but assuming purely repulsive interactions with the same potential cores were also performed. The study includes both singleparticle dynamic properties, such as the velocity autocorrelation functions, and collective dynamic properties, such as the intermediate scattering funcfunctions, and collective dynamic properties, such as the intermediate scattering functions, the dynamic structure factors, the longitudinal and transverse current correlations, and the transport coefficients.

Gamma stochastic volatility models

This paper presents gamma stochastic volatility models and investigates its distributional and time series properties. The parameter estimators obtained by the method of moments are shown analytically to be consistent and asymptotically normal. The simulation results indicate that the estimators behave well. The insample analysis shows that return models with gamma autoregressive stochastic volatility processes capture the leptokurtic nature of return distributions and the slowly decaying autocorrelation functions of squared stock index returns for the USA and UK. In comparison with GARCH and EGARCH models, the gamma autoregressive model picks up the persistence in volatility for the US and UK index returns but not the volatility persistence for the Canadian and Japanese index returns. The out-of-sample analysis indicates that the gamma autoregressive model has a superior volatility forecasting performance compared to GARCH and EGARCH models.

Threshold Autoregressive Model for a Time Series Data

In this paper we try to fit a threshold autoregressive (TAR) model to time series data of monthly coconut oil prices at Cochin market. The procedure proposed by Tsay [7] for fitting the TAR model is briefly presented. The fitted model is compared with a simple autoregressive (AR) model. The results are in favour of TAR process. Thus the monthly coconut oil prices exhibit a type of non-linearity which can be accounted for by a threshold model.

Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Ensemble prediction for nowcasting with a convection-permitting model - II: forecast error statistics

A 24-member ensemble of 1-h high-resolution forecasts over the Southern United Kingdom is used to study short-range forecast error statistics. The initial conditions are found from perturbations from an ensemble transform Kalman filter. Forecasts from this system are assumed to lie within the bounds of forecast error of an operational forecast system. Although noisy, this system is capable of producing physically reasonable statistics which are analysed and compared to statistics implied from a variational assimilation system. The variances for temperature errors for instance show structures that reflect convective activity. Some variables, notably potential temperature and specific humidity perturbations, have autocorrelation functions that deviate from 3-D isotropy at the convective-scale (horizontal scales less than 10 km). Other variables, notably the velocity potential for horizontal divergence perturbations, maintain 3-D isotropy at all scales. Geostrophic and hydrostatic balances are studied by examining correlations between terms in the divergence and vertical momentum equations respectively. Both balances are found to decay as the horizontal scale decreases. It is estimated that geostrophic balance becomes less important at scales smaller than 75 km, and hydrostatic balance becomes less important at scales smaller than 35 km, although more work is required to validate these findings. The implications of these results for high-resolution data assimilation are discussed.

The persistence of solar activity indicators and the descent of the sun into Maunder Minimum conditions

The recent low and prolonged minimum of the solar cycle, along with the slow growth in activity of the new cycle, has led to suggestions that the Sun is entering a Grand Solar Minimum (GSMi), potentially as deep as the Maunder Minimum (MM). This raises questions about the persistence and predictability of solar activity. We study the autocorrelation functions and predictability R^2_L(t) of solar indices, particularly group sunspot number R_G and heliospheric modulation potential phi for which we have data during the descent into the MM. For R_G and phi, R^2_L (t) > 0.5 for times into the future of t = 4 and 3 solar cycles, respectively: sufficient to allow prediction of a GSMi onset. The lower predictability of sunspot number R_Z is discussed. The current declines in peak and mean R_G are the largest since the onset of the MM and exceed those around 1800 which failed to initiate a GSMi.

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

Impact of long-range correlations on trend detection in total ozone

Total ozone trends are typically studied using linear regression models that assume a first-order autoregression of the residuals [so-called AR(1) models]. We consider total ozone time series over 60°S–60°N from 1979 to 2005 and show that most latitude bands exhibit long-range correlated (LRC) behavior, meaning that ozone autocorrelation functions decay by a power law rather than exponentially as in AR(1). At such latitudes the uncertainties of total ozone trends are greater than those obtained from AR(1) models and the expected time required to detect ozone recovery correspondingly longer. We find no evidence of LRC behavior in southern middle-and high-subpolar latitudes (45°–60°S), where the long-term ozone decline attributable to anthropogenic chlorine is the greatest. We thus confirm an earlier prediction based on an AR(1) analysis that this region (especially the highest latitudes, and especially the South Atlantic) is the optimal location for the detection of ozone recovery, with a statistically significant ozone increase attributable to chlorine likely to be detectable by the end of the next decade. In northern middle and high latitudes, on the other hand, there is clear evidence of LRC behavior. This increases the uncertainties on the long-term trend attributable to anthropogenic chlorine by about a factor of 1.5 and lengthens the expected time to detect ozone recovery by a similar amount (from ∼2030 to ∼2045). If the long-term changes in ozone are instead fit by a piecewise-linear trend rather than by stratospheric chlorine loading, then the strong decrease of northern middle- and high-latitude ozone during the first half of the 1990s and its subsequent increase in the second half of the 1990s projects more strongly on the trend and makes a smaller contribution to the noise. This both increases the trend and weakens the LRC behavior at these latitudes, to the extent that ozone recovery (according to this model, and in the sense of a statistically significant ozone increase) is already on the verge of being detected. The implications of this rather controversial interpretation are discussed.

Field-perpendicular and field-aligned plasma flows observed by EISCAT during a prolonged period of northward IMF

The effect of a prolonged period of strongly northward Interplanetary Magnetic Field (IMF) on the high-latitude F-region is studied using data from the EISCAT Common Programme Zero mode of operation on 11–12 August 1982. The analysis of the raw autocorrelation functions is kept to the directly derived parameters Ne, Te, Ti and velocity, and limits are defined for the errors introduced by assumptions about ion composition and by changes in the transmitted power and system constant. Simple data-cleaning criteria are employed to eliminate problems due to coherent signals and large background noise levels. The observed variations in plasma densities, temperatures and velocities are interpreted in terms of supporting data from ISEE-3 and local riometers and magnetometers. Both field-aligned and field-perpendicular plasma flows at Tromsø showed effects of the northward IMF: convection was slow and irregular and field-aligned flow profiles were characteristic of steady-state polar wind outflow with flux of order 1012 m−2 s−1. This period followed a strongly southward IMF which had triggered a substorm. The substorm gave enhanced convection, with a swing to equatorward flow and large (5 × 1012 m−2 s−1), steady-state field-aligned fluxes, leading to the possibility of O+ escape into the magnetosphere. The apparent influence of the IMF over both field-perpendicular and field-aligned flows is explained in terms of the cross-cap potential difference and the location of the auroral oval.

Indagine delle proprietà statistiche di serie temporali di posizione applicata al caso della stazione permanente GPS della base Mario Zucchelli in Terra Vittoria (Antartide)

Da ormai sette anni la stazione permanente GPS di Baia Terranova acquisisce dati giornalieri che opportunamente elaborati consentono di contribuire alla comprensione della dinamica antartica e a verificare se modelli globali di natura geofisica siano aderenti all’area di interesse della stazione GPS permanente. Da ricerche bibliografiche condotte si è dedotto che una serie GPS presenta molteplici possibili perturbazioni principalmente dovute a errori nella modellizzazione di alcuni dati ancillari necessari al processamento. Non solo, da alcune analisi svolte, è emerso come tali serie temporali ricavate da rilievi geodetici, siano afflitte da differenti tipologie di rumore che possono alterare, se non opportunamente considerate, i parametri di interesse per le interpretazioni geofisiche del dato. Il lavoro di tesi consiste nel comprendere in che misura tali errori, possano incidere sui parametri dinamici che caratterizzano il moto della stazione permanente, facendo particolare riferimento alla velocità del punto sul quale la stazione è installata e sugli eventuali segnali periodici che possono essere individuati.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers [Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013)1751-811310.1088/1751-8113/46/3/035501; Nath, Phys. Rev. E 88, 013010 (2013)PLEEE81539-375510.1103/PhysRevE.88.013010] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000 K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Bridging large and small scales of water models using hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework

This thesis presents a two-dimensional water model investigation and development of a multiscale method for the modelling of large systems, such as virus in water or peptide immersed in the solvent. We have implemented a two-dimensional ‘Mercedes Benz’ (MB) or BN2D water model using Molecular Dynamics. We have studied its dynamical and structural properties dependence on the model’s parameters. For the first time we derived formulas to calculate thermodynamic properties of the MB model in the microcanonical (NVE) ensemble. We also derived equations of motion in the isothermal–isobaric (NPT) ensemble. We have analysed the rotational degree of freedom of the model in both ensembles. We have developed and implemented a self-consistent multiscale method, which is able to communicate micro- and macro- scales. This multiscale method assumes, that matter consists of the two phases. One phase is related to micro- and the other to macroscale. We simulate the macro scale using Landau Lifshitz-Fluctuating Hydrodynamics, while we describe the microscale using Molecular Dynamics. We have demonstrated that the communication between the disparate scales is possible without introduction of fictitious interface or approximations which reduce the accuracy of the information exchange between the scales. We have investigated control parameters, which were introduced to control the contribution of each phases to the matter behaviour. We have shown, that microscales inherit dynamical properties of the macroscales and vice versa, depending on the concentration of each phase. We have shown, that Radial Distribution Function is not altered and velocity autocorrelation functions are gradually transformed, from Molecular Dynamics to Fluctuating Hydrodynamics description, when phase balance is changed. In this work we test our multiscale method for the liquid argon, BN2D and SPC/E water models. For the SPC/E water model we investigate microscale fluctuations which are computed using advanced mapping technique of the small scales to the large scales, which was developed by Voulgarakisand et. al.