Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

The spatial patterns of the tau immunopositive neuronal cytoplasmic inclusions (NCI) in the tauopathies

Tau positive neuronal cytoplasmic inclusions (NCI) are the ‘hallmark’ pathological feature of several neurodegenerative diseases collectively known as the tauopathies. This study compared the spatial patterns of various types of NCI in selected tauopathies including the neurofibrillary tangles (NFT) in Alzheimer's disease (AD) and progressive supranuclear palsy (PSP), Pick bodies (PB) in Pick’s disease (PiD), and the tau positive (tau+) neurons in corticobasal degeneration (CBD). In the cerebral cortex of these disorders, the tau+ NCI were distributed in clusters and in a significant proportion of analyses, the clusters were distributed with a regular periodicity parallel to the pia mater. The inclusions in AD, PiD and CBD exhibited a similar range of spatial patterns but in PSP were less frequently clustered and more frequently randomly distributed. In gyri where the NCI were clustered, there was a significant difference in mean cluster size between disorders. Hence, clusters of NFT in AD were larger than those in PSP and the tau+ neurons in CBD and clusters of PB in PiD were larger than the tau+ neurons in CBD and the NFT in PSP. The cluster size of the tau+ neurons in CBD was similar to the NFT in PSP. The data suggest that the formation of clusters of NCI, regularly distributed parallel to the pia mater, is a common feature of the tauopathies indicating similar patterns of cortical degeneration and pathogenic mechanisms across different diseases. Furthermore, the data suggest that cortical degeneration affecting the short and long cortico-cortical pathways may be a characteristic of the tauopathies.

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

Techniques for determining bias and stability in satellite altimeters

The case for monitoring large-scale sea level variability is established in the context of the estimation of the extent of anthropogenic climate change. Satellite altimeters are identified as having the potential to monitor this change with high resolution and accuracy. Possible sources of systematic errors and instabilities in these instruments which would be hurdles to the most accurate monitoring of such ocean signals are examined. Techniques for employing tide gauges to combat such inaccuracies are proposed and developed. The tide gauge at Newhaven in Sussex is used in conjunction with the nearby satellite laser ranger and high-resolution ocean models to estimate the absolute bias of the TOPEX, Poseidon, ERS 1 and ERS 2 altimeters. The theory which underlies the augmentation of altimeter measurements with tide gauge data is developed. In order to apply this, the tide gauges of the World Ocean Circulation Experiment are assessed and their suitability for altimeter calibration is determined. A reliable subset of these gauges is derived. A method of intra-altimeter calibration is developed using these tide gauges to remove the effect of variability over long time scales. In this way the long-term instability in the TOPEX range measurement is inferred and the drift arising from the on-board ultra stable oscillator is thus detected. An extension to this work develops a method for inter-altimeter calibration, allowing the systematic differences between unconnected altimeters to be measured. This is applied to the TOPEX and ERS 1 altimeters.

Spatial patterns of FUS-immunoreactive neuronal cytoplasmic inclusions (NCI) in neuronal intermediate filament inclusion disease (NIFID)

Neuronal intermediate filament inclusion disease (NIFID), a rare form of frontotemporal lobar degeneration (FTLD), is characterized neuropathologically by focal atrophy of the frontal and temporal lobes, neuronal loss, gliosis, and neuronal cytoplasmic inclusions (NCI) containing epitopes of ubiquitin and neuronal intermediate filament (IF) proteins. Recently, the 'fused in sarcoma' (FUS) protein (encoded by the FUS gene) has been shown to be a component of the inclusions of NIFID. To further characterize FUS proteinopathy in NIFID, we studied the spatial patterns of the FUS-immunoreactive NCI in frontal and temporal cortex of 10 cases. In the cerebral cortex, sectors CA1/2 of the hippocampus, and the dentate gyrus (DG), the FUS-immunoreactive NCI were frequently clustered and the clusters were regularly distributed parallel to the tissue boundary. In a proportion of cortical gyri, cluster size of the NCI approximated to those of the columns of cells was associated with the cortico-cortical projections. There were no significant differences in the frequency of different types of spatial patterns with disease duration or disease stage. Clusters of NCI in the upper and lower cortex were significantly larger using FUS compared with phosphorylated, neurofilament heavy polypeptide (NEFH) or a-internexin (INA) immunohistochemistry (IHC). We concluded: (1) FUS-immunoreactive NCI exhibit similar spatial patterns to analogous inclusions in the tauopathies and synucleinopathies, (2) clusters of FUS-immunoreactive NCI are larger than those revealed by NEFH or ???, and (3) the spatial patterns of the FUS-immunoreactive NCI suggest the degeneration of the cortico-cortical projections in NIFID.

Spatial patterns of TDP-43 neuronal cytoplasmic inclusions (NCI) in fifteen cases of frontotemporal lobar degeneration with TDP-43 proteinopathy (FTLD-TDP)

Neuronal cytoplasmic inclusions (NCI) immunoreactive for transactive response DNA-binding protein (TDP-43) are the pathological hallmark of frontotemporal lobar degeneration with TDP-43 proteinopathy (FTLD-TDP). We studied the spatial patterns of the TDP-43 immunoreactive NCI in the frontal and temporal cortex of 15 cases of FTLD-TDP. The NCI were distributed parallel to the tissue boundary predominantly in regular clusters 50-400 µm in diameter. In five cortical areas, the size of the clusters approximated to the cells of the cortico-cortical pathways. In most regions, cluster size was smaller than 400 µm. There were no significant differences in spatial patterns between familial and sporadic cases. Cluster size of the NCI was not correlated with disease duration, brain weight, Braak stage, or disease subtype. The spatial pattern of the NCI was similar to that of neuronal inclusions in other neurodegenerative diseases and may reflect a common pattern of degeneration involving the cortico-cortical projections.

Time scale analysis for fluidized bed melt granulation I: granule-granule and granule-droplet collision rates

Fluidized bed spray granulators (FBMG) are widely used in the process industry for particle size growth; a desirable feature in many products, such as granulated food and medical tablets. In this paper, the first in a series of four discussing the rate of various microscopic events occurring in FBMG, theoretical analysis coupled with CFD simulations have been used to predict granule–granule and droplet–granule collision time scales. The granule–granule collision time scale was derived from principles of kinetic theory of granular flow (KTGF). For the droplet–granule collisions, two limiting models were derived; one is for the case of fast droplet velocity, where the granule velocity is considerable lower than that of the droplet (ballistic model) and another for the case where the droplet is traveling with a velocity similar to the velocity of the granules. The hydrodynamic parameters used in the solution of the above models were obtained from the CFD predictions for a typical spray fluidized bed system. The granule–granule collision rate within an identified spray zone was found to fall approximately within the range of 10-2–10-3 s, while the droplet–granule collision was found to be much faster, however, slowing rapidly (exponentially) when moving away from the spray nozzle tip. Such information, together with the time scale analysis of droplet solidification and spreading, discussed in part II and III of this study, are useful for probability analysis of the various event occurring during a granulation process, which then lead to be better qualitative and, in part IV, quantitative prediction of the aggregation rate.

Fluctuation-induced traffic congestion in heterogeneous networks

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic away from failed or congested elements. Here we model another type of the network reaction to congestion - a sharp reduction of the input traffic rate through congested routes which occurs on much shorter time scales. We consider the onset of congestion in the Internet where local mismatch between demand and capacity results in traffic losses and show that it can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution. They result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible. © Copyright EPLA, 2012.

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.

Unifractality and multifractality in the Italian stock market

Tests for random walk behaviour in the Italian stock market are presented, based on an investigation of the fractal properties of the log return series for the Mibtel index. The random walk hypothesis is evaluated against alternatives accommodating either unifractality or multifractality. Critical values for the test statistics are generated using Monte Carlo simulations of random Gaussian innovations. Evidence is reported of multifractality, and the departure from random walk behaviour is statistically significant on standard criteria. The observed pattern is attributed primarily to fat tails in the return probability distribution, associated with volatility clustering in returns measured over various time scales. © 2009 Elsevier Inc. All rights reserved.

Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

Fluctuation-driven traffic congestion in a scale-free model of the Internet

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analysing network failures caused by hardware faults or overload. There network reaction was modelled as rerouting of traffic away from failed or congested elements. Here we model network reaction to congestion on much shorter time scales when the input traffic rate through congested routes is reduced. As an example we consider the Internet where local mismatch between demand and capacity results in traffic losses. We describe the onset of congestion as a phase transition characterised by strong, albeit relatively short-lived, fluctuations of losses caused by noise in input traffic and exacerbated by the heterogeneous nature of the network manifested in a power-law load distribution. The fluctuations may result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible. © 2013 IEEE.

Ginzburg-Landau turbulence in quasi-CW Raman fiber lasers

Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers. Fiber lasers operating via Raman gain or based on rare-earth-doped active fibers are widely used as sources of CW radiation. However, these lasers are only quasi-CW: their intensity fluctuates strongly on short time scales. Here the framework of the complex Ginzburg-Landau equations, which are well known as an efficient model of mode-locked fiber lasers, is applied for the description of quasi-CW fiber lasers. The vector Ginzburg-Landau model of a Raman fiber laser describes the experimentally observed turbulent-like intensity dynamics, as well as polarization rogue waves. Our results open debates about the common underlying physics of operation of very different laser types - quasi-CW lasers and passively mode-locked lasers.

Unveiling temporal correlations characteristic of a phase transition in the output intensity of a fiber laser

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

Geochemical variation among small eruptive centers in the central SVZ of the Andes: An evaluation of subduction, mantle and crustal influences

Subduction zone magmatism is an important and extensively studied topic in igneous geochemistry. Recent studies focus on from where arc magmas are generated, how subduction components (fluids or melts) are fluxed into the source of the magmas, and whether or how the subduction components affect partial melting processes beneath volcanic arcs at convergent boundaries. ^ At 39.5°S in the Central Southern Volcanic Zone of the Andes, Volcano Villarrica is surrounded by a suite of Small Eruptive Centers (SEC). The SECs are located mostly to the east and northeast of the stratovolcano and aligned along the Liquine-Ofqui Fault Zone, the major fracture system in this area. Former studies observed the geochemical patterns of the SECs differ distinctively from those of V. Villarrica and suggested there may be a relationship between the compositions of the volcanic units and their edifice sizes. This work is a comprehensive geochemical study on the SECs near V. Villarrica, using a variety of geochemical tracers and tools including major, trace and REE elements, Li-Be-B elements, Sr-Nd-Pb isotopes and short-lived isotopes such as U-series and 10Be. In this work, systematic differences between the elemental and isotopic compositions of the SECs and those of V. Villarrica are revealed and more importantly, modeled in terms of magmatic processes occurring at continental arc margins. Detailed modeling calculations in this work reconstruct chemical compositions of the primary magmas, source compositions, compositions and percentages of different subduction endmembers mixed into the source, degrees of partial melting and different time scales of the SECs and V. Villarrica, respectively. Geochemical characteristics and possible origins of the two special SECs—andesitic Llizan, with crustal signatures, and Rucapillan, to the northwest toward the trench, are also discussed in this work. ^