Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

On the use of a time sequence of surface pressures in four-dimensional data assimilation

The possibility of using a time sequence of surface pressure observations in four-dimensional data assimilation is being investigated. It is shown that a linear multilevel quasi-geostrophic model can be updated successfully with surface data alone, provided the number of time levels are at least as many as the number of vertical levels. It is further demonstrated that current statistical analysis procedures are very inefficient to assimilate surface observations, and it is shown by numerical experiments that the vertical interpolation must be carried out using the structure of the most dominating baroclinic mode in order to obtain a satisfactory updating. Different possible ways towards finding a practical solution are being discussed.

Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

Current problems in four-dimensional data assimilation

The purpose of this lecture is to review recent development in data analysis, initialization and data assimilation. The development of 3-dimensional multivariate schemes has been very timely because of its suitability to handle the many different types of observations during FGGE. Great progress has taken place in the initialization of global models by the aid of non-linear normal mode technique. However, in spite of great progress, several fundamental problems are still unsatisfactorily solved. Of particular importance is the question of the initialization of the divergent wind fields in the Tropics and to find proper ways to initialize weather systems driven by non-adiabatic processes. The unsatisfactory ways in which such processes are being initialized are leading to excessively long spin-up times.

Four-dimensional data assimilation and balanced dynamics

The problem of spurious excitation of gravity waves in the context of four-dimensional data assimilation is investigated using a simple model of balanced dynamics. The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode, and can be initialized such that the model evolves on a so-called slow manifold, where the fast motion is suppressed. Identical twin assimilation experiments are performed, comparing the extended and ensemble Kalman filters (EKF and EnKF, respectively). The EKF uses a tangent linear model (TLM) to estimate the evolution of forecast error statistics in time, whereas the EnKF uses the statistics of an ensemble of nonlinear model integrations. Specifically, the case is examined where the true state is balanced, but observation errors project onto all degrees of freedom, including the fast modes. It is shown that the EKF and EnKF will assimilate observations in a balanced way only if certain assumptions hold, and that, outside of ideal cases (i.e., with very frequent observations), dynamical balance can easily be lost in the assimilation. For the EKF, the repeated adjustment of the covariances by the assimilation of observations can easily unbalance the TLM, and destroy the assumptions on which balanced assimilation rests. It is shown that an important factor is the choice of initial forecast error covariance matrix. A balance-constrained EKF is described and compared to the standard EKF, and shown to offer significant improvement for observation frequencies where balance in the standard EKF is lost. The EnKF is advantageous in that balance in the error covariances relies only on a balanced forecast ensemble, and that the analysis step is an ensemble-mean operation. Numerical experiments show that the EnKF may be preferable to the EKF in terms of balance, though its validity is limited by ensemble size. It is also found that overobserving can lead to a more unbalanced forecast ensemble and thus to an unbalanced analysis.

Wave-breaking characteristics of Northern Hemisphere winter blocking: a two-dimensional approach

This paper generalises and applies recently developed blocking diagnostics in a two- dimensional latitude-longitude context, which takes into consideration both mid- and high-latitude blocking. These diagnostics identify characteristics of the associated wave-breaking as seen in the potential temperature (θ) on the dynamical tropopause, in particular the cyclonic or anticyclonic Direction of wave-Breaking (DB index), and the Relative Intensity (RI index) of the air masses that contribute to blocking formation. The methodology is extended to a 2-D domain and a cluster technique is deployed to classify mid- and high-latitude blocking according to the wave-breaking characteristics. Mid-latitude blocking is observed over Europe and Asia, where the meridional gradient of θ is generally weak, whereas high-latitude blocking is mainly present over the oceans, to the north of the jet-stream, where the meridional gradient of θ is much stronger. They occur respectively on the equatorward and poleward flank of the jet- stream, where the horizontal shear ∂u/∂y is positive in the first case and negative in the second case. A regional analysis is also conducted. It is found that cold-anticyclonic and cyclonic blocking divert the storm-track respectively to the south and to the north over the East Atlantic and western Europe. Furthermore, warm-cyclonic blocking over the Pacific and cold-anticyclonic blocking over Europe are identified as the most persistent types and are associated with large amplitude anomalies in temperature and precipitation. Finally, the high-latitude, cyclonic events seem to correlate well with low- frequency modes of variability over the Pacific and Atlantic Ocean.

Metabifurcation analysis of a mean field model of the cortex

Mean field models (MFMs) of cortical tissue incorporate salient, average features of neural masses in order to model activity at the population level, thereby linking microscopic physiology to macroscopic observations, e.g., with the electroencephalogram (EEG). One of the common aspects of MFM descriptions is the presence of a high-dimensional parameter space capturing neurobiological attributes deemed relevant to the brain dynamics of interest. We study the physiological parameter space of a MFM of electrocortical activity and discover robust correlations between physiological attributes of the model cortex and its dynamical features. These correlations are revealed by the study of bifurcation plots, which show that the model responses to changes in inhibition belong to two archetypal categories or “families”. After investigating and characterizing them in depth, we discuss their essential differences in terms of four important aspects: power responses with respect to the modeled action of anesthetics, reaction to exogenous stimuli such as thalamic input, and distributions of model parameters and oscillatory repertoires when inhibition is enhanced. Furthermore, while the complexity of sustained periodic orbits differs significantly between families, we are able to show how metamorphoses between the families can be brought about by exogenous stimuli. We here unveil links between measurable physiological attributes of the brain and dynamical patterns that are not accessible by linear methods. They instead emerge when the nonlinear structure of parameter space is partitioned according to bifurcation responses. We call this general method “metabifurcation analysis”. The partitioning cannot be achieved by the investigation of only a small number of parameter sets and is instead the result of an automated bifurcation analysis of a representative sample of 73,454 physiologically admissible parameter sets. Our approach generalizes straightforwardly and is well suited to probing the dynamics of other models with large and complex parameter spaces.

The stability of a two-dimensional vorticity filament under uniform strain

The quantitative effects of uniform strain and background rotation on the stability of a strip of constant vorticity (a simple shear layer) are examined. The thickness of the strip decreases in time under the strain, so it is necessary to formulate the linear stability analysis for a time-dependent basic flow. The results show that even a strain rate γ (scaled with the vorticity of the strip) as small as 0.25 suppresses the conventional Rayleigh shear instability mechanism, in the sense that the r.m.s. wave steepness cannot amplify by more than a certain factor, and must eventually decay. For γ < 0.25 the amplification factor increases as γ decreases; however, it is only 3 when γ e 0.065. Numerical simulations confirm the predictions of linear theory at small steepness and predict a threshold value necessary for the formation of coherent vortices. The results help to explain the impression from numerous simulations of two-dimensional turbulence reported in the literature that filaments of vorticity infrequently roll up into vortices. The stabilization effect may be expected to extend to two- and three-dimensional quasi-geostrophic flows.

Rossby waves and two-dimensional turbulence in a large-scale zonal jet

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field. Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ[identical with] (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ [identical with] (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences. The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to K Kβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [double less-than sign] κ for typical eddy length and velocity scales.

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Performance analysis of MIMO MRC in 3D mobile-to-mobile double-correlated channels

In this paper, we consider multiple-input multiple- output (MIMO) maximal ratio combining (MRC) systems and assess the system performance in terms of average symbol error probability (SEP), outage probability and ergodic capacity in double-correlated Rayleigh-and-Lognormal fading channels. In order to derive the receive and transmit correlation functions needed for the performance analysis, a three-dimensional (3D) MIMO mobile-to-mobile (M-to-M) channel model, which takes into account the effects of fast fading and shadowing is used. Numerical results are provided to show the effects of system parameters, such as maximum elevation angle of scatterers, orientation angle of antenna array in the x-y plane, angle between x-y plane and the antenna array orientation, and degree of scattering in the x-y plane, on the system performance.

A three-dimensional open-framework indium selenide: [C7H10N][In9Se14]

An open-framework indium selenide, [C7H10N][In9Se14], has been prepared under solvothermal conditions in the presence of 3,5-dimethylpyridine, and characterized by single crystal diffraction, thermogravimetry, elemental analysis, FTIR spectroscopy and UV-Vis diffuse reflectance. The crystal structure of [C7H10N][In9Se14] contains an unusual building unit, in which corner-linked and edge-linked InSe45- tetrahedra coexist. The presence of one-dimensional circular channels, of ca. 6 Å diameter, results in approximately 25% of solvent accessible void space.

The lottery-panel task for bi-dimensional parameter-free elicitation of risk attitudes

We propose first, a simple task for the eliciting attitudes toward risky choice, the SGG lottery-panel task, which consists in a series of lotteries constructed to compensate riskier options with higher risk-return trade-offs. Using Principal Component Analysis technique, we show that the SGG lottery-panel task is capable of capturing two dimensions of individual risky decision making i.e. subjects’ average risk taking and their sensitivity towards variations in risk-return. From the results of a large experimental dataset, we confirm that the task systematically captures a number of regularities such as: A tendency to risk averse behavior (only around 10% of choices are compatible with risk neutrality); An attraction to certain payoffs compared to low risk lotteries, compatible with over-(under-) weighting of small (large) probabilities predicted in PT and; Gender differences, i.e. males being consistently less risk averse than females but both genders being similarly responsive to the increases in risk-premium. Another interesting result is that in hypothetical choices most individuals increase their risk taking responding to the increase in return to risk, as predicted by PT, while across panels with real rewards we see even more changes, but opposite to the expected pattern of riskier choices for higher risk-returns. Therefore, we conclude from our data that an “economic anomaly” emerges in the real reward choices opposite to the hypothetical choices. These findings are in line with Camerer's (1995) view that although in many domains, paid subjects probably do exert extra mental effort which improves their performance, choice over money gambles is not likely to be a domain in which effort will improve adherence to rational axioms (p. 635). Finally, we demonstrate that both dimensions of risk attitudes, average risk taking and sensitivity towards variations in the return to risk, are desirable not only to describe behavior under risk but also to explain behavior in other contexts, as illustrated by an example. In the second study, we propose three additional treatments intended to elicit risk attitudes under high stakes and mixed outcome (gains and losses) lotteries. Using a dataset obtained from a hypothetical implementation of the tasks we show that the new treatments are able to capture both dimensions of risk attitudes. This new dataset allows us to describe several regularities, both at the aggregate and within-subjects level. We find that in every treatment over 70% of choices show some degree of risk aversion and only between 0.6% and 15.3% of individuals are consistently risk neutral within the same treatment. We also confirm the existence of gender differences in the degree of risk taking, that is, in all treatments females prefer safer lotteries compared to males. Regarding our second dimension of risk attitudes we observe, in all treatments, an increase in risk taking in response to risk premium increases. Treatment comparisons reveal other regularities, such as a lower degree of risk taking in large stake treatments compared to low stake treatments and a lower degree of risk taking when losses are incorporated into the large stake lotteries. Results that are compatible with previous findings in the literature, for stake size effects (e.g., Binswanger, 1980; Antoni Bosch-Domènech & Silvestre, 1999; Hogarth & Einhorn, 1990; Holt & Laury, 2002; Kachelmeier & Shehata, 1992; Kühberger et al., 1999; B. J. Weber & Chapman, 2005; Wik et al., 2007) and domain effect (e.g., Brooks and Zank, 2005, Schoemaker, 1990, Wik et al., 2007). Whereas for small stake treatments, we find that the effect of incorporating losses into the outcomes is not so clear. At the aggregate level an increase in risk taking is observed, but also more dispersion in the choices, whilst at the within-subjects level the effect weakens. Finally, regarding responses to risk premium, we find that compared to only gains treatments sensitivity is lower in the mixed lotteries treatments (SL and LL). In general sensitivity to risk-return is more affected by the domain than the stake size. After having described the properties of risk attitudes as captured by the SGG risk elicitation task and its three new versions, it is important to recall that the danger of using unidimensional descriptions of risk attitudes goes beyond the incompatibility with modern economic theories like PT, CPT etc., all of which call for tests with multiple degrees of freedom. Being faithful to this recommendation, the contribution of this essay is an empirically and endogenously determined bi-dimensional specification of risk attitudes, useful to describe behavior under uncertainty and to explain behavior in other contexts. Hopefully, this will contribute to create large datasets containing a multidimensional description of individual risk attitudes, while at the same time allowing for a robust context, compatible with present and even future more complex descriptions of human attitudes towards risk.

Unsteady flow simulation of a vertical axis augmented wind turbine: a two-dimensional study

As the integration of vertical axis wind turbines in the built environment is a promising alternative to horizontal axis wind turbines, a 2D computational investigation of an augmented wind turbine is proposed and analysed. In the initial CFD analysis, three parameters are carefully investigated: mesh resolution; turbulence model; and time step size. It appears that the mesh resolution and the turbulence model affect result accuracy; while the time step size examined, for the unsteady nature of the flow, has small impact on the numerical results. In the CFD validation of the open rotor with secondary data, the numerical results are in good agreement in terms of shape. It is, however, observed a discrepancy factor of 2 between numerical and experimental data. Successively, the introduction of an omnidirectional stator around the wind turbine increases the power and torque coefficients by around 30–35% when compared to the open case; but attention needs to be given to the orientation of the stator blades for optimum performance. It is found that the power and torque coefficients of the augmented wind turbine are independent of the incident wind speed considered.

Bilayer graphene formed by passage of current through graphite: evidence for a three-dimensional structure

The passage of an electric current through graphite or few-layer graphene can result in a striking structural transformation, but there is disagreement about the precise nature of this process. Some workers have interpreted the phenomenon in terms of the sublimation and edge reconstruction of essentially flat graphitic structures. An alternative explanation is that the transformation actually involves a change from a flat to a three-dimensional structure. Here we describe detailed studies of carbon produced by the passage of a current through graphite which provide strong evidence that the transformed carbon is indeed three-dimensional. The evidence comes primarily from images obtained in the scanning transmission electron microscope using the technique of high-angle annular dark-field imaging, and from a detailed analysis of electron energy loss spectra. We discuss the possible mechanism of the transformation, and consider potential applications of “three-dimensional bilayer graphene”.