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Register a new userUniversal fluctuations in tropospheric radar measurements
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Authors
Andrea Barucci
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Radar data collected at an experimental facility arranged on purpose suggest that the footprint of atmospheric turbulence might be encoded in the radar signal statistics. Radar data probability distributions are calculated and nicely fitted by a one parameter family of generalized Gumbel (GG) distributions, G(a). A relation between the wind strength and the measured shape parameter a is obtained. Strong wind fluctuations return pronounced asymmetric leptokurtic profiles, while Gaussian profiles are eventually recovered as the wind fluctuations decrease. Besides stressing the crucial impact of air turbulence for radar applications, we also confirm the adequacy of G(a) statistics for highly correlated complex systems.
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Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW.
Recent work by Sromovsky et al. (2017, Icarus 291, 232-244) suggested that all red colour in Jupiters atmosphere could be explained by a single colour-carrying compound, a so-called universal chromophore. We tested this hypothesis on ground-based spectroscopic observations in the visible and near-infrared (480-930 nm) from the VLT/MUSE instrument between 2014 and 2018, retrieving a chromophore absorption spectrum directly from the North Equatorial Belt, and applying it to model spatial variations in colour, tropospheric cloud and haze structure on Jupiter. We found that we could model both the belts and the Great Red Spot of Jupiter using the same chromophore compound, but that this chromophore must exhibit a steeper blue-absorption gradient than the proposed chromophore of Carlson et al. (2016, Icarus 274, 106-115). We retrieved this chromophore to be located no deeper than 0.2+/-0.1 bars in the Great Red Spot and 0.7+/-0.1 bars elsewhere on Jupiter. However, we also identified some spectral variability between 510 nm and 540 nm that could not be accounted for by a universal chromophore. In addition, we retrieved a thick, global cloud layer at 1.4+/-0.3 bars that was relatively spatially invariant in altitude across Jupiter. We found that this cloud layer was best characterised by a real refractive index close to that of ammonia ice in the belts and the Great Red Spot, and poorly characterised by a real refractive index of 1.6 or greater. This may be the result of ammonia cloud at higher altitude obscuring a deeper cloud layer of unknown composition.
We study bounds on ratios of fluctuations in steady-state time-reversal heat engines controlled by multi affinities. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower-bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian universal curve. We derive the functional form of the global PDF in terms of the source PDF of the individual events in the system. A single parameter distinguishes the global PDF and is related to the exponent of the source PDF. When normalized, the global PDF is shown to be insensitive to this parameter and importantly we obtain the previously demonstrated universality from an uncorrelated Gaussian source PDF. The second and third moments of the global PDF are more sensitive, providing a powerful tool to probe the degree of complexity of physical systems.
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed automatically by an equipartition relation, while the q-parameter is related to the scaled variance and to the expectation value of the particle number. For the binomial distribution q is smaller, for the negative binomial q is larger than one. These results also represent an approximation for general particle number distributions in the reservoir up to second order in the canonical expansion. For general systems the average phase-space volume ratio expanded to second order delivers a q parameter related to the heat capacity and to the variance of the temperature. However, q differing from one leads to non-additivity of the Boltzmann-Gibbs entropy. We demonstrate that a deformed entropy, K(S), can be constructed and used for demanding additivity. This requirement leads to a second order differential equation for K(S). Finally, the generalized q-entropy formula contains the Tsallis, Renyi and Boltzmann-Gibbs-Shannon expressions as particular cases. For diverging temperature variance we obtain a novel entropy formula.
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