Thermographic Monitoring of Scum Accumulation beneath Floating Covers

Large sheets of high-density polyethene geomembrane are used as floating covers on some of the wastewater treatment lagoons at the Melbourne Water Corporation’s Western Treatment Plant. These covers provide an airtight seal for the anaerobic digestion of sewage and allow for harvesting the methane-rich biogas, which is then used to generate electricity. There is a potential for scum to develop under the covers during the anaerobic digestion of the raw sewage by microorganisms. Due to the nature of the operating environment of the lagoons and the vast size (450 m × 170 m) of these covers, a safe non-contact method to monitor the development and movement of the scum is preferred. This paper explores the potential of using a new thermographic approach to identify and monitor the scum under the covers. The approach exploits naturally occurring variations in solar intensity as a trigger for generating a transient thermal response that is then fitted to an exponential decay law to determine a cooling constant. This approach is investigated experimentally using a laboratory-scale test rig. A finite element (FE) model is constructed and shown to reliably predict the experimentally observed thermal transients and cooling constants. This FE model is then set up to simulate progressive scum accumulation with time, using a specified scumberg geometry and a stepwise change in thermal properties. The results indicate a detectable change in the cooling constant at different locations on the cover, thereby providing a quantitative basis for characterising the scum accumulation beneath the cover. The practical application and limitations of these results are briefly discussed.

On the recent claim of correlation between radioactive decay rates and space weather

In recent literature, several authors have challenged the validity of the exponential-decay law, based on observed variations in radioactive decay rate measurements beyond statistical accuracy. Tentative explanations have been sought in external interferences influencing the decay process, such as interactions of the nuclei with solar and cosmic neutrinos. Given the important implications of such statements on theoretical and practical level, one would expect that they are backed up with radionuclide metrology of the highest quality. In reality, they share the common traits of using poor metrology and incomplete uncertainty analysis with respect to the stability of the measurement technique. In this paper, new claims of correlations between decay rates and space weather are questioned.

ANALYSIS OF FRACTAL–FRACTIONAL MALARIA TRANSMISSION MODEL

In this paper, the malaria transmission (MT) model under control strategies is considered using the Liouville–Caputo fractional order (FO) derivatives with exponential decay law and power-law. For the solutions we are using an iterative technique involving Laplace transform. We examined the uniqueness and existence (UE) of the solutions by applying the fixed-point theory. Also, fractal–fractional operators that include power-law and exponential decay law are considered. Numerical results of the MT model are obtained for the particular values of the FO derivatives [Formula: see text] and [Formula: see text].

CAUCHY PROBLEMS WITH FRACTAL–FRACTIONAL OPERATORS AND APPLICATIONS TO GROUNDWATER DYNAMICS

As the Riemann–Liouville derivative is a derivative of a convolution of a function and the power law, the fractal–fractional derivative of a function is the fractal derivative of a convolution of that function with the power law or exponential decay. In order to further open new doors on ongoing investigations with field of partial differential equations with non-conventional differential operators, we introduce in this paper new Cauchy problems with fractal–fractional differential operators. We consider two cases, when the operator is constructed with power law and when it is constructed with exponential decay law with Delta-Dirac property. For each case, we present the conditions under which the exact solution exists and is unique. We suggest a suitable and accurate numerical scheme that can be used to solve such differential equation numerically. We present illustrative examples where an application to a partial differential equation and to a model of groundwater flow within the confined aquifer are done with numerical simulations provided. The clear variation of water level shows the impact of the fractal–fractional derivative on the dynamics.

Probing Nonexponential Decay in Floquet–Bloch Bands

Exponential decay laws describe systems ranging from unstable nuclei to fluorescent molecules, in which the probability of jumping to a lower-energy state in any given time interval is static and history-independent. These decays, involving only a metastable state and fluctuations of the quantum vacuum, are the most fundamental nonequilibrium process and provide a microscopic model for the origins of irreversibility. Despite the fact that the apparently universal exponential decay law has been precisely tested in a variety of physical systems, it is a surprising truth that quantum mechanics requires that spontaneous decay processes have nonexponential time dependence at both very short and very long times. Cold-atom experiments have proven to be powerful probes of fundamental decay processes; in this article, we propose the use of Bose condensates in Floquet–Bloch bands as a probe of long-time nonexponential decay in single isolated emitters. We identify a range of parameters that should enable observation of long-time deviations and experimentally demonstrate a key element of the scheme: tunable decay between quasi-energy bands in a driven optical lattice.

Solar radiative transfer in Antarctic blue ice: spectral considerations, subsurface enhancement, inclusions, and meteorites

We describe and validate a Monte Carlo model to track photons over the full range of solar wavelengths as they travel into optically thick Antarctic blue ice. The model considers both reflection and transmission of radiation at the surface of blue ice, scattering by air bubbles within it, and spectral absorption due to the ice. The ice surface is treated as planar whilst bubbles are considered to be spherical scattering centres using the Henyey–Greenstein approximation. Using bubble radii and number concentrations that are representative of Antarctic blue ice, we calculate spectral albedos and spectrally integrated downwelling and upwelling radiative fluxes as functions of depth and find that, relative to the incident irradiance, there is a marked subsurface enhancement in the downwelling flux and accordingly also in the mean irradiance. This is due to the interaction between the refractive air–ice interface and the scattering interior and is particularly notable at blue and UV wavelengths which correspond to the minimum of the absorption spectrum of ice. In contrast the absorption path length at IR wavelengths is short and consequently the attenuation is more complex than can be described by a simple Lambert–Beer style exponential decay law – instead we present a triple-exponential fit to the net irradiance against depth. We find that there is a moderate dependence on the solar zenith angle and surface conditions such as altitude and cloud optical depth. Representative broadband albedos for blue ice are calculated in the range from 0.585 to 0.621. For macroscopic absorbing inclusions we observe both geometry- and size-dependent self-shadowing that reduces the fractional irradiance incident on an inclusion's surface. Despite this, the inclusions act as local photon sinks and are subject to fluxes that are several times the magnitude of the single-scattering contribution. Such enhancement may have consequences for the energy budget in regions of the cryosphere where particulates are present near the surface. These results also have particular relevance to measurements of the internal radiation field: account must be taken of both self-shadowing and the optical effect of introducing the detector. Turning to the particular example of englacial meteorites, our modelling predicts iron meteorites to reside at much reduced depths than previously suggested in the literature (< 10 cm vs. ∼ 40 cm) and further shows a size dependency that may explain the observed bias in their Antarctic size distribution.

Comparative study for target fragmentation in 4He and 6Li interactions with emulsion nuclei at Elab = 3.7A GeV

The multiplicity characteristics of the grey and black particles are studied in 3.7A GeV 4He and 6Li interactions with emulsion nuclei. The dependence on the system size is examined. The data are classified according the emission direction in the 4π space. The forward or backward emitted grey particle multiplicities distributions are approximated by exponential decay law. The black particle distributions also have the decay shapes, except for the CNO target nuclei; they are shoulder-shaped curves. The production probabilities and average multiplicities increase linearly with the target size. Multiplicity correlations are carried out. Regarding the nuclear limiting fragmentation hypothesis, the grey and black particle productions are independent of the projectile size.