Retrieval of the piecewise-constant mass density in the Bergman wave equation

This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy, isotropic, homogeneous fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, generally-lossy, flat-plane layer in which the mass density and wavespeed are different from those of the host. The focus is on the inverse problem of the retrieval of the layer mass density. The data is the transmitted pressure field, obtained by simulation (resolution of the forward problem) in exact, explicit form via the domain integral form of the Bergman wave equation. This solution is exact and more explicit in terms of the mass-density contrast (between the host and layer) than the classical solution obtained by separation of variables. A perturbation technique enables the solution (in its form obtained by the domain integral method) to be cast as a series of powers of the mass density contrast, the first three terms of which are employed as the trial models in the treatment of the inverse problem. The aptitude of these models to retrieve the mass density contrast is demonstrated both theoretically and numerically.

Cumulants of the chiral order parameter in a nonequilibrium Bjorken expansion with a QCD critical point

To understand experimentally obtained net-proton number cumulants in the search for the QCD critical point, we study a dynamical model based on an effective quark-meson Lagrangian with chiral symmetry. We investigate the evolution of the expanding medium created in a heavy-ion collision using a spatially homogeneous fluid and a time-dependent order parameter, the sigma field evolved by a Langevin equation. We extract cumulants of the sigma field along a parametrized freeze-out curve and match the obtained freeze-out points to corresponding beam energies. These cumulants can be related to cumulants of the net-proton number through the sigma-proton coupling to provide a qualitative comparison to experimental data from STAR’s beam energy scan program. We demonstrate that the presence of the spinodal or mixed phase region around the first-order chiral phase transition allows for a wide interval of cumulants at the lowest beam energies.

Nonlinear Analysis of Tropical Waves and Cyclogenesis Excited by Pressure Disturbance in Atmosphere

The horizontal equations of motion for an inviscid homogeneous fluid under the influence of pressure disturbance and waves are applied to investigate the nonlinear process of solitary waves and cyclone genesis forced by a moving pressure disturbance in atmosphere. Based on the reductive perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies the Korteweg–de Vries equation with a forcing term (fKdV equation for short), which describes the physics of a shallow layer of fluid subject to external pressure forcing. Then, with the help of Hirota’s direct method, the analytic solutions of the fKdV equation are studied and some exact vortex solutions are given as examples, from which one can see that the solitary waves and vortex multi-pole structures can be excited by external pressure forcing in atmosphere, such as pressure perturbation and waves. It is worthy to point out that cyclone and waves can be excited by different type of moving atmospheric pressure forcing source.

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear current. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive the modal equations from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (group speed, wave action conservation law) and to constructing more general ‘hybrid solutions’ consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. Detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions (i.e. eigenfunctions of the relevant spectral problems) for the surface waves in homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a large family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. Global and local measures of the deformation of wavefronts are introduced and evaluated.

CFD Analysis on Biogas Bubble Creation Within a Stirred Tank of a Wastewater Treatment Plant

A mixing strategy for assuring a homogeneous fluid flow inside wastewater treatment plants (WWTPs) is a necessity, in order to keep continuous contacts of substrates and degraders. On the other hand, mixing is an energy-demanding process. Therefore, the power consumption for mixing the fluid flow within bioreactors affects the overall efficiency of WWTPs. The current study aims at evaluating the incorporation of biogas bubble creation on the mixing of WWTP tanks. Computational fluid dynamics (CFD) enables simulating hydrodynamics of multiphase fluid flows injected with bubble parcels. The case is a cylindrical stirred tank, in which the fluid flow is agitated via a rotating mixer. Mixer rotates at various speeds; and for each case, the ultimate fluid flow is captured both with and without bubble creation. Non-Newtonian characteristics of the fluid flow within the tank are considered and k–ε turbulence closure is selected for the model. By a two-way coupling of an Eulerian-Lagrangian platform, velocity fields and the amount of dead volume are analyzed and discussed. Our key finding is that the biogas bubble creation contributes to the reduction of dead volume inside the WWTP tank, when there is no external rotating mixing, or once the amount of mixer rotation speed is low.

Temperature profiles due to continuous hot water injection into homogeneous fluid-saturated porous media through a line source

We report a theoretical study to determine the temperature profiles due to the continuous andconstant injection of hot water through a line source, into a homogeneous fluid-saturated porous medium which has had initially a constant temperature T∞. In our treatment we have taken in to account the simultaneous injection of constant fluxes of volume fluid, q, and of heat, φ. By using a far-field description, we found similarity solutions for the dimensionless temperature depending on the Peclet number, P e, as the single parameter of the problem.

Gravitational Collapse and Singularity Removal in Rastall Theory

In the present work, we study spherically symmetric gravitational collapse of a homogeneous fluid in the framework of Rastall gravity. Considering a nonlinear equation of state (EoS) for the fluid profiles, we search for a class of nonsingular collapse solutions and the possibility of singularity removal. We find that depending on the model parameters, the collapse scenario halts at a minimum value of the scale factor at which a bounce occurs. The collapse process then enters an expanding phase in the postbounce regime, and consequently the formation of a spacetime singularity is prevented. We also find that, in comparison to the singular case where the apparent horizon forms to cover the singularity, the formation of apparent horizon can be delayed allowing thus the bounce to be causally connected to the external universe. The nonsingular solutions we obtain satisfy the weak energy condition (WEC) which is crucial for physical validity of the model.

A quantitative interpretation of the saturation exponent in Archie’s equations

Saturation exponent is an important parameter in Archie’s equations; however, there has been no well-accepted physical interpretation for the saturation exponent. We have theoretically derived Archie’s equations from the Maxwell–Wagner theory on the assumption of homogeneous fluid distribution in the pore space of clay-free porous rocks. Further theoretical derivations showed that the saturation exponent is in essence the cementation exponent for the water–air mixture and is quantitatively and explicitly related to the aspect ratio of the air bubbles in the pores. The results have provided a theoretical backup for the empirically obtained Archie’s equations and have offered a more physical and quantitative understanding of the saturation exponent.

Mapping coral calcification strategies from in situ boron isotope and trace element measurements of the tropical coral Siderastrea siderea

Boron isotopic and elemental analysis of coral aragonite can give important insights into the calcification strategies employed in coral skeletal construction. Traditional methods of analysis have limited spatial (and thus temporal) resolution, hindering attempts to unravel skeletal heterogeneity. Laser ablation mass spectrometry allows a much more refined view, and here we employ these techniques to explore boron isotope and co-varying elemental ratios in the tropical coral Siderastrea siderea. We generate two-dimensional maps of the carbonate parameters within the calcification medium that deposited the skeleton, which reveal large heterogeneities in carbonate chemistry across the macro-structure of a coral polyp. These differences have the potential to bias proxy interpretations, and indicate that different processes facilitated precipitation of different parts of the coral skeleton: the low-density columella being precipitated from a fluid with a carbonate composition closer to seawater, compared to the high-density inter-polyp walls where aragonite saturation was ~ 5 times that of external seawater. Therefore, the skeleton does not precipitate from a spatially homogeneous fluid and its different parts may thus have varying sensitivity to environmental stress. This offers new insights into the mechanisms behind the response of the S. siderea skeletal phenotype to ocean acidification.

Mathematical Modelling and Simulation of liquid steel flow phenomena and temperature distribution in an optimized tundish design of a continuous caster

The objective of this study was to analyze the fluid flow of molten steel in a continuous casting tundish using numerical simulations for better inclusion floatation and its separation. The tundish geometry was designed using Autodesk FUSION 360 and the analysis were performed on ANSYS FLUENT. The investigations were done on steady-state as well as transient conditions. To scale back vortexing and turbulence within the tundish, turbo stoppers and flow modulators, e.g. dam and weirs were placed for an optimized and efficient flow inside the tundish and its behavior on the spacious flow structure was explored. The strategic placements of the flow modifiers produced higher turbulence in the recess region of the tundish resulting in better turbulent flow withinside the inlet region of the tundish. Thereby a more homogeneous fluid flow is formed with better conditions for particle separation. Analysing the flow behavior we have determined the inclusion floatation using particle tracking method form dense discrete phase modelling along with multiphase eulerian-lagragian model. Reduction in dead volumes was achieved in the spatial flow due to better intermixing which further reduced the metal loss and increased the yield of the tundish using the fluid flow analysis. Analyzing eddy formations in the spatial geometry of the tundish structure made it easy to evenly distributes the flow-induced shear. This determined the lesser turbulence on the free surface of the steel flow resulting in less reduction of the liquid steel surface.