Results For Initial Conditions Research Articles

An experimental and numerical study of evaporite mineral dissolution and density-driven flow in porous media

Subsurface mineral dissolution problems exhibit complex behaviors, which are difficult to model and validate numerically. Controlled, physically-validated experimental problems can be used to better understand mineral dissolution and subsequent numerical representation, bridging the gap between numerical models and field observations. The objective of this work was to collect the first controlled, physical measurements in a porous aquifer overlying an evaporite mineral, and to create a numerical model of the system. The problem studied was modified from the classic HYDROCOIN Level 1 Case 5 problem. Three flow gradients in a porous aquifer were investigated in duplicate in a 2-D box-problem. The duplicate measurements had high variability, shown by numerical modeling to be a result of initial conditions, variable flux representing dissolution, sharp gradients, and variable dispersivity. The physical measurements of parameters and fields were important for calibration success. The numerical models, including sensitivity analyses, were capable of simulating flow patterns, observed concentrations, and peaks resulting from observed initial conditions. The numerical models were a key tool in understanding factors influencing the flow and spread of salt within the system. The models were limited by the ability to detail physical observations, difficult in both the laboratory and for potential field applications. The results provided insight in the HYDROCOIN Level 1 Case 5 numerical simulations, with flow appearing to be swept-forward; however, observed concentrations were lower than commonly modeled.

Optimisation of culture conditions and development of a novel fed‐batch strategy for high production of β‐galactosidase by Kluyveromyces lactis

SummaryThe aim of this study was to enhance β‐galactosidase production by Kluyveromyces lactis CICC1773. Firstly, the optimum culture conditions were obtained by response surface methodology, and the maximum β‐galactosidase activity reached 20.6 U mL−1, about two‐fold increase than that of the initial conditions (initial fermentation medium and conditions). To further improve β‐galactosidase production, a new fed‐batch strategy based on pH feedback control was developed successfully in a 7‐L fermenter, using 400 g L−1 lactose as feeding medium. As a result, the β‐galactosidase activity and productivity reached up to 111.61 U mL−1 and 5.31 U/(mL·h), enhanced by 15.3‐fold and 17.6‐fold superior than the results of initial conditions, respectively. To our knowledge, β‐galactosidase activity obtained was the highest value among the results reported by nonrecombinant strains. These results demonstrated that the new fed‐batch strategy based on optimum culture conditions could be automatic control easily and be conductive to further scale up for industrial fermentation.

On $F^\varepsilon _2$-planar mappings of (pseudo-) Riemannian manifolds

We study special $F$-planar mappings between two $n$-dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced $PQ^{\varepsilon }$-projectivity of Riemannian metrics, $\varepsilon \ne 1,1+n$. Later these mappings were studied by Matveev and Rosemann. They found that for $\varepsilon =0$ they are projective. We show that $PQ^{\varepsilon }$-projective equivalence corresponds to a special case of $F$-planar mapping studied by Mikeš and Sinyukov (1983) and ${F_2}$-planar mappings (Mikeš, 1994), with $F=Q$. Moreover, the tensor $P$ is derived from the tensor $Q$ and the non-zero number $\varepsilon $. For this reason we suggest to rename $PQ^{\varepsilon }$ as ${F_2^{\varepsilon }}$. We use earlier results derived for ${F}$- and ${F_2}$-planar mappings and find new results. For these mappings we find the fundamental partial differential equations in closed linear Cauchy type form and we obtain new results for initial conditions.

In Situ PLIF and Particle Image Velocimetry Measurements of the Primary Entrainment Fuel Jet in a Naturally Aspirated Water Heater

The time-averaged characteristics of a fuel jet have been measured via acetone planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) in the primary mixing region of an operating gas-fired water heater. These measurements allow for experimental characterization of the cross-sectional scalar and velocity fields as well as the estimation of the mass entrainment as the flow enters the burner in a practical system. In these experiments, reasonable results were obtained when only the fuel jet was seeded with acetone or PIV particles rather than the entire flow, thus demonstrating the potential for simplified experimental configurations in some applications where controlling or seeding the entire flow may be difficult. The entrainment characteristics of the fuel jet are compared with benchmarks from literature. The commercial device exhibits a larger mass entrainment rate than is found in typical free jets that have been studied in the literature. This may be a result of the jet's low Reynolds number (9,600) in comparison with other literature studies, and a result of initial conditions.

Can the Tully-Fisher Relation Be the Result of Initial Conditions?

We use Monte Carlo realizations of halo formation histories and a spherical accretion model to calculate the expected scatter in the velocity dispersions of galactic halos of a given mass due to differences in their formation times. Assuming that the rotational velocity of a spiral galaxy is determined by the velocity dispersion of its halo and that its luminosity is related to its total baryonic mass, this scatter translates to a minimum intrinsic scatter in the Tully-Fisher relation. For popular cosmological models we find that the scatter due to variations in formation histories is by itself greater than allowed by observations. Unless halos of spiral galaxies formed at high redshift (z>1) and did not later accrete any significant amount of mass, the Tully-Fisher relation is not likely to be the direct result of cosmological initial conditions but rather a consequence of a subsequent feedback process.