Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

Analytical solution for tidal propagation in a coupled semi-confined/phreatic coastal aquifer

An analytical solution is derived for tidal fluctuations in a coupled coastal aquifer system consisting of a semi-confined aquifer, a thin semi-permeable layer and a phreatic aquifer. Based on the solution, we study the interactions (via leakage) between the confined and unconfined aquifers in response to tides. The results show that, under certain conditions, leakage from the confined aquifer can affect considerably the tidal water table fluctuation in the phreatic aquifer and vice versa. Ignoring these effects could lead to errors in estimating aquifer properties based on tidal signals. (C) 2002 Elsevier Science Ltd. All rights reserved.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

A comparison of the self-association behavior of the plant cyclotides kalata B1 and kalata B2 via analytical ultracentrifugation

The recently discovered cyclotides kalata B1 and kalata B2 are miniproteins containing a head-to-tail cyclized backbone and a cystine knot motif, in which disulfide bonds and the connecting backbone segments form a ring that is penetrated by the third disulfide bond. This arrangement renders the cyclotides extremely stable against thermal and enzymatic decay, making them a possible template onto which functionalities can be grafted.We have compared the hydrodynamic properties of two prototypic cyclotides, kalata B1 and kalata B2, using analytical ultracentrifugation techniques. Direct evidence for oligomerization of kalata B2 was shown by sedimentation velocity experiments in which a method for determining size distribution of polydisperse molecules in solution was employed. The shape of the oligomers appears to be spherical. Both sedimentation velocity and equilibrium experiments indicate that in phosphate buffer kalata B1 exists mainly as a monomer, even at millimolar concentrations. In contrast, at 1.6 mM, kalata B2 exists as an equilibrium mixture of monomer (30%), tetramer (42%), octamer (25%), and possibly a small proportion of higher oligomers. The results from the sedimentation equilibrium experiments show that this self-association is concentration dependent and reversible. We link our findings to the three-dimensional structures of both cyclotides, and propose two putative interaction interfaces on opposite sides of the kalata B2 molecule, one involving a hydrophobic interaction with the Phe(6), and the second involving a charge-charge interaction with the Asp(25) residue. An understanding of the factors affecting solution aggregation is of vital importance for future pharmaceutical application of these molecules.

Thermogravimetric analytical procedures for determining reactivities of chars from New Zealand coals

Tightly constrained thermogravimetric experimental procedures (particle size < 212 mu m, sample mass 15.5 mg, CO2 reactant gas, near isothermal conditions) allow the reactivity of chars from high volatile New Zealand coals to be determined to a repeatability of +/-0.07 h(-1) at 900 degrees C and +/-0.5 h(-1) at 1100 degrees C. The procedure also provides proximate analyses information and affords a quick (< 90 min) comparison between different coal types as well as indicating likely operating conditions and problems associated with a particular coal or blend. A clear difference is evident between reactivities of differing New Zealand coal ranks. Between 900 and 1100 degrees C, bituminous coals increase thirtyfold in reactivity compared with fourfold for subbituminous, with the latter being three to five times greater in reactivity at higher temperature. (C) 1997 Elsevier Science B.V.

Evaluation of lignin contents in tropical forages using different analytical methods and their correlations with degradation of insoluble fiber

We compared the lignin contents of tropical forages by different analytical methods and evaluated their correlations with parameters related to the degradation of neutral detergent fiber (NDF). The lignin content was evaluated by five methods: cellulose solubilization in sulfuric acid [Lignin (sa)], oxidation with potassium permanganate [Lignin (pm)], the Klason lignin method (KL), solubilization in acetyl bromide from acid detergent fiber (ABLadf) and solubilization in acetyl bromide from the cell wall (ABLcw). Samples from ten grasses and ten legumes were used. The lignin content values obtained by gravimetric methods were also corrected for protein contamination, and the corrected values were referred to as Lignin (sa)p, Lignin (pm)p and KLp. The indigestible fraction of NDF (iNDF), the discrete lag (LAG) and the fractional rate of degradation (kd) of NDF were estimated using an in vitro assay. Correcting for protein resulted in reductions (P < 0.05) in the lignin contents as measured by the Lignin (sa), Lignin (pm) and, especially, the KL methods. There was an interaction (P < 0.05) of analytical method and forage group for lignin content. In general, LKp method provided the higher (P < 0.05) lignin contents. The estimates of lignin content obtained by the Lignin (sa)p, Lignin (pm)p and LKp methods were associated (P > 0.05) with all of the NDF degradation parameters. However, the strongest correlation coefficients for all methods evaluated were obtained with Lignin (pm)p and KLp. The lignin content estimated by the ABLcw method did not correlate (P > 0.05) with any parameters of NDF degradation. There was a correlation (P < 0.05) between the lignin content estimated by the ABLadf method and iNDF content. Nonetheless, this correlation was weaker than those found with gravimetric methods. From these results, we concluded that the gravimetric methods produce residues that are contaminated by nitrogenous compounds. Adjustment for these contaminants is suggested, particularly for the KL method, to express lignin content with greater accuracy. The relationships between lignin content measurements and NDF degradation parameters can be better determined using KLp and Lignin (pm)p methods. (C) 2011 Elsevier B.V. All rights reserved.

Analytical solution and numerical model for the interface in a stratified long wave system

For a two layered long wave propagation, linearized governing equations, which were derived earlier from the Euler equations of mass and momentum assuming negligible friction and interfacial mixing are solved analytically using Fourier transform. For the solution, variations of upper layer water level is assumed to be sinosoidal having known amplitude and variations of interface level is solved. As the governing equations are too complex to solve it analytically, density of upper layer fluid is assumed as very close to the density of lower layer fluid to simplify the lower layer equation. A numerical model is developed using the staggered leap-forg scheme for computation of water level and discharge in one dimensional propagation having known amplitude for the variations of upper layer water level and interface level to be solved. For the numerical model, water levels (upper layer and interface) at both the boundaries are assumed to be known from analytical solution. Results of numerical model are verified by comparing with the analytical solutions for different time period. Good agreements between analytical solution and numerical model are found for the stated boundary condition. The reliability of the developed numerical model is discussed, using it for different a (ratio of density of fluid in the upper layer to that in the lower layer) and p (ratio of water depth in the lower layer to that in the upper layer) values. It is found that as ‘CX’ increases amplification of interface also increases for same upper layer amplitude. Again for a constant lower layer depth, as ‘p’ increases amplification of interface. also increases for same upper layer amplitude.

A potential role for the analytical ultracentrifuge in the experimental measurement of protein valence

A method is described whereby sedimentation velocity is combined with equilibrium dialysis to determine the net charge (valence) of a protein by using chromate as an indicator ion for assessing the extent of the Donnan redistribution of small ions. The procedure has been used in experiments on bovine serum albumin under slightly alkaline conditions (pH 8.0, I 0.05) to illustrate its application to a system in which the indicator ion and protein both bear net negative charge and on lysozyme under slightly acidic conditions (pH 5.0, I 0.10) to illustrate the situation where chromate is a counterion. (C) 2001 Elsevier Science.