We study hydroelastic waves in interfacial flow of two-dimensional irrotational fluids. Each of the fluids is taken to be of infinite extent in one vertical direction, and bounded by a free surface in the other vertical direction. Elastic effects are considered at the free surface; this can describe physical settings such as the ocean bounded above by a layer of ice. A previous study proved well-posedness without considering the mass of the elastic surface; we now consider the effect of this mass. Under the assumption that a certain integral equation is solvable, we prove well-posedness of the initial value problem for the system. We are able to demonstrate that in some cases, such as the case of small mass parameter, the integral equation is indeed solvable. The proof uses geometric dependent variables, a normalized arclength parameterization, and a small-scale decomposition in the evolution equations.© 2016. This manuscript version is made available under the Elsevier user license http://www.elsevier.com/open-access/userlicense/1.0/ sheet strength. We must then evolve γ and the position of the free surface in order to have a solution of the problem.Considering interfacial potential flows with surface tension accounted for at the free boundary, Hou, Lowengrub, and Shelley (HLS) introduced a non-stiff numerical method [18], [19]. The second author subsequently used the elements of their formulation of the problem to prove well-posedness for the vortex sheet with surface tension and for interfacial Darcy flow [3], [4]. The significant elements of the formulation involve making a geometric description of the free surface rather than using Cartesian coordinates, using an artificial tangential velocity to enforce a favorable parameterization, and isolating the leading-order terms in the evolution equation (i.e., making a small-scale decomposition). Other analytical works which subsequently used these ideas include [5], [6], [11], [12], [13], [14], [15], [31], [32].Also using the HLS framework is the paper of the second author and Siegel which proves well-posedness of the hydroelastic initial value problem in the simpler case that the mass of the elastic sheet is neglected [7]. In the present, more general case, there are many additional terms to estimate in the evolution equation for γ. The greater difficulty, however, lies with the fact that the equation specifying the evolution of γ is actually an integral equation for γ t ; while this is also the case when the mass of the sheet is neglected, the form of the integral equation without mass is much more straightfoward. In particular, the integral equation which needed to be solved in [7] is the same integral equation which was proved to be solvable by Baker, Meiron, and Orszag in [8]. This result has been used many times in the literature, including, for example, in [3], [12], and [30]. In the present case, with a much more complicated integral equation to solve, we are not able to guarantee that it is always solvable. We prove well-posedness under the assumption th...

Truncated series models of gravity water waves are popular for use in simulation. Recent work has shown that these models need not inherit the well-posedness properties of the full equations of motion (the irrotational, incompressible Euler equations). We show that if one adds a sufficiently strong dispersive term to a quadratic truncated series model, the system then has a well-posed initial value problem. Such dispersion can be relevant in certain physical contexts, such as in the case of a bending force present at the free surface, as in a hydroelastic sheet.

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Variations of extracellular polymeric substances (EPS) and its components with sludge granulation were examined in a lab-scale sequencing batch reactor (SBR) which was fed with sodium nitrate and sodium acetate. Ultrasonication plus cation exchange resin (CER) were used as the EPS extraction method. Results showed that after approximately 90 d cultivation, the sludge in the reactor was almost granulated. The content of extracellular polysaccharides increased from 10.36 mg/g-VSS (volatile suspended solids) at start-up with flocculent sludge to 23.18 mg/g-VSS at 91 d with matured granular sludge, while the content of extracellular proteins were almost unchanged. Polysaccharides were the major components of EPS in anoxic granular sludge, accounting for about 70.6-79.0%, while proteins and DNA accounted for about 16.5-18.9% and 4.6-9.9%, respectively. It is proposed that EPS play a positive role in anoxic sludge granulation and polysaccharides might be strongly involved in aggregation of flocs into granules.