A model of two incompressible, Newtonian fluids coupled across a common interface is studied. The nonlinearity of the coupling condition exacerbates the problem of decoupling the fluid calculations in each subdomain, a natural parallelization strategy employed in current climate models. A specialized partitioned time stepping method is studied which decouples the discrete fluid equations without sacrificing stability and maintaining convergence. This is accomplished through explicit updating of the size of the jump in tangential velocities across the fluid-fluid interface by a geometric averaging of this data over the previous two time levels. A full numerical analysis is presented and computational tests are performed demonstrating the robustness of this method.

Solubility data for poly(3-hexylthiophene) (P3HT) in 29 pure solvents are presented and discussed in detail. Functional solubility parameter (FSP) and convex solubility parameter (CSP) computations are performed and the CSP and FSP results are compared to previously reported Hansen solubility parameters (HSPs) and to the parameters calculated using additive functional group contribution methods. The empirical data reveals experimental solubility parameters with substantial polar (d P ) and hydrogen-bonding (d H ) components, which are not intrinsic to the structure of the P3HT polymer. Despite these apparent irregularities, it is shown that the predictor method based on the solubility function, f, does provide a reliable way to quantitatively evaluate the solubility of P3HT in other solvents in terms of a given set of empirical solubility data. The solubility behavior is further investigated using linear solvation energy relationship (LSER) modeling and COSMO-RS computations of the activity coefficients of P3HT. The LSER model reveals that (1) the cavity term, d T , is the dominant factor governing the solubility behavior of P3HT and (2) the solvent characteristics that dictate the structural order (crystallinity) of P3HT aggregates do not similarly influence the overall solubility behavior of the polymer.This article, which investigates the solubility characteristics of P3HT using complementary experimental and computational Additional Supporting Information may be found in the online version of this article. FIGURE 4 (a) Comparison of the activity coefficients calculated using COSMO-RS and eq 2. (b) Graph showing the correlation between the activity coefficient term, -ln(c), computed with COSMO-RS and the experimental mole fraction solubility of P3HT. Although the trend is not linear, as described by eq 2, there is clearly a monotonic relationship between the theoretical activity coefficient and the solubility.

Abstract. There have been many numerical simulations but few analytical results of stability and accuracy of algorithms for computational modeling of fluid-fluid and fluid-structure interaction problems, where two domains corresponding to different fluids (ocean-atmosphere) or a fluid and deformable solid (blood flow) are separated by an interface. As a simplified model of the first examples, this report considers two heat equations in Ω 1 , Ω 2 ⊂ R 2 adjoined by an interface I = Ω 1 ∩ Ω 2 ⊂ R. The heat equations are coupled by a condition that allows energy to pass back and forth across the interface I while preserving the total global energy of the monolithic, coupled problem. To compute approximate solutions to the above problem only using subdomain solvers, two first order in time, fully discrete methods are presented. The methods consist of an implicit-explicit (IMEX) approach, in which the action across I is lagged and a partitioned method based on passing interface values back and forth across I. Stability and convergence results are derived for both schemes. Numerical experiments that support the theoretical results are presented.

We consider a cantilevered (clamped-free) beam in an axial potential flow. Certain flow velocities may bring about a bounded-response instability in the structure, termed flutter. As a preliminary analysis, we employ the theory of large deflections and utilize a piston-theoretic approximation of the flow for appropriate parameters, yielding a nonlinear (Berger/Woinowsky-Krieger) beam equation with a non-dissipative RHS. As we obtain this structural model via a simplification, we arrive at a nonstandard nonlinear boundary condition that necessitates careful well-posedness analysis. We account for rotational inertia effects in the beam and discuss technical issues that necessitate this feature.We demonstrate nonlinear semigroup well-posedness of the model with the rotational inertia terms. For the case with no rotational inertia, we utilize a Galerkin approach to establish existence of weak, possibly non-unique, solutions. For the former, inertial model, we prove that the associated non-gradient dynamical system has a compact global attractor. Finally, we study stability regimes and post-flutter dynamics (non-stationary end behaviors) using numerical methods for models with, and without, the rotational inertia terms.

The determination of solubility parameters for solutes represents a challenging mathematical problem of locating the central tendency of solvent affinity based on a limited set of data taken from experimental observations. At present, the most commonly used methods for computing solubility parameters of a solute require a binary classification of solvent affinity for the solute and employ a spherical/ellipsoidal compatibility region in the three-dimensional Hansen solubility parameter space. Utilizing a binary classification requires an arbitrary solubility threshold, and an ellipsoidal fitting model imposes a symmetry on the intermolecular forces that is rarely reflected by the experimental data. To overcome these issues, an approach that makes use of accurate solubility data to describe a three-dimensional solubility function, f, is introduced. The principles of the approach are discussed in detail and the procedures for constructing the solubility function and computing solubility parameters are described. An example using PCBM solubility data available in the literature demonstrates the new method. Lastly, a method that employs f as a predictor of solubility in arbitrary solvents with a proposed measure of reliability is presented.