We prove the existence of complex geometrical optics solutions for Lipschitz conductivities. Moreover we show that, in dimensions n ≥ 3 that one can uniquely recover a W 3/2,∞ conductivity from its associated Dirichlet-to-Neumann map or voltage to current map.
We present a simple yet effective approach for learning word sense embeddings. In contrast to existing techniques, which either directly learn sense representations from corpora or rely on sense inventories from lexical resources, our approach can induce a sense inventory from existing word embeddings via clustering of ego-networks of related words. An integrated WSD mechanism enables labeling of words in context with learned sense vectors, which gives rise to downstream applications. Experiments show that the performance of our method is comparable to state-of-the-art unsupervised WSD systems.
We present a system for taxonomy construction that reached the first place in all subtasks of the SemEval 2016 challenge on Taxonomy Extraction Evaluation. Our simple yet effective approach harvests hypernyms with substring inclusion and Hearst-style lexicosyntactic patterns from domain-specific texts obtained via language model based focused crawling. Extracted taxonomies are evaluated on English, Dutch, French and Italian for three domains each (Food, Environment and Science). Evaluations against a gold standard and by human judgment show that our method outperforms more complex and knowledge-rich approaches on most domains and languages. Furthermore, to adapt the method to a new domain or language, only a small amount of manual labour is needed.
We present a novel formulation of the Pairwise Force Smoothed Particle Hydrodynamics Model (PF-SPH) and use it to simulate two-and threephase flows in bounded domains. In the PF-SPH model, the Navier-Stokes equations are discretized with the Smoothed Particle Hydrodynamics (SPH) method and the Young-Laplace boundary condition at the fluid-fluid interface and the Young boundary condition at the fluid-fluid-solid interface are replaced with pairwise forces added into the Navier-Stokes equations. We derive a relationship between the parameters in the pairwise forces and the surface tension and static contact angle. Next, we demonstrate the accuracy of the model under static and dynamic conditions. Finally, to demonstrate the capabilities and robustness of the model we use it to simulate flow of three fluids in a porous medium.
Abstract. We study suspensions of rigid particles (inclusions) in a viscous incompressible fluid. The particles are close to touching one another, so that the suspension is near the packing limit, and the flow at small Reynolds number is modeled by the Stokes equations. The objective is to determine the dependence of the effective viscosity μ on the geometric properties of the particle array. We study spatially irregular arrays, for which the volume fraction alone is not sufficient to estimate the effective viscosity. We use the notion of the interparticle distance parameter δ, based on the Voronoi tessellation, and we obtain a discrete network approximation of μ , as δ → 0. The asymptotic formulas for μ , derived in dimensions two and three, take into account translational and rotational motions of the particles. The leading term in the asymptotics is rigorously justified in two dimensions by constructing matching upper and lower variational bounds on μ . While the upper bound is obtained by patching together local approximate solutions, the construction of the lower bound cannot be obtained by a similar local analysis because the boundary conditions at fluid-solid interfaces must be resolved for all particles simultaneously. We observe that satisfying these boundary conditions, as well as the incompressibility condition, amounts to solving a certain algebraic system. The matrix of this system is determined by the total number of particles and their coordination numbers (number of neighbors of each particle). We show that the solvability of this system is determined by the properties of the network graph (which is uniquely defined by the array of particles) as well as by the conditions imposed at the external boundary.
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